## Copy this file to 3DLDF-1.1.4/ ## Delete 3DLDF-1.1.4/DOC/TEXINFO/EPS. ## Apply the patch like this: ## patch -p1 -i 3DLDF-1.1.4-1.1.5.1.diff ## ## See 3DLDF-1.1.5.1/README for more information. ## diff -Naur 3DLDF-1.1.4/.rcsfreeze.log 3DLDF-1.1.5.1/.rcsfreeze.log --- 3DLDF-1.1.4/.rcsfreeze.log 2003-12-10 18:37:30.000000000 +0100 +++ 3DLDF-1.1.5.1/.rcsfreeze.log 2004-01-14 21:56:16.000000000 +0100 @@ -1,3 +1,8 @@ +Version: C_4(C_4), Date: Wed Jan 14 21:56:09 MET 2004 +----------- + Release 1.1.5. +----------- + Version: C_3(C_3), Date: Wed Dec 10 18:36:59 MET 2003 ----------- Release 1.1.4. diff -Naur 3DLDF-1.1.4/AUTHORS 3DLDF-1.1.5.1/AUTHORS --- 3DLDF-1.1.4/AUTHORS 2003-12-09 21:19:53.000000000 +0100 +++ 3DLDF-1.1.5.1/AUTHORS 2004-01-16 17:25:40.000000000 +0100 @@ -1,9 +1,9 @@ AUTHORS -$Id: AUTHORS,v 1.4 2003/12/09 20:19:53 lfinsto1 Exp $ +$Id: AUTHORS,v 1.5 2004/01/16 16:25:39 lfinsto1 Exp $ This file is part of 3DLDF, a package for three-dimensional drawing. -Copyright (C) 2003 Laurence D. Finston. +Copyright (C) 2003, 2004 Laurence D. Finston. 3DLDF is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by diff -Naur 3DLDF-1.1.4/CWEB/.rcsfreeze.log 3DLDF-1.1.5.1/CWEB/.rcsfreeze.log --- 3DLDF-1.1.4/CWEB/.rcsfreeze.log 2003-12-10 18:37:52.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/.rcsfreeze.log 2004-01-14 21:53:23.000000000 +0100 @@ -1,3 +1,8 @@ +Version: C_5(C_5), Date: Wed Jan 14 21:53:16 MET 2004 +----------- + Release 1.1.5. +----------- + Version: C_4(C_4), Date: Wed Dec 10 18:37:40 MET 2003 ----------- Release 1.1.4. diff -Naur 3DLDF-1.1.4/CWEB/3DLDFmp.mp 3DLDF-1.1.5.1/CWEB/3DLDFmp.mp --- 3DLDF-1.1.4/CWEB/3DLDFmp.mp 2003-12-10 15:37:15.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/3DLDFmp.mp 2004-01-16 19:20:02.000000000 +0100 @@ -3,7 +3,7 @@ %% * Copyright and License.@> %%% This file is part of 3DLDF, a package for three-dimensional drawing. -%%% Copyright (C) 2003 Laurence D. Finston. +%%% Copyright (C) 2003, 2004 Laurence D. Finston. %%% 3DLDF is free software; you can redistribute it and/or modify %%% it under the terms of the GNU General Public License as published by @@ -30,8 +30,7 @@ %%% s246794@stud.uni-goettingen.de -%%%%% $Id: 3DLDFmp.mp,v 1.1 2003/11/28 13:35:19 lfinsto1 Exp $ - +%%%%% $Id: 3DLDFmp.mp,v 1.5 2004/01/12 21:25:37 lfinsto1 Exp $ input boxes; @@ -47,5 +46,6 @@ bye; - + + diff -Naur 3DLDF-1.1.4/CWEB/3DLDFprg.dvi 3DLDF-1.1.5.1/CWEB/3DLDFprg.dvi --- 3DLDF-1.1.4/CWEB/3DLDFprg.dvi 2003-12-10 18:45:10.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/3DLDFprg.dvi 2004-01-16 18:31:55.000000000 +0100 @@ -1,21 +1,58 @@ -÷ƒ’À;è TeX output 2003.12.10:1845‹ÿÿÿÿ Šn ý‘ìó !",š +÷ƒ’À;è TeX output 2004.01.16:1821‹ ÿÿÿÿ Šn ý•UJ’šc!óÙ“ R„›cmr7«3DLDF:––›The“ProgramŽŸ¾[’µÇ®V‘þ©ersion‘–›1.1.5.1Ž¤’”òßb²y––›Laurence“D.“FinstonŽ¡’Í ŸóKñ`y -cmsy10·xóKñ`y +cmr10¬Jan¸ãuary‘UU2004ŽŸjì[’˜•Section‘ P¸ãageŽŽ¤ Cop•¸ãyrigh“t–UUand“License‘¸Ø.Ž–.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž“.Ž‘ ÁC1‘1ŽŽ©óò"V -cmr10«1›ó|{Ycmr8­3DLDFPRÃŽG’TrCOPYRIGHT–ÕXAND“LICENSE˜«1Ž €n ý•@Póò"V +cmbx10­In®9troQÇduction‘ ü(óßêÌ«preproGcessor“commandsŽ¡for–^àconditional“compilation.‘ŽgThere's“a“di erenš¸ãt“v˜ersion“of“this“ le“in“eac˜h“of“the“subGdirectories“used“forŽ¡compiling–UUwith“a“di erenš¸ãt“com˜bination“of“opGerating“system,“compiler,“and“compiler“v˜ersion.Ž¡‘ -[¬LDF‘T2003.07.25.«]Ž‘Y;MoGdi ed–UUthe“conditional“constructions“go•¸ãv“erning–UUcompilation“sligh¸ãtly‘ÿ*ª.Ž¡‘ -[¬LDF‘T2003.08.14.«]Ž‘Z3£Noš¸ãw–€½including“Ègetopt.h“«for“the“GCC‘€pv˜ersions“under“Lin˜ux.‘óÿIt's“for“proGcessing“theŽ¡command–UUline“options.Ž¡‘ -[¬LDF‘T2003.08.14.«]Ž‘Z›No¸ãw–_µincluding“Èstreambuf.h«,›¢Lif“ÝLDF_GCC_2_95Ž‘HE®«is“de ned,˜otherwise“Èios«.‘æThis“is“forŽ¡stream‘UUformatting.Ž¡‘ -[¬LDF‘T2003.08.29.«]Ž‘YFdRemo•¸ãv“ed–“~Ègetopt.h“«to“Èmain.web«,‘£bGecause“it's“only“used“there.‘,ATO‘“nDO:“Mo•¸ãv“e–“~the“restŽ¡of–UUthe“include“commands“to“the“ les“where“they're“needed,“Âand–ÕTget“rid“of“this“ le«.Ž¡‘ -[¬LDF‘T2003.09.03.«]Ž‘YÎAdded–9#Âde neŽ‘"cºÝLDF_PUBLICŽ‘[…=«in“order“to“bGe“able“to“conditionally“include“Èplfmvar.h«.Ž¡The–latter“is“not“included“in“the“v¸ãersion“for“distribution.‘ïInstead,‘‰…the“preproGcessor“v‘ÿqÇariables“are“de ned“orŽ¡unde ned‘UUhere.Ž¡‘ -[¬LDF‘T2003.11.12.«]Ž‘ZCáRemo•¸ãv“ed–ûthe“vš¸ãersion“con˜trol“iden˜ti ers“from“the“CWEB‘© les“for“the“distribution“ofŽ¡3DLDF–UU1.1.‘qÇThey're“still“used“in“mš¸ãy“dev˜elopmen˜t“v˜ersions.Ž¦ŸüÈ„`ÕÁGŽŽŸÂ6.– üCon guration‘æÕ le.“«This–dsection“includes“Èconfig.h«,‘h[whicš¸ãh“is“generated“b˜y“ÝconfigureŽ‘3*Ú«.‘ŸoThis“is“newŽ¡in–Zâ3DLDF‘Zá1.1.‘‚nThe“ÝconfigureŽ‘6|«script“generated“bš¸ãy“AutoGconf“tests“whether“certain“library“ les“are“presen˜t,Ž¡and–œÿde nes“preprošGcessor“v‘ÿqÇariables“in“Èconfig.h“«accordingly‘ÿ*ª.‘HÅThese“can“b˜e“used“for“conditionally“compilingŽ¡coGde,›­uso–›Õthat“library“ les“are“only“included“if“they“are“really“presen•¸ãt.‘EGHo“w“ev“er,˜it–›Õwill“bGe“necessary“to“addŽ¡coGde–‚ofor“handling“the“case“that“they“aren't“presen•¸ãt.‘+{I›‚9ha“v“en't–‚odone“this“y¸ãet,‘¬although“I˜ha•¸ãv“e–‚oput“in“conditionalŽ¡coGde–UUusing“these“v‘ÿqÇariables“in“a“couple“of“places.›qÇTO“DO:“W‘ÿ*ªork“on“this.˜[¬LDF‘T2003.11.12.«]ŽŽ¡‘ -Auto•Gconf›do“es˜not˜p“er˜default˜c•¸ãhec“k˜the˜v“ersion˜of˜the˜compiler˜that's˜used,‘0íand˜I'm˜not˜sure˜whetherŽ¡this–ë¡wš¸ãould“really“bGe“sensible.‘4¬3DLDF‘ë{already“con˜tains“conditionally“compiled“coGde“based“on“whether“theŽ¡DEC›…–¬C‘€Ÿÿ®+‘ÿ+ŽŽ‘Í«compiler,‘Òor–…åthe“GNU˜¬C‘€Ÿÿ®+‘ÿ+ŽŽ‘Í«compiler“(GCC)˜vš¸ãersion“2.95“or“v˜ersion“3.3“is“used.‘vIf“the“DECŽ¡compiler–›Úis“used,‘í{the“preprošGcessor“v‘ÿqÇariables“ÝLDF_GCC_2_95Ž‘H½ø«or“ÝLDF_GCC_3_3Ž‘C}û«m¸ãust“b˜e“unde ned“b¸ãy“handŽ¡bGelo¸ãw.›ÄIt–Æde nes“Ý__DECCXXŽ‘2€«itself.˜If“GCC‘Åûis“used,›âIone“of“them“m¸ãust“bGe“de ned,˜and“the“other“unde ned.Ž¡P¸ãer–à default,‘÷÷ÝLDF_GCC_3_3Ž‘@Þ«is“de ned“and“ÝLDF_GCC_2_95Ž‘EG„«is“unde ned.‘JàThis“is“bGecause“GCC‘à‚3.3“is,‘÷÷in“general,Ž¡an›ßüimpro•¸ãv“emen“t˜o“v“er˜GCC›ßØ2.95.‘»Ho“w“ev“er,‘¥I˜usually–ßüuse“GCC˜2.95“mš¸ãyself,‘¥bGecause“linking“is“signi can˜tlyŽ¡faster–UUon“the“computer“I“use.‘qÇ[¬LDF‘T2003.11.12.«]ŽŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.11.12.«]Ž‘Y;Added–UUthis“section.Ž¦ŸüÈ„`ÕÁGŽŽŽŽŒ‹è Šn ý‘ì«4–­CONFIGURA‘ÿJªTION‘ÕXFILE’cr3DLDFPRÃŽG“·x«6Ž €n ý•@P·h‘ª¨Ýloader.hŽ‘5°ù­6‘ª¨·i‘ÇŽ¤ «#ÂincludeŽ‘'Ø~Ý"config.h"ŽŽŸ ­See–ÕXalso“sections“7,“8,“and“9.ŽŸÂ7.‘ üLibrary‘ÕT les.ŽŸ·h‘ª¨Ýloader.hŽ‘5°ù­6‘ª¨·i‘Ç«+·Ž¡«#Âde neŽ‘!ÖÝLDF_PUBLICŽŽ¡«#ÂifdefŽ‘áeÝLDF_PUBLICŽŽ¡«#Âde neŽ‘!ÖÝ_GNU_SOURCEŽŽ¡«#Âde neŽ‘!ÖÝLDF_GCC_3_3ŽŽ¡«#ÂundefŽ‘ ó*ÝLDF_GCC_2_95ŽŽ¡«#ÂundefŽ‘ ó*Ý__DECCXXŽ‘_y{ó  b> +cmtex10´.webŽ‘Ú¶¬ les,“so˜that˜cw•¸ãea“v“eŽ¡proGcesses–UUthem“as“if“they“w¸ãere“all“one“ le.ŽŽŽŒ‹p£ Šn ý‘ì¬2–¯INTRÃŽODUCTION‘€(®3DLDF.WEB¯)’ê•Y3DLDF-1.1.5.1“°x¬2Ž €n ý•@P‘ +T‘ÿ*ªo–#+write“mš¸ãy“´.webŽ‘̲¬ les,‘-4I‘#wrote“a“´cweb-modeŽ‘6 £¬for“Emacs“and“a“n˜um˜bGer“of“Emacs-Lisp“functions“to“go“withŽ¤ it.‘0±It–”øis“not“curren¸ãtly“included“in“the“3DLDF›”èdistribution“(V‘ÿ*ªersion“1.1.5.1),‘¤ábut“I˜ma¸ãy“include“it“in“a“laterŽ¡v•¸ãersion.‘püHo“w“ev“er,‘SmGNU‘Ròis–Róat“wš¸ãork“at“an“ocial“cw˜eb-moGde“of“its“o˜wn,‘Smso“y˜ou“migh˜t“w˜an˜t“to“use“it“instead,Ž¡if–UUit's“a¸ãv‘ÿqÇailable.Ž¡‘ +Plurals–kof“tš¸ãypGes“are“t˜ypGeset“with“the“\s"“in“the“same“fon˜t“as“the“t˜ypGe,–ppe.g.,“\­P•®9oin“tsŽ‘ #„¬"–kand“not“\­P•®9oin“tŽ‘šH¬s".Ž¡It's–¢Ínot“considered“go•Go“d›¢Ít¸ãyp“ographical˜practice˜to˜t¸ãyp“eset˜w•¸ãords˜with˜letters˜from˜di eren“t˜fon“ts.‘6EThe˜secondŽ¡example–èdoGes“ha•¸ãv“e–èthe“adv‘ÿqÇanš¸ãtage“that“it's“somewhat“clearer“what“the“actual“name“of“the“t˜ypGe“is,‘ýîbut“I‘çùthinkŽ¡the–UU rst“argumenš¸ãt“is“w˜eigh˜tier.Ž¡‘ +See–™®http://www-cs-faculty.stanford.edu/knuth/cweb.html“¬for“more“information“abGout“CWEB.“TheŽ¡WEB–UU(for“Pš¸ãascal)“and“CWEB“pac˜k‘ÿqÇages“are“a˜v‘ÿqÇailable“from“the“CT‘ÿ*ªAN“arc˜hiv˜e,“®ftp.dante.de“¬andŽ¡®http:://www.dante.de¬.Ž¡‘ +Donald–}¹Kn¸ãuth's“b•Go“oks‘}¹±T‘þKßÓVEŽ‘Í-XŽ‘á¡:‘ãèThe›¹Pr–ÿ}'o“gr“am‘B¬and‘}¹±MET‘ÿ;¼AF¾“ONT:˜The˜Pr“o“gr“am‘B¬eacš¸ãh–}¹include“a“section“\Ho˜wŽ¡to–UUread“a“WEB",“whicš¸ãh“ma˜y“bGe“helpful.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.11.18.¬]Ž‘YXChanged–Nrname“of“this“ le“from“®cweavedriver.web“¬to“®cwdriver.web¬.‘o{It“noš¸ãw“has“few˜erŽ¡than–UU8“letters“and“can“bGe“used“under“DOS.Ž¡‘ +[²LDF‘T2003.08.16.¬]Ž‘X£ƒChanged–ðname“of“this“ le“from“®cwdriver.web“¬to“®3DLDF.web“¬sometime“since“2002.11.18.Ž¡F‘ÿ*ªorgot–UUto“note“it“here.Ž¡‘ +[²LDF‘T2003.11.12.¬]Ž‘ZCáRemo•¸ãv“ed–ûthe“vš¸ãersion“con˜trol“iden˜ti ers“from“the“CWEB‘© les“for“the“distribution“ofŽ¡3DLDF–UU1.1.‘qÇThey're“still“used“in“mš¸ãy“dev˜elopmen˜t“v˜ersions.Ž©ŸüÈ„`ÕÁGŽŽŸ­3.– üF‘ÿ +«ormatting‘r©commands.“®cweave–ÿˆ¬formats“\´==Ž› b¬"“as“\°¬",‘±\´!=Ž˜¬"“as“\°6¬=",‘±and“\´!Ž‘Æe¬"“as“\°:¬".‘U.ProgrammersŽ¡who–UUuse“these“tokš¸ãens“m˜ust“t˜ypGe“them“as“\´==Ž› b¬",“\´!=Ž˜¬,“and“\®!¬".Ž¡‘ +The–ïÏfolloš¸ãwing“formatting“commands“are“for“t˜ypGes“de ned“in“²C‘€Ÿÿ³+‘ÿ+ŽŽ›6ï¬or“in“the“²C‘€Ÿÿ³+‘ÿ+ŽŽ˜¬Standard“Library‘ÿ*ª,‘but“notŽ¡handled–UUcorrectly“b¸ãy“®cweave¬.Ž¦‘ +­formatŽ‘3c(±bitsetŽ‘T.#intŽŽ¡‘ +­formatŽ‘3c(±b–ÿ}'o“olŽ‘MžÝintŽŽ¡‘ +­formatŽ‘3c(±b–ÿ}'o“olsŽ‘Q5b–ÿ}'o“olŽŽ¡‘ +­formatŽ‘3c(±ifstr–ÿ}'e“amŽ‘_ _intŽŽ¡‘ +­formatŽ‘3c(±key‘‰ffŽ‘®typ‘ÿ}'eŽ‘`¢intŽŽ¡‘ +­formatŽ‘3c(±mapp–ÿ}'e“d‘‰ffŽ‘®typ“eŽ‘r=–intŽŽ¡‘ +­formatŽ‘3c(±mapŽ‘OCOintŽŽ¡‘ +­formatŽ‘3c(±ofstr–ÿ}'e“amŽ‘a«¿intŽŽ¡‘ +­formatŽ‘3c(±statŽ‘MUintŽŽ¡‘ +­formatŽ‘3c(±stringstr–ÿ}'e“amŽ‘rhÞintŽŽ¡‘ +­formatŽ‘3c(±numeric‘‰ffŽ‘®limitsŽ‘|¨õintŽŽ¡‘ +­formatŽ‘3c(±p‘ÿ}'airŽ‘NMpintŽŽ¡‘ +­formatŽ‘3c(±stringŽ‘VscharŽŽ¡‘ +­formatŽ‘3c(±tmŽ‘HµintŽŽ¡‘ +­formatŽ‘3c(±valarr‘ÿ}'ayŽ‘`bintŽŽ¡‘ +­formatŽ‘3c(±ve‘ÿ}'ctorŽ‘W?0intŽŽŽŽŒ‹€ Šn ý‘ì°x¬4–¯3DLDF-1.1.5.1’û:vFÃŽORMA‘ÿJªTTING‘ÕXCOMMANDS“¬3Ž €n ý•@P­4.‘ ü¬This–±Àsection“conš¸ãtains“commands“for“inputting“the“®CWEB‘±¨¬source“ les,‘ÈÚwhic˜h“are“in˜visible“in“the“®cweaveŽ¤ ¬output.Ž©Ÿ­5.› üPreproQÇcessor–ÕTv‘ÿ\rariables“and“library“ les˜(®loader.web­).‘/_+¬[²LDF‘T2002.10.15.¬]Ž‘~geIt–UUw¸ãould,“ofŽ¡course,‘¢b•Ge›’»p“ossible˜to˜put˜this˜co“de˜in•¸ãto˜a˜´.hŽ‘+ج le˜directly‘ÿ*ª,‘¢but˜it's˜con“v“enien“t˜to˜ha“v“e˜a˜®CWEB‘’¬¬ le˜so˜that˜itŽ¡can–UUbGe“´cweavedŽ‘+ðý¬along“with“the“rest“of“3DLDF.Ž¡‘ +[²LDF‘T2003.07.18.¬]Ž‘Y;Set–MUthe“preproGcessor“macro“´LDF_GCC_3_3Ž‘@àñ¬to“1“in“order“to“compile“using“gcc“v¸ãersion“3.3Ž¡20030226–=„(prerelease)“(SuSE›=HLin¸ãux).‘*TSet“it“to“0“in“order“to“compile“using“GCC˜v¸ãersion“2.95.3“20010315Ž¡(SuSE).–UUThis“can“bšGe“faster“than“using“GCC“3.3,“esp˜ecially“with“resp˜ect“to“linking.ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.08.21.¬]Ž‘YSÝNoš¸ãw– ÷including“®plfmvar.h¬.‘T¬It“con˜tains“#­de neŽ‘!éx¬and“#­undefŽ‘!>̬preproGcessor“commandsŽ¡for–^àconditional“compilation.‘ŽgThere's“a“di erenš¸ãt“v˜ersion“of“this“ le“in“eac˜h“of“the“subGdirectories“used“forŽ¡compiling–UUwith“a“di erenš¸ãt“com˜bination“of“opGerating“system,“compiler,“and“compiler“v˜ersion.Ž¡‘ +[²LDF‘T2003.07.25.¬]Ž‘Y;MoGdi ed–UUthe“conditional“constructions“go•¸ãv“erning–UUcompilation“sligh¸ãtly‘ÿ*ª.Ž¡‘ +[²LDF‘T2003.08.14.¬]Ž‘Z3£Noš¸ãw–€½including“®getopt.h“¬for“the“GCC‘€pv˜ersions“under“Lin˜ux.‘óÿIt's“for“proGcessing“theŽ¡command–UUline“options.Ž¡‘ +[²LDF‘T2003.08.14.¬]Ž‘Z›No¸ãw–_µincluding“®streambuf.h¬,›¢Lif“´LDF_GCC_2_95Ž‘HE®¬is“de ned,˜otherwise“®ios¬.‘æThis“is“forŽ¡stream‘UUformatting.Ž¡‘ +[²LDF‘T2003.08.29.¬]Ž‘Y;Remo•¸ãv“ed–UU®getopt.h“¬to“®main.web¬,“bGecause“it's“only“used“there.Ž¡‘ +[²LDF‘T2003.09.03.¬]Ž‘YÎAdded–9#­de neŽ‘"cº´LDF_PUBLICŽ‘[…=¬in“order“to“bGe“able“to“conditionally“include“®plfmvar.h¬.Ž¡The–latter“is“not“included“in“the“v¸ãersion“for“distribution.‘ïInstead,‘‰…the“preproGcessor“v‘ÿqÇariables“are“de ned“orŽ¡unde ned‘UUhere.Ž¡‘ +[²LDF‘T2003.11.12.¬]Ž‘ZCáRemo•¸ãv“ed–ûthe“vš¸ãersion“con˜trol“iden˜ti ers“from“the“CWEB‘© les“for“the“distribution“ofŽ¡3DLDF–UU1.1.‘qÇThey're“still“used“in“mš¸ãy“dev˜elopmen˜t“v˜ersions.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h‘ª¨¬V‘ÿ*ªersion–UUconš¸ãtrol“iden˜ti er‘@¯5‘ª¨°i‘ÇŽ¡‘ +­staticŽ‘)HÚstringŽ‘Jn'±r‘ÿ}'cs‘‰ffŽ‘®idŽ‘g(¬=‘Ç´"$Id:® ´loader.web,v® ´1Ž‘kÆÜ.4® ´2004/01/12® ´21:30:Ž’ÔÆ 27® ´lfinsto1® ´Exp® ´$"Ž’3ÌÒ¬;Ž¤ ¯See–»Talso“sections“13,–Àˆ53,“63,“76,“93,“164,“241,“250,“307,“635,“659,“696,“982,“1017,“1099,“1141,“1273,“1317,“1331,“1443,“1451,“1470,Ž© +‘1536,–ÕXand“1543.Ž¡This–¹Ðco -cmmi10±=·‘ÿý«Just–UUto“bGe“extra“sure.‘qÇ[¬LDF‘T2003.09.03.«]Ž‘U$©·±=Ž¡«#ÂelseŽ‘&Øà±=·‘ÿý«Do‘UUnothing.‘o·±=Ž¡«#ÂendifŽŽ¡«#ÂifdefŽ‘áeÝ__DECCXXŽŽ¡«#Âde neŽ‘!ÖÝ__USE_STD_IOSTREAMŽ’”¤ ±=·‘ÿý«Needed–UUfor“"sstream"“bGelo¸ãw.‘o·±=Ž¡«#ÂendifŽŽ¡«#ÂincludeŽ‘'Ø~ÝŽŽ¡«#ÂincludeŽ‘'Ø~ÝŽŽ¡«#ÂincludeŽ‘'Ø~ÝŽŽ¡«#ÂifdefŽ‘áeÝ__GNUC__ŽŽ¡«#ÂifŽ‘ ´øÝHAVE_FLOAT_HŽŽ¡«#ÂincludeŽ‘'Ø~ÝŽ‘kžÌ±=·‘ÿý«[¬LDF‘T2002.12.13.«]Ž‘T7Needed–UUfor“ÝFLT_MAXŽ‘(›¨«.‘o·±=Ž¡«#ÂendifŽŽ¡«#ÂendifŽŽ¡«#ÂincludeŽ‘'Ø~ÝŽŽ¡«#ÂincludeŽ‘'Ø~ÝŽŽ¡«#ÂincludeŽ‘'Ø~ÝŽŽ¡«#ÂifdefŽ‘áeÝLDF_GCC_2_95Ž‘ngª±=·‘ÿý«F‘ÿ*ªor–UUstream“formatting.‘qÇ[¬LDF‘T2003.08.14.«]Ž‘U$©·±=Ž¡«#ÂincludeŽ‘'Ø~ÝŽŽ¡«#ÂelseŽŽ¡«#ÂincludeŽ‘'Ø~ÝŽŽ¡«#ÂendifŽŽ¡«#ÂincludeŽ‘'Ø~ÝŽŽ¡«#ÂincludeŽ‘'Ø~ÝŽŽ¡«#ÂifdefŽ‘áeÝ__DECCXXŽŽ¡«#ÂincludeŽ‘'Ø~ÝŽŽ¡«#ÂelseŽŽ¡«#ÂifdefŽ‘áeÝLDF_GCC_3_3ŽŽ¡«#ÂincludeŽ‘'Ø~ÝŽŽ¡«#ÂelseŽŽ¡«#ÂifdefŽ‘áeÝLDF_GCC_2_95ŽŽ¡«#ÂifŽ‘ ´øÝHAVE_LIMITS_HŽŽ¡«#ÂincludeŽ‘'Ø~ÝŽŽ¡«#ÂendifŽŽ¡«#ÂendifŽŽ¡«#ÂendifŽŽ¡«#ÂendifŽŽ¡«#ÂincludeŽ‘'Ø~ÝŽŽ¡«#ÂincludeŽ‘'Ø~ÝŽŽ¡«#ÂifdefŽ‘áeÝLDF_GCC_3_3ŽŽ¡«#ÂincludeŽ‘'Ø~ÝŽŽŽŽŒ‹0  Šn ý‘ì·x«7–­3DLDFPRÃŽG’4˜ŠLIBRAR‘ÿJªY‘ÕXFILES“«5Ž €n ý•@P#ÂelseŽŽ¤ «#ÂifdefŽ‘áeÝLDF_GCC_2_95ŽŽ¡«#ÂincludeŽ‘'Ø~ÝŽŽ¡«#ÂendifŽŽ¡«#ÂendifŽŽ¡«#ÂincludeŽ‘'Ø~ÝŽŽ¡«#ÂincludeŽ‘'Ø~ÝŽŽ¡«#ÂincludeŽ‘'Ø~ÝŽŽ¡«#ÂifdefŽ‘áeÝ__GNUC__ŽŽ¡«#ÂincludeŽ‘'Ø~ÝŽŽ¡«#ÂendifŽŽ¡«#ÂifŽ‘ ´øÝHAVE_STDLIB_HŽŽ¡«#ÂincludeŽ‘'Ø~ÝŽŽ¡«#ÂendifŽŽŸ8.‘ üÈstreambuf.h–K«is“included“abGo•¸ãv“e,–ˆ†if‘KÝLDF_GCC_2_95Ž‘Hp«is›Kde ned,“instead˜of˜Èios«,“whic¸ãh˜is˜included˜in˜allŽ¡other‘UUcases.‘qÇ[¬LDF‘T2003.08.14.«]ŽŽŸ·h‘ª¨Ýloader.hŽ‘5°ù­6‘ª¨·i‘Ç«+·Ž¡«#ÂincludeŽ‘'Ø~ÝŽŽ¡«#ÂincludeŽ‘'Ø~ÝŽŽ¡«#ÂincludeŽ‘'Ø~ÝŽŽŽŽŒ‹7Ë Šn ý‘ì«6–­LIBRAR‘ÿJªY‘ÕXFILES’4˜Š3DLDFPRÃŽG“·x«9Ž €n ý•@PÂ9.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ -«[¬LDF‘T2003.07.18.«]Ž‘X–yAdded–ã“\ÂusingŽ‘áÄnamespaceŽ‘W|ÏstdŽ‘e$Š«".‘KÜThis“is“needed“with“GCC›ãv3.3,‘úSbut“not“with“GCC˜2.95Ž¡or–UUthe“DEC“C++“compiler.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h‘ª¨Ýloader.hŽ‘5°ù­6‘ª¨·i‘Ç«+·Ž¤ ‘ -ÂusingŽ‘(S‡namespaceŽ‘a÷stdŽ‘qïà«;ŽŸÂ10.– üGlobal‘ÕTitems“(Èpspglb.webÂ).‘$I÷«Tš¸ãypGedefs,–UUglobal“v‘ÿqÇariables“and“constan˜ts,“and“some“non-classŽ¡functions.‘qÇ(Èpspglb.web«.)ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.11.12.«]Ž‘ZCáRemo•¸ãv“ed–ûthe“vš¸ãersion“con˜trol“iden˜ti ers“from“the“CWEB‘© les“for“the“distribution“ofŽ¡3DLDF–UU1.1.1.‘qÇThey're“still“used“in“mš¸ãy“dev˜elopmen˜t“v˜ersions.Ž¡‘ -[¬LDF‘T2003.12.01.«]Ž‘Y$Put–R>the“vš¸ãersion“con˜trol“iden˜ti ers“bac˜k“in˜to“the“release“v˜ersions,‘RÜbGecause“I'v˜e“put“themŽ¡in–UUtheir“oš¸ãwn“R˜CS“repGository‘ÿ*ª.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h‘ª¨«V‘ÿ*ªersion–UUconš¸ãtrol“iden˜ti er‘@­10‘ª¨·i‘ÇŽŸ ‘ -ÂstaticŽ‘)HÚstringŽ‘Jn'Ïr‘ÿ}'cs‘‰ffŽ‘®idŽ‘g(«=‘ÇÝ"$Id:È Ýpspglb.web,vÈ Ý1Ž‘kÆÜ.10È Ý2003/12/10È Ý16:34Ž’ÔÆ :02È Ýlfinsto1È ÝExpÈ Ý$"Ž’9 Ï«;Ž¤ ­See– -also“sections“37,–C54,“120,“196,“205,“262,“591,“615,“652,“938,“973,“1057,“1101,“1234,“1280,“1294,“1403,“1411,“1429,“1495,Ž© -‘and‘ÕX1502.Ž¡This–ÀècoŽŽ¤ ­See– -also“sections“38,–C55,“121,“197,“206,“263,“592,“616,“653,“939,“974,“1058,“1102,“1235,“1281,“1295,“1404,“1412,“1430,“1496,Ž¦‘and‘ÕX1503.Ž¡This–Àèco«v‘ÿqÇalue.‘ -ÝMAX_REAL_SQRTŽ‘Pøa«is“con•¸ãv“enien“t–pto“ha•¸ãv“e–pfor“testing“whenŽ¡computing‘UUdistances.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.09.25.«]Ž‘YâñAdded–0 this“section.‘èPreviously‘ÿ*ª,‘f¸I‘/Òdeclared“and“initialized“mš¸ãy“global“constan˜ts“in“theŽ¡header–%> le.‘ áThis“meanš¸ãt“that“eac˜h“compilation“unit“that“loaded“Èpspglb.h“«had“its“o˜wn“v˜ersion“of“ÝPIŽ‘+ «,Ž¡ÝINVALID_REALŽ‘?†D«,‘¹ketc.‘aýI‘¥Rdidn't–¥gknoš¸ãw“that“Ïc‘ÿ}'onstsŽ‘"ò:«had“in˜ternal“link‘ÿqÇage“b˜y“default“and“that“I‘¥Rcould“mak˜e“theirŽ¡link‘ÿqÇage–ÿ external“b¸ãy“using“ÂexternŽ‘(Æ—«in“the“declaration“with“the“initialization,‘)yand“put“a“second“declaration,Ž¡also–UUwith“ÂexternŽ‘$Ö«,“in“the“header“ le.‘qÇThis“is“what“I'vš¸ãe“done“no˜w.Ž¡‘ -[¬LDF‘T2003.06.03.«]Ž‘Y;Added‘UUÝINVALID_REAL_SHORTŽ‘b[‡«.Ž¦ŸüÈ„`ÕÁGŽŽŸÂ25.‘ üF‘ÿ -«or‘ÕTcompilation.Ž¦·h–ª¨«Global‘UUconstan¸ãts‘@­19“·i‘Ç«+·Ž¡‘ -ÂexternŽ‘.×constŽ‘LHyrealŽ‘bû§ÝPIŽ‘pÉ!«=‘Ç4±:«0ŽŽ‘Ç·‘8àÏatanŽ‘ªÀ«(1±:«0ŽŽ‘ Ç);ŽŽŽŒ‹ xµ Šn ý‘ì«12›­F•ÃŽOR‘ÕXCOMPILA‘ÿJªTION’<¼3DLDFPR“G˜·x«25Ž €n ý•@P‘ -ÂexternŽ‘.×constŽ‘LHyrealu½‰™šs4Ž‘ÔwpairŽ‘{¸úÝINVALID_REAL_PAIRŽ’Õ/«(ÝINVALID_REALŽ‘?†D±;‘ª¨ÝINVALID_REALŽ‘A0ì«);Ž¤ ‘ -ÂexternŽ‘.×constŽ‘LHyrealu½‰™šs4Ž‘ÔwshortŽ’²7ÝINVALID_REAL_SHORTŽ’à¸i«(ÝINVALID_REALŽ‘?†D±;‘ª¨«0Ž‘ª©);Ž¡#ÂifdefŽ‘áeÝ__DECCXXŽŽ¡‘ -ÂexternŽ‘.×constŽ‘LHyrealŽ‘bû§ÝMAX_REAL_SQRTŽ’ª‰«=‘ÇÏsqrtŽ‘w«(ÝMAX_REALŽ‘*†P«);Ž¡#ÂendifŽŽ©26.‘ ü«[¬LDF‘T2002.12.10.«]Ž‘Zˆ6URš¸ãGENT:–UUFind“out“wh˜y“ÏsqrtŽ‘N«(‘ª®)“doGesn't“w˜ork.ŽŸ·h–ª¨«Global‘UUconstan¸ãts‘@­19“·i‘Ç«+·Ž¡«#ÂifdefŽ‘áeÝ__GNUC__ŽŽ¡‘ -ÂexternŽ‘.×constŽ‘LHyrealŽ‘bû§ÝMAX_REAL_SQRTŽ’ª‰«=‘Ç1±:«84467–8à·“«10Ÿü^ÿ®+19ŽŽŽ‘Cc«;Ž¡#ÂendifŽŽ¦27.‘ üF‘ÿ -«or–ÕTthe“header“ le.ŽŸ·h›ª¨«Declarations–UUfor“the“header“ le‘@­18˜·i‘Ç«+·Ž¡‘ -ÂexternŽ‘.×constŽ‘LHyrealŽ‘bû§ÝPIŽ‘n «;Ž¡‘ -ÂexternŽ‘.×constŽ‘LHyrealŽ‘bû§ÝINVALID_REALŽ’¢ë«;Ž¡‘ -ÂexternŽ‘.×constŽ‘LHyrealu½‰™šs4Ž‘ÔwpairŽ‘{¸úÝINVALID_REAL_PAIRŽ’Õ/«;Ž¡‘ -ÂexternŽ‘.×constŽ‘LHyrealu½‰™šs4Ž‘ÔwshortŽ’²7ÝINVALID_REAL_SHORTŽ’à¸i«;Ž¡‘ -ÂexternŽ‘.×constŽ‘LHyrealŽ‘bû§ÝMAX_REALŽ’÷«;Ž¡‘ -ÂexternŽ‘.×constŽ‘LHyrealŽ‘bû§ÝMAX_REAL_SQRTŽ’§Áè«;Ž¦Â28.‘ üUtilit®9y‘ÕTfunctions.Ž¦29.› üSolv®9e–´ùquadratic“equation.˜«[¬LDF‘T2002.09.03.«]Ž‘ZlTO‘9+DO:–93Ma¸ãybGe“add“functions“for“solving“cubic“andŽ¡quartic–UUequations,“if“this“is“practicable.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.06.1.«]Ž‘Th=Changed–UUreturn“tš¸ãypGe“from“ÂpairŽ‘Ñf·hÂrealŽ‘]Ù±;‘ª¨ÂrealŽ‘·i“«to“Ârealu½‰™šs4Ž‘ÔwpairŽ‘/p«,“whic˜h“is“equiv‘ÿqÇalen˜t.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h›ª¨«Declare–UUutilit¸ãy“functions‘@­21˜·i‘Ç«+·ŽŸ ‘ -Ârealu½‰™šs4Ž‘ÔwpairŽ‘9p‚Ïsolve‘‰ffŽ‘®quadr‘ÿ}'aticŽ‘{%<«(ÂrealŽ‘³.±aŽ‘ü^;‘ª¨ÂrealŽ‘]Ö±bŽ‘¨€;‘ª¨ÂrealŽ‘]Ö±cŽ‘±±«);ŽŽŽŒ‹ ‡¤ Šn ý‘ì·x«30‘­3DLDFPRÃŽG’ç’˜SOL‘ÿ8VE–ÕXQUADRA›ÿJªTIC“EQUA˜TION‘«13Ž €n ý•@PÂ30.Ž©·h›ª¨«De ne–UUutilit¸ãy“functions‘@­22˜·i‘Ç«+·Ž¤ ‘ -Ârealu½‰™šs4Ž‘ÔwpairŽ‘9p‚Ïsolve‘‰ffŽ‘®quadr‘ÿ}'aticŽ‘{%<«(ÂrealŽ‘³.±aŽ‘ü^;‘ª¨ÂrealŽ‘]Ö±bŽ‘¨€;‘ª¨ÂrealŽ‘]Ö±cŽ‘±±«)Ž¡‘ -·fŽ¡‘Ârealu½‰™šs4Ž‘ÔwpairŽ‘Cpƒ±pŽ‘Hxƒ«;Ž¦‘ÂtryŽ‘)3·fŽ¡‘±pŽ‘#:Ï rstŽ‘|«=‘Ç(·Ž‘DZbŽ‘J¨«+‘8àÏsqrtŽ‘èÙ«((±bŽ–ƒŠ·‘8à±bŽ“«)–8à·“«(4Ž›8á·“±aŽ‘ ºð·“±cŽ‘Œ»«)))±=«(2Ž˜·“±aŽ‘‚«);Ž¡‘·gŽ¦‘Âcatc®9hŽ‘.í׫(–ª¨±:“:“:Ž‘ÿ÷«)Ž¡‘·fŽ¡‘±pŽ‘#:Ï rstŽ‘|«=‘ÇÝINVALID_REALŽ‘BM\«;Ž¡‘·gŽ¦‘ÂtryŽ‘)3·fŽ¡‘±pŽ‘#:Ïse–ÿ}'c“ondŽ‘ nß«=‘Ç(·Ž‘DZbŽ‘J¨·‘8àÏsqrtŽ‘èÙ«((±bŽ–ƒŠ·‘8à±bŽ“«)–8à·“«(4Ž›8á·“±aŽ‘ ºð·“±cŽ‘Œ»«)))±=«(2Ž˜·“±aŽ‘‚«);Ž¡‘·gŽ¦‘Âcatc®9hŽ‘.í׫(–ª¨±:“:“:Ž‘ÿ÷«)Ž¡‘·fŽ¡‘±pŽ‘#:Ïse–ÿ}'c“ondŽ‘ nß«=‘ÇÝINVALID_REALŽ‘BM\«;Ž¡‘·gŽ¦‘ÂreturnŽ‘7æ¼±pŽ‘<;Ž¡‘ -·gŽŸÂ31.– üDynamic‘{TalloQÇcation.“«[¬LDF‘T2002.10.02.«]Ž‘[TO›å‰DO:–å®T‘ÿ*ªry“to“get“this“to“w•¸ãork.‘"ÒI˜ha“v“en't–å®bGeen“able“toŽ¡get–UUthis“template“function“to“instan¸ãtiate“correctly‘ÿ*ª.Ž¦·h›ª¨«Declare–UUutilit¸ãy“functions‘@­21˜·i‘Ç«+·Ž¡«#ÂifŽ‘ ´ø«0ŽŽ¡‘ -ÂtemplateŽ‘6Ñ_·hÂclassŽ‘àQ±CŽ‘"½·i‘UU±CŽ‘ 2!·Ž‘2"Ïcr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘?Áæ«(±CŽ‘ -¬·‘8à±cŽ‘ 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-«[¬LDF‘T2002.04.10.«]Ž‘YÔöAdded–"the“forw¸ãard“declaration“of“Âb•QÇo“olu½‰™šs4Ž–Ôwrealu½‰™šs4Ž“pQÇoin®9tŽ‘Qq«.‘×øIt's“needed“bGecause“it's“used“asŽ¡the–sreturn“v‘ÿqÇalue“of“ÂP•®9oin“tŽ‘¿«::‘Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘N–Ú«(‘ª®),›Ówhic¸ãh“is,˜of“course,˜declared“within“the“declaration“of“ÂclassŽŽ¡P•®9oin“tŽ‘šH«.›g~Ho•¸ãw“ev“er,‘&aÂb•QÇo“olu½‰™šs4Ž–Ôwrealu½‰™šs4Ž“pQÇoin®9tŽ‘UT«can–ü’only“bGe“de ned“Ïafter‘ÂP•®9oin“tŽ‘$¦ù«is“de ned.˜This“forw¸ãard“declarationŽ¡solv¸ães–UUthe“problem.Ž¡‘ -[¬LDF‘T2003.07.16.«]Ž‘Xî¿Added–;Ùforwš¸ãard“declaration“of“ÂEllipseŽ‘%$²«.‘iHIt's“needed,‘@òbGecause“I'v˜e“declared“ÂEllipseŽ‘(`‹«to“bGeŽ¡a‘!ÂfriendŽ›$S«of‘!ÂP®9athŽ‘²x«.‘`\F–ÿ*ªormerly“,‘+‡ÂCircleŽ‘$¯Ç«w¸ãas–!a“ÂfriendŽ˜«of“ÂP®9athŽ‘²x«,‘+‡but“noš¸ãw“it“m˜ust“bšGe“ÂEllipseŽ‘% 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üPutting–ÕTI/O“together.Ž¡52.‘ ü«This–UUis“what's“compiled.Ž¦‘ -·h–ª¨«Include‘UU les‘@­11“·iŽ¤ ‘ -h‘ª¨«V‘ÿ*ªersion–UUconš¸ãtrol“iden˜ti er‘@­10‘ª¨·iŽ¡‘ -h–ª¨«Global‘UUv‘ÿqÇariables‘@­15“·iŽ¡‘ -h›ª¨«De ne–UUI/O“functions‘@­43˜·iŽŽŽŒ‹Î Šn ý‘ì«20›­PUTTING–ÕXI/O“TOGETHER’þê&3DLDFPRÃŽG˜·x«53Ž €n ý•@PÂ53.‘ ü«This–UUis“what's“written“to“Èio.h«.Ž©·h‘ª¨Ýio.hŽ‘ ±­53‘ª¨·i‘ÇŽ¤ ‘ -h‘ª¨ÂexternŽ‘%È~«v‘ÿqÇariable‘UUdeclarations‘@­40‘ª¨·iŽ¡‘ -h›ª¨«Declare–UUI/O“functions‘@­42˜·iŽŸÂ54.– üColor“(Ècolors.webÂ).ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.11.12.«]Ž‘ZCáRemo•¸ãv“ed–ûthe“vš¸ãersion“con˜trol“iden˜ti ers“from“the“CWEB‘© les“for“the“distribution“ofŽ¡3DLDF–UU1.1.‘qÇThey're“still“used“in“mš¸ãy“dev˜elopmen˜t“v˜ersions.Ž¡‘ -[¬LDF‘T2003.12.10.«]Ž‘YQ‘Put–ž«the“vš¸ãersion“con˜trol“iden˜ti 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-ÂclassŽ‘$àRColorŽ‘D…E·fŽ¡‘ÂstringŽ‘5%OÏnameŽ‘MëS«;Ž¡‘Âb•QÇo“olŽ‘-¡hÏuse‘‰ffŽ‘®nameŽ‘X#²«;Ž¡‘Âb•QÇo“olŽ‘-¡hÏon‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘eFZ«;‘±=·‘ÿý«LDF‘UU2002.10.06.‘qÇAdded.‘o·±=Ž¡‘ÂrealŽ‘*³0Ïr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘Mþ¶«;Ž¡‘ÂrealŽ‘*³0Ïgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘W´¼«;Ž¡‘ÂrealŽ‘*³0Ïblue‘‰ffŽ‘®p‘ÿ}'artŽ‘R6.«;Ž¦‘ -ÂpublicŽ‘)=Ö«:‘·h–ª¨«Declare‘UUÂColorŽ‘"úH«functions‘@­58“·iŽ¡‘ -g«;ŽŸ ­This–ÕXcoJ«=‘DZcŽ‘ó:Ïget‘‰ffŽ–®blue‘‰ffŽ“p‘ÿ}'artŽ‘7¶º«(‘ª¨);Ž¡‘ÂifŽ‘´ú«(±nŽ‘Dz·6«=‘ÇÝ""Ž‘Z·^‘8à±uŽ‘ -¹v·‘ÇÏtrueŽ‘‹°«)‘·fŽ¡‘Ïuse‘‰ffŽ‘®nameŽ‘KIe«=‘ÇÏtrueŽ‘‹°«;Ž¡‘·gŽ¡‘ÂelseŽ‘+ØáÏuse‘‰ffŽ‘®nameŽ‘Y"C«=‘ÇÏfalseŽ‘v\«;Ž¡‘Ïon‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘Nl «=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿý«LDF‘UU2002.10.06.‘qÇAdded.‘o·±=Ž¡‘ÂreturnŽ‘4‘g«;Ž¡‘ -·gŽ¤Â62.‘ üName–ÕTand“unsigned“short“argumen®9ts.Ž¡63.‘ üConstructor.Ž¦·h–ª¨«Declare‘UUÂColorŽ‘"úH«functions‘@­58“·i‘Ç«+·Ž¤ ‘ -ÂColorŽ‘&OŸ«(ÂconstŽ‘]stringŽ‘?´å±nŽ‘Eµ;‘ª¨ÂconstŽ‘ ÅunsignedŽ‘PqNshortŽ‘nnl±rŽ‘s8€;‘ª¨ÂconstŽ‘ ÅunsignedŽ‘PqNshortŽ‘nnl±gŽ‘sO;‘ª¨ÂconstŽ‘ ÅunsignedŽ‘PqNshortŽŽ¡‘±bŽ‘"J­;‘ª¨ÂconstŽ‘ÕJb•QÇo“olŽ‘9v°±uŽ‘A÷F«=‘ÇÏtrueŽ‘‹°«);ŽŽŽŒ‹âT Šn ý‘ì«22›­CONSTR•ÃŽUCTOR’)B|3DLDFPR“G˜·x«64Ž €n ý•@PÂ64.Ž©·h–ª¨«De ne‘UUÂColorŽ‘"úH«functions‘@­59“·i‘Ç«+·Ž¤ ‘ -ÂColorŽ‘'O£«::‘ÂColorŽ‘O¢«(ÂconstŽ‘GNstringŽ‘?‰G±nŽ‘E‰á;‘ª¨ÂconstŽ‘ñöunsignedŽ‘PE°shortŽ‘n,ÿ±rŽ‘r÷;‘ª¨ÂconstŽ‘ñöunsignedŽ‘PE°shortŽ‘n,ÿ±gŽ‘sMâ;‘ª¨ÂconstŽ‘ñöunsignedŽŽ¡‘2shortŽ‘Oʨ±bŽ‘TR;‘ª¨ÂconstŽ‘ÕJb•QÇo“olŽ‘9v°±uŽ‘?0.«)Ž¡‘ -:‘qÇÏnameŽ‘7Ë«(±nŽ‘š«)‘UU·fŽ¡‘ÏnameŽ‘/«=‘DZnŽ‘Dz«;Ž¡‘ÂifŽ‘´ú«(±nŽ‘Dz·6«=‘ÇÝ""Ž‘Z·^‘8à±uŽ‘ -¹v·‘ÇÏtrueŽ‘‹°«)‘·fŽ¡‘Ïuse‘‰ffŽ‘®nameŽ‘KIe«=‘ÇÏtrueŽ‘‹°«;Ž¡‘·gŽ¡‘ÂelseŽ‘+ØáÏuse‘‰ffŽ‘®nameŽ‘Y"C«=‘ÇÏfalseŽ‘v\«;Ž¡‘Ïon‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘Nl «=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿý«LDF‘UU2002.10.06.‘qÇAdded.‘o·±=Ž¡‘Ïr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘: «=‘DZrŽ‘‘,=«255±:«0ŽŽ‘Ç!;Ž¡‘Ïgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘CȦ«=‘DZgŽ‘çû=«255±:«0ŽŽ‘Ç!;Ž¡‘Ïblue‘‰ffŽ‘®p‘ÿ}'artŽ‘>J«=‘DZbŽ‘Â=«255±:«0ŽŽ‘Ç!;Ž¡‘ -·gŽŸÂ65.‘ üSetting‘ÕTfunction.Ž¦·h–ª¨«Declare‘UUÂColorŽ‘"úH«functions‘@­58“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘# ÏsetŽ‘0ƒˆ«(ÂconstŽ‘7ÍstringŽ‘?jE±nŽ‘Ejß;‘ª¨ÂconstŽ‘âuunsignedŽ‘P&®shortŽ‘mþ|±rŽ‘rÈ;‘ª¨ÂconstŽ‘âuunsignedŽ‘P&®shortŽ‘mþ|±gŽ‘s_;‘ª¨ÂconstŽ‘âuunsignedŽ‘P&®shortŽŽ¡‘±bŽ‘"J­;‘ª¨ÂconstŽ‘ÕJb•QÇo“olŽ‘9v°±uŽ‘A÷F«=‘ÇÏfalseŽ‘v\«);ŽŸÂ66.Ž¦·h–ª¨«De ne‘UUÂColorŽ‘"úH«functions‘@­59“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"Ý3ColorŽ‘@,Õ«::‘ÏsetŽ‘xˆ«(ÂconstŽ‘ üstringŽ‘?£±nŽ‘E=;‘ª¨ÂconstŽ‘´¤unsignedŽ‘OË shortŽ‘mu ±rŽ‘r?;‘ª¨ÂconstŽ‘´¤unsignedŽ‘OË shortŽ‘mu ±gŽ‘r•ì;‘ª¨ÂconstŽ‘´¤unsignedŽŽ¡‘2shortŽ‘Oʨ±bŽ‘TR;‘ª¨ÂconstŽ‘ÕJb•QÇo“olŽ‘9v°±uŽ‘?0.«)Ž¡‘ -·fŽ¡‘ÏnameŽ‘/«=‘DZnŽ‘Dz«;Ž¡‘ÂifŽ‘´ú«(±nŽ‘Dz·6«=‘ÇÝ""Ž‘Z·^‘8à±uŽ‘ -¹v·‘ÇÏtrueŽ‘‹°«)‘·fŽ¡‘Ïuse‘‰ffŽ‘®nameŽ‘KIe«=‘ÇÏtrueŽ‘‹°«;Ž¡‘·gŽ¡‘ÂelseŽ‘+ØáÏuse‘‰ffŽ‘®nameŽ‘Y"C«=‘ÇÏfalseŽ‘v\«;Ž¡‘Ïr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘: «=‘DZrŽ‘‘,=«255±:«0ŽŽ‘Ç!;Ž¡‘Ïgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘CȦ«=‘DZgŽ‘çû=«255±:«0ŽŽ‘Ç!;Ž¡‘Ïblue‘‰ffŽ‘®p‘ÿ}'artŽ‘>J«=‘DZbŽ‘Â=«255±:«0ŽŽ‘Ç!;Ž¡‘ -·gŽ©Â67.› üThree–—Þreal“argumen®9ts.˜«[¬LDF‘T2002.10.09.«]Ž‘[1`Added–þthe“follo¸ãwing“constructor“and“setting“function.Ž¡They– äare“for“unnamed“ÂColorsŽ‘$⾫.‘tThe“DEC‘ µcompiler“can't“distinguish“bGet•¸ãw“een‘ äÂrealŽ‘q¡«and‘ äÂunsignedŽ‘4õshortŽŽ¡«argumenš¸ãts,‘óso–Û/the“o˜v˜erloaded“functions“m˜ust“di er“in“another“w˜a˜y‘ÿ*ª.‘IIn“this“case,‘óthese“v˜ersions“ha˜v˜e“no“ÏnameŽŽ¡«argumen•¸ãt.‘‘ÀI‘µ:bGeliev“e–µSthat“users“are“most“likš¸ãely“to“declare“ÂColorsŽ‘(C€«using“ÂrealŽ‘È«argumen˜ts“when“they“plan“toŽ¡moGdify–Àthem,›*xin“whic¸ãh“case“the“ÏoutputŽ‘ /«(‘ª®)“function“should“write“the“red,˜green“and“blue“v‘ÿqÇalues“to“Ïout‘‰ffŽ‘®str–ÿ}'e“amŽŽ¡«rather–e*than“ÏnameŽ‘+.«.‘¡EIf“it“turns“out“to“bšGe“necessary‘ÿ*ª,‘imore“constructors“can“b˜e“added“or“the“existing“ones“canŽ¡bGe‘UUc¸ãhanged.Ž¦Â68.‘ üConstructor.ŽŸ·h–ª¨«Declare‘UUÂColorŽ‘"úH«functions‘@­58“·i‘Ç«+·Ž¡‘ -ÂColorŽ‘&OŸ«(ÂconstŽ‘*¢realŽ‘4ÝбrŽ‘9§ä;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±gŽ‘;©[;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±bŽ‘:Ó"«);ŽŽŽŒ‹ìö Šn ý‘ì·x«69›­3DLDFPR•ÃŽG’)B|CONSTR“UCTOR˜«23Ž €n ý•@PÂ69.Ž©·h–ª¨«De ne‘UUÂColorŽ‘"úH«functions‘@­59“·i‘Ç«+·Ž¤ ‘ -ÂColorŽ‘'O£«::‘ÂColorŽ‘O¢«(ÂconstŽ‘*¢realŽ‘4ÝбrŽ‘9§ä;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±gŽ‘;©[;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±bŽ‘:Ó"«)Ž¡‘ -·fŽ¡‘ÏnameŽ‘/«=‘ÇÝ""Ž‘ Íz«;Ž¡‘Ïuse‘‰ffŽ‘®nameŽ‘AId«=‘ÇÏfalseŽ‘v\«;Ž¡‘Ïon‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘Nl «=‘ÇÏfalseŽ‘v\«;Ž¡‘ÂifŽ‘´ú«(±rŽ‘‘,<‘Ç«0Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘6F0·‘‡Ý"WARNING!È ÝInÈ ÝColor::Ž‘nKColor()È Ý(threeÈ ÝrealÈ Ž’×Ýarguments):\n"Ž’'&Ô·Ž¡‘2Ý"RedÈ ÝpartÈ ÝargumentÈ Ý<Ž’šÿÉÈ Ý0.È ÝSettingÈ Ýred_parŽ’ÿtÈ ÝtoÈ Ý0.\n\n"Ž’C…Ñ«;Ž¡‘Ïr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘D¡«=‘Ç0Ž‘Ç;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(±rŽ‘‘,>‘Ç«1Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘6F0·‘‡Ý"WARNING!È ÝInÈ ÝColor::Ž‘nKColor()È Ý(threeÈ ÝrealÈ Ž’×Ýarguments):\n"Ž’'&Ô·Ž¡‘2Ý"RedÈ ÝpartÈ ÝargumentÈ Ý>Ž’šÿÉÈ Ý1.È ÝSettingÈ Ýred_parŽ’ÿtÈ ÝtoÈ Ý1.\n\n"Ž’C…Ñ«;Ž¡‘Ïr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘D¡«=‘Ç1Ž‘Ç;Ž¡‘·gŽ¡‘ÂelseŽ‘+ØáÏr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘Që«=‘DZrŽ‘‘,«;Ž¡‘ÂifŽ‘´ú«(±gŽ‘çû<‘Ç«0Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘6F0·‘‡Ý"WARNING!È ÝInÈ ÝColor::Ž‘nKColor()È Ý(threeÈ ÝrealÈ Ž’×Ýarguments):\n"Ž’'&Ô·Ž¡‘2Ý"GreenÈ ÝpartÈ ÝargumentŽ’šÿÉÈ Ý<È Ý0.È ÝSettingÈ ÝgreenŽ’ÿ_partÈ ÝtoÈ Ý0.\n\n"Ž’X…Å«;Ž¡‘Ïgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘Mȧ«=‘Ç0Ž‘Ç;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(±gŽ‘çû>‘Ç«1Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘6F0·‘‡Ý"WARNING!È ÝInÈ ÝColor::Ž‘nKColor()È Ý(threeÈ ÝrealÈ Ž’×Ýarguments):\n"Ž’'&Ô·Ž¡‘2Ý"GreenÈ ÝpartÈ ÝargumentŽ’šÿÉÈ Ý>È Ý1.È ÝSettingÈ ÝgreenŽ’ÿ_partÈ ÝtoÈ Ý1.\n\n"Ž’X…Å«;Ž¡‘Ïgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘Mȧ«=‘Ç1Ž‘Ç;Ž¡‘·gŽ¡‘ÂelseŽ‘+ØáÏgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘[¡…«=‘DZgŽ‘çû«;Ž¡‘ÂifŽ‘´ú«(±bŽ‘Â<‘Ç«0Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘6F0·‘‡Ý"WARNING!È ÝInÈ ÝColor::Ž‘nKColor()È Ý(threeÈ ÝrealÈ Ž’×Ýarguments):\n"Ž’'&Ô·Ž¡‘2Ý"BlueÈ ÝpartÈ ÝargumentÈ Ž’šÿÉÝ<È Ý0.È ÝSettingÈ Ýblue_pŽ’ÿartÈ ÝtoÈ Ý0.\n\n"Ž’NË«;Ž¡‘Ïblue‘‰ffŽ‘®p‘ÿ}'artŽ‘HJ«=‘Ç0Ž‘Ç;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(±bŽ‘Â>‘Ç«1Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘6F0·‘‡Ý"WARNING!È ÝInÈ ÝColor::Ž‘nKColor()È Ý(threeÈ ÝrealÈ Ž’×Ýarguments):\n"Ž’'&Ô·Ž¡‘2Ý"BlueÈ ÝpartÈ ÝargumentÈ Ž’šÿÉÝ>È Ý1.È ÝSettingÈ Ýblue_pŽ’ÿartÈ ÝtoÈ Ý1.\n\n"Ž’NË«;Ž¡‘Ïblue‘‰ffŽ‘®p‘ÿ}'artŽ‘HJ«=‘Ç1Ž‘Ç;Ž¡‘·gŽ¡‘ÂelseŽ‘+ØáÏblue‘‰ffŽ‘®p‘ÿ}'artŽ‘V"÷«=‘DZbŽ‘«;Ž¡‘ÂreturnŽ‘4‘g«;Ž¡‘ -·gŽŸÂ70.‘ üSetting‘ÕTfunction.Ž¦·h–ª¨«Declare‘UUÂColorŽ‘"úH«functions‘@­58“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙÏsetŽ‘0v]«(ÂconstŽ‘*¢realŽ‘4ÝбrŽ‘9§ä;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±gŽ‘;©[;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±bŽ‘:Ó"«);ŽŽŽŒ‹úf Šn ý‘ì«24–­SETTING‘ÕXFUNCTION’u@3DLDFPRÃŽG“·x«71Ž €n ý•@PÂ71.Ž©·h–ª¨«De ne‘UUÂColorŽ‘"úH«functions‘@­59“·i‘Ç«+·Ž¤ ‘ -Âv®9oidŽ‘"ýÙColorŽ‘@M{«::‘ÏsetŽ‘xˆ«(ÂconstŽ‘*¢realŽ‘4ÝбrŽ‘9§ä;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±gŽ‘;©[;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±bŽ‘:Ó"«)Ž¡‘ -·fŽ¡‘ÏnameŽ‘/«=‘ÇÝ""Ž‘ Íz«;Ž¡‘Ïuse‘‰ffŽ‘®nameŽ‘AId«=‘ÇÏfalseŽ‘v\«;Ž¡‘Ïon‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘Nl «=‘ÇÏfalseŽ‘v\«;Ž¡‘ÂifŽ‘´ú«(±rŽ‘‘,<‘Ç«0Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘6F0·‘‡Ý"WARNING!È ÝInÈ ÝColor::Ž‘nKColor()È Ý(threeÈ ÝrealÈ Ž’×Ýarguments):\n"Ž’'&Ô·Ž¡‘2Ý"RedÈ ÝpartÈ ÝargumentÈ Ý<Ž’šÿÉÈ Ý0.È ÝSettingÈ Ýred_parŽ’ÿtÈ ÝtoÈ Ý0.\n\n"Ž’C…Ñ«;Ž¡‘Ïr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘D¡«=‘Ç0Ž‘Ç;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(±rŽ‘‘,>‘Ç«1Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘6F0·‘‡Ý"WARNING!È ÝInÈ ÝColor::Ž‘nKColor()È Ý(threeÈ ÝrealÈ Ž’×Ýarguments):\n"Ž’'&Ô·Ž¡‘2Ý"RedÈ ÝpartÈ ÝargumentÈ Ý>Ž’šÿÉÈ Ý1.È ÝSettingÈ Ýred_parŽ’ÿtÈ ÝtoÈ Ý1.\n\n"Ž’C…Ñ«;Ž¡‘Ïr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘D¡«=‘Ç1Ž‘Ç;Ž¡‘·gŽ¡‘ÂelseŽ‘+ØáÏr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘Që«=‘DZrŽ‘‘,«;Ž¡‘ÂifŽ‘´ú«(±gŽ‘çû<‘Ç«0Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘6F0·‘‡Ý"WARNING!È ÝInÈ ÝColor::Ž‘nKColor()È Ý(threeÈ ÝrealÈ Ž’×Ýarguments):\n"Ž’'&Ô·Ž¡‘2Ý"GreenÈ ÝpartÈ ÝargumentŽ’šÿÉÈ Ý<È Ý0.È ÝSettingÈ ÝgreenŽ’ÿ_partÈ ÝtoÈ Ý0.\n\n"Ž’X…Å«;Ž¡‘Ïgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘Mȧ«=‘Ç0Ž‘Ç;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(±gŽ‘çû>‘Ç«1Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘6F0·‘‡Ý"WARNING!È ÝInÈ ÝColor::Ž‘nKColor()È Ý(threeÈ ÝrealÈ Ž’×Ýarguments):\n"Ž’'&Ô·Ž¡‘2Ý"GreenÈ ÝpartÈ ÝargumentŽ’šÿÉÈ Ý>È Ý1.È ÝSettingÈ ÝgreenŽ’ÿ_partÈ ÝtoÈ Ý1.\n\n"Ž’X…Å«;Ž¡‘Ïgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘Mȧ«=‘Ç1Ž‘Ç;Ž¡‘·gŽ¡‘ÂelseŽ‘+ØáÏgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘[¡…«=‘DZgŽ‘çû«;Ž¡‘ÂifŽ‘´ú«(±bŽ‘Â<‘Ç«0Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘6F0·‘‡Ý"WARNING!È ÝInÈ ÝColor::Ž‘nKColor()È Ý(threeÈ ÝrealÈ Ž’×Ýarguments):\n"Ž’'&Ô·Ž¡‘2Ý"BlueÈ ÝpartÈ ÝargumentÈ Ž’šÿÉÝ<È Ý0.È ÝSettingÈ Ýblue_pŽ’ÿartÈ ÝtoÈ Ý0.\n\n"Ž’NË«;Ž¡‘Ïblue‘‰ffŽ‘®p‘ÿ}'artŽ‘HJ«=‘Ç0Ž‘Ç;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(±bŽ‘Â>‘Ç«1Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘6F0·‘‡Ý"WARNING!È ÝInÈ ÝColor::Ž‘nKColor()È Ý(threeÈ ÝrealÈ Ž’×Ýarguments):\n"Ž’'&Ô·Ž¡‘2Ý"BlueÈ ÝpartÈ ÝargumentÈ Ž’šÿÉÝ>È Ý1.È ÝSettingÈ Ýblue_pŽ’ÿartÈ ÝtoÈ Ý1.\n\n"Ž’NË«;Ž¡‘Ïblue‘‰ffŽ‘®p‘ÿ}'artŽ‘HJ«=‘Ç1Ž‘Ç;Ž¡‘·gŽ¡‘ÂelseŽ‘+ØáÏblue‘‰ffŽ‘®p‘ÿ}'artŽ‘V"÷«=‘DZbŽ‘«;Ž¡‘ -·gŽŸÂ72.‘ üPseudo-constructor–ÕTfor“dynamic“alloQÇcation.Ž¦·h–ª¨«Declare‘UUÂColorŽ‘"úH«functions‘@­58“·i‘Ç«+·Ž¡‘ -ÂinlineŽ‘)ŠIstaticŽ‘HÓ"ColorŽ‘hx·Ž‘mxÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“c‘ÿ}'olorŽ’µË8«(‘ª¨)Ž¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EnteringÈ ÝColor::creŽ‘kÆÜate_new_color().\n"Ž’Ð «;Ž¦‘ÂColorŽ‘3¤õ·Ž‘8¤ö±cŽ‘?¿é«=‘ÇÂnewŽ‘Ïœ«(ÂColorŽ‘Ož«);Ž¦‘±cŽ‘SÝŸ~ŽŽ‘SÞÏon‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘V¿è«=‘ÇÏtrueŽ‘‹°«;Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ExitingÈ ÝColor::creaŽ‘kÆÜte_new_color().\n"Ž’ÊÍ«;ŽŽŽŒ‹/ Šn ý‘ì·x«72‘­3DLDFPR•ÃŽG’„ PSEUDO-CONSTR“UCTOR›ÕXF“OR˜D“YNAMIC˜ALLOCA‘ÿJªTION‘«25Ž €n ý•@P‘ÂreturnŽ‘7æ¼±cŽ‘<:—«;Ž¤ ‘ -·gŽ©Â73.– üAssignmen®9t.“«[¬LDF‘T2002.09.24.«]Ž‘Zˆ6Added–UUthis“opGerator“function.ŽŸ·h–ª¨«Declare‘UUÂColorŽ‘"úH«functions‘@­58“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙopQÇeratorŽ‘N”Ž«=Ž‘V[¬(ÂconstŽ‘*¢ColorŽ‘=Ï•«&Ž‘E–³±cŽ‘Iꎫ);Ž¦Â74.ŽŸ·h–ª¨«De ne‘UUÂColorŽ‘"úH«functions‘@­59“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙColorŽ‘@M{«::Ž‘FÛ¹ÂopQÇeratorŽ‘rrn«=Ž‘z9Œ(ÂconstŽ‘*¢ColorŽ‘=Ï•«&Ž‘E–³±cŽ‘Iꎫ)Ž¡‘ -·fŽ¡‘ÏnameŽ‘/«=‘ÇÝ""Ž‘ Íz«;Ž¡‘Ïuse‘‰ffŽ‘®nameŽ‘AId«=‘ÇÏfalseŽ‘v\«;Ž¡‘Ïr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘: «=‘DZcŽ‘ó:Ïr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘#K†«;Ž¡‘Ïgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘CȦ«=‘DZcŽ‘ó:Ïgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘-Œ«;Ž¡‘Ïblue‘‰ffŽ‘®p‘ÿ}'artŽ‘>J«=‘DZcŽ‘ó:Ïblue‘‰ffŽ‘®p‘ÿ}'artŽ‘'‚þ«;Ž¡‘ -·gŽ¦Â75.– üEqualit®9y‘ÿ -«.“«[¬LDF‘T2002.09.25.«]Ž‘Z@ÀChanged– ßso“that“only“Ïr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘&Ye«,‘*Ïgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘3+•«and“Ïblue‘‰ffŽ‘®p‘ÿ}'artŽ‘-ž¼«are“compared.Ž¡This›{Ðw•¸ãa“y‘ÿ*ª,‘…nÂColorsŽ‘'Ú«that˜di er˜only˜in˜ÏnameŽ‘½¤«and/or˜Ïuse‘‰ffŽ‘®nameŽ‘1yê«are˜considered˜to˜bGe˜equal.‘å7[¬LDF‘T2002.09.24.«]ŽŽ¡Added–UUthis“opGerator“function.ŽŸ·h–ª¨«Declare‘UUÂColorŽ‘"úH«functions‘@­58“·i‘Ç«+·Ž¡‘ -Âb•QÇo“olŽ‘#¡gopQÇeratorŽ‘O8·Ž‘Vÿ:«(ÂconstŽ‘*¢ColorŽ‘=Ï•«&Ž‘E–³±cŽ‘Iꎫ)‘UUÂconstŽ‘*¢«;Ž¦Â76.ŽŸ·h–ª¨«De ne‘UUÂColorŽ‘"úH«functions‘@­59“·i‘Ç«+·Ž¡‘ -Âb•QÇo“olŽ‘#¡gColorŽ‘@ñ «::Ž‘GGÂopQÇeratorŽ‘sü·Ž‘zÝ«(ÂconstŽ‘*¢ColorŽ‘=Ï•«&Ž‘E–³±cŽ‘Iꎫ)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7漫((Ïr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘&ž·‘DZcŽ›ó:Ïr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘#K†«)–8à·^“«(Ïgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘/Ȥ·‘DZcŽ˜:Ïgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘-Œ«)“·^“«(Ïblue‘‰ffŽ‘®p‘ÿ}'artŽ‘*J·‘DZcŽ˜:Ïblue‘‰ffŽ‘®p‘ÿ}'artŽ‘'‚þ«));Ž¡‘ -·gŽ¦Â77.– üInequalit®9y‘ÿ -«.“«[¬LDF‘T2002.09.24.«]Ž‘Zˆ6Added–UUthis“opGerator“function.ŽŸ·h–ª¨«Declare‘UUÂColorŽ‘"úH«functions‘@­58“·i‘Ç«+·Ž¡‘ -Âb•QÇo“olŽ‘#¡gopQÇeratorŽ‘O8·6«=Ž‘Vÿ:(ÂconstŽ‘*¢ColorŽ‘=Ï•«&Ž‘E–³±cŽ‘Iꎫ)‘UUÂconstŽ‘*¢«;Ž¦Â78.ŽŸ·h–ª¨«De ne‘UUÂColorŽ‘"úH«functions‘@­59“·i‘Ç«+·Ž¡‘ -Âb•QÇo“olŽ‘#¡gColorŽ‘@ñ «::Ž‘GGÂopQÇeratorŽ‘sü·6«=Ž‘zÝ(ÂconstŽ‘*¢ColorŽ‘=Ï•«&Ž‘E–³±cŽ‘Iꎫ)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼·:«(·Ž‘ÏthisŽ‘²Ï·‘DZcŽ‘ó«);Ž¡‘ -·gŽ¦Â79.‘ üMoQÇdifying.Ž¦80.‘ üSet‘ÕTname.ŽŸ·h–ª¨«Declare‘UUÂColorŽ‘"úH«functions‘@­58“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙÏset‘‰ffŽ‘®nameŽ‘Kt«(ÂconstŽ‘*¢stringŽ‘?Oï±sŽ‘Cÿï«);ŽŽŽŒ‹ï Šn ý‘ì«26–­SET‘ÕXNAME’>ý–3DLDFPRÃŽG“·x«81Ž €n ý•@PÂ81.Ž©·h–ª¨«De ne‘UUÂColorŽ‘"úH«functions‘@­59“·i‘Ç«+·Ž¤ ‘ -Âv®9oidŽ‘"ýÙColorŽ‘@M{«::‘Ïset‘‰ffŽ‘®nameŽ‘)ví«(ÂconstŽ‘*¢stringŽ‘?Oï±sŽ‘Cÿï«)Ž¡‘ -·fŽ¡‘ÏnameŽ‘/«=‘DZsŽ‘w«;Ž¡‘ -·gŽŸÂ82.‘ üSet–ÕTuse“name.Ž¦·h–ª¨«Declare‘UUÂColorŽ‘"úH«functions‘@­58“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙÏset‘‰ffŽ–®use‘‰ffŽ“nameŽ‘]1«(ÂconstŽ‘*¢b•QÇo“olŽ‘7̱bŽ‘<²«);ŽŸÂ83.Ž¦·h–ª¨«De ne‘UUÂColorŽ‘"úH«functions‘@­59“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙColorŽ‘@M{«::‘Ïset‘‰ffŽ–®use‘‰ffŽ“nameŽ‘;33«(ÂconstŽ‘*¢b•QÇo“olŽ‘7̱bŽ‘<²«)Ž¡‘ -·fŽ¡‘Ïuse‘‰ffŽ‘®nameŽ‘AId«=‘DZbŽ‘«;Ž¡‘ -·gŽŸÂ84.‘ üMoQÇdify‘ÿ -«.Ž¦·h–ª¨«Declare‘UUÂColorŽ‘"úH«functions‘@­58“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙÏmo‘ÿ}'difyŽ‘ACÚ«(ÂconstŽ‘*¢realŽ‘4ÝбrŽ‘9§ä;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±gŽ‘>ps«=‘Ç0Ž–DZ;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±bŽ‘=š:«=‘Ç0Ž“);ŽŽŽŒ‹T Šn ý‘ì·x«85–­3DLDFPRÃŽG’HèJMODIFY“«27Ž €n ý•@PÂ85.Ž©·h–ª¨«De ne‘UUÂColorŽ‘"úH«functions‘@­59“·i‘Ç«+·Ž¤ ‘ -Âv®9oidŽ‘"ýÙColorŽ‘@M{«::‘Ïmo‘ÿ}'difyŽ‘F«(ÂconstŽ‘*¢realŽ‘4ÝбrŽ‘9§ä;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±gŽ‘;©[;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±bŽ‘:Ó"«)Ž¡‘ -·fŽ¡‘Ïr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘: «+=ŽŽ‘Lgô±rŽ‘Q2«;Ž¡‘Ïgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘CȦ«+=ŽŽ‘Vú±gŽ‘[>Ý«;Ž¡‘Ïblue‘‰ffŽ‘®p‘ÿ}'artŽ‘>J«+=ŽŽ‘PŸl±bŽ‘Tê«;Ž¡‘ÂifŽ‘´ú«(Ïr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘&ž±>‘Ç«1Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘3|Á·‘ÇÝ"WARNING!È ÝInÈ ÝColor::Ž‘kÆÜmodify():\n"Ž’®8·‘ÇÝ"red_partÈ ÝisÈ ÝgreaterŽ‘kÆÜÈ ÝthanÈ Ý1:È Ý"Ž’£”>·‘ÇÏr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘(Ù¶·Ž¡‘2Ïend‘‚ØlŽ‘H¸ß·‘ÇÝ"SettingÈ Ýred_partÈ ÝtoŽ‘kÆÜÈ Ý1.\n\n"Ž’–M,«;Ž¡‘Ïr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘D¡«=‘Ç1Ž‘Ç;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(Ïr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘&ž±<‘Ç«0Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘3Ù·‘#mÝ"WARNING!È ÝInÈ ÝColor::Ž‘l#1modify():\n"Ž’®Ìâ·‘#mÝ"red_partÈ ÝisÈ ÝlessÈ ÝthŽ‘l#1anÈ Ý0:È Ý"Ž’”Œñ·‘#mÏr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘)’`·Ž¡‘2Ïend‘‚ØlŽ‘H¸ß·‘ÇÝ"SettingÈ Ýred_partÈ ÝtoŽ‘kÆÜÈ Ý0.\n\n"Ž’–M,«;Ž¡‘Ïr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘D¡«=‘Ç0Ž‘Ç;Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(Ïgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘/Ȥ±>‘Ç«1Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘4w0·‘Á‡Ý"WARNING!È ÝInÈ ÝColor::Ž‘lÁKmodify():\n"Ž—° ·‘Á‡Ý"green_partÈ ÝisÈ ÝgreatŽ‘lÁKerÈ ÝthanÈ Ý1:È Ý"Ž“·Ž¡‘2Ïgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘aÈ©·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÝ"SettingÈ Ýgreen_partÈ Ž‘kÆÜÝtoÈ Ý1.\n\n"Ž’ Í&«;Ž¡‘Ïgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘Mȧ«=‘Ç1Ž‘Ç;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(Ïgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘/Ȥ±<‘Ç«0Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘3|Á·‘ÇÝ"WARNING!È ÝInÈ ÝColor::Ž‘kÆÜmodify():\n"Ž’®8·‘ÇÝ"green_partÈ ÝisÈ ÝlessÈ Ž‘kÆÜÝthanÈ Ý0:È Ý"Ž’žTA·‘ÇÏgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘2¼·Ž¡‘2Ïend‘‚ØlŽ‘H¸ß·‘ÇÝ"SettingÈ Ýgreen_partÈ Ž‘kÆÜÝtoÈ Ý0.\n\n"Ž’ Í&«;Ž¡‘Ïgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘Mȧ«=‘Ç0Ž‘Ç;Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(Ïblue‘‰ffŽ‘®p‘ÿ}'artŽ‘*J±>‘Ç«1Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘4—ø·‘âOÝ"WARNING!È ÝInÈ ÝColor::Ž‘lâmodify():\n"Ž’°J¦·‘âOÝ"blue_partÈ ÝisÈ ÝgreateŽ‘lârÈ ÝthanÈ Ý1:È Ý"Ž’« -©·Ž¡‘2Ïblue‘‰ffŽ‘®p‘ÿ}'artŽ‘\J·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÝ"SettingÈ Ýblue_partÈ ÝtŽ‘kÆÜoÈ Ý1.\n\n"Ž’›)«;Ž¡‘Ïblue‘‰ffŽ‘®p‘ÿ}'artŽ‘HJ«=‘Ç1Ž‘Ç;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(Ïblue‘‰ffŽ‘®p‘ÿ}'artŽ‘*J±<‘Ç«0Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘3 º·‘ëÝ"WARNING!È ÝInÈ ÝColor::Ž‘kêÕmodify():\n"Ž’®\*·‘ëÝ"blue_partÈ ÝisÈ ÝlessÈ ÝtŽ‘kêÕhanÈ Ý0:È Ý"Ž’™\6·‘ëÏblue‘‰ffŽ‘®p‘ÿ}'artŽ‘-Y ·Ž¡‘2Ïend‘‚ØlŽ‘H¸ß·‘ÇÝ"SettingÈ Ýblue_partÈ ÝtŽ‘kÆÜoÈ Ý0.\n\n"Ž’›)«;Ž¡‘Ïblue‘‰ffŽ‘®p‘ÿ}'artŽ‘HJ«=‘Ç0Ž‘Ç;Ž¡‘·gŽ¡‘ÂreturnŽ‘4‘g«;Ž¡‘ -·gŽŸÂ86.‘ üSet–ÕTred“part.Ž¦·h–ª¨«Declare‘UUÂColorŽ‘"úH«functions‘@­58“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙÏset‘‰ffŽ›®r–ÿ}'e“d‘‰ffŽ˜p“artŽ‘UúD«(ÂconstŽ‘*¢realŽ‘4ÝбrŽ‘9§ä«);ŽŽŽŒ‹#† Šn ý‘ì«28›­SET–ÕXRED“P–ÿJªAR“T’,ÏL3DLDFPRÃŽG˜·x«87Ž €n ý•@PÂ87.Ž©·h–ª¨«De ne‘UUÂColorŽ‘"úH«functions‘@­59“·i‘Ç«+·Ž¤ ‘ -Âv®9oidŽ‘"ýÙColorŽ‘@M{«::‘Ïset‘‰ffŽ›®r–ÿ}'e“d‘‰ffŽ˜p“artŽ‘3üo«(ÂconstŽ‘*¢realŽ‘4ÝбrŽ‘9§ä«)Ž¡‘ -·fŽ¡‘ÂifŽ‘´ú«(±rŽ‘‘,>‘Ç«1Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘3|×·‘Ç.Ý"WARNING!È ÝInÈ ÝColor::Ž‘kÆòset_red_part():\n"Ž’Í”R·‘Ç.Ý"rÈ ÝisÈ ÝgreaterÈ ÝthanÈ Ý1Ž‘kÆò:È Ý"Ž‘~Ô·‘Ç.±rŽ‘ -Xp·‘Ç.Ïend‘‚ØlŽ‘€·Ž¡‘2Ý"SettingÈ Ýred_partÈ ÝtoŽ’šÿÉÈ Ý1.\n\n"Ž’ņ«;Ž¡‘Ïr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘D¡«=‘Ç1Ž‘Ç;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(±rŽ‘‘,<‘Ç«0Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘3Öp·‘ ÇÝ"WARNING!È ÝInÈ ÝColor::Ž‘l ‹set_red_part():\n"Ž’ÎG„·‘ ÇÝ"rÈ ÝisÈ ÝlessÈ ÝthanÈ Ý0:È Ý"Ž‘oǺ·‘ DZrŽ‘ ¢·‘ ÇÏend‘‚ØlŽ‘3P·Ž¡‘2Ý"SettingÈ Ýred_partÈ ÝtoŽ’šÿÉÈ Ý0.\n\n"Ž’ņ«;Ž¡‘Ïr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘D¡«=‘Ç0Ž‘Ç;Ž¡‘·gŽ¡‘ÂelseŽ‘+ØáÏr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘Që«=‘DZrŽ‘‘,«;Ž¡‘ÂreturnŽ‘4‘g«;Ž¡‘ -·gŽŸÂ88.‘ üSet–ÕTgreen“part.Ž¦·h–ª¨«Declare‘UUÂColorŽ‘"úH«functions‘@­58“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙÏset‘‰ffŽ›®gr–ÿ}'e“en‘‰ffŽ˜p“artŽ‘_°J«(ÂconstŽ‘*¢realŽ‘4ÝбgŽ‘9þ³«);ŽŸÂ89.Ž¦·h–ª¨«De ne‘UUÂColorŽ‘"úH«functions‘@­59“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙColorŽ‘@M{«::‘Ïset‘‰ffŽ›®gr–ÿ}'e“en‘‰ffŽ˜p“artŽ‘=²u«(ÂconstŽ‘*¢realŽ‘4ÝбgŽ‘9þ³«)Ž¡‘ -·fŽ¡‘ÂifŽ‘´ú«(±gŽ‘çû>‘Ç«1Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘4¨·‘YÿÝ"WARNING!È ÝInÈ ÝColor::Ž‘lYÃset_green_part():\n"Ž’Ù9î·‘YÿÝ"gÈ ÝisÈ ÝgreaterÈ ÝthanÈ Ý1Ž‘lYÃ:È Ý"Ž‘ú!·‘Yÿ±gŽ‘ Ôá·Ž¡‘2Ïend‘‚ØlŽ‘H¸ß·‘ÇÝ"SettingÈ Ýgreen_partÈ Ž‘kÆÜÝtoÈ Ý1.\n\n"Ž’ Í&«;Ž¡‘Ïgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘Mȧ«=‘Ç1Ž‘Ç;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(±gŽ‘çû<‘Ç«0Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘3˜Ç·‘ãÝ"WARNING!È ÝInÈ ÝColor::Ž‘kââset_green_part():\n"Ž’ØL,·‘ãÝ"gÈ ÝisÈ ÝlessÈ ÝthanÈ Ý0:È Ý"Ž‘oLh·‘ã±gŽ‘ -ç·‘ãÏend‘‚ØlŽ‘·þ·Ž¡‘2Ý"SettingÈ Ýgreen_partÈ Ž’šÿÉÝtoÈ Ý0.\n\n"Ž’Ы;Ž¡‘Ïgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘Mȧ«=‘Ç0Ž‘Ç;Ž¡‘·gŽ¡‘ÂelseŽ‘+ØáÏgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘[¡…«=‘DZgŽ‘çû«;Ž¡‘ÂreturnŽ‘4‘g«;Ž¡‘ -·gŽŸÂ90.‘ üSet–ÕTblue“part.Ž¦·h–ª¨«Declare‘UUÂColorŽ‘"úH«functions‘@­58“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙÏset‘‰ffŽ–®blue‘‰ffŽ“p‘ÿ}'artŽ‘Z1¼«(ÂconstŽ‘*¢realŽ‘4ÝбbŽ‘9(z«);ŽŽŽŒ‹0W Šn ý‘ì·x«91›­3DLDFPRÃŽG’'ÜSET–ÕXBLUE“P–ÿJªAR“T˜«29Ž €n ý•@PÂ91.Ž©·h–ª¨«De ne‘UUÂColorŽ‘"úH«functions‘@­59“·i‘Ç«+·Ž¤ ‘ -Âv®9oidŽ‘"ýÙColorŽ‘@M{«::‘Ïset‘‰ffŽ–®blue‘‰ffŽ“p‘ÿ}'artŽ‘83ç«(ÂconstŽ‘*¢realŽ‘4ÝбbŽ‘9(z«)Ž¡‘ -·fŽ¡‘ÂifŽ‘´ú«(±bŽ‘Â>‘Ç«1Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘43å·‘~<Ý"WARNING!È ÝInÈ ÝColor::Ž‘l~set_blue_part():\n"Ž’ÔBk·‘~<Ý"bÈ ÝisÈ ÝgreaterÈ ÝthanÈ Ý1Ž‘l~:È Ý"Ž’€B›·‘~<±bŽ‘ G"·Ž¡‘2Ïend‘‚ØlŽ‘H¸ß·‘ÇÝ"SettingÈ Ýblue_partÈ ÝtŽ‘kÆÜoÈ Ý1.\n\n"Ž’›)«;Ž¡‘Ïblue‘‰ffŽ‘®p‘ÿ}'artŽ‘HJ«=‘Ç1Ž‘Ç;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(±bŽ‘Â<‘Ç«0Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘3»g·‘¾Ý"WARNING!È ÝInÈ ÝColor::Ž‘l‚set_blue_part():\n"Ž’ÓQo·‘¾Ý"bÈ ÝisÈ ÝlessÈ ÝthanÈ Ý0:È Ý"Ž‘o‘¨·‘¾±bŽ‘ -V&·‘¾Ïend‘‚ØlŽ‘ý>·Ž¡‘2Ý"SettingÈ Ýblue_partÈ ÝtŽ’šÿÉoÈ Ý0.\n\n"Ž’ÊÆ«;Ž¡‘Ïblue‘‰ffŽ‘®p‘ÿ}'artŽ‘HJ«=‘Ç0Ž‘Ç;Ž¡‘·gŽ¡‘ÂelseŽ‘+ØáÏblue‘‰ffŽ‘®p‘ÿ}'artŽ‘V"÷«=‘DZbŽ‘«;Ž¡‘ÂreturnŽ‘4‘g«;Ž¡‘ -·gŽŸÂ92.‘ üSho®9w.Ž¦·h–ª¨«Declare‘UUÂColorŽ‘"úH«functions‘@­58“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙÏshowŽ‘9ˆØ«(ÂstringŽ‘!%MÏtextŽ‘5D1«=‘ÇÝ""Ž‘ Íz«)‘UUÂconstŽ‘*¢«;ŽŸÂ93.Ž¦·h–ª¨«De ne‘UUÂColorŽ‘"úH«functions‘@­59“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙColorŽ‘@M{«::‘ÏshowŽ‘‹«(ÂstringŽ‘!%MÏtextŽ‘2}«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂifŽ‘´ú«(ÏtextŽ‘ä·‘ÇÝ""Ž‘ Íz«)‘ÏtextŽ‘ä«=‘ÇÝ"Color:"Ž‘-Mh«;Ž¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÏtextŽ‘åü·‘ÇÏend‘‚ØlŽ‘¸Ú«;Ž¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"nameÈ Ý==È Ý"Ž‘:”z·‘ÇÏget‘‰ffŽ‘®nameŽ‘+ÀØ«(‘ª¨)–Ç·“Ïend‘‚ØlŽ‘¸Ú«;Ž¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"use_nameÈ Ý==È Ý"Ž‘O”n·‘ÇÏget‘‰ffŽ–®use‘‰ffŽ“nameŽ‘=}«(‘ª¨)–Ç·“Ïend‘‚ØlŽ‘¸Ú«;Ž¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"red_partÈ Ý==È Ý"Ž‘O”n·‘ÇÏget‘‰ffŽ›®r–ÿ}'e“d‘‰ffŽ˜p“artŽ‘6FZ«(‘ª¨)–Ç·“Ïend‘‚ØlŽ‘¸Ú«;Ž¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"green_partÈ Ý==È Ý"Ž‘Zh·‘ÇÏget‘‰ffŽ›®gr–ÿ}'e“en‘‰ffŽ˜p“artŽ‘?ü`«(‘ª¨)–Ç·“Ïend‘‚ØlŽ‘¸Ú«;Ž¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"blue_partÈ Ý==È Ý"Ž‘TÔk·‘ÇÏget‘‰ffŽ–®blue‘‰ffŽ“p‘ÿ}'artŽ‘:}Ò«(‘ª¨)–Ç·“Ïend‘‚ØlŽ‘ò·“Ïend‘‚ØlŽ‘¸Ú«;Ž¡‘ÂreturnŽ‘4‘g«;Ž¡‘ -·gŽ¤Â94.‘ üReturning–ÕTelemen®9ts“and“information.Ž¡95.‘ üIs–ÕTon“free“store.Ž¦·h–ª¨«Declare‘UUÂColorŽ‘"úH«functions‘@­58“·i‘Ç«+·Ž¤ ‘ -ÂinlineŽ‘)ŠIb•QÇo“olŽ‘C+¯Ïis‘‰ffŽ–®on‘‰ffŽ“fr–ÿ}'e“e‘‰ffŽ‘®stor“eŽ’…¦„«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼Ïon‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘o‹®«;Ž¡‘ -·gŽŸÂ96.› üGet–WƒColor“parts.˜«[¬LDF‘T2002.09.24.«]Ž‘ZùjThese–Ɖfunctions“alw•¸ãa“ys–Ɖreturn“a“ÂrealŽ‘$b«;‘ÿ"the“argumen¸ãt“Ïde‘ÿ}'cimalŽŽ¡«can't–UUmak¸ãe“them“return“an“ÂunsignedŽ‘3ŒcshortŽ‘N±«.ŽŽŽŒ‹:\ Šn ý‘ì«30›­GET–ÕXRED“P–ÿJªAR“T’*Ý(3DLDFPRÃŽG˜·x«97Ž €n ý•@PÂ97.‘ üGet–ÕTred“part.Ž©·h–ª¨«Declare‘UUÂColorŽ‘"úH«functions‘@­58“·i‘Ç«+·Ž¤ ‘ -ÂinlineŽ‘)ŠIrealŽ‘@=wÏget‘‰ffŽ›®r–ÿ}'e“d‘‰ffŽ˜p“artŽ‘s¼¹«(Âb•QÇo“olŽ‘¡fÏde‘ÿ}'cimalŽ‘>©Þ«=‘ÇÏfalseŽ‘v\«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂifŽ‘´ú«(Ïde‘ÿ}'cimalŽ‘"A`«)‘ÂreturnŽ‘(æºÏtruncŽ‘Aõ«((Ïr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘%„f·‘8à«255ŽŽ‘8ã)–8à+“±:«5ŽŽ‘ ÿþ);Ž¡‘ÂelseŽ‘+ØáreturnŽ‘O¿›Ïr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘s !«;Ž¡‘ -·gŽŸÂ98.‘ üGet–ÕTgreen“part.Ž¦·h–ª¨«Declare‘UUÂColorŽ‘"úH«functions‘@­58“·i‘Ç«+·Ž¡‘ -ÂinlineŽ‘)ŠIrealŽ‘@=wÏget‘‰ffŽ›®gr–ÿ}'e“en‘‰ffŽ˜p“artŽ‘}r¿«(Âb•QÇo“olŽ‘¡fÏde‘ÿ}'cimalŽ‘>©Þ«=‘ÇÏfalseŽ‘v\«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂifŽ‘´ú«(Ïde‘ÿ}'cimalŽ‘"A`«)‘ÂreturnŽ‘(æºÏtruncŽ‘Aõ«((Ïgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘/:l·‘8à«255ŽŽ‘8ã)–8à+“±:«5ŽŽ‘ ÿþ);Ž¡‘ÂelseŽ‘+ØáreturnŽ‘O¿›Ïgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘|Á'«;Ž¡‘ -·gŽŸÂ99.‘ üGet–ÕTblue“part.Ž¦·h–ª¨«Declare‘UUÂColorŽ‘"úH«functions‘@­58“·i‘Ç«+·Ž¡‘ -ÂinlineŽ‘)ŠIrealŽ‘@=wÏget‘‰ffŽ–®blue‘‰ffŽ“p‘ÿ}'artŽ‘wô1«(Âb•QÇo“olŽ‘¡fÏde‘ÿ}'cimalŽ‘>©Þ«=‘ÇÏfalseŽ‘v\«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂifŽ‘´ú«(Ïde‘ÿ}'cimalŽ‘"A`«)‘ÂreturnŽ‘(æºÏtruncŽ‘Aõ«((Ïblue‘‰ffŽ‘®p‘ÿ}'artŽ‘)»Þ·‘8à«255ŽŽ‘8ã)–8à+“±:«5ŽŽ‘ ÿþ);Ž¡‘ÂelseŽ‘+ØáreturnŽ‘O¿›Ïblue‘‰ffŽ‘®p‘ÿ}'artŽ‘wB™«;Ž¡‘ -·gŽŸÂ100.‘ üGet–ÕTuse“name.Ž¦·h–ª¨«Declare‘UUÂColorŽ‘"úH«functions‘@­58“·i‘Ç«+·Ž¡‘ -Âb•QÇo“olŽ‘#¡gÏget‘‰ffŽ–®use‘‰ffŽ“nameŽ‘^Wm«(‘ª®)‘UUÂconstŽ‘*¢«;ŽŸÂ101.Ž¦·h–ª¨«De ne‘UUÂColorŽ‘"úH«functions‘@­59“·i‘Ç«+·Ž¡‘ -Âb•QÇo“olŽ‘#¡gColorŽ‘@ñ «::‘Ïget‘‰ffŽ–®use‘‰ffŽ“nameŽ‘;¶ -«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼Ïuse‘‰ffŽ‘®nameŽ‘bi«;Ž¡‘ -·gŽŸÂ102.‘ üGet‘ÕTname.Ž¦·h–ª¨«Declare‘UUÂColorŽ‘"úH«functions‘@­58“·i‘Ç«+·Ž¡‘ -ÂinlineŽ‘)ŠIstringŽ‘J¯–Ïget‘‰ffŽ‘®nameŽ‘s©V«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼ÏnameŽ‘P¬À«;Ž¡‘ -·gŽŸÂ103.‘ üOutput‘ÕTopQÇerator.Ž¦·h›ª¨«Declare–UUnon-mem¸ãbGer“functions“for“ÂColorŽ‘#ä÷­103˜·i‘ÇŽ¡‘ -Ïostr–ÿ}'e“amŽ‘/«&‘8àÂopQÇeratorŽ‘-Ï•·Ž‘7Ï–«(Ïostr–ÿ}'e“amŽ‘%«&‘8à±oŽ‘Ä;‘ª¨ÂconstŽ‘ÕJColorŽ‘?z=«&Ž‘GA[±cŽ‘K•6«);ŽŸ ­This–ÕXco‘h«;Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(ÏnameŽ‘·‘ÇÝ""Ž‘ Íz«)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘8(¢·‘rùÝ"ERROR!È ÝInÈ ÝColor::deŽ‘pr½fine_colors_mp():\n"Ž’ákâ·Ž¡‘2Ý"nameÈ ÝisÈ Ýempty.È ÝNotŽ’šÿÉÈ ÝdoingÈ ÝanythingÈ ÝandÈ Ž’ÿÝreturning.\n"Ž’KŒæ·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘>‘h«;Ž¡‘·gŽ¡‘Ïout‘‰ffŽ‘®str–ÿ}'e“amŽ‘FlÀ·‘,"Ý"colorÈ Ý"Ž‘0Þ”·‘,"ÏnameŽ–H·‘,"Ý";"Ž‘ž£·‘,"Ý"È Ý"Ž›Þ ·‘,"ÏnameŽ“·‘,"Ý"È Ý=È Ý("Ž‘&^š·‘,"Ïget‘‰ffŽ›®r–ÿ}'e“d‘‰ffŽ˜p“artŽ‘6«d«(‘ª¨)–,"·“Ý",È Ý"Ž˜·Ž¡‘(Ïget‘‰ffŽ›®gr–ÿ}'e“en‘‰ffŽ˜p“artŽ‘e5L«(›ª¨)–Ç·“Ý",È Ý"Ž‘Œ·“Ïget‘‰ffŽ–®blue‘‰ffŽ“p‘ÿ}'artŽ‘:}Ò«(˜)“·“Ý");\n"Ž‘%”†·“Ï ushŽ‘€«;Ž¡‘ÂreturnŽ‘4‘g«;Ž¡‘ -·gŽŸÂ107.– üInitialize‘ÃColors.“«[¬LDF‘T2002.09.25.«]Ž‘\x=This–E\function“presuppGoses“the“existence“of“ÂnamespaceŽŽ¡ColorsŽ‘ ØÚ«.Ž¦·h–ª¨«Declare‘UUÂColorŽ‘"úH«functions‘@­58“·i‘Ç«+·Ž¡‘ -ÂstaticŽ‘)HÚv®9oidŽ‘BF²Ïinitialize‘‰ffŽ‘®c‘ÿ}'olorsŽ’†Í«(‘ª®);ŽŽŽŒ‹ Oï Šn ý‘ì«32–­INITIALIZE‘ÕXÂCOLORS’­3DLDFPRÃŽG“·x«108Ž €n ý•@PÂ108.Ž©·h–ª¨«De ne‘UUÂColorŽ‘"úH«functions‘@­59“·i‘Ç«+·Ž¤ ‘ -Âv®9oidŽ‘"ýÙColorŽ‘@M{«::‘Ïinitialize‘‰ffŽ‘®c‘ÿ}'olorsŽ‘DÀ«(‘ª®)Ž¡‘ -·fŽ¡‘ÂusingŽ‘2SˆnamespaceŽ‘k÷ColorsŽ’ŒÏÜ«;Ž¦‘ÂifŽ‘´ú«(·:Ïout‘‰ffŽ‘®str–ÿ}'e“amŽ‘/@œ±:Ïis‘‰ffŽ‘®op‘ÿ}'enŽ‘ «(‘ª¨))‘·fŽ¡‘Ïc‘ÿ}'errŽ‘8-·‘P„Ý"ERROR!È ÝInÈ ÝColor::inŽ‘pPHitialize_colors():\nŽ’ÙP "Ž’æfõ·Ž¡‘2Ý"out_streamÈ ÝisÈ ÝcloseŽ’šÿÉd!È ÝReturning.\n"Ž’÷·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘>‘h«;Ž¡‘·gŽ¡‘Ïout‘‰ffŽ‘®str–ÿ}'e“amŽ‘F¶·‘ÇÝ"%%%È ÝColorÈ ÝdefinitioŽ‘kÆÜns.\n\n"Ž’–M,«;Ž¡#ÂifŽ‘ Öo«0Ž‘$Öq±=·‘!t«[¬LDF‘T2002.09.25.«]Ž‘TK%These–vÌcolors“are“already“de ned“in“MET‘ÿ*ªAPOST‘vÄand“their“de nitions“areŽ¡‘(not–UUlikš¸ãely“to“c˜hange.‘qÇHo˜w˜ev˜er,“if“they“do,“I“can“commen˜t“these“function“calls“bac˜k“in.‘o·±=Ž¡‘Ïr–ÿ}'e“dŽ‘"s/±:Ïde ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn«(‘ª¨);Ž¡‘Ïgr–ÿ}'e“enŽ‘+å±:Ïde ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn«(‘ª¨);Ž¡‘ÏblueŽ‘&by±:Ïde ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn«(‘ª¨);Ž¡‘ÏblackŽ‘+ Ö±:Ïde ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn«(‘ª¨);Ž¡‘ÏwhiteŽ‘,Á±:Ïde ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn«(‘ª¨);Ž¡‘Ïb–ÿ}'ackgr“oundŽ‘Euø±:Ïde ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn«(‘ª¨);Ž¡#ÂendifŽŽ¡‘Ïyel‘‚ØlowŽ‘0k³±:Ïde ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn«(‘ª¨);Ž¡‘ÏcyanŽ‘)w‘±:Ïde ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn«(‘ª¨);Ž¡‘ÏmagentaŽ‘9Ò±:Ïde ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn«(‘ª¨);Ž¡‘Ïor‘ÿ}'angeŽ‘2)±:Ïde ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn«(‘ª¨);Ž¡‘ÏvioletŽ‘,·±:Ïde ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn«(‘ª¨);Ž¡‘ÏpurpleŽ‘097±:Ïde ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn«(‘ª¨);Ž¡‘Ïyel‘‚Ølow‘‰ffŽ‘®gr–ÿ}'e“enŽ‘Jhl±:Ïde ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn«(‘ª¨);Ž¡‘Ïgr–ÿ}'e“en‘‰ffŽ‘®yel‘‚ØlowŽ‘J·–±:Ïde ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn«(‘ª¨);Ž¡‘Ïblue‘‰ffŽ‘®violetŽ‘A„j±:Ïde ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn«(‘ª¨);Ž¡‘Ïgr‘ÿ}'ayŽ‘'ªÿ±:Ïde ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn«(‘ª¨);Ž¡‘Ïlight‘‰ffŽ‘®gr‘ÿ}'ayŽ‘>ܱ:Ïde ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn«(‘ª¨);Ž¡‘Ïviolet‘‰ffŽ‘®r–ÿ}'e“dŽ‘=b£±:Ïde ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn«(‘ª¨);Ž¡‘Ïdefault‘‰ffŽ‘®b–ÿ}'ackgr“oundŽ‘fF!±:Ïde ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn«(‘ª¨);Ž¡‘±=·‘ÿý«[¬LDF‘T2002.09.25.«]Ž‘T7Curren¸ãtly‘ÿ*ª,–UUthis“function“doGes“nothing“if“I'm“using“all“of“the“colors.‘o·±=Ž¡‘Ïout‘‰ffŽ‘®str–ÿ}'e“amŽ‘F¶·‘ÇÝ"\n%%%È ÝEndÈ ÝofÈ ÝColorÈ Ž‘kÆÜÝdefinitions.\n\n"Ž’Å«;Ž¡‘ÂreturnŽ‘4‘g«;Ž¡‘ -·gŽŸÂ109.– üNamespace‘ :Colors.“«Here–'(I‘'can“put“either“·h›ª¨«Ma‘Ž8jor“ÂColorsŽ‘(@­112˜·i“«or“·h˜«All“ÂColorsŽ‘(@­0˜·i“«in¸ãto“·h˜«DeclareŽ¡ÂnamespaceŽ‘9‡ÀColorsŽ‘^ ž­109‘ª¨·i«,›?&and–9›commen¸ãt“out“the“other,˜depGending“on“what“I‘9”w•¸ãan“t.‘h‰This›9›prev“en“ts˜toGo˜m“uc“hŽ¡unneeded–cošGde“from“b˜eing“pro˜cessed.‘[V·h›ª¨«All“ÂColorsŽ‘(*Þ­0˜·i“«is“vš¸ãery“long,‘xso“I‘ïneither“w˜an˜t“to“compile“it,‘xwrite“theŽ¡ÂexternŽ‘#ôí«declarations–,lfrom“it“to“Ècolors.h«,›4›nor“prin¸ãt“out“the“coGde“when“I‘,brun“Ècweave«,˜unless“I‘,breally“w•¸ãan“t‘,ltoŽ¡use‘UUit.‘qÇ[¬LDF‘T2002.09.25.«]ŽŽ¦·h–ª¨«Declare‘UUÂnamespaceŽ‘<øÏColorsŽ‘b­­109“·i‘ÇŽ¡‘ -h–ª¨«Ma‘Ž8jor‘UUÂColorsŽ›(n3­112“·i‘±=·“h“«All‘UUÂColorsŽ˜­0“·i‘ÿý±=Ž¤ ­This–ÕXco±;‘ª¨«173ŽŽ–ª«±;‘ª¨«255ŽŽ“±;‘ª¨«47ŽŽ‘ ªª);‘±=·‘ÿý«Orange.‘o·±=Ž¡‘ÂexternŽ‘8ØconstŽ‘VHzColorŽ‘uímÏor‘ÿ}'angeŽ’“ð”«(Ý"orange"Ž‘*†P±;‘ª¨«255ŽŽ–ª«±;‘ª¨«165ŽŽ“±;‘ª¨«0Ž‘ª©±;‘ª¨ÏtrueŽ‘o@«);‘±=·‘ÿý«Violet.‘o·±=Ž¡‘ÂexternŽ‘8ØconstŽ‘VHzColorŽ‘uímÏvioletŽ’Ž¤€«(Ý"violet"Ž‘*†P±;‘ª¨«238ŽŽ–ª«±;‘ª¨«130ŽŽ“±;‘ª¨«238ŽŽ“±;‘ª¨ÏtrueŽ‘o@«);Ž¡‘ÂexternŽ‘8ØconstŽ‘VHzColorŽ‘uímÏpurpleŽ’’&¢«(Ý"purple"Ž‘*†P±;‘ª¨«160ŽŽ–ª«±;‘ª¨«32ŽŽ‘ ªª±;‘ª¨«240ŽŽ“±;‘ª¨ÏtrueŽ‘o@«);Ž¡‘ÂexternŽ‘8ØconstŽ‘VHzColorŽ‘uímÏblue‘‰ffŽ‘®violetŽ’£qÕ«(Ý"blue_violet"Ž‘DÆA±;‘ª¨«138ŽŽ–ª«±;‘ª¨«43ŽŽ‘ ªª±;‘ª¨«226ŽŽ“);‘±=·‘ÿý«Green.‘o·±=Ž¡‘ÂexternŽ‘8ØconstŽ‘VHzColorŽ‘uímÏyel‘‚Ølow‘‰ffŽ‘®gr–ÿ}'e“enŽ’¬U׫(Ý"yellow_green"Ž‘J>±;‘ª¨«154ŽŽ–ª«±;‘ª¨«205ŽŽ“±;‘ª¨«50ŽŽ‘ ªª);Ž¡‘±=·‘ÿý«\Un•¸ãbun“t"–UUColors“(blacš¸ãks,“whites,“and“gra˜ys).‘o·±=Ž¡‘ÂexternŽ‘8ØconstŽ‘VHzColorŽ‘uímÏblackŽ’ŒûA«(Ý"black"Ž‘%FS±;‘ª¨«0Ž–ª©±;‘ª¨«0Ž“±;‘ª¨«0Ž“±;‘ª¨ÏtrueŽ‘o@«);Ž¡‘ÂexternŽ‘8ØconstŽ‘VHzColorŽ‘uímÏwhiteŽ’ï,«(Ý"white"Ž‘%FS±;‘ª¨«255ŽŽ–ª«±;‘ª¨«255ŽŽ“±;‘ª¨«255ŽŽ“±;‘ª¨ÏtrueŽ‘o@«);Ž¡‘ÂexternŽ‘8ØconstŽ‘VHzColorŽ‘uímÏgr‘ÿ}'ayŽ’‰˜j«(Ý"gray"Ž‘ V±;‘ª¨«192ŽŽ–ª«±;‘ª¨«192ŽŽ“±;‘ª¨«192ŽŽ“);Ž¡‘ÂexternŽ‘8ØconstŽ‘VHzColorŽ‘uímÏlight‘‰ffŽ‘®gr‘ÿ}'ayŽ’ŸîG«(Ý"light_gray"Ž‘?†D±;‘ª¨«211ŽŽ–ª«±;‘ª¨«211ŽŽ“±;‘ª¨«211ŽŽ“);Ž¡‘±=·‘ð6«Defaults.‘l…[¬LDF‘T2002.09.27.«]Ž‘SdøNote–EŽthat“Ïdefault‘‰ffŽ‘®c‘ÿ}'olorŽ‘:Ái«,‘HµÏhelp‘‰ffŽ‘®c‘ÿ}'olorŽ‘2H·«and“Ïb–ÿ}'ackgr“ound‘‰ffŽ‘®c“olorŽ‘PÏt«are“pGoin¸ãtersŽ¡‘(and–Óthat“Ïdefault‘‰ffŽ‘®b–ÿ}'ackgr“oundŽ‘YEÅ«is“a“plain“ÂColorŽ‘Ïq«.‘ñ@It“can“bGe“used“to“access“the“original“bac¸ãkgroundŽ¡‘(color–UU(currenš¸ãtly“white),“if“the“user“pGoin˜ts“the“Ïb–ÿ}'ackgr“ound‘‰ffŽ‘®c“olorŽ‘Pï«at“some“other“ÂColorŽ‘¤ó«.‘o·±=Ž¡‘ÂexternŽ‘8ØconstŽ‘VHzColorŽ‘uímÏdefault‘‰ffŽ‘®b–ÿ}'ackgr“oundŽ’È3Œ«(Ý"default_background"Ž‘i†,±;‘ª¨«255ŽŽ–ª«±;‘ª¨«255ŽŽ“±;‘ª¨«255ŽŽ“±;‘ª¨ÏtrueŽ‘o@«);Ž¡‘ÂexternŽ‘8ØconstŽ‘VHzColorŽ‘uím·Ž‘zínÏdefault‘‰ffŽ‘®c‘ÿ}'olorŽ’µ0a«=‘Ç&Ž‘ -Ž6ÏblackŽ‘!œ -«;Ž¡‘ÂexternŽ‘8ØconstŽ‘VHzColorŽ‘uím·Ž‘zínÏb–ÿ}'ackgr“ound‘‰ffŽ‘®c“olorŽ’ÇøÞ«=‘Ç&Ž‘ -Ž6Ïdefault‘‰ffŽ‘®b–ÿ}'ackgr“oundŽ‘\ÔU«;Ž¡‘ÂexternŽ‘8ØconstŽ‘VHzColorŽ‘uím·Ž‘zínÏhelp‘‰ffŽ‘®c‘ÿ}'olorŽ’©nú«=‘Ç&Ž‘ -Ž6Ïgr–ÿ}'e“enŽ‘"sC«;‘±=·‘ÿý«LDF‘UU2002.10.26.‘qÇAdded.‘o·±=Ž¡‘=·‘7«[¬LDF‘T2002.09.25.«]Ž‘T«!!‘{uTO›XŽDO:‘XÏdefault‘‰ffŽ‘®b–ÿ}'ackgr“oundŽ‘X÷=«is–Xa“con•¸ãv“enience,‘Y^in–Xcase“I˜cš¸ãhange“\bac˜kground"Ž¡‘(in–S8the“MET›ÿ*ªAPOST‘S7coGde.‘qChec¸ãk“MET˜APOST–S7došGcumen¸ãtation!!‘qI“b˜eliev¸ãe–S8it“has“something“similar.Ž¡‘(·±=ŽŽŽŒ‹"j‹ Šn ý‘ì«34›­INTERNAL–ÕX(WITH“INITIALIZA‘ÿJªTION)’Ð3DLDFPRÃŽG˜·x«112Ž €n ý•@P‘ -·gŽ¤ ­This–ÕXco§«;Ž¡‘ÂexternŽ‘8ØColorŽ‘WÂË·Ž‘\ÂÌÏhelp‘‰ffŽ‘®c‘ÿ}'olorŽ’ˆ}@«;‘±=·‘ÿý«LDF‘UU2002.10.26.‘qÇAdded.‘o·±=Ž¡‘ÂexternŽ‘8ØColorŽ‘WÂË·Ž‘\ÂÌÏb–ÿ}'ackgr“ound‘‰ffŽ‘®c“olorŽ’§$«;Ž¡‘ -·gŽ¤ ­This–ÕXco‘«declaration‘@­110˜·iŽ¡«abGo•¸ãv“e.Ž¡‘ -Ý@Ž‘Æf«i–UUÈcolall.web“«(Commen¸ãted“out).Ž¦Â115.‘ üGlobal‘ÕTconstan®9ts.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.10.26.«]Ž‘Y;Added‘UUÏhelp‘‰ffŽ–®c›ÿ}'olor‘‰ffŽ“ve˜ctorŽ‘L®(«.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Global‘UUconstan¸ãts‘@­19“·i‘Ç«+·Ž¤ ‘ -ÂnamespaceŽ‘C£{ColorsŽ‘gѪ·fŽ¡‘ÂexternŽ‘8ØconstŽ‘VHzv®9ectorŽ‘uò·hÂconstŽ‘*¢ColorŽ‘=Ï•·Ž‘BÏ–i‘UUÏdefault‘‰ffŽ–®c›ÿ}'olor‘‰ffŽ“ve˜ctorŽ‘Xo«(1Ž‘±;‘ª¨Ïdefault‘‰ffŽ‘®c‘ÿ}'olorŽ‘9&ƒ«);ŽŽŽŒ‹#ƒ¸ Šn ý‘ì·x«115–­3DLDFPRÃŽG’ É%GLOBAL‘ÕXCONST‘ÿJªANTS“«35Ž €n ý•@P‘ÂexternŽ‘8ØconstŽ‘VHzv®9ectorŽ‘uò·hÂconstŽ‘*¢ColorŽ‘=Ï•·Ž‘BÏ–i‘UUÏhelp‘‰ffŽ–®c›ÿ}'olor‘‰ffŽ“ve˜ctorŽ‘L®(«(1Ž‘±;‘ª¨Ïhelp‘‰ffŽ‘®c‘ÿ}'olorŽ‘-e«);Ž¤ ‘±=·‘ÿý«LDF‘UU2002.10.26.‘qÇAdded.‘o·±=Ž¡‘ÂexternŽ‘8ØconstŽ‘VHzv®9ectorŽ‘uò·hÂconstŽ‘*¢ColorŽ‘=Ï•·Ž‘BÏ–i‘UUÏb–ÿ}'ackgr“ound‘‰ffŽ›®c“olor‘‰ffŽ˜ve“ctorŽ‘k8 «(1Ž‘±;‘ª¨Ïb–ÿ}'ackgr“ound‘‰ffŽ‘®c“olorŽ‘Kï«);Ž¡‘ -·gŽ©Â116.ŽŸ·h‘ª¨ÂexternŽ‘%È~«global–UUconstan¸ãt“declarations‘@­116‘ª¨·i‘ÇŽ¡‘ -ÂnamespaceŽ‘C£{ColorsŽ‘gѪ·fŽ¡‘ÂexternŽ‘8ØconstŽ‘VHzv®9ectorŽ‘uò·hÂconstŽ‘*¢ColorŽ‘=Ï•·Ž‘BÏ–i‘UUÏdefault‘‰ffŽ–®c›ÿ}'olor‘‰ffŽ“ve˜ctorŽ‘Xo«;Ž¡‘ÂexternŽ‘8ØconstŽ‘VHzv®9ectorŽ‘uò·hÂconstŽ‘*¢ColorŽ‘=Ï•·Ž‘BÏ–i‘UUÏhelp‘‰ffŽ–®c›ÿ}'olor‘‰ffŽ“ve˜ctorŽ‘L®(«;‘±=·‘ÿý«LDF‘UU2002.10.26.‘qÇAdded.‘o·±=Ž¡‘ÂexternŽ‘8ØconstŽ‘VHzv®9ectorŽ‘uò·hÂconstŽ‘*¢ColorŽ‘=Ï•·Ž‘BÏ–i‘UUÏb–ÿ}'ackgr“ound‘‰ffŽ›®c“olor‘‰ffŽ˜ve“ctorŽ‘k8 «;Ž¡‘ -·gŽŸ ­This–ÕXcoÅH­56“·iŽ¡‘ -h–ª¨«Declare‘UUÂnamespaceŽ‘<øÏColorsŽ‘b­­109“·iŽ¡‘ -h–ª¨«De ne‘UUÂColorŽ‘"úH«functions‘@­59“·iŽ¡‘ -h›ª¨«De ne–UUnon-mem¸ãbGer“functions“for“ÂColorŽ‘#ä÷­104˜·iŽ¡‘ -h–ª¨«Global‘UUconstan¸ãts‘@­19“·iŽŽŽŒ‹$“ - Šn ý‘ì«36›­PUTTING–ÕXÂCOLOR“­TOGETHER’Þ¶X3DLDFPRÃŽG˜·x«119Ž €n ý•@PÂ119.‘ ü«This–`àis“written“to“Ècolors.h«.‘ KBUG‘`¢FIX:“The“preprošGcessor“\Âde neŽ‘H«"“command“m¸ãust“b˜e“here,‘‘ÄotherwiseŽ¤ it's–UUnot“written“to“the“header“ le.‘qÇUsing“\@±dŽ‘4r«"“abšGo•¸ãv“e–UUdo˜esn't“do“it.Ž©ëî·h‘ª¨Ýcolors.hŽ‘5°ù­119‘ª¨·i‘ÇŽ¡‘ -h–ª¨«De ne‘UUÂclassŽ‘5¦ColorŽ‘>ÅH­56“·iŽ¡‘ -h‘ª¨ÂexternŽ‘%È~namespaceŽ‘_køColorsŽ’ƒš'«declaration‘@­110‘ª¨·iŽ¡‘ -h›ª¨«Declare–UUnon-mem¸ãbGer“functions“for“ÂColorŽ‘#ä÷­103˜·iŽ¡‘ -h‘ª¨ÂexternŽ‘%È~«global–UUconstan¸ãt“declarations‘@­116‘ª¨·iŽŸÂ120.– üT‘ÿ -«ransformations“(Ètransform.webÂ).ŽŸ&Ÿû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.11.12.«]Ž‘ZCáRemo•¸ãv“ed–ûthe“vš¸ãersion“con˜trol“iden˜ti ers“from“the“CWEB‘© les“for“the“distribution“ofŽ¡3DLDF–UU1.1.‘qÇThey're“still“used“in“mš¸ãy“dev˜elopmen˜t“v˜ersions.Ž¡‘ -[¬LDF‘T2003.12.10.«]Ž‘YQ‘Put–ž«the“vš¸ãersion“con˜trol“iden˜ti ers“bac˜k“in˜to“m˜y“release“v˜ersions“for“3DLDF‘ž™1.1.4.‘MÊI'v˜eŽ¡already–"¯put“some“of“them“bacš¸ãk“in,‘,Ñno˜w“I'm“doing“the“rest“of“them.‘`åHo˜w˜ev˜er,‘,Ñthe“release“v˜ersions“are“no˜w“inŽ¡their–UUoš¸ãwn“R˜CS“repGository‘ÿ*ª.ŽŸŸüÈ„`ÕÁGŽŽ¦·h‘ª¨«V‘ÿ*ªersion–UUconš¸ãtrol“iden˜ti er‘@­10‘ª¨·i‘Ç«+·Ž¡‘ -ÂstaticŽ‘)HÚstringŽ‘Jn'Ïr‘ÿ}'cs‘‰ffŽ‘®idŽ‘g(«=‘ÇÝ"$Id:È Ýtransfor.web,vŽ‘kÆÜÈ Ý1.3È Ý2003/12/10È Ý16:5Ž’ÔÆ 2:21È Ýlfinsto1È ÝExpÈ Ý$"Ž’>LÌ«;ŽŸÂ121.‘ üInclude‘ÕT les.Ž¦·h–ª¨«Include‘UU les‘@­11“·i‘Ç«+·Ž¡«#ÂincludeŽ‘'Ø~Ý"loader.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"pspglb.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"io.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"colors.h"ŽŽŸÂ122.› üT‘ÿ -«ransform–class“de nition.˜«The‘œÂT‘ÿ -«ransformŽ‘:¤µ«class–œhas“a“4–¿o·“«4–œtransformation“matrix“as“its“onlyŽ¡data–I—memš¸ãbGer“and“a“n˜um˜bGer“of“mem˜bGer“functions.‘mÝÂP•®9oin“tsŽ‘$‘a«,‘KðÂPicturesŽ‘-q9«,‘Kðand“ÏF‘ÿ;¼o‘ÿ}'cusesŽ‘)«con˜tain“ÂT‘ÿ -«ransformsŽ‘?ç«asŽ¡data‘UUmem¸ãbGers.Ž¡‘ -!!‘qÇRemem¸ãbGer–UUto“add“items“to“ÂopQÇeratorŽ‘.ì -«=Ž‘6³((‘ª¨)“if“if“I“add“them“to“the“class“de nition“here.ŽŸ&Ÿû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.07.04.«]Ž‘YŠÛRemo•¸ãv“ed‘×õÂfriendŽ‘%ÁO«declaration–×õfor“ÂF‘ÿ -«oQÇcusŽ‘ ÍA«.‘ù¦I'v¸ãe“added“Ïset‘‰ffŽ‘®elementŽ‘6xÌ«(›ª®)“and“Ïget‘‰ffŽ‘®elementŽ‘6û£«(˜),Ž¡whic¸ãh–UUare“used“in“the“ÂF‘ÿ -«oQÇcusŽ‘#Ÿö«functions,“so“the“latter“need“no“longer“bGe“a“ÂfriendŽ‘$¼«of“ÂT‘ÿ -«ransformŽ‘7ÈÒ«.ŽŸŸüÈ„`ÕÁGŽŽ¦‘ -ÂformatŽ‘3c(ÏT‘ÿ;¼r‘ÿ}'ansformŽ‘j|ÎintŽŽ¦·h–ª¨«De ne‘UUÂclassŽ‘5¦T‘ÿ -«ransformŽ‘Vé'­122“·i‘ÇŽ¡‘ -ÂclassŽ‘$àRT‘ÿ -«ransformŽ‘\©$·fŽ¡‘ÂfriendŽ‘5f¼classŽ‘PG P•®9oin“tŽ‘káU«;Ž¡‘ÂMatrixŽ‘;({ÏmatrixŽ‘Yh«;‘±=·‘EN«When–š¦I'vš¸ãe“got“things“w˜orking,‘«ûI‘š•can“try“to“optimize“use“of“storage“b˜y“notŽ¡‘(storing–dthe“parts“of“the“matrix“that“I‘d -don't“need.‘òThis“is“a“little“complicated,‘g¼bGecause“the“ro¸ãw“orŽ¡‘(column–UUwhicš¸ãh“isn't“needed“di ers“bGet˜w˜een“the“ane“and“p•Gersp“ectiv˜e‘UUtransformations.‘o·±=Ž¦‘ -ÂpublicŽ‘)=Ö«:‘·h–ª¨«Declare‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­124“·iŽ¡‘ -g«;ŽŸ ëî­This–ÕXcos~«(‘ª®);Ž¤ ­See–´?also“sections“126,–ºÝ128,“130,“132,“134,“136,“138,“140,“142,“145,“147,“150,“152,“155,“157,“158,“160,“166,“167,“168,“171,“173,“176,ŽŸ -‘178,–ÕX181,“and“187.Ž¡This–ÕXcos~«(ÂrealŽ‘³.±rŽ‘}B«);Ž¡Â127.ŽŸ·h–ª¨«De ne‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­125“·i‘Ç«+·Ž¦‘ -ÂT‘ÿ -«ransformŽ‘?s‚«::‘ÂT‘ÿ -«ransformŽ‘5s«(ÂrealŽ‘³.±rŽ‘}B«)Ž¦‘ -·fŽ¦‘ÂforŽ‘%舫(Âin®9tŽ‘¤÷±iŽ‘Þ«=‘Ç0Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«4Ž“;‘ÿý±iŽ‘ññŸÿ®+‘ÿ+ŽŽ‘¹«)Ž¦‘ÂforŽ‘/艫(Âin®9tŽ‘¤÷±jŽ‘Ó«=‘Ç0Ž–Ç;‘ÿý±jŽ‘ wÙ<‘Ç«4Ž“;‘ÿý±jŽ‘ -0ÁŸÿ®+‘ÿ+ŽŽ‘÷á«)‘ÏmatrixŽ‘#?›«[±iŽ‘qô«][±jŽ‘°Ä«]–Ç=“±rŽ‘‘,«;Ž¦‘ -·gŽ¡Â128.› üConstructor–0&with“16“real“argumen®9ts.˜«[¬LDF‘T2002.09.06.«]Ž‘[µËAdded–‚êthis“constructor.‘ú‡This“con-Ž¦structor–UUmak¸ães“it“pšGossible“to“sp˜ecify“all“of“the“elemen¸ãts“of“ÏmatrixŽ‘!”ð«.ŽŸ·h–ª¨«Declare‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­124“·i‘Ç«+·Ž¦‘ -ÂT‘ÿ -«ransformŽ‘>s~«(ÂrealŽ‘Í’Ïr0‘‰ffŽ‘®0Ž‘*ÉÚ±;‘ª¨ÂrealŽ‘x:Ïr0‘‰ffŽ‘®1Ž–,t‚±;‘ª¨ÂrealŽ‘x:Ïr0‘‰ffŽ‘®2Ž“±;‘ª¨ÂrealŽ‘x:Ïr0‘‰ffŽ‘®3Ž“±;‘ª¨ÂrealŽ‘x:Ïr1‘‰ffŽ‘®0Ž“±;‘ª¨ÂrealŽ‘x:Ïr1‘‰ffŽ‘®1Ž“±;‘ª¨ÂrealŽ‘x:Ïr1‘‰ffŽ‘®2Ž“±;‘ª¨ÂrealŽ‘x:Ïr1‘‰ffŽ‘®3Ž“±;‘ª¨ÂrealŽŽ¦‘Ïr2‘‰ffŽ‘®0Ž‘1üK±;‘ª¨ÂrealŽ‘]ÖÏr2‘‰ffŽ‘®1Ž–,Z±;‘ª¨ÂrealŽ‘]ÖÏr2‘‰ffŽ‘®2Ž“±;‘ª¨ÂrealŽ‘]ÖÏr2‘‰ffŽ‘®3Ž“±;‘ª¨ÂrealŽ‘]ÖÏr3‘‰ffŽ‘®0Ž“±;‘ª¨ÂrealŽ‘]ÖÏr3‘‰ffŽ‘®1Ž“±;‘ª¨ÂrealŽ‘]ÖÏr3‘‰ffŽ‘®2Ž“±;‘ª¨ÂrealŽ‘]ÖÏr3‘‰ffŽ‘®3Ž“«);ŽŽŽŒ‹&§± Šn ý‘ì«38‘­CONSTRšÃŽUCTOR–ÕXWITH“16“ÂREAL“­AR˜GUMENTS’ !3DLDFPR˜G‘·x«129Ž €n ý•@PÂ129.Ž©·h–ª¨«De ne‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­125“·i‘Ç«+·Ž¤ ‘ -ÂT‘ÿ -«ransformŽ‘?s‚«::‘ÂT‘ÿ -«ransformŽ‘5s«(ÂrealŽ‘UNÏr0‘‰ffŽ‘®0Ž‘*Q–±;‘ª¨ÂrealŽ‘ÿöÏr0‘‰ffŽ‘®1Ž–+ü>±;‘ª¨ÂrealŽ‘ÿöÏr0‘‰ffŽ‘®2Ž“±;‘ª¨ÂrealŽ‘ÿöÏr0‘‰ffŽ‘®3Ž“±;‘ª¨ÂrealŽ‘ÿöÏr1‘‰ffŽ‘®0Ž“±;‘ª¨ÂrealŽ‘ÿöÏr1‘‰ffŽ‘®1Ž“±;‘ª¨ÂrealŽ‘ÿöÏr1‘‰ffŽ‘®2Ž“±;‘ª¨ÂrealŽŽ¡‘2Ïr1‘‰ffŽ‘®3Ž‘EüM±;‘ª¨ÂrealŽ‘]ÖÏr2‘‰ffŽ‘®0Ž–,Z±;‘ª¨ÂrealŽ‘]ÖÏr2‘‰ffŽ‘®1Ž“±;‘ª¨ÂrealŽ‘]ÖÏr2‘‰ffŽ‘®2Ž“±;‘ª¨ÂrealŽ‘]ÖÏr2‘‰ffŽ‘®3Ž“±;‘ª¨ÂrealŽ‘]ÖÏr3‘‰ffŽ‘®0Ž“±;‘ª¨ÂrealŽ‘]ÖÏr3‘‰ffŽ‘®1Ž“±;‘ª¨ÂrealŽ‘]ÖÏr3‘‰ffŽ‘®2Ž“±;‘ª¨ÂrealŽ‘]ÖÏr3‘‰ffŽ‘®3Ž“«)Ž¡‘ -·fŽ¡‘ÏmatrixŽ‘2?«[0Ž–][0Ž“]–Ç=“Ïr0‘‰ffŽ‘®0Ž‘Ã`«;Ž¡‘ÏmatrixŽ‘2?«[0Ž–][1Ž“]–Ç=“Ïr0‘‰ffŽ‘®1Ž‘Ã`«;Ž¡‘ÏmatrixŽ‘2?«[0Ž–][2Ž“]–Ç=“Ïr0‘‰ffŽ‘®2Ž‘Ã`«;Ž¡‘ÏmatrixŽ‘2?«[0Ž–][3Ž“]–Ç=“Ïr0‘‰ffŽ‘®3Ž‘Ã`«;Ž¡‘ÏmatrixŽ‘2?«[1Ž–][0Ž“]–Ç=“Ïr1‘‰ffŽ‘®0Ž‘Ã`«;Ž¡‘ÏmatrixŽ‘2?«[1Ž–][1Ž“]–Ç=“Ïr1‘‰ffŽ‘®1Ž‘Ã`«;Ž¡‘ÏmatrixŽ‘2?«[1Ž–][2Ž“]–Ç=“Ïr1‘‰ffŽ‘®2Ž‘Ã`«;Ž¡‘ÏmatrixŽ‘2?«[1Ž–][3Ž“]–Ç=“Ïr1‘‰ffŽ‘®3Ž‘Ã`«;Ž¡‘ÏmatrixŽ‘2?«[2Ž–][0Ž“]–Ç=“Ïr2‘‰ffŽ‘®0Ž‘Ã`«;Ž¡‘ÏmatrixŽ‘2?«[2Ž–][1Ž“]–Ç=“Ïr2‘‰ffŽ‘®1Ž‘Ã`«;Ž¡‘ÏmatrixŽ‘2?«[2Ž–][2Ž“]–Ç=“Ïr2‘‰ffŽ‘®2Ž‘Ã`«;Ž¡‘ÏmatrixŽ‘2?«[2Ž–][3Ž“]–Ç=“Ïr2‘‰ffŽ‘®3Ž‘Ã`«;Ž¡‘ÏmatrixŽ‘2?«[3Ž–][0Ž“]–Ç=“Ïr3‘‰ffŽ‘®0Ž‘Ã`«;Ž¡‘ÏmatrixŽ‘2?«[3Ž–][1Ž“]–Ç=“Ïr3‘‰ffŽ‘®1Ž‘Ã`«;Ž¡‘ÏmatrixŽ‘2?«[3Ž–][2Ž“]–Ç=“Ïr3‘‰ffŽ‘®2Ž‘Ã`«;Ž¡‘ÏmatrixŽ‘2?«[3Ž–][3Ž“]–Ç=“Ïr3‘‰ffŽ‘®3Ž‘Ã`«;Ž¡‘ -·gŽŸÂ130.– üAssignmen®9t.“«Sets‘fÏmatrixŽ›%`g«to–fbGe“iden¸ãtical“to“the“ÏmatrixŽ˜«of“another“ÂT‘ÿ -«ransformŽ‘8ã«.–"û!!“Remem¸ãbGer‘ftoŽ¡add–UUitems“here“if“I“add“them“to“the“class“de nition.Ž¦·h–ª¨«Declare‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­124“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ -«ransformŽ‘AÈÓopQÇeratorŽ‘m_ˆ«=Ž‘u&¦(ÂconstŽ‘*¢T‘ÿ -«ransformŽ‘Uót«&Ž‘]º’±tŽ‘aW«);ŽŸÂ131.Ž¦·h–ª¨«De ne‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­125“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ +cmmi10µ=°‘ÿý¬Needed–UUfor“"sstream"“bGelo¸ãw.‘o°µ=Ž¡¬#­endifŽŽ¡¬#­includeŽ‘'Ø~´ŽŽ¡¬#­includeŽ‘'Ø~´ŽŽ¡¬#­includeŽ‘'Ø~´ŽŽ¡¬#­ifdefŽ‘áe´__GNUC__ŽŽ¡¬#­ifŽ‘ ´ø´HAVE_FLOAT_HŽŽ¡¬#­includeŽ‘'Ø~´Ž‘kžÌµ=°‘ÿý¬[²LDF‘T2002.12.13.¬]Ž‘T7Needed–UUfor“´FLT_MAXŽ‘(›¨¬.‘o°µ=Ž¡¬#­endifŽŽ¡¬#­endifŽŽ¡¬#­includeŽ‘'Ø~´ŽŽ¡¬#­includeŽ‘'Ø~´ŽŽ¡¬#­includeŽ‘'Ø~´ŽŽ¡¬#­ifdefŽ‘áe´LDF_GCC_2_95Ž‘ngªµ=°‘ÿý¬F‘ÿ*ªor–UUstream“formatting.‘qÇ[²LDF‘T2003.08.14.¬]Ž‘U$©°µ=Ž¡¬#­includeŽ‘'Ø~´ŽŽ¡¬#­elseŽŽ¡¬#­includeŽ‘'Ø~´ŽŽ¡¬#­endifŽŽ¡¬#­includeŽ‘'Ø~´ŽŽ¡¬#­includeŽ‘'Ø~´ŽŽ¡¬#­includeŽ‘'Ø~´ŽŽ¡¬#­ifdefŽ‘áe´LDF_GCC_3_3ŽŽ¡¬#­includeŽ‘'Ø~´ŽŽ¡¬#­elseŽŽŽŽŒ‹ u Šn ý‘ì°x¬7–¯3DLDF-1.1.5.1’,$ôLIBRAR‘ÿJªY‘ÕXFILES“¬5Ž €n ý•@P#­ifdefŽ‘áe´LDF_GCC_2_95ŽŽ¤ ¬#­includeŽ‘'Ø~´ŽŽ¡¬#­endifŽŽ¡¬#­endifŽŽ¡¬#­includeŽ‘'Ø~´ŽŽ¡¬#­includeŽ‘'Ø~´ŽŽ¡¬#­includeŽ‘'Ø~´ŽŽ¡¬#­ifdefŽ‘áe´__GNUC__ŽŽ¡¬#­includeŽ‘'Ø~´ŽŽ¡¬#­endifŽŽ¡¬#­ifdefŽ‘áe´__DECCXXŽŽ¡¬#­includeŽ‘'Ø~´ŽŽ¡¬#­elifŽ‘,´HAVE_STDLIB_HŽŽ¡¬#­includeŽ‘'Ø~´ŽŽ¡¬#­endifŽŽ©8.‘ ü®streambuf.h–K¬is“included“abGo•¸ãv“e,–ˆ†if‘K´LDF_GCC_2_95Ž‘Hp¬is›Kde ned,“instead˜of˜®ios¬,“whic¸ãh˜is˜included˜in˜allŽ¡other‘UUcases.‘qÇ[²LDF‘T2003.08.14.¬]ŽŽŸ°h–ª¨¬Include‘UU les‘@¯6“°i‘Ǭ+°Ž¡¬#­includeŽ‘'Ø~´ŽŽ¡¬#­includeŽ‘'Ø~´ŽŽ¡¬#­includeŽ‘'Ø~´ŽŽ¦­9.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.07.18.¬]Ž‘X–yAdded–ã“\­usingŽ‘áÄnamespaceŽ‘W|±stdŽ‘e$Š¬".‘KÜThis“is“needed“with“GCC›ãv3.3,‘úSbut“not“with“GCC˜2.95Ž¡or–UUthe“DEC“C++“compiler.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Include‘UU les‘@¯6“°i‘Ǭ+°Ž¤ ‘ +­usingŽ‘(S‡namespaceŽ‘a÷stdŽ‘qïà¬;Ž¦­10.‘ üPutting–ÕT®loader“­together.Ž¦11.‘ ü¬This–K is“what's“compiled.‘nZIt's“not“necessary“to“include“®stdlib.h“¬when“using“GCC›K 3.3,‘Mbut“I˜think“it'sŽ¡safer.‘qÇ[²LDF‘T2004.01.06.¬]ŽŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2004.01.06.¬]Ž‘X¡åAdded–îÿthis“section.‘O«It“simpli es“the“rules“for“building“the“executable“´3dldfŽ‘ ¤W¬if“®loader.cŽ¡¬is‘UUcompiled.Ž¤ŸüÈ„`ÕÁGŽŽ¡#­ifdefŽ‘áe´__DECCXXŽŽ¤ ¬#­includeŽ‘'Ø~´ŽŽ¡¬#­elifŽ‘,´HAVE_STDLIB_HŽŽ¡¬#­includeŽ‘'Ø~´ŽŽ¡¬#­endifŽŽ¡¬#­includeŽ‘'Ø~´ŽŽ¡‘ +­usingŽ‘(S‡namespaceŽ‘a÷stdŽ‘qïà¬;ŽŸ‘ +°h‘ª¨¬V‘ÿ*ªersion–UUconš¸ãtrol“iden˜ti er‘@¯5‘ª¨°iŽŽŽŒ‹©Ù Šn ý‘ì¬6›¯PUTTING–ÕX®LOADER“¯TOGETHER’éâÇ3DLDF-1.1.5.1˜°x¬12Ž €n ý•@P­12.‘ ü¬This–UUis“what's“written“to“the“®loader.h¬.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ© ‘ +¬[²LDF‘T2004.01.06.¬]Ž‘Y;Added–UUthis“section.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h‘ª¨´loader.hŽ‘5°ù¯12‘ª¨°i‘ÇŽ¦‘ +h–ª¨¬Include‘UU les‘@¯6“°iŽŸ­13.– üGlobal‘ÕTitems“(®pspglb.web­).‘$I÷¬Tš¸ãypGedefs,–UUglobal“v‘ÿqÇariables“and“constan˜ts,“and“some“non-classŽ¦functions.‘qÇ(®pspglb.web¬.)ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ +¬[²LDF‘T2003.11.12.¬]Ž‘ZCáRemo•¸ãv“ed–ûthe“vš¸ãersion“con˜trol“iden˜ti ers“from“the“CWEB‘© les“for“the“distribution“ofŽ¦3DLDF–UU1.1.1.‘qÇThey're“still“used“in“mš¸ãy“dev˜elopmen˜t“v˜ersions.Ž¦‘ +[²LDF‘T2003.12.10.¬]Ž‘YQ‘Put–ž«the“vš¸ãersion“con˜trol“iden˜ti ers“bac˜k“in˜to“m˜y“release“v˜ersions“for“3DLDF‘ž™1.1.4.‘MÊI'v˜eŽ¦already–"¯put“some“of“them“bacš¸ãk“in,‘,Ñno˜w“I'm“doing“the“rest“of“them.‘`åHo˜w˜ev˜er,‘,Ñthe“release“v˜ersions“are“no˜w“inŽ¦their–UUoš¸ãwn“R˜CS“repGository‘ÿ*ª.Ž¡ŸüÈ„`ÕÁGŽŽ¡°h‘ª¨¬V‘ÿ*ªersion–UUconš¸ãtrol“iden˜ti er‘@¯5‘ª¨°i‘Ǭ+°Ž¦‘ +­staticŽ‘)HÚstringŽ‘Jn'±r‘ÿ}'cs‘‰ffŽ‘®idŽ‘g(¬=‘Ç´"$Id:® ´pspglb.web,v® ´1Ž‘kÆÜ.14® ´2004/01/16® ´16:30Ž’ÔÆ :41® ´lfinsto1® ´Exp® ´$"Ž’9 Ϭ;ŽŸ­14.‘ üInclude‘ÕT les.Ž¡°h–ª¨¬Include‘UU les‘@¯6“°i‘Ǭ+°Ž¦¬#­includeŽ‘'Ø~´"loader.h"ŽŽ¦¬#­ifdefŽ‘áe´__DECCXXŽŽ¦¬#­includeŽ‘'Ø~´ŽŽ¦¬#­elseŽŽ¦¬#­ifdefŽ‘áe´LDF_GCC_3_3ŽŽ¦¬#­includeŽ‘'Ø~´ŽŽ¦¬#­elseŽŽ¦¬#­ifdefŽ‘áe´LDF_GCC_2_95ŽŽ¦¬#­ifŽ‘ ´ø´HAVE_LIMITS_HŽŽ¦¬#­includeŽ‘'Ø~´ŽŽ¦¬#­endifŽŽ¦¬#­endifŽŽ¦¬#­endifŽŽ¦¬#­endifŽŽ¦¬#­includeŽ‘'Ø~´ŽŽŸ­15.– üT®9ypQÇe‘¸Ãde nitions.“¬[²LDF‘T2002.10.15.¬]Ž‘[MúCurrenš¸ãtly‘ÿ*ª,‘LŠall– oating“pGoin˜t“v‘ÿqÇariables“are“declared“as“­realsŽ‘.¬.Ž¦I'vš¸ãe–ßde ned“­realŽ‘Ù¬in“order“to“mak˜e“it“easy“to“switc˜h“bGet˜w˜een“using“± o‘ÿ}'atsŽ‘ ð¬and“±doublesŽ‘(ݬsimply“b˜y“c˜hangingŽ¦the–UUv‘ÿqÇalue“of“the“#­ifŽ‘ ´ø¬expression.Ž¦‘ +I‘oÁtry–oÈto“a•¸ãv“oid–oÈusing“preprošGcessor“commands“(see“In¸ãtro˜duction),‘vdbut“this“is“one“of“the“cases“where“there'sŽ¦no–»bšGetter“alternativ¸ãe“to“using“the“prepro˜cessor“(I‘º©don't“consider“commenš¸ãting“out“the“un˜w˜an˜ted“v˜ersionŽ¦preferable–UUto“using“the“preproGcessor).ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ +¬[²LDF‘T2002.04.10.¬]Ž‘Y;Added–UUformatting“commands.Ž¦‘ +[²LDF‘T2002.04.10.¬]Ž‘Y;Added–UUdeclaration“of“­b•QÇo“olu½‰™šs4Ž‘ÔwrealŽ‘1@¬.Ž¦‘ +[²LDF‘T2002.12.11.¬]Ž‘ZIAdded–Îcthe“macros“´LDF_REAL_FLOATŽ‘S£¬and“´LDF_REAL_DOUBLEŽ‘Tž¬.‘ÜñThey're“needed“bGelo¸ãw,Ž¦where‘UU´MAX_REALŽ‘10ú¬and‘UU´INVALID_REALŽ‘F0î¬are–UUdeclared“in“the“GNU/Linš¸ãux“v˜ersion“(using“GCC).Ž¦‘ +[²LDF‘T2003.06.03.¬]Ž‘Y;Added‘UU±r–ÿ}'e“al‘‰ffŽ‘®shortŽ‘-Ȭ¬.‘qÇIt's–UUthe“return“t¸ãypGe“of“­PlaneŽ‘!6¼¬::‘±get‘‰ffŽ‘®distanc‘ÿ}'eŽ‘5y½¬(‘ª®).ŽŽŽŒ‹±E Šn ý‘ì°x¬15–¯3DLDF-1.1.5.1’5=TYPE‘ÕXDEFINITIONS“¬7Ž €n ý•@P‘ +[²LDF‘T2003.12.30.¬]Ž‘WëÉNo¸ãw–8ãusing“#“­de neŽ‘"ºG¬instead“of“@µdŽ‘mU¬for“the“de nitions“of“´LDF_REAL_FLOATŽ‘Nx¬and“´LDF_REAL_DOUBLEŽ‘Q¬.Ÿ€„ +Ž¤ If–F<@µdŽ‘ z®¬is“used,›‚vthe“de nitions“are“only“written“to“®pspglb.c¬.‘D|Using“#“­de neŽ‘"Ž½¬,˜and“writing“°h‘ª¨¬T¸ãypGe“de ni-Ž¡tions‘@¯15‘ª¨°i–UU¬to“®pspglb.h“¬makš¸ães“the“de nitions“a˜v‘ÿqÇailable“to“the“ les“that“include“®pspglb.h¬.Ž¤ŸüÈ„`ÕÁGŽŽ¡‘ +­formatŽ‘3c(±r–ÿ}'e“alŽ‘L¹â o‘ÿ}'atŽŽ¤ ‘ +­formatŽ‘3c(±r–ÿ}'e“al‘‰ffŽ‘®p“airŽ‘aq…r–ÿ}'e“alŽŽ¡‘ +­formatŽ‘3c(±b–ÿ}'o“ol‘‰ffŽ‘®p“airŽ‘bV€r–ÿ}'e“al‘‰ffŽ‘®p“airŽŽ¡‘ +­formatŽ‘3c(±r–ÿ}'e“al‘‰ffŽ‘®p“airŽ‘aq…r–ÿ}'e“al‘‰ffŽ‘®shortŽŽ¡‘ +­formatŽ‘3c(±MatrixŽ‘Z intŽŽ©°h–ª¨¬T¸ãypGe‘UUde nitions‘@¯15“°i‘ÇŽ¡¬#­de neŽ‘!Ö´LDF_REAL_FLOATŽ‘sùi¬1ŽŽ¡#­de neŽ‘!Ö´LDF_REAL_DOUBLEŽ‘y9f¬0ŽŽ¡#­ifŽ‘ ´ø´LDF_REAL_FLOATŽŽ¡‘ +­t®9ypQÇedefŽ‘4_š oatŽ‘N{©realŽ‘aÙ‚¬;Ž¡#­elifŽ‘,´LDF_REAL_DOUBLEŽŽ¡‘ +­t®9ypQÇedefŽ‘4_šdoubleŽ‘Y©àrealŽ‘m¹¬;Ž¡#­elseŽ‘&Øàµ=°‘ÿý¬Default.‘qÇLDF‘UU2003.12.17.‘o°µ=Ž¡‘ +­t®9ypQÇedefŽ‘4_š oatŽ‘N{©realŽ‘aÙ‚¬;Ž¡#­endifŽŽ¡‘ +t®9ypQÇedefŽ‘4_šrealŽ‘KÈMatrixŽ‘n ›¬[4Ž–][4Ž“];Ž¡‘ +­t®9ypQÇedefŽ‘4_špairŽ‘HÛ«°h­realŽ‘]Ùµ;‘ª¨­realŽ‘°i‘UU­realu½‰™šs4Ž‘ÔwpairŽ‘/p¬;Ž¡‘ +­t®9ypQÇedefŽ‘4_špairŽ‘HÛ«°h­realŽ‘]Ùµ;‘ª¨­signedŽ‘%žshortŽ‘?ì°i‘UU­realu½‰™šs4Ž‘ÔwshortŽ‘5i¾¬;Ž¡‘ +­t®9ypQÇedefŽ‘4_špairŽ‘HÛ«°h­b•QÇo“olŽ‘Lµ;‘ª¨­b•QÇo“olŽ‘ö¹°i‘UU­b•QÇo“olu½‰™šs4Ž‘ÔwpairŽ‘2^¹¬;Ž¡‘ +­t®9ypQÇedefŽ‘4_špairŽ‘HÛ«°h­b•QÇo“olŽ‘Lµ;‘ª¨­realŽ‘°i‘UU­b•QÇo“olu½‰™šs4Ž‘ÔwrealŽ‘1@¬;Ž¤ ¯See–ÕXalso“sections“312,“313,“315,“and“317.Ž¡This–ÕXco‘Ǭ(‘ª¨).Ž¦The–UUv›ÿqÇalue“of“´MAX_REAL_SQRTŽ‘Kpë¬is“set“after“this.‘qÇTheir“v˜alues“should“nevš¸ãer“c˜hange“after“this!Ž¦‘ +´MAX_REAL_SQRTŽ‘R—¬m¸ãust–UUbšGe“initialized“here,“b˜ecause“it's“used“in“­P•®9oin“tŽ‘::‘±magnitudeŽ‘/=v¬(‘ª®).‘qÇ[²LDF‘T2003.12.29.¬]ŽŽ¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Global‘UUv‘ÿqÇariables‘@¯18“°i‘Ǭ+°Ž¦¬#­ifdefŽ‘áe´__DECCXXŽŽ¦‘ +­n®9umericu½‰™šs4Ž‘ÔwlimitsŽ‘Sï °h­realŽ‘]Ù°i‘UU±r–ÿ}'e“al‘‰ffŽ‘®limitsŽ‘0x¬;Ž¦‘ +­externŽ‘.×constŽ‘LHyrealŽ‘bû§´INVALID_REALŽ’¥I¬=‘DZr–ÿ}'e“al‘‰ffŽ‘®limitsŽ‘/‡;µ:±maxŽ‘¤›¬(‘ª¨);Ž¦#­elseŽŽ¦¬#­ifŽ‘ ´ø´LDF_REAL_DOUBLEŽŽ¦‘ +­externŽ‘.×constŽ‘LHyrealŽ‘bû§´INVALID_REALŽ’¥I¬=‘Ç´DBL_MAXŽ‘( k¬;Ž¦#­elseŽ‘&Øàµ=°‘ÿý´LDF_REAL_FLOATŽ‘O;¬,–UUor“not“spGeci ed.‘qÇLDF“2003.12.08.‘o°µ=Ž¦‘ +­externŽ‘.×constŽ‘LHyrealŽ‘bû§´INVALID_REALŽ’¥I¬=‘Ç´FLT_MAXŽ‘( k¬;Ž¦#­endifŽŽ¦¬#­endifŽŽ¦‘ +realŽ‘ ³/´MAX_REALŽ‘N—¬=‘Ç0Ž‘Ç;Ž¦‘ +­realŽ‘ ³/´MAX_REAL_SQRTŽ‘h@ˆ¬=‘Ç0Ž‘Ç;ŽŸ­20.‘ ü¬[²LDF‘T2003.08.14.¬]Ž‘Zùì´VERBOSE_GLOBALŽ’¨Ç5¬is‘Ç ±falseŽ‘=Z¬bš¸ãy–Ç default.‘ÆêIt“is“set“to“±trueŽ‘R®¬b˜y“the“command“line“optionŽ¦\®--verbose¬".‘qÇIf‘UU´VERBOSE_GLOBALŽ‘P°è¬is‘UU±trueŽ›í¬,–UUthe“loGcal“±verb‘ÿ}'oseŽ‘'<¬v‘ÿqÇariables“in“functions“are“set“to“±trueŽ˜¬.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ +¬[²LDF‘T2003.08.14.¬]Ž‘Y;Added‘UU´VERBOSE_GLOBALŽ‘P°è¬and‘UU´SILENT_GLOBALŽ‘H–¬.Ž¡ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Global‘UUv‘ÿqÇariables‘@¯18“°i‘Ǭ+°Ž¦‘ +­b•QÇo“olŽ‘#¡g´VERBOSE_GLOBALŽ‘pn½¬=‘DZfalseŽ‘v\¬;Ž¦‘ +­b•QÇo“olŽ‘#¡g´SILENT_GLOBALŽ‘k.À¬=‘DZfalseŽ‘v\¬;ŽŽŽŒ‹ ÊŠ Šn ý‘ì°x¬21–¯3DLDF-1.1.5.1’É'FÃŽOR‘ÕXCOMPILA‘ÿJªTION“¬9Ž €n ý•@P­21.Ž©°h›ª¨¬Declarations–UUfor“the“header“ le‘@¯21˜°i‘ÇŽ¤ ‘ +­externŽ‘.×b•QÇo“olŽ‘G¿=´VERBOSE_GLOBALŽ’‘Å{¬;Ž¡‘ +­externŽ‘.×b•QÇo“olŽ‘G¿=´SILENT_GLOBALŽ’Œ…~¬;Ž¡‘ +­externŽ‘.×constŽ‘LHyb•QÇo“olŽ‘eéß±ldf‘‰ffŽ›®r–ÿ}'e“al‘‰ffŽ˜ o“atŽ’›Ö¦¬;Ž¡‘ +­externŽ‘.×constŽ‘LHyb•QÇo“olŽ‘eéß±ldf‘‰ffŽ›®r–ÿ}'e“al‘‰ffŽ˜doubleŽ’¤¬;Ž¡‘ +­externŽ‘.×realŽ‘DÑ´MAX_REALŽ‘oWU¬;Ž¡‘ +­externŽ‘.×realŽ‘DÑ´MAX_REAL_SQRTŽ’‰—F¬;Ž¤ ¯See–ÕXalso“sections“23,“26,“29,“235,“237,“303,“320,“631,“655,“and“692.Ž¡This–ÕXco le.‘ áThis“meanš¸ãt“that“eac˜h“compilation“unit“that“loaded“®pspglb.h“¬had“its“o˜wn“v˜ersion“of“´PIŽ‘+ ¬,Ž¡´INVALID_REALŽ‘?†D¬,‘¹ketc.‘aýI‘¥Rdidn't–¥gknoš¸ãw“that“±c‘ÿ}'onstsŽ‘"ò:¬had“in˜ternal“link‘ÿqÇage“b˜y“default“and“that“I‘¥Rcould“mak˜e“theirŽ¡link‘ÿqÇage–ÿ external“b¸ãy“using“­externŽ‘(Æ—¬in“the“declaration“with“the“initialization,‘)yand“put“a“second“declaration,Ž¡also–UUwith“­externŽ‘$Ö¬,“in“the“header“ le.‘qÇThis“is“what“I'vš¸ãe“done“no˜w.Ž¡‘ +[²LDF‘T2003.06.03.¬]Ž‘Y;Added‘UU´INVALID_REAL_SHORTŽ‘b[‡¬.Ž¦ŸüÈ„`ÕÁGŽŽŸ­28.‘ üF‘ÿ +«or‘ÕTcompilation.Ž¦°h–ª¨¬Global‘UUconstan¸ãts‘@¯22“°i‘Ǭ+°Ž¡‘ +­externŽ‘.×constŽ‘LHyrealŽ‘bû§´PIŽ‘pÉ!¬=‘Ç4µ:¬0ŽŽ‘Ç°‘8à±atanŽ‘ªÀ¬(1µ:¬0ŽŽ‘ Ç);Ž¡‘ +­externŽ‘.×constŽ‘LHyrealu½‰™šs4Ž‘ÔwpairŽ‘{¸ú´INVALID_REAL_PAIRŽ’Õ/¬(´INVALID_REALŽ‘?†Dµ;‘ª¨´INVALID_REALŽ‘A0ì¬);Ž¡‘ +­externŽ‘.×constŽ‘LHyrealu½‰™šs4Ž‘ÔwshortŽ’²7´INVALID_REAL_SHORTŽ’à¸i¬(´INVALID_REALŽ‘?†Dµ;‘ª¨¬0Ž‘ª©);ŽŽŽŒ‹ ëÑ Šn ý‘ì¬12›¯FÃŽOR–ÕXTHE“HEADER“FILE’þŸ 3DLDF-1.1.5.1˜°x¬29Ž €n ý•@P­29.‘ üF‘ÿ +«or–ÕTthe“header“ le.Ž©°h›ª¨¬Declarations–UUfor“the“header“ le‘@¯21˜°i‘Ǭ+°Ž¤ ‘ +­externŽ‘.×constŽ‘LHyrealŽ‘bû§´PIŽ‘n ¬;Ž¡‘ +­externŽ‘.×constŽ‘LHyrealŽ‘bû§´INVALID_REALŽ’¢ë¬;Ž¡‘ +­externŽ‘.×constŽ‘LHyrealu½‰™šs4Ž‘ÔwpairŽ‘{¸ú´INVALID_REAL_PAIRŽ’Õ/¬;Ž¡‘ +­externŽ‘.×constŽ‘LHyrealu½‰™šs4Ž‘ÔwshortŽ’²7´INVALID_REAL_SHORTŽ’à¸i¬;Ž¤­30.‘ üUtilit®9y‘ÕTfunctions.Ž¡31.› üSolv®9e–´ùquadratic“equation.˜¬[²LDF‘T2002.09.03.¬]Ž‘ZlTO‘9+DO:–93Ma¸ãybGe“add“functions“for“solving“cubic“andŽ¤ quartic–UUequations,“if“this“is“practicable.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.06.1.¬]Ž‘Th=Changed–UUreturn“tš¸ãypGe“from“­pairŽ‘Ñf°h­realŽ‘]Ùµ;‘ª¨­realŽ‘°i“¬to“­realu½‰™šs4Ž‘ÔwpairŽ‘/p¬,“whic˜h“is“equiv‘ÿqÇalen˜t.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h›ª¨¬Declare–UUutilit¸ãy“functions‘@¯24˜°i‘Ǭ+°Ž¡‘ +­realu½‰™šs4Ž‘ÔwpairŽ‘9p‚±solve‘‰ffŽ‘®quadr‘ÿ}'aticŽ‘{%<¬(­realŽ‘³.µaŽ‘ü^;‘ª¨­realŽ‘]ÖµbŽ‘¨€;‘ª¨­realŽ‘]ÖµcŽ‘±±¬);ŽŽŽŒ‹ 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les“for“the“distribution“ofŽ¡3DLDF–UU1.1.‘qÇThey're“still“used“in“mš¸ãy“dev˜elopmen˜t“v˜ersions.Ž¡‘ +[²LDF‘T2003.12.10.¬]Ž‘YQ‘Put–ž«the“vš¸ãersion“con˜trol“iden˜ti ers“bac˜k“in˜to“m˜y“release“v˜ersions“for“3DLDF‘ž™1.1.4.‘MÊI'v˜eŽ¡already–"¯put“some“of“them“bacš¸ãk“in,‘,Ñno˜w“I'm“doing“the“rest“of“them.‘`åHo˜w˜ev˜er,‘,Ñthe“release“v˜ersions“are“no˜w“inŽ¡their–UUoš¸ãwn“R˜CS“repGository‘ÿ*ª.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h‘ª¨¬V‘ÿ*ªersion–UUconš¸ãtrol“iden˜ti er‘@¯5‘ª¨°i‘Ǭ+°Ž¡‘ +­staticŽ‘)HÚstringŽ‘Jn'±r‘ÿ}'cs‘‰ffŽ‘®idŽ‘g(¬=‘Ç´"$Id:® ´colors.web,v® ´1Ž‘kÆÜ.7® ´2004/01/12® ´21:27:Ž’ÔÆ 38® ´lfinsto1® ´Exp® ´$"Ž’3ÌÒ¬;ŽŸ­94.‘ üInclude‘ÕT les.Ž¦°h–ª¨¬Include‘UU les‘@¯6“°i‘Ǭ+°Ž¡¬#­includeŽ‘'Ø~´"loader.h"ŽŽ¡¬#­includeŽ‘'Ø~´"pspglb.h"ŽŽ¡¬#­includeŽ‘'Ø~´"creatnew.h"ŽŽ¡¬#­includeŽ‘'Ø~´"io.h"ŽŽŸ­95.› üColor–xØclass“de nition.˜¬[²LDF‘T2002.09.25.¬]Ž‘[f!!‘WRememš¸ãbGer–ã…to“c˜hange“the“constructors,‘setting“func-Ž¡tions,–UUand“assignmenš¸ãt“opGerator“if“I“add“or“c˜hange“an˜ything“here!!ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.10.06.¬]Ž‘Y;Added.‘qDZon‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘<¹¬.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬De ne‘UU­classŽ‘5¦ColorŽ‘>ÅH¯95“°i‘ÇŽ¡‘ +­classŽ‘$àRColorŽ‘D…E°fŽ¡‘­stringŽ‘5%O±nameŽ‘MëS¬;Ž¡‘­b•QÇo“olŽ‘-¡h±use‘‰ffŽ‘®nameŽ‘X#²¬;Ž¡‘­b•QÇo“olŽ‘-¡h±on‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘eFZ¬;Ž¡‘­realŽ‘*³0±r–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘Mþ¶¬;Ž¡‘­realŽ‘*³0±gr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘W´¼¬;Ž¡‘­realŽ‘*³0±blue‘‰ffŽ‘®p‘ÿ}'artŽ‘R6.¬;Ž¦‘ +­publicŽ‘)=Ö¬:‘°h–ª¨¬Declare‘UU­ColorŽ‘"úH¬functions‘@¯97“°iŽ¡‘ +g¬;ŽŸ ¯This–ÕXcoJ¬=‘ǵcŽ‘ó:±get‘‰ffŽ–®blue‘‰ffŽ“p‘ÿ}'artŽ‘7¶º¬(‘ª¨);Ž¡‘­ifŽ‘´ú¬(µnŽ‘Dz°6¬=‘Ç´""Ž‘Z°^‘8àµuŽ‘ +¹v°‘DZtrueŽ‘‹°¬)‘°fŽ¡‘±use‘‰ffŽ‘®nameŽ‘KIe¬=‘DZtrueŽ‘‹°¬;Ž¡‘°gŽ¡‘­elseŽ‘+Øá±use‘‰ffŽ‘®nameŽ‘Y"C¬=‘DZfalseŽ‘v\¬;Ž¡‘±on‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘Nl ¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý¬LDF‘UU2002.10.06.‘qÇAdded.‘o°µ=Ž¡‘­returnŽ‘4‘g¬;Ž¡‘ +°gŽ¤­101.‘ üName–ÕTand“unsigned“short“argumen®9ts.Ž¡102.‘ üConstructor.Ž¦°h–ª¨¬Declare‘UU­ColorŽ‘"úH¬functions‘@¯97“°i‘Ǭ+°Ž¤ ‘ +­ColorŽ‘&OŸ¬(­constŽ‘]stringŽ‘?´åµnŽ‘Eµ;‘ª¨­constŽ‘ ÅunsignedŽ‘PqNshortŽ‘nnlµrŽ‘s8€;‘ª¨­constŽ‘ ÅunsignedŽ‘PqNshortŽ‘nnlµgŽ‘sO;‘ª¨­constŽ‘ ÅunsignedŽ‘PqNshortŽŽ¡‘µbŽ‘"J­;‘ª¨­constŽ‘ÕJb•QÇo“olŽ‘9v°µuŽ‘A÷F¬=‘DZtrueŽ‘‹°¬);ŽŽŽŒ‹ǹ Šn ý‘ì°x¬103–¯3DLDF-1.1.5.1’ÎåCONSTRÃŽUCTOR“¬31Ž €n ý•@P­103.Ž©°h–ª¨¬De ne‘UU­ColorŽ‘"úH¬functions‘@¯98“°i‘Ǭ+°Ž¤ ‘ +­ColorŽ‘'O£¬::‘­ColorŽ‘O¢¬(­constŽ‘GNstringŽ‘?‰GµnŽ‘E‰á;‘ª¨­constŽ‘ñöunsignedŽ‘PE°shortŽ‘n,ÿµrŽ‘r÷;‘ª¨­constŽ‘ñöunsignedŽ‘PE°shortŽ‘n,ÿµgŽ‘sMâ;‘ª¨­constŽ‘ñöunsignedŽŽ¡‘2shortŽ‘OʨµbŽ‘TR;‘ª¨­constŽ‘ÕJb•QÇo“olŽ‘9v°µuŽ‘?0.¬)Ž¡‘ +:‘qDZnameŽ‘7ˬ(µnŽ‘š¬)‘UU°fŽ¡‘±nameŽ‘/¬=‘ǵnŽ‘Dz¬;Ž¡‘­ifŽ‘´ú¬(µnŽ‘Dz°6¬=‘Ç´""Ž‘Z°^‘8àµuŽ‘ +¹v°‘DZtrueŽ‘‹°¬)‘°fŽ¡‘±use‘‰ffŽ‘®nameŽ‘KIe¬=‘DZtrueŽ‘‹°¬;Ž¡‘°gŽ¡‘­elseŽ‘+Øá±use‘‰ffŽ‘®nameŽ‘Y"C¬=‘DZfalseŽ‘v\¬;Ž¡‘±on‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘Nl ¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý¬LDF‘UU2002.10.06.‘qÇAdded.‘o°µ=Ž¡‘±r–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘: ¬=‘ǵrŽ‘‘,=¬255µ:¬0ŽŽ‘Ç!;Ž¡‘±gr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘CȦ¬=‘ǵgŽ‘çû=¬255µ:¬0ŽŽ‘Ç!;Ž¡‘±blue‘‰ffŽ‘®p‘ÿ}'artŽ‘>J¬=‘ǵbŽ‘Â=¬255µ:¬0ŽŽ‘Ç!;Ž¡‘ +°gŽŸ­104.‘ üSetting‘ÕTfunction.Ž¦°h–ª¨¬Declare‘UU­ColorŽ‘"úH¬functions‘@¯97“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘# ±setŽ‘0ƒˆ¬(­constŽ‘7ÍstringŽ‘?jEµnŽ‘Ejß;‘ª¨­constŽ‘âuunsignedŽ‘P&®shortŽ‘mþ|µrŽ‘rÈ;‘ª¨­constŽ‘âuunsignedŽ‘P&®shortŽ‘mþ|µgŽ‘s_;‘ª¨­constŽ‘âuunsignedŽ‘P&®shortŽŽ¡‘µbŽ‘"J­;‘ª¨­constŽ‘ÕJb•QÇo“olŽ‘9v°µuŽ‘A÷F¬=‘DZfalseŽ‘v\¬);ŽŸ­105.Ž¦°h–ª¨¬De ne‘UU­ColorŽ‘"úH¬functions‘@¯98“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"Ý3ColorŽ‘@,Õ¬::‘±setŽ‘xˆ¬(­constŽ‘ üstringŽ‘?£µnŽ‘E=;‘ª¨­constŽ‘´¤unsignedŽ‘OË shortŽ‘mu µrŽ‘r?;‘ª¨­constŽ‘´¤unsignedŽ‘OË shortŽ‘mu µgŽ‘r•ì;‘ª¨­constŽ‘´¤unsignedŽŽ¡‘2shortŽ‘OʨµbŽ‘TR;‘ª¨­constŽ‘ÕJb•QÇo“olŽ‘9v°µuŽ‘?0.¬)Ž¡‘ +°fŽ¡‘±nameŽ‘/¬=‘ǵnŽ‘Dz¬;Ž¡‘­ifŽ‘´ú¬(µnŽ‘Dz°6¬=‘Ç´""Ž‘Z°^‘8àµuŽ‘ +¹v°‘DZtrueŽ‘‹°¬)‘°fŽ¡‘±use‘‰ffŽ‘®nameŽ‘KIe¬=‘DZtrueŽ‘‹°¬;Ž¡‘°gŽ¡‘­elseŽ‘+Øá±use‘‰ffŽ‘®nameŽ‘Y"C¬=‘DZfalseŽ‘v\¬;Ž¡‘±r–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘: ¬=‘ǵrŽ‘‘,=¬255µ:¬0ŽŽ‘Ç!;Ž¡‘±gr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘CȦ¬=‘ǵgŽ‘çû=¬255µ:¬0ŽŽ‘Ç!;Ž¡‘±blue‘‰ffŽ‘®p‘ÿ}'artŽ‘>J¬=‘ǵbŽ‘Â=¬255µ:¬0ŽŽ‘Ç!;Ž¡‘ +°gŽ©­106.› üThree–áØreal“argumen®9ts.˜¬[²LDF‘T2002.10.09.¬]Ž‘Z“Added–`7the“follo¸ãwing“constructor“and“setting“function.Ž¡They– äare“for“unnamed“­ColorsŽ‘$⾬.‘tThe“DEC‘ µcompiler“can't“distinguish“bGet•¸ãw“een‘ ä­realŽ‘q¡¬and‘ ä­unsignedŽ‘4õshortŽŽ¡¬argumenš¸ãts,‘óso–Û/the“o˜v˜erloaded“functions“m˜ust“di er“in“another“w˜a˜y‘ÿ*ª.‘IIn“this“case,‘óthese“v˜ersions“ha˜v˜e“no“±nameŽŽ¡¬argumen•¸ãt.‘‘ÀI‘µ:bGeliev“e–µSthat“users“are“most“likš¸ãely“to“declare“­ColorsŽ‘(C€¬using“­realŽ‘Ȭargumen˜ts“when“they“plan“toŽ¡moGdify–Àthem,›*xin“whic¸ãh“case“the“±outputŽ‘ /¬(‘ª®)“function“should“write“the“red,˜green“and“blue“v‘ÿqÇalues“to“±out‘‰ffŽ‘®str–ÿ}'e“amŽŽ¡¬rather–e*than“±nameŽ‘+.¬.‘¡EIf“it“turns“out“to“bšGe“necessary‘ÿ*ª,‘imore“constructors“can“b˜e“added“or“the“existing“ones“canŽ¡bGe‘UUc¸ãhanged.Ž¦­107.‘ üConstructor.ŽŸ°h–ª¨¬Declare‘UU­ColorŽ‘"úH¬functions‘@¯97“°i‘Ǭ+°Ž¡‘ +­ColorŽ‘&OŸ¬(­constŽ‘*¢realŽ‘4ÝеrŽ‘9§ä;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµgŽ‘;©[;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµbŽ‘:Ó"¬);ŽŽŽŒ‹ Ò{ Šn ý‘ì¬32–¯CONSTRÃŽUCTOR’Îå3DLDF-1.1.5.1“°x¬108Ž €n ý•@P­108.Ž©°h–ª¨¬De ne‘UU­ColorŽ‘"úH¬functions‘@¯98“°i‘Ǭ+°Ž¤ ‘ +­ColorŽ‘'O£¬::‘­ColorŽ‘O¢¬(­constŽ‘*¢realŽ‘4ÝеrŽ‘9§ä;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµgŽ‘;©[;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµbŽ‘:Ó"¬)Ž¡‘ +°fŽ¡‘±nameŽ‘/¬=‘Ç´""Ž‘ Íz¬;Ž¡‘±use‘‰ffŽ‘®nameŽ‘AId¬=‘DZfalseŽ‘v\¬;Ž¡‘±on‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘Nl ¬=‘DZfalseŽ‘v\¬;Ž¡‘­ifŽ‘´ú¬(µrŽ‘‘,<‘Ǭ0Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘6F0°‘‡´"WARNING!® ´In® ´Color::Ž‘nKColor()® ´(three® ´real® Ž’×´arguments):\n"Ž’'&Ô°Ž¡‘2´"Red® ´part® ´argument® ´<Ž’šÿÉ® ´0.® ´Setting® ´red_parŽ’ÿt® ´to® ´0.\n\n"Ž’C…Ѭ;Ž¡‘±r–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘D¡¬=‘Ç0Ž‘Ç;Ž¡‘°gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(µrŽ‘‘,>‘Ǭ1Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘6F0°‘‡´"WARNING!® ´In® ´Color::Ž‘nKColor()® ´(three® ´real® Ž’×´arguments):\n"Ž’'&Ô°Ž¡‘2´"Red® ´part® ´argument® ´>Ž’šÿÉ® ´1.® ´Setting® ´red_parŽ’ÿt® ´to® ´1.\n\n"Ž’C…Ѭ;Ž¡‘±r–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘D¡¬=‘Ç1Ž‘Ç;Ž¡‘°gŽ¡‘­elseŽ‘+Øá±r–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘Që¬=‘ǵrŽ‘‘,¬;Ž¡‘­ifŽ‘´ú¬(µgŽ‘çû<‘Ǭ0Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘6F0°‘‡´"WARNING!® ´In® ´Color::Ž‘nKColor()® ´(three® ´real® Ž’×´arguments):\n"Ž’'&Ô°Ž¡‘2´"Green® ´part® ´argumentŽ’šÿÉ® ´<® ´0.® ´Setting® ´greenŽ’ÿ_part® ´to® ´0.\n\n"Ž’X…Ŭ;Ž¡‘±gr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘Mȧ¬=‘Ç0Ž‘Ç;Ž¡‘°gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(µgŽ‘çû>‘Ǭ1Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘6F0°‘‡´"WARNING!® ´In® ´Color::Ž‘nKColor()® ´(three® ´real® Ž’×´arguments):\n"Ž’'&Ô°Ž¡‘2´"Green® ´part® ´argumentŽ’šÿÉ® ´>® ´1.® ´Setting® ´greenŽ’ÿ_part® ´to® ´1.\n\n"Ž’X…Ŭ;Ž¡‘±gr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘Mȧ¬=‘Ç1Ž‘Ç;Ž¡‘°gŽ¡‘­elseŽ‘+Øá±gr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘[¡…¬=‘ǵgŽ‘çû¬;Ž¡‘­ifŽ‘´ú¬(µbŽ‘Â<‘Ǭ0Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘6F0°‘‡´"WARNING!® ´In® ´Color::Ž‘nKColor()® ´(three® ´real® Ž’×´arguments):\n"Ž’'&Ô°Ž¡‘2´"Blue® ´part® ´argument® Ž’šÿÉ´<® ´0.® ´Setting® ´blue_pŽ’ÿart® ´to® ´0.\n\n"Ž’Nˬ;Ž¡‘±blue‘‰ffŽ‘®p‘ÿ}'artŽ‘HJ¬=‘Ç0Ž‘Ç;Ž¡‘°gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(µbŽ‘Â>‘Ǭ1Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘6F0°‘‡´"WARNING!® ´In® ´Color::Ž‘nKColor()® ´(three® ´real® Ž’×´arguments):\n"Ž’'&Ô°Ž¡‘2´"Blue® ´part® ´argument® Ž’šÿÉ´>® ´1.® ´Setting® ´blue_pŽ’ÿart® ´to® ´1.\n\n"Ž’Nˬ;Ž¡‘±blue‘‰ffŽ‘®p‘ÿ}'artŽ‘HJ¬=‘Ç1Ž‘Ç;Ž¡‘°gŽ¡‘­elseŽ‘+Øá±blue‘‰ffŽ‘®p‘ÿ}'artŽ‘V"÷¬=‘ǵbŽ‘¬;Ž¡‘­returnŽ‘4‘g¬;Ž¡‘ +°gŽŸ­109.‘ üSetting‘ÕTfunction.Ž¦°h–ª¨¬Declare‘UU­ColorŽ‘"úH¬functions‘@¯97“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙ±setŽ‘0v]¬(­constŽ‘*¢realŽ‘4ÝеrŽ‘9§ä;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµgŽ‘;©[;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµbŽ‘:Ó"¬);ŽŽŽŒ‹!ßõ Šn ý‘ì°x¬110–¯3DLDF-1.1.5.1’©SETTING‘ÕXFUNCTION“¬33Ž €n ý•@P­110.Ž©°h–ª¨¬De ne‘UU­ColorŽ‘"úH¬functions‘@¯98“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘"ýÙColorŽ‘@M{¬::‘±setŽ‘xˆ¬(­constŽ‘*¢realŽ‘4ÝеrŽ‘9§ä;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµgŽ‘;©[;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµbŽ‘:Ó"¬)Ž¡‘ +°fŽ¡‘±nameŽ‘/¬=‘Ç´""Ž‘ Íz¬;Ž¡‘±use‘‰ffŽ‘®nameŽ‘AId¬=‘DZfalseŽ‘v\¬;Ž¡‘±on‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘Nl ¬=‘DZfalseŽ‘v\¬;Ž¡‘­ifŽ‘´ú¬(µrŽ‘‘,<‘Ǭ0Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘6F0°‘‡´"WARNING!® ´In® ´Color::Ž‘nKColor()® ´(three® ´real® Ž’×´arguments):\n"Ž’'&Ô°Ž¡‘2´"Red® ´part® ´argument® ´<Ž’šÿÉ® ´0.® ´Setting® ´red_parŽ’ÿt® ´to® ´0.\n\n"Ž’C…Ѭ;Ž¡‘±r–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘D¡¬=‘Ç0Ž‘Ç;Ž¡‘°gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(µrŽ‘‘,>‘Ǭ1Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘6F0°‘‡´"WARNING!® ´In® ´Color::Ž‘nKColor()® ´(three® ´real® Ž’×´arguments):\n"Ž’'&Ô°Ž¡‘2´"Red® ´part® ´argument® ´>Ž’šÿÉ® ´1.® ´Setting® ´red_parŽ’ÿt® ´to® ´1.\n\n"Ž’C…Ѭ;Ž¡‘±r–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘D¡¬=‘Ç1Ž‘Ç;Ž¡‘°gŽ¡‘­elseŽ‘+Øá±r–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘Që¬=‘ǵrŽ‘‘,¬;Ž¡‘­ifŽ‘´ú¬(µgŽ‘çû<‘Ǭ0Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘6F0°‘‡´"WARNING!® ´In® ´Color::Ž‘nKColor()® ´(three® ´real® Ž’×´arguments):\n"Ž’'&Ô°Ž¡‘2´"Green® ´part® ´argumentŽ’šÿÉ® ´<® ´0.® ´Setting® ´greenŽ’ÿ_part® ´to® ´0.\n\n"Ž’X…Ŭ;Ž¡‘±gr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘Mȧ¬=‘Ç0Ž‘Ç;Ž¡‘°gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(µgŽ‘çû>‘Ǭ1Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘6F0°‘‡´"WARNING!® ´In® ´Color::Ž‘nKColor()® ´(three® ´real® Ž’×´arguments):\n"Ž’'&Ô°Ž¡‘2´"Green® ´part® ´argumentŽ’šÿÉ® ´>® ´1.® ´Setting® ´greenŽ’ÿ_part® ´to® ´1.\n\n"Ž’X…Ŭ;Ž¡‘±gr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘Mȧ¬=‘Ç1Ž‘Ç;Ž¡‘°gŽ¡‘­elseŽ‘+Øá±gr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘[¡…¬=‘ǵgŽ‘çû¬;Ž¡‘­ifŽ‘´ú¬(µbŽ‘Â<‘Ǭ0Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘6F0°‘‡´"WARNING!® ´In® ´Color::Ž‘nKColor()® ´(three® ´real® Ž’×´arguments):\n"Ž’'&Ô°Ž¡‘2´"Blue® ´part® ´argument® Ž’šÿÉ´<® ´0.® ´Setting® ´blue_pŽ’ÿart® ´to® ´0.\n\n"Ž’Nˬ;Ž¡‘±blue‘‰ffŽ‘®p‘ÿ}'artŽ‘HJ¬=‘Ç0Ž‘Ç;Ž¡‘°gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(µbŽ‘Â>‘Ǭ1Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘6F0°‘‡´"WARNING!® ´In® ´Color::Ž‘nKColor()® ´(three® ´real® Ž’×´arguments):\n"Ž’'&Ô°Ž¡‘2´"Blue® ´part® ´argument® Ž’šÿÉ´>® ´1.® ´Setting® ´blue_pŽ’ÿart® ´to® ´1.\n\n"Ž’Nˬ;Ž¡‘±blue‘‰ffŽ‘®p‘ÿ}'artŽ‘HJ¬=‘Ç1Ž‘Ç;Ž¡‘°gŽ¡‘­elseŽ‘+Øá±blue‘‰ffŽ‘®p‘ÿ}'artŽ‘V"÷¬=‘ǵbŽ‘¬;Ž¡‘ +°gŽŸ­111.‘ üPseudo-constructor–ÕTfor“dynamic“alloQÇcation.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.12.30.¬]Ž‘WëÉReplaced‘8ã­ColorŽ‘ˆ…¬::‘±cr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“c‘ÿ}'olorŽ‘IS&¬(‘ª®)–8ãwith“spGecializations“of“­templateŽ‘/ +A°h­classŽ‘ÃßµCŽ‘! «°i“µCŽ‘ +¯°Ž‘°±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘>¥t¬(‘ª¨).Ÿ€„ +Ž¡¦ŸüÈ„`ÕÁGŽŽŸ­112.‘ üP•®9oin“ter‘ÕTargumen“t.Ž¦°h›ª¨¬Declare–UUnon-mem¸ãbGer“template“functions“for“­ColorŽ‘#ä÷¯112˜°i‘ÇŽ¡‘ +­ColorŽ‘)¤ô°Ž‘.¤õ±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘^4¹¬(­constŽ‘*¢ColorŽ‘=Ï•°Ž‘BÏ–µcŽ‘G#q¬);ŽŽŽŒ‹"ëÅ Šn ý‘ì¬34–¯POINTER‘ÕXARÃŽGUMENT’ÿ3DLDF-1.1.5.1“°x¬112Ž €n ý•@P¯See–ÕXalso“section“113.ŽŸ This–ÕXcoJ¬=‘ǵcŽ‘ó:±blue‘‰ffŽ‘®p‘ÿ}'artŽ‘'‚þ¬;Ž¦‘ +°gŽŸ­116.– üEqualit®9y‘ÿ +«.“¬[²LDF‘T2002.09.25.¬]Ž‘YªŒChanged–w«so“that“only“±r–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘%Ã1¬,‘¤±gr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘27¬and“±blue‘‰ffŽ‘®p‘ÿ}'artŽ‘,rT¬are“compared.Ž¦This›{Ðw•¸ãa“y‘ÿ*ª,‘…n­ColorsŽ‘'Ú¬that˜di er˜only˜in˜±nameŽ‘½¤¬and/or˜±use‘‰ffŽ‘®nameŽ‘1yê¬are˜considered˜to˜bGe˜equal.‘å7[²LDF‘T2002.09.24.¬]ŽŽ¦Added–UUthis“opGerator“function.Ž¡°h–ª¨¬Declare‘UU­ColorŽ‘"úH¬functions‘@¯97“°i‘Ǭ+°Ž¦‘ +­b•QÇo“olŽ‘#¡gopQÇeratorŽ‘O8°Ž‘Vÿ:¬(­constŽ‘*¢ColorŽ‘=Ï•¬&Ž‘E–³µcŽ‘Iꎬ)‘UU­constŽ‘*¢¬;ŽŸ­117.Ž¡°h–ª¨¬De ne‘UU­ColorŽ‘"úH¬functions‘@¯98“°i‘Ǭ+°Ž¦‘ +­b•QÇo“olŽ‘#¡gColorŽ‘@ñ ¬::Ž‘GG­opQÇeratorŽ‘sü°Ž‘zݬ(­constŽ‘*¢ColorŽ‘=Ï•¬&Ž‘E–³µcŽ‘Iꎬ)‘UU­constŽŽ¦‘ +°fŽ¦‘­returnŽ‘7漬((±r–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘&ž°‘ǵcŽ›ó:±r–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘#K†¬)–8à°^“¬(±gr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘/Ȥ°‘ǵcŽ˜:±gr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘-Œ¬)“°^“¬(±blue‘‰ffŽ‘®p‘ÿ}'artŽ‘*J°‘ǵcŽ˜:±blue‘‰ffŽ‘®p‘ÿ}'artŽ‘'‚þ¬));Ž¦‘ +°gŽŸ­118.– üInequalit®9y‘ÿ +«.“¬[²LDF‘T2002.09.24.¬]Ž‘Zˆ6Added–UUthis“opGerator“function.Ž¡°h–ª¨¬Declare‘UU­ColorŽ‘"úH¬functions‘@¯97“°i‘Ǭ+°Ž¦‘ +­b•QÇo“olŽ‘#¡gopQÇeratorŽ‘O8°6¬=Ž‘Vÿ:(­constŽ‘*¢ColorŽ‘=Ï•¬&Ž‘E–³µcŽ‘Iꎬ)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹#ù9 Šn ý‘ì°x¬119–¯3DLDF-1.1.5.1’'â#INEQUALITY“¬35Ž €n ý•@P­119.Ž©°h–ª¨¬De ne‘UU­ColorŽ‘"úH¬functions‘@¯98“°i‘Ǭ+°Ž¤ ‘ +­b•QÇo“olŽ‘#¡gColorŽ‘@ñ ¬::Ž‘GG­opQÇeratorŽ‘sü°6¬=Ž‘zÝ(­constŽ‘*¢ColorŽ‘=Ï•¬&Ž‘E–³µcŽ‘Iꎬ)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼°:¬(°Ž‘±thisŽ‘²Ï°‘ǵcŽ‘ó¬);Ž¡‘ +°gŽ¤­120.‘ üMoQÇdifying.Ž¡121.‘ üSet–ÕTon“free“store.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ +¬[²LDF‘T2003.12.30.¬]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­ColorŽ‘"úH¬functions‘@¯97“°i‘Ǭ+°Ž¡‘ +­b•QÇo“olŽ‘#¡g±set‘‰ffŽ–®on‘‰ffŽ“fr–ÿ}'e“e‘‰ffŽ‘®stor“eŽ‘j÷>¬(­b•QÇo“olŽ‘¡fµbŽ‘ ³(¬=‘DZtrueŽ‘‹°¬);ŽŸ­122.Ž¦°h–ª¨¬De ne‘UU­ColorŽ‘"úH¬functions‘@¯98“°i‘Ǭ+°Ž¡‘ +­b•QÇo“olŽ‘#¡gColorŽ‘@ñ ¬::‘±set‘‰ffŽ–®on‘‰ffŽ“fr–ÿ}'e“e‘‰ffŽ‘®stor“eŽ‘HUÛ¬(­b•QÇo“olŽ‘¡fµbŽ‘ì¬)Ž¡‘ +°fŽ¡‘±on‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘Nl ¬=‘ǵbŽ‘¬;Ž¡‘­returnŽ‘7æ¼µbŽ‘<1f¬;Ž¡‘ +°gŽŸ­123.‘ üSet‘ÕTname.Ž¦°h–ª¨¬Declare‘UU­ColorŽ‘"úH¬functions‘@¯97“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙ±set‘‰ffŽ‘®nameŽ‘Kt¬(­constŽ‘*¢stringŽ‘?OïµsŽ‘Cÿï¬);ŽŸ­124.Ž¦°h–ª¨¬De ne‘UU­ColorŽ‘"úH¬functions‘@¯98“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙColorŽ‘@M{¬::‘±set‘‰ffŽ‘®nameŽ‘)ví¬(­constŽ‘*¢stringŽ‘?OïµsŽ‘Cÿï¬)Ž¡‘ +°fŽ¡‘±nameŽ‘/¬=‘ǵsŽ‘w¬;Ž¡‘ +°gŽŸ­125.‘ üSet–ÕTuse“name.Ž¦°h–ª¨¬Declare‘UU­ColorŽ‘"úH¬functions‘@¯97“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙ±set‘‰ffŽ–®use‘‰ffŽ“nameŽ‘]1¬(­constŽ‘*¢b•QÇo“olŽ‘7̵bŽ‘<²¬);ŽŸ­126.Ž¦°h–ª¨¬De ne‘UU­ColorŽ‘"úH¬functions‘@¯98“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙColorŽ‘@M{¬::‘±set‘‰ffŽ–®use‘‰ffŽ“nameŽ‘;33¬(­constŽ‘*¢b•QÇo“olŽ‘7̵bŽ‘<²¬)Ž¡‘ +°fŽ¡‘±use‘‰ffŽ‘®nameŽ‘AId¬=‘ǵbŽ‘¬;Ž¡‘ +°gŽŸ­127.‘ üMoQÇdify‘ÿ +«.Ž¦°h–ª¨¬Declare‘UU­ColorŽ‘"úH¬functions‘@¯97“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙ±mo‘ÿ}'difyŽ‘ACÚ¬(­constŽ‘*¢realŽ‘4ÝеrŽ‘9§ä;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµgŽ‘>ps¬=‘Ç0Ž–ǵ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµbŽ‘=š:¬=‘Ç0Ž“);ŽŽŽŒ‹$K Šn ý‘ì¬36–¯MODIFY’;t³3DLDF-1.1.5.1“°x¬128Ž €n ý•@P­128.Ž©°h–ª¨¬De ne‘UU­ColorŽ‘"úH¬functions‘@¯98“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘"ýÙColorŽ‘@M{¬::‘±mo‘ÿ}'difyŽ‘F¬(­constŽ‘*¢realŽ‘4ÝеrŽ‘9§ä;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµgŽ‘;©[;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµbŽ‘:Ó"¬)Ž¡‘ +°fŽ¡‘±r–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘: ¬+=ŽŽ‘LgôµrŽ‘Q2¬;Ž¡‘±gr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘CȦ¬+=ŽŽ‘VúµgŽ‘[>ݬ;Ž¡‘±blue‘‰ffŽ‘®p‘ÿ}'artŽ‘>J¬+=ŽŽ‘PŸlµbŽ‘Tê¬;Ž¡‘­ifŽ‘´ú¬(±r–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘&žµ>‘Ǭ1Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘3|Á°‘Ç´"WARNING!® ´In® ´Color::Ž‘kÆÜmodify():\n"Ž’®8°‘Ç´"red_part® ´is® ´greaterŽ‘kÆÜ® ´than® ´1:® ´"Ž’£”>°‘DZr–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘(Ù¶°Ž¡‘2±end‘‚ØlŽ‘H¸ß°‘Ç´"Setting® ´red_part® ´toŽ‘kÆÜ® ´1.\n\n"Ž’–M,¬;Ž¡‘±r–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘D¡¬=‘Ç1Ž‘Ç;Ž¡‘°gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±r–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘&žµ<‘Ǭ0Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘3Ù°‘#m´"WARNING!® ´In® ´Color::Ž‘l#1modify():\n"Ž’®Ìâ°‘#m´"red_part® ´is® ´less® ´thŽ‘l#1an® ´0:® ´"Ž’”Œñ°‘#m±r–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘)’`°Ž¡‘2±end‘‚ØlŽ‘H¸ß°‘Ç´"Setting® ´red_part® ´toŽ‘kÆÜ® ´0.\n\n"Ž’–M,¬;Ž¡‘±r–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘D¡¬=‘Ç0Ž‘Ç;Ž¡‘°gŽ¡‘­ifŽ‘´ú¬(±gr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘/Ȥµ>‘Ǭ1Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘4w0°‘Á‡´"WARNING!® ´In® ´Color::Ž‘lÁKmodify():\n"Ž—° °‘Á‡´"green_part® ´is® ´greatŽ‘lÁKer® ´than® ´1:® ´"Ž“°Ž¡‘2±gr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘aÈ©°‘DZend‘‚ØlŽ‘ò°‘Ç´"Setting® ´green_part® Ž‘kÆÜ´to® ´1.\n\n"Ž’ Í&¬;Ž¡‘±gr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘Mȧ¬=‘Ç1Ž‘Ç;Ž¡‘°gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±gr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘/Ȥµ<‘Ǭ0Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘3|Á°‘Ç´"WARNING!® ´In® ´Color::Ž‘kÆÜmodify():\n"Ž’®8°‘Ç´"green_part® ´is® ´less® Ž‘kÆÜ´than® ´0:® ´"Ž’žTA°‘DZgr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘2¼°Ž¡‘2±end‘‚ØlŽ‘H¸ß°‘Ç´"Setting® ´green_part® Ž‘kÆÜ´to® ´0.\n\n"Ž’ Í&¬;Ž¡‘±gr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘Mȧ¬=‘Ç0Ž‘Ç;Ž¡‘°gŽ¡‘­ifŽ‘´ú¬(±blue‘‰ffŽ‘®p‘ÿ}'artŽ‘*Jµ>‘Ǭ1Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘4—ø°‘âO´"WARNING!® ´In® ´Color::Ž‘lâmodify():\n"Ž’°J¦°‘âO´"blue_part® ´is® ´greateŽ‘lâr® ´than® ´1:® ´"Ž’« +©°Ž¡‘2±blue‘‰ffŽ‘®p‘ÿ}'artŽ‘\J°‘DZend‘‚ØlŽ‘ò°‘Ç´"Setting® ´blue_part® ´tŽ‘kÆÜo® ´1.\n\n"Ž’›)¬;Ž¡‘±blue‘‰ffŽ‘®p‘ÿ}'artŽ‘HJ¬=‘Ç1Ž‘Ç;Ž¡‘°gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±blue‘‰ffŽ‘®p‘ÿ}'artŽ‘*Jµ<‘Ǭ0Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘3 º°‘ë´"WARNING!® ´In® ´Color::Ž‘kêÕmodify():\n"Ž’®\*°‘ë´"blue_part® ´is® ´less® ´tŽ‘kêÕhan® ´0:® ´"Ž’™\6°‘ë±blue‘‰ffŽ‘®p‘ÿ}'artŽ‘-Y °Ž¡‘2±end‘‚ØlŽ‘H¸ß°‘Ç´"Setting® ´blue_part® ´tŽ‘kÆÜo® ´0.\n\n"Ž’›)¬;Ž¡‘±blue‘‰ffŽ‘®p‘ÿ}'artŽ‘HJ¬=‘Ç0Ž‘Ç;Ž¡‘°gŽ¡‘­returnŽ‘4‘g¬;Ž¡‘ +°gŽŸ­129.‘ üSet–ÕTred“part.Ž¦°h–ª¨¬Declare‘UU­ColorŽ‘"úH¬functions‘@¯97“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙ±set‘‰ffŽ›®r–ÿ}'e“d‘‰ffŽ˜p“artŽ‘UúD¬(­constŽ‘*¢realŽ‘4ÝеrŽ‘9§ä¬);ŽŽŽŒ‹% 4 Šn ý‘ì°x¬130›¯3DLDF-1.1.5.1’[µSET–ÕXRED“P–ÿJªAR“T˜¬37Ž €n ý•@P­130.Ž©°h–ª¨¬De ne‘UU­ColorŽ‘"úH¬functions‘@¯98“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘"ýÙColorŽ‘@M{¬::‘±set‘‰ffŽ›®r–ÿ}'e“d‘‰ffŽ˜p“artŽ‘3üo¬(­constŽ‘*¢realŽ‘4ÝеrŽ‘9§ä¬)Ž¡‘ +°fŽ¡‘­ifŽ‘´ú¬(µrŽ‘‘,>‘Ǭ1Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘3|×°‘Ç.´"WARNING!® ´In® ´Color::Ž‘kÆòset_red_part():\n"Ž’Í”R°‘Ç.´"r® ´is® ´greater® ´than® ´1Ž‘kÆò:® ´"Ž‘~Ô°‘Ç.µrŽ‘ +Xp°‘Ç.±end‘‚ØlŽ‘€°Ž¡‘2´"Setting® ´red_part® ´toŽ’šÿÉ® ´1.\n\n"Ž’ņ¬;Ž¡‘±r–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘D¡¬=‘Ç1Ž‘Ç;Ž¡‘°gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(µrŽ‘‘,<‘Ǭ0Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘3Öp°‘ Ç´"WARNING!® ´In® ´Color::Ž‘l ‹set_red_part():\n"Ž’ÎG„°‘ Ç´"r® ´is® ´less® ´than® ´0:® ´"Ž‘oǺ°‘ ǵrŽ‘ ¢°‘ DZend‘‚ØlŽ‘3P°Ž¡‘2´"Setting® ´red_part® ´toŽ’šÿÉ® ´0.\n\n"Ž’ņ¬;Ž¡‘±r–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘D¡¬=‘Ç0Ž‘Ç;Ž¡‘°gŽ¡‘­elseŽ‘+Øá±r–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘Që¬=‘ǵrŽ‘‘,¬;Ž¡‘­returnŽ‘4‘g¬;Ž¡‘ +°gŽŸ­131.‘ üSet–ÕTgreen“part.Ž¦°h–ª¨¬Declare‘UU­ColorŽ‘"úH¬functions‘@¯97“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙ±set‘‰ffŽ›®gr–ÿ}'e“en‘‰ffŽ˜p“artŽ‘_°J¬(­constŽ‘*¢realŽ‘4ÝеgŽ‘9þ³¬);ŽŸ­132.Ž¦°h–ª¨¬De ne‘UU­ColorŽ‘"úH¬functions‘@¯98“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙColorŽ‘@M{¬::‘±set‘‰ffŽ›®gr–ÿ}'e“en‘‰ffŽ˜p“artŽ‘=²u¬(­constŽ‘*¢realŽ‘4ÝеgŽ‘9þ³¬)Ž¡‘ +°fŽ¡‘­ifŽ‘´ú¬(µgŽ‘çû>‘Ǭ1Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘4¨°‘Yÿ´"WARNING!® ´In® ´Color::Ž‘lYÃset_green_part():\n"Ž’Ù9î°‘Yÿ´"g® ´is® ´greater® ´than® ´1Ž‘lYÃ:® ´"Ž‘ú!°‘YÿµgŽ‘ Ôá°Ž¡‘2±end‘‚ØlŽ‘H¸ß°‘Ç´"Setting® ´green_part® Ž‘kÆÜ´to® ´1.\n\n"Ž’ Í&¬;Ž¡‘±gr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘Mȧ¬=‘Ç1Ž‘Ç;Ž¡‘°gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(µgŽ‘çû<‘Ǭ0Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘3˜Ç°‘ã´"WARNING!® ´In® ´Color::Ž‘kââset_green_part():\n"Ž’ØL,°‘ã´"g® ´is® ´less® ´than® ´0:® ´"Ž‘oLh°‘ãµgŽ‘ +ç°‘ã±end‘‚ØlŽ‘·þ°Ž¡‘2´"Setting® ´green_part® Ž’šÿÉ´to® ´0.\n\n"Ž’Ь;Ž¡‘±gr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘Mȧ¬=‘Ç0Ž‘Ç;Ž¡‘°gŽ¡‘­elseŽ‘+Øá±gr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘[¡…¬=‘ǵgŽ‘çû¬;Ž¡‘­returnŽ‘4‘g¬;Ž¡‘ +°gŽŸ­133.‘ üSet–ÕTblue“part.Ž¦°h–ª¨¬Declare‘UU­ColorŽ‘"úH¬functions‘@¯97“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙ±set‘‰ffŽ–®blue‘‰ffŽ“p‘ÿ}'artŽ‘Z1¼¬(­constŽ‘*¢realŽ‘4ÝеbŽ‘9(z¬);ŽŽŽŒ‹& + Šn ý‘ì¬38›¯SET–ÕXBLUE“P–ÿJªAR“T’h}3DLDF-1.1.5.1˜°x¬134Ž €n ý•@P­134.Ž©°h–ª¨¬De ne‘UU­ColorŽ‘"úH¬functions‘@¯98“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘"ýÙColorŽ‘@M{¬::‘±set‘‰ffŽ–®blue‘‰ffŽ“p‘ÿ}'artŽ‘83ç¬(­constŽ‘*¢realŽ‘4ÝеbŽ‘9(z¬)Ž¡‘ +°fŽ¡‘­ifŽ‘´ú¬(µbŽ‘Â>‘Ǭ1Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘43å°‘~<´"WARNING!® ´In® ´Color::Ž‘l~set_blue_part():\n"Ž’ÔBk°‘~<´"b® ´is® ´greater® ´than® ´1Ž‘l~:® ´"Ž’€B›°‘~<µbŽ‘ G"°Ž¡‘2±end‘‚ØlŽ‘H¸ß°‘Ç´"Setting® ´blue_part® ´tŽ‘kÆÜo® ´1.\n\n"Ž’›)¬;Ž¡‘±blue‘‰ffŽ‘®p‘ÿ}'artŽ‘HJ¬=‘Ç1Ž‘Ç;Ž¡‘°gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(µbŽ‘Â<‘Ǭ0Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘3»g°‘¾´"WARNING!® ´In® ´Color::Ž‘l‚set_blue_part():\n"Ž’ÓQo°‘¾´"b® ´is® ´less® ´than® ´0:® ´"Ž‘o‘¨°‘¾µbŽ‘ +V&°‘¾±end‘‚ØlŽ‘ý>°Ž¡‘2´"Setting® ´blue_part® ´tŽ’šÿÉo® ´0.\n\n"Ž’ÊƬ;Ž¡‘±blue‘‰ffŽ‘®p‘ÿ}'artŽ‘HJ¬=‘Ç0Ž‘Ç;Ž¡‘°gŽ¡‘­elseŽ‘+Øá±blue‘‰ffŽ‘®p‘ÿ}'artŽ‘V"÷¬=‘ǵbŽ‘¬;Ž¡‘­returnŽ‘4‘g¬;Ž¡‘ +°gŽŸ­135.‘ üSho®9w.Ž¦°h–ª¨¬Declare‘UU­ColorŽ‘"úH¬functions‘@¯97“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙ±showŽ‘9ˆØ¬(­stringŽ‘!%M±textŽ‘5D1¬=‘Ç´""Ž‘ Íz¬)‘UU­constŽ‘*¢¬;ŽŸ­136.Ž¦°h–ª¨¬De ne‘UU­ColorŽ‘"úH¬functions‘@¯98“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙColorŽ‘@M{¬::‘±showŽ‘‹¬(­stringŽ‘!%M±textŽ‘2}¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­ifŽ‘´ú¬(±textŽ‘ä°‘Ç´""Ž‘ Íz¬)‘±textŽ‘ä¬=‘Ç´"Color:"Ž‘-Mh¬;Ž¡‘±c‘ÿ}'outŽ‘* Q°‘DZtextŽ‘åü°‘DZend‘‚ØlŽ‘¸Ú¬;Ž¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"name® ´==® ´"Ž‘:”z°‘DZget‘‰ffŽ‘®nameŽ‘+Àج(‘ª¨)–Ç°“±end‘‚ØlŽ‘¸Ú¬;Ž¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"use_name® ´==® ´"Ž‘O”n°‘DZget‘‰ffŽ–®use‘‰ffŽ“nameŽ‘=}¬(‘ª¨)–Ç°“±end‘‚ØlŽ‘¸Ú¬;Ž¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"red_part® ´==® ´"Ž‘O”n°‘DZget‘‰ffŽ›®r–ÿ}'e“d‘‰ffŽ˜p“artŽ‘6FZ¬(‘ª¨)–Ç°“±end‘‚ØlŽ‘¸Ú¬;Ž¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"green_part® ´==® ´"Ž‘Zh°‘DZget‘‰ffŽ›®gr–ÿ}'e“en‘‰ffŽ˜p“artŽ‘?ü`¬(‘ª¨)–Ç°“±end‘‚ØlŽ‘¸Ú¬;Ž¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"blue_part® ´==® ´"Ž‘TÔk°‘DZget‘‰ffŽ–®blue‘‰ffŽ“p‘ÿ}'artŽ‘:}Ò¬(‘ª¨)–Ç°“±end‘‚ØlŽ‘ò°“±end‘‚ØlŽ‘¸Ú¬;Ž¡‘­returnŽ‘4‘g¬;Ž¡‘ +°gŽ¤­137.‘ üReturning–ÕTelemen®9ts“and“information.Ž¡138.‘ üIs–ÕTon“free“store.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ +¬[²LDF‘T2004.01.06.¬]Ž‘Y;Made‘UUnon-inline.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­ColorŽ‘"úH¬functions‘@¯97“°i‘Ǭ+°Ž¡‘ +­b•QÇo“olŽ‘#¡g±is‘‰ffŽ–®on‘‰ffŽ“fr–ÿ}'e“e‘‰ffŽ‘®stor“eŽ‘f<¬(‘ª®)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹'$ Šn ý‘ì°x¬139›¯3DLDF-1.1.5.1’ /IS–ÕXON“FREE“STORE˜¬39Ž €n ý•@P­139.ŽŸ°h–ª¨¬De ne‘UU­ColorŽ‘"úH¬functions‘@¯98“°i‘Ǭ+°Ž¤ ‘ +­b•QÇo“olŽ‘#¡gColorŽ‘@ñ ¬::‘±is‘‰ffŽ–®on‘‰ffŽ“fr–ÿ}'e“e‘‰ffŽ‘®stor“eŽ‘CzÙ¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼±on‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘o‹®¬;Ž¡‘ +°gŽ©­140.› üGet–Ç Color“parts.˜¬[²LDF‘T2002.09.24.¬]Ž‘Z{ÊThese–Héfunctions“alw•¸ãa“ys–Héreturn“a“­realŽ‘¦Â¬;‘M the“argumen¸ãt“±de‘ÿ}'cimalŽŽ¡¬can't–UUmak¸ãe“them“return“an“­unsignedŽ‘3ŒcshortŽ‘N±¬.Ž¦­141.‘ üGet–ÕTred“part.ŽŸ°h–ª¨¬Declare‘UU­ColorŽ‘"úH¬functions‘@¯97“°i‘Ǭ+°Ž¡‘ +­inlineŽ‘)ŠIrealŽ‘@=w±get‘‰ffŽ›®r–ÿ}'e“d‘‰ffŽ˜p“artŽ‘s¼¹¬(­b•QÇo“olŽ‘¡f±de‘ÿ}'cimalŽ‘>©Þ¬=‘DZfalseŽ‘v\¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­ifŽ‘´ú¬(±de‘ÿ}'cimalŽ‘"A`¬)‘­returnŽ‘(溱truncŽ‘Aõ¬((±r–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘%„f°‘8à¬255ŽŽ‘8ã)–8à+“µ:¬5ŽŽ‘ ÿþ);Ž¡‘­elseŽ‘+ØáreturnŽ‘O¿›±r–ÿ}'e“d‘‰ffŽ‘®p“artŽ‘s !¬;Ž¡‘ +°gŽ¦­142.‘ üGet–ÕTgreen“part.ŽŸ°h–ª¨¬Declare‘UU­ColorŽ‘"úH¬functions‘@¯97“°i‘Ǭ+°Ž¡‘ +­inlineŽ‘)ŠIrealŽ‘@=w±get‘‰ffŽ›®gr–ÿ}'e“en‘‰ffŽ˜p“artŽ‘}r¿¬(­b•QÇo“olŽ‘¡f±de‘ÿ}'cimalŽ‘>©Þ¬=‘DZfalseŽ‘v\¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­ifŽ‘´ú¬(±de‘ÿ}'cimalŽ‘"A`¬)‘­returnŽ‘(溱truncŽ‘Aõ¬((±gr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘/:l°‘8à¬255ŽŽ‘8ã)–8à+“µ:¬5ŽŽ‘ ÿþ);Ž¡‘­elseŽ‘+ØáreturnŽ‘O¿›±gr–ÿ}'e“en‘‰ffŽ‘®p“artŽ‘|Á'¬;Ž¡‘ +°gŽ¦­143.‘ üGet–ÕTblue“part.ŽŸ°h–ª¨¬Declare‘UU­ColorŽ‘"úH¬functions‘@¯97“°i‘Ǭ+°Ž¡‘ +­inlineŽ‘)ŠIrealŽ‘@=w±get‘‰ffŽ–®blue‘‰ffŽ“p‘ÿ}'artŽ‘wô1¬(­b•QÇo“olŽ‘¡f±de‘ÿ}'cimalŽ‘>©Þ¬=‘DZfalseŽ‘v\¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­ifŽ‘´ú¬(±de‘ÿ}'cimalŽ‘"A`¬)‘­returnŽ‘(溱truncŽ‘Aõ¬((±blue‘‰ffŽ‘®p‘ÿ}'artŽ‘)»Þ°‘8à¬255ŽŽ‘8ã)–8à+“µ:¬5ŽŽ‘ ÿþ);Ž¡‘­elseŽ‘+ØáreturnŽ‘O¿›±blue‘‰ffŽ‘®p‘ÿ}'artŽ‘wB™¬;Ž¡‘ +°gŽ¦­144.‘ üGet–ÕTuse“name.ŽŸ°h–ª¨¬Declare‘UU­ColorŽ‘"úH¬functions‘@¯97“°i‘Ǭ+°Ž¡‘ +­b•QÇo“olŽ‘#¡g±get‘‰ffŽ–®use‘‰ffŽ“nameŽ‘^Wm¬(‘ª®)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹(.û Šn ý‘ì¬40›¯GET–ÕXUSE“NAME’ãß3DLDF-1.1.5.1˜°x¬145Ž €n ý•@P­145.Ž©°h–ª¨¬De ne‘UU­ColorŽ‘"úH¬functions‘@¯98“°i‘Ǭ+°Ž¤ ‘ +­b•QÇo“olŽ‘#¡gColorŽ‘@ñ ¬::‘±get‘‰ffŽ–®use‘‰ffŽ“nameŽ‘;¶ +¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼±use‘‰ffŽ‘®nameŽ‘bi¬;Ž¡‘ +°gŽŸ­146.‘ üGet‘ÕTname.Ž¦°h–ª¨¬Declare‘UU­ColorŽ‘"úH¬functions‘@¯97“°i‘Ǭ+°Ž¡‘ +­inlineŽ‘)ŠIstringŽ‘J¯–±get‘‰ffŽ‘®nameŽ‘s©V¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼±nameŽ‘P¬À¬;Ž¡‘ +°gŽŸ­147.‘ üOutput‘ÕTopQÇerator.Ž¦°h›ª¨¬Declare–UUnon-mem¸ãbGer“non-template“functions“for“­ColorŽ‘#ä÷¯147˜°i‘ÇŽ¡‘ +±ostr–ÿ}'e“amŽ‘/¬&‘8à­opQÇeratorŽ‘-Ï•°Ž‘7Ï–¬(±ostr–ÿ}'e“amŽ‘%¬&‘8àµoŽ‘Ä;‘ª¨­constŽ‘ÕJColorŽ‘?z=¬&Ž‘GA[µcŽ‘K•6¬);ŽŸ ¯This–ÕXco‘h¬;Ž¡‘°gŽ¡‘­ifŽ‘´ú¬(±nameŽ‘°‘Ç´""Ž‘ Íz¬)‘°fŽ¡‘±c‘ÿ}'errŽ‘8(¢°‘rù´"ERROR!® ´In® ´Color::deŽ‘pr½fine_colors_mp():\n"Ž’ákâ°Ž¡‘2´"name® ´is® ´empty.® ´NotŽ’šÿÉ® ´doing® ´anything® ´and® Ž’ÿ´returning.\n"Ž’KŒæ°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘>‘h¬;Ž¡‘°gŽ¡‘±out‘‰ffŽ‘®str–ÿ}'e“amŽ‘FlÀ°‘,"´"color® ´"Ž‘0Þ”°‘,"±nameŽ–H°‘,"´";"Ž‘ž£°‘,"´"® ´"Ž›Þ °‘,"±nameŽ“°‘,"´"® ´=® ´("Ž‘&^š°‘,"±get‘‰ffŽ›®r–ÿ}'e“d‘‰ffŽ˜p“artŽ‘6«d¬(‘ª¨)–,"°“´",® ´"Ž˜°Ž¡‘(±get‘‰ffŽ›®gr–ÿ}'e“en‘‰ffŽ˜p“artŽ‘e5L¬(›ª¨)–Ç°“´",® ´"Ž‘Œ°“±get‘‰ffŽ–®blue‘‰ffŽ“p‘ÿ}'artŽ‘:}Ò¬(˜)“°“´");\n"Ž‘%”†°“± ushŽ‘€¬;Ž¡‘­returnŽ‘4‘g¬;Ž¡‘ +°gŽŸ­151.– üInitialize‘ÃColors.“¬[²LDF‘T2002.09.25.¬]Ž‘\x=This–E\function“presuppGoses“the“existence“of“­namespaceŽŽ¡ColorsŽ‘ ØÚ¬.Ž¦°h–ª¨¬Declare‘UU­ColorŽ‘"úH¬functions‘@¯97“°i‘Ǭ+°Ž¡‘ +­staticŽ‘)HÚv®9oidŽ‘BF²±initialize‘‰ffŽ‘®c‘ÿ}'olorsŽ’†ͬ(‘ª®);ŽŽŽŒ‹*?» Šn ý‘ì¬42–¯INITIALIZE‘ÕX­COLORS’ýr¯3DLDF-1.1.5.1“°x¬152Ž €n ý•@P­152.Ž©°h–ª¨¬De ne‘UU­ColorŽ‘"úH¬functions‘@¯98“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘"ýÙColorŽ‘@M{¬::‘±initialize‘‰ffŽ‘®c‘ÿ}'olorsŽ‘DÀ¬(‘ª®)Ž¡‘ +°fŽ¡‘­usingŽ‘2SˆnamespaceŽ‘k÷ColorsŽ’ŒÏܬ;Ž¦‘­ifŽ‘´ú¬(°:±out‘‰ffŽ‘®str–ÿ}'e“amŽ‘/@œµ:±is‘‰ffŽ‘®op‘ÿ}'enŽ‘ ¬(‘ª¨))‘°fŽ¡‘±c‘ÿ}'errŽ‘8-°‘P„´"ERROR!® ´In® ´Color::inŽ‘pPHitialize_colors():\nŽ’ÙP "Ž’æfõ°Ž¡‘2´"out_stream® ´is® ´closeŽ’šÿÉd!® ´Returning.\n"Ž’÷°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘>‘h¬;Ž¡‘°gŽ¡‘±out‘‰ffŽ‘®str–ÿ}'e“amŽ‘F¶°‘Ç´"%%%® ´Color® ´definitioŽ‘kÆÜns.\n\n"Ž’–M,¬;Ž¡#­ifŽ‘ Öo¬0Ž‘$Öqµ=°‘!t¬[²LDF‘T2002.09.25.¬]Ž‘TK%These–vÌcolors“are“already“de ned“in“MET‘ÿ*ªAPOST‘vÄand“their“de nitions“areŽ¡‘(not–UUlikš¸ãely“to“c˜hange.‘qÇHo˜w˜ev˜er,“if“they“do,“I“can“commen˜t“these“function“calls“bac˜k“in.‘o°µ=Ž¡‘±r–ÿ}'e“dŽ‘"s/µ:±de ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn¬(‘ª¨);Ž¡‘±gr–ÿ}'e“enŽ‘+åµ:±de ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn¬(‘ª¨);Ž¡‘±blueŽ‘&byµ:±de ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn¬(‘ª¨);Ž¡‘±blackŽ‘+ Öµ:±de ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn¬(‘ª¨);Ž¡‘±whiteŽ‘,Áµ:±de ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn¬(‘ª¨);Ž¡‘±b–ÿ}'ackgr“oundŽ‘Euøµ:±de ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn¬(‘ª¨);Ž¡#­endifŽŽ¡‘±yel‘‚ØlowŽ‘0k³µ:±de ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn¬(‘ª¨);Ž¡‘±cyanŽ‘)w‘µ:±de ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn¬(‘ª¨);Ž¡‘±magentaŽ‘9Òµ:±de ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn¬(‘ª¨);Ž¡‘±or‘ÿ}'angeŽ‘2)µ:±de ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn¬(‘ª¨);Ž¡‘±violetŽ‘,·µ:±de ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn¬(‘ª¨);Ž¡‘±purpleŽ‘097µ:±de ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn¬(‘ª¨);Ž¡‘±yel‘‚Ølow‘‰ffŽ‘®gr–ÿ}'e“enŽ‘Jhlµ:±de ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn¬(‘ª¨);Ž¡‘±gr–ÿ}'e“en‘‰ffŽ‘®yel‘‚ØlowŽ‘J·–µ:±de ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn¬(‘ª¨);Ž¡‘±blue‘‰ffŽ‘®violetŽ‘A„jµ:±de ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn¬(‘ª¨);Ž¡‘±gr‘ÿ}'ayŽ‘'ªÿµ:±de ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn¬(‘ª¨);Ž¡‘±light‘‰ffŽ‘®gr‘ÿ}'ayŽ‘>ܵ:±de ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn¬(‘ª¨);Ž¡‘±violet‘‰ffŽ‘®r–ÿ}'e“dŽ‘=b£µ:±de ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn¬(‘ª¨);Ž¡‘±default‘‰ffŽ‘®b–ÿ}'ackgr“oundŽ‘fF!µ:±de ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn¬(‘ª¨);Ž¡‘µ=°‘ÿý¬[²LDF‘T2002.09.25.¬]Ž‘T7Curren¸ãtly‘ÿ*ª,–UUthis“function“doGes“nothing“if“I'm“using“all“of“the“colors.‘o°µ=Ž¡‘±out‘‰ffŽ‘®str–ÿ}'e“amŽ‘F¶°‘Ç´"\n%%%® ´End® ´of® ´Color® Ž‘kÆÜ´definitions.\n\n"Ž’Ŭ;Ž¡‘­returnŽ‘4‘g¬;Ž¡‘ +°gŽŸ­153.– üNamespace‘ :Colors.“¬Here–'(I‘'can“put“either“°h›ª¨¬Ma‘Ž8jor“­ColorsŽ‘(@¯156˜°i“¬or“°h˜¬All“­ColorsŽ‘(@¯0˜°i“¬in¸ãto“°h˜¬DeclareŽ¡­namespaceŽ‘9‡ÀColorsŽ‘^ ž¯153‘ª¨°i¬,›?&and–9›commen¸ãt“out“the“other,˜depGending“on“what“I‘9”w•¸ãan“t.‘h‰This›9›prev“en“ts˜toGo˜m“uc“hŽ¡unneeded–cošGde“from“b˜eing“pro˜cessed.‘[V°h›ª¨¬All“­ColorsŽ‘(*Þ¯0˜°i“¬is“vš¸ãery“long,‘xso“I‘ïneither“w˜an˜t“to“compile“it,‘xwrite“theŽ¡­externŽ‘#ôí¬declarations–,lfrom“it“to“®colors.h¬,›4›nor“prin¸ãt“out“the“coGde“when“I‘,brun“®cweave¬,˜unless“I‘,breally“w•¸ãan“t‘,ltoŽ¡use‘UUit.‘qÇ[²LDF‘T2002.09.25.¬]ŽŽ¦°h–ª¨¬Declare‘UU­namespaceŽ‘<øÏColorsŽ‘b­¯153“°i‘ÇŽ¡‘ +h–ª¨¬Ma‘Ž8jor‘UU­ColorsŽ›(n3¯156“°i‘µ=°“h“¬All‘UU­ColorsŽ˜¯0“°i‘ÿýµ=Ž¤ ¯This–ÕXcoµ;‘ª¨¬173ŽŽ–ª«µ;‘ª¨¬255ŽŽ“µ;‘ª¨¬47ŽŽ‘ ªª);‘µ=°‘ÿý¬Orange.‘o°µ=Ž¡‘­externŽ‘8ØconstŽ‘VHzColorŽ‘uím±or‘ÿ}'angeŽ’“ð”¬(´"orange"Ž‘*†Pµ;‘ª¨¬255ŽŽ–ª«µ;‘ª¨¬165ŽŽ“µ;‘ª¨¬0Ž‘ª©µ;‘ª¨±trueŽ‘o@¬);‘µ=°‘ÿý¬Violet.‘o°µ=Ž¡‘­externŽ‘8ØconstŽ‘VHzColorŽ‘uím±violetŽ’Ž¤€¬(´"violet"Ž‘*†Pµ;‘ª¨¬238ŽŽ–ª«µ;‘ª¨¬130ŽŽ“µ;‘ª¨¬238ŽŽ“µ;‘ª¨±trueŽ‘o@¬);Ž¡‘­externŽ‘8ØconstŽ‘VHzColorŽ‘uím±purpleŽ’’&¢¬(´"purple"Ž‘*†Pµ;‘ª¨¬160ŽŽ–ª«µ;‘ª¨¬32ŽŽ‘ ªªµ;‘ª¨¬240ŽŽ“µ;‘ª¨±trueŽ‘o@¬);Ž¡‘­externŽ‘8ØconstŽ‘VHzColorŽ‘uím±blue‘‰ffŽ‘®violetŽ’£qÕ¬(´"blue_violet"Ž‘DÆAµ;‘ª¨¬138ŽŽ–ª«µ;‘ª¨¬43ŽŽ‘ ªªµ;‘ª¨¬226ŽŽ“);‘µ=°‘ÿý¬Green.‘o°µ=Ž¡‘­externŽ‘8ØconstŽ‘VHzColorŽ‘uím±yel‘‚Ølow‘‰ffŽ‘®gr–ÿ}'e“enŽ’¬U׬(´"yellow_green"Ž‘J>µ;‘ª¨¬154ŽŽ–ª«µ;‘ª¨¬205ŽŽ“µ;‘ª¨¬50ŽŽ‘ ªª);Ž¡‘µ=°‘ÿý¬\Un•¸ãbun“t"–UUColors“(blacš¸ãks,“whites,“and“gra˜ys).‘o°µ=Ž¡‘­externŽ‘8ØconstŽ‘VHzColorŽ‘uím±blackŽ’ŒûA¬(´"black"Ž‘%FSµ;‘ª¨¬0Ž–ª©µ;‘ª¨¬0Ž“µ;‘ª¨¬0Ž“µ;‘ª¨±trueŽ‘o@¬);Ž¡‘­externŽ‘8ØconstŽ‘VHzColorŽ‘uím±whiteŽ’ï,¬(´"white"Ž‘%FSµ;‘ª¨¬255ŽŽ–ª«µ;‘ª¨¬255ŽŽ“µ;‘ª¨¬255ŽŽ“µ;‘ª¨±trueŽ‘o@¬);Ž¡‘­externŽ‘8ØconstŽ‘VHzColorŽ‘uím±gr‘ÿ}'ayŽ’‰˜j¬(´"gray"Ž‘ Vµ;‘ª¨¬192ŽŽ–ª«µ;‘ª¨¬192ŽŽ“µ;‘ª¨¬192ŽŽ“);Ž¡‘­externŽ‘8ØconstŽ‘VHzColorŽ‘uím±light‘‰ffŽ‘®gr‘ÿ}'ayŽ’ŸîG¬(´"light_gray"Ž‘?†Dµ;‘ª¨¬211ŽŽ–ª«µ;‘ª¨¬211ŽŽ“µ;‘ª¨¬211ŽŽ“);Ž¡‘µ=°‘ð6¬Defaults.‘l…[²LDF‘T2002.09.27.¬]Ž‘SdøNote–EŽthat“±default‘‰ffŽ‘®c‘ÿ}'olorŽ‘:Ái¬,‘Hµ±help‘‰ffŽ‘®c‘ÿ}'olorŽ‘2H·¬and“±b–ÿ}'ackgr“ound‘‰ffŽ‘®c“olorŽ‘PÏt¬are“pGoin¸ãtersŽ¡‘(and–Óthat“±default‘‰ffŽ‘®b–ÿ}'ackgr“oundŽ‘YEŬis“a“plain“­ColorŽ‘Ïq¬.‘ñ@It“can“bGe“used“to“access“the“original“bac¸ãkgroundŽ¡‘(color–UU(currenš¸ãtly“white),“if“the“user“pGoin˜ts“the“±b–ÿ}'ackgr“ound‘‰ffŽ‘®c“olorŽ‘Pï¬at“some“other“­ColorŽ‘¤ó¬.‘o°µ=Ž¡‘­externŽ‘8ØconstŽ‘VHzColorŽ‘uím±default‘‰ffŽ‘®b–ÿ}'ackgr“oundŽ’È3Œ¬(´"default_background"Ž‘i†,µ;‘ª¨¬255ŽŽ–ª«µ;‘ª¨¬255ŽŽ“µ;‘ª¨¬255ŽŽ“µ;‘ª¨±trueŽ‘o@¬);Ž¡‘­externŽ‘8ØconstŽ‘VHzColorŽ‘uím°Ž‘zín±default‘‰ffŽ‘®c‘ÿ}'olorŽ’µ0a¬=‘Ç&Ž‘ +Ž6±blackŽ‘!œ +¬;Ž¡‘­externŽ‘8ØconstŽ‘VHzColorŽ‘uím°Ž‘zín±b–ÿ}'ackgr“ound‘‰ffŽ‘®c“olorŽ’ÇøÞ¬=‘Ç&Ž‘ +Ž6±default‘‰ffŽ‘®b–ÿ}'ackgr“oundŽ‘\ÔU¬;Ž¡‘­externŽ‘8ØconstŽ‘VHzColorŽ‘uím°Ž‘zín±help‘‰ffŽ‘®c‘ÿ}'olorŽ’©nú¬=‘Ç&Ž‘ +Ž6±gr–ÿ}'e“enŽ‘"sC¬;‘µ=°‘ÿý¬LDF‘UU2002.10.26.‘qÇAdded.‘o°µ=Ž¡‘=°‘7¬[²LDF‘T2002.09.25.¬]Ž‘T«!!‘{uTO›XŽDO:‘X±default‘‰ffŽ‘®b–ÿ}'ackgr“oundŽ‘X÷=¬is–Xa“con•¸ãv“enience,‘Y^in–Xcase“I˜cš¸ãhange“\bac˜kground"Ž¡‘(in–S8the“MET›ÿ*ªAPOST‘S7coGde.‘qChec¸ãk“MET˜APOST–S7došGcumen¸ãtation!!‘qI“b˜eliev¸ãe–S8it“has“something“similar.Ž¡‘(°µ=ŽŽŽŒ‹,V? Šn ý‘ì¬44›¯INTERNAL–ÕX(WITH“INITIALIZA‘ÿJªTION)’Ç£é3DLDF-1.1.5.1˜°x¬156Ž €n ý•@P‘ +°gŽ¤ ¯This–ÕXco§¬;Ž¡‘­externŽ‘8ØColorŽ‘WÂË°Ž‘\Â̱help‘‰ffŽ‘®c‘ÿ}'olorŽ’ˆ}@¬;‘µ=°‘ÿý¬LDF‘UU2002.10.26.‘qÇAdded.‘o°µ=Ž¡‘­externŽ‘8ØColorŽ‘WÂË°Ž‘\Â̱b–ÿ}'ackgr“ound‘‰ffŽ‘®c“olorŽ’§$¬;Ž¡‘ +°gŽ¤ ¯This–ÕXco‘¬declaration‘@¯154˜°iŽ¡¬abGo•¸ãv“e.Ž¡‘ +´@Ž‘Æf¬i–UU®colall.web“¬(Commen¸ãted“out).Ž¦­159.‘ üGlobal‘ÕTconstan®9ts.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.10.26.¬]Ž‘Y;Added‘UU±help‘‰ffŽ–®c›ÿ}'olor‘‰ffŽ“ve˜ctorŽ‘L®(¬.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Global‘UUconstan¸ãts‘@¯22“°i‘Ǭ+°Ž¤ ‘ +­namespaceŽ‘C£{ColorsŽ‘gѪ°fŽ¡‘­externŽ‘8ØconstŽ‘VHzv®9ectorŽ‘uò°h­constŽ‘*¢ColorŽ‘=Ï•°Ž‘BÏ–i‘UU±default‘‰ffŽ–®c›ÿ}'olor‘‰ffŽ“ve˜ctorŽ‘Xo¬(1Ž‘µ;‘ª¨±default‘‰ffŽ‘®c‘ÿ}'olorŽ‘9&ƒ¬);ŽŽŽŒ‹-op Šn ý‘ì°x¬159–¯3DLDF-1.1.5.1’UGLOBAL‘ÕXCONST‘ÿJªANTS“¬45Ž €n ý•@P‘­externŽ‘8ØconstŽ‘VHzv®9ectorŽ‘uò°h­constŽ‘*¢ColorŽ‘=Ï•°Ž‘BÏ–i‘UU±help‘‰ffŽ–®c›ÿ}'olor‘‰ffŽ“ve˜ctorŽ‘L®(¬(1Ž‘µ;‘ª¨±help‘‰ffŽ‘®c‘ÿ}'olorŽ‘-e¬);Ž¤ ‘µ=°‘ÿý¬LDF‘UU2002.10.26.‘qÇAdded.‘o°µ=Ž¡‘­externŽ‘8ØconstŽ‘VHzv®9ectorŽ‘uò°h­constŽ‘*¢ColorŽ‘=Ï•°Ž‘BÏ–i‘UU±b–ÿ}'ackgr“ound‘‰ffŽ›®c“olor‘‰ffŽ˜ve“ctorŽ‘k8 ¬(1Ž‘µ;‘ª¨±b–ÿ}'ackgr“ound‘‰ffŽ‘®c“olorŽ‘Kï¬);Ž¡‘ +°gŽ©­160.ŽŸ°h‘ª¨­externŽ‘%È~¬global–UUconstan¸ãt“declarations‘@¯160‘ª¨°i‘ÇŽ¡‘ +­namespaceŽ‘C£{ColorsŽ‘gѪ°fŽ¡‘­externŽ‘8ØconstŽ‘VHzv®9ectorŽ‘uò°h­constŽ‘*¢ColorŽ‘=Ï•°Ž‘BÏ–i‘UU±default‘‰ffŽ–®c›ÿ}'olor‘‰ffŽ“ve˜ctorŽ‘Xo¬;Ž¡‘­externŽ‘8ØconstŽ‘VHzv®9ectorŽ‘uò°h­constŽ‘*¢ColorŽ‘=Ï•°Ž‘BÏ–i‘UU±help‘‰ffŽ–®c›ÿ}'olor‘‰ffŽ“ve˜ctorŽ‘L®(¬;‘µ=°‘ÿý¬LDF‘UU2002.10.26.‘qÇAdded.‘o°µ=Ž¡‘­externŽ‘8ØconstŽ‘VHzv®9ectorŽ‘uò°h­constŽ‘*¢ColorŽ‘=Ï•°Ž‘BÏ–i‘UU±b–ÿ}'ackgr“ound‘‰ffŽ›®c“olor‘‰ffŽ˜ve“ctorŽ‘k8 ¬;Ž¡‘ +°gŽŸ ¯This–ÕXcoÅH¯95“°iŽ¡‘ +h–ª¨¬Declare‘UU­namespaceŽ‘<øÏColorsŽ‘b­¯153“°iŽ¡‘ +h–ª¨¬De ne‘UU­ColorŽ‘"úH¬functions‘@¯98“°iŽ¡‘ +h›ª¨¬Declare–UUnon-mem¸ãbGer“template“functions“for“­ColorŽ‘#ä÷¯112˜°iŽ¡‘ +h›ª¨¬De ne–UUnon-mem¸ãbGer“non-template“functions“for“­ColorŽ‘#ä÷¯148˜°iŽ¡‘ +h–ª¨¬Global‘UUconstan¸ãts‘@¯22“°iŽŽŽŒ‹.~Ä Šn ý‘ì¬46›¯PUTTING–ÕX­COLOR“¯TOGETHER’ÖBÂ3DLDF-1.1.5.1˜°x¬163Ž €n ý•@P­163.‘ ü¬This–UUis“written“to“®colors.h¬.Ž©ëî°h‘ª¨´colors.hŽ‘5°ù¯163‘ª¨°i‘ÇŽ¤ ‘ +h–ª¨¬De ne‘UU­classŽ‘5¦ColorŽ‘>ÅH¯95“°iŽ¡‘ +h‘ª¨­externŽ‘%È~namespaceŽ‘_køColorsŽ’ƒš'¬declaration‘@¯154‘ª¨°iŽ¡‘ 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+°fŽ¡‘±matrixŽ‘2?¬[0Ž–][0Ž“]–Ç=“±r0‘‰ffŽ‘®0Ž‘Ã`¬;Ž¡‘±matrixŽ‘2?¬[0Ž–][1Ž“]–Ç=“±r0‘‰ffŽ‘®1Ž‘Ã`¬;Ž¡‘±matrixŽ‘2?¬[0Ž–][2Ž“]–Ç=“±r0‘‰ffŽ‘®2Ž‘Ã`¬;Ž¡‘±matrixŽ‘2?¬[0Ž–][3Ž“]–Ç=“±r0‘‰ffŽ‘®3Ž‘Ã`¬;Ž¡‘±matrixŽ‘2?¬[1Ž–][0Ž“]–Ç=“±r1‘‰ffŽ‘®0Ž‘Ã`¬;Ž¡‘±matrixŽ‘2?¬[1Ž–][1Ž“]–Ç=“±r1‘‰ffŽ‘®1Ž‘Ã`¬;Ž¡‘±matrixŽ‘2?¬[1Ž–][2Ž“]–Ç=“±r1‘‰ffŽ‘®2Ž‘Ã`¬;Ž¡‘±matrixŽ‘2?¬[1Ž–][3Ž“]–Ç=“±r1‘‰ffŽ‘®3Ž‘Ã`¬;Ž¡‘±matrixŽ‘2?¬[2Ž–][0Ž“]–Ç=“±r2‘‰ffŽ‘®0Ž‘Ã`¬;Ž¡‘±matrixŽ‘2?¬[2Ž–][1Ž“]–Ç=“±r2‘‰ffŽ‘®1Ž‘Ã`¬;Ž¡‘±matrixŽ‘2?¬[2Ž–][2Ž“]–Ç=“±r2‘‰ffŽ‘®2Ž‘Ã`¬;Ž¡‘±matrixŽ‘2?¬[2Ž–][3Ž“]–Ç=“±r2‘‰ffŽ‘®3Ž‘Ã`¬;Ž¡‘±matrixŽ‘2?¬[3Ž–][0Ž“]–Ç=“±r3‘‰ffŽ‘®0Ž‘Ã`¬;Ž¡‘±matrixŽ‘2?¬[3Ž–][1Ž“]–Ç=“±r3‘‰ffŽ‘®1Ž‘Ã`¬;Ž¡‘±matrixŽ‘2?¬[3Ž–][2Ž“]–Ç=“±r3‘‰ffŽ‘®2Ž‘Ã`¬;Ž¡‘±matrixŽ‘2?¬[3Ž–][3Ž“]–Ç=“±r3‘‰ffŽ‘®3Ž‘Ã`¬;Ž¡‘ +°gŽŸ­174.– üAssignmen®9t.“¬Sets‘f±matrixŽ›%`g¬to–fbGe“iden¸ãtical“to“the“±matrixŽ˜¬of“another“­T‘ÿ +«ransformŽ‘8ã¬.–"û!!“Remem¸ãbGer‘ftoŽ¡add–UUitems“here“if“I“add“them“to“the“class“de nition.Ž¦°h–ª¨¬Declare‘UU­T‘ÿ +«ransformŽ‘;'¬functions‘@¯168“°i‘Ǭ+°Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓopQÇeratorŽ‘m_ˆ¬=Ž‘u&¦(­constŽ‘*¢T‘ÿ +«ransformŽ‘Uót¬&Ž‘]º’µtŽ‘aW¬);ŽŸ­175.Ž¦°h–ª¨¬De ne‘UU­T‘ÿ +«ransformŽ‘;'¬functions‘@¯169“°i‘Ǭ+°Ž¡‘ +­T‘ÿ «ransformŽ‘AÈÓT‘ÿ -«ransformŽ‘w S·‘ÇÏsetwŽ‘I«(7Ž›)–Ç·“Ïsetpr–ÿ}'e“cisionŽ‘6‡ «(3Ž˜)“·“ÏmatrixŽ‘!³«[±iŽ‘qô«][±jŽ‘°Ä«]“·“Ý"È Ý"Ž‘ w«;Ž¡‘·gŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÏend‘‚ØlŽ‘¸Ú«;Ž¡‘·gŽ¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ -·gŽ©Â149.– üAne‘2ctransformations.“«[¬LDF‘T2002.10.16.«]Ž‘Yú†The–Ç¥functions“for“the“ane“transformations“all“returnŽ¡a‘TªÂT‘ÿ -«ransformŽ‘;Ñ«represenš¸ãting–Tªthe“transformation,‘TÌnot“·Ž‘T«ÏthisŽ‘@a«.‘qŽThis“mak˜es“it“pGossible“to“c˜hain“expressions“usingŽ¡ÂopQÇeratorŽ‘+–µ·«=ŽŽŽ‘8]Ô(‘ª¨),‘UUe.g.,Ž¦‘(ÂP•®9oin“tŽ‘Fï¡Ïpt0Ž‘VXÜ«;Ž¡‘(ÂP•®9oin“tŽ‘Fï¡Ïpt1Ž‘VXÜ«(1Ž‘±;‘ª¨«2Ž–ª©±;‘ª¨«3Ž“);Ž¡‘(ÂP•®9oin“tŽ‘Fï¡Ïpt2Ž‘VXÜ«(3Ž‘±;‘ª¨«4Ž–ª©±;‘ª¨«5Ž“);Ž¡‘(ÂT‘ÿ -«ransformŽ‘_ÈÖ±tŽ‘ceH«;Ž¡‘(±tŽ‘+œv:Ïr‘ÿ}'otateŽ‘o>«(90ŽŽ‘ -±;‘ª¨«90ŽŽ– ªª±;‘ª¨«90ŽŽ“);Ž¡‘(Ïpt0Ž‘:0W·«=ŽŽ‘I¾ŽÏpt1Ž‘[îá·«=ŽŽ‘k}Ïpt2Ž‘}­k·«=ŽŽ’;¢±tŽ’Ø«;Ž¦Ïpt0Ž‘i;«,‘UUÏpt1Ž‘¾«,–UUand“Ïpt2Ž‘å«are“all“rotated“90Ÿü^ÿóO!â…cmsy7ºŽ‘î9«around“the“x,“y‘ÿ*ª,“and“z-axes.Ž¦Â150.‘ üScale.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.10.15.«]Ž‘XÁBUG‘FIX:–-If“the“absolute“v‘ÿqÇalue“of“an“argumenš¸ãt“is“±<“ÏepsilonŽ‘"}1«(‘ª®),‘ithe“argumen˜t“is“no˜w“setŽ¡to–§Ç0“instead“of“1.‘iSetting“it“to“1“causes“no“scaling“to“takš¸ãe“place,‘¼cwhic˜h“is“not“the“e ect“of“m˜ultiplying“theŽ¡corresp•Gonding›UUco“ordinate˜b•¸ãy˜a˜n“um“bGer˜of˜v“ery˜small˜magnitude.Ž¡‘ -[¬LDF‘T2003.03.25.«]Ž‘Y;BUG–UUFIX:“Fixed“conditional“that“tests“whether“all“the“argumen¸ãts“are“1.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­124“·i‘Ç«+·ŽŸ ‘ -ÂT‘ÿ -«ransformŽ‘AÈÓÏsc‘ÿ}'aleŽ‘W}Å«(ÂrealŽ‘³.±xŽ‘jJ;‘ª¨ÂrealŽ‘]Ö±yŽ‘ gæ«=‘Ç1Ž–DZ;‘ª¨ÂrealŽ‘]Ö±zŽ‘ < «=‘Ç1Ž“);ŽŽŽŒ‹+Úè Šn ý‘ì·x«151–­3DLDFPRÃŽG’KrESCALE“«43Ž €n ý•@PÂ151.Ž©·h–ª¨«De ne‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­125“·i‘Ç«+·Ž¤ ‘ -ÂT‘ÿ +«ransformŽ‘w S°‘DZsetwŽ‘I¬(7Ž›)–Ç°“±setpr–ÿ}'e“cisionŽ‘6‡ ¬(3Ž˜)“°“±matrixŽ‘!³¬[µiŽ‘qô¬][µjŽ‘°Ä¬]“°“´"® ´"Ž‘ w¬;Ž¡‘°gŽ¡‘±c‘ÿ}'outŽ‘4 R°‘DZend‘‚ØlŽ‘¸Ú¬;Ž¡‘°gŽ¡‘±c‘ÿ}'outŽ‘* Q°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘ +°gŽ©­194.– üAne‘2ctransformations.“¬[²LDF‘T2002.10.16.¬]Ž‘Yú†The–Ç¥functions“for“the“ane“transformations“all“returnŽ¡a‘Tª­T‘ÿ +«ransformŽ‘;Ѭrepresenš¸ãting–Tªthe“transformation,‘TÌnot“°Ž‘T«±thisŽ‘@a¬.‘qŽThis“mak˜es“it“pGossible“to“c˜hain“expressions“usingŽ¡­opQÇeratorŽ‘+–µ°¬=ŽŽŽ‘8]Ô(‘ª¨),‘UUe.g.,Ž¦‘(­P•®9oin“tŽ‘Fpt0Ž‘VXܬ;Ž¡‘(­P•®9oin“tŽ‘Fpt1Ž‘VXܬ(1Ž‘µ;‘ª¨¬2Ž–ª©µ;‘ª¨¬3Ž“);Ž¡‘(­P•®9oin“tŽ‘Fpt2Ž‘VXܬ(3Ž‘µ;‘ª¨¬4Ž–ª©µ;‘ª¨¬5Ž“);Ž¡‘(­T‘ÿ +«ransformŽ‘_ÈÖµtŽ‘ceH¬;Ž¡‘(µtŽ‘+œv:±r‘ÿ}'otateŽ‘o>¬(90ŽŽ‘ +µ;‘ª¨¬90ŽŽ– ªªµ;‘ª¨¬90ŽŽ“);Ž¡‘(±pt0Ž‘:0W°¬=ŽŽ‘I¾Ž±pt1Ž‘[îá°¬=ŽŽ‘k}±pt2Ž‘}­k°¬=ŽŽ’;¢µtŽ’ج;Ž¦±pt0Ž‘i;¬,‘UU±pt1Ž‘¾¬,–UUand“±pt2Ž‘å¬are“all“rotated“90Ÿü^ÿó O!â…cmsy7¶Ž‘î9¬around“the“x,“y‘ÿ*ª,“and“z-axes.Ž¦­195.‘ üScale.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.10.15.¬]Ž‘XÁBUG‘FIX:–-If“the“absolute“v‘ÿqÇalue“of“an“argumenš¸ãt“is“µ<“±epsilonŽ‘"}1¬(‘ª®),‘ithe“argumen˜t“is“no˜w“setŽ¡to–§Ç0“instead“of“1.‘iSetting“it“to“1“causes“no“scaling“to“takš¸ãe“place,‘¼cwhic˜h“is“not“the“e ect“of“m˜ultiplying“theŽ¡corresp•Gonding›UUco“ordinate˜b•¸ãy˜a˜n“um“bGer˜of˜v“ery˜small˜magnitude.Ž¡‘ +[²LDF‘T2003.03.25.¬]Ž‘Y;BUG–UUFIX:“Fixed“conditional“that“tests“whether“all“the“argumen¸ãts“are“1.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­T‘ÿ +«ransformŽ‘;'¬functions‘@¯168“°i‘Ǭ+°ŽŸ ‘ +­T‘ÿ +«ransformŽ‘AÈÓ±sc‘ÿ}'aleŽ‘W}Ŭ(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ gæ¬=‘Ç1Ž–ǵ;‘ª¨­realŽ‘]ÖµzŽ‘ < ¬=‘Ç1Ž“);ŽŽŽŒ‹5É’ Šn ý‘ì°x¬196–¯3DLDF-1.1.5.1’Bþ¯SCALE“¬53Ž €n ý•@P­196.Ž©°h–ª¨¬De ne‘UU­T‘ÿ +«ransformŽ‘;'¬functions‘@¯169“°i‘Ǭ+°Ž¤ ‘ +­T‘ÿ «ransformŽ‘AÈÓT‘ÿ -«ransformŽ‘w«(ÂrealŽ‘³.ÏxyŽ‘!—±;‘ª¨ÂrealŽ‘]ÖÏxzŽ‘"Õ¨±;‘ª¨ÂrealŽ‘]ÖÏyxŽ‘#“„±;‘ª¨ÂrealŽ‘]ÖÏyzŽ‘# ±;‘ª¨ÂrealŽ‘]ÖÏzxŽ‘"ÏA±;‘ª¨ÂrealŽ‘]ÖÏzyŽ‘"´ð«)Ž¡‘ -·fŽ¡‘ÂT‘ÿ -«ransformŽ‘KÈÔ±tŽ‘OeF«;Ž¡‘ÂrealŽ‘*³0ÏepsŽ‘<œ -«=‘ÇÏepsilonŽ‘"6«(‘ª¨);Ž¦‘ÂifŽ‘´ú«(ÏfabsŽ‘2Ò«(ÏxyŽ‘ -ãç«)–DZ<“ÏepsŽ‘èÚ«)‘ÏxyŽ‘ªÿ«=“0Ž‘Ç;Ž¡‘ÂifŽ‘´ú«(ÏfabsŽ‘2Ò«(ÏxzŽ‘ -wÒ«)–DZ<“ÏepsŽ‘èÚ«)‘ÏxzŽ‘>ê«=“0Ž‘Ç;Ž¡‘ÂifŽ‘´ú«(ÏfabsŽ‘2Ò«(ÏyxŽ‘ 5®«)–DZ<“ÏepsŽ‘èÚ«)‘ÏyxŽ‘üÆ«=“0Ž‘Ç;Ž¡‘ÂifŽ‘´ú«(ÏfabsŽ‘2Ò«(ÏyzŽ‘ -¯H«)–DZ<“ÏepsŽ‘èÚ«)‘ÏyzŽ‘v`«=“0Ž‘Ç;Ž¡‘ÂifŽ‘´ú«(ÏfabsŽ‘2Ò«(ÏzxŽ‘ -qk«)–DZ<“ÏepsŽ‘èÚ«)‘ÏzxŽ‘8ƒ«=“0Ž‘Ç;Ž¡‘ÂifŽ‘´ú«(ÏfabsŽ‘2Ò«(ÏzyŽ‘ -W«)–DZ<“ÏepsŽ‘èÚ«)‘ÏzyŽ‘2«=“0Ž‘Ç;Ž¡‘ÂifŽ‘´ú«(ÏxyŽ‘ ªÿ·‘Ç«0Ž– ÿù·^‘8àÏxzŽ‘wÊ·‘Ç«0Ž“·^‘8àÏyxŽ‘5¦·‘Ç«0Ž“·^‘8àÏyzŽ‘¯@·‘Ç«0Ž“·^‘8àÏzxŽ‘qc·‘Ç«0Ž“·^‘8àÏzyŽ‘W·‘Ç«0Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘8Ôð·‘GÝ"WARNING!È ÝInÈ ÝTransfoŽ‘q rm::shear():\n"Ž’È„·Ž¡‘2Ý"AllÈ ÝargumentsÈ ÝareÈ Ý0Ž’šÿÉ.È ÝReturningÈ ÝidentitŽ’ÿyÈ Ýtransformation."Ž’eÌ×·‘ÇÏend‘‚ØlŽ–ò·‘ÇÏend‘‚ØlŽ“·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½±tŽ‘Eƒ/«;Ž¡‘·gŽ¡‘±tŽ‘œt:ÏmatrixŽ‘?›«[1Ž–][0Ž“]–Ç=“ÏxyŽ‘ ªÿ«;Ž¡‘±tŽ‘œt:ÏmatrixŽ‘?›«[2Ž–][0Ž“]–Ç=“ÏxzŽ‘ >ê«;Ž¡‘±tŽ‘œt:ÏmatrixŽ‘?›«[0Ž–][1Ž“]–Ç=“ÏyxŽ‘ üÆ«;Ž¡‘±tŽ‘œt:ÏmatrixŽ‘?›«[2Ž–][1Ž“]–Ç=“ÏyzŽ‘ v`«;Ž¡‘±tŽ‘œt:ÏmatrixŽ‘?›«[0Ž–][2Ž“]–Ç=“ÏzxŽ‘ 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üShift–›with“m®9ultiplication.˜«[¬LDF‘T2002.08.22.«]Ž‘Z®¶Added–{Õthis“function.‘åHIt“takš¸ães“ÂrealŽ‘Uƒ«argumen˜ts“andŽ¡mš¸ãultiplies–UUthe“appropriate“elemen˜ts“of“ÏmatrixŽ‘$êE«b˜y“them.Ž¦·h–ª¨«Declare‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­124“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ -«ransformŽ‘AÈÓÏshift‘‰ffŽ‘®timesŽ‘pµ«(ÂrealŽ‘³.±xŽ‘jJ;‘ª¨ÂrealŽ‘]Ö±yŽ‘ gæ«=‘Ç1Ž–DZ;‘ª¨ÂrealŽ‘]Ö±zŽ‘ < «=‘Ç1Ž“);ŽŸÂ159.Ž¦·h–ª¨«De ne‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­125“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ +«ransformŽ‘w“±epsŽ‘èÚ¬)“?“µxŽ‘ EL¬:“0Ž‘Ç;Ž¡‘µtŽ‘œt:±matrixŽ‘?›¬[3Ž–][1Ž“]–Ç=“(±fabsŽ‘2Ò¬(µyŽ‘Bø¬)“µ>“±epsŽ‘èÚ¬)“?“µyŽ‘ +Ñ(¬:“0Ž‘Ç;Ž¡‘µtŽ‘œt:±matrixŽ‘?›¬[3Ž–][2Ž“]–Ç=“(±fabsŽ‘2Ò¬(µzŽ‘¬)“µ>“±epsŽ‘èÚ¬)“?“µzŽ‘ +¥N¬:“0Ž‘Ç;Ž¡‘µtŽ‘œt:±cle‘ÿ}'anŽ‘A‚¬(‘ª¨);Ž¡‘(°Ž‘±thisŽ‘ë·¬)‘Ç°¬=ŽŽ‘UOµtŽ‘ñÁ¬;Ž¡‘±cle‘ÿ}'anŽ‘+A„¬(‘ª®);Ž¡‘­returnŽ‘7æ¼µtŽ‘;ƒ.¬;Ž¡‘ +°gŽŽŽŒ‹7Ûb Šn ý‘ì°x¬202–¯3DLDF-1.1.5.1’!!­POINT‘ÕX¯ARÃŽGUMENT“¬55Ž €n ý•@P­202.› üP•®9oin“t‘Àargumen“t.˜¬[²LDF‘T2002.04.24.¬]Ž‘\2èAdded–this“function.‘ qÞIt“m¸ãust“bGe“de ned“in“®points.web¬,Ž¤ bšGecause‘UU­P•®9oin“tŽ‘"Dò¬is–UUan“incomplete“t¸ãyp˜e“here.Ž©°h–ª¨¬Declare‘UU­T‘ÿ +«ransformŽ‘;'¬functions‘@¯168“°i‘Ǭ+°Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓ±shiftŽ‘UæP¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié]¬);ŽŸ­203.› üShift–›with“m®9ultiplication.˜¬[²LDF‘T2002.08.22.¬]Ž‘Z®¶Added–{Õthis“function.‘åHIt“takš¸ães“­realŽ‘Uƒ¬argumen˜ts“andŽ¡mš¸ãultiplies–UUthe“appropriate“elemen˜ts“of“±matrixŽ‘$êE¬b˜y“them.Ž¦°h–ª¨¬Declare‘UU­T‘ÿ +«ransformŽ‘;'¬functions‘@¯168“°i‘Ǭ+°Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓ±shift‘‰ffŽ‘®timesŽ‘pµ¬(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ gæ¬=‘Ç1Ž–ǵ;‘ª¨­realŽ‘]ÖµzŽ‘ < ¬=‘Ç1Ž“);ŽŸ­204.Ž¦°h–ª¨¬De ne‘UU­T‘ÿ +«ransformŽ‘;'¬functions‘@¯169“°i‘Ǭ+°Ž¡‘ +­T‘ÿ «ransformŽ‘AÈÓT‘ÿ -«ransformŽ‘wÙí±=«180±:«0ŽŽ‘Ç!;‘±=·‘ÿý«Con•¸ãv“ert–UUto“radians.‘o·±=Ž¦‘ÏssinŽ‘(ì/«=‘ÇÏsinŽ‘Õm«(±xŽ‘·«);Ž¦‘Ïc–ÿ}'c“osŽ‘)|Á«=‘ÇÏc‘ÿ}'osŽ‘f«(±xŽ‘·«);Ž¦‘ÂforŽ‘%舫(±iŽ‘9 «=‘Ç0Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«4Ž“;‘ÿý±iŽ‘ññŸÿ®+‘ÿ+ŽŽ‘¹«)‘·fŽ¦‘Ïtemp1Ž‘<÷m«=‘Ç(Ït‘‰ffŽ‘®xŽ› [9±:ÏmatrixŽ‘?›«[±iŽ‘qô«][1Ž‘]–8à·“Ïc–ÿ}'c“osŽ‘)“·“«(Ït‘‰ffŽ‘®xŽ˜±:ÏmatrixŽ‘?›«[±iŽ‘qô«][2Ž‘]“·“ÏssinŽ‘]õ«);Ž¦‘Ïtemp2Ž‘<÷m«=‘Ç(Ït‘‰ffŽ‘®xŽ› [9±:ÏmatrixŽ‘?›«[±iŽ‘qô«][1Ž‘]–8à·“ÏssinŽ‘]õ«)“+“(Ït‘‰ffŽ‘®xŽ˜±:ÏmatrixŽ‘?›«[±iŽ‘qô«][2Ž‘]“·“Ïc–ÿ}'c“osŽ‘);Ž¦‘Ït‘‰ffŽ‘®xŽ‘+[<±:ÏmatrixŽ‘?›«[±iŽ‘qô«][2Ž‘]–Ç=“(ÏfabsŽ‘2Ò«(Ïtemp2Ž‘0R«)“·“ÏepsŽ‘èÚ«)“?“Ïtemp2Ž‘!¾‚«:“0Ž‘Ç;Ž¦‘Ït‘‰ffŽ‘®xŽ‘+[<±:ÏmatrixŽ‘?›«[±iŽ‘qô«][1Ž‘]–Ç=“(ÏfabsŽ‘2Ò«(Ïtemp1Ž‘0R«)“·“ÏepsŽ‘èÚ«)“?“Ïtemp1Ž‘!¾‚«:“0Ž‘Ç;Ž¦‘·gŽ¦‘ -g‘±=·‘ÿýÂifŽ‘_·±=ŽŸÂ163.‘ ü«Rotation–UUaround“the“y-axis.Ž¡·h–ª¨«De ne‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­125“·i‘Ç«+·Ž¦‘ -ÂifŽ‘´ù«(±yŽ‘ -·6«=‘Ç0Ž‘Ç)‘·f‘±=·‘ÿý«!!‘qÇRevš¸ãersed–UUdirection“of“rotation“bGecause“I“didn't“lik˜e“the“w˜a˜y“it“w˜as.‘o·±=Ž¦‘yŽ‘ -·«=ŽŽ‘+˜I·Ž‘3_gÝPIŽ‘>eɱ=«180±:«0ŽŽ‘Ç!;Ž¦‘ÏssinŽ‘(ì/«=‘ÇÏsinŽ‘Õm«(±yŽ‘Bø«);Ž¦‘Ïc–ÿ}'c“osŽ‘)|Á«=‘ÇÏc‘ÿ}'osŽ‘f«(±yŽ‘Bø«);Ž¦‘ÂforŽ‘%舫(±iŽ‘9 «=‘Ç0Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«4Ž“;‘ÿý±iŽ‘ññŸÿ®+‘ÿ+ŽŽ‘¹«)‘·fŽ¦‘Ïtemp1Ž‘<÷m«=‘Ç(Ït‘‰ffŽ‘®yŽ› @è±:ÏmatrixŽ‘?›«[±iŽ‘qô«][0Ž‘]–8à·“Ïc–ÿ}'c“osŽ‘)“+“(Ït‘‰ffŽ‘®yŽ˜±:ÏmatrixŽ‘?›«[±iŽ‘qô«][2Ž‘]“·“ÏssinŽ‘]õ«);Ž¦‘Ïtemp2Ž‘<÷m«=‘Ç(·Ž‘ÇÏt‘‰ffŽ‘®yŽ‘±:ÏmatrixŽ›?›«[±iŽ‘qô«][0Ž‘]–8à·“ÏssinŽ‘]õ«)“+“(Ït‘‰ffŽ‘®yŽ‘ @è±:ÏmatrixŽ˜«[±iŽ‘qô«][2Ž‘]“·“Ïc–ÿ}'c“osŽ‘);Ž¦‘Ït‘‰ffŽ‘®yŽ‘+@ë±:ÏmatrixŽ‘?›«[±iŽ‘qô«][2Ž‘]–Ç=“(ÏfabsŽ‘2Ò«(Ïtemp2Ž‘0R«)“·“ÏepsŽ‘èÚ«)“?“Ïtemp2Ž‘!¾‚«:“0Ž‘Ç;Ž¦‘Ït‘‰ffŽ‘®yŽ‘+@ë±:ÏmatrixŽ‘?›«[±iŽ‘qô«][0Ž‘]–Ç=“(ÏfabsŽ‘2Ò«(Ïtemp1Ž‘0R«)“·“ÏepsŽ‘èÚ«)“?“Ïtemp1Ž‘!¾‚«:“0Ž‘Ç;Ž¦‘·gŽ¦‘ -g‘±=·‘ÿýÂifŽ‘_·±=ŽŽŽŒ‹// Šn ý‘ì·x«164›­3DLDFPR•ÃŽG’Ç7wR“OT–ÿJªA“TION–ÕXARÃŽOUND“THE“MAIN“AXES˜«47Ž €n ý•@PÂ164.‘ ü«Rotation–UUaround“the“z-axis.Ž©·h–ª¨«De ne‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­125“·i‘Ç«+·Ž¤ ‘ -ÂifŽ‘´ù«(±zŽ‘Þ6·6«=‘Ç0Ž‘Ç)‘·fŽ¡‘±zŽ‘Þ8·«=ŽŽ‘+loÝPIŽ‘6rѱ=«180±:«0ŽŽ‘Ç!;Ž¡‘ÏssinŽ‘(ì/«=‘ÇÏsinŽ‘Õm«(±zŽ‘«);Ž¡‘Ïc–ÿ}'c“osŽ‘)|Á«=‘ÇÏc‘ÿ}'osŽ‘f«(±zŽ‘«);Ž¡‘ÂforŽ‘%舫(Âin®9tŽ‘¤÷±iŽ‘Þ«=‘Ç0Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«4Ž“;‘ÿý±iŽ‘ññŸÿ®+‘ÿ+ŽŽ‘¹«)‘·fŽ¡‘Ïtemp1Ž‘<÷m«=‘Ç(Ït‘‰ffŽ‘®zŽ› ÔÓ±:ÏmatrixŽ‘?›«[±iŽ‘qô«][0Ž‘]–8à·“Ïc–ÿ}'c“osŽ‘)“·“«(Ït‘‰ffŽ‘®zŽ˜±:ÏmatrixŽ‘?›«[±iŽ‘qô«][1Ž‘]“·“ÏssinŽ‘]õ«);Ž¡‘Ïtemp2Ž‘<÷m«=‘Ç(Ït‘‰ffŽ‘®zŽ› ÔÓ±:ÏmatrixŽ‘?›«[±iŽ‘qô«][0Ž‘]–8à·“ÏssinŽ‘]õ«)“+“(Ït‘‰ffŽ‘®zŽ˜±:ÏmatrixŽ‘?›«[±iŽ‘qô«][1Ž‘]“·“Ïc–ÿ}'c“osŽ‘);Ž¡‘Ït‘‰ffŽ‘®zŽ‘*ÔÖ±:ÏmatrixŽ‘?›«[±iŽ‘qô«][1Ž‘]–Ç=“(ÏfabsŽ‘2Ò«(Ïtemp2Ž‘0R«)“·“ÏepsŽ‘èÚ«)“?“Ïtemp2Ž‘!¾‚«:“0Ž‘Ç;Ž¡‘Ït‘‰ffŽ‘®zŽ‘*ÔÖ±:ÏmatrixŽ‘?›«[±iŽ‘qô«][0Ž‘]–Ç=“(ÏfabsŽ‘2Ò«(Ïtemp1Ž‘0R«)“·“ÏepsŽ‘èÚ«)“?“Ïtemp1Ž‘!¾‚«:“0Ž‘Ç;Ž¡‘·gŽ¡‘ -g‘±=·‘ÿýÂifŽ‘_·±=Ž¡‘ -Ït‘‰ffŽ‘®al‘‚ØlŽ‘ ·«=ŽŽ‘/œùÏt‘‰ffŽ‘®xŽ‘<ø2«;Ž¡‘ -Ït‘‰ffŽ‘®al‘‚ØlŽ‘ ·«=ŽŽ‘/œùÏt‘‰ffŽ‘®yŽ‘<Ýá«;Ž¡‘ -Ït‘‰ffŽ‘®al‘‚ØlŽ‘ ·«=ŽŽ‘/œùÏt‘‰ffŽ‘®zŽ‘Ùíµ=¬180µ:¬0ŽŽ‘Ç!;‘µ=°‘ÿý¬Con•¸ãv“ert–UUto“radians.‘o°µ=Ž¦‘±ssinŽ‘(ì/¬=‘DZsinŽ‘Õm¬(µxŽ‘·¬);Ž¦‘±c–ÿ}'c“osŽ‘)|Á¬=‘DZc‘ÿ}'osŽ‘f¬(µxŽ‘·¬);Ž¦‘­forŽ‘%般(µiŽ‘9 ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ4Ž“;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)‘°fŽ¦‘±temp1Ž‘<÷m¬=‘Ç(±t‘‰ffŽ‘®xŽ› [9µ:±matrixŽ‘?›¬[µiŽ‘qô¬][1Ž‘]–8à°“±c–ÿ}'c“osŽ‘)“°“¬(±t‘‰ffŽ‘®xŽ˜µ:±matrixŽ‘?›¬[µiŽ‘qô¬][2Ž‘]“°“±ssinŽ‘]õ¬);Ž¦‘±temp2Ž‘<÷m¬=‘Ç(±t‘‰ffŽ‘®xŽ› [9µ:±matrixŽ‘?›¬[µiŽ‘qô¬][1Ž‘]–8à°“±ssinŽ‘]õ¬)“+“(±t‘‰ffŽ‘®xŽ˜µ:±matrixŽ‘?›¬[µiŽ‘qô¬][2Ž‘]“°“±c–ÿ}'c“osŽ‘);Ž¦‘±t‘‰ffŽ‘®xŽ‘+[<µ:±matrixŽ‘?›¬[µiŽ‘qô¬][2Ž‘]–Ç=“(±fabsŽ‘2Ò¬(±temp2Ž‘0R¬)“°“±epsŽ‘èÚ¬)“?“±temp2Ž‘!¾‚¬:“0Ž‘Ç;Ž¦‘±t‘‰ffŽ‘®xŽ‘+[<µ:±matrixŽ‘?›¬[µiŽ‘qô¬][1Ž‘]–Ç=“(±fabsŽ‘2Ò¬(±temp1Ž‘0R¬)“°“±epsŽ‘èÚ¬)“?“±temp1Ž‘!¾‚¬:“0Ž‘Ç;Ž¦‘°gŽ¦‘ +g‘µ=°‘ÿý­ifŽ‘_°µ=ŽŸ­208.‘ ü¬Rotation–UUaround“the“y-axis.Ž¡°h–ª¨¬De ne‘UU­T‘ÿ +«ransformŽ‘;'¬functions‘@¯169“°i‘Ǭ+°Ž¦‘ +­ifŽ‘´ù¬(µyŽ‘ +°6¬=‘Ç0Ž‘Ç)‘°f‘µ=°‘ÿý¬!!‘qÇRevš¸ãersed–UUdirection“of“rotation“bGecause“I“didn't“lik˜e“the“w˜a˜y“it“w˜as.‘o°µ=Ž¦‘yŽ‘ +°¬=ŽŽ‘+˜I°Ž‘3_g´PIŽ‘>eɵ=¬180µ:¬0ŽŽ‘Ç!;Ž¦‘±ssinŽ‘(ì/¬=‘DZsinŽ‘Õm¬(µyŽ‘Bø¬);Ž¦‘±c–ÿ}'c“osŽ‘)|Á¬=‘DZc‘ÿ}'osŽ‘f¬(µyŽ‘Bø¬);Ž¦‘­forŽ‘%般(µiŽ‘9 ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ4Ž“;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)‘°fŽ¦‘±temp1Ž‘<÷m¬=‘Ç(±t‘‰ffŽ‘®yŽ› @èµ:±matrixŽ‘?›¬[µiŽ‘qô¬][0Ž‘]–8à°“±c–ÿ}'c“osŽ‘)“+“(±t‘‰ffŽ‘®yŽ˜µ:±matrixŽ‘?›¬[µiŽ‘qô¬][2Ž‘]“°“±ssinŽ‘]õ¬);Ž¦‘±temp2Ž‘<÷m¬=‘Ç(°Ž‘DZt‘‰ffŽ‘®yŽ‘µ:±matrixŽ›?›¬[µiŽ‘qô¬][0Ž‘]–8à°“±ssinŽ‘]õ¬)“+“(±t‘‰ffŽ‘®yŽ‘ @èµ:±matrixŽ˜¬[µiŽ‘qô¬][2Ž‘]“°“±c–ÿ}'c“osŽ‘);Ž¦‘±t‘‰ffŽ‘®yŽ‘+@ëµ:±matrixŽ‘?›¬[µiŽ‘qô¬][2Ž‘]–Ç=“(±fabsŽ‘2Ò¬(±temp2Ž‘0R¬)“°“±epsŽ‘èÚ¬)“?“±temp2Ž‘!¾‚¬:“0Ž‘Ç;Ž¦‘±t‘‰ffŽ‘®yŽ‘+@ëµ:±matrixŽ‘?›¬[µiŽ‘qô¬][0Ž‘]–Ç=“(±fabsŽ‘2Ò¬(±temp1Ž‘0R¬)“°“±epsŽ‘èÚ¬)“?“±temp1Ž‘!¾‚¬:“0Ž‘Ç;Ž¦‘°gŽ¦‘ +g‘µ=°‘ÿý­ifŽ‘_°µ=ŽŽŽŒ‹9ðå Šn ý‘ì°x¬209‘¯3DLDF-1.1.5.1’¾ÃáRšÃŽOT–ÿJªA“TION–ÕXAR˜OUND“THE“MAIN“AXES‘¬57Ž €n ý•@P­209.‘ ü¬Rotation–UUaround“the“z-axis.Ž©°h–ª¨¬De ne‘UU­T‘ÿ +«ransformŽ‘;'¬functions‘@¯169“°i‘Ǭ+°Ž¤ ‘ +­ifŽ‘´ù¬(µzŽ‘Þ6°6¬=‘Ç0Ž‘Ç)‘°fŽ¡‘µzŽ‘Þ8°¬=ŽŽ‘+lo´PIŽ‘6rѵ=¬180µ:¬0ŽŽ‘Ç!;Ž¡‘±ssinŽ‘(ì/¬=‘DZsinŽ‘Õm¬(µzŽ‘¬);Ž¡‘±c–ÿ}'c“osŽ‘)|Á¬=‘DZc‘ÿ}'osŽ‘f¬(µzŽ‘¬);Ž¡‘­forŽ‘%般(­in®9tŽ‘¤÷µiŽ‘Þ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ4Ž“;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)‘°fŽ¡‘±temp1Ž‘<÷m¬=‘Ç(±t‘‰ffŽ‘®zŽ› ÔÓµ:±matrixŽ‘?›¬[µiŽ‘qô¬][0Ž‘]–8à°“±c–ÿ}'c“osŽ‘)“°“¬(±t‘‰ffŽ‘®zŽ˜µ:±matrixŽ‘?›¬[µiŽ‘qô¬][1Ž‘]“°“±ssinŽ‘]õ¬);Ž¡‘±temp2Ž‘<÷m¬=‘Ç(±t‘‰ffŽ‘®zŽ› ÔÓµ:±matrixŽ‘?›¬[µiŽ‘qô¬][0Ž‘]–8à°“±ssinŽ‘]õ¬)“+“(±t‘‰ffŽ‘®zŽ˜µ:±matrixŽ‘?›¬[µiŽ‘qô¬][1Ž‘]“°“±c–ÿ}'c“osŽ‘);Ž¡‘±t‘‰ffŽ‘®zŽ‘*ÔÖµ:±matrixŽ‘?›¬[µiŽ‘qô¬][1Ž‘]–Ç=“(±fabsŽ‘2Ò¬(±temp2Ž‘0R¬)“°“±epsŽ‘èÚ¬)“?“±temp2Ž‘!¾‚¬:“0Ž‘Ç;Ž¡‘±t‘‰ffŽ‘®zŽ‘*ÔÖµ:±matrixŽ‘?›¬[µiŽ‘qô¬][0Ž‘]–Ç=“(±fabsŽ‘2Ò¬(±temp1Ž‘0R¬)“°“±epsŽ‘èÚ¬)“?“±temp1Ž‘!¾‚¬:“0Ž‘Ç;Ž¡‘°gŽ¡‘ +g‘µ=°‘ÿý­ifŽ‘_°µ=Ž¡‘ +±t‘‰ffŽ‘®al‘‚ØlŽ‘ °¬=ŽŽ‘/œù±t‘‰ffŽ‘®xŽ‘<ø2¬;Ž¡‘ +±t‘‰ffŽ‘®al‘‚ØlŽ‘ °¬=ŽŽ‘/œù±t‘‰ffŽ‘®yŽ‘<Ýá¬;Ž¡‘ +±t‘‰ffŽ‘®al‘‚ØlŽ‘ °¬=ŽŽ‘/œù±t‘‰ffŽ‘®zŽ‘‰ffŠ=Ÿ š‘ƒŽŸü^ÿ®1ŽŽ‘ -«StoGer,‘N¸Josef.›oÏNumerische–ŒLMathematik“1«.˜Ac•¸ãh“te,‘N¸neu›Mb•Gearb“eitete˜und˜erw¸ãeiterte˜Au age.‘oSpringer-V‘ÿ*ªerlag.Ž¡Berlin–UU1999.‘qÇISBN“3-540-66154-9,“page“205.ŽŽŽŒ‹36ã Šn ý‘ì·x«182›­3DLDFPRÃŽG’Â3¾ÂCONST–ÕX­VERSION“(NO“ASSIGNMENT)˜«51Ž €n ý•@PÂ182.Ž¤·h–ª¨«De ne‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­125“·i‘Ç«+·Ž© ‘ -ÂT‘ÿ +«ransformŽ‘w‰ffŠ=Ÿ š‘ƒŽŸü^ÿ³1ŽŽ‘ +¬StoGer,‘N¸Josef.›o±Numerische–ŒLMathematik“1¬.˜Ac•¸ãh“te,‘N¸neu›Mb•Gearb“eitete˜und˜erw¸ãeiterte˜Au age.‘oSpringer-V‘ÿ*ªerlag.Ž¡Berlin–UU1999.‘qÇISBN“3-540-66154-9,“page“205.ŽŽŽŒ‹=%ª Šn ý‘ì°x¬227›¯3DLDF-1.1.5.1’¹À(­CONST–ÕX¯VERSION“(NO“ASSIGNMENT)˜¬61Ž €n ý•@P­227.Ž¤°h–ª¨¬De ne‘UU­T‘ÿ +«ransformŽ‘;'¬functions‘@¯169“°i‘Ǭ+°Ž© ‘ +­T‘ÿ «ransformŽ‘AÈÓT‘ÿ -«ransformŽ‘w S·‘ÇÝ"matrixÈ Ý=\n"Ž‘BM\«;Ž¦‘·gŽ¦‘ÂforŽ‘/艫(±iŽ‘9 «=‘Ç0Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«4Ž“;‘ÿý±iŽ‘ññŸÿ®+‘ÿ+ŽŽ‘¹«)‘·fŽ¦‘(ÂforŽ‘9芫(±jŽ‘wÜ«=‘Ç0Ž–Ç;‘ÿý±jŽ‘ wÙ<‘Ç«4Ž“;‘ÿý±jŽ‘ -0ÁŸÿ®+‘ÿ+ŽŽ‘÷á«)‘·fŽ¦‘2±tŽ‘5œw:ÏmatrixŽ‘?›«[±iŽ›qô«][±jŽ‘°Ä«]–Ç=“ÏmatrixŽ‘!³«[±iŽ˜«][±jŽ‘°Ä«];Ž¦‘2ÂifŽ‘=´ý«(ÝDEBUGŽ‘ÆY«)‘·fŽ¦‘<Ïc‘ÿ}'outŽ‘R U·‘ÇÏmatrixŽ‘!³«[±iŽ‘qô«][±jŽ‘°Ä«]–Ç·“Ý"È Ý"Ž‘ w«;Ž¦‘2·gŽ¦‘(gŽ¦‘(ÂifŽ‘3´ü«(ÝDEBUGŽ‘ÆY«)‘·fŽ¦‘2Ïc‘ÿ}'outŽ‘H T·‘ÇÝ"\n"Ž‘Mt«;Ž¦‘(·gŽ¦‘gŽ¦‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘·fŽ¦‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÝ"\n"Ž‘Mt«;Ž¦‘(±tŽ‘+œv:ÏshowŽ‘Šÿ«(Ý"t"Ž‘F_«);Ž¦‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÝ"EnterÈ ÝÈ ÝtoÈ ÝcŽ‘kÆÜontinue.\n\n"Ž’³T5·‘ÇÏ ushŽ‘€«;Ž¦‘(ÏgetcharŽ‘I&«(‘ª®);Ž¦‘·gŽ¡‘Âin®9tŽ‘/¤ú±pŽ‘4¬ú«[±nŽ‘š«];Ž¡‘ÂforŽ‘/艫(Âin®9tŽ‘¤÷±jŽ‘Ó«=‘Ç0Ž‘Ç;‘ÿý±jŽ‘ wÙ<‘ÇnŽ‘Dz«;‘ÿý±jŽ‘ -0ÁŸÿ®+‘ÿ+ŽŽ‘÷á«)‘±pŽ‘ -«[±jŽ‘°Ä«]–Ç=“±jŽ‘wÜ«;Ž¦‘ÂforŽ‘/艫(±jŽ‘wÜ«=‘Ç0Ž‘Ç;‘ÿý±jŽ‘ wÙ<‘ÇnŽ‘Dz«;‘ÿý±jŽ‘ -0ÁŸÿ®+‘ÿ+ŽŽ‘÷á«)‘UU·fŽŽŽŒ‹4? Šn ý‘ì«52›ÂCONST–ÕX­VERSION“(NO“ASSIGNMENT)’Â3¾3DLDFPRÃŽG˜·x«183Ž €n ý•@PÂ183.‘ ü«Piv•¸ãot‘UUsearc“h.Ž©·h–ª¨«De ne‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­125“·i‘Ç«+·Ž¤ ‘ -ÏmaxŽ‘ k´«=‘ÇÏfabsŽ‘ùê«(±tŽ‘œr:ÏmatrixŽ‘?›«[±jŽ–°Ä«][±jŽ“«]);Ž¡‘ -Ïr‘ÿ}'owŽ‘Ó„«=‘DZjŽ‘wÜ«;Ž¡‘ -ÂforŽ‘臫(±iŽ‘9 «=‘DZjŽ‘ °¼«+‘8à1Ž‘8á;‘ÿý±iŽ‘ 9 <‘ÇnŽ‘Dz«;‘ÿý±iŽ‘ññŸÿ®+‘ÿ+ŽŽ‘¹«)‘·fŽ¡‘ÂifŽ‘´ú«(ÏfabsŽ‘2Ò«(±tŽ‘œr:ÏmatrixŽ‘?›«[±iŽ‘qô«][±jŽ‘°Ä«])–DZ>“ÏmaxŽ‘k³«)‘·fŽ¡‘ÏmaxŽ‘4k¶«=‘ÇÏfabsŽ‘ùê«(±tŽ‘œr:ÏmatrixŽ‘?›«[±iŽ‘qô«][±jŽ‘°Ä«]);Ž¡‘Ïr‘ÿ}'owŽ‘1Ó†«=‘DZiŽ‘9 «;Ž¡‘·g‘±=·‘ÿýÂifŽ‘_·±=Ž¡‘ -·g‘±=·‘ÿý«inner‘UUÂforŽ‘胷±=Ž¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"maxÈ Ý==È Ý"Ž‘5T}·‘ÇÏmaxŽ‘2Ë·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"rowÈ Ý==È Ý"Ž‘5T}·‘ÇÏr‘ÿ}'owŽ‘š›·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ -·gŽ¡‘ -ÂifŽ‘´ù«(ÏmaxŽ‘k³·‘Ç«0Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘/“·‘`ëÝ"ERROR!È ÝInÈ ÝTransformŽ‘q`¯::inverse():\n"Ž’ÉÕ·Ž¡‘(Ý"MatrixÈ ÝisÈ Ýsingular.Ž’ÿÈÈ ÝReturningÈ ÝINVALID_Ž’ùÿŒTRANSFORM.\n"Ž’AŒå·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘7æ¼ÝINVALID_TRANSFORMŽ’‘¬ñ«;Ž¡‘ -·gŽŸÂ184.‘ ü«Ro•¸ãw‘UUexc“hange.Ž¦·h–ª¨«De ne‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­125“·i‘Ç«+·Ž¡‘ -ÂifŽ‘´ù«(Ïr‘ÿ}'owŽ‘Óƒ±>‘ÇjŽ‘wÜ«)‘·fŽ¡‘ÂforŽ‘%舫(±kŽ‘Ln«=‘Ç0Ž‘Ç;‘ÿý±kŽ‘ Lk<‘ÇnŽ‘Dz«;‘ÿý±kŽ‘ SŸÿ®+‘ÿ+ŽŽ‘Ìs«)‘·fŽ¡‘ÏhrŽ‘+±g«=‘DZtŽ‘cŠ:ÏmatrixŽ‘?›«[±jŽ‘°Ä«][±kŽ‘…V«];Ž¡‘±tŽ‘!œu:ÏmatrixŽ›?›«[±jŽ‘°Ä«][±kŽ‘…V«]–Ç=“±tŽ‘cŠ:ÏmatrixŽ˜«[Ïr‘ÿ}'owŽ‘ k«][±kŽ‘…V«];Ž¡‘±tŽ‘!œu:ÏmatrixŽ‘?›«[Ïr‘ÿ}'owŽ‘ k«][±kŽ‘…V«]–Ç=“ÏhrŽ‘ ±d«;Ž¡‘·g‘±=·‘ÿýÂforŽ‘“+·±=Ž¡‘ÏhiŽ‘ |N«=‘DZpŽ‘Ï«[±jŽ‘°Ä«];Ž¡‘±pŽ‘«[±jŽ‘°Ä«]–Ç=“±pŽ‘Ï«[Ïr‘ÿ}'owŽ‘ k«];Ž¡‘±pŽ‘«[Ïr‘ÿ}'owŽ‘ k«]–Ç=“ÏhiŽ‘ |L«;Ž¡‘ -·g‘±=·‘ÿýÂifŽ‘_·±=Ž¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"FinishedÈ ÝrowÈ ÝexchanŽ‘kÆÜge.\n"Ž’Ž”J·‘ÇÏ ushŽ‘€«;ŽŸÂ185.‘ ü«T‘ÿ*ªransformation.Ž¦·h–ª¨«De ne‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­125“·i‘Ç«+·Ž¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"t.matrix["Ž‘?Ôw·‘DZjŽ– ->ô·‘ÇÝ"]["Ž‘Œ·‘DZjŽ“·‘ÇÝ"]È Ý==È Ý"Ž‘*Ôƒ·‘DZtŽ‘cŠ:ÏmatrixŽ‘?›«[±jŽ–°Ä«][±jŽ“«]–Ç·“Ïend‘‚ØlŽ‘ò·“Ï ushŽ‘€«;Ž¡‘ -ÏhrŽ‘±e«=‘Ç1Ž‘DZ=tŽ‘œr:ÏmatrixŽ‘?›«[±jŽ–°Ä«][±jŽ“«];Ž¡‘ -ÂforŽ‘臫(±iŽ‘9 «=‘Ç0Ž‘Ç;‘ÿý±iŽ‘ 9 <‘ÇnŽ‘Dz«;‘ÿý±iŽ‘ññŸÿ®+‘ÿ+ŽŽ‘¹«)‘±tŽ‘œr:ÏmatrixŽ›?›«[±iŽ‘qô«][±jŽ‘°Ä«]–Ç=“ÏhrŽ‘êD·‘8à±tŽ‘ÕR:ÏmatrixŽ˜«[±iŽ‘qô«][±jŽ‘°Ä«];Ž¡‘ -±tŽ‘ œs:ÏmatrixŽ‘?›«[±jŽ–°Ä«][±jŽ“«]–Ç=“ÏhrŽ‘ ±d«;Ž¡‘ -ÂforŽ‘臫(±kŽ‘Ln«=‘Ç0Ž‘Ç;‘ÿý±kŽ‘ Lk<‘ÇnŽ‘Dz«;‘ÿý±kŽ‘ SŸÿ®+‘ÿ+ŽŽ‘Ìs«)Ž¡‘ÂifŽ‘´ú«(±kŽ‘Ln·6«=‘DZjŽ‘wÜ«)‘·fŽ¡‘ÂforŽ‘/艫(±iŽ‘9 «=‘Ç0Ž‘Ç;‘ÿý±iŽ‘ 9 <‘ÇnŽ‘Dz«;‘ÿý±iŽ‘ññŸÿ®+‘ÿ+ŽŽ‘¹«)Ž¡‘(ÂifŽ‘3´ü«(±iŽ‘9 ·6«=‘DZjŽ‘wÜ«)‘±tŽ‘œr:ÏmatrixŽ–?›«[±iŽ›qô«][±kŽ‘…V«]‘Ç·«=ŽŽ‘l±tŽ‘¸Þ:ÏmatrixŽ“«[±iŽ˜«][±jŽ›°Ä«]–8à·“±tŽ‘ÕR:ÏmatrixŽ‘?›«[±jŽ˜«][±kŽ‘…V«];Ž¡‘±tŽ‘!œu:ÏmatrixŽ‘?›«[±jŽ‘°Ä«][±kŽ‘…V«]‘Ç·«=ŽŽ‘UO·Ž‘mÏhrŽ‘%¹«;Ž¡‘·gŽ¡‘ -g‘±=·‘ÿý«outer‘UUÂforŽ‘胷±=Ž¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"FinishedÈ ÝTransformaŽ‘kÆÜtion.\n"Ž’™D·‘ÇÏ ushŽ‘€«;ŽŽŽŒ‹5Gƒ Šn ý‘ì·x«186›­3DLDFPRÃŽG’Â3¾ÂCONST–ÕX­VERSION“(NO“ASSIGNMENT)˜«53Ž €n ý•@PÂ186.‘ ü«Column‘UUexc¸ãhange.Ž©·h–ª¨«De ne‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­125“·i‘Ç«+·Ž¤ ‘ -ÂforŽ‘臫(±iŽ‘9 «=‘Ç0Ž‘Ç;‘ÿý±iŽ‘ 9 <‘ÇnŽ‘Dz«;‘ÿý±iŽ‘ññŸÿ®+‘ÿ+ŽŽ‘¹«)‘·fŽ¡‘ÂforŽ‘%舫(±kŽ‘Ln«=‘Ç0Ž‘Ç;‘ÿý±kŽ‘ Lk<‘ÇnŽ‘Dz«;‘ÿý±kŽ‘ SŸÿ®+‘ÿ+ŽŽ‘Ìs«)‘ÏhvŽ‘Ln«[±pŽ‘«[±kŽ›…V«]]–Ç=“±tŽ‘cŠ:ÏmatrixŽ‘?›«[±iŽ‘qô«][±kŽ˜«];Ž¡‘ÂforŽ‘%舫(±kŽ‘Ln«=‘Ç0Ž‘Ç;‘ÿý±kŽ‘ Lk<‘ÇnŽ‘Dz«;‘ÿý±kŽ‘ SŸÿ®+‘ÿ+ŽŽ‘Ìs«)‘±tŽ‘œr:ÏmatrixŽ‘?›«[±iŽ‘qô«][±kŽ›…V«]–Ç=“ÏhvŽ‘†«[±kŽ˜«];Ž¡‘ -·g‘±=·‘ÿýÂforŽ‘“+·±=Ž¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"FinishedÈ ÝcolumnÈ ÝexcŽ‘kÆÜhange.\n"Ž’žTA·‘ÇÏ ushŽ‘€«;Ž¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"ExitingÈ ÝTransform::Ž‘kÆÜinverse()."Ž’¨Ô;·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ -·gŽ¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ExitingÈ ÝTransform::Ž‘kÆÜinverse()."Ž’¨Ô;·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ -ÂreturnŽ‘-æ»±tŽ‘1ƒ-«;‘qÇ·gŽŸÂ187.‘ üNon-const– -°vš®9ersion“(with“assignmen˜t).‘ ü«[¬LDF‘T2002.10.20.«]Ž‘[•8Added–bWthis“function.‘˜ÍI‘bthough¸ãt“ofŽ¡calling–÷ain“\ÏinvertŽ‘ã(«(‘ª®)",›ãbut“I‘÷7decided“against“it,˜bGecause“I‘÷7thoughš¸ãt“ha˜ving“t˜w˜o“functions“called“\ÏinverseŽ‘ ‡«(‘ª®)"Ž¡and–UU\ÏinvertŽ‘ã(«(‘ª®)"“w¸ãould“bGe“confusing.Ž¡‘ -There–œfis“no“pGoinš¸ãt“in“calling“this“function“with“ÏassignŽ‘"µ ·‘=ŠÏfalseŽ‘ìΫ,‘®+since“it“is“equiv‘ÿqÇalen˜t“to“the“ÂconstŽ‘"«v˜ersionŽ¡abGo•¸ãv“e–Ëãwith“no“argumenš¸ãt.‘C÷If“it“is“called“with“ÏassignŽ‘!n·‘ÇÏfalseŽ‘v\«,‘ç`a“w˜arning“is“issued,‘ç`the“ÂconstŽ‘ m«v˜ersion“is“in˜v˜ok˜ed,Ž¡and–UUits“return“v‘ÿqÇalue“is“returned.Ž¦·h–ª¨«Declare‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­124“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ -«ransformŽ‘AÈÓÏinverseŽ‘a×Z«(Âb•QÇo“olŽ‘¡fÏassignŽ‘5|‚«);ŽŸÂ188.Ž¦·h–ª¨«De ne‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­125“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ +«ransformŽ‘w S°‘Ç´"matrix® ´=\n"Ž‘BM\¬;Ž¦‘°gŽ¦‘­forŽ‘/艬(µiŽ‘9 ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ4Ž“;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)‘°fŽ¦‘(­forŽ‘9芬(µjŽ‘wܬ=‘Ç0Ž–Ç;‘ÿýµjŽ‘ wÙ<‘Ǭ4Ž“;‘ÿýµjŽ‘ +0ÁŸÿ³+‘ÿ+ŽŽ‘÷á¬)‘°fŽ¦‘2µtŽ‘5œw:±matrixŽ‘?›¬[µiŽ›qô¬][µjŽ‘°Ä¬]–Ç=“±matrixŽ‘!³¬[µiŽ˜¬][µjŽ‘°Ä¬];Ž¦‘2­ifŽ‘=´ý¬(´DEBUGŽ‘ÆY¬)‘°fŽ¦‘<±c‘ÿ}'outŽ‘R U°‘DZmatrixŽ‘!³¬[µiŽ‘qô¬][µjŽ‘°Ä¬]–Ç°“´"® ´"Ž‘ w¬;Ž¦‘2°gŽ¦‘(gŽ¦‘(­ifŽ‘3´ü¬(´DEBUGŽ‘ÆY¬)‘°fŽ¦‘2±c‘ÿ}'outŽ‘H T°‘Ç´"\n"Ž‘Mt¬;Ž¦‘(°gŽ¦‘gŽ¦‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘°fŽ¦‘(±c‘ÿ}'outŽ‘> S°‘Ç´"\n"Ž‘Mt¬;Ž¦‘(µtŽ‘+œv:±showŽ‘Šÿ¬(´"t"Ž‘F_¬);Ž¦‘(±c‘ÿ}'outŽ‘> S°‘Ç´"Enter® ´® ´to® ´cŽ‘kÆÜontinue.\n\n"Ž’³T5°‘DZ ushŽ‘€¬;Ž¦‘(±getcharŽ‘I&¬(‘ª®);Ž¦‘°gŽ¡‘­in®9tŽ‘/¤úµpŽ‘4¬ú¬[µnŽ‘š¬];Ž¡‘­forŽ‘/艬(­in®9tŽ‘¤÷µjŽ‘Ó¬=‘Ç0Ž‘Ç;‘ÿýµjŽ‘ wÙ<‘ÇnŽ‘Dz¬;‘ÿýµjŽ‘ +0ÁŸÿ³+‘ÿ+ŽŽ‘÷á¬)‘µpŽ‘ +¬[µjŽ‘°Ä¬]–Ç=“µjŽ‘wܬ;Ž¦‘­forŽ‘/艬(µjŽ‘wܬ=‘Ç0Ž‘Ç;‘ÿýµjŽ‘ wÙ<‘ÇnŽ‘Dz¬;‘ÿýµjŽ‘ +0ÁŸÿ³+‘ÿ+ŽŽ‘÷á¬)‘UU°fŽŽŽŒ‹>-ê Šn ý‘ì¬62›­CONST–ÕX¯VERSION“(NO“ASSIGNMENT)’¹À(3DLDF-1.1.5.1˜°x¬228Ž €n ý•@P­228.‘ ü¬Piv•¸ãot‘UUsearc“h.Ž©°h–ª¨¬De ne‘UU­T‘ÿ +«ransformŽ‘;'¬functions‘@¯169“°i‘Ǭ+°Ž¤ ‘ +±maxŽ‘ k´¬=‘DZfabsŽ‘ùê¬(µtŽ‘œr:±matrixŽ‘?›¬[µjŽ–°Ä¬][µjŽ“¬]);Ž¡‘ +±r‘ÿ}'owŽ‘Ó„¬=‘ǵjŽ‘wܬ;Ž¡‘ +­forŽ‘臬(µiŽ‘9 ¬=‘ǵjŽ‘ °¼¬+‘8à1Ž‘8á;‘ÿýµiŽ‘ 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SŸÿ³+‘ÿ+ŽŽ‘Ìs¬)‘°fŽ¡‘±hrŽ‘+±g¬=‘ǵtŽ‘cŠ:±matrixŽ‘?›¬[µjŽ‘°Ä¬][µkŽ‘…V¬];Ž¡‘µtŽ‘!œu:±matrixŽ›?›¬[µjŽ‘°Ä¬][µkŽ‘…V¬]–Ç=“µtŽ‘cŠ:±matrixŽ˜¬[±r‘ÿ}'owŽ‘ k¬][µkŽ‘…V¬];Ž¡‘µtŽ‘!œu:±matrixŽ‘?›¬[±r‘ÿ}'owŽ‘ k¬][µkŽ‘…V¬]–Ç=“±hrŽ‘ ±d¬;Ž¡‘°g‘µ=°‘ÿý­forŽ‘“+°µ=Ž¡‘±hiŽ‘ |N¬=‘ǵpŽ‘Ϭ[µjŽ‘°Ä¬];Ž¡‘µpŽ‘¬[µjŽ‘°Ä¬]–Ç=“µpŽ‘Ϭ[±r‘ÿ}'owŽ‘ k¬];Ž¡‘µpŽ‘¬[±r‘ÿ}'owŽ‘ k¬]–Ç=“±hiŽ‘ |L¬;Ž¡‘ +°g‘µ=°‘ÿý­ifŽ‘_°µ=Ž¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Finished® ´row® ´exchanŽ‘kÆÜge.\n"Ž’Ž”J°‘DZ ushŽ‘€¬;ŽŸ­230.‘ ü¬T‘ÿ*ªransformation.Ž¦°h–ª¨¬De ne‘UU­T‘ÿ +«ransformŽ‘;'¬functions‘@¯169“°i‘Ǭ+°Ž¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"t.matrix["Ž‘?Ôw°‘ǵjŽ– +>ô°‘Ç´"]["Ž‘Œ°‘ǵjŽ“°‘Ç´"]® ´==® ´"Ž‘*Ôƒ°‘ǵtŽ‘cŠ:±matrixŽ‘?›¬[µjŽ–°Ä¬][µjŽ“¬]–Ç°“±end‘‚ØlŽ‘ò°“± ushŽ‘€¬;Ž¡‘ +±hrŽ‘±e¬=‘Ç1Ž‘ǵ=tŽ‘œr:±matrixŽ‘?›¬[µjŽ–°Ä¬][µjŽ“¬];Ž¡‘ +­forŽ‘臬(µiŽ‘9 ¬=‘Ç0Ž‘Ç;‘ÿýµiŽ‘ 9 <‘ÇnŽ‘Dz¬;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)‘µtŽ‘œr:±matrixŽ›?›¬[µiŽ‘qô¬][µjŽ‘°Ä¬]–Ç=“±hrŽ‘êD°‘8àµtŽ‘ÕR:±matrixŽ˜¬[µiŽ‘qô¬][µjŽ‘°Ä¬];Ž¡‘ +µtŽ‘ œs:±matrixŽ‘?›¬[µjŽ–°Ä¬][µjŽ“¬]–Ç=“±hrŽ‘ ±d¬;Ž¡‘ +­forŽ‘臬(µkŽ‘Ln¬=‘Ç0Ž‘Ç;‘ÿýµkŽ‘ Lk<‘ÇnŽ‘Dz¬;‘ÿýµkŽ‘ SŸÿ³+‘ÿ+ŽŽ‘Ìs¬)Ž¡‘­ifŽ‘´ú¬(µkŽ‘Ln°6¬=‘ǵjŽ‘wܬ)‘°fŽ¡‘­forŽ‘/艬(µiŽ‘9 ¬=‘Ç0Ž‘Ç;‘ÿýµiŽ‘ 9 <‘ÇnŽ‘Dz¬;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)Ž¡‘(­ifŽ‘3´ü¬(µiŽ‘9 °6¬=‘ǵjŽ‘wܬ)‘µtŽ‘œr:±matrixŽ–?›¬[µiŽ›qô¬][µkŽ‘…V¬]‘Ç°¬=ŽŽ‘lµtŽ‘¸Þ:±matrixŽ“¬[µiŽ˜¬][µjŽ›°Ä¬]–8à°“µtŽ‘ÕR:±matrixŽ‘?›¬[µjŽ˜¬][µkŽ‘…V¬];Ž¡‘µtŽ‘!œu:±matrixŽ‘?›¬[µjŽ‘°Ä¬][µkŽ‘…V¬]‘Ç°¬=ŽŽ‘UO°Ž‘m±hrŽ‘%¹¬;Ž¡‘°gŽ¡‘ +g‘µ=°‘ÿý¬outer‘UU­forŽ‘胰µ=Ž¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Finished® ´TransformaŽ‘kÆÜtion.\n"Ž’™D°‘DZ ushŽ‘€¬;ŽŽŽŒ‹?6P Šn ý‘ì°x¬231›¯3DLDF-1.1.5.1’¹À(­CONST–ÕX¯VERSION“(NO“ASSIGNMENT)˜¬63Ž €n ý•@P­231.‘ ü¬Column‘UUexc¸ãhange.Ž©°h–ª¨¬De ne‘UU­T‘ÿ +«ransformŽ‘;'¬functions‘@¯169“°i‘Ǭ+°Ž¤ ‘ +­forŽ‘臬(µiŽ‘9 ¬=‘Ç0Ž‘Ç;‘ÿýµiŽ‘ 9 <‘ÇnŽ‘Dz¬;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)‘°fŽ¡‘­forŽ‘%般(µkŽ‘Ln¬=‘Ç0Ž‘Ç;‘ÿýµkŽ‘ Lk<‘ÇnŽ‘Dz¬;‘ÿýµkŽ‘ SŸÿ³+‘ÿ+ŽŽ‘Ìs¬)‘±hvŽ‘Ln¬[µpŽ‘¬[µkŽ›…V¬]]–Ç=“µtŽ‘cŠ:±matrixŽ‘?›¬[µiŽ‘qô¬][µkŽ˜¬];Ž¡‘­forŽ‘%般(µkŽ‘Ln¬=‘Ç0Ž‘Ç;‘ÿýµkŽ‘ Lk<‘ÇnŽ‘Dz¬;‘ÿýµkŽ‘ SŸÿ³+‘ÿ+ŽŽ‘Ìs¬)‘µtŽ‘œr:±matrixŽ‘?›¬[µiŽ‘qô¬][µkŽ›…V¬]–Ç=“±hvŽ‘†¬[µkŽ˜¬];Ž¡‘ +°g‘µ=°‘ÿý­forŽ‘“+°µ=Ž¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"Finished® ´column® ´excŽ‘kÆÜhange.\n"Ž’žTA°‘DZ ushŽ‘€¬;Ž¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"Exiting® ´Transform::Ž‘kÆÜinverse()."Ž’¨Ô;°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Exiting® ´Transform::Ž‘kÆÜinverse()."Ž’¨Ô;°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘ +­returnŽ‘-滵tŽ‘1ƒ-¬;‘qÇ°gŽŸ­232.‘ üNon-const– +°vš®9ersion“(with“assignmen˜t).‘ ü¬[²LDF‘T2002.10.20.¬]Ž‘[•8Added–bWthis“function.‘˜ÍI‘bthough¸ãt“ofŽ¡calling–÷ain“\±invertŽ‘ã(¬(‘ª®)",›ãbut“I‘÷7decided“against“it,˜bGecause“I‘÷7thoughš¸ãt“ha˜ving“t˜w˜o“functions“called“\±inverseŽ‘ ‡¬(‘ª®)"Ž¡and–UU\±invertŽ‘ã(¬(‘ª®)"“w¸ãould“bGe“confusing.Ž¡‘ +There–œfis“no“pGoinš¸ãt“in“calling“this“function“with“±assignŽ‘"µ °‘=Š±falseŽ‘ìά,‘®+since“it“is“equiv‘ÿqÇalen˜t“to“the“­constŽ‘"¬v˜ersionŽ¡abGo•¸ãv“e–Ëãwith“no“argumenš¸ãt.‘C÷If“it“is“called“with“±assignŽ‘!n°‘DZfalseŽ‘v\¬,‘ç`a“w˜arning“is“issued,‘ç`the“­constŽ‘ m¬v˜ersion“is“in˜v˜ok˜ed,Ž¡and–UUits“return“v‘ÿqÇalue“is“returned.Ž¦°h–ª¨¬Declare‘UU­T‘ÿ +«ransformŽ‘;'¬functions‘@¯168“°i‘Ǭ+°Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓ±inverseŽ‘a×Z¬(­b•QÇo“olŽ‘¡f±assignŽ‘5|‚¬);ŽŸ­233.Ž¦°h–ª¨¬De ne‘UU­T‘ÿ +«ransformŽ‘;'¬functions‘@¯169“°i‘Ǭ+°Ž¡‘ +­T‘ÿ «ransformŽ‘AÈÓT‘ÿ -«ransformŽ‘wuC«&Ž‘FÄç«&Ž‘FŒ±;‘ª¨ÂconstŽ‘ÕJrealŽ‘33#«)–Ç=“0Ž‘Ç;Ž¡‘ -ÂvirtualŽ‘/ÔT‘ÿ -«ransformŽ‘gV¦opQÇeratorŽ’’í[·«=ŽŽŽ’Ÿ´z(ÂconstŽ‘*¢T‘ÿ -«ransformŽ‘Uót«&Ž‘]º’)–Ç=“0Ž‘Ç;Ž¡‘ -ÂvirtualŽ‘/Ôv®9oidŽ‘H‹¬Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ’Ž«‹«(Âv®9oidŽ‘¨ƒ«)–Ç=“0Ž‘Ç;Ž¡‘ -ÂvirtualŽ‘/Ôb•QÇo“olŽ‘I/:Ïset‘‰ffŽ‘®extr‘ÿ}'emesŽ‘ðë(‘ª®)–Ç=“0Ž‘Ç;Ž¡‘ -ÂvirtualŽ‘/ÔrealŽ‘FAÏget‘‰ffŽ–®minimum‘‰ffŽ“zŽ’‰žÚ«(‘ª®)‘UUÂconstŽ‘ ñº«=‘Ç0Ž‘Ç;Ž¡‘ -ÂvirtualŽ‘/ÔrealŽ‘FAÏget‘‰ffŽ–®maximum‘‰ffŽ“zŽ’Š®«(‘ª®)‘UUÂconstŽ‘ ñº«=‘Ç0Ž‘Ç;Ž¡‘ -ÂvirtualŽ‘/ÔrealŽ‘FAÏget‘‰ffŽ–®me‘ÿ}'an‘‰ffŽ“zŽ‘v÷ «(‘ª®)‘UUÂconstŽ‘ ñº«=‘Ç0Ž‘Ç;Ž¡‘ -ÂvirtualŽ‘/ÔconstŽ‘M¸vv‘ÿ\ralarra®9yŽ‘w··hÂrealŽ‘]Ù·i‘UUÏget‘‰ffŽ‘®extr‘ÿ}'emesŽ‘:™µ«(‘ª®)‘UUÂconstŽ‘ ñº«=‘Ç0Ž‘Ç;Ž¡‘ -ÂvirtualŽ‘/Ôv®9oidŽ‘H‹¬Ïsuppr‘ÿ}'ess‘‰ffŽ‘®outputŽ’r.«(‘ª®)–Ç=“0Ž‘Ç;Ž¡‘ -ÂvirtualŽ‘/Ôv®9oidŽ‘H‹¬Ïunsuppr‘ÿ}'ess‘‰ffŽ‘®outputŽ’˜oR«(‘ª®)–Ç=“0Ž‘Ç;–UU·g“«;ŽŸÂ201.‘ üStatic–ÕTdata“mem®9bQÇers.Ž¦·h–ª¨«De ne‘UUÂstaticŽ‘"ž.ShapQÇeŽ‘Dß«mem¸ãbGer‘UUv‘ÿqÇariables‘@­201“·i‘ÇŽ¡‘ -ÂconstŽ‘(*£signedŽ‘Kš™shortŽ‘ieLÌ«;ŽŸÂ206.‘ üInclude‘ÕT les.Ž¦·h–ª¨«Include‘UU les‘@­11“·i‘Ç«+·Ž¡«#ÂincludeŽ‘'Ø~Ý"loader.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"pspglb.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"io.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"colors.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"transfor.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"shapes.h"ŽŽ©Â207.– üLabšQÇel.“«[¬LDF‘T2002.10.20.«]Ž‘Zì ÂLab˜elsŽ‘oÖ«are–¹+the“only“ob‘Ž8jects,‘Ò!other“than“ÂShap˜esŽ‘'.t«,‘Ò!that“can“bGe“put“on¸ãtoŽ¡ÂPicturesŽ‘*%I«.‘[ºThey–/are“created“b¸ãy“the“functions“Ïlab‘ÿ}'elŽ‘‡Ç«(›ª®)“and“Ïdotlab‘ÿ}'elŽ‘%"«(˜),‘ jwhicš¸ãh“are“curren˜tly“de ned“for“ÂP•®9oin“tsŽŽ¡«and‘UUÂP®9athsŽ‘ oõ«.Ž¦Â208.› üLabQÇel–þxclass“de nition.˜«A‘yÂLabQÇelŽ‘#3«conš¸ãtains–ya“pGoin˜ter“to“a“ÂP•®9oin“tŽ‘c«,‘‚ whic˜h“is“its“loGcation,‘‚ a“Âb•QÇo“olŽ‘>G«toŽ¡indicate–.gwhether“the“labšGel“should“ha•¸ãv“e–.ga“dot“or“not,‘d«a“ÂstringŽ‘&,Æ«for“the“text“of“the“lab˜el“and“a“ÂstringŽ‘&,Æ«forŽ¡pšGositioning–¬áthe“text“with“resp˜ect“to“the“lab˜el.‘xlÏptŽ‘ ê«m¸ãust“b˜e“a“p˜oin¸ãter,‘ÂÅb˜ecause“ÂP•®9oin“tŽ‘"ô -«is“an“incomplete“t¸ãyp˜eŽ¡here.‘¶—Ïp‘ÿ}'ositionŽ‘.Þ«can–ðbGe“anš¸ãy“of“the“strings“used“in“MET‘ÿ*ªAF˜ONT,“i.e.,‘GVÝ"top"Ž– ¯«,‘GVÝ"bot"Ž“«,‘GVÝ"lft"Ž“«,‘GVÝ"rt"Ž‘Ͳ«,‘GVÝ"llft"Ž‘$M¬«,Ž¡Ý"ulft"Ž‘ V«,‘UUÝ"lrt"Ž›®«,–UUor“Ý"urt"Ž˜«.Ž¡‘ -[¬LDF‘T2002.10.09.«]Ž‘Y;ÂLabQÇelsŽ‘}(/«are–UUcurrenš¸ãtly“only“ev˜er“created“on“the“free“store.Ž¤‘ -ÂformatŽ‘3c(ÏL–ÿ}'ab“elŽ‘Sa±intŽŽ¡·h–ª¨«De ne‘UUclasses‘@­208“·i‘ÇŽ¤ ‘ -ÂclassŽ‘$àRLabQÇelŽ‘Dw -·fŽ¡‘ÂfriendŽ‘5f¼classŽ‘PG P•®9oin“tŽ‘káU«;Ž¡‘ÂfriendŽ‘5f¼classŽ‘PG PictureŽ‘uã«;Ž¡‘ÂP•®9oin“tŽ‘2Ž‘7ï ÏptŽ‘AÔ=«;Ž¡‘Âb•QÇo“olŽ‘-¡hÏdotŽ‘<¢u«;Ž¡‘ÂstringŽ‘5%OÏtextŽ‘F}«;Ž¡‘ÂstringŽ‘5%OÏp‘ÿ}'ositionŽ‘Xi¦«;Ž¡‘ -ÂpublicŽ‘)=Ö«:‘ÂstaticŽ‘$HÙb•QÇo“olŽ‘=ê?ÝDO_LABELSŽ‘m°Œ«;ŽŸ‘·h–ª¨«Declare‘UUÂLabQÇelŽ‘"ì «functions‘@­210“·iŽ¡‘ -g«;Ž¤ ­See–ÕXalso“section“216.Ž¡This–ÕXcouC«&Ž‘Fclass“de nition.˜«[¬LDF‘T2002.08.06.«]Ž‘Z¯DNote–|cthat“ÂLabQÇelŽ‘#:)«has“a“ÂpublicŽ‘&6›staticŽ‘E¦‚«data“mem¸ãbGerŽ¤ named‘ÖYÝDO_LABELSŽ‘3œ¦«,‘öšwhicš¸ãh–ÖYis“used“for“globally“enabling“or“suppressing“putting“ÂLabQÇelsŽ‘(wQ«on˜to“ÂPicturesŽ‘1Ñû«(seeŽ¡abGo•¸ãv“e).Ž¡‘ -ÂPictureŽ‘0œ«::‘Ïdo‘‰ffŽ‘®lab‘ÿ}'elsŽ‘';ç«,›ø¹on–Ø the“other“hand,˜is“for“enabling“or“suppressing“the“output“of“ÂLabQÇelsŽ‘(zµ«for“a“singleŽ¡ÂPictureŽ‘%œ «.‘œ¾If–c§a“ÂPictureŽ‘.c[«is“output“when“Ïdo‘‰ffŽ‘®lab‘ÿ}'elsŽ‘/1«is“ÏfalseŽ‘v’«for“that“ÂPictureŽ‘)ÿ´«,‘§«¶ Šn ý‘ì«62›­DEF‘ÿ8A•ÃŽUL‘ÿJªT‘ÕXCONSTR“UCTOR’ùQ÷3DLDFPR“G˜·x«219Ž €n ý•@PÂ219.Ž©·h–ª¨«De ne‘UUÂPictureŽ‘,F·«functions‘@­219“·i‘ÇŽ¤ ‘ -ÂPictureŽ‘0œ«::‘ÂPictureŽ‘&œ«(‘ª®)Ž¡‘ -:‘qÇÏdo‘‰ffŽ‘®lab‘ÿ}'elsŽ‘*­ª«(ÏtrueŽ‘Ę«)‘UU·f‘ª¨gŽ¤ ­See–ùalso“sections“226,–ð228,“232,“236,“239,“242,“245,“247,“249,“251,“373,“396,“543,“544,“545,“546,“548,“549,“550,“551,“552,“553,ŽŸ -‘and‘ÕX554.Ž¡This–ÕXcoŸÓVEŽ‘ãxXŽ‘i¡macro“for“\POR›ÿ*ªTING".“!!‘¥­POR˜TING.“[¬LDF‘T2002.12.05.«]Ž‘R€)Mo•¸ãv“edŽ¡to–”žÈpoints.web“«bGecause“ÂPictureŽ‘)0¯«::‘Ïcle‘ÿ}'arŽ‘(Ý«(›ª®)“and“ÂLabQÇelŽ‘Ö«::‘Ïget‘‰ffŽ‘®c‘ÿ}'opyŽ‘%ø«(˜)“are“unde ned“in“this“ le.‘1ŠThis“didn't“causeŽ¡a–UUproblem“with“the“DEC“compiler,“but“it“doGes“with“the“GNU“Compiler.ŽŸ·h–ª¨«Declare‘UUÂPictureŽ‘,F·«functions‘@­218“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙopQÇeratorŽ‘N”Ž«=Ž‘V[¬(ÂconstŽ‘*¢PictureŽ‘G«&Ž‘Nã"±pŽ‘Së"«);Ž¦Â223.‘ üAdding‘ÕTelemen®9ts.Ž¦224.– üAdd‘/çPicture.“«This–¤function“m¸ãust“bšGe“de ned“in“Èpoints.web«,‘·Èb˜ecause“it“uses“ÂP•®9oin“tŽ‘>_«,‘·Èwhic¸ãh“is“anŽ¡incompletely–UUde ned“ÂclassŽ‘5¦«here.Ž¡‘ -[¬LDF‘T2002.04.17.«]Ž‘Y73It–„Mseems“to“bšGe“most“useful“to“ha•¸ãv“e–„Mthe“argumen¸ãt“ÂPictureŽ‘,¤§±pŽ‘50ô«b˜e“non-ÂconstŽ‘ÕM«,‘ in“order“toŽ¡bGe–ò¢able“to“shift“it“and“add“it“to“·Ž‘ò£ÏthisŽ‘Ðû«mš¸ãultiple“times.‘PáF‘ÿ*ªor“this“to“w˜ork,‘_it“m˜ust“bšGe“p˜ossible“to“set“±pŽ‘ú¢:Ïtr‘ÿ}'ansformŽŽ¡«to–BËthe“iden•¸ãtit“y–BËmatrix“afterwš¸ãards.‘:)It“is“pGossible“to“do“this“explicitly“b˜y“calling“Ïr–ÿ}'eset‘‰ffŽ‘®tr“ansformŽ‘Gõ$«(‘ª®)“on“theŽ¡ÂPictureŽ‘)h«folloš¸ãwing–z[the“call“to“ÂopQÇeratorŽ‘/«+=ŽŽŽ‘>ŸL(‘ª¨),‘ƒœbut“it's“more“con˜v˜enien˜t“to“ha˜v˜e“it“done“automatically‘ÿ*ª.‘àÙIf“itŽ¡turns–UUout“to“bGe“useful,“I“can“add“a“ÂconstŽ‘!÷«v¸ãersion“of“this“function.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.04.17.«]Ž‘Y;Added–UUthis“declaration.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂPictureŽ‘,F·«functions‘@­218“·i‘Ç«+·ŽŸ ‘ -Âv®9oidŽ‘"ýÙopQÇeratorŽ‘N”Ž«+=ŽŽŽ‘^"Ê(ÂconstŽ‘*¢PictureŽ‘G«&Ž‘Nã"±pŽ‘Së"«);Ž¦Â225.‘ üAdd‘ÕTShapQÇe.Ž¡·h–ª¨«Declare‘UUÂPictureŽ‘,F·«functions‘@­218“·i‘Ç«+·ŽŸ ‘ -Âv®9oidŽ‘"ýÙopQÇeratorŽ‘N”Ž«+=ŽŽŽ‘^"Ê(ÂShapQÇeŽ‘"Ab·Ž‘'Ac±sŽ‘+ñc«);ŽŽŽŒ‹?µñ Šn ý‘ì·x«226–­3DLDFPRÃŽG’*çADD‘ÕXÂSHAPE“«63Ž €n ý•@PÂ226.Ž©·h–ª¨«De ne‘UUÂPictureŽ‘,F·«functions‘@­219“·i‘Ç«+·Ž¤ ‘ -Âv®9oidŽ‘"ýÙPictureŽ‘I™ê«::Ž‘P((ÂopQÇeratorŽ‘{¾Ý«+=ŽŽŽ’‹M(ÂShapQÇeŽ‘"Ab·Ž‘'Ac±sŽ‘+ñc«)Ž¡‘ -·fŽ¡‘Ïshap‘ÿ}'esŽ‘0:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(±sŽ‘°«);Ž¡‘ -·gŽŸÂ227.‘ üAdd‘ÕTLabQÇel.Ž¦·h–ª¨«Declare‘UUÂPictureŽ‘,F·«functions‘@­218“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙopQÇeratorŽ‘N”Ž«+=ŽŽŽ‘^"Ê(ÂLabQÇelŽ‘–¸·Ž‘$–¹Ïlab‘ÿ}'elŽ‘9 Q«);ŽŸÂ228.Ž¦·h–ª¨«De ne‘UUÂPictureŽ‘,F·«functions‘@­219“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙPictureŽ‘I™ê«::Ž‘P((ÂopQÇeratorŽ‘{¾Ý«+=ŽŽŽ’‹M(ÂLabQÇelŽ‘–¸·Ž‘$–¹Ïlab‘ÿ}'elŽ‘9 Q«)Ž¡‘ -·fŽ¡‘Ïlab‘ÿ}'elsŽ‘,Tò±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(Ïlab‘ÿ}'elŽ‘t˜«);Ž¡‘ -·gŽŸÂ229.– üSuppress‘Ê•LabQÇels.“«[¬LDF‘T2002.04.25.«]Ž‘[]yAdded–*˜this“function.‘ñ‘Sometimes“it's“irritating“to“ha•¸ãv“e‘*˜theŽ¡labšGels–½“when“a“ÂPictureŽ‘-3«is“copied“and“transformed,‘×¢and“b˜oth“the“original“and“the“transformed“v¸ãersions“areŽ¡output.Ž¦·h–ª¨«Declare‘UUÂPictureŽ‘,F·«functions‘@­218“·i‘Ç«+·Ž¡‘ -ÂinlineŽ‘)ŠIv®9oidŽ‘Bˆ!Ïsuppr–ÿ}'ess‘‰ffŽ‘®lab“elsŽ’‚´S«(‘ª®)Ž¡‘ -·fŽ¡‘Ïdo‘‰ffŽ‘®lab‘ÿ}'elsŽ‘=ý«=‘ÇÏfalseŽ‘v\«;Ž¡‘ -·gŽŸÂ230.‘ üUnsuppress‘ÕTLabQÇels.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.12.20.«]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂPictureŽ‘,F·«functions‘@­218“·i‘Ç«+·Ž¡‘ -ÂinlineŽ‘)ŠIv®9oidŽ‘Bˆ!Ïunsuppr–ÿ}'ess‘‰ffŽ‘®lab“elsŽ’±w«(‘ª®)Ž¡‘ -·fŽ¡‘Ïdo‘‰ffŽ‘®lab‘ÿ}'elsŽ‘=ý«=‘ÇÏtrueŽ‘‹°«;Ž¡‘ -·gŽŸÂ231.‘ üKill‘ÕTLabQÇels.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.05.07.«]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂPictureŽ‘,F·«functions‘@­218“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙÏkil‘‚Øl‘‰ffŽ‘®lab‘ÿ}'elsŽ‘LJË«(‘ª®);ŽŽŽŒ‹@à  Šn ý‘ì«64–­KILL‘ÕXÂLABELS’#ÿ'­3DLDFPRÃŽG“·x«232Ž €n ý•@PÂ232.ŽŸ·h–ª¨«De ne‘UUÂPictureŽ‘,F·«functions‘@­219“·i‘Ç«+·Ž¤ ‘ -Âv®9oidŽ‘"ýÙPictureŽ‘I™ê«::‘Ïkil‘‚Øl‘‰ffŽ‘®lab‘ÿ}'elsŽ‘*Lö«(‘ª®)Ž¡‘ -·fŽ¡‘Ïlab‘ÿ}'elsŽ‘,Tò±:Ïcle‘ÿ}'arŽ‘(Ù«(‘ª¨);Ž¡‘ -·gŽ©Â233.– üT‘ÿ -«ransformations.“«T‘ÿ*ªransformations–Êyfor“ÂPicturesŽ‘3º;«are“sa•¸ãv“ed–Êyup,‘'Áand“then“pGerformed“when“theŽ¡ÂPictureŽ‘(ñb«is‘UUoutput.Ž¦Â234.‘ üAne‘ÕTtransformations.Ž¦235.‘ üScale.ŽŸ·h–ª¨«Declare‘UUÂPictureŽ‘,F·«functions‘@­218“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ -«ransformŽ‘AÈÓÏsc‘ÿ}'aleŽ‘W}Å«(ÂrealŽ‘³.±xŽ‘jJ;‘ª¨ÂrealŽ‘]Ö±yŽ‘ gæ«=‘Ç1Ž–DZ;‘ª¨ÂrealŽ‘]Ö±zŽ‘ < «=‘Ç1Ž“);Ž¦Â236.ŽŸ·h–ª¨«De ne‘UUÂPictureŽ‘,F·«functions‘@­219“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ -«ransformŽ‘AÈÓPictureŽ‘hdä«::‘Ïsc‘ÿ}'aleŽ‘´ö«(ÂrealŽ‘³.±xŽ‘jJ;‘ª¨ÂrealŽ‘]Ö±yŽ‘ Î;‘ª¨ÂrealŽ‘]Ö±zŽ‘tô«)Ž¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼Ïtr‘ÿ}'ansformŽ‘c™ý±:Ïsc‘ÿ}'aleŽ‘´ò«(±xŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁÆ«);Ž¡‘ -·gŽ¦Â237.– üShift.“«(T‘ÿ*ªranslation.)Ž¦Â238.‘ üreal‘ÕTv®9ersion.ŽŸ·h–ª¨«Declare‘UUÂPictureŽ‘,F·«functions‘@­218“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ -«ransformŽ‘AÈÓÏshiftŽ‘UæP«(ÂrealŽ‘³.±xŽ‘jJ;‘ª¨ÂrealŽ‘]Ö±yŽ‘ gæ«=‘Ç0Ž–DZ;‘ª¨ÂrealŽ‘]Ö±zŽ‘ < «=‘Ç0Ž“);Ž¦Â239.‘ üÏshiftŽ‘y«(‘ª®)–¨dreturns“a“ÂT‘ÿ -«ransformŽ‘;ÄE«represenš¸ãting“the“shift,‘½(Ïnot‘›<·Ž‘ ›=ÏthisŽ‘†ó«.‘jõThis“mak˜es“it“pGossible“to“apply“theŽ¡transformation–UUto“other“ob‘Ž8jects.ŽŸ·h–ª¨«De ne‘UUÂPictureŽ‘,F·«functions‘@­219“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ -«ransformŽ‘AÈÓPictureŽ‘hdä«::‘ÏshiftŽ‘«(ÂrealŽ‘³.±xŽ‘jJ;‘ª¨ÂrealŽ‘]Ö±yŽ‘ Î;‘ª¨ÂrealŽ‘]Ö±zŽ‘tô«)Ž¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼Ïtr‘ÿ}'ansformŽ‘c™ý±:ÏshiftŽ‘}«(±xŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁÆ«);Ž¡‘ -·gŽ¦Â240.› üP•®9oin“t‘¥lv“ersion.˜«This–èäfunction“m¸ãust“de ned“in“Èpoints.web«,‘MÇbGecause“ÂP•®9oin“tŽ‘%l«is“an“incompletelyŽ¡de ned–UUt¸ãypGe“here.ŽŸ·h–ª¨«Declare‘UUÂPictureŽ‘,F·«functions‘@­218“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ -«ransformŽ‘AÈÓÏshiftŽ‘UæP«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]±pŽ‘Ié]«);Ž¦Â241.› üRotation–yaround“the“main“axes.˜Ïr‘ÿ}'otateŽ‘%ï:«(‘ª®)–ã®will“pšGerform“rotation“ab˜out“the“x,‘Dy“and“z-axes“inŽ¡that–ô"order“if“called“with“mš¸ãultiple,‘“non-zero“argumen˜ts.‘QaRotation“only“abGout“the“y“and/or“z-axis“requires“oneŽ¡or›UUt•¸ãw“o˜dumm“y˜0˜argumen“ts˜so˜that˜Ïr‘ÿ}'otateŽ‘Ä“«(‘ª®)˜\kno“ws"˜abGout˜whic“h˜axis˜(or˜axes)˜to˜rotate.ŽŸ·h–ª¨«Declare‘UUÂPictureŽ‘,F·«functions‘@­218“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ -«ransformŽ‘AÈÓÏr‘ÿ}'otateŽ‘\8«(ÂconstŽ‘*¢realŽ‘4ÝбxŽ‘:”ì;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±yŽ‘>’ˆ«=‘Ç0Ž–DZ;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±zŽ‘>f®«=‘Ç0Ž“);ŽŽŽŒ‹AËG Šn ý‘ì·x«242›­3DLDFPR•ÃŽG’Ç7wR“OT–ÿJªA“TION–ÕXARÃŽOUND“THE“MAIN“AXES˜«65Ž €n ý•@PÂ242.Ž©·h–ª¨«De ne‘UUÂPictureŽ‘,F·«functions‘@­219“·i‘Ç«+·Ž¤ ‘ -ÂT‘ÿ -«ransformŽ‘AÈÓPictureŽ‘hdä«::‘Ïr‘ÿ}'otateŽ‘oB«(ÂconstŽ‘*¢realŽ‘4ÝбxŽ‘:”ì;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±yŽ‘;Ëp;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±zŽ‘;Ÿ–«)Ž¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼Ïtr‘ÿ}'ansformŽ‘c™ý±:Ïr‘ÿ}'otateŽ‘o>«(±xŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁÆ«);Ž¡‘ -·gŽŸÂ243.› üRotation–·×around“an“arbitrary“axis.˜«[¬LDF‘T2002.05.03.«]Ž‘Zn’This–;±function“is“de ned“in“Èpoints.web«,Ž¡bGecause–UUit“has“ÂP•®9oin“tŽ›"Dò«argumen¸ãts,“and“ÂP•®9oin“tŽ˜«is“an“incomplete“t¸ãypGe“in“this“ le.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.05.03.«]Ž‘Y;Added–UUthis“declaration.Ž¡‘ -[¬LDF‘T2003.05.02.«]Ž‘YËSChanged–mname“of“this“function“from“Ïr–ÿ}'otate‘‰ffŽ‘®ar“oundŽ‘@„ü«(›ª®)“to“Ïr‘ÿ}'otateŽ‘‡««(˜).‘»This“function“no¸ãwŽ¡o•¸ãv“erloads‘UUÏr‘ÿ}'otateŽ‘Ä“«(‘ª®)–UUwith“three“ÂrealŽ‘ƒ«argumen¸ãts.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂPictureŽ‘,F·«functions‘@­218“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ -«ransformŽ‘AÈÓÏr‘ÿ}'otateŽ‘\8«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]Ïp0Ž‘Pø±;‘ª¨ÂconstŽ‘ÕJP•®9oin“tŽ‘>Äç«&Ž‘FŒÏp1Ž‘R¢Å±;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆxÏangleŽ‘Qã«=‘Ç180ŽŽ‘Ç);Ž¡‘±=·‘ÿý«Remem¸ãbGer–UUto“add“shear!‘o·±=ŽŸÂ244.‘ üSet‘ÕTtransform.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.01.17.«]Ž‘Y;Made–UUnon-inline“and“c¸ãhanged“±tŽ‘ -G«from“plain“ÂT‘ÿ -«ransformŽ‘;'«to“ÂconstŽ‘!÷T‘ÿ -«ransformŽ‘YHÉ«&Ž‘aç.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂPictureŽ‘,F·«functions‘@­218“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ -«ransformŽ‘AÈÓÏset‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘},ù«(ÂconstŽ‘*¢T‘ÿ -«ransformŽ‘Uót«&Ž‘]º’±tŽ‘aW«);ŽŸÂ245.Ž¦·h–ª¨«De ne‘UUÂPictureŽ‘,F·«functions‘@­219“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ -«ransformŽ‘AÈÓPictureŽ‘hdä«::‘Ïset‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘‡_«::Ž‘EÝPERSPŽ‘_Ûö±;‘ª¨ÂrealŽŽ¡‘ÏfactorŽ‘> è«=‘ +«ransformŽ‘wuC¬&Ž‘FÄç¬&Ž‘FŒµ;‘ª¨­constŽ‘ÕJrealŽ‘33#¬)–Ç=“0Ž‘Ç;Ž¡‘ +­virtualŽ‘/ÔT‘ÿ +«ransformŽ‘gV¦opQÇeratorŽ’’í[°¬=ŽŽŽ’Ÿ´z(­constŽ‘*¢T‘ÿ +«ransformŽ‘Uót¬&Ž‘]º’)–Ç=“0Ž‘Ç;Ž¡‘ +­virtualŽ‘/Ôv®9oidŽ‘H‹¬±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ’Ž«‹¬(­v®9oidŽ‘¨ƒ¬)–Ç=“0Ž‘Ç;Ž¡‘ +­virtualŽ‘/Ôb•QÇo“olŽ‘I/:±set‘‰ffŽ‘®extr‘ÿ}'emesŽ‘ðì(‘ª®)–Ç=“0Ž‘Ç;Ž¡‘ +­virtualŽ‘/ÔrealŽ‘FA±get‘‰ffŽ–®minimum‘‰ffŽ“zŽ’‰žÚ¬(‘ª®)‘UU­constŽ‘ ñº¬=‘Ç0Ž‘Ç;Ž¡‘ +­virtualŽ‘/ÔrealŽ‘FA±get‘‰ffŽ–®maximum‘‰ffŽ“zŽ’Š®¬(‘ª®)‘UU­constŽ‘ ñº¬=‘Ç0Ž‘Ç;Ž¡‘ +­virtualŽ‘/ÔrealŽ‘FA±get‘‰ffŽ–®me‘ÿ}'an‘‰ffŽ“zŽ‘v÷ ¬(‘ª®)‘UU­constŽ‘ ñº¬=‘Ç0Ž‘Ç;Ž¡‘ +­virtualŽ‘/ÔconstŽ‘M¸vv‘ÿ\ralarra®9yŽ‘w·°h­realŽ‘]Ù°i‘UU±get‘‰ffŽ‘®extr‘ÿ}'emesŽ‘:™µ¬(‘ª®)‘UU­constŽ‘ ñº¬=‘Ç0Ž‘Ç;Ž¡‘ +­virtualŽ‘/Ôv®9oidŽ‘H‹¬±suppr‘ÿ}'ess‘‰ffŽ‘®outputŽ’r.¬(‘ª®)–Ç=“0Ž‘Ç;Ž¡‘ +­virtualŽ‘/Ôv®9oidŽ‘H‹¬±unsuppr‘ÿ}'ess‘‰ffŽ‘®outputŽ’˜oR¬(‘ª®)–Ç=“0Ž‘Ç;–UU°g“¬;ŽŸ­246.‘ üStatic–ÕTdata“mem®9bQÇers.Ž¦°h–ª¨¬De ne‘UU­staticŽ‘"ž.ShapQÇeŽ‘D߬mem¸ãbGer‘UUv‘ÿqÇariables‘@¯246“°i‘ÇŽ¡‘ +­constŽ‘(*£signedŽ‘Kš™shortŽ‘ieL̬;ŽŸ­251.‘ üInclude‘ÕT les.Ž¦°h–ª¨¬Include‘UU les‘@¯6“°i‘Ǭ+°Ž¡¬#­includeŽ‘'Ø~´"loader.h"ŽŽ¡¬#­includeŽ‘'Ø~´"pspglb.h"ŽŽ¡¬#­includeŽ‘'Ø~´"io.h"ŽŽ¡¬#­includeŽ‘'Ø~´"colors.h"ŽŽ¡¬#­includeŽ‘'Ø~´"transfor.h"ŽŽ¡¬#­includeŽ‘'Ø~´"shapes.h"ŽŽ©­252.– üLabšQÇel.“¬[²LDF‘T2002.10.20.¬]Ž‘Zì ­Lab˜elsŽ‘oÖ¬are–¹+the“only“ob‘Ž8jects,‘Ò!other“than“­Shap˜esŽ‘'.t¬,‘Ò!that“can“bGe“put“on¸ãtoŽ¡­PicturesŽ‘*%I¬.‘[ºThey–/are“created“b¸ãy“the“functions“±lab‘ÿ}'elŽ‘‡Ç¬(›ª®)“and“±dotlab‘ÿ}'elŽ‘%"¬(˜),‘ jwhicš¸ãh“are“curren˜tly“de ned“for“­P•®9oin“tsŽŽ¡¬and‘UU­P®9athsŽ‘ oõ¬.Ž¦­253.› üLabQÇel–þxclass“de nition.˜¬A‘y­LabQÇelŽ‘#3¬conš¸ãtains–ya“pGoin˜ter“to“a“­P•®9oin“tŽ‘c¬,‘‚ whic˜h“is“its“loGcation,‘‚ a“­b•QÇo“olŽ‘>G¬toŽ¡indicate–.gwhether“the“labšGel“should“ha•¸ãv“e–.ga“dot“or“not,‘d«a“­stringŽ‘&,Ƭfor“the“text“of“the“lab˜el“and“a“­stringŽ‘&,ƬforŽ¡pšGositioning–¬áthe“text“with“resp˜ect“to“the“lab˜el.‘xl±ptŽ‘ ê¬m¸ãust“b˜e“a“p˜oin¸ãter,‘ÂÅb˜ecause“­P•®9oin“tŽ‘"ô +¬is“an“incomplete“t¸ãyp˜eŽ¡here.‘¶—±p‘ÿ}'ositionŽ‘.Þ¬can–ðbGe“anš¸ãy“of“the“strings“used“in“MET‘ÿ*ªAF˜ONT,“i.e.,‘GV´"top"Ž– ¯¬,‘GV´"bot"Ž“¬,‘GV´"lft"Ž“¬,‘GV´"rt"Ž‘Ͳ¬,‘GV´"llft"Ž‘$M¬¬,Ž¡´"ulft"Ž‘ V¬,‘UU´"lrt"Ž›®¬,–UUor“´"urt"Ž˜¬.Ž¡‘ +[²LDF‘T2002.10.09.¬]Ž‘Y;­LabQÇelsŽ‘}(/¬are–UUcurrenš¸ãtly“only“ev˜er“created“on“the“free“store.Ž¤‘ +­formatŽ‘3c(±L–ÿ}'ab“elŽ‘Sa±intŽŽ¡°h–ª¨¬De ne‘UUclasses‘@¯253“°i‘ÇŽ¤ ‘ +­classŽ‘$àRLabQÇelŽ‘Dw +°fŽ¡‘­friendŽ‘5f¼classŽ‘PG P•®9oin“tŽ‘káU¬;Ž¡‘­friendŽ‘5f¼classŽ‘PG PictureŽ‘uã¬;Ž¡‘­P•®9oin“tŽ‘2Ž‘7ï ±ptŽ‘AÔ=¬;Ž¡‘­b•QÇo“olŽ‘-¡h±dotŽ‘<¢u¬;Ž¡‘­stringŽ‘5%O±textŽ‘F}¬;Ž¡‘­stringŽ‘5%O±p‘ÿ}'ositionŽ‘Xi¦¬;Ž¡‘ +­publicŽ‘)=Ö¬:‘­staticŽ‘$HÙb•QÇo“olŽ‘=ê?´DO_LABELSŽ‘m°Œ¬;ŽŸ‘°h–ª¨¬Declare‘UU­LabQÇelŽ‘"ì ¬functions‘@¯255“°iŽ¡‘ +g¬;Ž¤ ¯See–ÕXalso“section“261.Ž¡This–ÕXcouC¬&Ž‘Fclass“de nition.˜¬[²LDF‘T2002.08.06.¬]Ž‘Z¯DNote–|cthat“­LabQÇelŽ‘#:)¬has“a“­publicŽ‘&6›staticŽ‘E¦‚¬data“mem¸ãbGerŽ¤ named‘ÖY´DO_LABELSŽ‘3œ¦¬,‘öšwhicš¸ãh–ÖYis“used“for“globally“enabling“or“suppressing“putting“­LabQÇelsŽ‘(wQ¬on˜to“­PicturesŽ‘1Ñû¬(seeŽ¡abGo•¸ãv“e).Ž¡‘ +­PictureŽ‘0œ¬::‘±do‘‰ffŽ‘®lab‘ÿ}'elsŽ‘';ç¬,›ø¹on–Ø the“other“hand,˜is“for“enabling“or“suppressing“the“output“of“­LabQÇelsŽ‘(zµ¬for“a“singleŽ¡­PictureŽ‘%œ ¬.‘œ¾If–c§a“­PictureŽ‘.c[¬is“output“when“±do‘‰ffŽ‘®lab‘ÿ}'elsŽ‘/1¬is“±falseŽ‘v’¬for“that“­PictureŽ‘)ÿ´¬,‘§ŸÓVEŽ‘ãxXŽ‘i¡macro“for“\POR›ÿ*ªTING".“!!‘¥­POR˜TING.“[²LDF‘T2002.12.05.¬]Ž‘R€)Mo•¸ãv“edŽ¡to–”ž®points.web“¬bGecause“­PictureŽ‘)0¯¬::‘±cle‘ÿ}'arŽ‘(ݬ(›ª®)“and“­LabQÇelŽ‘Ö¬::‘±get‘‰ffŽ‘®c‘ÿ}'opyŽ‘%ø¬(˜)“are“unde ned“in“this“ le.‘1ŠThis“didn't“causeŽ¡a–UUproblem“with“the“DEC“compiler,“but“it“doGes“with“the“GNU“Compiler.ŽŸ°h–ª¨¬Declare‘UU­PictureŽ‘,F·¬functions‘@¯263“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙopQÇeratorŽ‘N”Ž¬=Ž‘V[¬(­constŽ‘*¢PictureŽ‘G¬&Ž‘Nã"µpŽ‘Së"¬);Ž¦­268.‘ üAdding‘ÕTelemen®9ts.Ž¦269.– üAdd‘/çPicture.“¬This–¤function“m¸ãust“bšGe“de ned“in“®points.web¬,‘·Èb˜ecause“it“uses“­P•®9oin“tŽ‘>_¬,‘·Èwhic¸ãh“is“anŽ¡incompletely–UUde ned“­classŽ‘5¦¬here.Ž¡‘ +[²LDF‘T2002.04.17.¬]Ž‘Y73It–„Mseems“to“bšGe“most“useful“to“ha•¸ãv“e–„Mthe“argumen¸ãt“­PictureŽ‘,¤§µpŽ‘50ô¬b˜e“non-­constŽ‘ÕM¬,‘ in“order“toŽ¡bGe–ò¢able“to“shift“it“and“add“it“to“°Ž‘ò£±thisŽ‘Ðû¬mš¸ãultiple“times.‘PáF‘ÿ*ªor“this“to“w˜ork,‘_it“m˜ust“bšGe“p˜ossible“to“set“µpŽ‘ú¢:±tr‘ÿ}'ansformŽŽ¡¬to–BËthe“iden•¸ãtit“y–BËmatrix“afterwš¸ãards.‘:)It“is“pGossible“to“do“this“explicitly“b˜y“calling“±r–ÿ}'eset‘‰ffŽ‘®tr“ansformŽ‘Gõ$¬(‘ª®)“on“theŽ¡­PictureŽ‘)h¬folloš¸ãwing–z[the“call“to“­opQÇeratorŽ‘/¬+=ŽŽŽ‘>ŸL(‘ª¨),‘ƒœbut“it's“more“con˜v˜enien˜t“to“ha˜v˜e“it“done“automatically‘ÿ*ª.‘àÙIf“itŽ¡turns–UUout“to“bGe“useful,“I“can“add“a“­constŽ‘!÷¬v¸ãersion“of“this“function.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.04.17.¬]Ž‘Y;Added–UUthis“declaration.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­PictureŽ‘,F·¬functions‘@¯263“°i‘Ǭ+°ŽŸ ‘ +­v®9oidŽ‘"ýÙopQÇeratorŽ‘N”Ž¬+=ŽŽŽ‘^"Ê(­constŽ‘*¢PictureŽ‘G¬&Ž‘Nã"µpŽ‘Së"¬);Ž¦­270.‘ üAdd‘ÕTShapQÇe.Ž¡°h–ª¨¬Declare‘UU­PictureŽ‘,F·¬functions‘@¯263“°i‘Ǭ+°ŽŸ ‘ +­v®9oidŽ‘"ýÙopQÇeratorŽ‘N”Ž¬+=ŽŽŽ‘^"Ê(­ShapQÇeŽ‘"Ab°Ž‘'AcµsŽ‘+ñc¬);ŽŽŽŒ‹I¤Ë Šn ý‘ì°x¬271–¯3DLDF-1.1.5.1’!¢QADD‘ÕX­SHAPE“¬73Ž €n ý•@P­271.Ž©°h–ª¨¬De ne‘UU­PictureŽ‘,F·¬functions‘@¯264“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘"ýÙPictureŽ‘I™ê¬::Ž‘P((­opQÇeratorŽ‘{¾Ý¬+=ŽŽŽ’‹M(­ShapQÇeŽ‘"Ab°Ž‘'AcµsŽ‘+ñc¬)Ž¡‘ +°fŽ¡‘±shap‘ÿ}'esŽ‘0:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(µsŽ‘°¬);Ž¡‘ +°gŽŸ­272.‘ üAdd‘ÕTLabQÇel.Ž¦°h–ª¨¬Declare‘UU­PictureŽ‘,F·¬functions‘@¯263“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙopQÇeratorŽ‘N”Ž¬+=ŽŽŽ‘^"Ê(­LabQÇelŽ‘–¸°Ž‘$–¹±lab‘ÿ}'elŽ‘9 Q¬);ŽŸ­273.Ž¦°h–ª¨¬De ne‘UU­PictureŽ‘,F·¬functions‘@¯264“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙPictureŽ‘I™ê¬::Ž‘P((­opQÇeratorŽ‘{¾Ý¬+=ŽŽŽ’‹M(­LabQÇelŽ‘–¸°Ž‘$–¹±lab‘ÿ}'elŽ‘9 Q¬)Ž¡‘ +°fŽ¡‘±lab‘ÿ}'elsŽ‘,Tòµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(±lab‘ÿ}'elŽ‘t˜¬);Ž¡‘ +°gŽŸ­274.– üSuppress‘Ê•LabQÇels.“¬[²LDF‘T2002.04.25.¬]Ž‘[]yAdded–*˜this“function.‘ñ‘Sometimes“it's“irritating“to“ha•¸ãv“e‘*˜theŽ¡labšGels–½“when“a“­PictureŽ‘-3¬is“copied“and“transformed,‘×¢and“b˜oth“the“original“and“the“transformed“v¸ãersions“areŽ¡output.Ž¦°h–ª¨¬Declare‘UU­PictureŽ‘,F·¬functions‘@¯263“°i‘Ǭ+°Ž¡‘ +­inlineŽ‘)ŠIv®9oidŽ‘Bˆ!±suppr–ÿ}'ess‘‰ffŽ‘®lab“elsŽ’‚´S¬(‘ª®)Ž¡‘ +°fŽ¡‘±do‘‰ffŽ‘®lab‘ÿ}'elsŽ‘=ý¬=‘DZfalseŽ‘v\¬;Ž¡‘ +°gŽŸ­275.‘ üUnsuppress‘ÕTLabQÇels.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.12.20.¬]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­PictureŽ‘,F·¬functions‘@¯263“°i‘Ǭ+°Ž¡‘ +­inlineŽ‘)ŠIv®9oidŽ‘Bˆ!±unsuppr–ÿ}'ess‘‰ffŽ‘®lab“elsŽ’±w¬(‘ª®)Ž¡‘ +°fŽ¡‘±do‘‰ffŽ‘®lab‘ÿ}'elsŽ‘=ý¬=‘DZtrueŽ‘‹°¬;Ž¡‘ +°gŽŸ­276.‘ üKill‘ÕTLabQÇels.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.05.07.¬]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­PictureŽ‘,F·¬functions‘@¯263“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙ±kil‘‚Øl‘‰ffŽ‘®lab‘ÿ}'elsŽ‘LJˬ(‘ª®);ŽŽŽŒ‹J±þ Šn ý‘ì¬74–¯KILL‘ÕX­LABELS’‹‘¯3DLDF-1.1.5.1“°x¬277Ž €n ý•@P­277.ŽŸ°h–ª¨¬De ne‘UU­PictureŽ‘,F·¬functions‘@¯264“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘"ýÙPictureŽ‘I™ê¬::‘±kil‘‚Øl‘‰ffŽ‘®lab‘ÿ}'elsŽ‘*Lö¬(‘ª®)Ž¡‘ +°fŽ¡‘±lab‘ÿ}'elsŽ‘,Tòµ:±cle‘ÿ}'arŽ‘(Ù¬(‘ª¨);Ž¡‘ +°gŽ©­278.– üT‘ÿ +«ransformations.“¬T‘ÿ*ªransformations–Êyfor“­PicturesŽ‘3º;¬are“sa•¸ãv“ed–Êyup,‘'Áand“then“pGerformed“when“theŽ¡­PictureŽ‘(ñb¬is‘UUoutput.Ž¦­279.‘ üAne‘ÕTtransformations.Ž¦280.‘ üScale.ŽŸ°h–ª¨¬Declare‘UU­PictureŽ‘,F·¬functions‘@¯263“°i‘Ǭ+°Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓ±sc‘ÿ}'aleŽ‘W}Ŭ(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ gæ¬=‘Ç1Ž–ǵ;‘ª¨­realŽ‘]ÖµzŽ‘ < ¬=‘Ç1Ž“);Ž¦­281.ŽŸ°h–ª¨¬De ne‘UU­PictureŽ‘,F·¬functions‘@¯264“°i‘Ǭ+°Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓPictureŽ‘hdä¬::‘±sc‘ÿ}'aleŽ‘´ö¬(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ Î;‘ª¨­realŽ‘]ÖµzŽ‘tô¬)Ž¡‘ +°fŽ¡‘­returnŽ‘7æ¼±tr‘ÿ}'ansformŽ‘c™ýµ:±sc‘ÿ}'aleŽ‘´ò¬(µxŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁƬ);Ž¡‘ +°gŽ¦­282.– üShift.“¬(T‘ÿ*ªranslation.)Ž¦­283.‘ üreal‘ÕTv®9ersion.ŽŸ°h–ª¨¬Declare‘UU­PictureŽ‘,F·¬functions‘@¯263“°i‘Ǭ+°Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓ±shiftŽ‘UæP¬(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ gæ¬=‘Ç0Ž–ǵ;‘ª¨­realŽ‘]ÖµzŽ‘ < ¬=‘Ç0Ž“);Ž¦­284.‘ ü±shiftŽ‘y¬(‘ª®)–¨dreturns“a“­T‘ÿ +«ransformŽ‘;ÄE¬represenš¸ãting“the“shift,‘½(±not‘›<°Ž‘ ›=±thisŽ‘†ó¬.‘jõThis“mak˜es“it“pGossible“to“apply“theŽ¡transformation–UUto“other“ob‘Ž8jects.ŽŸ°h–ª¨¬De ne‘UU­PictureŽ‘,F·¬functions‘@¯264“°i‘Ǭ+°Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓPictureŽ‘hdä¬::‘±shiftŽ‘¬(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ Î;‘ª¨­realŽ‘]ÖµzŽ‘tô¬)Ž¡‘ +°fŽ¡‘­returnŽ‘7æ¼±tr‘ÿ}'ansformŽ‘c™ýµ:±shiftŽ‘}¬(µxŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁƬ);Ž¡‘ +°gŽ¦­285.› üP•®9oin“t‘¥lv“ersion.˜¬This–èäfunction“m¸ãust“de ned“in“®points.web¬,‘MÇbGecause“­P•®9oin“tŽ‘%l¬is“an“incompletelyŽ¡de ned–UUt¸ãypGe“here.ŽŸ°h–ª¨¬Declare‘UU­PictureŽ‘,F·¬functions‘@¯263“°i‘Ǭ+°Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓ±shiftŽ‘UæP¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié]¬);Ž¦­286.› üRotation–yaround“the“main“axes.˜±r‘ÿ}'otateŽ‘%ï:¬(‘ª®)–ã®will“pšGerform“rotation“ab˜out“the“x,‘Dy“and“z-axes“inŽ¡that–ô"order“if“called“with“mš¸ãultiple,‘“non-zero“argumen˜ts.‘QaRotation“only“abGout“the“y“and/or“z-axis“requires“oneŽ¡or›UUt•¸ãw“o˜dumm“y˜0˜argumen“ts˜so˜that˜±r‘ÿ}'otateŽ‘Ä“¬(‘ª®)˜\kno“ws"˜abGout˜whic“h˜axis˜(or˜axes)˜to˜rotate.ŽŸ°h–ª¨¬Declare‘UU­PictureŽ‘,F·¬functions‘@¯263“°i‘Ǭ+°Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓ±r‘ÿ}'otateŽ‘\8¬(­constŽ‘*¢realŽ‘4ÝеxŽ‘:”ì;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµyŽ‘>’ˆ¬=‘Ç0Ž–ǵ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµzŽ‘>f®¬=‘Ç0Ž“);ŽŽŽŒ‹Kº' Šn ý‘ì°x¬287‘¯3DLDF-1.1.5.1’¾ÃáRšÃŽOT–ÿJªA“TION–ÕXAR˜OUND“THE“MAIN“AXES‘¬75Ž €n ý•@P­287.Ž©°h–ª¨¬De ne‘UU­PictureŽ‘,F·¬functions‘@¯264“°i‘Ǭ+°Ž¤ ‘ +­T‘ÿ +«ransformŽ‘AÈÓPictureŽ‘hdä¬::‘±r‘ÿ}'otateŽ‘oB¬(­constŽ‘*¢realŽ‘4ÝеxŽ‘:”ì;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµyŽ‘;Ëp;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµzŽ‘;Ÿ–¬)Ž¡‘ +°fŽ¡‘­returnŽ‘7æ¼±tr‘ÿ}'ansformŽ‘c™ýµ:±r‘ÿ}'otateŽ‘o>¬(µxŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁƬ);Ž¡‘ +°gŽŸ­288.› üRotation–·×around“an“arbitrary“axis.˜¬[²LDF‘T2002.05.03.¬]Ž‘Zn’This–;±function“is“de ned“in“®points.web¬,Ž¡bGecause–UUit“has“­P•®9oin“tŽ›"Dò¬argumen¸ãts,“and“­P•®9oin“tŽ˜¬is“an“incomplete“t¸ãypGe“in“this“ le.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.05.03.¬]Ž‘Y;Added–UUthis“declaration.Ž¡‘ +[²LDF‘T2003.05.02.¬]Ž‘YËSChanged–mname“of“this“function“from“±r–ÿ}'otate‘‰ffŽ‘®ar“oundŽ‘@„ü¬(›ª®)“to“±r‘ÿ}'otateŽ‘‡«¬(˜).‘»This“function“no¸ãwŽ¡o•¸ãv“erloads‘UU±r‘ÿ}'otateŽ‘Ä“¬(‘ª®)–UUwith“three“­realŽ‘ƒ¬argumen¸ãts.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­PictureŽ‘,F·¬functions‘@¯263“°i‘Ǭ+°Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓ±r‘ÿ}'otateŽ‘\8¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±p0Ž‘Pøµ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±p1Ž‘R¢Åµ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±angleŽ‘Qã¬=‘Ç180ŽŽ‘Ç);Ž¡‘µ=°‘ÿý¬Remem¸ãbGer–UUto“add“shear!‘o°µ=ŽŸ­289.‘ üSet‘ÕTtransform.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.01.17.¬]Ž‘Y;Made–UUnon-inline“and“c¸ãhanged“µtŽ‘ +G¬from“plain“­T‘ÿ +«ransformŽ‘;'¬to“­constŽ‘!÷T‘ÿ +«ransformŽ‘YHɬ&Ž‘aç.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­PictureŽ‘,F·¬functions‘@¯263“°i‘Ǭ+°Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓ±set‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘},ù¬(­constŽ‘*¢T‘ÿ +«ransformŽ‘Uót¬&Ž‘]º’µtŽ‘aW¬);ŽŸ­290.Ž¦°h–ª¨¬De ne‘UU­PictureŽ‘,F·¬functions‘@¯264“°i‘Ǭ+°Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓPictureŽ‘hdä¬::‘±set‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘‡_¬::Ž‘E´PERSPŽ‘_Ûöµ;‘ª¨­realŽŽ¡‘±factorŽ‘> è¬=‘ 1Ž‘ -±;‘ª¨ÂconstŽ‘!0¨unsignedŽ‘RÃshortŽ‘qéÏsort‘‰ffŽ‘®valueŽ’¢Ý6«=‘ -ÂSortingŽ‘+tQ«::Ž‘2ÝMAX_ZŽ‘LÈè±;‘ª¨ÂconstŽ‘!0¨b•QÇo“olŽŽ¡‘Ïdo‘‰ffŽ‘®warningsŽ‘W»Ÿ«=‘†ÚÏtrueŽ‘Kr±;‘ª¨ÂconstŽ‘ HXrealŽ‘7n”Ïmin‘‰ffŽ–®x‘‰ffŽ“pr‘ÿ}'ojŽ‘jƼ«=‘†Ú·Ž‘ Mø«40ŽŽ‘Mú±;‘ª¨ÂconstŽ‘ HXrealŽ‘7n”Ïmax‘‰ffŽ–®x‘‰ffŽ“pr‘ÿ}'ojŽ‘kÖa«=‘†Ú40ŽŽ‘ †Ü±;‘ª¨ÂconstŽ‘ HXrealŽŽ¡‘Ïmin‘‰ffŽ–®y‘‰ffŽ“pr‘ÿ}'ojŽ‘QºD«=‘±}·Ž‘ x›«40ŽŽ–x±;‘ª¨ÂconstŽ‘ aîrealŽ‘7¡ÀÏmax‘‰ffŽ–®y‘‰ffŽ“pr‘ÿ}'ojŽ‘lk¦«=‘±}40ŽŽ‘ ±±;‘ª¨ÂconstŽ‘ aîrealŽ‘7¡ÀÏmin‘‰ffŽ–®z‘‰ffŽ“pr‘ÿ}'ojŽ‘j—¾«=‘±}·Ž‘ x›«40ŽŽ“±;‘ª¨ÂconstŽ‘ aîrealŽŽ¡‘Ïmax‘‰ffŽ–®z‘‰ffŽ“pr‘ÿ}'ojŽ‘QA«=‘Ç40ŽŽ‘ Ç);Ž¦Â254.‘ üNo–ÕTF‘ÿ -«oQÇcus“argumen®9t.ŽŸ·h–ª¨«Declare‘UUÂPictureŽ‘,F·«functions‘@­218“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘#ç«ÏoutputŽ‘@öë«(ÂconstŽ‘tunsignedŽ‘P5TshortŽ‘néÉÏpr‘ÿ}'ojŽ’†*U«=‘LÉÂPro‘£ŽjectionsŽ‘?-«::Ž‘E§kÝPERSPŽ‘`mı;‘ª¨ÂrealŽ‘G¨ÏfactorŽ‘8˜O«=‘LÉ1Ž‘ Lʱ;‘ª¨ÂconstŽŽ¡‘unsignedŽ‘Nª1shortŽ‘lçôÏsort‘‰ffŽ‘®valueŽ’œY«=‘†÷ÂSortingŽ‘)ñA«::Ž‘0ÝMAX_ZŽ‘KEر;‘ª¨ÂconstŽ‘ Hjb•QÇo“olŽ‘:\ðÏdo‘‰ffŽ‘®warningsŽ‘t©«=‘†÷ÏtrueŽ‘K±;‘ª¨ÂconstŽ‘ HjrealŽŽ¡‘Ïmin‘‰ffŽ–®x‘‰ffŽ“pr‘ÿ}'ojŽ‘Q€é«=‘¯˜·Ž‘ v¶«40ŽŽ–v¸±;‘ª¨ÂconstŽ‘ `ÊrealŽ‘7ŸxÏmax‘‰ffŽ–®x‘‰ffŽ“pr‘ÿ}'ojŽ‘l0«=‘¯˜40ŽŽ‘ ¯š±;‘ª¨ÂconstŽ‘ `ÊrealŽ‘7ŸxÏmin‘‰ffŽ–®y‘‰ffŽ“pr‘ÿ}'ojŽ‘kWÔ«=‘¯˜·Ž‘ v¶«40ŽŽ“±;‘ª¨ÂconstŽ‘ `ÊrealŽŽ¡‘Ïmax‘‰ffŽ–®y‘‰ffŽ“pr‘ÿ}'ojŽ‘Qß„«=‘Ç40ŽŽ– DZ;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆxÏmin‘‰ffŽ–®z‘‰ffŽ“pr‘ÿ}'ojŽ‘h”«=‘Ç·Ž‘ -Ž6«40ŽŽ‘Ž8±;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆxÏmax‘‰ffŽ–®z‘‰ffŽ“pr‘ÿ}'ojŽ‘i£¶«=‘Ç40ŽŽ“);Ž¦Â255.– üClear.“«De ned–UUin“Èpoints.web«.ŽŸ·h–ª¨«Declare‘UUÂPictureŽ‘,F·«functions‘@­218“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙÏcle‘ÿ}'arŽ‘9&²«(‘ª®);Ž¦Â256.– üReset‘ÕTtransform.“«[¬LDF‘T2002.04.17.«]Ž‘Zˆ6Added–UUthis“function.ŽŸ·h–ª¨«Declare‘UUÂPictureŽ‘,F·«functions‘@­218“·i‘Ç«+·Ž¡‘ -ÂinlineŽ‘)ŠIv®9oidŽ‘Bˆ!Ïr–ÿ}'eset‘‰ffŽ‘®tr“ansformŽ’†:z«(‘ª®)Ž¡‘ -·fŽ¡‘Ïtr‘ÿ}'ansformŽ‘?³C±:Ïr‘ÿ}'esetŽ‘Æ·«(‘ª¨);Ž¡‘ -·gŽ¦Â257.‘ üGlobal‘ÕTv‘ÿ\rariables.ŽŸ·h–ª¨«Global‘UUv‘ÿqÇariables‘@­15“·i‘Ç«+·Ž¡‘ -ÂPictureŽ‘2ñcÏcurr–ÿ}'ent‘‰ffŽ‘®pictur“eŽ‘u*«;Ž¦Â258.ŽŸ·h›ª¨«Declarations–UUfor“the“header“ le‘@­18˜·i‘Ç«+·Ž¡‘ -ÂexternŽ‘.×PictureŽ‘W9Ïcurr–ÿ}'ent‘‰ffŽ‘®pictur“eŽ’™5«;Ž¦Â259.‘ üPutting–ÕTPicture“and“LabQÇel“together.ŽŽŽŒ‹Déx Šn ý‘ì«68›­PUTTING–ÕXÂPICTURE“­AND“ÂLABEL“­TOGETHER’“ þ3DLDFPRÃŽG˜·x«260Ž €n ý•@PÂ260.‘ ü«This–UUis“what's“compiled.ŽŸ‘ -·h–ª¨«Include‘UU les‘@­11“·iŽ¤ ‘ -h‘ª¨«V‘ÿ*ªersion–UUconš¸ãtrol“iden˜ti er‘@­10‘ª¨·iŽ¡‘ -h›ª¨«Declare–UUnamespace“ÂPro‘£ŽjectionsŽ‘Aa¹­211˜·iŽ¡‘ -h›ª¨«Declare–UUnamespace“ÂSortingŽ‘,ÿŸ­213˜·iŽ¡‘ -h–ª¨«De ne‘UUclasses‘@­208“·iŽ¡‘ -h–ª¨«Initialize‘UUÂstaticŽ‘"ž.LabQÇelŽ‘B4æ«data‘UUmem¸ãbGers‘@­209“·iŽ¡‘ -h–ª¨«Global‘UUv‘ÿqÇariables‘@­15“·iŽ¡‘ -h–ª¨«De ne‘UUÂPictureŽ‘,F·«functions‘@­219“·iŽŽŽŒ‹Eû; Šn ý‘ì·x«261›­3DLDFPRÃŽG’“ þPUTTING–ÕXÂPICTURE“­AND“ÂLABEL“­TOGETHER˜«69Ž €n ý•@PÂ261.‘ ü«This–UUis“what's“written“to“Èpictures.h«.Ž©·h‘ª¨Ýpictures.hŽ‘@0ó­261‘ª¨·i‘ÇŽ¤ ‘ -h‘ª¨ÂexternŽ‘%È~«declaration–UUof“namespace“ÂPro‘£ŽjectionsŽ‘Aa¹­212‘ª¨·iŽ¡‘ -h‘ª¨ÂexternŽ‘%È~«declaration–UUof“namespace“ÂSortingŽ‘,ÿŸ­214‘ª¨·iŽ¡‘ -h–ª¨«De ne‘UUclasses‘@­208“·iŽ¡‘ -h›ª¨«Declarations–UUfor“the“header“ le‘@­18˜·iŽŸÂ262.› üP•®9oin“t˜(Èpoints.webÂ).Ž¡‘ -«[¬LDF‘T2002.10.20.«]Ž‘Y¤ÂP•®9oin“tŽ‘x ª«is–_¾the“most“basic“dra•¸ãw“able–_¾(not“ llable!)–‘tš¸ãypGe.“All–_¾of“the“other“ÂShapQÇesŽ‘*4Å«con˜tainŽ¡ÂP•®9oin“tsŽ‘%r«and–Üîare“ultimately“de ned“b¸ãy“their“ÂP•®9oin“tsŽ‘)Ý`«and“the“relationships“among“them.‘ “It“is“thereforeŽ¡understandable–yythat“Èpoints.web“«is“b¸ãy“far“the“largest“of“the“source“ les“of“3DLDF‘ypand“that“ÂP•®9oin“tŽ‘":«has“theŽ¡most–]ÿfunctions“of“anš¸ãy“class“in“3DLDF.“Man˜y“of“the“functions“in“the“other“classes“do“little“more“than“applyŽ¡the‘UUÂP•®9oin“tŽ‘"Dò«v¸ãersion–UUof“the“function“to“their“ÂP•®9oin“tsŽ‘#xÙ«.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.11.12.«]Ž‘ZCáRemo•¸ãv“ed–ûthe“vš¸ãersion“con˜trol“iden˜ti ers“from“the“CWEB‘© les“for“the“distribution“ofŽ¡3DLDF–UU1.1.‘qÇThey're“still“used“in“mš¸ãy“dev˜elopmen˜t“v˜ersions.Ž¡‘ -[¬LDF‘T2003.12.10.«]Ž‘YQ‘Put–ž«the“vš¸ãersion“con˜trol“iden˜ti ers“bac˜k“in˜to“m˜y“release“v˜ersions“for“3DLDF‘ž™1.1.4.‘MÊI'v˜eŽ¡already–"¯put“some“of“them“bacš¸ãk“in,‘,Ñno˜w“I'm“doing“the“rest“of“them.‘`åHo˜w˜ev˜er,‘,Ñthe“release“v˜ersions“are“no˜w“inŽ¡their–UUoš¸ãwn“R˜CS“repGository‘ÿ*ª.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h‘ª¨«V‘ÿ*ªersion–UUconš¸ãtrol“iden˜ti er‘@­10‘ª¨·i‘Ç«+·Ž¡‘ -ÂstaticŽ‘)HÚstringŽ‘Jn'Ïr‘ÿ}'cs‘‰ffŽ‘®idŽ‘g(«=‘ÇÝ"$Id:È Ýpoints.web,vÈ Ý1Ž‘kÆÜ.3È Ý2003/12/10È Ý16:21:Ž’ÔÆ 48È Ýlfinsto1È ÝExpÈ Ý$"Ž’3ÌÒ«;ŽŸÂ263.‘ üInclude‘ÕT les.Ž¦·h–ª¨«Include‘UU les‘@­11“·i‘Ç«+·Ž¡«#ÂincludeŽ‘'Ø~Ý"loader.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"pspglb.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"io.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"colors.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"transfor.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"shapes.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"pictures.h"ŽŽŸÂ264.› üP•®9oin“t–ÕTclass“de nition.˜«[¬LDF‘T2002.10.20.«]ŽŽ¡·Ž‘ -Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘ZiT«con¸ãtains–UUthe“cošGordinates“of“the“ÂP•®9oin“tŽ‘"Dò«in“the“global“co˜ordinate“system.Ž¡·Ž‘ -Ïuser‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘U w«and‘UUÏview‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘OY«are–UUnot“curren¸ãtly“used.Ž¡·Ž‘ -Ïuser‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘T»<«is–inš¸ãtended“for“use“with“a“user-de ned“coGordinate“system.‘W F‘ÿ*ªor“example,‘&it“ma˜y“bGe“con˜v˜e-Ž¡‘ +µ;‘ª¨­constŽ‘!0¨unsignedŽ‘RÃshortŽ‘qé±sort‘‰ffŽ‘®valueŽ’¢Ý6¬=‘ +­SortingŽ‘+tQ¬::Ž‘2´MAX_ZŽ‘LÈèµ;‘ª¨­constŽ‘!0¨b•QÇo“olŽŽ¡‘±do‘‰ffŽ‘®warningsŽ‘W»Ÿ¬=‘†Ú±trueŽ‘Krµ;‘ª¨­constŽ‘ HXrealŽ‘7n”±min‘‰ffŽ–®x‘‰ffŽ“pr‘ÿ}'ojŽ‘jƼ¬=‘†Ú°Ž‘ Mø¬40ŽŽ‘Múµ;‘ª¨­constŽ‘ HXrealŽ‘7n”±max‘‰ffŽ–®x‘‰ffŽ“pr‘ÿ}'ojŽ‘kÖa¬=‘†Ú40ŽŽ‘ †Üµ;‘ª¨­constŽ‘ HXrealŽŽ¡‘±min‘‰ffŽ–®y‘‰ffŽ“pr‘ÿ}'ojŽ‘QºD¬=‘±}°Ž‘ x›¬40ŽŽ–xµ;‘ª¨­constŽ‘ aîrealŽ‘7¡À±max‘‰ffŽ–®y‘‰ffŽ“pr‘ÿ}'ojŽ‘lk¦¬=‘±}40ŽŽ‘ ±µ;‘ª¨­constŽ‘ aîrealŽ‘7¡À±min‘‰ffŽ–®z‘‰ffŽ“pr‘ÿ}'ojŽ‘j—¾¬=‘±}°Ž‘ x›¬40ŽŽ“µ;‘ª¨­constŽ‘ aîrealŽŽ¡‘±max‘‰ffŽ–®z‘‰ffŽ“pr‘ÿ}'ojŽ‘QA¬=‘Ç40ŽŽ‘ Ç);Ž¦­299.‘ üNo–ÕTF‘ÿ +«oQÇcus“argumen®9t.ŽŸ°h–ª¨¬Declare‘UU­PictureŽ‘,F·¬functions‘@¯263“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘#竱outputŽ‘@öë¬(­constŽ‘tunsignedŽ‘P5TshortŽ‘néɱpr‘ÿ}'ojŽ’†*U¬=‘LÉ­Pro‘£ŽjectionsŽ‘?-¬::Ž‘E§k´PERSPŽ‘`mĵ;‘ª¨­realŽ‘G¨±factorŽ‘8˜O¬=‘LÉ1Ž‘ Lʵ;‘ª¨­constŽŽ¡‘unsignedŽ‘Nª1shortŽ‘lçô±sort‘‰ffŽ‘®valueŽ’œY¬=‘†÷­SortingŽ‘)ñA¬::Ž‘0´MAX_ZŽ‘KEص;‘ª¨­constŽ‘ Hjb•QÇo“olŽ‘:\ð±do‘‰ffŽ‘®warningsŽ‘t©¬=‘†÷±trueŽ‘Kµ;‘ª¨­constŽ‘ HjrealŽŽ¡‘±min‘‰ffŽ–®x‘‰ffŽ“pr‘ÿ}'ojŽ‘Q€é¬=‘¯˜°Ž‘ v¶¬40ŽŽ–v¸µ;‘ª¨­constŽ‘ `ÊrealŽ‘7Ÿx±max‘‰ffŽ–®x‘‰ffŽ“pr‘ÿ}'ojŽ‘l0¬=‘¯˜40ŽŽ‘ ¯šµ;‘ª¨­constŽ‘ `ÊrealŽ‘7Ÿx±min‘‰ffŽ–®y‘‰ffŽ“pr‘ÿ}'ojŽ‘kWÔ¬=‘¯˜°Ž‘ v¶¬40ŽŽ“µ;‘ª¨­constŽ‘ `ÊrealŽŽ¡‘±max‘‰ffŽ–®y‘‰ffŽ“pr‘ÿ}'ojŽ‘Qß„¬=‘Ç40ŽŽ– ǵ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±min‘‰ffŽ–®z‘‰ffŽ“pr‘ÿ}'ojŽ‘h”¬=‘Ç°Ž‘ +Ž6¬40ŽŽ‘Ž8µ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±max‘‰ffŽ–®z‘‰ffŽ“pr‘ÿ}'ojŽ‘i£¶¬=‘Ç40ŽŽ“);Ž¦­300.– üClear.“¬De ned–UUin“®points.web¬.ŽŸ°h–ª¨¬Declare‘UU­PictureŽ‘,F·¬functions‘@¯263“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙ±cle‘ÿ}'arŽ‘9&²¬(‘ª®);Ž¦­301.– üReset‘ÕTtransform.“¬[²LDF‘T2002.04.17.¬]Ž‘Zˆ6Added–UUthis“function.ŽŸ°h–ª¨¬Declare‘UU­PictureŽ‘,F·¬functions‘@¯263“°i‘Ǭ+°Ž¡‘ +­inlineŽ‘)ŠIv®9oidŽ‘Bˆ!±r–ÿ}'eset‘‰ffŽ‘®tr“ansformŽ’†:z¬(‘ª®)Ž¡‘ +°fŽ¡‘±tr‘ÿ}'ansformŽ‘?³Cµ:±r‘ÿ}'esetŽ‘Æ·¬(‘ª¨);Ž¡‘ +°gŽ¦­302.‘ üGlobal‘ÕTv‘ÿ\rariables.ŽŸ°h–ª¨¬Global‘UUv‘ÿqÇariables‘@¯18“°i‘Ǭ+°Ž¡‘ +­PictureŽ‘2ñc±curr–ÿ}'ent‘‰ffŽ‘®pictur“eŽ‘u*¬;Ž¦­303.ŽŸ°h›ª¨¬Declarations–UUfor“the“header“ le‘@¯21˜°i‘Ǭ+°Ž¡‘ +­externŽ‘.×PictureŽ‘W9±curr–ÿ}'ent‘‰ffŽ‘®pictur“eŽ’™5¬;Ž¦­304.‘ üPutting–ÕTPicture“and“LabQÇel“together.ŽŽŽŒ‹NØa Šn ý‘ì¬78›¯PUTTING–ÕX­PICTURE“¯AND“­LABEL“¯TOGETHER’Š­h3DLDF-1.1.5.1˜°x¬305Ž €n ý•@P­305.‘ ü¬This–UUis“what's“compiled.ŽŸ‘ +°h–ª¨¬Include‘UU les‘@¯6“°iŽ¤ ‘ +h‘ª¨¬V‘ÿ*ªersion–UUconš¸ãtrol“iden˜ti er‘@¯5‘ª¨°iŽ¡‘ +h›ª¨¬Declare–UUnamespace“­Pro‘£ŽjectionsŽ‘Aa¹¯256˜°iŽ¡‘ +h›ª¨¬Declare–UUnamespace“­SortingŽ‘,ÿŸ¯258˜°iŽ¡‘ +h–ª¨¬De ne‘UUclasses‘@¯253“°iŽ¡‘ +h–ª¨¬Initialize‘UU­staticŽ‘"ž.LabQÇelŽ‘B4æ¬data‘UUmem¸ãbGers‘@¯254“°iŽ¡‘ +h–ª¨¬Global‘UUv‘ÿqÇariables‘@¯18“°iŽ¡‘ +h–ª¨¬De ne‘UU­PictureŽ‘,F·¬functions‘@¯264“°iŽŽŽŒ‹Oê( Šn ý‘ì°x¬306›¯3DLDF-1.1.5.1’Š­hPUTTING–ÕX­PICTURE“¯AND“­LABEL“¯TOGETHER˜¬79Ž €n ý•@P­306.‘ ü¬This–UUis“what's“written“to“®pictures.h¬.Ž©°h‘ª¨´pictures.hŽ‘@0ó¯306‘ª¨°i‘ÇŽ¤ ‘ +h‘ª¨­externŽ‘%È~¬declaration–UUof“namespace“­Pro‘£ŽjectionsŽ‘Aa¹¯257‘ª¨°iŽ¡‘ +h‘ª¨­externŽ‘%È~¬declaration–UUof“namespace“­SortingŽ‘,ÿŸ¯259‘ª¨°iŽ¡‘ +h–ª¨¬De ne‘UUclasses‘@¯253“°iŽ¡‘ +h›ª¨¬Declarations–UUfor“the“header“ le‘@¯21˜°iŽŸ­307.› üP•®9oin“t˜(®points.web­).Ž¡‘ +¬[²LDF‘T2002.10.20.¬]Ž‘Y¤­P•®9oin“tŽ‘x ª¬is–_¾the“most“basic“dra•¸ãw“able–_¾(not“ llable!)–‘tš¸ãypGe.“All–_¾of“the“other“­ShapQÇesŽ‘*4Ŭcon˜tainŽ¡­P•®9oin“tsŽ‘%r¬and–Üîare“ultimately“de ned“b¸ãy“their“­P•®9oin“tsŽ‘)Ý`¬and“the“relationships“among“them.‘ “It“is“thereforeŽ¡understandable–yythat“®points.web“¬is“b¸ãy“far“the“largest“of“the“source“ les“of“3DLDF‘ypand“that“­P•®9oin“tŽ‘":¬has“theŽ¡most–]ÿfunctions“of“anš¸ãy“class“in“3DLDF.“Man˜y“of“the“functions“in“the“other“classes“do“little“more“than“applyŽ¡the‘UU­P•®9oin“tŽ‘"Dò¬v¸ãersion–UUof“the“function“to“their“­P•®9oin“tsŽ‘#xÙ¬.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.11.12.¬]Ž‘ZCáRemo•¸ãv“ed–ûthe“vš¸ãersion“con˜trol“iden˜ti ers“from“the“CWEB‘© les“for“the“distribution“ofŽ¡3DLDF–UU1.1.‘qÇThey're“still“used“in“mš¸ãy“dev˜elopmen˜t“v˜ersions.Ž¡‘ +[²LDF‘T2003.12.10.¬]Ž‘YQ‘Put–ž«the“vš¸ãersion“con˜trol“iden˜ti ers“bac˜k“in˜to“m˜y“release“v˜ersions“for“3DLDF‘ž™1.1.4.‘MÊI'v˜eŽ¡already–"¯put“some“of“them“bacš¸ãk“in,‘,Ñno˜w“I'm“doing“the“rest“of“them.‘`åHo˜w˜ev˜er,‘,Ñthe“release“v˜ersions“are“no˜w“inŽ¡their–UUoš¸ãwn“R˜CS“repGository‘ÿ*ª.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h‘ª¨¬V‘ÿ*ªersion–UUconš¸ãtrol“iden˜ti er‘@¯5‘ª¨°i‘Ǭ+°Ž¡‘ +­staticŽ‘)HÚstringŽ‘Jn'±r‘ÿ}'cs‘‰ffŽ‘®idŽ‘g(¬=‘Ç´"$Id:® ´points.web,v® ´1Ž‘kÆÜ.6® ´2004/01/12® ´21:32:Ž’ÔÆ 01® ´lfinsto1® ´Exp® ´$"Ž’3ÌÒ¬;ŽŸ­308.‘ üInclude‘ÕT les.Ž¦°h–ª¨¬Include‘UU les‘@¯6“°i‘Ǭ+°Ž¡¬#­includeŽ‘'Ø~´"loader.h"ŽŽ¡¬#­includeŽ‘'Ø~´"pspglb.h"ŽŽ¡¬#­includeŽ‘'Ø~´"creatnew.h"ŽŽ¡¬#­includeŽ‘'Ø~´"io.h"ŽŽ¡¬#­includeŽ‘'Ø~´"colors.h"ŽŽ¡¬#­includeŽ‘'Ø~´"transfor.h"ŽŽ¡¬#­includeŽ‘'Ø~´"shapes.h"ŽŽ¡¬#­includeŽ‘'Ø~´"pictures.h"ŽŽŸ­309.› üP•®9oin“t–ÕTclass“de nition.˜¬[²LDF‘T2002.10.20.¬]ŽŽ¡°Ž‘ +±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘ZiT¬con¸ãtains–UUthe“cošGordinates“of“the“­P•®9oin“tŽ‘"Dò¬in“the“global“co˜ordinate“system.Ž¡°Ž‘ +±user‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘U w¬and‘UU±view‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘OY¬are–UUnot“curren¸ãtly“used.Ž¡°Ž‘ +±user‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘T»<¬is–inš¸ãtended“for“use“with“a“user-de ned“coGordinate“system.‘W F‘ÿ*ªor“example,‘&it“ma˜y“bGe“con˜v˜e-Ž¡‘ nienš¸ãt–@âto“de ne“a“coGordinate“system“based“on“a“plane“de ned“b˜y“an“ob‘Ž8ject“in“a“dra˜wing.‘jöThe“user-de nedŽ¡‘ -cošGordinate–:ysystem“will“b˜e“de ned“in“terms“of“the“global“co˜ordinate“system“and“the“Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Sˆð«canŽ¡‘ -bGe–UUderivš¸ãed“from“the“Ïuser‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘N`Ë«b˜y“using“the“appropriate“transformation.Ž¡·Ž‘ -Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘k]:«is–§&used“for“pro‘Ž8jecting“the“three-dimensional“ÂP•®9oin“tsŽ‘%qЫonš¸ãto“t˜w˜o-dimensions“for“output.Ž¡‘ +cošGordinate–:ysystem“will“b˜e“de ned“in“terms“of“the“global“co˜ordinate“system“and“the“±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Sˆð¬canŽ¡‘ +bGe–UUderivš¸ãed“from“the“±user‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘N`ˬb˜y“using“the“appropriate“transformation.Ž¡°Ž‘ +±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘k]:¬is–§&used“for“pro‘Ž8jecting“the“three-dimensional“­P•®9oin“tsŽ‘%qЬonš¸ãto“t˜w˜o-dimensions“for“output.Ž¡‘ Currenš¸ãtly‘ÿ*ª,‘÷½the–×Bonly“pro‘Ž8jection“routines“are“for“p•Gersp“ectiv˜e–×Band“parallel“pro‘Ž8jection.‘÷I‘× plan“to“add“othersŽ¡‘ -(axionometric,‘UUetc.)‘qÇsoGon.Ž¡·Ž‘ -Ïtr‘ÿ}'ansformŽ‘8yå«is–Æ£used“for“storing“the“transformations“that“are“applied“the“ÂP•®9oin“tŽ‘`ë«.‘B7It“is“not“necessary“to“upGdateŽ¡‘ -Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘[I-«(or‘5.Ïuser‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘KëO«,‘m#if–5.they're“bGeing“used)“ev¸ãery“time“a“ÂP•®9oin“tŽ‘$¤«is“transformed.‘QTheŽ¡‘ -transformations–¨÷can“bšGe“sa•¸ãv“ed–¨÷up“and“their“result“applied“to“the“ÂP•®9oin“tŽ‘"ì6«when“needed.‘l­This“will“b˜e“whenŽ¡‘ -the‘m‚ÂP•®9oin“tŽ‘"uL«or–m‚the“ÂShapQÇeŽ‘%Ç«or“ÂLabQÇelŽ‘#g«conš¸ãtaining“it“is“output,‘sor“when“a“function“(suc˜h“as“Ïget‘‰ffŽ‘®xŽ‘ûé«(‘ª®))“requiresŽ¡‘ -up-to-date–UUcoGordinate“v‘ÿqÇalues.Ž¡·Ž‘ -Ïdr‘ÿ}'awdot‘‰ffŽ‘®valueŽ‘GJÊ«,‘Ïdr–ÿ}'awdot‘‰ffŽ‘®c“olorŽ‘C•œ«,‘and‘\KÏp‘ÿ}'enŽ‘ÒI«are–\Kused“in“the“draš¸ãwing“and“undra˜wing“functions“and“inŽ¡‘ -ÂP•®9oin“tŽ‘&šM«::‘ÏoutputŽ‘D«(‘ª®).‘qÇThey–UUare“explained“bGelo¸ãw.ŽŽŽŒ‹Fý¹ Šn ý‘ì«70›ÂPOINT–ÕX­CLASS“DEFINITION’ì~é3DLDFPRÃŽG˜·x«264Ž €n ý•@P·Ž‘ -Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘bç«is–Œ•used“in“outputting“ÂPicturesŽ‘.±Þ«.‘ˆIt's“for“culling“ÂP•®9oin“tsŽ‘)<®«that“are“in¸ãvisible“using“aŽ¤ ‘ -particular‘UUÂF‘ÿ -«oQÇcusŽ‘ J¡«,–UUor“that“lie“outside“the“bGoundaries“passed“as“argumen¸ãts“to“ÂPictureŽ‘)ñf«::‘ÏoutputŽ‘D«(‘ª®).Ž¡·Ž‘ -Ïdo‘‰ffŽ‘®outputŽ‘8Ä«is–Íçfor“enabling“or“suppressing“output“of“a“ÂP•®9oin“tŽ‘h/«.‘Û|It's“needed“when“a“ÂP•®9oin“tŽ‘#6«has“bGeen“culled,Ž¡‘ -as–X describšGed“ab˜o•¸ãv“e.‘yäCulling–X do˜es“not“actually“remo•¸ãv“e–X a“ÂP•®9oin“tŽ‘"JZ«(or“an¸ãy“other“ÂShapQÇeŽ‘"D«)“from“a“ÂPictureŽ‘(ô«,‘X¶soŽ¡‘ +(axionometric,‘UUetc.)‘qÇsoGon.Ž¡°Ž‘ +±tr‘ÿ}'ansformŽ‘8yå¬is–Æ£used“for“storing“the“transformations“that“are“applied“the“­P•®9oin“tŽ‘`ë¬.‘B7It“is“not“necessary“to“upGdateŽ¡‘ +±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘[I-¬(or‘5.±user‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘KëO¬,‘m#if–5.they're“bGeing“used)“ev¸ãery“time“a“­P•®9oin“tŽ‘$¤¬is“transformed.‘QTheŽ¡‘ +transformations–¨÷can“bšGe“sa•¸ãv“ed–¨÷up“and“their“result“applied“to“the“­P•®9oin“tŽ‘"ì6¬when“needed.‘l­This“will“b˜e“whenŽ¡‘ +the‘m‚­P•®9oin“tŽ‘"uL¬or–m‚the“­ShapQÇeŽ‘%Ǭor“­LabQÇelŽ‘#g¬conš¸ãtaining“it“is“output,‘sor“when“a“function“(suc˜h“as“±get‘‰ffŽ‘®xŽ‘ûé¬(‘ª®))“requiresŽ¡‘ +up-to-date–UUcoGordinate“v‘ÿqÇalues.Ž¡°Ž‘ +±dr‘ÿ}'awdot‘‰ffŽ‘®valueŽ‘GJʬ,‘±dr–ÿ}'awdot‘‰ffŽ‘®c“olorŽ‘C•œ¬,‘and‘\K±p‘ÿ}'enŽ‘ÒI¬are–\Kused“in“the“draš¸ãwing“and“undra˜wing“functions“and“inŽ¡‘ +­P•®9oin“tŽ‘&šM¬::‘±outputŽ‘D¬(‘ª®).‘qÇThey–UUare“explained“bGelo¸ãw.ŽŽŽŒ‹P즠Šn ý‘ì¬80›­POINT–ÕX¯CLASS“DEFINITION’ä S3DLDF-1.1.5.1˜°x¬309Ž €n ý•@P°Ž‘ +±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘bç¬is–Œ•used“in“outputting“­PicturesŽ‘.±Þ¬.‘ˆIt's“for“culling“­P•®9oin“tsŽ‘)<®¬that“are“in¸ãvisible“using“aŽ¤ ‘ +particular‘UU­F‘ÿ +«oQÇcusŽ‘ J¡¬,–UUor“that“lie“outside“the“bGoundaries“passed“as“argumen¸ãts“to“­PictureŽ‘)ñf¬::‘±outputŽ‘D¬(‘ª®).Ž¡°Ž‘ +±do‘‰ffŽ‘®outputŽ‘8Ĭis–Íçfor“enabling“or“suppressing“output“of“a“­P•®9oin“tŽ‘h/¬.‘Û|It's“needed“when“a“­P•®9oin“tŽ‘#6¬has“bGeen“culled,Ž¡‘ +as–X describšGed“ab˜o•¸ãv“e.‘yäCulling–X do˜es“not“actually“remo•¸ãv“e–X a“­P•®9oin“tŽ‘"JZ¬(or“an¸ãy“other“­ShapQÇeŽ‘"D¬)“from“a“­PictureŽ‘(ô¬,‘X¶soŽ¡‘ a›]Æw•¸ãa“y˜of˜suppressing˜output˜is˜needed.‘‹Ho“w“ev“er,‘_ãit˜m“ust˜b•Ge˜p“ossible˜to˜enable˜output˜again,‘_ãb“ecause˜theŽ¡‘ -ÂPictureŽ‘2ñc«maš¸ãy–UUbGe“output“again“using“a“di eren˜t“ÂF‘ÿ -«oQÇcusŽ‘#Ÿö«and/or“di eren˜t“v‘ÿqÇalues“for“the“bGoundaries.Ž¡·Ž‘ -Ïme–ÿ}'asur“ement‘‰ffŽ‘®unitsŽ‘`G#«is–ðNa“ÂstringŽ‘#°”«that“is“attacš¸ãhed“to“the“n˜umerical“v‘ÿqÇalues“of“the“Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘d–¯«whenŽ¡‘ -the–7¼MET‘ÿ*ªAPOST‘7´coGde“is“output“to“Ïout‘‰ffŽ‘®str–ÿ}'e“amŽ‘2xX«.‘géIt“is“currenš¸ãtly“Ý"cm"Ž‘õÔ«and“at“the“presen˜t“time“(2002.10.20),Ž¡‘ +­PictureŽ‘2ñc¬maš¸ãy–UUbGe“output“again“using“a“di eren˜t“­F‘ÿ +«oQÇcusŽ‘#Ÿö¬and/or“di eren˜t“v‘ÿqÇalues“for“the“bGoundaries.Ž¡°Ž‘ +±me–ÿ}'asur“ement‘‰ffŽ‘®unitsŽ‘`G#¬is–ðNa“­stringŽ‘#°”¬that“is“attacš¸ãhed“to“the“n˜umerical“v‘ÿqÇalues“of“the“±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘d–¯¬whenŽ¡‘ +the–7¼MET‘ÿ*ªAPOST‘7´coGde“is“output“to“±out‘‰ffŽ‘®str–ÿ}'e“amŽ‘2xX¬.‘géIt“is“currenš¸ãtly“´"cm"Ž‘õÔ¬and“at“the“presen˜t“time“(2002.10.20),Ž¡‘ it's–1}not“a“go•Go“d–1}idea“to“use“more“than“one“v‘ÿqÇalue“for“a“single“dra¸ãwing.‘?Changing“this“will“only“bGecomeŽ¡‘ -urgen¸ãt–UUwhen“I“start“writing“the“input“routine.‘qÇTO“DO.ŽŸ¿åŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.04.01.«]Ž‘YR\Added‘ŸvÝWORLD_VALUESŽ‘C%º«,‘±þÝPROJ_VALUESŽ–=øE«,‘±þÝUSER_VALUESŽ“«,‘±þand‘ŸvÝVIEW_VALUESŽ‘=彫.‘P*They–Ÿvare“usedŽ¡in‘UUÏlab‘ÿ}'elŽ‘Éí«(‘ª®)–UUfor“labGelling“ÂP•®9oin“tsŽ‘&Î.«using“the“v‘ÿqÇalues“in“Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘PiS«,“Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘b h«,“etc.Ž¡‘ -[¬LDF‘T2003.05.06.«]Ž‘YDÛChanged‘‘õÝWORLD_VALUEŽ‘=Ø<«,‘¡ÝPROJ_VALUEŽ–8§h«,‘¡ÝUSER_VALUEŽ“«,‘¡and‘‘õÝVIEW_VALUEŽ‘<*4«to‘‘õÝWORLD_VALUESŽ‘C9«,Ž¡ÝPROJ_VALUESŽ‘:FG«,‘UUÝUSER_VALUESŽ›=›œ«,–UUand“ÝVIEW_VALUESŽ˜«.‘qÇAdded“ÝWORLD_VALUES_X_YŽ‘WÛ«,“ÝPROJ_VALUES_X_YŽ‘R›«,Ž¡ÝUSER_VALUES_X_YŽ‘OF;«,–UUand“ÝVIEW_VALUES_X_YŽ‘Uðå«for“suppressing“the“z-coGordinate.Ž¡‘ -[¬LDF‘T2003.05.20.«]Ž‘Y;Added‘UUÝWORLD_VALUES_ZŽ‘M[“«.ŽŸŸüÈ„`ÕÁGŽŽ¤ó‘ -ÂformatŽ‘3c(ÏPointŽ‘UøShap‘ÿ}'eŽŽ¡·h–ª¨«De ne‘UUÂclassŽ‘5¦P•®9oin“tŽ‘>ò­264“·i‘ÇŽ¤ ‘ -ÂclassŽ‘$àRP•®9oin“tŽ‘CÏï«:‘qÇÂprotectedŽ‘86´ShapQÇeŽ‘Zx·fŽ¡‘ÂfriendŽ‘5f¼T‘ÿ +urgen¸ãt–UUwhen“I“start“writing“the“input“routine.‘qÇTO“DO.ŽŸ¿åŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.04.01.¬]Ž‘YR\Added‘Ÿv´WORLD_VALUESŽ‘C%º¬,‘±þ´PROJ_VALUESŽ–=øE¬,‘±þ´USER_VALUESŽ“¬,‘±þand‘Ÿv´VIEW_VALUESŽ‘=彬.‘P*They–Ÿvare“usedŽ¡in‘UU±lab‘ÿ}'elŽ‘Éí¬(‘ª®)–UUfor“labGelling“­P•®9oin“tsŽ‘&Î.¬using“the“v‘ÿqÇalues“in“±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘PiS¬,“±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘b h¬,“etc.Ž¡‘ +[²LDF‘T2003.05.06.¬]Ž‘YDÛChanged‘‘õ´WORLD_VALUEŽ‘=Ø<¬,‘¡´PROJ_VALUEŽ–8§h¬,‘¡´USER_VALUEŽ“¬,‘¡and‘‘õ´VIEW_VALUEŽ‘<*4¬to‘‘õ´WORLD_VALUESŽ‘C9¬,Ž¡´PROJ_VALUESŽ‘:FG¬,‘UU´USER_VALUESŽ›=›œ¬,–UUand“´VIEW_VALUESŽ˜¬.‘qÇAdded“´WORLD_VALUES_X_YŽ‘WÛ¬,“´PROJ_VALUES_X_YŽ‘R›¬,Ž¡´USER_VALUES_X_YŽ‘OF;¬,–UUand“´VIEW_VALUES_X_YŽ‘Uðå¬for“suppressing“the“z-coGordinate.Ž¡‘ +[²LDF‘T2003.05.20.¬]Ž‘Y;Added‘UU´WORLD_VALUES_ZŽ‘M[“¬.ŽŸŸüÈ„`ÕÁGŽŽ¤ó‘ +­formatŽ‘3c(±PointŽ‘UøShap‘ÿ}'eŽŽ¡°h–ª¨¬De ne‘UU­classŽ‘5¦P•®9oin“tŽ‘>ò¯309“°i‘ÇŽ¤ ‘ +­classŽ‘$àRP•®9oin“tŽ‘CÏï¬:‘qÇ­protectedŽ‘86´ShapQÇeŽ‘Zx°fŽ¡‘­friendŽ‘5f¼T‘ÿ «ransformŽ‘m/ŽT‘ÿ -«ransformŽ’¢£«::Ž’©1MÏalign‘‰ffŽ–®with‘‰ffŽ“axisŽ’éãÅ«(ÂP•®9oin“tŽ‘šH±;‘ª¨ÂP•®9oin“tŽ‘Dð±;‘ª¨Âc®9harŽ‘¿œ«);Ž¡‘ -Âpriv‘ÿ\rateŽ‘-¨«:‘ÂT‘ÿ -«ransformŽ‘<ÈÒÏtr‘ÿ}'ansformŽ‘h|«;Ž¡‘Âb•QÇo“olŽ‘-¡hÏon‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘eFZ«;Ž¡‘Âv‘ÿ\ralarra®9yŽ‘=ZC·hÂrealŽ‘]Ù·i‘UUÏworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘PiS«;Ž¡‘Âv‘ÿ\ralarra®9yŽ‘=ZC·hÂrealŽ‘]Ù·i‘UUÏuser‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘K 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ä«;Ž¡‘Ïthir‘ÿ}'dŽ‘3Üm±:bŽ‘«=‘ÇÏar‘ÿ}'gŽ‘—±:Ïthir‘ÿ}'dŽ‘Üj±:bŽ‘Jª«;Ž¡‘Ïthir‘ÿ}'dŽ‘3Üm±:ÏptŽ‘ «µ«=‘ÇÏar‘ÿ}'gŽ‘—±:Ïthir‘ÿ}'dŽ‘Üj±:ÏptŽ‘ ä«;Ž¡‘ÏfourthŽ‘9xü±:bŽ‘«=‘ÇÏar‘ÿ}'gŽ‘—±:ÏfourthŽ‘xù±:bŽ‘Jª«;Ž¡‘ÏfourthŽ‘9xü±:ÏptŽ‘ «µ«=‘ÇÏar‘ÿ}'gŽ‘—±:ÏfourthŽ‘xù±:ÏptŽ‘ ä«;Ž¡‘·gŽ¡‘ -g«;ŽŽŽŒ‹J8S Šn ý‘ì«74‘­DEF‘ÿ8A•ÃŽUL‘ÿJªT›ÕXCONSTR“UCTOR˜F“OR˜ÂBOOL‘°¡‰ffs4Ž–#ÕPOINT‘°¡‰ffs4Ž“QUADR®9UPLE‘HzÇ­3DLDFPRÃŽG‘·x«271Ž €n ý•@PÂ271.‘ üDefault–ÕTConstructor“for“b•QÇo“ol‘°¡‰ffs4Ž›#Õp“oin®9t‘°¡‰ffs4Ž˜quadruple.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ -«LDF‘ê—2003.06.1.›NO–ÏrrŽ‘HTç±;‘ª¨ÂconstŽ‘ÕJP•®9oin“tŽ‘>Äç«&Ž‘FŒÏpptŽ‘U«)Ž¡‘:‘qDZbŽ‘¼q«(ÏbbŽ‘ -W «)±;‘ÿýrŽ‘ Ê«(ÏrrŽ‘ -Q«)±;‘ÿýÏptŽ‘äš«(ÏpptŽ‘ «)–UU·f‘ª¨g‘±=·‘ÿý«Construcor“with“Âb•QÇo“olŽ‘¡f«,“ÂrealŽ‘³.«,“and“ÂP•®9oin“tŽ‘"Dò«argumen¸ãts.‘o·±=Ž¦‘Âv®9oidŽ‘,ýÚopQÇeratorŽ‘X”«=Ž‘`[­(ÂconstŽ‘*¢b•QÇo“olu½‰™šs4Ž–Ôwrealu½‰™šs4Ž“pQÇoin®9tŽ‘nqX«&Ž‘v8vÏbrpŽ’…Jd«)‘±=·‘ÿý«Assignmen¸ãt‘UUopGerator.‘o·±=Ž¡‘·fŽ¡‘±bŽ‘%Å«=‘ÇÏbrpŽ‘Ù±:bŽ‘Jª«;Ž¡‘±rŽ‘%‘/«=‘ÇÏbrpŽ‘Ù±:rŽ‘Ê«;Ž¡‘ÏptŽ‘*«¸«=‘ÇÏbrpŽ‘Ù±:ÏptŽ‘ ä«;Ž¡‘·gŽ¡‘ -g«;ŽŽŽŒ‹KD; Šn ý‘ì·x«273‘­3DLDFPR•ÃŽG‘s,~DEF‘ÿ8A“UL‘ÿJªT›ÕXCONSTR“UCTOR˜F“OR˜ÂBOOL‘°¡‰ffs4Ž–#ÕREAL‘°¡‰ffs4Ž“POINT‘«75Ž €n ý•@PÂ273.‘ üDefault–ÕTConstructor“for“b•QÇo“ol‘°¡‰ffs4Ž–#Õreal‘°¡‰ffs4Ž“pQÇoin®9t.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ -«LDF‘82003.06.1.›h Added–8!this“section.˜Rede ned“the“default“constructor“Âb•QÇo“olu½‰™šs4Ž–Ôwrealu½‰™šs4Ž“pQÇoin®9tŽ‘P)‚«(Âv®9oidŽ‘¨ƒ«),‘=ùso“that“±bŽŽ¡«is–|êset“to“ÏfalseŽ‘,.«,‘†Ð±rŽ‘ ÍΫis“set“to“ÝINVALID_REALŽ‘C.«,›†Ðand“ÏptŽ‘Þq«is“set“to“ÝINVALID_BOOL_POINTŽ‘bƒ«.‘è‡In“order“to“do“this,˜it“w¸ãasŽ¡necessary–Ígto“remo•¸ãv“e–Ígthe“de nition“from“the“declaration“of“Âb•QÇo“olu½‰™šs4Ž–Ôwrealu½‰™šs4Ž“pQÇoin®9tŽ‘O¾È«,‘è—bGecause“when“the“compiler“seesŽ¡it,‘UUÝINVALID_REALŽ‘F0î«and‘UUÝINVALID_POINTŽ‘Kpë«aren't–UUde ned“y¸ãet.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«De ne‘UUÂb•QÇo“olu½‰™šs4Ž–Ôwrealu½‰™šs4Ž“pQÇoin®9tŽ‘Sœ «functions‘@­273“·i‘ÇŽ¤ ‘ -Âb•QÇo“olu½‰™šs4Ž–Ôwrealu½‰™šs4Ž“pQÇoin®9tŽ‘Wñf«::‘Âb•QÇo“olu½‰™šs4Ž–Ôwrealu½‰™šs4Ž“pQÇoin®9tŽ‘Mñe«(‘ª®)Ž¡‘ -:‘qDZbŽ‘¼q«(ÏfalseŽ‘¯D«)±;‘ÿýrŽ‘ Ê«(ÝINVALID_REALŽ‘?†D«)±;‘ÿýÏptŽ‘äš«(ÝINVALID_POINTŽ‘DÆA«)‘UU·f‘ª¨gŽŸ ­This–ÕXco’ˆ«=‘ÇÝCURR_YŽ–"Ín±;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±zŽ‘>f®«=‘ÇÝCURR_ZŽ“«);ŽŸÿõÂ283.Ž¦·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«constructors‘@­280“·i‘Ç«+·Ž¡‘ -ÂP•®9oin“tŽ‘&šM«::‘ÂP•®9oin“tŽ‘šL«(ÂconstŽ‘*¢realŽ‘4ÝбxŽ‘:”ì;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±yŽ‘;Ëp;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±zŽ‘;Ÿ–«)Ž¡‘ -·fŽ¡‘h›ª¨«Initialize–UUcoGordinates“and“limits‘@­278˜·iŽ¡‘Ïon‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘Nl «=‘ÇÏfalseŽ‘v\«;Ž¡‘Ïdo‘‰ffŽ‘®outputŽ‘A½M«=‘ÇÏtrueŽ‘‹°«;Ž¡#ÂifŽ‘ hÍ«0Ž‘$hϱ=·‘³Ò«[¬LDF‘T2002.10.23.«]Ž‘SoáÏuser‘‰ffŽ‘®tr‘ÿ}'ansformŽ’˜ «is– *not“currenš¸ãtly“in“use.‘XdIt“is“in˜tended“for“use“in“implemen˜tingŽ¡‘(user-de ned–UUcoGordinate“systems.‘o·±=Ž¡‘ÂifŽ‘´ú«(Ïuser‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘A¦ü±:Ïis‘‰ffŽ‘®identityŽ‘-2¢«(‘ª¨))Ž¡#ÂendifŽŽ¡‘Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘k«[0Ž‘]–Ç=“±xŽ‘~4«;Ž¡‘Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘a«[1Ž‘]–Ç=“±yŽ‘ -«;Ž¡‘Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘a«[2Ž‘]–Ç=“±zŽ‘Þ6«;Ž¡‘Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘a«[3Ž‘]–Ç=“1Ž‘Ç;Ž¡‘ -·gŽŸÿõÂ284.‘ üSetting‘ÕTfunction.ŽŸ¿øŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.12.01.«]Ž‘Y;Made–UUargumen¸ãts“ÂconstŽ‘*¢«.Ž¡‘ -[¬LDF‘T2003.03.25.«]Ž‘Y$½Changed–q×this“function,‘xøso“that“it“returns“·Ž‘qØÏthisŽ‘Ïe«instead“of“Âv®9oidŽ‘Z«.‘ÇNThis“mak¸ães“it“pGossibleŽ¡to–UUcš¸ãhain“in˜v˜oGcations“of“this“function.ŽŸŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘ÇŽ¡‘ -ÂconstŽ‘(*£P•®9oin“tŽ‘G@«&Ž‘Ná^ÏsetŽ‘\Yâ«(ÂconstŽ‘*¢realŽ‘4ÝбxŽ‘:”ì;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±yŽ‘>’ˆ«=‘ÇÝCURR_YŽ–"Ín±;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±zŽ‘>f®«=‘ÇÝCURR_ZŽ“«);Ž© ÿü­See–´?also“sections“288,–ºÝ291,“293,“295,“297,“299,“301,“302,“304,“307,“308,“309,“312,“314,“317,“319,“322,“324,“327,“329,“332,“334,“337,Ž¤ -‘339,–áú341,“342,“344,“345,“349,“352,“354,“356,“357,“360,“362,“364,“368,“370,“375,“377,“392,“394,“398,“402,“404,“406,“410,“412,Ž¡‘414,–áú416,“419,“420,“422,“423,“425,“426,“428,“429,“431,“433,“438,“440,“442,“444,“445,“447,“449,“451,“457,“461,“463,“466,“468,Ž¡‘474,–ÕX477,“479,“481,“483,“485,“488,“492,“494,“496,“498,“500,“502,“504,“507,“509,“511,“513,“516,“523,“525,“528,“and“529.Ž¦This–ÕXcoOœ«to‘UUÏtrueŽ‘í«.Ž¡‘ -[¬LDF‘T2002.10.11.«]Ž‘X•3It–âMis“used“in“v‘ÿqÇarious“ÂP•®9oin“tŽ‘!^â«functions,‘ùOand“in“ÂP®9athŽ‘Uþ«and“some“classes“deriv¸ãed“from“ÂP®9athŽ‘s±«,Ž¡currenš¸ãtly‘N¡ÂEllipseŽ‘$7z«,‘ƒ,ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘Dà«,‘ƒ,and‘N¡ÂRectangleŽ‘4Ž6«.‘6It–N¡is“in˜tended“that“ob‘Ž8jects“of“these“t˜ypšGes“b˜e“declared,‘ƒ,i.e.,Ž¡unlikš¸ãe‘—ÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘kû/«,‘ñthey–—are“not“mean˜t“to“bGe“used“only“as“base“classes.‘VˆÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽŽ¡«doGes–UUnot“use“Ïcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“p‘ÿ}'ointŽ‘L+Q«(‘ª®)“and“it“is“unlik¸ãely“that“other“classes“of“this“kind“will“use“it.Ž¦Â291.‘ üOptional–ÕTpQÇoinš®9ter“argumen˜t.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.10.29.«]Ž‘YuMade–Úthis“function“non-ÂinlineŽ‘4ó«.›tAdded“argumen¸ãt“ÂconstŽ‘"ŠkP•®9oin“tŽ‘AÿB·Ž‘FÿC±pŽ‘LC«.˜If“±pŽ‘ ‡±·6«=‘¥"0Ž‘¥#,‘ûÝthe“newŽ¡ÂP•®9oin“tŽ‘ï«is–UUassigned“to“using“the“v‘ÿqÇalues“from“±pŽ‘]U«.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·ŽŸ ‘ 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-·fŽ¡‘ÂP•®9oin“tŽ‘2Ž‘7ï ±aŽ‘?ÿè«=‘ÇÂnewŽ‘Ïœ«(ÂP•®9oin“tŽ‘šH«);Ž¦‘±aŽ‘I2Ÿ~ŽŽ‘I3Ïon‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘Wµ=«=‘ÇÏtrueŽ‘‹°«;Ž¡‘±aŽ‘I2Ÿ~ŽŽ‘I3ÏsetŽ‘*Á·«(±xŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁÆ«);Ž¡‘ÂreturnŽ‘7æ¼±aŽ‘=/ì«;Ž¡‘ -·gŽŸÂ297.‘ üDestructor.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.08.27.«]Ž‘Y(½Added–u×a“ÂvirtualŽ‘)$,«destructor“with“an“empt¸ãy“de nition,‘}øbGecause“GCC‘uÏwith“the“\È-Wall«"Ž¡option–UUissued“the“folloš¸ãwing“w˜arning:‘qÇ\`class“P˜oin˜t'“has“virtual“functions“but“non-virtual“destructor".Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/Ô·Ž‘7TòÂP•®9oin“tŽ‘Rï:«(‘ª¨);ŽŸÂ298.Ž¦·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¡‘ -ÂP•®9oin“tŽ‘&šM«::Ž‘-(‹·Ž‘4ï©ÂP•®9oin“tŽ‘P‰ñ«(‘ª¨)Ž¡‘ -·f‘ª¨gŽŸÂ299.‘ üAssignmen®9t.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.03.25.«]Ž‘Yd¦Changed–±Àthis“function,‘ÈÚso“that“it“returns“±pŽ‘ 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XshortŽ‘mÖûÏpr‘ÿ}'ojŽ’€Ê¾±;‘ª¨ÂrealŽ‘]ÖÏfactorŽ‘3a´«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂP•®9oin“tŽ‘2pŽ‘7÷Ÿ«(·Ž‘ÏthisŽ‘ë·«);Ž¡‘Âv‘ÿ\ralarra®9yŽ‘=ZC·hÂrealŽ‘]Ù·i‘UU±vŽ‘ Q*«=‘DZpŽ‘Ï:Ïget‘‰ffŽ–®al‘‚Øl‘‰ffŽ“c–ÿ}'o“or“dsŽ‘:§«(Ïc–ÿ}'o“or“dsŽ‘ Œ±;‘ª¨Ïdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘'Sà±;‘ª¨Ïdo‘‰ffŽ‘®applyŽ‘'µ}±;‘ª¨fŽ‘£Ž«);Ž¦‘ÂreturnŽ‘7æ¼±vŽ‘=y«;Ž¡‘ -·gŽŽŽŒ‹T¯é Šn ý‘ì«84–­GET‘ÕXCOORD’2=33DLDFPRÃŽG“·x«316Ž €n ý•@PÂ316.– üGet‘…ïcoQÇord.“«[¬LDF‘T2002.09.14.«]Ž‘[!ÈAdded‘îçÏget‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘,K׫(‘ª®).‘>}Fixing–îça“bug“that“caused“Ïget‘‰ffŽ‘®xŽ‘}N«(Ý'p'Ž‘F_«),–Letc.,“toŽ¤ call‘UUÏpr–ÿ}'oje“ctŽ‘!Ìc«(›ª®)–UUm¸ãultiple“times“when“doing“ÂP®9athŽ‘潫::‘ÏoutputŽ‘D«(˜).Ž©Â317.– üNon-const‘Mv®9ersion.“«[¬LDF‘T2002.10.27.«]Ž‘YéíThe–· argumen¸ãt“±cŽ‘ Áó«refers“to“either“the“x,–Ö´y‘ÿ*ª,“z,“or–· w“coGordinate.ŽŸ·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘!ëxÏget‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘JHh«(Âc®9harŽ‘¢’±cŽ‘öm;‘ª¨Âc®9harŽ‘M:Ïc–ÿ}'o“or“dsŽ‘=&U«=‘ÏÝ'w'Ž‘î±;‘ª¨ÂconstŽ‘! “b•QÇo“olŽ‘;çBÏdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘f` «=‘ÏÏtrueŽ‘”'±;‘ª¨ÂconstŽ‘! “b•QÇo“olŽŽ¡‘Ïdo‘‰ffŽ‘®applyŽ‘GÈJ«=‘½rÏtrueŽ‘‚ -±;‘ª¨ÂF‘ÿ -«oQÇcusŽ‘"‰·Ž‘'‰±fŽ‘1?r«=‘½r0Ž‘½s±;‘ª¨ÂconstŽ‘ iunsignedŽ‘Q3øshortŽ‘o’kÏpr‘ÿ}'ojŽ’†C «=‘½rÂPro‘£ŽjectionsŽ‘>‰Ö«::Ž‘EÝPERSPŽ‘_Þm±;‘ª¨ÂrealŽŽ¡‘ÏfactorŽ‘;Êù«=‘Ç1Ž‘Ç);Ž¦Â318.Ž©·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘ eaP•®9oin“tŽ‘<ÿ­«::‘Ïget‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘)\ô«(Âc®9harŽ‘{±cŽ‘pV;‘ª¨Âc®9harŽ‘Ç#Ïc–ÿ}'o“or“dsŽ‘6Я±;‘ª¨ÂconstŽ‘‡|b•QÇo“olŽ‘8ÛÏdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘^„L±;‘ª¨ÂconstŽ‘‡|b•QÇo“olŽ‘8ÛÏdo‘‰ffŽ‘®applyŽ‘^åé±;‘ª¨ÂF‘ÿ -«oQÇcusŽ‘!§{·Ž‘&§|±fŽ‘, b;‘ª¨ÂconstŽŽ¡‘2unsignedŽ‘b7shortŽ’€¶Ïpr‘ÿ}'ojŽ’’õy±;‘ª¨ÂrealŽ‘]ÖÏfactorŽ‘3a´«)Ž¡‘ -·fŽ¡‘ÂifŽ‘´ú«(Ïdo‘‰ffŽ‘®applyŽ‘& -Õ«)‘Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Kß«(‘ª®);Ž¡‘ÂifŽ‘´ú«(±fŽ‘¿þ·‘Ç«0Ž‘Ç)‘±fŽ‘ ¿þ«=‘Ç&Ž‘ -Ž6Ïdefault‘‰ffŽ‘®fo‘ÿ}'cusŽ‘Bl4«;Ž¦‘ÂunsignedŽ‘D7shortŽ‘b³ÏctrŽ‘o»¡«;Ž¦‘±cŽ‘õ«=‘ÇÏtolowerŽ‘#í«(±cŽ‘SÛ«);Ž¡‘ÂifŽ‘´ú«(±cŽ‘ó·‘ÇÝ'x'Ž‘ w«)‘ÏctrŽ‘«=‘Ç0Ž‘Ç;Ž¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(±cŽ‘ó·‘ÇÝ'y'Ž‘ w«)‘ÏctrŽ‘«=‘Ç1Ž‘Ç;Ž¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(±cŽ‘ó·‘ÇÝ'z'Ž‘ w«)‘ÏctrŽ‘«=‘Ç2Ž‘Ç;Ž¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(±cŽ‘ó·‘ÇÝ'w'Ž‘ w«)‘ÏctrŽ‘«=‘Ç3Ž‘Ç;Ž¡‘ÂelseŽ‘+Øá·fŽ¡‘Ïc‘ÿ}'errŽ‘4)«·‘tÝ"ERROR!È ÝInÈ ÝPoint::geŽ‘lsÆt_coord():È Ý"Ž’¯n ·‘tÝ"InvalidÈ ÝcÈ Ýargument:Ž‘lsÆÈ Ý"Ž‘zî*·‘t±cŽ‘ ;ß·‘tÝ".\n"Ž‘!®]·Ž¡‘2Ý"UsingÈ Ýx\n"Ž‘o d·‘ÇÏ ushŽ‘€«;Ž¡‘ÏctrŽ‘. «=‘Ç0Ž‘Ç;Ž¡‘·gŽ¡‘Ïc–ÿ}'o“or“dsŽ‘2Ц«=‘ÇÏtolowerŽ‘#í«(Ïc–ÿ}'o“or“dsŽ‘ Œ«);Ž¡‘ÂifŽ‘´ú«(Ïc–ÿ}'o“or“dsŽ‘Ф·‘ÇÝ'w'Ž‘ w«)‘ÂreturnŽ‘(æºÏworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘uú¸«[ÏctrŽ‘ ¹î«];Ž¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(Ïc–ÿ}'o“or“dsŽ‘Ф·‘ÇÝ'u'Ž‘ w«)‘ÂreturnŽ‘(æºÏuser‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘pœÛ«[ÏctrŽ‘ ¹î«];Ž¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(Ïc–ÿ}'o“or“dsŽ‘Ф·‘ÇÝ'p'Ž‘ w«)‘·fŽ¡‘ÂifŽ‘)´û«(Ïdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘%©8«)‘Ïpr–ÿ}'oje“ctŽ‘#w«(·Ž‘±fŽ‘ -øç;‘ª¨Ïpr‘ÿ}'ojŽ‘žk±;‘ª¨ÏfactorŽ‘®†«);Ž¡‘ÂreturnŽ‘Aæ½Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ’ œÐ«[ÏctrŽ‘ ¹î«];Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(Ïc–ÿ}'o“or“dsŽ‘Ф·‘ÇÝ'v'Ž‘ w«)‘ÂreturnŽ‘(æºÏview‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘q@i«[ÏctrŽ‘ ¹î«];Ž¡‘ÂelseŽ‘+Øá·fŽ¡‘Ïc‘ÿ}'errŽ‘4 ø·‘WOÝ"ERROR!È ÝInÈ ÝPoint::geŽ‘lWt_coord().È ÝInvalidÈ ÝaŽ’ÕV×rgumentÈ ÝcharÈ Ýcoords:Ž’>V›È Ý"Ž’L´L·‘WOÏc–ÿ}'o“or“dsŽ‘"¸*·Ž¡‘2Ïend‘‚ØlŽ‘H¸ß·‘ÇÝ"ReturningÈ ÝINVALID_RŽ‘kÆÜEAL.\n\n"Ž’žTA·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½ÝINVALID_REALŽ’m«;Ž¡‘·gŽ¡‘ -gŽŸÂ319.‘ üconst‘ÕTv®9ersion.Ž¦·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘!ëxÏget‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘JHh«(Âc®9harŽ‘¢’±cŽ‘öm;‘ª¨Âc®9harŽ‘M:Ïc–ÿ}'o“or“dsŽ‘=&U«=‘ÏÝ'w'Ž‘î±;‘ª¨ÂconstŽ‘! “b•QÇo“olŽ‘;çBÏdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘f` «=‘ÏÏtrueŽ‘”'±;‘ª¨ÂconstŽ‘! “b•QÇo“olŽŽ¡‘Ïdo‘‰ffŽ‘®applyŽ‘GÈJ«=‘½rÏtrueŽ‘‚ -±;‘ª¨ÂF‘ÿ -«oQÇcusŽ‘"‰·Ž‘'‰±fŽ‘1?r«=‘½r0Ž‘½s±;‘ª¨ÂconstŽ‘ iunsignedŽ‘Q3øshortŽ‘o’kÏpr‘ÿ}'ojŽ’†C «=‘½rÂPro‘£ŽjectionsŽ‘>‰Ö«::Ž‘EÝPERSPŽ‘_Þm±;‘ª¨ÂrealŽŽ¡‘ÏfactorŽ‘;Êù«=‘Ç1Ž‘Ç)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹UÂ_ Šn ý‘ì·x«320–­3DLDFPRÃŽG’onÂCONST‘ÕX­VERSION“«85Ž €n ý•@PÂ320.Ž©·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¤ ‘ -ÂrealŽ‘ eaP•®9oin“tŽ‘<ÿ­«::‘Ïget‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘)\ô«(Âc®9harŽ‘{±cŽ‘pV;‘ª¨Âc®9harŽ‘Ç#Ïc–ÿ}'o“or“dsŽ‘6Я±;‘ª¨ÂconstŽ‘‡|b•QÇo“olŽ‘8ÛÏdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘^„L±;‘ª¨ÂconstŽ‘‡|b•QÇo“olŽ‘8ÛÏdo‘‰ffŽ‘®applyŽ‘^åé±;‘ª¨ÂF‘ÿ -«oQÇcusŽ‘!§{·Ž‘&§|±fŽ‘, b;‘ª¨ÂconstŽŽ¡‘2unsignedŽ‘b7shortŽ’€¶Ïpr‘ÿ}'ojŽ’’õy±;‘ª¨ÂrealŽ‘]ÖÏfactorŽ‘3a´«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂP•®9oin“tŽ‘2pŽ‘7÷Ÿ«(·Ž‘ÏthisŽ‘ë·«);Ž¦‘ÂreturnŽ‘7æ¼±pŽ‘<î¼:Ïget‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘(\ð«(±cŽ‘SÛ;‘ª¨Ïc–ÿ}'o“or“dsŽ‘´4±;‘ª¨Ïdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘'Sà±;‘ª¨Ïdo‘‰ffŽ‘®applyŽ‘'µ}±;‘ª¨fŽ‘£Ž;‘ª¨Ïpr‘ÿ}'ojŽ‘žk±;‘ª¨ÏfactorŽ‘®†«);Ž¡‘ -·gŽ¤Â321.‘ üGet‘ÕTx.Ž¡322.‘ üNon-const‘ÕTv®9ersion.Ž¦·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¤ ‘ -ÂrealŽ‘!$åÏget‘‰ffŽ‘®xŽ‘7³L«(Âc®9harŽ‘ÛÿÏc–ÿ}'o“or“dsŽ‘9j'«=‘„œÝ'w'Ž‘Êû±;‘ª¨ÂconstŽ‘ Gb•QÇo“olŽ‘:ZÏdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘c‡ð«=‘„œÏtrueŽ–I4±;‘ª¨ÂconstŽ‘ Gb•QÇo“olŽ‘:ZÏdo‘‰ffŽ‘®applyŽ‘cé«=‘„œÏtrueŽ“±;‘ª¨ÂF‘ÿ -«oQÇcusŽŽ¡‘·Ž‘#±fŽ‘+À«=‘Ç0Ž–DZ;‘ª¨ÂconstŽ‘ÕJunsignedŽ‘P XshortŽ‘mÖûÏpr‘ÿ}'ojŽ’ƒ‘Ö«=‘ÇÂPro‘£ŽjectionsŽ‘=“|«::Ž‘D!ºÝPERSPŽ‘^è±;‘ª¨ÂrealŽ‘]ÖÏfactorŽ‘6(Ì«=‘Ç1Ž“);ŽŸÂ323.Ž¦·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘ žHP•®9oin“tŽ‘=8”«::‘Ïget‘‰ffŽ‘®xŽ‘Žk«(Âc®9harŽ‘UbÏc–ÿ}'o“or“dsŽ‘5^î±;‘ª¨ÂconstŽ‘Àcb•QÇo“olŽ‘9LâÏdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘^ö±;‘ª¨ÂconstŽ‘Àcb•QÇo“olŽ‘9LâÏdo‘‰ffŽ‘®applyŽ‘_W·±;‘ª¨ÂF‘ÿ -«oQÇcusŽ‘!àb·Ž‘&àc±fŽ‘,ÙI;‘ª¨ÂconstŽ‘ÀcunsignedŽŽ¡‘2shortŽ‘OʨÏpr‘ÿ}'ojŽ‘b¾k±;‘ª¨ÂrealŽ‘]ÖÏfactorŽ‘3a´«)Ž¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼Ïget‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘`C¬«(Ý'x'Ž‘F_±;‘ª¨Ïc–ÿ}'o“or“dsŽ‘´4±;‘ª¨Ïdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘'Sà±;‘ª¨Ïdo‘‰ffŽ‘®applyŽ‘'µ}±;‘ª¨fŽ‘£Ž;‘ª¨Ïpr‘ÿ}'ojŽ‘žk±;‘ª¨ÏfactorŽ‘®†«);Ž¡‘ -·gŽŸÂ324.‘ üconst‘ÕTv®9ersion.Ž¦·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘!$åÏget‘‰ffŽ‘®xŽ‘7³L«(Âc®9harŽ‘ÛÿÏc–ÿ}'o“or“dsŽ‘9j'«=‘„œÝ'w'Ž‘Êû±;‘ª¨ÂconstŽ‘ Gb•QÇo“olŽ‘:ZÏdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘c‡ð«=‘„œÏtrueŽ–I4±;‘ª¨ÂconstŽ‘ Gb•QÇo“olŽ‘:ZÏdo‘‰ffŽ‘®applyŽ‘cé«=‘„œÏtrueŽ“±;‘ª¨ÂF‘ÿ -«oQÇcusŽŽ¡‘·Ž‘#±fŽ‘+À«=‘Ç0Ž–DZ;‘ª¨ÂconstŽ‘ÕJunsignedŽ‘P XshortŽ‘mÖûÏpr‘ÿ}'ojŽ’ƒ‘Ö«=‘ÇÂPro‘£ŽjectionsŽ‘=“|«::Ž‘D!ºÝPERSPŽ‘^è±;‘ª¨ÂrealŽ‘]ÖÏfactorŽ‘6(Ì«=‘Ç1Ž“)‘UUÂconstŽ‘*¢«;ŽŸÂ325.Ž¦·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘ žHP•®9oin“tŽ‘=8”«::‘Ïget‘‰ffŽ‘®xŽ‘Žk«(Âc®9harŽ‘UbÏc–ÿ}'o“or“dsŽ‘5^î±;‘ª¨ÂconstŽ‘Àcb•QÇo“olŽ‘9LâÏdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘^ö±;‘ª¨ÂconstŽ‘Àcb•QÇo“olŽ‘9LâÏdo‘‰ffŽ‘®applyŽ‘_W·±;‘ª¨ÂF‘ÿ -«oQÇcusŽ‘!àb·Ž‘&àc±fŽ‘,ÙI;‘ª¨ÂconstŽ‘ÀcunsignedŽŽ¡‘2shortŽ‘OʨÏpr‘ÿ}'ojŽ‘b¾k±;‘ª¨ÂrealŽ‘]ÖÏfactorŽ‘3a´«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼Ïget‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘`C¬«(Ý'x'Ž‘F_±;‘ª¨Ïc–ÿ}'o“or“dsŽ‘´4±;‘ª¨Ïdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘'Sà±;‘ª¨Ïdo‘‰ffŽ‘®applyŽ‘'µ}±;‘ª¨fŽ‘£Ž;‘ª¨Ïpr‘ÿ}'ojŽ‘žk±;‘ª¨ÏfactorŽ‘®†«);Ž¡‘ -·gŽ¤Â326.‘ üGet‘ÕTy‘ÿ -«.Ž¡327.‘ üNon-const‘ÕTv®9ersion.Ž¦·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¤ ‘ -ÂrealŽ‘!%>Ïget‘‰ffŽ‘®yŽ‘7™T«(Âc®9harŽ‘ÜXÏc–ÿ}'o“or“dsŽ‘9k«=‘…0Ý'w'Ž‘˱;‘ª¨ÂconstŽ‘ GYb•QÇo“olŽ‘:ZÎÏdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘c‰6«=‘…0ÏtrueŽ–Iȱ;‘ª¨ÂconstŽ‘ GYb•QÇo“olŽ‘:ZÎÏdo‘‰ffŽ‘®applyŽ‘cêÓ«=‘…0ÏtrueŽ“±;‘ª¨ÂF‘ÿ -«oQÇcusŽŽ¡‘·Ž‘#±fŽ‘+À«=‘Ç0Ž–DZ;‘ª¨ÂconstŽ‘ÕJunsignedŽ‘P XshortŽ‘mÖûÏpr‘ÿ}'ojŽ’ƒ‘Ö«=‘ÇÂPro‘£ŽjectionsŽ‘=“|«::Ž‘D!ºÝPERSPŽ‘^è±;‘ª¨ÂrealŽ‘]ÖÏfactorŽ‘6(Ì«=‘Ç1Ž“);ŽŽŽŒ‹VÓL Šn ý‘ì«86–­NON-ÂCONST‘ÕX­VERSION’ÿAÖ3DLDFPRÃŽG“·x«328Ž €n ý•@PÂ328.Ž©·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¤ ‘ -ÂrealŽ‘ ŸÕP•®9oin“tŽ‘=:!«::‘Ïget‘‰ffŽ‘®yŽ‘t«(Âc®9harŽ‘VïÏc–ÿ}'o“or“dsŽ‘5`{±;‘ª¨ÂconstŽ‘Áðb•QÇo“olŽ‘9OüÏdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘^ù4±;‘ª¨ÂconstŽ‘Áðb•QÇo“olŽ‘9OüÏdo‘‰ffŽ‘®applyŽ‘_Zѱ;‘ª¨ÂF‘ÿ -«oQÇcusŽ‘!áï·Ž‘&áð±fŽ‘,ÚÖ;‘ª¨ÂconstŽ‘ÁðunsignedŽŽ¡‘2shortŽ‘OʨÏpr‘ÿ}'ojŽ‘b¾k±;‘ª¨ÂrealŽ‘]ÖÏfactorŽ‘3a´«)Ž¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼Ïget‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘`C¬«(Ý'y'Ž‘F_±;‘ª¨Ïc–ÿ}'o“or“dsŽ‘´4±;‘ª¨Ïdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘'Sà±;‘ª¨Ïdo‘‰ffŽ‘®applyŽ‘'µ}±;‘ª¨fŽ‘£Ž;‘ª¨Ïpr‘ÿ}'ojŽ‘žk±;‘ª¨ÏfactorŽ‘®†«);Ž¡‘ -·gŽŸÂ329.‘ üconst‘ÕTv®9ersion.Ž¦·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘!%>Ïget‘‰ffŽ‘®yŽ‘7™T«(Âc®9harŽ‘ÜXÏc–ÿ}'o“or“dsŽ‘9k«=‘…0Ý'w'Ž‘˱;‘ª¨ÂconstŽ‘ GYb•QÇo“olŽ‘:ZÎÏdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘c‰6«=‘…0ÏtrueŽ–Iȱ;‘ª¨ÂconstŽ‘ GYb•QÇo“olŽ‘:ZÎÏdo‘‰ffŽ‘®applyŽ‘cêÓ«=‘…0ÏtrueŽ“±;‘ª¨ÂF‘ÿ -«oQÇcusŽŽ¡‘·Ž‘#±fŽ‘+À«=‘Ç0Ž–DZ;‘ª¨ÂconstŽ‘ÕJunsignedŽ‘P XshortŽ‘mÖûÏpr‘ÿ}'ojŽ’ƒ‘Ö«=‘ÇÂPro‘£ŽjectionsŽ‘=“|«::Ž‘D!ºÝPERSPŽ‘^è±;‘ª¨ÂrealŽ‘]ÖÏfactorŽ‘6(Ì«=‘Ç1Ž“)‘UUÂconstŽ‘*¢«;ŽŸÂ330.Ž¦·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘ ŸÕP•®9oin“tŽ‘=:!«::‘Ïget‘‰ffŽ‘®yŽ‘t«(Âc®9harŽ‘VïÏc–ÿ}'o“or“dsŽ‘5`{±;‘ª¨ÂconstŽ‘Áðb•QÇo“olŽ‘9OüÏdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘^ù4±;‘ª¨ÂconstŽ‘Áðb•QÇo“olŽ‘9OüÏdo‘‰ffŽ‘®applyŽ‘_Zѱ;‘ª¨ÂF‘ÿ -«oQÇcusŽ‘!áï·Ž‘&áð±fŽ‘,ÚÖ;‘ª¨ÂconstŽ‘ÁðunsignedŽŽ¡‘2shortŽ‘OʨÏpr‘ÿ}'ojŽ‘b¾k±;‘ª¨ÂrealŽ‘]ÖÏfactorŽ‘3a´«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼Ïget‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘`C¬«(Ý'y'Ž‘F_±;‘ª¨Ïc–ÿ}'o“or“dsŽ‘´4±;‘ª¨Ïdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘'Sà±;‘ª¨Ïdo‘‰ffŽ‘®applyŽ‘'µ}±;‘ª¨fŽ‘£Ž;‘ª¨Ïpr‘ÿ}'ojŽ‘žk±;‘ª¨ÏfactorŽ‘®†«);Ž¡‘ -·gŽ¤Â331.‘ üGet‘ÕTz.Ž¡332.‘ üNon-const‘ÕTv®9ersion.Ž¦·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¤ ‘ -ÂrealŽ‘!&ªÏget‘‰ffŽ‘®zŽ‘7.««(Âc®9harŽ‘ÝÄÏc–ÿ}'o“or“dsŽ‘9nß«=‘‡Ý'w'Ž‘Íî±;‘ª¨ÂconstŽ‘ HÅb•QÇo“olŽ‘:]¦Ïdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘cŽm«=‘‡ÏtrueŽ–L'±;‘ª¨ÂconstŽ‘ HÅb•QÇo“olŽ‘:]¦Ïdo‘‰ffŽ‘®applyŽ‘cð -«=‘‡ÏtrueŽ“±;‘ª¨ÂF‘ÿ -«oQÇcusŽŽ¡‘·Ž‘#±fŽ‘+À«=‘Ç0Ž–DZ;‘ª¨ÂconstŽ‘ÕJunsignedŽ‘P XshortŽ‘mÖûÏpr‘ÿ}'ojŽ’ƒ‘Ö«=‘ÇÂPro‘£ŽjectionsŽ‘=“|«::Ž‘D!ºÝPERSPŽ‘^è±;‘ª¨ÂrealŽ‘]ÖÏfactorŽ‘6(Ì«=‘Ç1Ž“);ŽŸÂ333.Ž¦·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘ ¦0P•®9oin“tŽ‘=@|«::‘Ïget‘‰ffŽ‘®zŽ‘«(Âc®9harŽ‘]JÏc–ÿ}'o“or“dsŽ‘5fÖ±;‘ª¨ÂconstŽ‘ÈKb•QÇo“olŽ‘9\²Ïdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘_ê±;‘ª¨ÂconstŽ‘ÈKb•QÇo“olŽ‘9\²Ïdo‘‰ffŽ‘®applyŽ‘_g‡±;‘ª¨ÂF‘ÿ -«oQÇcusŽ‘!èJ·Ž‘&èK±fŽ‘,á1;‘ª¨ÂconstŽ‘ÈKunsignedŽŽ¡‘2shortŽ‘OʨÏpr‘ÿ}'ojŽ‘b¾k±;‘ª¨ÂrealŽ‘]ÖÏfactorŽ‘3a´«)Ž¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼Ïget‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘`C¬«(Ý'z'Ž‘F_±;‘ª¨Ïc–ÿ}'o“or“dsŽ‘´4±;‘ª¨Ïdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘'Sà±;‘ª¨Ïdo‘‰ffŽ‘®applyŽ‘'µ}±;‘ª¨fŽ‘£Ž;‘ª¨Ïpr‘ÿ}'ojŽ‘žk±;‘ª¨ÏfactorŽ‘®†«);Ž¡‘ -·gŽŸÂ334.‘ üconst‘ÕTv®9ersion.Ž¦·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘!&ªÏget‘‰ffŽ‘®zŽ‘7.««(Âc®9harŽ‘ÝÄÏc–ÿ}'o“or“dsŽ‘9nß«=‘‡Ý'w'Ž‘Íî±;‘ª¨ÂconstŽ‘ HÅb•QÇo“olŽ‘:]¦Ïdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘cŽm«=‘‡ÏtrueŽ–L'±;‘ª¨ÂconstŽ‘ HÅb•QÇo“olŽ‘:]¦Ïdo‘‰ffŽ‘®applyŽ‘cð -«=‘‡ÏtrueŽ“±;‘ª¨ÂF‘ÿ -«oQÇcusŽŽ¡‘·Ž‘#±fŽ‘+À«=‘Ç0Ž–DZ;‘ª¨ÂconstŽ‘ÕJunsignedŽ‘P XshortŽ‘mÖûÏpr‘ÿ}'ojŽ’ƒ‘Ö«=‘ÇÂPro‘£ŽjectionsŽ‘=“|«::Ž‘D!ºÝPERSPŽ‘^è±;‘ª¨ÂrealŽ‘]ÖÏfactorŽ‘6(Ì«=‘Ç1Ž“)‘UUÂconstŽ‘*¢«;ŽŸÂ335.Ž¦·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘ ¦0P•®9oin“tŽ‘=@|«::‘Ïget‘‰ffŽ‘®zŽ‘«(Âc®9harŽ‘]JÏc–ÿ}'o“or“dsŽ‘5fÖ±;‘ª¨ÂconstŽ‘ÈKb•QÇo“olŽ‘9\²Ïdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘_ê±;‘ª¨ÂconstŽ‘ÈKb•QÇo“olŽ‘9\²Ïdo‘‰ffŽ‘®applyŽ‘_g‡±;‘ª¨ÂF‘ÿ -«oQÇcusŽ‘!èJ·Ž‘&èK±fŽ‘,á1;‘ª¨ÂconstŽ‘ÈKunsignedŽŽ¡‘2shortŽ‘OʨÏpr‘ÿ}'ojŽ‘b¾k±;‘ª¨ÂrealŽ‘]ÖÏfactorŽ‘3a´«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼Ïget‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘`C¬«(Ý'z'Ž‘F_±;‘ª¨Ïc–ÿ}'o“or“dsŽ‘´4±;‘ª¨Ïdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘'Sà±;‘ª¨Ïdo‘‰ffŽ‘®applyŽ‘'µ}±;‘ª¨fŽ‘£Ž;‘ª¨Ïpr‘ÿ}'ojŽ‘žk±;‘ª¨ÏfactorŽ‘®†«);Ž¡‘ -·gŽŸÂ336.‘ 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¬)–UU°f‘ª¨g‘µ=°‘ÿý¬Construcor“with“­b•QÇo“olŽ‘¡f¬,“­realŽ‘³.¬,“and“­P•®9oin“tŽ‘"Dò¬argumen¸ãts.‘o°µ=Ž¦‘­v®9oidŽ‘,ýÚopQÇeratorŽ‘X”¬=Ž‘`[­(­constŽ‘*¢b•QÇo“olu½‰™šs4Ž–Ôwrealu½‰™šs4Ž“pQÇoin®9tŽ‘nqX¬&Ž‘v8v±brpŽ’…Jd¬)‘µ=°‘ÿý¬Assignmen¸ãt‘UUopGerator.‘o°µ=Ž¡‘°fŽ¡‘µbŽ‘%Ŭ=‘DZbrpŽ‘Ùµ:bŽ‘Jª¬;Ž¡‘µrŽ‘%‘/¬=‘DZbrpŽ‘Ùµ:rŽ‘ʬ;Ž¡‘±ptŽ‘*«¸¬=‘DZbrpŽ‘Ùµ:±ptŽ‘ ä¬;Ž¡‘°gŽ¡‘ +g¬;ŽŽŽŒ‹U3R Šn ý‘ì°x¬318‘¯3DLDF-1.1.5.1‘j¸èDEF‘ÿ8A•ÃŽUL‘ÿJªT›ÕXCONSTR“UCTOR˜F“OR˜­BOOL‘°¡‰ffs4Ž–#ÕREAL‘°¡‰ffs4Ž“POINT‘¬85Ž €n ý•@P­318.‘ üDefault–ÕTConstructor“for“b•QÇo“ol‘°¡‰ffs4Ž–#Õreal‘°¡‰ffs4Ž“pQÇoin®9t.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ +¬LDF‘82003.06.1.›h Added–8!this“section.˜Rede ned“the“default“constructor“­b•QÇo“olu½‰™šs4Ž–Ôwrealu½‰™šs4Ž“pQÇoin®9tŽ‘P)‚¬(­v®9oidŽ‘¨ƒ¬),‘=ùso“that“µbŽŽ¡¬is–|êset“to“±falseŽ‘,.¬,‘†ÐµrŽ‘ Íάis“set“to“´INVALID_REALŽ‘C.¬,›†Ðand“±ptŽ‘Þq¬is“set“to“´INVALID_BOOL_POINTŽ‘bƒ¬.‘è‡In“order“to“do“this,˜it“w¸ãasŽ¡necessary–Ígto“remo•¸ãv“e–Ígthe“de nition“from“the“declaration“of“­b•QÇo“olu½‰™šs4Ž–Ôwrealu½‰™šs4Ž“pQÇoin®9tŽ‘O¾È¬,‘è—bGecause“when“the“compiler“seesŽ¡it,‘UU´INVALID_REALŽ‘F0î¬and‘UU´INVALID_POINTŽ‘Kpë¬aren't–UUde ned“y¸ãet.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬De ne‘UU­b•QÇo“olu½‰™šs4Ž–Ôwrealu½‰™šs4Ž“pQÇoin®9tŽ‘Sœ ¬functions‘@¯318“°i‘ÇŽ¤ ‘ +­b•QÇo“olu½‰™šs4Ž–Ôwrealu½‰™šs4Ž“pQÇoin®9tŽ‘Wñf¬::‘­b•QÇo“olu½‰™šs4Ž–Ôwrealu½‰™šs4Ž“pQÇoin®9tŽ‘Mñe¬(‘ª®)Ž¡‘ +:‘qǵbŽ‘¼q¬(±falseŽ‘¯D¬)µ;‘ÿýrŽ‘ ʬ(´INVALID_REALŽ‘?†D¬)µ;‘ÿý±ptŽ‘䚬(´INVALID_POINTŽ‘DÆA¬)‘UU°f‘ª¨gŽŸ ¯This–ÕXco’ˆ¬=‘Ç´CURR_YŽ–"Ínµ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµzŽ‘>f®¬=‘Ç´CURR_ZŽ“¬);ŽŸÿõ­328.Ž¦°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬constructors‘@¯325“°i‘Ǭ+°Ž¡‘ +­P•®9oin“tŽ‘&šM¬::‘­P•®9oin“tŽ‘šL¬(­constŽ‘*¢realŽ‘4ÝеxŽ‘:”ì;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµyŽ‘;Ëp;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµzŽ‘;Ÿ–¬)Ž¡‘ +°fŽ¡‘h›ª¨¬Initialize–UUcoGordinates“and“limits‘@¯323˜°iŽ¡‘±on‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘Nl ¬=‘DZfalseŽ‘v\¬;Ž¡‘±do‘‰ffŽ‘®outputŽ‘A½M¬=‘DZtrueŽ‘‹°¬;Ž¡#­ifŽ‘ hͬ0Ž‘$hϵ=°‘³Ò¬[²LDF‘T2002.10.23.¬]Ž‘Soá±user‘‰ffŽ‘®tr‘ÿ}'ansformŽ’˜ ¬is– *not“currenš¸ãtly“in“use.‘XdIt“is“in˜tended“for“use“in“implemen˜tingŽ¡‘(user-de ned–UUcoGordinate“systems.‘o°µ=Ž¡‘­ifŽ‘´ú¬(±user‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘A¦üµ:±is‘‰ffŽ‘®identityŽ‘-2¢¬(‘ª¨))Ž¡#­endifŽŽ¡‘±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘k¬[0Ž‘]–Ç=“µxŽ‘~4¬;Ž¡‘±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘a¬[1Ž‘]–Ç=“µyŽ‘ +¬;Ž¡‘±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘a¬[2Ž‘]–Ç=“µzŽ‘Þ6¬;Ž¡‘±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘a¬[3Ž‘]–Ç=“1Ž‘Ç;Ž¡‘ +°gŽŸÿõ­329.‘ üSetting‘ÕTfunction.ŽŸ¿øŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.12.01.¬]Ž‘Y;Made–UUargumen¸ãts“­constŽ‘*¢¬.Ž¡‘ +[²LDF‘T2003.03.25.¬]Ž‘Y$½Changed–q×this“function,‘xøso“that“it“returns“°Ž‘qرthisŽ‘Ïe¬instead“of“­v®9oidŽ‘Z¬.‘ÇNThis“mak¸ães“it“pGossibleŽ¡to–UUcš¸ãhain“in˜v˜oGcations“of“this“function.ŽŸŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘ÇŽ¡‘ +­constŽ‘(*£P•®9oin“tŽ‘G@¬&Ž‘Ná^±setŽ‘\Yâ¬(­constŽ‘*¢realŽ‘4ÝеxŽ‘:”ì;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµyŽ‘>’ˆ¬=‘Ç´CURR_YŽ–"Ínµ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµzŽ‘>f®¬=‘Ç´CURR_ZŽ“¬);Ž© ÿü¯See–´?also“sections“333,–ºÝ338,“340,“342,“344,“346,“349,“350,“352,“355,“357,“360,“362,“365,“367,“370,“372,“375,“377,“380,“382,“384,“385,Ž¤ +‘387,–áú389,“393,“396,“398,“400,“401,“404,“406,“408,“412,“414,“419,“421,“436,“438,“442,“446,“448,“450,“454,“456,“458,“460,“463,Ž¡‘464,–áú466,“467,“469,“470,“472,“473,“475,“477,“482,“484,“486,“488,“489,“491,“493,“495,“501,“505,“507,“510,“512,“518,“521,“523,Ž¡‘525,–ÕX527,“529,“532,“536,“538,“540,“542,“544,“546,“548,“551,“553,“555,“557,“560,“567,“569,“572,“and“573.Ž¦This–ÕXcoïÿµ<‘à?­P•®9oin“tŽ‘#ZƵ>–à?¬(‘ª®)“is“mean¸ãt“to“bGe“usedŽ¡instead–É/of“­newŽ‘E¬(‘ª®)“for“dynamic“alloGcation“of“­P•®9oin“tsŽ‘#쳬.‘ÍUIt“calls“the“default“constructor“(without“argumen¸ãts)Ž¡and–UUthen“sets“±on‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘>Oœ¬to“±trueŽ‘í¬.Ž¡‘ +[²LDF‘T2002.10.11.¬]Ž‘X•3It–âMis“used“in“v‘ÿqÇarious“­P•®9oin“tŽ‘!^â¬functions,‘ùOand“in“­P®9athŽ‘Uþ¬and“some“classes“deriv¸ãed“from“­P®9athŽ‘s±¬,Ž¡currenš¸ãtly‘N¡­EllipseŽ‘$7z¬,‘ƒ,­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘Dà¬,‘ƒ,and‘N¡­RectangleŽ‘4Ž6¬.‘6It–N¡is“in˜tended“that“ob‘Ž8jects“of“these“t˜ypšGes“b˜e“declared,‘ƒ,i.e.,Ž¡unlikš¸ãe‘—­Regu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘kû/¬,‘ñthey–—are“not“mean˜t“to“bGe“used“only“as“base“classes.‘Vˆ­Regu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽŽ¡¬doGes–UUnot“use“±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<“­P•®9oin“tŽ‘"Dòµ>“¬(‘ª®)“and“it“is“unlik¸ãely“that“other“classes“of“this“kind“will“use“it.ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.12.30.¬]Ž‘WëÉReplaced–8ãthe“non-template“±cr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“p‘ÿ}'ointŽ‘K߬(›ª®)“functions“with“v¸ãersions“of“the“±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘1ȧ¬(˜)Ÿ€„ +Ž¡template–n‚function.‘½NI‘n|bšGeliev¸ãe“the“de nitions“shouldn't“b˜e“necessary‘ÿ*ª,‘tÍbut“at“presen¸ãt“they“are.‘½NWithout“them,Ž¡the–UUtemplates“aren't“instan¸ãtiated.Ž¡‘ +[²LDF‘T2003.12.30.¬]Ž‘Y;Changed–UUthe“argumenš¸ãt.‘qÇIt's“no˜w“a“­constŽ‘!÷P•®9oin“tŽ‘@o”°Ž‘Eo•¬.Ž¡‘ +[²LDF‘T2003.12.30.¬]Ž‘YÂÿRemo•¸ãv“ed–default“argumen¸ãt“\0",‘>ÊbGecause“this“caused“a“compiler“error“when“using“theŽ¡DEC–UU²C‘€Ÿÿ³+‘ÿ+ŽŽ‘œu¬compiler.‘qÇApparenš¸ãtly‘ÿ*ª,“it“suces“to“declare“a“default“argumen˜t“in“the“template“declaration.Ž¦ŸüÈ„`ÕÁGŽŽŸ­336.‘ üP•®9oin“ter‘ÕTargumen“t.Ž¦°h›ª¨¬Declare–UUnon-mem¸ãbGer“template“functions“for“­P•®9oin“tŽ‘#/¡¯336˜°i‘ÇŽ¡‘ +­P•®9oin“tŽ‘(ïž°Ž‘-cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘]c¬(­constŽ‘*¢P•®9oin“tŽ‘=?°Ž‘B@µpŽ‘G"@¬);Ž¤ ¯See–ÕXalso“section“337.Ž¡This–ÕXco®¬=‘ǵpŽ‘Ï:±dr–ÿ}'awdot‘‰ffŽ‘®c“olorŽ‘YCan‘kI‘=mak¸ãeŽ¤ the‘9­F‘ÿ +«oQÇcusŽ‘#¾°Ž‘+ø¬argumenš¸ãt‘9­constŽ‘ㆬ?‘ZWhat–9is“the“syn˜tax“for“a“pGoin˜ter“to“a“­constŽ‘ㆬ,‘ras“oppšGosed“to“a“­constŽ‘ ñ¿¬p˜oin¸ãter?Ž¡LoGok–UUup!!‘qÇMakš¸ãe“sure“I“c˜hange“this“is“®3DLDF.texi“¬if“I“c˜hange“it“here!ŽŽŽŒ‹]“ΠŠn ý‘ì°x¬355–¯3DLDF-1.1.5.1’öÎ@NON-­CONST‘ÕX¯VERSION“¬93Ž €n ý•@P­355.– üNon-const‘ÕTv®9ersion.“¬[²LDF‘T2002.09.19.¬]Ž‘Zˆ6Added–UUthis“function.Ž©°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¤ ‘ +­v‘ÿ\ralarra®9yŽ‘3ZB°h­realŽ‘]Ù°i‘D±get‘‰ffŽ–®al‘‚Øl‘‰ffŽ“c–ÿ}'o“or“dsŽ‘>ÂW¬(­c®9harŽ‘08±c–ÿ}'o“or“dsŽ‘:J¾¬=‘ú´'w'Ž‘WYµ;‘ª¨­constŽ‘ ›9b•QÇo“olŽ‘;Ž±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘d¼À¬=‘ú±trueŽ‘Õ’µ;‘ª¨­constŽ‘ ›9b•QÇo“olŽŽ¡‘±do‘‰ffŽ‘®applyŽ‘GÈJ¬=‘½r±trueŽ‘‚ +µ;‘ª¨­F‘ÿ +«oQÇcusŽ‘"‰°Ž‘'‰µfŽ‘1?r¬=‘½r0Ž‘½sµ;‘ª¨­constŽ‘ iunsignedŽ‘Q3øshortŽ‘o’k±pr‘ÿ}'ojŽ’†C ¬=‘½r­Pro‘£ŽjectionsŽ‘>‰Ö¬::Ž‘E´PERSPŽ‘_Þmµ;‘ª¨­realŽŽ¡‘±factorŽ‘;Êù¬=‘Ç1Ž‘Ç);ŽŸ­356.Ž¦°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¡‘ +­v‘ÿ\ralarra®9yŽ‘3ZB°h­realŽ‘]Ù°i‘q2­P•®9oin“tŽ‘ ~¬::‘±get‘‰ffŽ–®al‘‚Øl‘‰ffŽ“c–ÿ}'o“or“dsŽ‘;§¬(­c®9harŽ‘†&±c–ÿ}'o“or“dsŽ‘5²µ;‘ª¨­constŽ‘ñ'b•QÇo“olŽ‘9®j±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘_W¢µ;‘ª¨­constŽ‘ñ'b•QÇo“olŽ‘9®j±do‘‰ffŽ‘®applyŽ‘_¹?µ;‘ª¨­F‘ÿ +«oQÇcusŽŽ¡‘2°Ž‘7µfŽ‘<øì;‘ª¨­constŽ‘ÕJunsignedŽ‘P XshortŽ‘mÖû±pr‘ÿ}'ojŽ’€Ê¾µ;‘ª¨­realŽ‘]Ö±factorŽ‘3a´¬)Ž¡‘ +°fŽ¡‘­ifŽ‘´ú¬(±do‘‰ffŽ‘®applyŽ‘& +Õ¬)‘±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘K߬(‘ª®);Ž¡‘±c–ÿ}'o“or“dsŽ‘2Ц¬=‘DZtolowerŽ‘#í¬(±c–ÿ}'o“or“dsŽ‘ Œ¬);Ž¡‘­ifŽ‘´ú¬(±c–ÿ}'o“or“dsŽ‘Ф°‘Ç´'w'Ž‘ w¬)‘­returnŽ‘(溱world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘uú¸¬;Ž¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±c–ÿ}'o“or“dsŽ‘Ф°‘Ç´'v'Ž‘ w¬)‘­returnŽ‘(溱view‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘q@i¬;Ž¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±c–ÿ}'o“or“dsŽ‘Ф°‘Ç´'u'Ž‘ w¬)‘­returnŽ‘(溱user‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘pœÛ¬;Ž¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±c–ÿ}'o“or“dsŽ‘Ф°‘Ç´'p'Ž‘ w¬)‘°fŽ¡‘­ifŽ‘)´û¬(±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘%©8¬)‘°fŽ¡‘(­ifŽ‘3´ü¬(µfŽ‘¿þ°‘Ǭ0Ž‘Ç)‘µfŽ‘ ¿þ¬=‘Ç&Ž‘ +Ž6±default‘‰ffŽ‘®fo‘ÿ}'cusŽ‘Bl4¬;Ž¡‘(±pr–ÿ}'oje“ctŽ‘Fw¬(°Ž‘µfŽ‘ +øç;‘ª¨±pr‘ÿ}'ojŽ‘žkµ;‘ª¨±factorŽ‘®†¬);Ž¡‘°gŽ¡‘­returnŽ‘Aæ½±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ’ œÐ¬;Ž¡‘°gŽ¡‘­elseŽ‘+Øá°fŽ¡‘±c‘ÿ}'errŽ‘8mŽ°‘·å´"ERROR!® ´In® ´Point::geŽ‘p·©t_all_coords():\n"Ž’×uÀ°Ž¡‘2´"Argument® ´coords® ´hasŽ’šÿÉ® ´invalid® ´value:® ´"Ž’ûß×°‘Ù±c–ÿ}'o“or“dsŽ‘*=>°Ž¡‘2´".® ´Returning® ´world® ´cŽ’šÿÉoordinates.\n"Ž’çÍ°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ’Žú»¬;Ž¡‘°gŽ¡‘ +gŽŸ­357.– üconst‘ÕTv®9ersion.“¬[²LDF‘T2002.09.19.¬]Ž‘Zˆ6Added–UUthis“function.Ž¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­v‘ÿ\ralarra®9yŽ‘3ZB°h­realŽ‘]Ù°i‘D±get‘‰ffŽ–®al‘‚Øl‘‰ffŽ“c–ÿ}'o“or“dsŽ‘>ÂW¬(­c®9harŽ‘08±c–ÿ}'o“or“dsŽ‘:J¾¬=‘ú´'w'Ž‘WYµ;‘ª¨­constŽ‘ ›9b•QÇo“olŽ‘;Ž±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘d¼À¬=‘ú±trueŽ‘Õ’µ;‘ª¨­constŽ‘ ›9b•QÇo“olŽŽ¡‘±do‘‰ffŽ‘®applyŽ‘GÈJ¬=‘½r±trueŽ‘‚ +µ;‘ª¨­F‘ÿ +«oQÇcusŽ‘"‰°Ž‘'‰µfŽ‘1?r¬=‘½r0Ž‘½sµ;‘ª¨­constŽ‘ iunsignedŽ‘Q3øshortŽ‘o’k±pr‘ÿ}'ojŽ’†C ¬=‘½r­Pro‘£ŽjectionsŽ‘>‰Ö¬::Ž‘E´PERSPŽ‘_Þmµ;‘ª¨­realŽŽ¡‘±factorŽ‘;Êù¬=‘Ç1Ž‘Ç)‘UU­constŽ‘*¢¬;ŽŸ­358.Ž¦°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¡‘ +­v‘ÿ\ralarra®9yŽ‘3ZB°h­realŽ‘]Ù°i‘q2­P•®9oin“tŽ‘ ~¬::‘±get‘‰ffŽ–®al‘‚Øl‘‰ffŽ“c–ÿ}'o“or“dsŽ‘;§¬(­c®9harŽ‘†&±c–ÿ}'o“or“dsŽ‘5²µ;‘ª¨­constŽ‘ñ'b•QÇo“olŽ‘9®j±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘_W¢µ;‘ª¨­constŽ‘ñ'b•QÇo“olŽ‘9®j±do‘‰ffŽ‘®applyŽ‘_¹?µ;‘ª¨­F‘ÿ +«oQÇcusŽŽ¡‘2°Ž‘7µfŽ‘<øì;‘ª¨­constŽ‘ÕJunsignedŽ‘P XshortŽ‘mÖû±pr‘ÿ}'ojŽ’€Ê¾µ;‘ª¨­realŽ‘]Ö±factorŽ‘3a´¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­P•®9oin“tŽ‘2pŽ‘7÷Ÿ¬(°Ž‘±thisŽ‘ë·¬);Ž¡‘­v‘ÿ\ralarra®9yŽ‘=ZC°h­realŽ‘]Ù°i‘UUµvŽ‘ Q*¬=‘ǵpŽ‘Ï:±get‘‰ffŽ–®al‘‚Øl‘‰ffŽ“c–ÿ}'o“or“dsŽ‘:§¬(±c–ÿ}'o“or“dsŽ‘ Œµ;‘ª¨±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘'Sàµ;‘ª¨±do‘‰ffŽ‘®applyŽ‘'µ}µ;‘ª¨fŽ‘£Ž¬);Ž¦‘­returnŽ‘7æ¼µvŽ‘=y¬;Ž¡‘ +°gŽŸ­359.– üGet‘…ïcoQÇord.“¬[²LDF‘T2002.09.14.¬]Ž‘[!ÈAdded‘îç±get‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘,K׬(‘ª®).‘>}Fixing–îça“bug“that“caused“±get‘‰ffŽ‘®xŽ‘}N¬(´'p'Ž‘F_¬),–Letc.,“toŽ¡call‘UU±pr–ÿ}'oje“ctŽ‘!Ìc¬(›ª®)–UUm¸ãultiple“times“when“doing“­P®9athŽ‘潬::‘±outputŽ‘D¬(˜).ŽŽŽŒ‹^Ÿ+ Šn ý‘ì¬94–¯NON-­CONST‘ÕX¯VERSION’öÎ@3DLDF-1.1.5.1“°x¬360Ž €n ý•@P­360.– üNon-const‘Mv®9ersion.“¬[²LDF‘T2002.10.27.¬]Ž‘YéíThe–· argumen¸ãt“µcŽ‘ Áó¬refers“to“either“the“x,–Ö´y‘ÿ*ª,“z,“or–· w“coGordinate.Ž©°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¤ ‘ +­realŽ‘!ëx±get‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘JHh¬(­c®9harŽ‘¢’µcŽ‘öm;‘ª¨­c®9harŽ‘M:±c–ÿ}'o“or“dsŽ‘=&U¬=‘Ï´'w'Ž‘îµ;‘ª¨­constŽ‘! “b•QÇo“olŽ‘;çB±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘f` ¬=‘ϱtrueŽ‘”'µ;‘ª¨­constŽ‘! “b•QÇo“olŽŽ¡‘±do‘‰ffŽ‘®applyŽ‘GÈJ¬=‘½r±trueŽ‘‚ +µ;‘ª¨­F‘ÿ +«oQÇcusŽ‘"‰°Ž‘'‰µfŽ‘1?r¬=‘½r0Ž‘½sµ;‘ª¨­constŽ‘ iunsignedŽ‘Q3øshortŽ‘o’k±pr‘ÿ}'ojŽ’†C ¬=‘½r­Pro‘£ŽjectionsŽ‘>‰Ö¬::Ž‘E´PERSPŽ‘_Þmµ;‘ª¨­realŽŽ¡‘±factorŽ‘;Êù¬=‘Ç1Ž‘Ç);ŽŸ­361.Ž¦°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¡‘ +­realŽ‘ eaP•®9oin“tŽ‘<ÿ­¬::‘±get‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘)\ô¬(­c®9harŽ‘{µcŽ‘pV;‘ª¨­c®9harŽ‘Ç#±c–ÿ}'o“or“dsŽ‘6Яµ;‘ª¨­constŽ‘‡|b•QÇo“olŽ‘8Û±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘^„Lµ;‘ª¨­constŽ‘‡|b•QÇo“olŽ‘8Û±do‘‰ffŽ‘®applyŽ‘^åéµ;‘ª¨­F‘ÿ +«oQÇcusŽ‘!§{°Ž‘&§|µfŽ‘, b;‘ª¨­constŽŽ¡‘2unsignedŽ‘b7shortŽ’€¶±pr‘ÿ}'ojŽ’’õyµ;‘ª¨­realŽ‘]Ö±factorŽ‘3a´¬)Ž¡‘ +°fŽ¡‘­ifŽ‘´ú¬(±do‘‰ffŽ‘®applyŽ‘& +Õ¬)‘±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘K߬(‘ª®);Ž¡‘­ifŽ‘´ú¬(µfŽ‘¿þ°‘Ǭ0Ž‘Ç)‘µfŽ‘ ¿þ¬=‘Ç&Ž‘ +Ž6±default‘‰ffŽ‘®fo‘ÿ}'cusŽ‘Bl4¬;Ž¦‘­unsignedŽ‘D7shortŽ‘b³±ctrŽ‘o»¡¬;Ž¦‘µcŽ‘õ¬=‘DZtolowerŽ‘#í¬(µcŽ‘SÛ¬);Ž¡‘­ifŽ‘´ú¬(µcŽ‘ó°‘Ç´'x'Ž‘ w¬)‘±ctrŽ‘¬=‘Ç0Ž‘Ç;Ž¡‘­elseŽ‘*.6ifŽ‘5ã.¬(µcŽ‘ó°‘Ç´'y'Ž‘ w¬)‘±ctrŽ‘¬=‘Ç1Ž‘Ç;Ž¡‘­elseŽ‘*.6ifŽ‘5ã.¬(µcŽ‘ó°‘Ç´'z'Ž‘ w¬)‘±ctrŽ‘¬=‘Ç2Ž‘Ç;Ž¡‘­elseŽ‘*.6ifŽ‘5ã.¬(µcŽ‘ó°‘Ç´'w'Ž‘ w¬)‘±ctrŽ‘¬=‘Ç3Ž‘Ç;Ž¡‘­elseŽ‘+Øá°fŽ¡‘±c‘ÿ}'errŽ‘4)«°‘t´"ERROR!® ´In® ´Point::geŽ‘lsÆt_coord():® ´"Ž’¯n °‘t´"Invalid® ´c® ´argument:Ž‘lsÆ® ´"Ž‘zî*°‘tµcŽ‘ ;ß°‘t´".\n"Ž‘!®]°Ž¡‘2´"Using® ´x\n"Ž‘o d°‘DZ ushŽ‘€¬;Ž¡‘±ctrŽ‘. ¬=‘Ç0Ž‘Ç;Ž¡‘°gŽ¡‘±c–ÿ}'o“or“dsŽ‘2Ц¬=‘DZtolowerŽ‘#í¬(±c–ÿ}'o“or“dsŽ‘ Œ¬);Ž¡‘­ifŽ‘´ú¬(±c–ÿ}'o“or“dsŽ‘Ф°‘Ç´'w'Ž‘ w¬)‘­returnŽ‘(溱world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘uú¸¬[±ctrŽ‘ ¹î¬];Ž¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±c–ÿ}'o“or“dsŽ‘Ф°‘Ç´'u'Ž‘ w¬)‘­returnŽ‘(溱user‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘pœÛ¬[±ctrŽ‘ ¹î¬];Ž¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±c–ÿ}'o“or“dsŽ‘Ф°‘Ç´'p'Ž‘ w¬)‘°fŽ¡‘­ifŽ‘)´û¬(±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘%©8¬)‘±pr–ÿ}'oje“ctŽ‘#w¬(°Ž‘µfŽ‘ +øç;‘ª¨±pr‘ÿ}'ojŽ‘žkµ;‘ª¨±factorŽ‘®†¬);Ž¡‘­returnŽ‘Aæ½±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ’ œÐ¬[±ctrŽ‘ ¹î¬];Ž¡‘°gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±c–ÿ}'o“or“dsŽ‘Ф°‘Ç´'v'Ž‘ w¬)‘­returnŽ‘(溱view‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘q@i¬[±ctrŽ‘ ¹î¬];Ž¡‘­elseŽ‘+Øá°fŽ¡‘±c‘ÿ}'errŽ‘4 ø°‘WO´"ERROR!® ´In® ´Point::geŽ‘lWt_coord().® ´Invalid® ´aŽ’ÕV×rgument® ´char® ´coords:Ž’>V›® ´"Ž’L´L°‘WO±c–ÿ}'o“or“dsŽ‘"¸*°Ž¡‘2±end‘‚ØlŽ‘H¸ß°‘Ç´"Returning® ´INVALID_RŽ‘kÆÜEAL.\n\n"Ž’žTA°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½´INVALID_REALŽ’m¬;Ž¡‘°gŽ¡‘ +gŽŸ­362.‘ üconst‘ÕTv®9ersion.Ž¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­realŽ‘!ëx±get‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘JHh¬(­c®9harŽ‘¢’µcŽ‘öm;‘ª¨­c®9harŽ‘M:±c–ÿ}'o“or“dsŽ‘=&U¬=‘Ï´'w'Ž‘îµ;‘ª¨­constŽ‘! “b•QÇo“olŽ‘;çB±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘f` ¬=‘ϱtrueŽ‘”'µ;‘ª¨­constŽ‘! “b•QÇo“olŽŽ¡‘±do‘‰ffŽ‘®applyŽ‘GÈJ¬=‘½r±trueŽ‘‚ +µ;‘ª¨­F‘ÿ +«oQÇcusŽ‘"‰°Ž‘'‰µfŽ‘1?r¬=‘½r0Ž‘½sµ;‘ª¨­constŽ‘ iunsignedŽ‘Q3øshortŽ‘o’k±pr‘ÿ}'ojŽ’†C ¬=‘½r­Pro‘£ŽjectionsŽ‘>‰Ö¬::Ž‘E´PERSPŽ‘_Þmµ;‘ª¨­realŽŽ¡‘±factorŽ‘;Êù¬=‘Ç1Ž‘Ç)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹_±= Šn ý‘ì°x¬363–¯3DLDF-1.1.5.1’ ûØ­CONST‘ÕX¯VERSION“¬95Ž €n ý•@P­363.Ž©°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¤ ‘ +­realŽ‘ eaP•®9oin“tŽ‘<ÿ­¬::‘±get‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘)\ô¬(­c®9harŽ‘{µcŽ‘pV;‘ª¨­c®9harŽ‘Ç#±c–ÿ}'o“or“dsŽ‘6Яµ;‘ª¨­constŽ‘‡|b•QÇo“olŽ‘8Û±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘^„Lµ;‘ª¨­constŽ‘‡|b•QÇo“olŽ‘8Û±do‘‰ffŽ‘®applyŽ‘^åéµ;‘ª¨­F‘ÿ +«oQÇcusŽ‘!§{°Ž‘&§|µfŽ‘, b;‘ª¨­constŽŽ¡‘2unsignedŽ‘b7shortŽ’€¶±pr‘ÿ}'ojŽ’’õyµ;‘ª¨­realŽ‘]Ö±factorŽ‘3a´¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­P•®9oin“tŽ‘2pŽ‘7÷Ÿ¬(°Ž‘±thisŽ‘ë·¬);Ž¦‘­returnŽ‘7æ¼µpŽ‘<î¼:±get‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘(\ð¬(µcŽ‘SÛ;‘ª¨±c–ÿ}'o“or“dsŽ‘´4µ;‘ª¨±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘'Sàµ;‘ª¨±do‘‰ffŽ‘®applyŽ‘'µ}µ;‘ª¨fŽ‘£Ž;‘ª¨±pr‘ÿ}'ojŽ‘žkµ;‘ª¨±factorŽ‘®†¬);Ž¡‘ +°gŽ¤­364.‘ üGet‘ÕTx.Ž¡365.‘ üNon-const‘ÕTv®9ersion.Ž¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¤ ‘ +­realŽ‘!$å±get‘‰ffŽ‘®xŽ‘7³L¬(­c®9harŽ‘Ûÿ±c–ÿ}'o“or“dsŽ‘9j'¬=‘„œ´'w'Ž‘Êûµ;‘ª¨­constŽ‘ Gb•QÇo“olŽ‘:Z±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘c‡ð¬=‘„œ±trueŽ–I4µ;‘ª¨­constŽ‘ Gb•QÇo“olŽ‘:Z±do‘‰ffŽ‘®applyŽ‘cé¬=‘„œ±trueŽ“µ;‘ª¨­F‘ÿ +«oQÇcusŽŽ¡‘°Ž‘#µfŽ‘+À¬=‘Ç0Ž–ǵ;‘ª¨­constŽ‘ÕJunsignedŽ‘P XshortŽ‘mÖû±pr‘ÿ}'ojŽ’ƒ‘Ö¬=‘Ç­Pro‘£ŽjectionsŽ‘=“|¬::Ž‘D!º´PERSPŽ‘^èµ;‘ª¨­realŽ‘]Ö±factorŽ‘6(̬=‘Ç1Ž“);ŽŸ­366.Ž¦°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¡‘ +­realŽ‘ žHP•®9oin“tŽ‘=8”¬::‘±get‘‰ffŽ‘®xŽ‘Žk¬(­c®9harŽ‘Ub±c–ÿ}'o“or“dsŽ‘5^îµ;‘ª¨­constŽ‘Àcb•QÇo“olŽ‘9Lâ±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘^öµ;‘ª¨­constŽ‘Àcb•QÇo“olŽ‘9Lâ±do‘‰ffŽ‘®applyŽ‘_W·µ;‘ª¨­F‘ÿ +«oQÇcusŽ‘!àb°Ž‘&àcµfŽ‘,ÙI;‘ª¨­constŽ‘ÀcunsignedŽŽ¡‘2shortŽ‘Oʨ±pr‘ÿ}'ojŽ‘b¾kµ;‘ª¨­realŽ‘]Ö±factorŽ‘3a´¬)Ž¡‘ +°fŽ¡‘­returnŽ‘7æ¼±get‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘`C¬¬(´'x'Ž‘F_µ;‘ª¨±c–ÿ}'o“or“dsŽ‘´4µ;‘ª¨±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘'Sàµ;‘ª¨±do‘‰ffŽ‘®applyŽ‘'µ}µ;‘ª¨fŽ‘£Ž;‘ª¨±pr‘ÿ}'ojŽ‘žkµ;‘ª¨±factorŽ‘®†¬);Ž¡‘ +°gŽŸ­367.‘ üconst‘ÕTv®9ersion.Ž¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­realŽ‘!$å±get‘‰ffŽ‘®xŽ‘7³L¬(­c®9harŽ‘Ûÿ±c–ÿ}'o“or“dsŽ‘9j'¬=‘„œ´'w'Ž‘Êûµ;‘ª¨­constŽ‘ Gb•QÇo“olŽ‘:Z±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘c‡ð¬=‘„œ±trueŽ–I4µ;‘ª¨­constŽ‘ Gb•QÇo“olŽ‘:Z±do‘‰ffŽ‘®applyŽ‘cé¬=‘„œ±trueŽ“µ;‘ª¨­F‘ÿ +«oQÇcusŽŽ¡‘°Ž‘#µfŽ‘+À¬=‘Ç0Ž–ǵ;‘ª¨­constŽ‘ÕJunsignedŽ‘P XshortŽ‘mÖû±pr‘ÿ}'ojŽ’ƒ‘Ö¬=‘Ç­Pro‘£ŽjectionsŽ‘=“|¬::Ž‘D!º´PERSPŽ‘^èµ;‘ª¨­realŽ‘]Ö±factorŽ‘6(̬=‘Ç1Ž“)‘UU­constŽ‘*¢¬;ŽŸ­368.Ž¦°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¡‘ +­realŽ‘ žHP•®9oin“tŽ‘=8”¬::‘±get‘‰ffŽ‘®xŽ‘Žk¬(­c®9harŽ‘Ub±c–ÿ}'o“or“dsŽ‘5^îµ;‘ª¨­constŽ‘Àcb•QÇo“olŽ‘9Lâ±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘^öµ;‘ª¨­constŽ‘Àcb•QÇo“olŽ‘9Lâ±do‘‰ffŽ‘®applyŽ‘_W·µ;‘ª¨­F‘ÿ +«oQÇcusŽ‘!àb°Ž‘&àcµfŽ‘,ÙI;‘ª¨­constŽ‘ÀcunsignedŽŽ¡‘2shortŽ‘Oʨ±pr‘ÿ}'ojŽ‘b¾kµ;‘ª¨­realŽ‘]Ö±factorŽ‘3a´¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼±get‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘`C¬¬(´'x'Ž‘F_µ;‘ª¨±c–ÿ}'o“or“dsŽ‘´4µ;‘ª¨±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘'Sàµ;‘ª¨±do‘‰ffŽ‘®applyŽ‘'µ}µ;‘ª¨fŽ‘£Ž;‘ª¨±pr‘ÿ}'ojŽ‘žkµ;‘ª¨±factorŽ‘®†¬);Ž¡‘ +°gŽ¤­369.‘ üGet‘ÕTy‘ÿ +«.Ž¡370.‘ üNon-const‘ÕTv®9ersion.Ž¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¤ ‘ +­realŽ‘!%>±get‘‰ffŽ‘®yŽ‘7™T¬(­c®9harŽ‘ÜX±c–ÿ}'o“or“dsŽ‘9k¬=‘…0´'w'Ž‘˵;‘ª¨­constŽ‘ GYb•QÇo“olŽ‘:Zαdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘c‰6¬=‘…0±trueŽ–Iȵ;‘ª¨­constŽ‘ GYb•QÇo“olŽ‘:Zαdo‘‰ffŽ‘®applyŽ‘cêÓ¬=‘…0±trueŽ“µ;‘ª¨­F‘ÿ +«oQÇcusŽŽ¡‘°Ž‘#µfŽ‘+À¬=‘Ç0Ž–ǵ;‘ª¨­constŽ‘ÕJunsignedŽ‘P XshortŽ‘mÖû±pr‘ÿ}'ojŽ’ƒ‘Ö¬=‘Ç­Pro‘£ŽjectionsŽ‘=“|¬::Ž‘D!º´PERSPŽ‘^èµ;‘ª¨­realŽ‘]Ö±factorŽ‘6(̬=‘Ç1Ž“);ŽŽŽŒ‹`Àú Šn ý‘ì¬96–¯NON-­CONST‘ÕX¯VERSION’öÎ@3DLDF-1.1.5.1“°x¬371Ž €n ý•@P­371.Ž©°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¤ ‘ +­realŽ‘ ŸÕP•®9oin“tŽ‘=:!¬::‘±get‘‰ffŽ‘®yŽ‘t¬(­c®9harŽ‘Vï±c–ÿ}'o“or“dsŽ‘5`{µ;‘ª¨­constŽ‘Áðb•QÇo“olŽ‘9Oü±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘^ù4µ;‘ª¨­constŽ‘Áðb•QÇo“olŽ‘9Oü±do‘‰ffŽ‘®applyŽ‘_Zѵ;‘ª¨­F‘ÿ +«oQÇcusŽ‘!áï°Ž‘&áðµfŽ‘,ÚÖ;‘ª¨­constŽ‘ÁðunsignedŽŽ¡‘2shortŽ‘Oʨ±pr‘ÿ}'ojŽ‘b¾kµ;‘ª¨­realŽ‘]Ö±factorŽ‘3a´¬)Ž¡‘ +°fŽ¡‘­returnŽ‘7æ¼±get‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘`C¬¬(´'y'Ž‘F_µ;‘ª¨±c–ÿ}'o“or“dsŽ‘´4µ;‘ª¨±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘'Sàµ;‘ª¨±do‘‰ffŽ‘®applyŽ‘'µ}µ;‘ª¨fŽ‘£Ž;‘ª¨±pr‘ÿ}'ojŽ‘žkµ;‘ª¨±factorŽ‘®†¬);Ž¡‘ +°gŽŸ­372.‘ üconst‘ÕTv®9ersion.Ž¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­realŽ‘!%>±get‘‰ffŽ‘®yŽ‘7™T¬(­c®9harŽ‘ÜX±c–ÿ}'o“or“dsŽ‘9k¬=‘…0´'w'Ž‘˵;‘ª¨­constŽ‘ GYb•QÇo“olŽ‘:Zαdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘c‰6¬=‘…0±trueŽ–Iȵ;‘ª¨­constŽ‘ GYb•QÇo“olŽ‘:Zαdo‘‰ffŽ‘®applyŽ‘cêÓ¬=‘…0±trueŽ“µ;‘ª¨­F‘ÿ +«oQÇcusŽŽ¡‘°Ž‘#µfŽ‘+À¬=‘Ç0Ž–ǵ;‘ª¨­constŽ‘ÕJunsignedŽ‘P XshortŽ‘mÖû±pr‘ÿ}'ojŽ’ƒ‘Ö¬=‘Ç­Pro‘£ŽjectionsŽ‘=“|¬::Ž‘D!º´PERSPŽ‘^èµ;‘ª¨­realŽ‘]Ö±factorŽ‘6(̬=‘Ç1Ž“)‘UU­constŽ‘*¢¬;ŽŸ­373.Ž¦°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¡‘ +­realŽ‘ ŸÕP•®9oin“tŽ‘=:!¬::‘±get‘‰ffŽ‘®yŽ‘t¬(­c®9harŽ‘Vï±c–ÿ}'o“or“dsŽ‘5`{µ;‘ª¨­constŽ‘Áðb•QÇo“olŽ‘9Oü±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘^ù4µ;‘ª¨­constŽ‘Áðb•QÇo“olŽ‘9Oü±do‘‰ffŽ‘®applyŽ‘_Zѵ;‘ª¨­F‘ÿ +«oQÇcusŽ‘!áï°Ž‘&áðµfŽ‘,ÚÖ;‘ª¨­constŽ‘ÁðunsignedŽŽ¡‘2shortŽ‘Oʨ±pr‘ÿ}'ojŽ‘b¾kµ;‘ª¨­realŽ‘]Ö±factorŽ‘3a´¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼±get‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘`C¬¬(´'y'Ž‘F_µ;‘ª¨±c–ÿ}'o“or“dsŽ‘´4µ;‘ª¨±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘'Sàµ;‘ª¨±do‘‰ffŽ‘®applyŽ‘'µ}µ;‘ª¨fŽ‘£Ž;‘ª¨±pr‘ÿ}'ojŽ‘žkµ;‘ª¨±factorŽ‘®†¬);Ž¡‘ +°gŽ¤­374.‘ üGet‘ÕTz.Ž¡375.‘ üNon-const‘ÕTv®9ersion.Ž¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¤ ‘ +­realŽ‘!&ª±get‘‰ffŽ‘®zŽ‘7.«¬(­c®9harŽ‘Ýıc–ÿ}'o“or“dsŽ‘9n߬=‘‡´'w'Ž‘Íîµ;‘ª¨­constŽ‘ HÅb•QÇo“olŽ‘:]¦±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘cŽm¬=‘‡±trueŽ–L'µ;‘ª¨­constŽ‘ HÅb•QÇo“olŽ‘:]¦±do‘‰ffŽ‘®applyŽ‘cð +¬=‘‡±trueŽ“µ;‘ª¨­F‘ÿ +«oQÇcusŽŽ¡‘°Ž‘#µfŽ‘+À¬=‘Ç0Ž–ǵ;‘ª¨­constŽ‘ÕJunsignedŽ‘P XshortŽ‘mÖû±pr‘ÿ}'ojŽ’ƒ‘Ö¬=‘Ç­Pro‘£ŽjectionsŽ‘=“|¬::Ž‘D!º´PERSPŽ‘^èµ;‘ª¨­realŽ‘]Ö±factorŽ‘6(̬=‘Ç1Ž“);ŽŸ­376.Ž¦°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¡‘ +­realŽ‘ ¦0P•®9oin“tŽ‘=@|¬::‘±get‘‰ffŽ‘®zŽ‘¬(­c®9harŽ‘]J±c–ÿ}'o“or“dsŽ‘5fÖµ;‘ª¨­constŽ‘ÈKb•QÇo“olŽ‘9\²±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘_êµ;‘ª¨­constŽ‘ÈKb•QÇo“olŽ‘9\²±do‘‰ffŽ‘®applyŽ‘_g‡µ;‘ª¨­F‘ÿ +«oQÇcusŽ‘!èJ°Ž‘&èKµfŽ‘,á1;‘ª¨­constŽ‘ÈKunsignedŽŽ¡‘2shortŽ‘Oʨ±pr‘ÿ}'ojŽ‘b¾kµ;‘ª¨­realŽ‘]Ö±factorŽ‘3a´¬)Ž¡‘ +°fŽ¡‘­returnŽ‘7æ¼±get‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘`C¬¬(´'z'Ž‘F_µ;‘ª¨±c–ÿ}'o“or“dsŽ‘´4µ;‘ª¨±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘'Sàµ;‘ª¨±do‘‰ffŽ‘®applyŽ‘'µ}µ;‘ª¨fŽ‘£Ž;‘ª¨±pr‘ÿ}'ojŽ‘žkµ;‘ª¨±factorŽ‘®†¬);Ž¡‘ +°gŽŸ­377.‘ üconst‘ÕTv®9ersion.Ž¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­realŽ‘!&ª±get‘‰ffŽ‘®zŽ‘7.«¬(­c®9harŽ‘Ýıc–ÿ}'o“or“dsŽ‘9n߬=‘‡´'w'Ž‘Íîµ;‘ª¨­constŽ‘ HÅb•QÇo“olŽ‘:]¦±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘cŽm¬=‘‡±trueŽ–L'µ;‘ª¨­constŽ‘ HÅb•QÇo“olŽ‘:]¦±do‘‰ffŽ‘®applyŽ‘cð +¬=‘‡±trueŽ“µ;‘ª¨­F‘ÿ +«oQÇcusŽŽ¡‘°Ž‘#µfŽ‘+À¬=‘Ç0Ž–ǵ;‘ª¨­constŽ‘ÕJunsignedŽ‘P XshortŽ‘mÖû±pr‘ÿ}'ojŽ’ƒ‘Ö¬=‘Ç­Pro‘£ŽjectionsŽ‘=“|¬::Ž‘D!º´PERSPŽ‘^èµ;‘ª¨­realŽ‘]Ö±factorŽ‘6(̬=‘Ç1Ž“)‘UU­constŽ‘*¢¬;ŽŸ­378.Ž¦°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¡‘ +­realŽ‘ ¦0P•®9oin“tŽ‘=@|¬::‘±get‘‰ffŽ‘®zŽ‘¬(­c®9harŽ‘]J±c–ÿ}'o“or“dsŽ‘5fÖµ;‘ª¨­constŽ‘ÈKb•QÇo“olŽ‘9\²±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘_êµ;‘ª¨­constŽ‘ÈKb•QÇo“olŽ‘9\²±do‘‰ffŽ‘®applyŽ‘_g‡µ;‘ª¨­F‘ÿ +«oQÇcusŽ‘!èJ°Ž‘&èKµfŽ‘,á1;‘ª¨­constŽ‘ÈKunsignedŽŽ¡‘2shortŽ‘Oʨ±pr‘ÿ}'ojŽ‘b¾kµ;‘ª¨­realŽ‘]Ö±factorŽ‘3a´¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼±get‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘`C¬¬(´'z'Ž‘F_µ;‘ª¨±c–ÿ}'o“or“dsŽ‘´4µ;‘ª¨±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘'Sàµ;‘ª¨±do‘‰ffŽ‘®applyŽ‘'µ}µ;‘ª¨fŽ‘£Ž;‘ª¨±pr‘ÿ}'ojŽ‘žkµ;‘ª¨±factorŽ‘®†¬);Ž¡‘ +°gŽŸ­379.‘ üGet‘ÕTw.ŽŽŽŒ‹aÑ# Šn ý‘ì°x¬380–¯3DLDF-1.1.5.1’öÎ@NON-­CONST‘ÕX¯VERSION“¬97Ž €n ý•@P­380.‘ üNon-const‘ÕTv®9ersion.Ž©°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¤ ‘ +­realŽ‘!’±get‘‰ffŽ‘®wŽ‘9­¬(­c®9harŽ‘Õ¬±c–ÿ}'o“or“dsŽ‘9YI¬=‘z´'w'Ž‘Àpµ;‘ª¨­constŽ‘ @­b•QÇo“olŽ‘:Mv±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘cp¿¬=‘z±trueŽ–>©µ;‘ª¨­constŽ‘ @­b•QÇo“olŽ‘:Mv±do‘‰ffŽ‘®applyŽ‘cÒ\¬=‘z±trueŽ“µ;‘ª¨­F‘ÿ +«oQÇcusŽŽ¡‘°Ž‘#µfŽ‘+À¬=‘Ç0Ž–ǵ;‘ª¨­constŽ‘ÕJunsignedŽ‘P XshortŽ‘mÖû±pr‘ÿ}'ojŽ’ƒ‘Ö¬=‘Ç­Pro‘£ŽjectionsŽ‘=“|¬::Ž‘D!º´PERSPŽ‘^èµ;‘ª¨­realŽ‘]Ö±factorŽ‘6(̬=‘Ç1Ž“);ŽŸ­381.Ž¦°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¡‘ +­realŽ‘ ‚P•®9oin“tŽ‘=N¬::‘±get‘‰ffŽ‘®wŽ‘o¬(­c®9harŽ‘9±c–ÿ}'o“or“dsŽ‘5B¨µ;‘ª¨­constŽ‘¤b•QÇo“olŽ‘9V±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘^½Žµ;‘ª¨­constŽ‘¤b•QÇo“olŽ‘9V±do‘‰ffŽ‘®applyŽ‘_+µ;‘ª¨­F‘ÿ +«oQÇcusŽ‘!Ä°Ž‘&ĵfŽ‘,½;‘ª¨­constŽ‘¤unsignedŽŽ¡‘2shortŽ‘Oʨ±pr‘ÿ}'ojŽ‘b¾kµ;‘ª¨­realŽ‘]Ö±factorŽ‘3a´¬)Ž¡‘ +°fŽ¡‘­returnŽ‘7æ¼±get‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘`C¬¬(´'w'Ž‘F_µ;‘ª¨±c–ÿ}'o“or“dsŽ‘´4µ;‘ª¨±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘'Sàµ;‘ª¨±do‘‰ffŽ‘®applyŽ‘'µ}µ;‘ª¨fŽ‘£Ž;‘ª¨±pr‘ÿ}'ojŽ‘žkµ;‘ª¨±factorŽ‘®†¬);Ž¡‘ +°gŽŸ­382.‘ üconst‘ÕTv®9ersion.Ž¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­realŽ‘!’±get‘‰ffŽ‘®wŽ‘9­¬(­c®9harŽ‘Õ¬±c–ÿ}'o“or“dsŽ‘9YI¬=‘z´'w'Ž‘Àpµ;‘ª¨­constŽ‘ @­b•QÇo“olŽ‘:Mv±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘cp¿¬=‘z±trueŽ–>©µ;‘ª¨­constŽ‘ @­b•QÇo“olŽ‘:Mv±do‘‰ffŽ‘®applyŽ‘cÒ\¬=‘z±trueŽ“µ;‘ª¨­F‘ÿ +«oQÇcusŽŽ¡‘°Ž‘#µfŽ‘+À¬=‘Ç0Ž–ǵ;‘ª¨­constŽ‘ÕJunsignedŽ‘P XshortŽ‘mÖû±pr‘ÿ}'ojŽ’ƒ‘Ö¬=‘Ç­Pro‘£ŽjectionsŽ‘=“|¬::Ž‘D!º´PERSPŽ‘^èµ;‘ª¨­realŽ‘]Ö±factorŽ‘6(̬=‘Ç1Ž“)‘UU­constŽ‘*¢¬;ŽŸ­383.Ž¦°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¡‘ +­realŽ‘ ‚P•®9oin“tŽ‘=N¬::‘±get‘‰ffŽ‘®wŽ‘o¬(­c®9harŽ‘9±c–ÿ}'o“or“dsŽ‘5B¨µ;‘ª¨­constŽ‘¤b•QÇo“olŽ‘9V±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘^½Žµ;‘ª¨­constŽ‘¤b•QÇo“olŽ‘9V±do‘‰ffŽ‘®applyŽ‘_+µ;‘ª¨­F‘ÿ +«oQÇcusŽ‘!Ä°Ž‘&ĵfŽ‘,½;‘ª¨­constŽ‘¤unsignedŽŽ¡‘2shortŽ‘Oʨ±pr‘ÿ}'ojŽ‘b¾kµ;‘ª¨­realŽ‘]Ö±factorŽ‘3a´¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼±get‘‰ffŽ‘®c–ÿ}'o“or“dŽ‘`C¬¬(´'w'Ž‘F_µ;‘ª¨±c–ÿ}'o“or“dsŽ‘´4µ;‘ª¨±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘'Sàµ;‘ª¨±do‘‰ffŽ‘®applyŽ‘'µ}µ;‘ª¨fŽ‘£Ž;‘ª¨±pr‘ÿ}'ojŽ‘žkµ;‘ª¨±factorŽ‘®†¬);Ž¡‘ +°gŽŸ­384.‘ üGet‘ÕTtransform.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.10.27.¬]Ž‘Y;Made–UUthis“function“­constŽ‘*¢¬.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­inlineŽ‘)ŠIT‘ÿ +«ransformŽ‘aS±get‘‰ffŽ‘®tr‘ÿ}'ansformŽ’:¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼±tr‘ÿ}'ansformŽ‘c™ý¬;Ž¡‘ +°gŽŸ­385.‘ üGet‘ÕTcop®9y‘ÿ «.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.10.27.«]Ž‘Y;Made–UUthis“function“ÂconstŽ‘*¢«.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¡‘ -ÂShapQÇeŽ‘,Ac·Ž‘1AdÏget‘‰ffŽ‘®c‘ÿ}'opyŽ‘V«(‘ª®)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹Xõÿ Šn ý‘ì«88–­GET‘ÕXCOPY’9qÙ3DLDFPRÃŽG“·x«343Ž €n ý•@PÂ343.Ž©·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¤ ‘ -ÂShapQÇeŽ‘,Ac·Ž‘1AdÂP•®9oin“tŽ‘MÛ°«::‘Ïget‘‰ffŽ‘®c‘ÿ}'opyŽ‘%ø«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂP•®9oin“tŽ‘2Ž‘7ï ±pŽ‘?¾¸«=‘ÇÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“p‘ÿ}'ointŽ‘K«(‘ª¨);Ž¦‘·Ž‘±pŽ‘ Ï«=‘Ç·Ž‘ÇÏthisŽ‘²Ï«;Ž¡‘ÂreturnŽ‘7æ¼staticu½‰™šs4Ž‘ÔwcastŽ‘ld^·hÂShapQÇeŽ‘"Ab·Ž‘'Aci«(±pŽ‘«);Ž¡‘ -·gŽŸÂ344.‘ üIs–ÕTon“free“store.Ž¦·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¡‘ -ÂinlineŽ‘)ŠIb•QÇo“olŽ‘C+¯Ïis‘‰ffŽ–®on‘‰ffŽ“fr–ÿ}'e“e‘‰ffŽ‘®stor“eŽ’…¦„«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼Ïon‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘o‹®«;Ž¡‘ -·gŽŸÂ345.– üSlopQÇe.“«[¬LDF‘T2002.10.27.«]Ž‘ZîYÏslop‘ÿ}'eŽ‘q&$«(‘ª®)–»xreturns“the“slopGe“of“the“Ïtr–ÿ}'ac“e‘{Ó«of–»xthe“line“from“·Ž‘»yÏthisŽ‘b§«to“±pŽ‘ ~ð«on“theŽ¡plane–UUindicated“bš¸ãy“the“Âc®9harŽ‘¿ž«argumen˜ts“±mŽ‘ra«and“±nŽ‘ Uï«.‘qÇThese“should“bGe“Ý'x'Ž››´«,“Ý'y'Ž˜«,“Ý'z'Ž˜«,“Ý'X'Ž˜«,“Ý'Y'Ž˜«,“or“Ý'Z'Ž˜«.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.10.27.«]Ž‘Y;No¸ãw–UUusing“Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘S¾¨«directly“instead“of“\get"“functions.Ž¡‘ -[¬LDF‘T2002.10.27.«]Ž‘Y;Changed–UUargumen¸ãt“±pŽ‘ ²ª«from“ÂconstŽ‘!÷P•®9oin“tŽ‘@o”«&Ž‘KŒto“ÂP•®9oin“tŽ‘ï«.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘ ³/Ïslop‘ÿ}'eŽ‘6êú«(ÂP•®9oin“tŽ‘ï±pŽ‘#÷;‘ª¨Âc®9harŽ‘ñ±mŽ‘&£À«=‘ÇÝ'x'Ž– w±;‘ª¨Âc®9harŽ‘ñ±nŽ‘#Ü£«=‘ÇÝ'y'Ž“«)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹Yn Šn ý‘ì·x«346–­3DLDFPRÃŽG’KmSLOPE“«89Ž €n ý•@PÂ346.Ž¤·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž© ‘ -ÂrealŽ‘ ³/P•®9oin“tŽ‘=M{«::‘Ïslop‘ÿ}'eŽ‘7Ï«(ÂP•®9oin“tŽ‘ï±pŽ‘#÷;‘ª¨Âc®9harŽ‘ñ±mŽ‘#ܨ;‘ª¨Âc®9harŽ‘ñ±nŽ‘!‹«)‘UUÂconstŽ‘*¢·f‘UUÂb•QÇo“olŽ‘ö»ÝDEBUGŽ‘:„,«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¡‘ÂP•®9oin“tŽ‘<ï ±aŽ‘B8Ы(·Ž‘ÏthisŽ‘ë·«);Ž¡‘±aŽ‘#I3:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨);Ž¦‘±pŽ‘#:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨);Ž¦‘ÂifŽ‘)´û«(±aŽ‘H·‘DZpŽ‘Ï«)‘·fŽ¦‘(Ïc‘ÿ}'errŽ‘=Èÿ·‘UÝ"ERROR!È ÝInÈ ÝPoint::slŽ‘lope():\n"Ž’žì»·‘UÝ"PointsÈ ÝareÈ ÝtheÈ ÝsameŽ‘l.È ÝReturningÈ ÝINVALID_Ž’ÕÝ\ŽŽ¦‘<REAL\n\n"Ž‘nk·‘ÇÏ ushŽ‘€«;Ž¦‘(ÂifŽ‘3´ü«(ÝDEBUGŽ‘ÆY«)‘·fŽ¦‘2±aŽ‘7I5:ÏshowŽ‘Šÿ«(Ý"a"Ž‘F_«);Ž¦‘2±pŽ‘7:ÏshowŽ‘Šÿ«(Ý"p"Ž‘F_«);Ž¦‘(·gŽ¦‘(ÂreturnŽ‘Kæ¾ÝINVALID_REALŽ’‹m«;Ž¦‘·gŽ¦‘±mŽ‘)ŽÒ«=‘ÇÏtolowerŽ‘#í«(±mŽ‘Ç·«);Ž¦‘±nŽ‘&ǵ«=‘ÇÏtolowerŽ‘#í«(±nŽ‘š«);Ž¦‘ÂifŽ‘)´û«(·:«((±mŽ‘ ŽÏ·‘ÇÝ'x'Ž–FW·_‘8à±mŽ› ǯ·‘ÇÝ'y'Ž“·_‘8à±mŽ˜·‘ÇÝ'z'Ž‘ w«)–8à·^“«(±nŽ‘Dz·‘ÇÝ'x'Ž›FW·_“±nŽ‘ ’·‘ÇÝ'y'Ž˜·_“±nŽ‘ ’·‘ÇÝ'z'Ž‘ w«)“·^“«(±mŽ‘ ŽÏ·6«=‘DZnŽ‘Dz«)))‘·fŽ¦‘(Ïc‘ÿ}'errŽ‘=Èÿ·‘UÝ"ERROR!È ÝInÈ ÝPoint::slŽ‘lope():\n"Ž’žì»·‘UÝ"OneÈ ÝorÈ ÝbothÈ ÝcharÈ ÝarŽ‘lgumentsÈ ÝareÈ ÝinvalidÈ Ž’ÕÝÝ\ŽŽ¦‘<orÈ ÝtheyÈ ÝareÈ ÝtheÈ ÝsameŽ’¤ÿÊ:È Ý"Ž’¸ A·‘DZmŽ‘Uç·‘ÇÝ",È Ý"Ž‘Œ·‘DZnŽ‘ ŽÊ·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÝ"ReturningÈ ÝINVALID_RŽ‘kÆÜEAL\n\n"Ž’™D·Ž¦‘<Ï ushŽ‘Q¹«;Ž¦‘(ÂreturnŽ‘Kæ¾ÝINVALID_REALŽ’‹m«;Ž¦‘·gŽ¡‘Âin®9tŽ‘/¤úÏctrŽ‘@&«=‘DZmŽ‘ ǯ·‘8àÝ'x'Ž‘?«;Ž¦‘ÂrealŽ‘4³1Ïa‘‰ffŽ–®m‘‰ffŽ“c–ÿ}'o“or“dŽ‘dI“«=‘DZaŽ‘H:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[ÏctrŽ‘ ¹î«];Ž¦‘ÂrealŽ‘4³1Ïp‘‰ffŽ–®m‘‰ffŽ“c–ÿ}'o“or“dŽ‘dI“«=‘DZpŽ‘Ï:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[ÏctrŽ‘ ¹î«];Ž¡‘ÏctrŽ‘. «=‘DZnŽ‘ ’·‘8àÝ'x'Ž‘?«;Ž¡‘ÂrealŽ‘4³1Ïa‘‰ffŽ–®n‘‰ffŽ“c–ÿ}'o“or“dŽ‘a»[«=‘DZaŽ‘H:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[ÏctrŽ‘ ¹î«];Ž¦‘ÂrealŽ‘4³1Ïp‘‰ffŽ–®n‘‰ffŽ“c–ÿ}'o“or“dŽ‘a»[«=‘DZpŽ‘Ï:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[ÏctrŽ‘ ¹î«];ŽŸÂ347.‘ ü«W‘ÿ*ªe–Upoften“use“Ïslop‘ÿ}'eŽ‘;«(‘ª®)“in“order“to“ nd“out“whether“a“line“has“slopGe“or“not,‘Uwso“an“error“message“is“outŽ¦of–tplace“here.‘y%A‘Hwš¸ãarning“is“toGo,–-¼probably‘ÿ*ª,“but–tI'm“lea˜ving“this“in“here“for“no˜w,‘-¼just“in“case“I‘Hc˜hange“m˜yŽ¦mind.Ž¡·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¦‘ -ÂifŽ‘´ù«(Ïa‘‰ffŽ–®m‘‰ffŽ“c–ÿ}'o“or“dŽ–/–b·‘ÇÏp‘‰ffŽ–®m‘‰ffŽ“c–ÿ}'o“or“dŽ“«)‘·fŽ¦«#ÂifŽ‘ ´ø«0ŽŽ¦‘Ïc‘ÿ}'errŽ‘.»Î·‘&Ý"WARNING!È ÝInÈ ÝPoint::Ž‘qêslope():\n"Ž’³RW·‘&±mŽ‘Ô·Ž¦‘(Ý"È ÝcoordinatesÈ ÝofÈ ÝpoiŽ’ÿÈntsÈ ÝareÈ ÝequalÈ Ý(noÈ ÝslŽ’ùÿŒope)!\n"Ž’'Lô·‘ÇÝ"ReturningÈ ÝINVALID_RŽ‘kÆÜEAL\n\n"Ž’–M,«;Ž¦#ÂendifŽŽ¦‘returnŽ‘7æ¼ÝINVALID_REALŽ‘wm«;Ž¦‘ -·gŽ¦‘ -ÂreturnŽ‘-滫(Ïa‘‰ffŽ–®n‘‰ffŽ“c–ÿ}'o“or“dŽ–,yò·‘8àÏp‘‰ffŽ–®n‘‰ffŽ“c–ÿ}'o“or“dŽ“«)±=«(Ïa‘‰ffŽ–®m‘‰ffŽ“c–ÿ}'o“or“dŽ–/*·‘8àÏp‘‰ffŽ–®m‘‰ffŽ“c–ÿ}'o“or“dŽ“«);‘UU·gŽŸÂ348.‘ üIs–ÕTon“segmen®9t.ŽŽŽŒ‹Z -– Šn ý‘ì«90–­NON-ÂCONSTŽ‘+½Ô­VERSION’þ®¡3DLDFPRÃŽG“·x«349Ž €n ý•@PÂ349.– üNon-constŽ‘Øëv®9ersion.“«[¬LDF‘T2002.10.29.«]Ž‘[Ïis‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ’˜Äa«(‘ª®)–\1returns“a“Âb•QÇo“olu½‰™šs4Ž‘ÔwrealŽ‘6£Ž«with“the“Âb•QÇo“olŽ‘s«in-Ž¤ dicating–=Vwhether“·Ž‘ =WÏthisŽ‘fc«lies“on“the“line“segmenš¸ãt“bGet˜w˜een“Ïp0Ž‘‘l«and“Ïp1Ž‘T«,‘wVand“a“ÂrealŽ‘Ø…«v‘ÿqÇalue“±t“«represen˜ting“theŽ¡distance–l¤of“·Ž‘l¥ÏthisŽ‘Äÿ«on“the“w•¸ãa“y–l¤from“Ïp0Ž‘ð«to“Ïp1Ž‘ƒd«.›·´If“the“Âb•QÇo“olŽ‘%Y«is“ÏtrueŽ‘1<«,‘rxthen“0–íñ±<«=“±t“<«=“1.˜If›l¤±t“<“«0˜or˜±t“>“«1,‘rxthenŽ¡·Ž‘ÏthisŽ‘Rã«lies–g,on“the“line“passing“through“Ïp0Ž‘å«and“Ïp1Ž‘}ì«,›k¢but“not“on“the“segmen¸ãt.‘§LIf“·Ž‘g-ÏthisŽ‘º«doGesn't“lie“on“the“line,˜±tŽ¡«will–UUbGe“ÝINVALID_REALŽ‘BÛ™«.Ž¡‘ -[¬LDF‘T2002.10.29.«]Ž‘Y;T‘ÿ*ªo›UUc•¸ãhec“k˜whether˜·Ž‘UVÏthisŽ‘–a«lies˜on˜the˜line,˜use˜Ïis‘‰ffŽ–®on‘‰ffŽ“lineŽ‘-°_«(‘ª®).ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.10.29.«]Ž‘XLJBUG‘‘FIX:–¡Added“coGde“to“c•¸ãhec“k–¡whether“the“unit“v¸ãectors“·Ž‘¢ÏthisŽ‘·Ñ·‘·yÏp0Ž›âÚ«and“Ïp1Ž˜·‘·yŽ‘·zÏthisŽ‘·Ñ«areŽ¡equal–gbGefore“calculating“±rŽ‘Ø{«.‘Z#Before“I‘Udid“this,‘—ÏtrueŽ‘ï–«wš¸ãas“returned“for“ÂP•®9oin“tsŽ‘&@R«that“w˜eren't“on“the“line“segmen˜t.Ž¡‘ -[¬LDF‘T2002.10.29.«]Ž‘Y;No¸ãw–UUusing“Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘S¾¨«directly“instead“of“Ïget‘‰ffŽ‘®xŽ‘㼫(›ª®),“Ïget‘‰ffŽ‘®yŽ‘Ék«(˜),“and“Ïget‘‰ffŽ‘®zŽ‘]V«(˜).Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·ŽŸ ‘ -Âb•QÇo“olu½‰™šs4Ž‘ÔwrealŽ‘;@‚Ïis‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘xuÑ«(ÂP•®9oin“tŽ‘ïÏp0Ž‘+]±;‘ª¨ÂP•®9oin“tŽ‘ šEÏp1Ž‘,±«);ŽŽŽŒ‹[ Šn ý‘ì·x«350–­3DLDFPRÃŽG’þ®¡NON-ÂCONSTŽ‘+½Ô­VERSION“«91Ž €n ý•@PÂ350.Ž¤·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž© ‘ -Âb•QÇo“olu½‰™šs4Ž‘ÔwrealŽ‘;@‚P•®9oin“tŽ‘WÚΫ::‘Ïis‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘>5S«(ÂP•®9oin“tŽ‘ïÏp0Ž‘+]±;‘ª¨ÂP•®9oin“tŽ‘ 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+ Šn ý‘ì«92–­NON-ÂCONSTŽ‘+½Ô­VERSION’þ®¡3DLDFPRÃŽG“·x«350Ž €n ý•@P‘ÂP•®9oin“tŽ‘<ï Ïv2Ž‘Hƒ‡«(·Ž‘ÇÏv1Ž‘[«);Ž©‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘·fŽ¤ ‘(Ïv2Ž‘3“ë±:ÏshowŽ‘Šÿ«(Ý"v2"Ž‘†\«);Ž¡‘·gŽ¡‘ÂifŽ‘)´û«(Ïv0Ž›Zÿ·6«=‘ÇÏv1Ž–“ß·^‘8àÏv0Ž“·6«=‘ÇÏv2Ž˜«)‘·fŽ¡‘(ÂifŽ‘3´ü«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"NotÈ ÝonÈ Ýline.\n"Ž‘WMP«;Ž¡‘(ÂreturnŽ‘Kæ¾pairŽ‘`bÏ·hÂb•QÇo“olŽ‘L±;‘ª¨ÂrealŽ‘·i«(ÏfalseŽ‘¯D±;‘ª¨ÝINVALID_REALŽ‘A0ì«);Ž¡‘·gŽ¡‘=ª³±=·‘ÿý«[¬LDF‘T2002.10.29.«]Ž‘T7End–UUof“new“coGde.‘o·±=ŽŸÂ351.‘ ü«[¬LDF‘T2002.10.29.«]Ž‘Zˆ6Calculate–UUhoš¸ãw“far“·Ž‘UVÏthisŽ‘–a«is“on“the“w˜a˜y“from“Ïp0Ž‘Áj«to“Ïp1Ž‘l«.Ž¡‘ -LDF‘&ÐUndated.‘bIThe–&Üv‘ÿqÇalue“±t“«can“bšGe“calculated“from“either“the“x,–0'y‘ÿ*ª,“or–&Üz-co˜ordinates.‘bIW‘ÿ*ªe“try“them“in“orderŽ¡and–çireturn“the“ rst“one“that“wš¸ãorks.‘M#Because“of“the“limited“precision“with“whic˜h“w˜e“are“w˜orking,‘ýeit's“pGossibleŽ¡that–¯the“v‘ÿqÇalue“of“±t“«can“di er,‘ÅodepšGending“on“what“co˜ordinates“are“used“to“calculate“it.‘~ÓIn“general,‘Åothis“willŽ¡not–bGe“signi 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-Âb•QÇo“olu½‰™šs4Ž‘ÔwrealŽ‘;@‚Ïis‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘xuÑ«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]Ïp0Ž‘Pø±;‘ª¨ÂconstŽ‘ÕJP•®9oin“tŽ‘>Äç«&Ž‘FŒÏp1Ž‘R¢Å«)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹]-è Šn ý‘ì·x«353–­3DLDFPRÃŽG’Ü9ÂCONSTŽ’@š ­VERSION“«93Ž €n ý•@PÂ353.Ž©·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¤ ‘ -Âb•QÇo“olu½‰™šs4Ž‘ÔwrealŽ‘;@‚P•®9oin“tŽ‘WÚΫ::‘Ïis‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘>5S«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]Ïp0Ž‘Pø±;‘ª¨ÂconstŽ‘ÕJP•®9oin“tŽ‘>Äç«&Ž‘FŒÏp1Ž‘R¢Å«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂP•®9oin“tŽ‘2aŽ‘88Ï«(·Ž‘ÏthisŽ‘ë·«);Ž¦‘ÂreturnŽ‘7æ¼±aŽ‘=/ì:Ïis‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘=5O«(Ïp0Ž‘ À±;‘ª¨Ïp1Ž‘ Áh«);Ž¡‘ -·gŽŸÂ354.› üIs–‰®on“line.˜«[¬LDF‘T2002.10.29.«]Ž‘ZFnTO‘|DO:–Maš¸ãybGe“add“a“non-ÂconstŽ‘èÚ«v˜ersion.‘[ÚThis“isn't“urgen˜t,‘ µthough.ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.10.29.«]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¡‘ 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-«[¬LDF‘T2003.06.04.«]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¡‘ -Âb•QÇo“olŽ‘#¡gÏis‘‰ffŽ–®on‘‰ffŽ“planeŽ‘U$A«(ÂconstŽ‘*¢PlaneŽ‘>aZ«&Ž‘F(x±pŽ‘K0x«)‘UUÂconstŽ‘*¢«;ŽŸÂ357.› üIs–öin“triangle.˜«[¬LDF‘T2003.06.11.«]Ž‘YÆThis–“P•®9oin“tŽ‘?VÏ«&Ž‘GíÏp1Ž–S4­±;‘ª¨ÂconstŽ‘ >P•®9oin“tŽ‘?VÏ«&Ž‘GíÏp2Ž“±;‘ª¨Âb•QÇo“olŽ‘•Ïverb‘ÿ}'oseŽ‘?g«=‘@¯ÏfalseŽ‘ïó«)Ž¡‘ÂconstŽ‘8ÕP«;Ž¤Â358.‘ üT‘ÿ -«ransformations.Ž¡359.‘ üAne‘ÕTtransformations.ŽŽŽŒ‹^= Šn ý‘ì«94‘­RšÃŽOT–ÿJªA“TION–ÕXAR˜OUND“THE“MAIN“AXES’Ç7w3DLDFPR˜G‘·x«360Ž €n ý•@PÂ360.‘ üRotation–ÕTaround“the“main“axes.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ -«[¬LDF‘T2003.01.22.«]Ž‘Y«µReplaced›øÏb•Go“dy˜of˜function.‘\4ÂT‘ÿ -«ransformŽ‘;ϵ«::‘Ïr‘ÿ}'otateŽ‘oB«(‘ª®)˜returns˜a˜ÂT‘ÿ -«ransformŽ‘’ˆ«=‘Ç0Ž–DZ;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±zŽ‘>f®«=‘Ç0Ž“);ŽŸÂ361.Ž¡·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¦‘ -ÂT‘ÿ 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4 Šn ý‘ì¬102–¯NON-­CONSTŽ‘+½Ô¯VERSION’ñ; +3DLDF-1.1.5.1“°x¬394Ž €n ý•@P‘­P•®9oin“tŽ‘<ï ±v2Ž‘Hƒ‡¬(°Ž‘DZv1Ž‘[¬);Ž©‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘°fŽ¤ ‘(±v2Ž‘3“ëµ:±showŽ‘Šÿ¬(´"v2"Ž‘†\¬);Ž¡‘°gŽ¡‘­ifŽ‘)´û¬(±v0Ž›Zÿ°6¬=‘DZv1Ž–“ß°^‘8à±v0Ž“°6¬=‘DZv2Ž˜¬)‘°fŽ¡‘(­ifŽ‘3´ü¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Not® ´on® ´line.\n"Ž‘WMP¬;Ž¡‘(­returnŽ‘Kæ¾pairŽ‘`bÏ°h­b•QÇo“olŽ‘Lµ;‘ª¨­realŽ‘°i¬(±falseŽ‘¯Dµ;‘ª¨´INVALID_REALŽ‘A0ì¬);Ž¡‘°gŽ¡‘=ª³µ=°‘ÿý¬[²LDF‘T2002.10.29.¬]Ž‘T7End–UUof“new“coGde.‘o°µ=ŽŸ­395.‘ ü¬[²LDF‘T2002.10.29.¬]Ž‘Zˆ6Calculate–UUhoš¸ãw“far“°Ž‘UV±thisŽ‘–a¬is“on“the“w˜a˜y“from“±p0Ž‘Áj¬to“±p1Ž‘l¬.Ž¡‘ +LDF‘&ÐUndated.‘bIThe–&Üv‘ÿqÇalue“µt“¬can“bšGe“calculated“from“either“the“x,–0'y‘ÿ*ª,“or–&Üz-co˜ordinates.‘bIW‘ÿ*ªe“try“them“in“orderŽ¡and–çireturn“the“ rst“one“that“wš¸ãorks.‘M#Because“of“the“limited“precision“with“whic˜h“w˜e“are“w˜orking,‘ýeit's“pGossibleŽ¡that–¯the“v‘ÿqÇalue“of“µt“¬can“di er,‘ÅodepšGending“on“what“co˜ordinates“are“used“to“calculate“it.‘~ÓIn“general,‘Åothis“willŽ¡not–bGe“signi canš¸ãt,‘Lsince“w˜e'll“mainly“bGe“needing“this“function“to“determine“whether“a“­P•®9oin“tŽ‘#Ðh¬is“on“a“lineŽ¡segmenš¸ãt;–UUthe“exact“v‘ÿqÇalue“of“µt“¬will“usually“not“bGe“signi can˜t.Ž¦°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¡‘ +­ifŽ‘´ù¬(±p1Ž‘ Àµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ›Mþ¬[0Ž‘]–Ç°6¬=“±p0Ž‘Ýص:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[0Ž‘])Ž¡‘µrŽ‘‘.¬=‘Ç(±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ›Mþ¬[0Ž‘]–²õ°“±p0Ž‘ ɵµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[0Ž–])µ=¬(±p1Ž‘ Àµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[0Ž“]–²õ°“±p0Ž‘ ɵµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[0Ž‘]);Ž¡‘ +­elseŽ‘ .5ifŽ‘+ã-¬(±p1Ž‘ Àµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ›Mþ¬[1Ž‘]–Ç°6¬=“±p0Ž‘Ýص:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[1Ž‘])Ž¡‘µrŽ‘‘.¬=‘Ç(±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ›Mþ¬[1Ž‘]–²õ°“±p0Ž‘ ɵµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[1Ž–])µ=¬(±p1Ž‘ Àµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[1Ž“]–²õ°“±p0Ž‘ ɵµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[1Ž‘]);Ž¡‘ +­elseŽ‘ .5ifŽ‘+ã-¬(±p1Ž‘ Àµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ›Mþ¬[2Ž‘]–Ç°6¬=“±p0Ž‘Ýص:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[2Ž‘])Ž¡‘µrŽ‘‘.¬=‘Ç(±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ›Mþ¬[2Ž‘]–²õ°“±p0Ž‘ ɵµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[2Ž–])µ=¬(±p1Ž‘ Àµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[2Ž“]–²õ°“±p0Ž‘ ɵµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[2Ž‘]);Ž¡‘ +­elseŽ‘!Øà°fŽ¡‘±c‘ÿ}'errŽ‘.ô°‘>u´"ERROR!® ´In® ´Point::isŽ‘q>9_on_segment()\n"Ž’Îæ°Ž¡‘(´"Can't® ´calculate® ´t.® Ž’ÿÈ´Returning® ´false® ´and® Ž’ùÿŒ´INVALID_REAL.\n\n"Ž’[ÌÖ°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘7æ¼pairŽ‘LbÍ°h­b•QÇo“olŽ‘Lµ;‘ª¨­realŽ‘°i¬(±falseŽ‘¯Dµ;‘ª¨´INVALID_REALŽ‘A0ì¬);Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(µrŽ‘‘,°‘Ǭ0Ž‘ ÿù°^‘8àµrŽ‘ Ê °‘Ǭ1Ž‘Ç)‘µbŽ‘ ¬=‘DZtrueŽ‘‹°¬;Ž¡‘ +­elseŽ‘!ØàµbŽ‘(ꢬ=‘DZfalseŽ‘v\¬;Ž¡‘ +­returnŽ‘-æ»pairŽ‘BbÌ°h­b•QÇo“olŽ‘Lµ;‘ª¨­realŽ‘°i¬(µbŽ‘Jª;‘ª¨rŽ‘t¼¬);‘UU°gŽŸ­396.‘ üconstŽ‘**v®9ersion.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.10.29.¬]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­b•QÇo“olu½‰™šs4Ž‘ÔwrealŽ‘;@‚±is‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘xuѬ(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±p0Ž‘Pøµ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±p1Ž‘R¢Å¬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹g ô Šn ý‘ì°x¬397–¯3DLDF-1.1.5.1’h¢­CONSTŽ’3&v¯VERSION“¬103Ž €n ý•@P­397.Ž©°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¤ ‘ +­b•QÇo“olu½‰™šs4Ž‘ÔwrealŽ‘;@‚P•®9oin“tŽ‘WÚά::‘±is‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘>5S¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±p0Ž‘Pøµ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±p1Ž‘R¢Å¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­P•®9oin“tŽ‘2aŽ‘88Ϭ(°Ž‘±thisŽ‘ë·¬);Ž¦‘­returnŽ‘7æ¼µaŽ‘=/ì:±is‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘=5O¬(±p0Ž‘ Àµ;‘ª¨±p1Ž‘ Áh¬);Ž¡‘ +°gŽŸ­398.› üIs–‰®on“line.˜¬[²LDF‘T2002.10.29.¬]Ž‘ZFnTO‘|DO:–Maš¸ãybGe“add“a“non-­constŽ‘èÚ¬v˜ersion.‘[ÚThis“isn't“urgen˜t,‘ µthough.ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.10.29.¬]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­b•QÇo“olu½‰™šs4Ž‘ÔwrealŽ‘;@‚±is‘‰ffŽ–®on‘‰ffŽ“lineŽ‘e›Œ¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±p0Ž‘Pøµ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±p1Ž‘R¢Å¬)‘UU­constŽ‘*¢¬;ŽŸ­399.Ž¦°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¡‘ +­b•QÇo“olu½‰™šs4Ž‘ÔwrealŽ‘;@‚P•®9oin“tŽ‘WÚά::‘±is‘‰ffŽ–®on‘‰ffŽ“lineŽ‘+[¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±p0Ž‘Pøµ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±p1Ž‘R¢Å¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­b•QÇo“olu½‰™šs4Ž‘ÔwrealŽ‘E@ƒ±brŽ‘Ro¬=‘DZis‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘?üg¬(±p0Ž‘ Àµ;‘ª¨±p1Ž‘ Áh¬);Ž¦‘­ifŽ‘´ú¬(±brŽ‘ +gsµ:±se–ÿ}'c“ondŽ‘ nß°6¬=‘Ç´INVALID_REALŽ‘BM\¬)‘±brŽ‘gsµ:± rstŽ‘|¬=‘DZtrueŽ‘‹°¬;Ž¡‘­returnŽ‘7æ¼±brŽ‘BN/¬;Ž¡‘ +°gŽŸ­400.› üIs–°ìon“Plane.˜¬[²LDF‘T2003.06.04.¬]Ž‘ZhŽThis–5­function“returns“±trueŽ‘úE¬,›<if“°Ž‘5®±thisŽ‘W¬lies“on“the“­PlaneŽ‘#L½µpŽ‘(T½¬,˜otherwiseŽ¡±falseŽ‘¯D¬.‘qÇIt–UUm¸ãust“bšGe“de ned“in“®planes.web¬,“b˜ecause“­PlaneŽ‘#Œ ¬is“an“incomplete“t¸ãyp˜e“here.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.06.04.¬]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­b•QÇo“olŽ‘#¡g±is‘‰ffŽ–®on‘‰ffŽ“planeŽ‘U$A¬(­constŽ‘*¢PlaneŽ‘>aZ¬&Ž‘F(xµpŽ‘K0x¬)‘UU­constŽ‘*¢¬;ŽŸ­401.› üIs–öin“triangle.˜¬[²LDF‘T2003.06.11.¬]Ž‘YÆThis–“P•®9oin“tŽ‘?VϬ&Ž‘Gí±p1Ž–S4­µ;‘ª¨­constŽ‘ >P•®9oin“tŽ‘?VϬ&Ž‘Gí±p2Ž“µ;‘ª¨­b•QÇo“olŽ‘•±verb‘ÿ}'oseŽ‘?g¬=‘@¯±falseŽ‘ïó¬)Ž¡‘­constŽ‘8ÕP¬;Ž¤­402.‘ üT‘ÿ +«ransformations.Ž¡403.‘ üAne‘ÕTtransformations.ŽŽŽŒ‹h ,! Šn ý‘ì¬104‘¯RšÃŽOT–ÿJªA“TION–ÕXAR˜OUND“THE“MAIN“AXES’¹Ãà3DLDF-1.1.5.1‘°x¬404Ž €n ý•@P­404.‘ üRotation–ÕTaround“the“main“axes.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ +¬[²LDF‘T2003.01.22.¬]Ž‘Y«µReplaced›øÏb•Go“dy˜of˜function.‘\4­T‘ÿ +«ransformŽ‘;ϵ¬::‘±r‘ÿ}'otateŽ‘oB¬(‘ª®)˜returns˜a˜­T‘ÿ +«ransformŽ‘’ˆ¬=‘Ç0Ž–ǵ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµzŽ‘>f®¬=‘Ç0Ž“);ŽŸ­405.Ž¡°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¦‘ +­T‘ÿ +«ransformŽ‘AÈÓP•®9oin“tŽ‘^c¬::‘±r‘ÿ}'otateŽ‘oB¬(­constŽ‘*¢realŽ‘4ÝеxŽ‘:”ì;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµyŽ‘;Ëp;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµzŽ‘;Ÿ–¬)Ž¦‘ +°fŽ¦‘­returnŽ‘7æ¼±tr‘ÿ}'ansformŽ‘c™ýµ:±r‘ÿ}'otateŽ‘o>¬(µxŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁƬ);Ž¦‘ +°gŽŸ­406.‘ üScale.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ +¬[²LDF‘T2003.01.22.¬]Ž‘Xr1Replaced›¿Kb•Go“dy˜of˜function.‘?Ä­T‘ÿ +«ransformŽ‘9³E¬::‘±sc‘ÿ}'aleŽ‘´ö¬(‘ª®)˜returns˜a˜­T‘ÿ +«ransformŽ‘9ò¬represen¸ãting˜theŽ¦rotation–UUonly‘ÿ*ª,“so“I“don't“need“to“use“a“loGcally“declared“­T‘ÿ +«ransformŽ‘;'µtŽ‘Bî¬in“this“function.Ž¡ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¦‘ +­T‘ÿ +«ransformŽ‘AÈÓ±sc‘ÿ}'aleŽ‘W}Ŭ(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ gæ¬=‘Ç1Ž–ǵ;‘ª¨­realŽ‘]ÖµzŽ‘ < ¬=‘Ç1Ž“);ŽŸ­407.Ž¡°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¦‘ +­T‘ÿ +«ransformŽ‘AÈÓP•®9oin“tŽ‘^c¬::‘±sc‘ÿ}'aleŽ‘´ö¬(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ Î;‘ª¨­realŽ‘]ÖµzŽ‘tô¬)Ž¦‘ +°fŽ¦‘­returnŽ‘7æ¼±tr‘ÿ}'ansformŽ‘c™ýµ:±sc‘ÿ}'aleŽ‘´ò¬(µxŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁƬ);Ž¦‘ +°gŽŸ­408.‘ üShear.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ +¬[²LDF‘T2003.01.22.¬]Ž‘YßžReplaced›,¸b•Go“dy˜of˜function.‘÷ï­T‘ÿ +«ransformŽ‘¬(‘ª®)˜returns˜a˜­T‘ÿ +«ransformŽ‘<Ìí¬represen¸ãtingŽ¦the–UUrotation“only‘ÿ*ª,“so“I“don't“need“to“use“a“loGcally“declared“­T‘ÿ +«ransformŽ‘;'µtŽ‘Bî¬in“this“function.Ž¡ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¦‘ +­T‘ÿ +«ransformŽ‘AÈÓ±she‘ÿ}'arŽ‘Yý ¬(­realŽ‘³.±xyŽ‘!—µ;‘ª¨­realŽ‘]Ö±xzŽ‘%œÀ¬=‘Ç0Ž–ǵ;‘ª¨­realŽ‘]Ö±yxŽ‘&Zœ¬=‘Ç0Ž“µ;‘ª¨­realŽ‘]Ö±yzŽ‘%Ô6¬=‘Ç0Ž“µ;‘ª¨­realŽ‘]Ö±zxŽ‘%–Y¬=‘Ç0Ž“µ;‘ª¨­realŽ‘]Ö±zyŽ‘%|¬=‘Ç0Ž“);ŽŸ­409.Ž¡°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¦‘ +­T‘ÿ +«ransformŽ‘AÈÓP•®9oin“tŽ‘^c¬::‘±she‘ÿ}'arŽ‘4>¬(­realŽ‘³.±xyŽ‘!—µ;‘ª¨­realŽ‘]Ö±xzŽ‘"Õ¨µ;‘ª¨­realŽ‘]Ö±yxŽ‘#“„µ;‘ª¨­realŽ‘]Ö±yzŽ‘# µ;‘ª¨­realŽ‘]Ö±zxŽ‘"ÏAµ;‘ª¨­realŽ‘]Ö±zyŽ‘"´ð¬)Ž¦‘ +°fŽ¦‘­returnŽ‘7æ¼±tr‘ÿ}'ansformŽ‘c™ýµ:±she‘ÿ}'arŽ‘4:¬(±xyŽ‘ +ãçµ;‘ª¨±xzŽ‘ "zµ;‘ª¨±yxŽ‘ àVµ;‘ª¨±yzŽ‘ Yðµ;‘ª¨±zxŽ‘ µ;‘ª¨±zyŽ‘ ¬);Ž¦‘ +°gŽ¤­410.‘ üShift.Ž¡411.‘ üP•®9oin“t‘ÕTv“ersions.ŽŽŽŒ‹i 9¢ Šn ý‘ì°x¬412›¯3DLDF-1.1.5.1’ÞRÁTHREE–ÕX­REAL“¯ARÃŽGUMENTS˜¬105Ž €n ý•@P­412.‘ üThree–ÕTreal“argumen®9ts.Ž¤°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž© ‘ +­T‘ÿ +«ransformŽ‘AÈÓ±shiftŽ‘UæP¬(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ gæ¬=‘Ç0Ž–ǵ;‘ª¨­realŽ‘]ÖµzŽ‘ < ¬=‘Ç0Ž“);ŽŸ­413.Ž¡°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¦‘ +­T‘ÿ +«ransformŽ‘AÈÓP•®9oin“tŽ‘^c¬::‘±shiftŽ‘¬(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ Î;‘ª¨­realŽ‘]ÖµzŽ‘tô¬)Ž¦‘ +°fŽ¦‘­T‘ÿ +«ransformŽ‘KÈÔµtŽ‘OeF¬;Ž¡‘­ifŽ‘´ú¬(µxŽ‘~4°6¬=‘Ç0Ž– ÿù°_‘8àµyŽ‘ +Bð°6¬=‘Ç0Ž“°_‘8àµzŽ‘ +°6¬=‘Ç0Ž‘Ç)‘±tr‘ÿ}'ansformŽ‘3zY°¬=ŽŽ‘CµtŽ‘F¥:±shiftŽ‘}¬(µxŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁƬ);Ž¦‘­returnŽ‘7æ¼µtŽ‘;ƒ.¬;Ž¦‘ +°gŽŸ­414.‘ üP•®9oin“t‘ÕTargumen“t.Ž¡°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¦‘ +­T‘ÿ +«ransformŽ‘AÈÓ±shiftŽ‘UæP¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié]¬);ŽŸ­415.Ž¡°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¦‘ +­T‘ÿ +«ransformŽ‘AÈÓP•®9oin“tŽ‘^c¬::‘±shiftŽ‘¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié]¬)Ž¦‘ +°fŽ¦‘­returnŽ‘7æ¼±shiftŽ‘L9¬(µpŽ‘:±get‘‰ffŽ‘®xŽ‘Žg¬(–ª¨)µ;“pŽ›²¨:±get‘‰ffŽ‘®yŽ‘t¬(“)µ;“pŽ˜:±get‘‰ffŽ‘®zŽ‘¬(“));Ž¦‘ +°gŽŸ­416.– üT‘ÿ +«ransform‘ÿ\vš®9ersion.“P˜oin˜tŽ‘+rÁ¬argumen¸ãt.‘{@[²LDF‘T2002.04.24.¬]Ž‘W†¢Added–X}this“function.‘{@It's“declared“inŽ¦®transfor.web¬,–UUbut“m¸ãust“bšGe“de ned“here,“b˜ecause“­P•®9oin“tŽ‘"Dò¬is“an“incomplete“t¸ãyp˜e“there.Ž¡°h–ª¨¬De ne‘UU­T‘ÿ +«ransformŽ‘;'¬functions‘@¯169“°i‘Ǭ+°Ž¦‘ +­T‘ÿ «ransformŽ‘AÈÓT‘ÿ -«ransformŽ‘wrid“of“loGcal“ÂT‘ÿ -«ransformŽ‘;Ýù±tŽ‘?zk«.›‘ƒIt“w¸ãasn't“needed.˜No¸ãw“just“returning“the“return“v‘ÿqÇalueŽ¡of‘UUÏtr‘ÿ}'ansformŽ‘/–±:Ïshift‘‰ffŽ‘®timesŽ‘.ì;«(‘ª¨).Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž© ‘ -ÂT‘ÿ -«ransformŽ‘AÈÓÏshift‘‰ffŽ‘®timesŽ‘pµ«(ÂrealŽ‘³.±xŽ‘jJ;‘ª¨ÂrealŽ‘]Ö±yŽ‘ gæ«=‘Ç1Ž–DZ;‘ª¨ÂrealŽ‘]Ö±zŽ‘ < «=‘Ç1Ž“);ŽŸÂ376.Ž¡·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¦‘ -ÂT‘ÿ -«ransformŽ‘AÈÓP•®9oin“tŽ‘^c«::‘Ïshift‘‰ffŽ‘®timesŽ‘/ì?«(ÂrealŽ‘³.±xŽ‘jJ;‘ª¨ÂrealŽ‘]Ö±yŽ‘ Î;‘ª¨ÂrealŽ‘]Ö±zŽ‘tô«)Ž¦‘ -·fŽ¦‘ÂreturnŽ‘7æ¼Ïtr‘ÿ}'ansformŽ‘c™ý±:Ïshift‘‰ffŽ‘®timesŽ‘.ì;«(±xŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁÆ«);Ž¦‘ -·gŽŸÂ377.‘ üP•®9oin“t‘ÕTargumen“t.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ -«[¬LDF‘T2003.01.19.«]Ž‘Y;Added–UUthis“function.Ž¡ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¦‘ -ÂT‘ÿ -«ransformŽ‘AÈÓÏshift‘‰ffŽ‘®timesŽ‘pµ«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]±pŽ‘Ié]«);ŽŸÂ378.Ž¡·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¦‘ -ÂT‘ÿ -«ransformŽ‘AÈÓP•®9oin“tŽ‘^c«::‘Ïshift‘‰ffŽ‘®timesŽ‘/ì?«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]±pŽ‘Ié]«)Ž¦‘ -·fŽ¦‘ÂreturnŽ‘7æ¼Ïtr‘ÿ}'ansformŽ‘c™ý±:Ïshift‘‰ffŽ‘®timesŽ‘.ì;«(±pŽ‘:Ïget‘‰ffŽ‘®xŽ‘Žg«(–ª¨)±;“pŽ›²¨:Ïget‘‰ffŽ‘®yŽ‘t«(“)±;“pŽ˜:Ïget‘‰ffŽ‘®zŽ‘«(“));Ž¦‘ -·gŽŸÂ379.› üAlignmen®9t–Ï?with“an“axis.˜«Declared–.§in“Ètransfor.web«.‘ý¼De ned“here,‘dûbGecause“it“needs“ÂP•®9oin“tsŽ‘$R+«.Ž¦[¬LDF‘T2002.10.23.«]Ž‘NÔÏalign‘‰ffŽ–®with‘‰ffŽ“axisŽ’†—«(‘ª®)–!:returns“the“ÂT‘ÿ -«ransformŽ‘:µñ«needed“to“alignŸü±È“·ŽŽ‘Â!‘þ㎎Ž‘gþ!ŽŽŸN8“±pŸÿ®0Ž‘|s±pŸÿ®1ŽŽŽŽŽ‘KZ«with“one“of“the“main“axes.Ž¦‘ -[¬LDF‘T2003.05.04.«]Ž‘Y;BUG:–UUTO“DO:“T‘ÿ*ªry“to“ nd“out“wh¸ãy“I“sometimes“get“erroneous“results“withŽ¦Ïr‘ÿ}'otateŽ‘o>«(ÂP•®9oin“tŽ‘šH±;‘ª¨ÂP•®9oin“tŽ‘Dð±;‘ª¨ÂrealŽ‘«)–UU(formerly“Ïr–ÿ}'otate‘‰ffŽ‘®ar“oundŽ‘?Áä«(‘ª®)).‘qÇI“think“the“problem“ma¸ãy“bGe“here.ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¦‘ -«[¬LDF‘T2002.12.10.«]Ž‘YÓ»Made– Õthis“function“a“ÂfriendŽ‘&S«in“ÂclassŽ‘̦P•®9oin“tŽ‘;fî«.‘ÔHNo¸ãw“calling“Ïp0Ž‘7•±:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨)“andŽ¦Ïp1Ž‘ À±:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨)–UUat“the“bGeginning“of“this“function“and“using“Ïp0Ž‘l±:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘PiS«andŽ¦Ïp1Ž‘ À±:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘PiS«directly–UUinstead“of“Ïget‘‰ffŽ‘®xŽ‘㼫(›ª®),“Ïget‘‰ffŽ‘®yŽ‘Ék«(˜),“and“Ïget‘‰ffŽ‘®zŽ‘]V«(˜).Ž¡ŸüÈ„`ÕÁGŽŽŽŽŒ‹ac Šn ý‘ì·x«380›­3DLDFPRÃŽG’ïàALIGNMENT–ÕXWITH“AN“AXIS˜«97Ž €n ý•@PÂ380.Ž©·h–ª¨«De ne‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­125“·i‘Ç«+·Ž¤ ‘ -ÂT‘ÿ +«ransformŽ‘wrid“of“loGcal“­T‘ÿ +«ransformŽ‘;ÝùµtŽ‘?zk¬.›‘ƒIt“w¸ãasn't“needed.˜No¸ãw“just“returning“the“return“v‘ÿqÇalueŽ¡of‘UU±tr‘ÿ}'ansformŽ‘/–µ:±shift‘‰ffŽ‘®timesŽ‘.ì;¬(‘ª¨).Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž© ‘ +­T‘ÿ +«ransformŽ‘AÈÓ±shift‘‰ffŽ‘®timesŽ‘pµ¬(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ gæ¬=‘Ç1Ž–ǵ;‘ª¨­realŽ‘]ÖµzŽ‘ < ¬=‘Ç1Ž“);ŽŸ­420.Ž¡°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¦‘ +­T‘ÿ +«ransformŽ‘AÈÓP•®9oin“tŽ‘^c¬::‘±shift‘‰ffŽ‘®timesŽ‘/ì?¬(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ Î;‘ª¨­realŽ‘]ÖµzŽ‘tô¬)Ž¦‘ +°fŽ¦‘­returnŽ‘7æ¼±tr‘ÿ}'ansformŽ‘c™ýµ:±shift‘‰ffŽ‘®timesŽ‘.ì;¬(µxŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁƬ);Ž¦‘ +°gŽŸ­421.‘ üP•®9oin“t‘ÕTargumen“t.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ +¬[²LDF‘T2003.01.19.¬]Ž‘Y;Added–UUthis“function.Ž¡ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¦‘ +­T‘ÿ +«ransformŽ‘AÈÓ±shift‘‰ffŽ‘®timesŽ‘pµ¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié]¬);ŽŸ­422.Ž¡°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¦‘ +­T‘ÿ +«ransformŽ‘AÈÓP•®9oin“tŽ‘^c¬::‘±shift‘‰ffŽ‘®timesŽ‘/ì?¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié]¬)Ž¦‘ +°fŽ¦‘­returnŽ‘7æ¼±tr‘ÿ}'ansformŽ‘c™ýµ:±shift‘‰ffŽ‘®timesŽ‘.ì;¬(µpŽ‘:±get‘‰ffŽ‘®xŽ‘Žg¬(–ª¨)µ;“pŽ›²¨:±get‘‰ffŽ‘®yŽ‘t¬(“)µ;“pŽ˜:±get‘‰ffŽ‘®zŽ‘¬(“));Ž¦‘ +°gŽŸ­423.› üAlignmen®9t–Ï?with“an“axis.˜¬Declared–.§in“®transfor.web¬.‘ý¼De ned“here,‘dûbGecause“it“needs“­P•®9oin“tsŽ‘$R+¬.Ž¦[²LDF‘T2002.10.23.¬]Ž‘NÔ±align‘‰ffŽ–®with‘‰ffŽ“axisŽ’†—¬(‘ª®)–!:returns“the“­T‘ÿ +«ransformŽ‘:µñ¬needed“to“alignŸü±È“°ŽŽ‘Â!‘þ㎎Ž‘gþ!ŽŽŸN8“µpŸÿ³0Ž‘|sµpŸÿ³1ŽŽŽŽŽ‘KZ¬with“one“of“the“main“axes.Ž¦‘ +[²LDF‘T2003.05.04.¬]Ž‘Y;BUG:–UUTO“DO:“T‘ÿ*ªry“to“ nd“out“wh¸ãy“I“sometimes“get“erroneous“results“withŽ¦±r‘ÿ}'otateŽ‘o>¬(­P•®9oin“tŽ‘šHµ;‘ª¨­P•®9oin“tŽ‘Dðµ;‘ª¨­realŽ‘¬)–UU(formerly“±r–ÿ}'otate‘‰ffŽ‘®ar“oundŽ‘?Áä¬(‘ª®)).‘qÇI“think“the“problem“ma¸ãy“bGe“here.ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ +¬[²LDF‘T2002.12.10.¬]Ž‘YÓ»Made– Õthis“function“a“­friendŽ‘&S¬in“­classŽ‘̦P•®9oin“tŽ‘;fî¬.‘ÔHNo¸ãw“calling“±p0Ž‘7•µ:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨)“andŽ¦±p1Ž‘ Àµ:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨)–UUat“the“bGeginning“of“this“function“and“using“±p0Ž‘lµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘PiS¬andŽ¦±p1Ž‘ Àµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘PiS¬directly–UUinstead“of“±get‘‰ffŽ‘®xŽ‘㼬(›ª®),“±get‘‰ffŽ‘®yŽ‘Ék¬(˜),“and“±get‘‰ffŽ‘®zŽ‘]V¬(˜).Ž¡ŸüÈ„`ÕÁGŽŽŽŽŒ‹k R¦ Šn ý‘ì°x¬424›¯3DLDF-1.1.5.1’âlêALIGNMENT–ÕXWITH“AN“AXIS˜¬107Ž €n ý•@P­424.Ž©°h–ª¨¬De ne‘UU­T‘ÿ +«ransformŽ‘;'¬functions‘@¯169“°i‘Ǭ+°Ž¤ ‘ +­T‘ÿ «ransformŽ‘AÈÓT‘ÿ -«ransformŽ‘wIGgument:È Ý"Ž’qY·Ž¡‘<ÏaxisŽ‘Qæ·‘ÇÏend‘‚ØlŽ–ò·‘ÇÝ"ReturningÈ ÝidentityÈ Ž‘kÆÜÝmatrix."Ž’™D·‘ÇÏend‘‚ØlŽ“·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾±tŽ‘Oƒ0«;Ž¡‘·gŽ¦‘ÂrealŽ‘4³1ÏangleŽ‘Ls„«;ŽŸÂ381.‘ ü«[¬LDF‘T2002.10.23.«]Ž‘[]ÓShift‘*òÏp0Ž›l¤«to–*òorigin,‘`Yand“shift“Ïp1Ž˜«the“same“w•¸ãa“y‘ÿ*ª,‘`Yso–*òthat“the“relationship“bGet•¸ãw“eenŽ¡them–UUremains“constan¸ãt.Ž¦·h–ª¨«De ne‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­125“·i‘Ç«+·Ž¡‘ -ÂifŽ‘´ù«(Ïp0Ž‘ÝØ·6«=‘ÇÏoriginŽ‘½9«)‘·fŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïp0Ž‘*ñ:ÏshowŽ‘Šÿ«(Ý"p0"Ž‘†\«);Ž¡‘Ïp1Ž‘*ñ:ÏshowŽ‘Šÿ«(Ý"p1"Ž‘†\«);Ž¡‘·gŽ¡‘±tŽ‘œt:ÏshiftŽ‘}«(·Ž‘ÇÏp0Ž‘ÝÞ«);Ž¡‘Ïp1Ž‘"ÝÚ·«=ŽŽ‘2l±tŽ‘6ƒ«;Ž¡‘Ïp1Ž‘ ±:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨);Ž¡‘Ïp0Ž‘ ±:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨);Ž¡‘ -·gŽ¦‘ -h–ª¨«Normalize›Y -pGoin¸ãt‘@­389“·i‘±=·‘²«[¬LDF‘T2002.10.23.«]Ž‘T¡T–ÿ*ªransform˜the˜ÂP•®9oin“tŽ‘"L\«so˜that˜it's˜x,›Y÷y“,˜and–Y -z“coGordinatesŽ¡‘2are–UUall“pšGositiv¸ãe.‘qÇSee“b˜elo¸ãw“for“the“explanation.‘o·±=Ž¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘(±tŽ‘+œv:ÏshowŽ‘Šÿ«(Ý"tÈ ÝoutsideÈ ÝofÈ ÝnormaŽ‘hÿÄlization"Ž’˜Æ«);Ž¡‘·gŽ¦‘ÂP•®9oin“tŽ‘<¼Ïpr‘ÿ}'oj‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“z‘‰ffŽ“planeŽ’ˆ,"«(Ïp1Ž‘ À«);‘±=·‘Ìv«[¬LDF‘T2002.10.23.«]Ž‘S¡)Get–!Îthe“pro‘Ž8jection“of“Ïp1Ž‘Z\«on“the“x-z“plane.‘ B·±=Ž¡‘ -Ïpr‘ÿ}'oj‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“z‘‰ffŽ“planeŽ‘Up -±:ÏshiftŽ‘}«(0Ž–±;‘ª¨·Ž‘ qÆÏp1Ž‘ˆ†±:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[1Ž“]);Ž¦‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘Ïpr‘ÿ}'oj‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“z‘‰ffŽ“planeŽ‘Pp ±:ÏshowŽ‘Šÿ«(Ý"proj_on_x_z_plane"Ž‘dF/«);ŽŽŽŒ‹bp1 Šn ý‘ì«98›­ALIGNMENT–ÕXWITH“AN“AXIS’ïà3DLDFPRÃŽG˜·x«382Ž €n ý•@PÂ382.‘ ü«[¬LDF‘T2002.10.23.«]Ž‘ZJœIf–»wš¸ãe're“aligning“with“the“x“or“y-axis,‘$ rotate“Ïp1Ž‘F6«on˜to“the“x-y“plane“and“then“to“theŽ¤ x-axis.Ž©·h–ª¨«De ne‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­125“·i‘Ç«+·Ž¡‘ -ÂifŽ‘´ù«(ÏaxisŽ‘à·‘ÇÝ'x'Ž‘FW·_‘8àÏaxisŽ‘<À·‘ÇÝ'y'Ž‘ w«)‘·fŽ¡‘ÂP•®9oin“tŽ‘2ïŸÏpt‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“axisŽ‘hЫ;Ž¦‘Ïpt‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“axisŽ‘I3±:ÏsetŽ‘ x„«(1Ž‘);Ž¡‘ÏangleŽ‘.‡m«=‘ÇÏpr‘ÿ}'oj‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“z‘‰ffŽ“planeŽ‘N7!±:ÏangleŽ‘ÀS«(Ïpt‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“axisŽ‘51«);Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"angleÈ ÝofÈ ÝprojectionŽ‘kÆÜ:È Ý"Ž‘~ÔS·‘ÇÏangleŽ‘Nƒ·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ÂifŽ‘´ú«(ÏangleŽ‘‡k·6«=‘Ç0Ž‘ ÿù·^‘8àÏangleŽ‘ÀK·6«=‘ÇÝINVALID_REALŽ‘BM\«)‘±tŽ‘ cŠ·«=ŽŽ‘ñÁÏp1Ž‘'±:Ïr‘ÿ}'otateŽ‘o>«(0Ž‘±;‘ª¨·Ž‘ qÆÏangleŽ‘!2«);Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïp1Ž‘À±:ÏshowŽ‘Šÿ«(Ý"p1È ÝafterÈ ÝrotationÈ ÝtŽ‘hÿÄoÈ Ýx-yÈ Ýplane"Ž’¨†«);Ž¡‘ÏangleŽ‘.‡m«=‘ÇÏp1Ž‘Ýر:ÏangleŽ‘ÀS«(Ïpt‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“axisŽ‘51«);Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"angleÈ ÝtoÈ Ýx-axis:È Ý"Ž‘iÔ_·‘ÇÏangleŽ‘Nƒ·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ÂifŽ‘´ú«(ÏangleŽ‘‡k·6«=‘Ç0Ž‘ ÿù·^‘8àÏangleŽ‘ÀK·6«=‘ÇÝINVALID_REALŽ‘BM\«)‘±tŽ‘ cŠ·«=ŽŽ‘ñÁÏp1Ž‘'±:Ïr‘ÿ}'otateŽ‘o>«(0Ž‘±;‘ª¨«0Ž‘ª©±;‘ª¨·Ž‘ qÆÏangleŽ‘!2«);Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïp1Ž‘À±:ÏshowŽ‘Šÿ«(Ý"p1È ÝafterÈ ÝrotationÈ ÝtŽ‘hÿÄoÈ Ýx-axis"Ž’˜Æ«);Ž¡‘ -·gŽŸÂ383.‘ ü«[¬LDF‘T2002.10.23.«]Ž‘YÇŠIf–”©wš¸ãe're“aligning“with“the“z-axis,‘»2rotate“Ïp1Ž‘@«on˜to“the“y-z“plane“and“then“to“the“z-axis.Ž¦·h–ª¨«De ne‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­125“·i‘Ç«+·Ž¡‘ -ÂelseŽ‘ .5ifŽ‘+ã-«(ÏaxisŽ‘à·‘ÇÝ'z'Ž‘ w«)–UU·f“ÂP•®9oin“tŽ‘"DòÏpt‘‰ffŽ–®on‘‰ffŽ“z‘‰ffŽ“axisŽ‘VÍV«;Ž¦‘ -Ïpt‘‰ffŽ–®on‘‰ffŽ“z‘‰ffŽ“axisŽ‘>ˆe±:ÏsetŽ‘ x„«(0Ž‘±;‘ª¨«0Ž–ª©±;‘ª¨«1Ž“);‘±=·‘<«[¬LDF‘T2002.10.23.«]Ž‘T€qThis–‘rassumes“that“Ïpr‘ÿ}'oj‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“z‘‰ffŽ“planeŽ‘O{±:Ïget‘‰ffŽ‘®zŽ‘«(‘ª¨)–+H·“«0Ž‘+I.‘&ItŽ¡‘should–UUbšGe,“but“if“it“isn't,“the“follo¸ãwing“error“handling“co˜de“tak¸ães“care“of“the“problem.‘o·±=Ž¡‘ -ÂifŽ‘´ù«(Ïpr‘ÿ}'oj‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“z‘‰ffŽ“planeŽ‘Kp ±:Ïget‘‰ffŽ‘®zŽ‘«(‘ª¨)–DZ<“«0Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘.ä·‘M<Ý"ERROR!È ÝInÈ ÝTransformŽ‘pM::align_with_axis():Ž’ÙLÄ\n"Ž’ðà_·Ž¡‘(Ý"proj_on_x_z_plane.gŽ’ÿÈet_z()È Ý<È Ý0\n"Ž’ØÛ·‘ Ý"@Ž‘lÏÈ ÝshouldÈ ÝensureÈ ÝthatÈ Ž’Õ“Ý"Ž’Ýð·Ž¡‘(Ý"thisÈ ÝvalueÈ ÝisÈ Ý>=È Ý0.Ž’ÿÈ\n"Ž’¤[2·‘ Ý"HandlingÈ ÝtheÈ Ýerror,Ž‘lÏÈ ÝbutÈ ÝfindÈ ÝoutÈ ÝwhyÈ ÝitŽ’Õ“È Ýhappened!"Ž’oå·Ž¡‘(Ïend‘‚ØlŽ‘>¸Þ·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘Ïpt‘‰ffŽ–®on‘‰ffŽ“z‘‰ffŽ“axisŽ‘Hˆf±:ÏsetŽ‘ x„«(0Ž‘±;‘ª¨«0Ž‘ª©±;‘ª¨·Ž‘ qÆ«1Ž‘qÇ);Ž¡‘ -·gŽŸÂ384.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.12.10.«]Ž‘Yð:Added–=Tthe“follo¸ãwing“conditional.‘)ÅT‘ÿ*ªrying“to“ x“a“bug“that“ošGccurred“while“p˜orting“toŽ¡GNU/Lin¸ãux.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«De ne‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­125“·i‘Ç«+·Ž¡‘ -ÂifŽ‘´ù«(Ïpr‘ÿ}'oj‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“z‘‰ffŽ“planeŽ‘Kp ±:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ›Mþ«[0Ž‘]–Ç·“«0Ž‘ ÿù·^‘8àÏpr‘ÿ}'oj‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“z‘‰ffŽ“planeŽ‘M¨é±:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜«[1Ž‘]“·“«0Ž›Ç)‘ÏangleŽ‘‡k«=“0Ž˜;Ž¡‘ -ÂelseŽ‘!ØàÏangleŽ‘<`K«=‘ÇÏpr‘ÿ}'oj‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“z‘‰ffŽ“planeŽ‘N7!±:ÏangleŽ‘ÀS«(Ïpt‘‰ffŽ–®on‘‰ffŽ“z‘‰ffŽ“axisŽ‘4ˆd«);ŽŸÂ385.Ž¦·h–ª¨«De ne‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­125“·i‘Ç«+·Ž¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"angleÈ ÝofÈ ÝprojectionŽ‘kÆÜ:È Ý"Ž‘~ÔS·‘ÇÏangleŽ‘Nƒ·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ -ÂifŽ‘´ù«(ÏangleŽ‘‡k·6«=‘Ç0Ž‘ ÿù·^‘8àÏangleŽ‘ÀK·6«=‘ÇÝINVALID_REALŽ‘BM\«)‘±tŽ‘ cŠ·«=ŽŽ‘ñÁÏp1Ž‘'±:Ïr‘ÿ}'otateŽ‘o>«(0Ž‘±;‘ª¨ÏangleŽ‘jû«);Ž¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘Ïp1Ž‘À±:ÏshowŽ‘Šÿ«(Ý"p1È ÝafterÈ ÝrotationÈ ÝtŽ‘hÿÄoÈ Ýz-yÈ Ýplane"Ž’¨†«);Ž¡‘ -Ïp1Ž‘Á±:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨);ŽŽŽŒ‹c|àŠn ý‘ì·x«386›­3DLDFPRÃŽG’ïàALIGNMENT–ÕXWITH“AN“AXIS˜«99Ž €n ý•@PÂ386.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ -«[¬LDF‘T2002.12.10.«]Ž‘Yð:Added–=Tthe“follo¸ãwing“conditional.‘)ÅT‘ÿ*ªrying“to“ x“a“bug“that“ošGccurred“while“p˜orting“toŽ¡GNU/Lin¸ãux.Ž¡‘ -[¬LDF‘T2003.06.13.«]Ž‘X=BUG‘ŠFIX:–Š9Changed“Ïpr‘ÿ}'oj‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“z‘‰ffŽ“planeŽ‘P„{«to“Ïp1Ž‘+2«in“the“\ÂifŽ‘_£«"“part“of“the“follo¸ãwing“conditional.Ž¡The–]/y-coGordinate“of“Ïpr‘ÿ}'oj‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“z‘‰ffŽ“planeŽ‘R*g«is“alw•¸ãa“ys–]/0,‘_&so“ÏangleŽ‘z±«wš¸ãas“alw˜a˜ys“set“to“0.‘‰VI‘]-disco˜v˜ered“this“bug“whenŽ¡I‘'‘tried–'œrotating“a“ÂP•®9oin“tŽ‘!逫in“the“plane“of“a“ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘GÍì«abGout“a“line“from“the“cen¸ãter“of“the“ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽŽ¡«in–UUthe“direction“of“its“normal,“and“the“resulting“ÂP•®9oin“tŽ‘"Dò«w¸ãas“not“in“the“same“plane.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«De ne‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­125“·i‘Ç«+·Ž¤ ‘ -ÂifŽ‘´ù«(Ïp1Ž‘ À±:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[1Ž‘]–Ç·“«0Ž›Ç)‘ÏangleŽ‘‡k«=“0Ž˜;Ž¡‘ -ÂelseŽ‘!ØàÏangleŽ‘<`K«=‘ÇÏp1Ž‘Ýر:ÏangleŽ‘ÀS«(Ïpt‘‰ffŽ–®on‘‰ffŽ“z‘‰ffŽ“axisŽ‘4ˆd«);Ž©Â387.ŽŸ·h–ª¨«De ne‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­125“·i‘Ç«+·Ž¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"angleÈ ÝtoÈ Ýz-axis:È Ý"Ž‘iÔ_·‘ÇÏangleŽ‘Nƒ·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ -ÂifŽ‘´ù«(ÏangleŽ‘‡k·6«=‘Ç0Ž‘ ÿù·^‘8àÏangleŽ‘ÀK·6«=‘ÇÝINVALID_REALŽ‘BM\«)‘±tŽ‘ cŠ·«=ŽŽ‘ñÁÏp1Ž‘'±:Ïr‘ÿ}'otateŽ‘o>«(·Ž‘ÇÏangleŽ‘‡q«);Ž¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘Ïp1Ž‘À±:ÏshowŽ‘Šÿ«(Ý"p1È ÝafterÈ ÝrotationÈ ÝtŽ‘hÿÄoÈ Ýz-axis"Ž’˜Æ«);Ž¡‘ -·gŽ¦Â388.‘ ü«[¬LDF‘T2002.10.23.«]Ž‘ZÚÖIf–§õwš¸ãe're“aligning“with“the“y-axis,‘¼Ïp1Ž‘{R«m˜ust“bGe“rotated“from“the“x-axis“(where“it“isŽ¡noš¸ãw)–UUaround“the“z-axis“b˜y“90Ÿü^ÿºŽ‘˜ä«.‘qÇThen“it“will“bGe“on“the“y-axis.ŽŸ·h–ª¨«De ne‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­125“·i‘Ç«+·Ž¡‘ -ÂifŽ‘´ù«(ÏaxisŽ‘à·‘ÇÝ'y'Ž‘ w«)‘·fŽ¡‘±tŽ‘cŒ·«=ŽŽ‘)ñÃÏp1Ž‘6ƒ±:Ïr‘ÿ}'otateŽ‘o>«(0Ž‘±;‘ª¨«0Ž‘ª©±;‘ª¨«90ŽŽ‘ ªª);Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïp1Ž‘À±:ÏshowŽ‘Šÿ«(Ý"p1È ÝafterÈ ÝrotationÈ ÝtŽ‘hÿÄoÈ Ýy-axis"Ž’˜Æ«);Ž¡‘ -·gŽ¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"p1.magnitude()È Ý==È Ý"Ž‘o\·‘ÇÏp1Ž‘Ýر:ÏmagnitudeŽ‘.=r«(‘ª¨)–Ç·“Ïend‘‚ØlŽ‘ò·“Ï ushŽ‘€«;Ž¡‘±tŽ‘œt:ÏshowŽ‘Šÿ«(Ý"tÈ ÝatÈ ÝendÈ ÝofÈ Ýalign_wŽ‘hÿÄith_axis()"Ž’£F «);Ž¡‘ -·gŽ¡‘ -Ž‘ÏthisŽ‘"²Ð·«=ŽŽ‘2A±tŽ‘5Ýy«;Ž¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ExitingÈ ÝTransform::Ž‘kÆÜalign_with_axis."Ž’ÈT)·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ -ÂreturnŽ‘-æ»±tŽ‘1ƒ-«;‘qÇ·gŽŽŽŒ‹d Šn ý‘ì«100–­NORMALIZE‘ÕXPOINT’>Ü3DLDFPRÃŽG“·x«389Ž €n ý•@PÂ389.– üNormalize‘ ŽpQÇoin®9t.“«It–'qmakš¸ães“it“easier“to“determine“the“correct“direction“of“rotation“to˜w˜ard“the“x-yŽ¤ or–xþy-z“plane“if“Ïp1Ž‘¾«'s“coGordinates“are“all“±>«=‘†0,‘èso“wš¸ãe“rotate“it“in“order“to“mak˜e“them“so.‘ÜÁThe“only“case“thatŽ¡requires–.‡more“than“a“rotation“around“a“single“axis“is“the“case“that“±xŸÿó 0e—rcmmi7´p®1Ž–›Å«,›6J±yŸÿ´p®1Ž“«,˜and–.‡±zŸÿ´p®1Ž‘ 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ÿù·^‘8àÏp1Ž‘O ±:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜«[1Ž‘]“±<“«0Ž‘ ÿù·^‘8àÏp1Ž‘O ±:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜«[2Ž‘]“±<“«0Ž‘Ç)Ž¡‘(±=·‘ÿý«x–UUpGositivš¸ãe,“y“negativ˜e,“z“negativ˜e.‘o·±=Ž¡‘tŽ‘$c·«=ŽŽ‘3ñÄÏp1Ž‘@„±:Ïr‘ÿ}'otateŽ‘o>«(180ŽŽ‘);Ž¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(Ïp1Ž‘ À±:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ›Mþ«[0Ž‘]–DZ<“«0Ž‘ ÿù·^‘8àÏp1Ž‘O ±:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜«[1Ž‘]“±<“«0Ž‘ ÿù·^‘8àÏp1Ž‘O ±:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜«[2Ž‘]“±<“«0Ž‘Ç)Ž¡‘±=·‘ÿý«All‘UUnegativ¸ãe.‘o·±=Ž¡‘·fŽ¡‘ÂrealŽ‘4³1±aŽ‘<Ãy«=‘ÇÏp1Ž‘Ýر:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[0Ž‘];Ž¦‘±tŽ‘$c·«=ŽŽ‘3ñÄÏp1Ž‘@„±:Ïr‘ÿ}'otateŽ‘o>«(180ŽŽ‘±;‘ª¨«180ŽŽ‘ª«);Ž¡‘±tŽ‘$c·«=ŽŽ‘3ñÄÏp1Ž‘@„±:ÏshiftŽ‘}«(±aŽ‘I0«);Ž¡‘±tŽ‘$c·«=ŽŽ‘3ñÄÏp1Ž‘@„±:Ïr‘ÿ}'otateŽ‘o>«(0Ž‘±;‘ª¨«180ŽŽ‘ª«);Ž¡‘±tŽ‘$c·«=ŽŽ‘3ñÄÏp1Ž‘@„±:ÏshiftŽ‘}«(·Ž‘DZaŽ‘ N«);Ž¡‘·gŽ¡‘Ïp1Ž‘ ±:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨);Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïp0Ž‘*ñ:ÏshowŽ‘Šÿ«(Ý"p0È ÝafterÈ ÝnormalizatŽ‘hÿÄion"Ž‘~† «);Ž¡‘Ïp1Ž‘*ñ:ÏshowŽ‘Šÿ«(Ý"p1È ÝafterÈ ÝnormalizatŽ‘hÿÄion"Ž‘~† 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µ:±showŽ‘Šÿ¬(´"proj_on_x_z_plane"Ž‘dF/¬);ŽŽŽŒ‹l _O Šn ý‘ì¬108›¯ALIGNMENT–ÕXWITH“AN“AXIS’âlê3DLDF-1.1.5.1˜°x¬426Ž €n ý•@P­426.‘ ü¬[²LDF‘T2002.10.23.¬]Ž‘ZJœIf–»wš¸ãe're“aligning“with“the“x“or“y-axis,‘$ rotate“±p1Ž‘F6¬on˜to“the“x-y“plane“and“then“to“theŽ¤ x-axis.Ž©°h–ª¨¬De ne‘UU­T‘ÿ +«ransformŽ‘;'¬functions‘@¯169“°i‘Ǭ+°Ž¡‘ +­ifŽ‘´ù¬(±axisŽ‘à°‘Ç´'x'Ž‘FW°_‘8à±axisŽ‘<À°‘Ç´'y'Ž‘ w¬)‘°fŽ¡‘­P•®9oin“tŽ‘2pt‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“axisŽ‘hЬ;Ž¦‘±pt‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“axisŽ‘I3µ:±setŽ‘ x„¬(1Ž‘);Ž¡‘±angleŽ‘.‡m¬=‘DZpr‘ÿ}'oj‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“z‘‰ffŽ“planeŽ‘N7!µ:±angleŽ‘ÀS¬(±pt‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“axisŽ‘51¬);Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"angle® ´of® ´projectionŽ‘kÆÜ:® ´"Ž‘~ÔS°‘DZangleŽ‘Nƒ°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘­ifŽ‘´ú¬(±angleŽ‘‡k°6¬=‘Ç0Ž‘ ÿù°^‘8à±angleŽ‘ÀK°6¬=‘Ç´INVALID_REALŽ‘BM\¬)‘µtŽ‘ cŠ°¬=ŽŽ‘ñÁ±p1Ž‘'µ:±r‘ÿ}'otateŽ‘o>¬(0Ž‘µ;‘ª¨°Ž‘ qƱangleŽ‘!2¬);Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±p1Ž‘Àµ:±showŽ‘Šÿ¬(´"p1® ´after® ´rotation® ´tŽ‘hÿÄo® ´x-y® ´plane"Ž’¨†¬);Ž¡‘±angleŽ‘.‡m¬=‘DZp1Ž‘Ýص:±angleŽ‘ÀS¬(±pt‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“axisŽ‘51¬);Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"angle® ´to® ´x-axis:® ´"Ž‘iÔ_°‘DZangleŽ‘Nƒ°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘­ifŽ‘´ú¬(±angleŽ‘‡k°6¬=‘Ç0Ž‘ ÿù°^‘8à±angleŽ‘ÀK°6¬=‘Ç´INVALID_REALŽ‘BM\¬)‘µtŽ‘ cŠ°¬=ŽŽ‘ñÁ±p1Ž‘'µ:±r‘ÿ}'otateŽ‘o>¬(0Ž‘µ;‘ª¨¬0Ž‘ª©µ;‘ª¨°Ž‘ qƱangleŽ‘!2¬);Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±p1Ž‘Àµ:±showŽ‘Šÿ¬(´"p1® ´after® ´rotation® ´tŽ‘hÿÄo® ´x-axis"Ž’˜Æ¬);Ž¡‘ +°gŽŸ­427.‘ ü¬[²LDF‘T2002.10.23.¬]Ž‘YÇŠIf–”©wš¸ãe're“aligning“with“the“z-axis,‘»2rotate“±p1Ž‘@¬on˜to“the“y-z“plane“and“then“to“the“z-axis.Ž¦°h–ª¨¬De ne‘UU­T‘ÿ +«ransformŽ‘;'¬functions‘@¯169“°i‘Ǭ+°Ž¡‘ +­elseŽ‘ .5ifŽ‘+ã-¬(±axisŽ‘à°‘Ç´'z'Ž‘ w¬)–UU°f“­P•®9oin“tŽ‘"Dò±pt‘‰ffŽ–®on‘‰ffŽ“z‘‰ffŽ“axisŽ‘VÍV¬;Ž¦‘ +±pt‘‰ffŽ–®on‘‰ffŽ“z‘‰ffŽ“axisŽ‘>ˆeµ:±setŽ‘ x„¬(0Ž‘µ;‘ª¨¬0Ž–ª©µ;‘ª¨¬1Ž“);‘µ=°‘<¬[²LDF‘T2002.10.23.¬]Ž‘T€qThis–‘rassumes“that“±pr‘ÿ}'oj‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“z‘‰ffŽ“planeŽ‘O{µ:±get‘‰ffŽ‘®zŽ‘¬(‘ª¨)–+H°“¬0Ž‘+I.‘&ItŽ¡‘should–UUbšGe,“but“if“it“isn't,“the“follo¸ãwing“error“handling“co˜de“tak¸ães“care“of“the“problem.‘o°µ=Ž¡‘ +­ifŽ‘´ù¬(±pr‘ÿ}'oj‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“z‘‰ffŽ“planeŽ‘Kp µ:±get‘‰ffŽ‘®zŽ‘¬(‘ª¨)–ǵ<“¬0Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘.ä°‘M<´"ERROR!® ´In® ´TransformŽ‘pM::align_with_axis():Ž’ÙLÄ\n"Ž’ðà_°Ž¡‘(´"proj_on_x_z_plane.gŽ’ÿÈet_z()® ´<® ´0\n"Ž’ØÛ°‘ ´"@Ž‘lÏ® ´should® ´ensure® ´that® Ž’Õ“´"Ž’Ýð°Ž¡‘(´"this® ´value® ´is® ´>=® ´0.Ž’ÿÈ\n"Ž’¤[2°‘ ´"Handling® ´the® ´error,Ž‘lÏ® ´but® ´find® ´out® ´why® ´itŽ’Õ“® ´happened!"Ž’oå°Ž¡‘(±end‘‚ØlŽ‘>¸Þ°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘±pt‘‰ffŽ–®on‘‰ffŽ“z‘‰ffŽ“axisŽ‘Hˆfµ:±setŽ‘ x„¬(0Ž‘µ;‘ª¨¬0Ž‘ª©µ;‘ª¨°Ž‘ qƬ1Ž‘qÇ);Ž¡‘ +°gŽŸ­428.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.12.10.¬]Ž‘Yð:Added–=Tthe“follo¸ãwing“conditional.‘)ÅT‘ÿ*ªrying“to“ x“a“bug“that“ošGccurred“while“p˜orting“toŽ¡GNU/Lin¸ãux.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬De ne‘UU­T‘ÿ +«ransformŽ‘;'¬functions‘@¯169“°i‘Ǭ+°Ž¡‘ +­ifŽ‘´ù¬(±pr‘ÿ}'oj‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“z‘‰ffŽ“planeŽ‘Kp µ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ›Mþ¬[0Ž‘]–Ç°“¬0Ž‘ ÿù°^‘8à±pr‘ÿ}'oj‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“z‘‰ffŽ“planeŽ‘M¨éµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[1Ž‘]“°“¬0Ž›Ç)‘±angleŽ‘‡k¬=“0Ž˜;Ž¡‘ +­elseŽ‘!Øà±angleŽ‘<`K¬=‘DZpr‘ÿ}'oj‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“z‘‰ffŽ“planeŽ‘N7!µ:±angleŽ‘ÀS¬(±pt‘‰ffŽ–®on‘‰ffŽ“z‘‰ffŽ“axisŽ‘4ˆd¬);ŽŸ­429.Ž¦°h–ª¨¬De ne‘UU­T‘ÿ +«ransformŽ‘;'¬functions‘@¯169“°i‘Ǭ+°Ž¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"angle® ´of® ´projectionŽ‘kÆÜ:® ´"Ž‘~ÔS°‘DZangleŽ‘Nƒ°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘ +­ifŽ‘´ù¬(±angleŽ‘‡k°6¬=‘Ç0Ž‘ ÿù°^‘8à±angleŽ‘ÀK°6¬=‘Ç´INVALID_REALŽ‘BM\¬)‘µtŽ‘ cŠ°¬=ŽŽ‘ñÁ±p1Ž‘'µ:±r‘ÿ}'otateŽ‘o>¬(0Ž‘µ;‘ª¨±angleŽ‘jû¬);Ž¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±p1Ž‘Àµ:±showŽ‘Šÿ¬(´"p1® ´after® ´rotation® ´tŽ‘hÿÄo® ´z-y® ´plane"Ž’¨†¬);Ž¡‘ +±p1Ž‘Áµ:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);ŽŽŽŒ‹m kä Šn ý‘ì°x¬430›¯3DLDF-1.1.5.1’âlêALIGNMENT–ÕXWITH“AN“AXIS˜¬109Ž €n ý•@P­430.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ +¬[²LDF‘T2002.12.10.¬]Ž‘Yð:Added–=Tthe“follo¸ãwing“conditional.‘)ÅT‘ÿ*ªrying“to“ x“a“bug“that“ošGccurred“while“p˜orting“toŽ¡GNU/Lin¸ãux.Ž¡‘ +[²LDF‘T2003.06.13.¬]Ž‘X=BUG‘ŠFIX:–Š9Changed“±pr‘ÿ}'oj‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“z‘‰ffŽ“planeŽ‘P„{¬to“±p1Ž‘+2¬in“the“\­ifŽ‘_£¬"“part“of“the“follo¸ãwing“conditional.Ž¡The–]/y-coGordinate“of“±pr‘ÿ}'oj‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“z‘‰ffŽ“planeŽ‘R*g¬is“alw•¸ãa“ys–]/0,‘_&so“±angleŽ‘z±¬wš¸ãas“alw˜a˜ys“set“to“0.‘‰VI‘]-disco˜v˜ered“this“bug“whenŽ¡I‘'‘tried–'œrotating“a“­P•®9oin“tŽ‘!逬in“the“plane“of“a“­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘GÍì¬abGout“a“line“from“the“cen¸ãter“of“the“­Regu½‰™šs4Ž‘ÔwP®9olygonŽŽ¡¬in–UUthe“direction“of“its“normal,“and“the“resulting“­P•®9oin“tŽ‘"Dò¬w¸ãas“not“in“the“same“plane.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬De ne‘UU­T‘ÿ +«ransformŽ‘;'¬functions‘@¯169“°i‘Ǭ+°Ž¤ ‘ +­ifŽ‘´ù¬(±p1Ž‘ Àµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ¬[1Ž‘]–Ç°“¬0Ž›Ç)‘±angleŽ‘‡k¬=“0Ž˜;Ž¡‘ +­elseŽ‘!Øà±angleŽ‘<`K¬=‘DZp1Ž‘Ýص:±angleŽ‘ÀS¬(±pt‘‰ffŽ–®on‘‰ffŽ“z‘‰ffŽ“axisŽ‘4ˆd¬);Ž©­431.ŽŸ°h–ª¨¬De ne‘UU­T‘ÿ +«ransformŽ‘;'¬functions‘@¯169“°i‘Ǭ+°Ž¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"angle® ´to® ´z-axis:® ´"Ž‘iÔ_°‘DZangleŽ‘Nƒ°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘ +­ifŽ‘´ù¬(±angleŽ‘‡k°6¬=‘Ç0Ž‘ ÿù°^‘8à±angleŽ‘ÀK°6¬=‘Ç´INVALID_REALŽ‘BM\¬)‘µtŽ‘ cŠ°¬=ŽŽ‘ñÁ±p1Ž‘'µ:±r‘ÿ}'otateŽ‘o>¬(°Ž‘DZangleŽ‘‡q¬);Ž¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±p1Ž‘Àµ:±showŽ‘Šÿ¬(´"p1® ´after® ´rotation® ´tŽ‘hÿÄo® ´z-axis"Ž’˜Æ¬);Ž¡‘ +°gŽ¦­432.‘ ü¬[²LDF‘T2002.10.23.¬]Ž‘ZÚÖIf–§õwš¸ãe're“aligning“with“the“y-axis,‘¼±p1Ž‘{R¬m˜ust“bGe“rotated“from“the“x-axis“(where“it“isŽ¡noš¸ãw)–UUaround“the“z-axis“b˜y“90Ÿü^ÿ¶Ž‘˜ä¬.‘qÇThen“it“will“bGe“on“the“y-axis.ŽŸ°h–ª¨¬De ne‘UU­T‘ÿ +«ransformŽ‘;'¬functions‘@¯169“°i‘Ǭ+°Ž¡‘ +­ifŽ‘´ù¬(±axisŽ‘à°‘Ç´'y'Ž‘ w¬)‘°fŽ¡‘µtŽ‘cŒ°¬=ŽŽ‘)ññp1Ž‘6ƒµ:±r‘ÿ}'otateŽ‘o>¬(0Ž‘µ;‘ª¨¬0Ž‘ª©µ;‘ª¨¬90ŽŽ‘ ªª);Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±p1Ž‘Àµ:±showŽ‘Šÿ¬(´"p1® ´after® ´rotation® ´tŽ‘hÿÄo® ´y-axis"Ž’˜Æ¬);Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"p1.magnitude()® ´==® ´"Ž‘o\°‘DZp1Ž‘Ýص:±magnitudeŽ‘.=r¬(‘ª¨)–Ç°“±end‘‚ØlŽ‘ò°“± ushŽ‘€¬;Ž¡‘µtŽ‘œt:±showŽ‘Šÿ¬(´"t® ´at® ´end® ´of® ´align_wŽ‘hÿÄith_axis()"Ž’£F ¬);Ž¡‘ +°gŽ¡‘ +Ž‘±thisŽ‘"²Ð°¬=ŽŽ‘2AµtŽ‘5Ýy¬;Ž¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Exiting® ´Transform::Ž‘kÆÜalign_with_axis."Ž’ÈT)°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘ +­returnŽ‘-滵tŽ‘1ƒ-¬;‘qÇ°gŽŽŽŒ‹n 2 Šn ý‘ì¬110–¯NORMALIZE‘ÕXPOINT’ËF3DLDF-1.1.5.1“°x¬433Ž €n ý•@P­433.– üNormalize‘ ŽpQÇoin®9t.“¬It–'qmakš¸ães“it“easier“to“determine“the“correct“direction“of“rotation“to˜w˜ard“the“x-yŽ¤ or–xþy-z“plane“if“±p1Ž‘¾¬'s“coGordinates“are“all“µ>¬=‘†0,‘èso“wš¸ãe“rotate“it“in“order“to“mak˜e“them“so.‘ÜÁThe“only“case“thatŽ¡requires–.‡more“than“a“rotation“around“a“single“axis“is“the“case“that“µxŸÿó 0e—rcmmi7·p³1Ž–›Å¬,›6JµyŸÿ·p³1Ž“¬,˜and–.‡µzŸÿ·p³1Ž‘ 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ÿù°^‘8à±p1Ž‘O µ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[1Ž‘]“°“¬0Ž‘ ÿù°^‘8à±p1Ž‘O µ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[2Ž‘]“µ<“¬0Ž‘Ç)Ž¡‘(µ=°‘ÿý¬x–UUpšGositiv¸ãe,“y“p˜ositivš¸ãe,“z“negativ˜e.‘o°µ=Ž¡‘tŽ‘$c°¬=ŽŽ‘3ñıp1Ž‘@„µ:±r‘ÿ}'otateŽ‘o>¬(°Ž‘Ǭ90ŽŽ‘Ç );Ž¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±p1Ž‘ Àµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ›Mþ¬[0Ž‘]–ǵ<“¬0Ž‘ ÿù°^‘8à±p1Ž‘O µ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[1Ž‘]“µ<“¬0Ž‘ ÿù°^‘8à±p1Ž‘O µ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[2Ž‘]“°“¬0Ž‘Ç)Ž¡‘(µ=°‘ÿý¬x–UUnegativš¸ãe,“y“negativ˜e,“z“pGositiv˜e.‘o°µ=Ž¡‘tŽ‘$c°¬=ŽŽ‘3ñıp1Ž‘@„µ:±r‘ÿ}'otateŽ‘o>¬(0Ž‘µ;‘ª¨¬0Ž‘ª©µ;‘ª¨¬180ŽŽ‘ª«);Ž¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±p1Ž‘ Àµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ›Mþ¬[0Ž‘]–ǵ<“¬0Ž‘ ÿù°^‘8à±p1Ž‘O µ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[1Ž‘]“°“¬0Ž‘ ÿù°^‘8à±p1Ž‘O µ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[2Ž‘]“µ<“¬0Ž‘Ç)Ž¡‘(µ=°‘ÿý¬x–UUnegativš¸ãe,“y“pGositiv˜e,“z“negativ˜e.‘o°µ=Ž¡‘tŽ‘$c°¬=ŽŽ‘3ñıp1Ž‘@„µ:±r‘ÿ}'otateŽ‘o>¬(0Ž‘µ;‘ª¨¬180ŽŽ‘ª«);Ž¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±p1Ž‘ Àµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ›Mþ¬[0Ž‘]–Ç°“¬0Ž‘ ÿù°^‘8à±p1Ž‘O µ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[1Ž‘]“µ<“¬0Ž‘ ÿù°^‘8à±p1Ž‘O µ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[2Ž‘]“µ<“¬0Ž‘Ç)Ž¡‘(µ=°‘ÿý¬x–UUpGositivš¸ãe,“y“negativ˜e,“z“negativ˜e.‘o°µ=Ž¡‘tŽ‘$c°¬=ŽŽ‘3ñıp1Ž‘@„µ:±r‘ÿ}'otateŽ‘o>¬(180ŽŽ‘);Ž¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±p1Ž‘ Àµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ›Mþ¬[0Ž‘]–ǵ<“¬0Ž‘ ÿù°^‘8à±p1Ž‘O µ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[1Ž‘]“µ<“¬0Ž‘ ÿù°^‘8à±p1Ž‘O µ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[2Ž‘]“µ<“¬0Ž‘Ç)Ž¡‘µ=°‘ÿý¬All‘UUnegativ¸ãe.‘o°µ=Ž¡‘°fŽ¡‘­realŽ‘4³1µaŽ‘<Ãy¬=‘DZp1Ž‘Ýص:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ¬[0Ž‘];Ž¦‘µtŽ‘$c°¬=ŽŽ‘3ñıp1Ž‘@„µ:±r‘ÿ}'otateŽ‘o>¬(180ŽŽ‘µ;‘ª¨¬180ŽŽ‘ª«);Ž¡‘µtŽ‘$c°¬=ŽŽ‘3ñıp1Ž‘@„µ:±shiftŽ‘}¬(µaŽ‘I0¬);Ž¡‘µtŽ‘$c°¬=ŽŽ‘3ñıp1Ž‘@„µ:±r‘ÿ}'otateŽ‘o>¬(0Ž‘µ;‘ª¨¬180ŽŽ‘ª«);Ž¡‘µtŽ‘$c°¬=ŽŽ‘3ñıp1Ž‘@„µ:±shiftŽ‘}¬(°Ž‘ǵaŽ‘ N¬);Ž¡‘°gŽ¡‘±p1Ž‘ µ:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±p0Ž‘*õ:±showŽ‘Šÿ¬(´"p0® ´after® ´normalizatŽ‘hÿÄion"Ž‘~† ¬);Ž¡‘±p1Ž‘*õ:±showŽ‘Šÿ¬(´"p1® ´after® ´normalizatŽ‘hÿÄion"Ž‘~† 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+°gŽŸ­438.› üP•®9ath‘**argumen“t.˜¬De ned–Ÿin“®paths.web¬,‘±‹bšGecause“­P®9athŽ‘Ϙ¬is“still“an“incomplete“t¸ãyp˜e“in“this“compi-Ž¦lation‘UUunit.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ +¬[²LDF‘T2002.04.07.¬]Ž‘Y;Added–UUdefault“v‘ÿqÇalue“for“±angleŽ‘jý°‘Ǭ180.Ž¦‘ +[²LDF‘T2003.05.02.¬]Ž‘YËSChanged–mname“of“this“function“from“±r–ÿ}'otate‘‰ffŽ‘®ar“oundŽ‘@„ü¬(›ª®)“to“±r‘ÿ}'otateŽ‘‡«¬(˜).‘»This“function“no¸ãwŽ¦o•¸ãv“erloads‘UU±r‘ÿ}'otateŽ‘Ä“¬(‘ª®)–UUwith“three“­realŽ‘ƒ¬argumen¸ãts.Ž¡ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¦‘ +­T‘ÿ +«ransformŽ‘AÈÓ±r‘ÿ}'otateŽ‘\8¬(­constŽ‘*¢P®9athŽ‘:[¬&Ž‘AØyµpŽ‘Fày;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±angleŽ‘Qã¬=‘Ç180ŽŽ‘Ç);ŽŽŽŒ‹p Œ Šn ý‘ì¬112–­TRANSF®9ORM‘ÕX¯VERSION’äƒ3DLDF-1.1.5.1“°x¬439Ž €n ý•@P­439.– üT‘ÿ +«ransform‘"v®9ersion.“¬Declared–˜in“®transfor.web¬.‘:[²LDF‘T2002.09.29.¬]Ž‘T…TO‘˜ DO:“P¸ãossible“BUG!!‘:Ac-Ž¤ 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üPro‘£Žjection.“«[¬LDF‘T2002.10.23.«]Ž‘\E™F‘ÿ*ªor–¸stš¸ãylistic“reasons,‘‚and“for“the“sak˜e“of“clean“programming,‘‚IŽ¡bGeliev¸ãe–_$that“the“programmer“who“uses“Ïpr–ÿ}'oje“ctŽ‘"Ö2«(›ª®)“should“ensure“that“Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘J«(˜)“has“bGeen“in•¸ãv“ok“edŽ¡ rst.‘Ä7Ho•¸ãw“ev“er,‘w®Ïtr‘ÿ}'ansformŽ‘2›¿«is›pÐc“hec“k“ed˜in˜Ïpr–ÿ}'oje“ctŽ‘!çÞ«(–ª®)˜and˜Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘I¯«(“)˜is˜in•¸ãv“ok“ed,–w®if˜required,“so˜in•¸ãv“okingŽ¡Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª®)–UUexplicitly“bšGeforehand“is“not“strictly“sp˜eaking“necessary‘ÿ*ª.Ž¦Ÿû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.09.09.«]Ž‘XmThe–º3new“vš¸ãersion“no˜w“almost“w˜orks“Added“division“of“Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘d*y«b˜y“the“v‘ÿqÇalueŽ¡calculated–Ø6for“±wŽ‘ EØ«.›úiHo•¸ãw“ev“er,‘øíit–Ø6doGesn't“w¸ãork“when“I‘Øuse“Ïhex‘‰ffŽ‘®p‘ÿ}'attern1Ž‘;¥~«(‘ª®).˜Find“out“wh¸ãy“not!!˜TO‘ØDO:“AddŽ¡routine–UUfor“calculating“±zŽ‘ls«.‘qÇThen“I“can“add“sorting“routine“in“ÂPictureŽ‘)ñf«::‘ÏoutputŽ‘D«(‘ª®).Ž¡‘ -[¬LDF‘T2002.09.14.«]Ž‘Y I‘m"bGeliev•¸ãe›m(I'v“e˜gotten˜the˜new˜v“ersion˜to˜w“ork˜no“w.‘¹ALOOK–m"UP:˜Do˜I“need˜to˜divide˜theŽ¡deriv•¸ãed‘]ï±zŽ‘ Òü«v‘ÿqÇalue›]ïb“y˜±wŽ‘ -Ë‘«?–‹–I‘]ídon't˜think˜it's˜necessary‘ÿ*ª.“Since˜the˜±zŽ‘ Òü«v‘ÿqÇalues˜of˜all˜of˜the˜ÂP•®9oin“tsŽ‘&ßb«w¸ãould˜bGe˜dividedŽ¡bš¸ãy–§·the“same“amoun˜t,‘¼Otheir“relativ˜e“pGositions“w˜ould“remain“the“same,‘¼Osince“only“the“relationship“\closer“orŽ¡further›UUa•¸ãw“a“y"˜matters,˜not˜the˜exact˜amoun“ts.Ž¡‘ -[¬LDF‘T2002.09.16.«]Ž‘YAdded‘a ÂF‘ÿ -«oQÇcusŽ‘#·Œ«argumenš¸ãt–a to“this“function.‘•(Default“is“Ïdefault‘‰ffŽ‘®fo‘ÿ}'cusŽ‘;?«,‘dbut“it“w˜as“necessaryŽ¡to–*write“a“dummš¸ãy“v˜ersion“of“this“function“in“order“to“mak˜e“this“w˜ork,‘3bšGecause“Ïdefault‘‰ffŽ‘®fo‘ÿ}'cusŽ‘>3«do˜esn't“exist“atŽ¡the–UUtime“that“this“declaration“is“compiled.Ž¡‘ -[¬LDF‘T2002.09.18.«]Ž‘X*Changed–aDname“of“this“function“from“Ïp–ÿ}'ersp‘‰ffŽ‘®tr“ansformŽ‘H`k«(‘ª®)“to“Ïpr–ÿ}'oje“ctŽ‘#9–«and“added“ÂT‘ÿ -«ransformŽŽ¡«argumen¸ãt.Ž¡‘ -[¬LDF‘T2003.05.09.«]Ž‘YøÐBUG‘E¬FIX:–EêAdded“loGop,‘‚setting“all“elemenš¸ãts“of“Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘gAç«to“0.‘C†This“w˜asŽ¡done–·in“the“conditionally“compiled“coGde“for“the“DEC›·compiler,‘ÏŽbut“I˜forgot“to“do“it“for“GCC˜when“addedŽ¡the–UUdeclaration“of“Ïtemp‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘QQ%«and“resized“it.‘qÇIt“tošGok“me“ab˜out“6{7“hours“to“ nd“this“bug!Ž©ŸüÈ„`ÕÁGŽŽŸÂ398.‘ üF‘ÿ +«ransformŽ‘w¬(±angleŽ‘ÀS¬);Ž¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±axisŽ‘à°‘Ç´'y'Ž‘ w¬)‘µtŽ‘œr:±r‘ÿ}'otateŽ‘o>¬(0Ž‘µ;‘ª¨±angleŽ‘jû¬);Ž¡‘­elseŽ‘+ØáµtŽ‘/uS:±r‘ÿ}'otateŽ‘o>¬(0Ž‘µ;‘ª¨¬0Ž‘ª©µ;‘ª¨±angleŽ‘jû¬);Ž¡‘µtŽ‘cŒ°¬=ŽŽ‘)ñõiŽ‘-c·¬;Ž¡‘µtŽ‘œt:±cle‘ÿ}'anŽ‘A‚¬(‘ª¨);Ž¡‘°Ž‘±thisŽ‘,²Ñ°¬=ŽŽ‘Äç¬&Ž‘FŒ±p1Ž‘R¢Åµ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±angleŽ‘NHˬ)Ž¡‘ +°fŽ¡‘­T‘ÿ +«ransformŽ‘KÈÔµtŽ‘OeF¬;ŽŸ‘µtŽ‘œt:±r‘ÿ}'otateŽ‘o>¬(±p0Ž‘ Àµ;‘ª¨±p1Ž‘ Áhµ;‘ª¨±angleŽ‘jû¬);Ž¡‘±tr‘ÿ}'ansformŽ‘Bz[°¬=ŽŽ‘R’µtŽ‘U¥¬;Ž¡‘­returnŽ‘7æ¼µtŽ‘;ƒ.¬;Ž¡‘ +°gŽŸ­441.– üPro‘£Žjection.“¬[²LDF‘T2002.10.23.¬]Ž‘\E™F‘ÿ*ªor–¸stš¸ãylistic“reasons,‘‚and“for“the“sak˜e“of“clean“programming,‘‚IŽ¡bGeliev¸ãe–_$that“the“programmer“who“uses“±pr–ÿ}'oje“ctŽ‘"Ö2¬(›ª®)“should“ensure“that“±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘J¬(˜)“has“bGeen“in•¸ãv“ok“edŽ¡ rst.‘Ä7Ho•¸ãw“ev“er,‘w®±tr‘ÿ}'ansformŽ‘2›¿¬is›pÐc“hec“k“ed˜in˜±pr–ÿ}'oje“ctŽ‘!çÞ¬(–ª®)˜and˜±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘I¯¬(“)˜is˜in•¸ãv“ok“ed,–w®if˜required,“so˜in•¸ãv“okingŽ¡±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª®)–UUexplicitly“bšGeforehand“is“not“strictly“sp˜eaking“necessary‘ÿ*ª.Ž¦Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.09.09.¬]Ž‘XmThe–º3new“vš¸ãersion“no˜w“almost“w˜orks“Added“division“of“±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘d*y¬b˜y“the“v‘ÿqÇalueŽ¡calculated–Ø6for“µwŽ‘ Eج.›úiHo•¸ãw“ev“er,‘øíit–Ø6doGesn't“w¸ãork“when“I‘Øuse“±hex‘‰ffŽ‘®p‘ÿ}'attern1Ž‘;¥~¬(‘ª®).˜Find“out“wh¸ãy“not!!˜TO‘ØDO:“AddŽ¡routine–UUfor“calculating“µzŽ‘ls¬.‘qÇThen“I“can“add“sorting“routine“in“­PictureŽ‘)ñf¬::‘±outputŽ‘D¬(‘ª®).Ž¡‘ +[²LDF‘T2002.09.14.¬]Ž‘Y I‘m"bGeliev•¸ãe›m(I'v“e˜gotten˜the˜new˜v“ersion˜to˜w“ork˜no“w.‘¹ALOOK–m"UP:˜Do˜I“need˜to˜divide˜theŽ¡deriv•¸ãed‘]ïµzŽ‘ Òü¬v‘ÿqÇalue›]ïb“y˜µwŽ‘ +Ë‘¬?–‹–I‘]ídon't˜think˜it's˜necessary‘ÿ*ª.“Since˜the˜µzŽ‘ Òü¬v‘ÿqÇalues˜of˜all˜of˜the˜­P•®9oin“tsŽ‘&ßb¬w¸ãould˜bGe˜dividedŽ¡bš¸ãy–§·the“same“amoun˜t,‘¼Otheir“relativ˜e“pGositions“w˜ould“remain“the“same,‘¼Osince“only“the“relationship“\closer“orŽ¡further›UUa•¸ãw“a“y"˜matters,˜not˜the˜exact˜amoun“ts.Ž¡‘ +[²LDF‘T2002.09.16.¬]Ž‘YAdded‘a ­F‘ÿ +«oQÇcusŽ‘#·Œ¬argumenš¸ãt–a to“this“function.‘•(Default“is“±default‘‰ffŽ‘®fo‘ÿ}'cusŽ‘;?¬,‘dbut“it“w˜as“necessaryŽ¡to–*write“a“dummš¸ãy“v˜ersion“of“this“function“in“order“to“mak˜e“this“w˜ork,‘3bšGecause“±default‘‰ffŽ‘®fo‘ÿ}'cusŽ‘>3¬do˜esn't“exist“atŽ¡the–UUtime“that“this“declaration“is“compiled.Ž¡‘ +[²LDF‘T2002.09.18.¬]Ž‘X*Changed–aDname“of“this“function“from“±p–ÿ}'ersp‘‰ffŽ‘®tr“ansformŽ‘H`k¬(‘ª®)“to“±pr–ÿ}'oje“ctŽ‘#9–¬and“added“­T‘ÿ +«ransformŽŽ¡¬argumen¸ãt.Ž¡‘ 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Q·‘ÇÝ"("Ž‘Ô·‘DZvŽ›ûÕ«[0Ž‘]–Ç·“Ý",È Ý"Ž‘Œ·“±vŽ˜«[1Ž‘]“·“Ý",È Ý"Ž‘Œ·“±vŽ˜«[2Ž‘]“·“Ý")\n"Ž‘ T‰·“Ï ushŽ‘€«;Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïtr‘ÿ}'ansformŽ‘I³D±:ÏshowŽ‘Šÿ«(Ý"TransformÈ ÝafterÈ ÝappŽ‘hÿÄly_transform"Ž’­Æ«);Ž¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"on_free_storeÈ Ý==È Ý"Ž‘iÔ_·‘ÇÏon‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘=3"·‘ÇÝ"\n"Ž‘Mt«;Ž¡‘·gŽ¡‘ -gŽŸÂ433.‘ üSho®9w‘ÕTtransform.Ž¦·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙÏshow‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘gSÅ«(ÂstringŽ‘!%MÏtextŽ‘5D1«=‘ÇÝ""Ž‘ Íz«);ŽŽŽŒ‹se– Šn ý‘ì·x«434›­3DLDFPR•ÃŽG’ ï6SHO“W‘ÕXTRANSF“ORM˜«115Ž €n ý•@PÂ434.Ž©·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¤ ‘ -Âv®9oidŽ‘"ýÙP•®9oin“tŽ‘?˜%«::‘Ïshow‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘EUð«(ÂstringŽ‘!%MÏtextŽ‘2}«)Ž¡‘ -·fŽ¡‘ÂifŽ‘´ú«(ÏtextŽ‘ä·‘ÇÝ""Ž‘ Íz«)‘ÏtextŽ‘ä«=‘ÇÝ"transform:"Ž‘BM\«;Ž¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÏtextŽ‘åü·‘ÇÏend‘‚ØlŽ‘¸Ú«;Ž¡‘Ïtr‘ÿ}'ansformŽ‘?³C±:ÏshowŽ‘Šÿ«(‘ª¨);Ž¡‘ -·gŽ¤Â435.‘ üOutputting.Ž¡436.– üOutput‘ ropQÇerator.“«[¬LDF‘T2002.10.26.«]Ž‘[8ÕThis–ôfunction“is“used“in“ÂP®9athŽ‘—\«::‘ÏoutputŽ‘D«(‘ª®)“for“writing“the“xŽ¤ and–‚Iy“v‘ÿqÇalues“of“the“Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘gº¥«to“Ïout‘‰ffŽ‘®str–ÿ}'e“amŽ‘3Âå«.‘ø¤All“coGde“using“this“function“m¸ãust“ensure“thatŽ¡Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(›ª®)–UUand“Ïpr–ÿ}'oje“ctŽ‘!Ìc«(˜)“are“called“Ï rst‘òØ«!ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.09.16.«]Ž‘Y;Remo•¸ãv“ed–UUcalls“to“Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Iu4«(›ª®)“and“Ïpr–ÿ}'oje“ctŽ‘!Ìc«(˜).Ž¦ŸüÈ„`ÕÁGŽŽ¦·h›ª¨«Declare–UUnon-mem¸ãbGer“functions“for“ÂP•®9oin“tsŽ‘'¸Ý­436˜·i‘ÇŽ¡‘ -Ïostr–ÿ}'e“amŽ‘/«&‘8àÂopQÇeratorŽ‘-Ï•·Ž‘7Ï–«(Ïostr–ÿ}'e“amŽ‘%«&‘8à±oŽ‘Ä;‘ª¨ÂP•®9oin“tŽ‘ šE«&Ž‘(ac±pŽ‘-ic«);Ž¤ ­See–ÕXalso“section“490.Ž¡This–ÕXco:«(‘ª®)–Hêis“a“pure“ÂvirtualŽ‘.ÊR«function“in“ÂShapQÇeŽ‘%4÷«.‘ L…It's“called“b¸ãyŽ¡ÂPictureŽ‘&œ«::‘ÏoutputŽ‘D«(‘ª®).‘E 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-ÂvirtualŽ‘/ÔrealŽ‘FAÏget‘‰ffŽ–®minimum‘‰ffŽ“zŽ’‰žÚ«(‘ª®)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹vL Šn ý‘ì«118›­GET–ÕXMINIMUM“Z’´3DLDFPRÃŽG˜·x«446Ž €n ý•@PÂ446.Ž©·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¤ ‘ -ÂrealŽ‘ ³/P•®9oin“tŽ‘=M{«::‘Ïget‘‰ffŽ–®minimum‘‰ffŽ“zŽ‘D]Ü«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EnteringÈ ÝPoint::getŽ‘kÆÜ_minimum_z()"Ž’³T5·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"minimum_zÈ Ý==È Ý"Ž‘TÔk·‘ÇÏpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘VËi«[4Ž‘]–Ç·“Ïend‘‚ØlŽ‘ò·“Ï ushŽ‘€«;Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ExitingÈ ÝPoint::get_Ž‘kÆÜminimum_z()"Ž’®8·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘7æ¼Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ’‹ë «[4Ž‘];Ž¡‘ -·gŽŸÂ447.› üGet–ÕTmaxim®9um“z.˜«[¬LDF‘T2002.09.17.«]Ž‘Zˆ6Added–UUthis“function.Ž¦·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/ÔrealŽ‘FAÏget‘‰ffŽ–®maximum‘‰ffŽ“zŽ’Š®«(‘ª®)‘UUÂconstŽ‘*¢«;ŽŸÂ448.Ž¦·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘ ³/P•®9oin“tŽ‘=M{«::‘Ïget‘‰ffŽ–®maximum‘‰ffŽ“zŽ‘Em«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EnteringÈ ÝPoint::getŽ‘kÆÜ_maximum_z()"Ž’³T5·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"maximum_zÈ Ý==È Ý"Ž‘TÔk·‘ÇÏpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘VËi«[5Ž‘]–Ç·“Ïend‘‚ØlŽ‘ò·“Ï ushŽ‘€«;Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ExitingÈ ÝPoint::get_Ž‘kÆÜmaximum_z()"Ž’®8·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘7æ¼Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ’‹ë «[5Ž‘];Ž¡‘ -·gŽŸÂ449.› üGet–ÕTmean“z.˜«[¬LDF‘T2003.05.16.«]Ž‘Zˆ6Added–UUthis“function.Ž¦·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/ÔrealŽ‘FAÏget‘‰ffŽ–®me‘ÿ}'an‘‰ffŽ“zŽ‘v÷ «(‘ª®)‘UUÂconstŽ‘*¢«;ŽŸÂ450.Ž¦·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘ ³/P•®9oin“tŽ‘=M{«::‘Ïget‘‰ffŽ–®me‘ÿ}'an‘‰ffŽ“zŽ‘1¶«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7漫((Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ«[4Ž›]–8à+“Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘V=1«[5Ž˜])±=«2Ž˜);Ž¡‘ -·gŽŸÂ451.– üSet‘írextremes.“«This–Héfunction“sets“\extreme"“v‘ÿqÇalues“for“the“x,–…Îy‘ÿ*ª,“and–Héz-coGordinates.‘LƒThis“is,‘…ÎofŽ¡course,›ßtrivial–Ñfor“ÂP•®9oin“tsŽ‘#ç«,˜bGecause“they“only“ha•¸ãv“e–Ñone“x,˜y“and“z-coGordinate.‘¼zSo“the“maxima“and“minimaŽ¡for–UUeacš¸ãh“coGordinate“are“alw˜a˜ys“the“same.Ž¡‘ -[¬LDF‘T2002.10.20.«]Ž‘Z¸ÎThe–èprogrammer“who“uses“Ïset‘‰ffŽ‘®extr‘ÿ}'emesŽ‘;Çq«(›ª®)“m¸ãust“ensure“that“Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘K%Ç«(˜)“andŽ¡Ïpr–ÿ}'oje“ctŽ‘w«(›ª®)–UUare“in•¸ãv“ok“ed–UUbGefore“Ïset‘‰ffŽ‘®extr‘ÿ}'emesŽ‘:Þ«(˜)!ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.09.17.«]Ž‘Y;Added–UUthis“function.Ž¡‘ -[¬LDF‘T2002.09.18.«]Ž‘Y;Changed–UUthe“name“of“this“function“from“Ïset‘‰ffŽ–®minimum‘‰ffŽ“zŽ‘F0V«(›ª®)“to“Ïset‘‰ffŽ‘®extr‘ÿ}'emesŽ‘:Þ«(˜).Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/Ôb•QÇo“olŽ‘I/:Ïset‘‰ffŽ‘®extr‘ÿ}'emesŽ‘ðë(‘ª®);ŽŽŽŒ‹w™K Šn ý‘ì·x«452–­3DLDFPRÃŽG’®SET‘ÕXEXTREMES“«119Ž €n ý•@PÂ452.Ž©·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¤ ‘ -Âb•QÇo“olŽ‘#¡gP•®9oin“tŽ‘@;³«::‘Ïset‘‰ffŽ‘®extr‘ÿ}'emesŽ‘7Á«(‘ª®)Ž¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EnteringÈ ÝPoint::setŽ‘kÆÜ_extremes()"Ž’®8·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ÂforŽ‘%舫(Âin®9tŽ‘¤÷±iŽ‘Þ«=‘Ç0Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«4Ž“;‘ÿý±iŽ‘ññŸÿ®+‘ÿ+ŽŽ‘¹«)‘·fŽ¡‘ÂifŽ‘)´û«(Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘^¶«[±iŽ‘qô«]–Ç·“ÝINVALID_REALŽ‘BM\«)‘·fŽ¡‘(Ïc‘ÿ}'errŽ‘=|·‘ÇÝ"ERROR!È ÝInÈ ÝPoint::seŽ‘kÆÜt_extremes():\n"Ž’Ã,·‘ÇÝ"projective_coordinaŽ‘kÆÜtes["Ž’‰TM·‘DZiŽ‘ $·‘ÇÝ"]"Ž‘Ô·Ž¡‘<Ý"È Ý==È ÝINVALID_REAL.\nŽ’¤ÿÊ"Ž’®&µ·‘`†Ý"SettingÈ ÝeveryÈ ÝelemeŽ‘l`JntÈ ÝinÈ Ýprojective_extŽ’Õ`remesÈ Ý"Ž’þç·Ž¡‘<Ý"toÈ ÝINVALID_REALÈ ÝandŽ’¤ÿÊÈ ÝreturningÈ Ýfalse.\n"Ž’M·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂforŽ‘9芫(Âin®9tŽ‘¤÷±jŽ‘Ó«=‘Ç0Ž–Ç;‘ÿý±jŽ‘ wÙ<‘Ç«6Ž“;‘ÿý±jŽ‘ -0ÁŸÿ®+‘ÿ+ŽŽ‘÷á«)‘Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘YQ«[±jŽ‘°Ä«]–Ç=“ÝINVALID_REALŽ‘BM\«;Ž¡‘(ÂreturnŽ‘Kæ¾ÏfalseŽ‘`–«;Ž¡‘·gŽ¡‘gŽ¡‘Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘hS«[0Ž›]–Ç=“Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘a}+«[0Ž˜];‘±=·–ÿý«min‘UUx“·±=Ž¡‘Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘hS«[1Ž›]–Ç=“Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘a}+«[0Ž˜];‘±=·–ÿý«max‘UUx“·±=Ž¡‘Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘hS«[2Ž›]–Ç=“Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘a}+«[1Ž˜];‘±=·–ÿý«min‘UUy“·±=Ž¡‘Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘hS«[3Ž›]–Ç=“Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘a}+«[1Ž˜];‘±=·–ÿý«max‘UUy“·±=Ž¡‘Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘hS«[4Ž›]–Ç=“Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘a}+«[2Ž˜];‘±=·–ÿý«min‘UUz“·±=Ž¡‘Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘hS«[5Ž›]–Ç=“Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘a}+«[2Ž˜];‘±=·–ÿý«max‘UUz“·±=Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ExitingÈ ÝPoint::setŽ‘kÆÜ_extremes()"Ž’®8·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘7æ¼ÏtrueŽ‘J«T«;Ž¡‘ -·gŽŸÂ453.– üComparison‘ÕTclasses.“«[¬LDF‘T2003.05.16.«]Ž‘Zˆ6The–UUfunction“classes“in“this“section“are“used“inŽ¡ÂPictureŽ‘&œ«::‘ÏoutputŽ‘D«(‘ª®)– õto“sort“the“pGoinš¸ãters“to“ÂShapQÇeŽ‘%÷«in“Âv®9ectorŽ‘"·=·hÂShapQÇeŽ‘!ù·Ž‘&ùi“ÏelementsŽ‘)òð«.‘Y§The“argumen˜t“Ïsort‘‰ffŽ‘®valueŽ‘.÷«,Ž¡whicš¸ãh–9pshould“bGe“one“of“the“constan˜ts“in“ÂnamespaceŽ‘<ÁSortingŽ‘b+K«,‘?determines“whic˜h“one“is“used,‘?or“if“ÏelementsŽŽ¡«shouldn't–UUbGe“sorted.Ž¡·Ž‘ -«If‘|õÂSortingŽ‘(ç?«::‘ÝMIN_ZŽ‘CR«is–|õpassed“to“ÂPictureŽ‘)«::‘ÏoutputŽ‘D«(‘ª®),‘¨<ÏComp–ÿ}'ar“e‘‰ffŽ–®minimum‘‰ffŽ“zŽ‘bsY«is“used“for“sorting.‘)¨The“elemen¸ãtsŽ¡‘ -are–UUsorted“in“descending“order“of“the“Ïminimum‘¸«z-v‘ÿqÇalue“from“their“Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘WY¦«.Ž¡·Ž‘ -«If‘dÂSortingŽ‘(ÎÙ«::‘ÝMAX_ZŽ‘*ì«is–dpassed“to“ÂPictureŽ‘) «::‘ÏoutputŽ‘D«(‘ª®),‘”·ÏComp–ÿ}'ar“e‘‰ffŽ–®maximum‘‰ffŽ“zŽ‘cW«is“used“for“sorting.‘!†The“elemen¸ãtsŽ¡‘ -are–UUthen“sorted“in“descending“order“of“the“Ïmaximum‘¸«z-v‘ÿqÇalue“from“their“Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘WY¦«.Ž¡·Ž‘ -«If‘ÂSortingŽ‘*f«::‘ÝMEAN_ZŽ‘$£v«is–passed“to“ÂPictureŽ‘*9-«::‘ÏoutputŽ‘D«(‘ª®),‘¯ÏComp–ÿ}'ar“e‘‰ffŽ›®me“an‘‰ffŽ˜zŽ‘Qò„«is“used“for“sorting.‘IThe“elemen¸ãtsŽ¡‘ +­realŽ‘ ³/±epsŽ‘2œ ¬=‘DZepsilonŽ‘"6¬(‘ª¨);Ž¦‘ +­ifŽ‘´ù¬(±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘^¶¬[3Ž‘]–Ç°“¬0Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘*”Ø°‘ß0´"ERROR!® ´In® ´Point::prŽ‘lÞôoject():® ´"Ž’¥Än°‘ß0´"projective_coordinaŽ‘lÞôtes[3]® ´==® ´0.\n"Ž’À_°Ž¡‘(´"This® ´will® ´cause® ´a® ´fŽ’ÿÈloating® ´point® ´error.Ž’ùÿŒ\n"Ž’4r°Ž¡‘(´"Setting® ´projective_Ž’ÿÈcoordinates® ´to® ´INVALŽ’ùÿŒID_REAL"Ž’'Lô°‘Ç´"® ´and® ´returning.\n"Ž‘iÔ_°‘DZ ushŽ‘€¬;Ž¡‘­forŽ‘%般(µiŽ‘9 ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ4Ž“;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)‘±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘c¶¬[µiŽ‘qô¬]–Ç=“´INVALID_REALŽ‘BM\¬;Ž¡‘­returnŽ‘7æ¼±falseŽ‘L–¬;Ž¡‘ +°gŽ¡‘ +­forŽ‘臬(µiŽ‘9 ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ4Ž“;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)‘°fŽ¡‘±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘r¶¬[µiŽ‘qô¬]‘ǵ=¬=ŽŽ‘UO±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘q b¬[3Ž‘];Ž¡‘­ifŽ‘´ú¬(±fabsŽ‘2Ò¬(±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘^¶¬[µiŽ›qô¬])–ǵ<“±epsŽ‘èÚ¬)‘±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘c¶¬[µiŽ˜¬]“=“0Ž‘Ç;Ž¡‘ +°g‘µ=°‘ž¬[²LDF‘T2002.09.14.¬]Ž‘TySet–Zöthe“µzŽ‘ Í +¬v‘ÿqÇalue“of“the“p•Gersp“ectiv¸ãe›Zöco“ordinates˜in˜order˜to˜b“e˜able˜to˜use˜it˜forŽ¡‘(m¸ãy–UUhidden“surface“algorith.‘o°µ=Ž¡‘ +±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘h¶¬[2Ž‘]–Ç=“(±fabsŽ‘2Ò¬(±save‘‰ffŽ‘®zŽ‘趬)“µ>“±epsŽ‘èÚ¬)“?“±save‘‰ffŽ‘®zŽ‘!væ¬:“0Ž‘Ç;Ž¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"Perspective® ´coordinŽ‘kÆÜates:\n("Ž’›)¬;Ž¡‘­forŽ‘%般(µiŽ‘9 ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ4Ž“;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘4 R°‘DZpr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘a}+¬[µiŽ‘qô¬];Ž¡‘­ifŽ‘)´û¬(µiŽ‘9 <‘Ǭ3Ž‘Ç)‘±c‘ÿ}'outŽ‘ O°‘Ç´",® ´"Ž‘Mt¬;Ž¡‘°gŽ¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´")\n"Ž‘ T‰°‘DZ ushŽ‘€¬;ŽŽŽŒ‹u ܼ Šn ý‘ì°x¬445–¯3DLDF-1.1.5.1’á(PERSPECTIVE‘ÕXPRÃŽOJECTION“¬117Ž €n ý•@P‘ +°gŽ¤ ‘ +­forŽ‘臬(µiŽ‘9 ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ2Ž“;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)Ž¡‘µ=°‘%d¬[²LDF‘T2002.11.07.¬]Ž‘TSKLUDGE.–z¼Added“this“loGop.‘áýThe“v‘ÿqÇalue“used“for“comparison“is“sligh¸ãtly“largerŽ¡‘(than–gÇone“that“arose“while“I‘gÂwš¸ãas“testing“the“constructor“of“±T‘ÿ;¼runc‘‰ffŽ‘®Octahe–ÿ}'dr“onŽ‘Tî¬.‘©±epsŽ‘2§¬w˜as“toGo“small.Ž¡‘(°µ=Ž¡‘­ifŽ‘´ú¬(±fabsŽ‘2Ò¬(±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘^¶¬[µiŽ›qô¬])–Ç°“¬10µ:¬0–8à°“¬10Ÿü^ÿ¶³05ŽŽŽ‘4þ¬)‘±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘c¶¬[µiŽ˜¬]“=“0Ž‘Ç;Ž¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Exiting® ´project().\Ž‘kÆÜn"Ž‘y”V°‘DZ ushŽ‘€¬;Ž¡‘ +­returnŽ‘-æ»±trueŽ‘@«S¬;‘qÇ°gŽ©­446.› üNo–i¿F‘ÿ +«oQÇcus“argumen®9t.˜¬[²LDF‘T2002.09.13.¬]Ž‘[ EAdded–Ödthis“function.‘ôõThis“dumm¸ãy“function“just“passesŽ¡±default‘‰ffŽ‘®fo‘ÿ}'cusŽ‘:7Ž¬to‘Y±pr–ÿ}'oje“ctŽ‘#*.¬(‘Y­constŽ‘ˆmF‘ÿ 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+­b•QÇo“olŽ‘#¡gP•®9oin“tŽ‘@;³¬::‘±pr–ÿ}'oje“ctŽ‘w¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S¬&Ž‘sóq±pr‘ÿ}'ojŽ’†ç4µ;‘ª¨­realŽ‘]Ö±factorŽ‘3a´¬)Ž¡‘ +°fŽ¡‘­returnŽ‘7æ¼±pr–ÿ}'oje“ctŽ‘V]ʬ(±default‘‰ffŽ‘®fo‘ÿ}'cusŽ‘7Ýþµ;‘ª¨±pr‘ÿ}'ojŽ‘žkµ;‘ª¨±factorŽ‘®†¬);Ž¡‘ +°gŽ¦­448.– üApplying‘ étransformations.“¬This–¸rv¸ãersion“applies“the“transformation“stored“in“­P•®9oin“tŽ‘R¾¬::‘±tr‘ÿ}'ansformŽ‘,³E¬.Ž¡!!‘]Add–Ra“vš¸ãersion“that“applies“a“­T‘ÿ +«ransformŽ‘9§¬supplied“as“an“argumen˜t!!‘][²LDF‘T2002.12.08.¬]Ž‘R WBUG‘QÓFIX:“See“bGelo˜w.ŽŸ°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙ±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘i¸¬(‘ª®);ŽŽŽŒ‹v ò“ Šn ý‘ì¬118›¯APPL–ÿJªYING‘ÕXTRANSFÃŽORMA“TIONS’Ò 3DLDF-1.1.5.1˜°x¬449Ž €n ý•@P­449.Ž©°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘"ýÙP•®9oin“tŽ‘?˜%¬::‘±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Gã¬(‘ª®)Ž¡‘ 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+­P®9athŽ‘%溱dr–ÿ}'awarr“owŽ‘TÙ~¬(­PictureŽ‘(ñb¬&Ž‘0¸€±pictur‘ÿ}'eŽ‘OÁVµ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒµpŽ‘K”;Ž¦‘­constŽ‘´µ;‘ª¨­stringŽ‘#å±pp‘ÿ}'enŽ‘;‚Z¬=‘8R´""Ž“¬)Ž¦‘­constŽ‘8ÕP¬;Ž¤­468.‘ üUndra®9w.Ž¡469.– üNormal‘¦žv®9ersion.“¬This–,¶function“m¸ãust“bšGe“de ned“in“®paths.web¬,‘4Öb˜ecause“it“uses“­P®9athŽ‘¾¬,‘4Öwhic¸ãh“is“anŽ¦incomplete–UUt¸ãypGe“here.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ +¬[²LDF‘T2002.4.8.¬]Ž‘OÈ?Added–UUthis“function.Ž¦‘ +[²LDF‘T2002.11.03.¬]Ž‘Y;Changed–UUthis“function,“so“that“it“returns“the“­P®9athŽ‘<±p‘ÿ}'aŽ‘*9R¬,“instead“of“­v®9oidŽ‘ýج.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¦‘ +­P®9athŽ‘'5±undr‘ÿ}'awŽ‘H[¬(­constŽ‘xþP•®9oin“tŽ‘?¶÷¬&Ž‘G~±ptŽ‘Qb²µ;‘ª¨­stringŽ‘$Q±ddashe‘ÿ}'dŽ‘LY»¬=‘ôY´""Ž–ú»µ;‘ª¨­stringŽ‘$Q±pp‘ÿ}'enŽ‘>Hͬ=‘ôY´""Ž“µ;‘ª¨­PictureŽŽ¦‘¬&Ž‘%Ç!±pictur‘ÿ}'eŽ‘G—¬=‘DZcurr–ÿ}'ent‘‰ffŽ‘®pictur“eŽ‘Dì߬);ŽŸ­470.‘ üPicture–ÕTargumen®9t“ rst.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ +¬[²LDF‘T2002.09.17.¬]Ž‘Y;Added–UUthis“function.‘qÇIt's“con•¸ãv“enien“t–UUfor“when“I“w•¸ãan“t–UUto“pass“a“­PictureŽ‘,F·¬argumen¸ãt.Ž¦‘ +[²LDF‘T2002.11.03.¬]Ž‘Y;Changed–UUthis“function,“so“that“it“returns“the“­P®9athŽ‘<±p‘ÿ}'aŽ‘*9R¬,“instead“of“­v®9oidŽ‘ýج.Ž¡ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¦‘ +­P®9athŽ‘%溱undr‘ÿ}'awŽ‘G ¹¬(­PictureŽ‘(ñb¬&Ž‘0¸€±pictur‘ÿ}'eŽ‘OÁVµ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±ptŽ‘Pp¢µ;‘ª¨­stringŽ‘"Ïõ±ddashe‘ÿ}'dŽ‘HÞ¬=‘Ç´""Ž– Ízµ;‘ª¨­stringŽ‘"Ïõ±pp‘ÿ}'enŽ‘:Í0¬=‘Ç´""Ž“¬);Ž¤­471.– üDra®9w‘+help.“¬[²LDF‘T2002.10.26.¬]Ž‘ZÒ˱dr‘ÿ}'aw‘‰ffŽ‘®helpŽ’…˜s¬(›ª®)–Ÿêis“lik¸ãe“±dr‘ÿ}'awŽ‘ÈŬ(˜),‘²except“that“the“­P®9athŽ‘Ñ8¬is“only“dra¸ãwn“ifŽ¦the‘wÀ­staticŽ‘"ãP®9athŽ‘>ì(¬data–wÀmemš¸ãbGer“±do‘‰ffŽ–®help‘‰ffŽ“linesŽ‘>±Ë°‘t±trueŽ‘Å ¬.‘ÙThis“is“con˜v˜enien˜t“for“dra˜wing“construction“lines“thatŽ¦shouldn't–UUbGe“output“in“the“ nal“vš¸ãersion“of“a“dra˜wing.‘qÇAlso,“the“default“color“is“°Ž‘UV­ColorsŽ‘*.4¬::Ž‘0¼r±help‘‰ffŽ‘®c‘ÿ}'olorŽ‘\væ¬.Ž¡­472.– 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üOutput‘ ropQÇerator.“¬[²LDF‘T2002.10.26.¬]Ž‘[8ÕThis–ôfunction“is“used“in“­P®9athŽ‘—\¬::‘±outputŽ‘D¬(‘ª®)“for“writing“the“xŽ¤ and–‚Iy“v‘ÿqÇalues“of“the“±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘gº¥¬to“±out‘‰ffŽ‘®str–ÿ}'e“amŽ‘3Âå¬.‘ø¤All“coGde“using“this“function“m¸ãust“ensure“thatŽ¡±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(›ª®)–UUand“±pr–ÿ}'oje“ctŽ‘!Ìc¬(˜)“are“called“± rst‘òج!ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.09.16.¬]Ž‘Y;Remo•¸ãv“ed–UUcalls“to“±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Iu4¬(›ª®)“and“±pr–ÿ}'oje“ctŽ‘!Ìc¬(˜).Ž¦ŸüÈ„`ÕÁGŽŽ¦°h›ª¨¬Declare–UUnon-mem¸ãbGer“non-template“functions“for“­P•®9oin“tŽ‘#/¡¯480˜°i‘ÇŽ¡‘ +±ostr–ÿ}'e“amŽ‘/¬&‘8à­opQÇeratorŽ‘-Ï•°Ž‘7Ï–¬(±ostr–ÿ}'e“amŽ‘%¬&‘8àµoŽ‘Ä;‘ª¨­P•®9oin“tŽ‘ šE¬&Ž‘(acµpŽ‘-ic¬);Ž¤ ¯See–ÕXalso“section“534.Ž¡This–ÕXco:¬(‘ª®)–Hêis“a“pure“­virtualŽ‘.ÊR¬function“in“­ShapQÇeŽ‘%4÷¬.‘ L…It's“called“b¸ãyŽ¡­PictureŽ‘&œ¬::‘±outputŽ‘D¬(‘ª®).‘E Eacš¸ãh–Ïof“the“­ShapQÇeŽ‘$ŠA¬pGoin˜ters“on“the“­v®9ectorŽ‘%H|±shap‘ÿ}'esŽ‘E¬in“the“­PictureŽ‘+:A¬m˜ust“bGe“\extracted".Ž¡F‘ÿ*ªor‘˜ý­P•®9oin“tsŽ‘$¼¬,‘éæthis–˜ýmeans“pro‘Ž8jecting“the“­P•®9oin“tŽ‘$ÌB¬using“the“­F‘ÿ +«oQÇcusŽ‘&'F¬passed“to“±extr‘ÿ}'actŽ‘#[l¬(‘ª®)“as“an“argumen¸ãt.‘<¿IfŽ¡±pr–ÿ}'oje“ctŽ‘w¬(›ª®)–UUsucceeds,“±extr‘ÿ}'actŽ‘"Ĭ(˜)“returns“a“­v®9ectorŽ‘&Tò¬conš¸ãtaining“±thisŽ‘A ¬.‘qÇOtherwise,“it“returns“an“empt˜y“­v®9ectorŽ‘"ÿ¬.Ž¡‘ +[²LDF‘T2002.10.26.¬]Ž‘YKNA‘˜W­v®9ectorŽ‘&Û¬is–˜hreturned“rather“than“±thisŽ‘†¬bš¸ãy“itself“bGecause“it“ma˜y“sometimes“bGe“useful“toŽ¡return– a“collection“of“­ShapQÇeŽ‘%(¬pGoinš¸ãters“rather“than“a“single“one.‘_XThis“w˜as“formerly“the“case“for“­CubQÇoidŽ‘(m£¬,‘)butŽ¡at–UUthe“presenš¸ãt“time,“no“v˜ersion“of“±extr‘ÿ}'actŽ‘"Ĭ(‘ª®)“returns“a“­v®9ectorŽ‘&Tò¬with“more“than“one“pGoin˜ter“to“­ShapQÇeŽ‘"Ab¬.ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.09.17.¬]Ž‘Y +WAdded‘Wq­constŽ‘!„/F‘ÿ +«oQÇcusŽ‘AÐì¬&Ž‘I˜ +µfŽ‘Rèa¬argumenš¸ãt–Wqand“error“handling“coGde.‘xNo˜w,‘W÷if“the“­P•®9oin“tŽ‘"I*¬cannotŽ¡bGe–fÝpro›Ž8jected“on¸ãto“the“pro˜jection“plane“using“the“­F‘ÿ +«oQÇcusŽ‘'õfŽ‘-»ì¬,‘ë>it“is“not“put“on¸ãto“the“­v®9ectorŽ‘%%°h­ShapQÇeŽ‘$Rê°Ž‘)RëiŽ¡­PictureŽ‘&œ¬::‘±elementsŽ‘'åÿ¬,–UUand“consequenš¸ãtly“nev˜er“reac˜hes“­PictureŽ‘)ñf¬::‘±outputŽ›D¬(‘ª®)“and“­P•®9oin“tŽ‘::‘±outputŽ˜¬(‘ª®).Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­v®9ectorŽ‘)ªI°h­ShapQÇeŽ‘"Ab°Ž‘'Aci‘UU±extr‘ÿ}'actŽ‘"Ĭ(­constŽ‘*¢F‘ÿ +«oQÇcusŽ‘>uC¬&Ž‘FuC¬&Ž‘F.\n"Ž’üM°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½µvŽ‘Gz¬;Ž¡‘°gŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘6¬e°‘S+´"world_coordinates:® Ž‘nRï ´("Ž’˜ìm°‘S+±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Rg)¬[0Ž‘]–S+°“´",® ´"Ž‘ ,²°Ž¡‘2±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘¬[1Ž›]–£Ø°“´",® ´"Ž‘Î °“±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘P·Ö¬[2Ž˜]“°“´",® ´"Ž‘Î °“±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘P·Ö¬[3Ž˜]“°Ž¡‘2´")\n"Ž‘R…°‘A'´"projective_coordinaŽ‘n@ëtes:® ´("Ž’˜Èe°‘A'±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘c÷:¬[0Ž‘]‘A'°Ž¡‘2´",® ´"Ž‘KÙ®°‘SM±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ›c `¬[1Ž‘]–SM°“´",® ´"Ž‘,ö°“±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ˜¬[2Ž‘]“°“´",® ´"Ž‘,ö°Ž¡‘2±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ’¶¬[3Ž‘]–Ç°“´")\n"Ž‘q¬;Ž¡‘°gŽ¡‘µvŽ‘4¿:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(±thisŽ‘붬);Ž¡‘­returnŽ‘7æ¼µvŽ‘=y¬;Ž¡‘ +°gŽŸ­488.– üGet‘3Lextremes.“¬[²LDF‘T2002.09.18.¬]Ž‘ZÙìAdded–§ this“function.‘fêAnš¸ãy“coGde“that“calls“±get‘‰ffŽ‘®extr‘ÿ}'emesŽ‘:ëk¬(‘ª®)“m˜ustŽ¡ensure–UUthat“±pr–ÿ}'oje“ctŽ‘!Ìc¬(‘ª®)“has“bGeen“in•¸ãv“ok“ed‘UU rst.Ž¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔinlineŽ‘OconstŽ‘mB¾v‘ÿ\ralarra®9yŽ’–œÿ°h­realŽ‘]Ù°i‘UU±get‘‰ffŽ‘®extr‘ÿ}'emesŽ‘:™µ¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ’‹ë ¬;Ž¡‘ +°gŽŸ­489.› üGet–ÕTminim®9um“z.˜¬[²LDF‘T2002.09.17.¬]Ž‘Zˆ6Added–UUthis“function.Ž¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔrealŽ‘FA±get‘‰ffŽ–®minimum‘‰ffŽ“zŽ’‰žÚ¬(‘ª®)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹€ +|´ Šn ý‘ì¬128›¯GET–ÕXMINIMUM“Z’¨3DLDF-1.1.5.1˜°x¬490Ž €n ý•@P­490.Ž©°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¤ ‘ +­realŽ‘ ³/P•®9oin“tŽ‘=M{¬::‘±get‘‰ffŽ–®minimum‘‰ffŽ“zŽ‘D]ܬ(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­b•QÇo“olŽ‘-¡h´DEBUGŽ‘K.Ù¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¦‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Entering® ´Point::getŽ‘kÆÜ_minimum_z()"Ž’³T5°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"minimum_z® ´==® ´"Ž‘TÔk°‘DZpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘VËi¬[4Ž‘]–Ç°“±end‘‚ØlŽ‘ò°“± ushŽ‘€¬;Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Exiting® ´Point::get_Ž‘kÆÜminimum_z()"Ž’®8°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘7æ¼±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ’‹ë ¬[4Ž‘];Ž¡‘ +°gŽŸ­491.› üGet–ÕTmaxim®9um“z.˜¬[²LDF‘T2002.09.17.¬]Ž‘Zˆ6Added–UUthis“function.Ž¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔrealŽ‘FA±get‘‰ffŽ–®maximum‘‰ffŽ“zŽ’Š®¬(‘ª®)‘UU­constŽ‘*¢¬;ŽŸ­492.Ž¦°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¡‘ +­realŽ‘ ³/P•®9oin“tŽ‘=M{¬::‘±get‘‰ffŽ–®maximum‘‰ffŽ“zŽ‘Em¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­b•QÇo“olŽ‘-¡h´DEBUGŽ‘K.Ù¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¦‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Entering® ´Point::getŽ‘kÆÜ_maximum_z()"Ž’³T5°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"maximum_z® ´==® ´"Ž‘TÔk°‘DZpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘VËi¬[5Ž‘]–Ç°“±end‘‚ØlŽ‘ò°“± ushŽ‘€¬;Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Exiting® ´Point::get_Ž‘kÆÜmaximum_z()"Ž’®8°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘7æ¼±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ’‹ë ¬[5Ž‘];Ž¡‘ +°gŽŸ­493.› üGet–ÕTmean“z.˜¬[²LDF‘T2003.05.16.¬]Ž‘Zˆ6Added–UUthis“function.Ž¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔrealŽ‘FA±get‘‰ffŽ–®me‘ÿ}'an‘‰ffŽ“zŽ‘v÷ ¬(‘ª®)‘UU­constŽ‘*¢¬;ŽŸ­494.Ž¦°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¡‘ +­realŽ‘ ³/P•®9oin“tŽ‘=M{¬::‘±get‘‰ffŽ–®me‘ÿ}'an‘‰ffŽ“zŽ‘1¶¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7漬((±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ¬[4Ž›]–8à+“±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘V=1¬[5Ž˜])µ=¬2Ž˜);Ž¡‘ +°gŽŸ­495.– üSet‘írextremes.“¬This–Héfunction“sets“\extreme"“v‘ÿqÇalues“for“the“x,–…Îy‘ÿ*ª,“and–Héz-coGordinates.‘LƒThis“is,‘…ÎofŽ¡course,›ßtrivial–Ñfor“­P•®9oin“tsŽ‘#ç¬,˜bGecause“they“only“ha•¸ãv“e–Ñone“x,˜y“and“z-coGordinate.‘¼zSo“the“maxima“and“minimaŽ¡for–UUeacš¸ãh“coGordinate“are“alw˜a˜ys“the“same.Ž¡‘ +[²LDF‘T2002.10.20.¬]Ž‘Z¸ÎThe–èprogrammer“who“uses“±set‘‰ffŽ‘®extr‘ÿ}'emesŽ‘;Çq¬(›ª®)“m¸ãust“ensure“that“±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘K%Ǭ(˜)“andŽ¡±pr–ÿ}'oje“ctŽ‘w¬(›ª®)–UUare“in•¸ãv“ok“ed–UUbGefore“±set‘‰ffŽ‘®extr‘ÿ}'emesŽ‘:Þ¬(˜)!ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.09.17.¬]Ž‘Y;Added–UUthis“function.Ž¡‘ +[²LDF‘T2002.09.18.¬]Ž‘Y;Changed–UUthe“name“of“this“function“from“±set‘‰ffŽ–®minimum‘‰ffŽ“zŽ‘F0V¬(›ª®)“to“±set‘‰ffŽ‘®extr‘ÿ}'emesŽ‘:Þ¬(˜).Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/Ôb•QÇo“olŽ‘I/:±set‘‰ffŽ‘®extr‘ÿ}'emesŽ‘ðì(‘ª®);ŽŽŽŒ‹ +ˆ· Šn ý‘ì°x¬496–¯3DLDF-1.1.5.1’:úSET‘ÕXEXTREMES“¬129Ž €n ý•@P­496.Ž©°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¤ ‘ +­b•QÇo“olŽ‘#¡gP•®9oin“tŽ‘@;³¬::‘±set‘‰ffŽ‘®extr‘ÿ}'emesŽ‘7Á¬(‘ª®)Ž¡‘ +°fŽ¡‘­b•QÇo“olŽ‘-¡h´DEBUGŽ‘K.Ù¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¦‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Entering® ´Point::setŽ‘kÆÜ_extremes()"Ž’®8°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘­forŽ‘%般(­in®9tŽ‘¤÷µiŽ‘Þ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ4Ž“;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)‘°fŽ¡‘­ifŽ‘)´û¬(±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘^¶¬[µiŽ‘qô¬]–Ç°“´INVALID_REALŽ‘BM\¬)‘°fŽ¡‘(±c‘ÿ}'errŽ‘=|°‘Ç´"ERROR!® ´In® ´Point::seŽ‘kÆÜt_extremes():\n"Ž’Ã,°‘Ç´"projective_coordinaŽ‘kÆÜtes["Ž’‰TM°‘ǵiŽ‘ $°‘Ç´"]"Ž‘Ô°Ž¡‘<´"® ´==® ´INVALID_REAL.\nŽ’¤ÿÊ"Ž’®&µ°‘`†´"Setting® ´every® ´elemeŽ‘l`Jnt® ´in® ´projective_extŽ’Õ`remes® ´"Ž’þç°Ž¡‘<´"to® ´INVALID_REAL® ´andŽ’¤ÿÊ® ´returning® ´false.\n"Ž’M°‘DZ ushŽ‘€¬;Ž¡‘(­forŽ‘9芬(­in®9tŽ‘¤÷µjŽ‘Ó¬=‘Ç0Ž–Ç;‘ÿýµjŽ‘ wÙ<‘Ǭ6Ž“;‘ÿýµjŽ‘ +0ÁŸÿ³+‘ÿ+ŽŽ‘÷á¬)‘±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘YQ¬[µjŽ‘°Ä¬]–Ç=“´INVALID_REALŽ‘BM\¬;Ž¡‘(­returnŽ‘Kæ¾±falseŽ‘`–¬;Ž¡‘°gŽ¡‘gŽ¡‘±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘hS¬[0Ž›]–Ç=“±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘a}+¬[0Ž˜];‘µ=°–ÿý¬min‘UUx“°µ=Ž¡‘±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘hS¬[1Ž›]–Ç=“±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘a}+¬[0Ž˜];‘µ=°–ÿý¬max‘UUx“°µ=Ž¡‘±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘hS¬[2Ž›]–Ç=“±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘a}+¬[1Ž˜];‘µ=°–ÿý¬min‘UUy“°µ=Ž¡‘±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘hS¬[3Ž›]–Ç=“±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘a}+¬[1Ž˜];‘µ=°–ÿý¬max‘UUy“°µ=Ž¡‘±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘hS¬[4Ž›]–Ç=“±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘a}+¬[2Ž˜];‘µ=°–ÿý¬min‘UUz“°µ=Ž¡‘±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘hS¬[5Ž›]–Ç=“±pr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘a}+¬[2Ž˜];‘µ=°–ÿý¬max‘UUz“°µ=Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Exiting® ´Point::setŽ‘kÆÜ_extremes()"Ž’®8°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘7æ¼±trueŽ‘J«T¬;Ž¡‘ +°gŽŸ­497.– üComparison‘ÕTclasses.“¬[²LDF‘T2003.05.16.¬]Ž‘Zˆ6The–UUfunction“classes“in“this“section“are“used“inŽ¡­PictureŽ‘&œ¬::‘±outputŽ‘D¬(‘ª®)– õto“sort“the“pGoinš¸ãters“to“­ShapQÇeŽ‘%÷¬in“­v®9ectorŽ‘"·=°h­ShapQÇeŽ‘!ù°Ž‘&ùi“±elementsŽ‘)òð¬.‘Y§The“argumen˜t“±sort‘‰ffŽ‘®valueŽ‘.÷¬,Ž¡whicš¸ãh–9pshould“bGe“one“of“the“constan˜ts“in“­namespaceŽ‘<ÁSortingŽ‘b+K¬,‘?determines“whic˜h“one“is“used,‘?or“if“±elementsŽŽ¡¬shouldn't–UUbGe“sorted.Ž¡°Ž‘ +¬If‘|õ­SortingŽ‘(ç?¬::‘´MIN_ZŽ‘CR¬is–|õpassed“to“­PictureŽ‘)¬::‘±outputŽ‘D¬(‘ª®),‘¨<±Comp–ÿ}'ar“e‘‰ffŽ–®minimum‘‰ffŽ“zŽ‘bsY¬is“used“for“sorting.‘)¨The“elemen¸ãtsŽ¡‘ +are–UUsorted“in“descending“order“of“the“±minimum‘¸¬z-v‘ÿqÇalue“from“their“±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘WY¦¬.Ž¡°Ž‘ +¬If‘d­SortingŽ‘(ÎÙ¬::‘´MAX_ZŽ‘*ì¬is–dpassed“to“­PictureŽ‘) ¬::‘±outputŽ‘D¬(‘ª®),‘”·±Comp–ÿ}'ar“e‘‰ffŽ–®maximum‘‰ffŽ“zŽ‘cW¬is“used“for“sorting.‘!†The“elemen¸ãtsŽ¡‘ 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-«[¬LDF‘T2003.05.16.«]Ž‘Y;Added–UUthis“ÂclassŽ‘àQ«.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h›ª¨«De ne–UUcomparison“classes‘@­454˜·i‘ÇŽ¦‘ -ÂclassŽ‘$àRCompareu½‰™šs4Ž–Ôwminim®9umu½‰™šs4Ž“zŽ’”Æý·fŽ¦‘ -ÂpublicŽ‘)=Ö«:‘Âin®9tŽ‘¤÷opQÇeratorŽ‘B;¬«(‘ª®)(ÂconstŽ‘*¢ShapQÇeŽ‘@l·Ž‘ElÏs1Ž‘P}±;‘ª¨ÂconstŽ‘ÕJShapQÇeŽ‘B¬·Ž‘G­Ïs2Ž‘R'½«)‘UUÂconstŽŽ¦‘·fŽ¦‘ÂreturnŽ‘Aæ½Ïs1Ž‘J÷ÍŸ±~ŽŽ‘P÷ÎÏget‘‰ffŽ–®minimum‘‰ffŽ“zŽ’”U¦«(›ª¨)–DZ>“Ïs2Ž‘ Ø(Ÿ±~ŽŽ‘Ø)Ïget‘‰ffŽ–®minimum‘‰ffŽ“zŽ‘U6«(˜);Ž¦‘·gŽ¦‘ -g«;Ž¤ ­See–ÕXalso“sections“455“and“456.Ž¡This–ÕXco“Ïs2Ž‘ Ø(Ÿ±~ŽŽ‘Ø)Ïget‘‰ffŽ–®maximum‘‰ffŽ“zŽ‘VE¦«(˜);Ž¦‘·gŽ¦‘ -g«;ŽŽŽŒ‹yº$ Šn ý‘ì·x«456›­3DLDFPRÃŽG’™.COMP‘ÿJªARE–ÕXMEAN“Z˜«121Ž €n ý•@PÂ456.‘ üCompare–ÕTmean“z.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ© ‘ -«[¬LDF‘T2002.09.17.«]Ž‘Y;Added–UUthis“ÂclassŽ‘àQ«.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h›ª¨«De ne–UUcomparison“classes‘@­454˜·i‘Ç«+·Ž¦‘ -ÂclassŽ‘$àRCompareu½‰™šs4Ž–Ôwmeanu½‰™šs4Ž“zŽ’€u·fŽ¦‘ -ÂpublicŽ‘)=Ö«:‘Âin®9tŽ‘¤÷opQÇeratorŽ‘B;¬«(‘ª®)(ÂconstŽ‘*¢ShapQÇeŽ‘@l·Ž‘ElÏs1Ž‘P}±;‘ª¨ÂconstŽ‘ÕJShapQÇeŽ‘B¬·Ž‘G­Ïs2Ž‘R'½«)‘UUÂconstŽŽ¦‘·fŽ¦‘ÂreturnŽ‘Dÿ«(((Ïs1Ž‘ Ÿ±~ŽŽ‘Ïget‘‰ffŽ–®minimum‘‰ffŽ“zŽ‘Rné«(›ª¨)–õ´+“Ïs1Ž‘ ÄŸ±~ŽŽ‘ÅÏget‘‰ffŽ–®maximum‘‰ffŽ“zŽ‘WtB«(˜))±=«2Ž‘)‘+±>Ž¦‘2«((Ïs2Ž‘ Ÿ±~ŽŽ‘Ïget‘‰ffŽ–®minimum‘‰ffŽ“zŽ‘Rné«(›ª¨)–8à+“Ïs2Ž‘ IðŸ±~ŽŽ‘IñÏget‘‰ffŽ–®maximum‘‰ffŽ“zŽ‘U·n«(˜))±=«2Ž‘));Ž¦‘·gŽ¦‘ -g«;ŽŸÂ457.– üOutput.“«[¬LDF‘T2002.10.26.«]Ž‘\V¼ÏoutputŽ‘yeü«(‘ª®)–#Ûis“a“pure“ÂvirtualŽ‘,€4«function“in“ÂShapQÇeŽ‘$è«.‘ ÝYAfter“the“ÂShapQÇeŽŽ¦«pGoinš¸ãters–¿on“the“Âv®9ectorŽ‘'éÆPictureŽ‘N…׫::‘Ïshap‘ÿ}'esŽ‘"L«ha˜v˜e“bGeen“extracted,‘RZÏoutputŽ‘!aš«(‘ª®)“is“called“for“eac˜h“of“the“ÂShapQÇesŽŽ¦«they–6¨pGoinš¸ãt“to“(except“for“the“ones,‘<Ëif“an˜y‘ÿ*ª,‘<Ëwhere“Ïpr–ÿ}'oje“ctŽ‘!­¶«(›ª®)“failed).‘gÏoutputŽ‘!vÍ«(˜)“writes“the“MET‘ÿ*ªAPOST‘6 coGde“toŽ¦Ïout‘‰ffŽ‘®str–ÿ}'e“amŽ‘/@œ«.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¦‘ -«[¬LDF‘T2002.09.16.«]Ž‘YAdded‘j!ÂF‘ÿ -«oQÇcusŽ‘#ÉŽ«argumen•¸ãt‘j!±fŽ‘ c«.‘°+I›jw“an“t–j!the“default“to“bGe“Ïdefault‘‰ffŽ‘®fo‘ÿ}'cusŽ‘;H«,‘oTbut“I˜can't“put“it“inŽ¦the–Þdeclaration,›Âas“I‘Énormally“do,˜bšGecause“Ïdefault‘‰ffŽ‘®fo‘ÿ}'cusŽ‘=麫hasn't“b˜een“de ned“y•¸ãet.‘WJI'v“e–Þput“it“in“the“de nition,Ž¦and––¿it“seems“to“wš¸ãork.‘6Sometimes“it“doGesn't,‘§and“I‘–®don't“kno˜w“wh˜y‘ÿ*ª,‘§nor“do“I‘–®kno˜w“wh˜y“it“w˜orks“this“time.Ž¦If–·ÿI‘·ærun“inš¸ãto“problems,‘Щthis“ma˜y“bGe“the“reason.‘™ÅIf“necessary‘ÿ*ª,‘ЩI‘·æcan“mak˜e“a“dumm˜y“v˜ersion“of“this“functionŽ¦with–UUno“argumenš¸ãt“that“calls“Ïthis‘'v«v˜ersion“with“Ïdefault‘‰ffŽ‘®fo‘ÿ}'cusŽ‘>ˆ¨«as“its“argumen˜t.Ž¦‘ -[¬LDF‘T2002.09.17.«]Ž‘YèChanged–lthe“argumenš¸ãt“±fŽ‘ Ðê«from“ÂF‘ÿ -«oQÇcusŽ‘#ÍP«to“ÂconstŽ‘!­QF‘ÿ -«oQÇcusŽ‘BŸ«&Ž‘IÕ½.‘µÍRemo˜v˜ed“the“in˜v˜oGcations“ofŽ¦Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(›ª®)–UUand“Ïpr–ÿ}'oje“ctŽ‘!Ìc«(˜)“and“error“handling“coGde“to“Ïextr‘ÿ}'actŽ‘"Ä«(˜).Ž¦‘ -[¬LDF‘T2002.10.23.«]Ž‘[hRemo•¸ãv“ed–µthe“argumenš¸ãt“±fŽ‘ ®«.‘ ‘Since“Ïextr‘ÿ}'actŽ‘$w‰«(‘ª®)“tak˜es“care“of“applying“Ïpr–ÿ}'oje“ctŽ‘$,(«(‘ª®),‘M theŽ¦Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®c“o“or“dinatesŽ‘c:Ыare–„½already“set,‘Зso“all“ÏoutputŽ‘!“ý«(‘ª®)“needs“to“do“is“write“them“to“Ïout‘‰ffŽ‘®str–ÿ}'e“amŽ‘8J«with“theŽ¦propGer–UUMET‘ÿ*ªAPOST“instructions.Ž¡ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¦‘ -Âv®9oidŽ‘"ýÙÏoutputŽ‘@ «(‘ª®);ŽŽŽŒ‹zÁ Šn ý‘ì«122–­OUTPUT’=\03DLDFPRÃŽG“·x«458Ž €n ý•@PÂ458.Ž©·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¤ ‘ -Âv®9oidŽ‘"ýÙP•®9oin“tŽ‘?˜%«::‘ÏoutputŽ‘D«(‘ª®)Ž¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EnteringÈ ÝPoint::outŽ‘kÆÜput().\n"Ž’žTA·‘ÇÏ ushŽ‘€«;Ž¡‘ÂifŽ‘´ú«(Ïdo‘‰ffŽ‘®outputŽ‘-½K·‘ÇÏfalseŽ‘v\«)‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"InÈ ÝPoint::output():Ž‘kÆÜÈ Ýdo_outputÈ Ý==È Ýfalse.Ž’ÔÆ È ÝReturning.\n"Ž’!“ö·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘>‘h«;Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(Ïdr‘ÿ}'awdot‘‰ffŽ‘®valueŽ‘@á·‘ÇÝDRAWDOTŽ‘( 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‘l‘pGermitted–À'as“in“MET‘ÿ*ªAPOST.“They“are“written“unc•¸ãhec“k“ed–À'to“Ïout‘‰ffŽ‘®str–ÿ}'e“amŽ‘3ë,‘ÚÛso“if“anŽ¡‘l‘inš¸ãv‘ÿqÇalid‘‹uÂstringŽ‘"æâ«is–‹uused,‘³Õit“w˜on't“cause“an“error“in“3DLDF,“but“it“will“in“MET‘ÿ*ªAPOST.Ž¡‘l‘The–ùüpGermitted“ÂstringsŽ‘,$H«are:‘»Ý"top"Ž‘'{j«(the“default),‘c%Ý"bot"Ž– 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üDotlabQÇel.“«TO‘ÅŠDO:–ÅéAdd“an“optional“Ïp‘ÿ}'enŽ‘¥…«argumen¸ãt.‘ÃIf“it's“used,‘"use“Ïdr‘ÿ}'awdotŽ‘(Yj«(‘ª®)“with“the“Ïp‘ÿ}'enŽŽ¡«argumen¸ãt,›ptogether–ò7with“Ïlab‘ÿ}'elŽ‘fÏ«(‘ª®).‘HnWhen“I‘òdo“this,˜I‘òshould“also“add“ÂrealŽ‘BG«argumen¸ãts“(to“bGoth“Ïlab‘ÿ}'elŽ‘fÏ«(‘ª®)“andŽ¡Ïdotlab‘ÿ}'elŽ‘!ÿó«(‘ª®))–,Äfor“shifting“the“pGosition“of“the“text,‘4áand“a“vš¸ãersion“with“a“ÂP•®9oin“tŽ‘!óЫargumen˜t“for“the“same“purpGose.Ž¡This–UUis“so“that“the“dot“wš¸ãon't“co˜v˜er“the“text.‘qÇ[¬LDF‘T2003.07.16.«]ŽŽŽŽŒ‹û Šn ý‘ì·x«466›­3DLDFPR•ÃŽG’ÿ€ÂSTRING‘ÕX­AR“GUMENT˜«127Ž €n ý•@PÂ466.‘ üstring‘ÕTargumen®9t.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ© ‘ -«[¬LDF‘T2003.07.09.«]Ž‘Y;Made‘UUÏtext‘‰ffŽ‘®strŽ‘'qî«and‘UUÏp‘ÿ}'osition‘‰ffŽ‘®strŽ‘9Œî«argumen¸ãts‘UUÂconstŽ‘*¢«.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¦‘ 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-·fŽ¡‘ÂP•®9oin“tŽ‘2aŽ‘88Ï«(·Ž‘ÏthisŽ‘ë·«);Ž¦‘±aŽ‘I2:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨);Ž¡‘±pŽ‘:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨);Ž¦‘ÂP•®9oin“tŽ‘2rŽ‘7¹³«;Ž¦‘±rŽ‘Ê:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ›Mþ«[0Ž‘]–—=“(±aŽ‘I0:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜«[1Ž‘]–\F·“±pŽ‘dF:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜«[2Ž‘])“·“«(±aŽ‘I0:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜«[2Ž‘]“·Ž¡‘(±pŽ‘-:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[1Ž‘]);‘±=·‘ÿý«x.‘o·±=Ž¡‘rŽ‘Ê:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ›Mþ«[1Ž‘]–—=“(±aŽ‘I0:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜«[2Ž‘]–\F·“±pŽ‘dF:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜«[0Ž‘])“·“«(±aŽ‘I0:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜«[0Ž‘]“·Ž¡‘(±pŽ‘-:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[2Ž‘]);‘±=·‘ÿý«y‘ÿ*ª.‘o·±=Ž¡‘rŽ‘Ê:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ›Mþ«[2Ž‘]–—=“(±aŽ‘I0:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜«[0Ž‘]–\F·“±pŽ‘dF:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜«[1Ž‘])“·“«(±aŽ‘I0:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜«[1Ž‘]“·Ž¡‘(±pŽ‘-:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[0Ž‘]);‘±=·‘ÿý«z.‘o·±=Ž¡‘ÂreturnŽ‘7æ¼±rŽ‘<°Ð«;Ž¡‘ -·gŽŸÂ502.– üMagnitude.“«[¬LDF‘T2002.10.27.«]ŽŽ¤Ùš‘ -The–UUmagnitude“of“a“ÂP•®9oin“tŽ‘"Dò«is“its“distance“from“the“origin“and“is“equal“to“Ÿ÷s0óú±u +¬[²LDF‘T2002.10.27.¬]Ž‘Y;Made–UUthis“function“and“the“argumen¸ãt“µrŽ‘ t¾­constŽ‘&J ¬.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­P•®9oin“tŽ‘(ïžopQÇeratorŽ‘T†Sµ=¬(­constŽ‘*¢realŽ‘4ÝеrŽ‘9§ä¬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹ 39 Šn ý‘ì°x¬541–¯3DLDF-1.1.5.1’äuÐVECTOR-SCALAR‘ÕXDIVISION“¬143Ž €n ý•@P­541.Ž©°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¤ ‘ +­P•®9oin“tŽ‘(ïžP•®9oin“tŽ‘E‰ê¬::Ž‘L(­opQÇeratorŽ‘w®Ýµ=¬(­constŽ‘*¢realŽ‘4ÝеrŽ‘9§ä¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­P•®9oin“tŽ‘2aŽ‘88Ϭ(°Ž‘±thisŽ‘ë·¬);Ž¦‘µaŽ‘I2:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¡‘µaŽ‘J=¬=ŽŽ‘+žµrŽ‘0h•¬;Ž¡‘­returnŽ‘7æ¼µaŽ‘=/ì¬;Ž¡‘ +°gŽŸ­542.‘ üDot‘ÕTproQÇduct.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.10.27.¬]Ž‘Xô2Changed–ALthis“function“and“argumenš¸ãt“µpŽ‘ Š˜¬to“­constŽ‘™¬.‘kNo˜w“using“±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘S––¬directlyŽ¡instead–UUof“±get‘‰ffŽ‘®xŽ‘㼬(›ª®),“±get‘‰ffŽ‘®yŽ‘Ék¬(˜),“and“±get‘‰ffŽ‘®zŽ‘]V¬(˜).Ž¡‘ +[²LDF‘T2003.07.11.¬]Ž‘Y;Changed,–UUso“that“if“the“dot“prošGduct“is“less“than“­P•®9oin“tŽ‘::‘±epsilonŽ‘ o¬(‘ª®),“0“will“b˜e“returned.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­realŽ‘ ³/±dot‘‰ffŽ‘®pr–ÿ}'o“ductŽ‘S3P¬(­P•®9oin“tŽ‘ïµpŽ‘#÷¬)‘UU­constŽ‘*¢¬;ŽŸ­543.Ž¦°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¡‘ +­realŽ‘ ³/P•®9oin“tŽ‘=M{¬::‘±dot‘‰ffŽ‘®pr–ÿ}'o“ductŽ‘3€%¬(­P•®9oin“tŽ‘ïµpŽ‘#÷¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­P•®9oin“tŽ‘2aŽ‘88Ϭ(°Ž‘±thisŽ‘ë·¬);Ž¦‘µaŽ‘I2:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¡‘µpŽ‘:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¦‘­realŽ‘+ØõµrŽ‘5S½¬=‘°´((µaŽ‘I0:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ›Mþ¬[0Ž‘]–ü¸°“µpŽ‘¸:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[0Ž‘])“+“(µaŽ‘I0:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[1Ž‘]“°Ž¡‘(µpŽ‘-:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ›Mþ¬[1Ž‘])–8à+“(µaŽ‘I0:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[2Ž‘]“°“µpŽ‘@à:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[2Ž‘]));Ž¦‘­ifŽ‘´ú¬(±fabsŽ‘2Ò¬(µrŽ‘ʬ)–ǵ<“­P•®9oin“tŽ‘ad¬::Ž‘%epsilonŽ‘E^¦¬(‘ª¨))‘µrŽ‘ ‘,¬=“0Ž‘Ç;Ž¡‘­returnŽ‘7æ¼µrŽ‘<°Ð¬;Ž¡‘ +°gŽŸ­544.‘ üCross‘ÕTproQÇduct.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.10.27.¬]Ž‘Xô2Changed–ALthis“function“and“argumenš¸ãt“µpŽ‘ Š˜¬to“­constŽ‘™¬.‘kNo˜w“using“±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘S––¬directlyŽ¡instead–UUof“±get‘‰ffŽ‘®xŽ‘㼬(›ª®),“±get‘‰ffŽ‘®yŽ‘Ék¬(˜),“and“±get‘‰ffŽ‘®zŽ‘]V¬(˜).Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­P•®9oin“tŽ‘(ïž±cr–ÿ}'oss‘‰ffŽ‘®pr“o“ductŽ‘c|‡¬(­P•®9oin“tŽ‘ïµpŽ‘#÷¬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹ :œ Šn ý‘ì¬144›¯CR•ÃŽOSS‘ÕXPR“ODUCT’¹ˆ3DLDF-1.1.5.1˜°x¬545Ž €n ý•@P­545.Ž©°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¤ ‘ +­P•®9oin“tŽ‘(ïžP•®9oin“tŽ‘E‰ê¬::‘±cr–ÿ}'oss‘‰ffŽ‘®pr“o“ductŽ‘;Œí¬(­P•®9oin“tŽ‘ïµpŽ‘#÷¬)‘UU­constŽŽ¡‘ 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-«[¬LDF‘T2002.10.27.«]Ž‘ZMade–j6this“function“ÂconstŽ‘?ƒ«.‘°kNo¸ãw“using“Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Uèj«directly“instead“of“Ïget‘‰ffŽ‘®xŽ‘ø«(‘ª®),Ž¡Ïget‘‰ffŽ‘®yŽ‘t«(›ª®),–UUand“Ïget‘‰ffŽ‘®zŽ‘]V«(˜).Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘ ³/ÏmagnitudeŽ‘Nð¡«(‘ª®)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹‡VE Šn ý‘ì·x«503›­3DLDFPR•ÃŽG’+úXMA“GNITUDE˜«135Ž €n ý•@PÂ503.Ž©·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¤ ‘ -ÂrealŽ‘ ³/P•®9oin“tŽ‘=M{«::‘ÏmagnitudeŽ‘/=v«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂrealŽ‘*³0±rŽ‘/}D«;Ž¡‘ÂrealŽ‘*³0ÏtempŽ‘A ¤«;Ž¡‘ÂP•®9oin“tŽ‘2aŽ‘88Ï«(·Ž‘ÏthisŽ‘ë·«);Ž¦‘±aŽ‘I2:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨);Ž¡‘ÂifŽ‘!™«((±aŽ›I0:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[0Ž‘]–íá±>“ÝMAX_REAL_SQRTŽ‘J´"«)–{—·_“«(±aŽ˜:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[1Ž‘]‘íá±>Ž¡‘2ÝMAX_REAL_SQRTŽ‘vÆF«)–8à·_“«(±aŽ‘I0:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[2Ž‘]–DZ>“ÝMAX_REAL_SQRTŽ‘GY«))‘·fŽ¡‘Ïc‘ÿ}'errŽ‘9Ü·‘d3Ý"ERROR:È ÝInÈ ÝPoint::maŽ‘qc÷gnitude().\n"Ž’¾Žk·Ž¡‘2Ý"PointÈ ÝhasÈ ÝaÈ 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<‘ÇÏtempŽ‘!Œ«)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘3|Á·‘ÇÝ"InÈ Ýmagnitude().\n"Ž‘g G«;Ž¡‘Ïc‘ÿ}'errŽ‘3ço·‘1ÆÝ"PointÈ ÝhasÈ ÝtooÈ ÝgreatŽ‘l1ŠÈ ÝaÈ Ýmagnitude!\n"Ž’À·Â«;‘±=·‘?ÿ«!!›1ÎThis‘•WÏshowŽ‘ V«(‘ª®)–•Woutputs“to“ÏstdoutŽ‘]{«.˜ItŽ¡‘2w¸ãould–UUbGe“nice“to“output“it“to“ÏstderrŽ‘!Ï=«instead.‘qÇMust“write“function“for“this.‘o·±=Ž¡‘Ïc‘ÿ}'errŽ‘3|Á·‘ÇÝ"ReturningÈ ÝINVALID_RŽ‘kÆÜEAL.\n"Ž’‘ /«;Ž¡‘ÂreturnŽ‘Aæ½ÝINVALID_REALŽ’m«;Ž¡‘·gŽ¡‘±rŽ‘‘.«+=ŽŽ‘-æ‚ÏtempŽ‘D@ö«;Ž¡‘ÂreturnŽ‘7æ¼ÏsqrtŽ‘I–µ«(±rŽ‘Ê«);Ž¡‘ -·gŽŸÂ504.‘ üAngle›ÕTbQÇet•®9w“een˜t“w“o˜v“ectors.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.10.27.«]Ž‘Y;Made–UUthis“function“ÂconstŽ‘*¢«.Ž¡‘ -[¬LDF‘T2003.07.27.«]Ž‘Y;Made–UUthe“argumenš¸ãt“±pŽ‘ ²ª«a“ÂconstŽ‘!÷P•®9oin“tŽ‘@o”«&Ž‘H6².‘qÇNo“longer“cop˜ying“·Ž‘UVÏthisŽ‘A «.‘qÇNo˜w“usingŽ¡Ïdot‘‰ffŽ‘®pr–ÿ}'o“ductŽ‘2€!«(‘ª®)–UUinstead“of“calculating“the“angle“\b¸ãy“hand".‘qÇSimpli ed“the“coGde“of“the“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘ 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ÝINVALID_RŽ’¤ÿÊEAL.\n"Ž’ÊF«;Ž¡‘ÂreturnŽ‘Aæ½ÝINVALID_REALŽ’m«;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(Ïp‘‰ffŽ‘®magŽ‘Úy·‘ÇÝINVALID_REALŽ‘BM\«)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘3|Á·‘ÇÝ"WARNING!È ÝInÈ Ýangle()Ž‘kÆÜ.È Ýp.magnitude()È ÝfailŽ’ÔÆ ed."Ž’í·‘ÇÝ"È ÝReturningÈ ÝINVALID_Ž‘kÆÜREAL.\n"Ž’–M,«;Ž¡‘ÂreturnŽ‘Aæ½ÝINVALID_REALŽ’m«;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(Ïp‘‰ffŽ‘®magŽ‘Úy·‘Ç«0Ž‘Ç)‘·fŽ¡‘ÂifŽ‘*軫(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'errŽ‘}¦·‘ÈÝ"WARNING!È ÝInÈ Ýangle()Ž‘mÇÄ.\n"Ž’ˆ ·‘ÈÝ"pÈ ÝhasÈ ÝmagnitudeÈ Ý0.\Ž‘mÇÄn"Ž‘}–&·Ž¡‘<Ý"ReturningÈ ÝINVALID_RŽ’¤ÿÊEAL.\n"Ž’ÊF«;Ž¡‘ÂreturnŽ‘Aæ½ÝINVALID_REALŽ’m«;Ž¡‘·gŽ¡‘ÂelseŽ‘+ØáreturnŽ‘O¿›«(180ŽŽ‘±=ÝPIŽ‘ ?B·‘8àÏac‘ÿ}'osŽ‘ô9«(Ïdot‘‰ffŽ‘®pr–ÿ}'o“ductŽ‘2€!«(±pŽ‘«)±=«(ÏmagŽ‘¾·‘8àÏp‘‰ffŽ‘®magŽ‘LA«)));Ž¡‘ -·gŽŸÂ506.‘ üUnit‘ÕTv®9ector.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.10.27.«]Ž‘Y·ùAdded–a“second“vš¸ãersion.‘If“ÏassignŽ‘#åB«is“not“used,‘1Ïunit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘4Æx«(‘ª®)“can“bGe“ÂconstŽ‘Ú`«,‘1so“I‘æno˜wŽ¡ha•¸ãv“e–<ça“ÂconstŽ‘!O«vš¸ãersion“with“no“argumen˜t“and“a“non-ÂconstŽ‘4«one“for“assignmen˜t“that“should“bGe“called“with“theŽ¡argumen¸ãt‘UUÏtrueŽ‘í«.Ž¦ŸüÈ„`ÕÁGŽŽŸÂ507.– üWith‘zÖassignmen®9t.“«This–¤vš¸ãersion“should“only“ev˜er“bGe“called“with“ÏtrueŽ‘Ñà«as“its“argumen˜t.‘WŒUsing“ÏfalseŽŽ¡«will–UUwš¸ãork,“unless“·Ž‘UVÏthisŽ‘–a«is“ÂconstŽ‘*¢«,“in“whic˜h“case“it“will“cause“an“compilation“error.‘qÇ[¬LDF‘T2002.10.27.«]ŽŽ¡‘ -If–˜Óthe“optional“ÏsilentŽ‘身argumenš¸ãt“is“ÏtrueŽ‘]k«,‘¾‡w˜arning“messages“will“bšGe“suppressed,–¾‡otherwise,“they–˜Ówill“b˜e“issued.Ž¡The‘ýIÂconstŽ‘"Ïß«v•¸ãersion›ýIbGelo“w˜can't˜ha“v“e˜an˜optional˜ÏsilentŽ‘ ±¦«argumen“t,‘'EbGecause˜that˜w“ould˜mak“e˜a˜call˜to˜thisŽ¡function–UUwith“one“argumenš¸ãt“am˜biguous.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.10.27.«]Ž‘Y;If‘UUÏmagnitudeŽ‘1’Ç«(›ª®)–UUfails,“Ïunit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘3êÊ«(˜)“no¸ãw“returns“ÝINVALID_POINTŽ‘Kpë«instead“of“ÏoriginŽ‘Kv«.Ž¡‘ -[¬LDF‘T2003.07.01.«]Ž‘XŽ'Added–ÛAthe“ÏsilentŽ‘m–«argumenš¸ãt“to“suppress“w˜arning“messages.‘II‘Û"k˜ept“getting“w˜arnings“whenŽ¡this–˜/function“wš¸ãas“called“from“in˜tersection“functions,‘¾in“cases“where“it“w˜asn't“a“problem,‘¾that“a“ÂP•®9oin“tŽ‘ ʦ«(v˜ector)Ž¡had–UU0“magnitude.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¡‘ -ÂP•®9oin“tŽ‘(ïžÏunit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘Y…«(ÂconstŽ‘*¢b•QÇo“olŽ‘7ÌÏassignŽ‘S§$±;‘ª¨ÂconstŽ‘ÕJb•QÇo“olŽ‘9v°ÏsilentŽ‘TôÜ«=‘ÇÏfalseŽ‘v\«);ŽŽŽŒ‹‰o  Šn ý‘ì·x«508–­3DLDFPRÃŽG’ ¨tWITH‘ÕXASSIGNMENT“«137Ž €n ý•@PÂ508.Ž©·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¤ ‘ -ÂP•®9oin“tŽ‘(ïžP•®9oin“tŽ‘E‰ê«::‘Ïunit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘1•y«(ÂconstŽ‘*¢b•QÇo“olŽ‘7ÌÏassignŽ‘S§$±;‘ª¨ÂconstŽ‘ÕJb•QÇo“olŽ‘9v°ÏsilentŽ‘R-Ä«)Ž¡‘ -·fŽ¡‘ÂifŽ‘´ú«(ÏassignŽ‘¢4·‘ÇÏfalseŽ‘v\«)‘·fŽ¡‘ÂifŽ‘)´û«(·:ÏsilentŽ‘·«)‘·fŽ¡‘(Ïc‘ÿ}'errŽ‘BNa·‘˜·Ý"WARNING!È ÝInÈ ÝPoint::Ž‘p˜{unit_vector():\n"Ž’Ñ÷g·Ž¡‘<Ý"Don'tÈ ÝcallÈ ÝthisÈ ÝfunŽ’¤ÿÊctionÈ ÝwithÈ ÝfalseÈ ÝasÈ Ž’ ÿŽÝitsÈ Ýargument.\n"Ž’hº·Ž¡‘<Ý"UseÈ Ýunit_vector()È ÝwŽ’¤ÿÊithoutÈ ÝanÈ ÝargumentÈ ÝiŽ’ ÿŽnstead.\n"Ž’Ik¼·Ž¡‘<Ý"CallingÈ Ýunit_vectorŽ’¤ÿÊ()È ÝwithoutÈ ÝanÈ ÝargumeŽ’ ÿŽnt.\n\n"Ž’;Lö·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¡‘ÂreturnŽ‘Aæ½Ïunit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘r|2«(‘ª®);Ž¡‘·gŽ¡‘Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Zá«(‘ª®);Ž¦‘ÂrealŽ‘*³0±mŽ‘6Aÿ«=‘ÇÏmagnitudeŽ‘1Š«(‘ª¨);Ž¦‘ÂifŽ‘´ú«(±mŽ‘ ŽÏ·‘Ç«0Ž‘Ç)Ž¡‘±=·‘ÿý«LDF–UU2002.04.10.‘qÇAdded“this“error“handling“coGde“for“the“case“where“*this“has“no“magnitude.‘o·±=Ž¡‘·fŽ¡‘ÂifŽ‘)´û«(·:ÏsilentŽ‘·«)‘·fŽ¡‘(Ïc‘ÿ}'errŽ‘BNa·‘˜·Ý"WARNING!È ÝInÈ ÝPoint::Ž‘p˜{unit_vector().\n"Ž’Ñ÷g·Ž¡‘<Ý"PointÈ Ý(vector)È ÝhasÈ Ž’¤ÿÊÝnoÈ Ýmagnitude.È ÝReturnŽ’ ÿŽingÈ ÝINVALID_POINT.\nŽ’vÿR\n"Ž’Š É·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¡‘ÂreturnŽ‘Aæ½ÝINVALID_POINTŽ’†¬þ«;Ž¡‘·gŽ¡‘ÂforŽ‘%舫(Âin®9tŽ‘¤÷±iŽ‘Þ«=‘Ç0Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«3Ž“;‘ÿý±iŽ‘ññŸÿ®+‘ÿ+ŽŽ‘¹«)‘Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Rþ«[±iŽ‘qô«]‘DZ=«=ŽŽ‘UO±mŽ‘«;Ž¡‘Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘a«[3Ž‘]–Ç=“1Ž‘Ç;‘±=·‘ÿý«[¬LDF‘T2002.10.27.«]Ž‘T7Setting–UUthe“w-cošGordinate“to“1,“just“to“b˜e“sure.‘o·±=Ž¡‘ÂreturnŽ‘7æ¼·Ž‘<æ½ÏthisŽ‘MÒs«;Ž¡‘ -·gŽŸÂ509.‘ üconst–ÕT(no“assignmen®9t).Ž¦·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¡‘ -ÂP•®9oin“tŽ‘(ïžÏunit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘Y…«(‘ª®)‘UUÂconstŽ‘*¢«;ŽŸÂ510.Ž¦·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¡‘ -ÂP•®9oin“tŽ‘(ïžP•®9oin“tŽ‘E‰ê«::‘Ïunit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘1•y«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂP•®9oin“tŽ‘2aŽ‘88Ï«(·Ž‘ÏthisŽ‘ë·«);Ž¦‘ÂreturnŽ‘7æ¼±aŽ‘=/ì:Ïunit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u«(ÏtrueŽ‘Ę«);Ž¡‘ -·gŽŸÂ511.‘ üMediation.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.12.09.«]Ž‘Y;Changed–UUfrom“a“non-memš¸ãbGer“to“a“ÂconstŽ‘!÷«mem˜bGer“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¡‘ -ÂP•®9oin“tŽ‘(ïžÏme‘ÿ}'diateŽ‘K­«(ÂP•®9oin“tŽ‘ï±pŽ‘#÷;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±rŽ‘>¤«=‘DZ:«5ŽŽ‘ -Ž6)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹Š~ Šn ý‘ì«138–­MEDIA‘ÿJªTION’/Ð 3DLDFPRÃŽG“·x«512Ž €n ý•@PÂ512.Ž©·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¤ ‘ -ÂP•®9oin“tŽ‘(ïžP•®9oin“tŽ‘E‰ê«::‘Ïme‘ÿ}'diateŽ‘#½y«(ÂP•®9oin“tŽ‘ï±pŽ‘#÷;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±rŽ‘;RŒ«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂP•®9oin“tŽ‘2tŽ‘6Œ«(·Ž‘ÏthisŽ‘ë·«);Ž¦‘±tŽ‘cŒ·«=ŽŽ‘)ñÃ(1Ž‘8á·‘8à±rŽ‘ô«);Ž¡‘±pŽ‘Ï·«=ŽŽ‘+]Q±rŽ‘0'e«;Ž¡‘ÂreturnŽ‘7漫(±tŽ‘ÕR«+‘8à±pŽ‘@à«);Ž¡‘ -·gŽŸÂ513.– üGet‘/normal.“Ïget‘‰ffŽ‘®normalŽ‘< -p«(‘ª®)–ĵm¸ãust“bšGe“de ned“in“Èpaths.web«,‘á¢b˜ecause“it“uses“a“ÂP®9athŽ‘Ϋin“its“de nition,Ž¡whicš¸ãh–UUis“an“incompletely“de ned“t˜ypGe“in“this“ le.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.07.11.«]Ž‘Y;Added–UUthis“declaration.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¡‘ -ÂP•®9oin“tŽ‘(ïžÏget‘‰ffŽ‘®normalŽ‘Yz«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]±pŽ‘Ié];‘ª¨ÂconstŽ‘ÕJP•®9oin“tŽ‘>Äç«&Ž‘FŒ±qŽ‘K^¯«)‘UUÂconstŽ‘*¢«;Ž¤Â514.‘ üComparison.Ž¡515.– üEqualit®9y‘ÿ -«.“«!!‘RˆI‘÷ma•¸ãy›÷™ha“v“e˜to˜adjust˜to˜v‘ÿqÇalue˜of˜ÏepsŽ‘[«.‘RˆIt˜w“ould˜b•Ge˜nice˜to˜b“e˜able˜to˜use˜ÏepsilonŽ‘"f«(‘ª®),‘ -XbutŽ¤ for– ,other“purpšGoses“ÏepsilonŽ‘"{0«(‘ª®)“m¸ãust“b˜e“smaller.‘YdT‘ÿ*ªransformations“seem“to“cause“fairly“large“inaccuracies“in“theŽ¡v‘ÿqÇalues–UUof“the“coGordinates,“so“I“need“greater“tolerance“in“the“functions“testing“for“equalitš¸ãy“and“inequalit˜y‘ÿ*ª.Ž¡‘ -This–1Øfunction“could“bGe“formš¸ãulated“more“succinctly‘ÿ*ª,‘8ñbut“I‘1Ïhad“some“trouble“getting“it“to“w˜ork“propGerly‘ÿ*ª,‘8ñsoŽ¡I'm–UUleaš¸ãving“it“in“its“more“v˜erbGose“form,“in“case“I“ha˜v˜e“to“debug“it“some“more.ŽŸÂ516.‘ üNon-const‘ÕTv®9ersion.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.10.27.«]Ž‘Y1ãRevised–~ýthis“function.›î¾No¸ãw“using“ÂP•®9oin“tŽ‘"˜B±aŽ‘+`o«and“ÂP•®9oin“tŽ‘"˜B±qŽ‘'jì«.˜Added“ÏfactorŽ‘"Ø«and“using“it“asŽ¡the–,Rargumen¸ãt“to“Ïcle‘ÿ}'anŽ‘mÔ«(‘ª®)“and“for“calculating“ÏepsŽ‘N«.‘dSince“this“function“is“an“opšGerator,‘4†it's“not“p˜ossible“to“passŽ¡ÏfactorŽ‘:[«as–6}an“argumenš¸ãt,‘nÇunfortunately‘ÿ*ª.‘?Using“Ïcle‘ÿ}'anŽ‘wÿ«(ÏfactorŽ‘Þ«)“mak˜es“it“pšGossible“to“compare“the“co˜ordinatesŽ¡with–¢0“directly“rather“than“using“ÏfabsŽ‘ÔÙ«(‘ª®)“and“ÏepsŽ‘ÃÉ«.‘WÝAlso,‘µ4ÂopQÇeratorŽ‘/Ké·Ž‘7«(‘ª¨)“no¸ãw“uses“Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘TX «directlyŽ¡rather–UUthan“Ïget‘‰ffŽ‘®xŽ‘㼫(›ª®),“Ïget‘‰ffŽ‘®yŽ‘Ék«(˜),“and“Ïget‘‰ffŽ‘®zŽ‘]V«(˜).Ž¡‘ -[¬LDF‘T2003.07.09.«]Ž‘Y;Made–UUthis“function“non-ÂconstŽ‘ÕM«,“and“added“ÂconstŽ‘!÷«vš¸ãersion“bGelo˜w.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¡‘ -Âb•QÇo“olŽ‘#¡gopQÇeratorŽ‘O8·Ž‘Vÿ:«(ÂP•®9oin“tŽ‘ï±pŽ‘#÷«);ŽŽŽŒ‹‹Š  Šn ý‘ì·x«517–­3DLDFPRÃŽG’úAÕNON-ÂCONST‘ÕX­VERSION“«139Ž €n ý•@PÂ517.Ž¤·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž© ‘ -Âb•QÇo“olŽ‘#¡gP•®9oin“tŽ‘@;³«::Ž‘FÉñÂopQÇeratorŽ‘r`¦·Ž‘z'Ä«(ÂP•®9oin“tŽ‘ï±pŽ‘#÷«)·f‘UUÂb•QÇo“olŽ‘ö»ÝDEBUGŽ‘:„,«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EnteringÈ ÝPoint::opeŽ‘kÆÜrator==()"Ž’£”>·‘ÇÝ"\n"Ž‘Œ·‘ÇÏ ushŽ‘€«;Ž¡‘ÂunsignedŽ‘N7shortŽ‘l´ÏfactorŽ’‰Ìª«=‘Ç10ŽŽ‘ Ç;‘±=·‘ÿý«LDF‘UU2002.10.27.‘qÇAdded.‘o·±=Ž¡‘Ïcle‘ÿ}'anŽ‘5A…«(ÏfactorŽ‘Þ«);Ž¦‘±pŽ‘#:Ïcle‘ÿ}'anŽ‘A‚«(ÏfactorŽ‘Þ«);Ž¡‘ÂrealŽ‘4³1ÏepsŽ‘Fœ «=‘ÇÏepsilonŽ‘"6«(‘ª¨)–8à·“ÏfactorŽ‘<¾«;‘±=·‘ÿý«This–UUcurrenš¸ãtly“mak˜es“ÏepsŽ‘Ìl·‘DZ:«0001.‘o·±=Ž¦‘ÂrealŽ‘4³1Ït‘‰ffŽ‘®xŽ‘DÕ‚«=‘ÇÏworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘OÛ«[0Ž‘];Ž¦‘ÂrealŽ‘4³1Ït‘‰ffŽ‘®yŽ‘D»1«=‘ÇÏworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘OÛ«[1Ž‘];Ž¦‘ÂrealŽ‘4³1Ït‘‰ffŽ‘®zŽ‘DO«=‘ÇÏworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘OÛ«[2Ž‘];Ž¦‘ÂrealŽ‘4³1Ïp‘‰ffŽ‘®xŽ‘FŸw«=‘DZpŽ‘Ï:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[0Ž‘];Ž¦‘ÂrealŽ‘4³1Ïp‘‰ffŽ‘®yŽ‘F…&«=‘DZpŽ‘Ï:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[1Ž‘];Ž¦‘ÂrealŽ‘4³1Ïp‘‰ffŽ‘®zŽ‘F«=‘DZpŽ‘Ï:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[2Ž‘];ŽŸÂ518.‘ üP•®9oin“tsŽ‘/À«are–™frequen¸ãtly“compared“to“ÝINVALID_POINTŽ‘HâÚ«,‘Njso“it's“bGest“to“suppress“debugging“output“forŽ¦these–UUcomparisons,“bGecause“they're“probably“not“the“ones“wš¸ãe're“in˜terested“in.Ž¡·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¦‘ -ÂifŽ‘Û«(Ït‘‰ffŽ‘®xŽ‘aÊ·‘‘ÝINVALID_REALŽ–Dß·_‘RDÏt‘‰ffŽ‘®yŽ‘™½·‘‘ÝINVALID_REALŽ“·_‘RDÏt‘‰ffŽ‘®zŽ‘-¨·‘‘ÝINVALID_REALŽ“·_‘RDÏp‘‰ffŽ‘®xŽ‘~·‘‘ÝINVALID_REALŽ“·_‘RDÏp‘‰ffŽ‘®yŽ‘c²·Ž¦‘(ÝINVALID_REALŽ‘i¿(·_‘8àÏp‘‰ffŽ‘®zŽ‘žÀ·‘ÇÝINVALID_REALŽ‘BM\«)‘ÝDEBUGŽ‘"q«=‘ÇÏfalseŽ‘v\«;ŽŸÂ519.‘ ü«Debugging‘UUoutput.Ž¡·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¦‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘·fŽ¦‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"t_xÈ Ý==È Ý"Ž‘5T}·‘ÇÏt‘‰ffŽ‘®xŽ‘éi·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¦‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"t_yÈ Ý==È Ý"Ž‘5T}·‘ÇÏt‘‰ffŽ‘®yŽ‘Ï·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¦‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"t_zÈ Ý==È Ý"Ž‘5T}·‘ÇÏt‘‰ffŽ‘®zŽ‘c·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¦‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"p_xÈ Ý==È Ý"Ž‘5T}·‘ÇÏp‘‰ffŽ‘®xŽ‘³^·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¦‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"p_yÈ Ý==È Ý"Ž‘5T}·‘ÇÏp‘‰ffŽ‘®yŽ‘™ ·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¦‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"p_zÈ Ý==È Ý"Ž‘5T}·‘ÇÏp‘‰ffŽ‘®zŽ‘,ø·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¦‘ -·gŽŸÂ520.‘ ü«Chec¸ãk–UUwhether“the“cošGordinates“of“b˜oth“ÂP•®9oin“tsŽ‘&Î.«are“all“0.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¦‘ -«[¬LDF‘T2002.10.27.«]Ž‘XTNo¸ãw–¡6that“Ïcle‘ÿ}'anŽ‘⸫(10ŽŽ› -)“and“±pŽ‘©6:Ïcle‘ÿ}'anŽ‘A‚«(10ŽŽ˜)“are“called“abGo•¸ãv“e,‘Åi³«blo˜c¸ãks“where“calculations“are“p˜erformed“b˜elo¸ãw,Ž¡just–UUin“case“o•¸ãv“er o“w‘UUoGccurs.Ž¡‘ -!!‘>BUnder–D)Linš¸ãux,‘ÝbGoth“this“function“and“the“v˜ersion“of“Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘UÑ«(‘ª®)“using“traces“ha˜v˜e“failed“inŽ¡the–cksame“cases,‘fñwhicš¸ãh“in˜v˜olv˜ed“coplanar“lines“whic˜h“had“bšGeen“rotated“ab˜out“the“z-axis“or“the“y“and“z-axes.Ž¡I‘€¥suspGect–€òit“has“to“do“with“the“routines“for“sine“and“cosine,‘ËÙsince“I'v¸ãe“had“trouble“with“rotation“in“theŽ¡constructors–UUfor“ÂP®9olyhedraŽ‘6Ö±«.‘qÇ[¬LDF‘T2003.06.29.«]ŽŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.04.10.«]Ž‘Y;Added–UUthis“function.‘qÇIt“replaces“the“old“vš¸ãersion,“bGelo˜w.Ž¡‘ -[¬LDF‘T2002.04.12.«]Ž‘YòÈRemo•¸ãv“ed–?âthe“de nition“of“this“function“to“Èlines.web«,‘z…bGecause“it“requires“the“use“ofŽ¡ÂLinesŽ‘á¿«,–UUand“ÂLineŽ‘-«is“an“incomplete“t¸ãypGe“here.Ž¡‘ -[¬LDF‘T2003.06.29.«]Ž‘YÝStarted–Ì÷using“this“vš¸ãersion“again.‘Ø®Bug“ xes“I'v˜e“made“elsewhere“seem“to“ha˜v˜e“made“itŽ¡function.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž¤ ‘ -ÂstaticŽ‘(Þºb•QÇo“olu½‰™šs4Ž‘Ôwp“oin®9tŽ‘a5Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointŽ’®³ «(ÂconstŽ‘À‚P•®9oin“tŽ‘ŸÓVEŽ‘ãxXŽ‘l/section“forŽ¡the–UUvš¸ãector“v˜ersion,“abGo˜v˜e,“for“more“information.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­284“·i‘Ç«+·Ž© ‘ -ÂstaticŽ‘)HÚb•QÇo“olu½‰™šs4Ž‘Ôwp“oin®9tŽ‘aðuÏinterse–ÿ}'ction‘‰ffŽ‘®p“ointŽ’¯‡K«(ÂP•®9oin“tŽ‘ïÏp0Ž‘+]±;‘ª¨ÂP•®9oin“tŽ‘ šEÏp1Ž‘,±±;‘ª¨ÂP•®9oin“tŽ‘ šEÏq0Ž–,.,±;‘ª¨ÂP•®9oin“tŽ‘ šEÏq1Ž“±;‘ª¨ÂconstŽ‘ÕJb•QÇo“olŽ‘9v°Ïtr–ÿ}'ac“eŽ‘OÁ«);ŽŸÂ530.Ž¡·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¦‘ -Âb•QÇo“olu½‰™šs4Ž‘Ôwp“oin®9tŽ‘BÑP•®9oin“tŽ‘_kL«::‘Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘N–Ú«(ÂP•®9oin“tŽ‘Ïp0Ž‘+/Á±;‘ª¨ÂP•®9oin“tŽ‘ éÏp1Ž‘,Úi±;‘ª¨ÂP•®9oin“tŽ‘ éÏq0Ž–,W±;‘ª¨ÂP•®9oin“tŽ‘ éÏq1Ž“±;‘ª¨ÂconstŽ‘þ®b•QÇo“olŽ‘9ÉxÏtr–ÿ}'ac“eŽ‘Oà‰«)·fŽ¦‘2Âb•QÇo“olŽ‘K¡kÝDEBUGŽ‘i.Ü«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘·fŽ¦‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÝ"EnteringÈ ÝPoint::intŽ‘kÆÜersection_point().\nŽ’ÔÆ "Ž’ÝT·‘ÇÏ ushŽ‘€«;Ž¦‘(Ïp0Ž‘4ı:ÏshowŽ‘Šÿ«(Ý"p0"Ž‘†\«);Ž¦‘(Ïp1Ž‘4ı:ÏshowŽ‘Šÿ«(Ý"p1"Ž‘†\«);Ž¦‘(Ïq0Ž‘3“ë±:ÏshowŽ‘Šÿ«(Ý"q0"Ž‘†\«);Ž¦‘(Ïq1Ž‘3“ë±:ÏshowŽ‘Šÿ«(Ý"q1"Ž‘†\«);Ž¦‘·gŽ¡‘Âb•QÇo“olu½‰™šs4Ž‘Ôwp“oin®9tŽ‘V§žÏbpŽ‘a‚«;‘±=·‘ÿý«Return‘UUv‘ÿqÇalue.‘o·±=Ž¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ErrorÈ ÝafterÈ ÝhereÈ Ý0.Ž‘kÆÜ\n"Ž‘~ÔS·‘ÇÏ ushŽ‘€«;ŽŸÂ531.‘ ü«Apply–¦the“transformations,‘%–so“wš¸ãe“ha˜v˜e“the“correct“v‘ÿqÇalues“for“x,–%–y‘ÿ*ª,“and–¦z“in“eac˜h“of“the“ÂP•®9oin“tsŽ‘#=*«.‘]âThenŽ¦assign–UUthem“to“v‘ÿqÇariables.Ž¡·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¦‘ -Ïp0Ž‘Á±:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨);Ž¦‘ -Ïp1Ž‘Á±:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨);Ž¦‘ -Ïq0Ž‘“è±:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨);Ž¦‘ -Ïq1Ž‘“è±:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨);Ž¡‘ -ÂrealŽ‘ ³/Ïp0‘‰ffŽ‘®xŽ‘7»å«=‘ÇÏp0Ž‘Ýر:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[0Ž‘];Ž¦‘ -ÂrealŽ‘ ³/Ïp0‘‰ffŽ‘®yŽ‘7¡”«=‘ÇÏp0Ž‘Ýر:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[1Ž‘];Ž¦‘ -ÂrealŽ‘ ³/Ïp0‘‰ffŽ‘®zŽ‘75«=‘ÇÏp0Ž‘Ýر:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[2Ž‘];Ž¦‘ -ÂrealŽ‘ ³/Ïp1‘‰ffŽ‘®xŽ‘7»å«=‘ÇÏp1Ž‘Ýر:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[0Ž‘];Ž¦‘ -ÂrealŽ‘ ³/Ïp1‘‰ffŽ‘®yŽ‘7¡”«=‘ÇÏp1Ž‘Ýر:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[1Ž‘];Ž¦‘ -ÂrealŽ‘ ³/Ïp1‘‰ffŽ‘®zŽ‘75«=‘ÇÏp1Ž‘Ýر:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[2Ž‘];Ž¦‘ -ÂrealŽ‘ ³/Ïq0‘‰ffŽ‘®xŽ‘79 «=‘ÇÏq0Ž‘Zÿ±:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[0Ž‘];Ž¦‘ -ÂrealŽ‘ ³/Ïq0‘‰ffŽ‘®yŽ‘7»«=‘ÇÏq0Ž‘Zÿ±:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[1Ž‘];Ž¦‘ -ÂrealŽ‘ ³/Ïq0‘‰ffŽ‘®zŽ‘6²¦«=‘ÇÏq0Ž‘Zÿ±:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[2Ž‘];Ž¦‘ -ÂrealŽ‘ ³/Ïq1‘‰ffŽ‘®xŽ‘79 «=‘ÇÏq1Ž‘Zÿ±:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[0Ž‘];Ž¦‘ -ÂrealŽ‘ ³/Ïq1‘‰ffŽ‘®yŽ‘7»«=‘ÇÏq1Ž‘Zÿ±:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[1Ž‘];Ž¦‘ -ÂrealŽ‘ ³/Ïq1‘‰ffŽ‘®zŽ‘6²¦«=‘ÇÏq1Ž‘Zÿ±:Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ«[2Ž‘];Ž¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ErrorÈ ÝafterÈ ÝhereÈ Ý1.Ž‘kÆÜ\n"Ž‘~ÔS·‘ÇÏ ushŽ‘€«;ŽŽŽŒ‹ÚU Šn ý‘ì«144›­TRA•ÃŽCE‘ÕXVERSION’S†3DLDFPR“G˜·x«532Ž €n ý•@PÂ532.‘ ü«Get‘UUdeltas.Ž©·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¤ ‘ -ÂrealŽ‘ ³/Ïdelta‘‰ffŽ–®x‘‰ffŽ“pŽ‘Jn«=‘ÇÏp1‘‰ffŽ‘®xŽ‘A–·‘8àÏp0‘‰ffŽ‘®xŽ‘z~«;Ž¡‘ -ÂrealŽ‘ ³/Ïdelta‘‰ffŽ–®y‘‰ffŽ“pŽ‘J¥|«=‘ÇÏp1‘‰ffŽ‘®yŽ‘'E·‘8àÏp0‘‰ffŽ‘®yŽ‘`-«;Ž¡‘ -ÂrealŽ‘ ³/Ïdelta‘‰ffŽ–®z‘‰ffŽ“pŽ‘Iá9«=‘ÇÏp1‘‰ffŽ‘®zŽ‘»0·‘8àÏp0‘‰ffŽ‘®zŽ‘ô«;Ž¡‘ -ÂrealŽ‘ ³/Ïdelta‘‰ffŽ–®x‘‰ffŽ“qŽ‘J,«=‘ÇÏq1‘‰ffŽ‘®xŽ‘¾½·‘8àÏq0‘‰ffŽ‘®xŽ‘÷¥«;Ž¡‘ -ÂrealŽ‘ ³/Ïdelta‘‰ffŽ–®y‘‰ffŽ“qŽ‘Jcˆ«=‘ÇÏq1‘‰ffŽ‘®yŽ‘¤l·‘8àÏq0‘‰ffŽ‘®yŽ‘ÝT«;Ž¡‘ -ÂrealŽ‘ ³/Ïdelta‘‰ffŽ–®z‘‰ffŽ“qŽ‘IŸE«=‘ÇÏq1‘‰ffŽ‘®zŽ‘8W·‘8àÏq0‘‰ffŽ‘®zŽ‘q?«;Ž¦‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ErrorÈ ÝafterÈ ÝhereÈ Ý2.Ž‘kÆÜ\n"Ž‘~ÔS·‘ÇÏ ushŽ‘€«;ŽŸÂ533.‘ ü«SlopGes–UUfor“lineŸü±È“·ŽŽ‘ö<‘þ㎎Ž‘gþ!ŽŽŸN8“±pŸÿ®0Ž‘|s±pŸÿ®1ŽŽŽŽŽ‘^;«.Ž¦·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘ ³/Ïslop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“x‘‰ffŽ“yŽ‘Sym«=–Ç(Ïdelta‘‰ffŽ–®x‘‰ffŽ“pŽ›)º×·6«=“0Ž‘Ç)“?“Ïdelta‘‰ffŽ–®y‘‰ffŽ“pŽ‘)òM±=Ïdelta‘‰ffŽ–®x‘‰ffŽ“pŽ˜«:“ÝINVALID_REALŽ‘BM\«;Ž¡‘ -ÂrealŽ‘ ³/Ïslop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“x‘‰ffŽ“zŽ‘S X«=–Ç(Ïdelta‘‰ffŽ–®x‘‰ffŽ“pŽ›)º×·6«=“0Ž‘Ç)“?“Ïdelta‘‰ffŽ–®z‘‰ffŽ“pŽ‘). -±=Ïdelta‘‰ffŽ–®x‘‰ffŽ“pŽ˜«:“ÝINVALID_REALŽ‘BM\«;Ž¡‘ -ÂrealŽ‘ ³/Ïslop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“z‘‰ffŽ“yŽ‘Rì «=–Ç(Ïdelta‘‰ffŽ–®z‘‰ffŽ“pŽ›). -·6«=“0Ž‘Ç)“?“Ïdelta‘‰ffŽ–®y‘‰ffŽ“pŽ‘)òM±=Ïdelta‘‰ffŽ–®z‘‰ffŽ“pŽ˜«:“ÝINVALID_REALŽ‘BM\«;Ž¦‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ErrorÈ ÝafterÈ ÝhereÈ Ý3.Ž‘kÆÜ\n"Ž‘~ÔS·‘ÇÏ ushŽ‘€«;ŽŸÂ534.‘ ü«SlopGes–UUfor“lineŸü±È“·ŽŽ‘e ‘þ㎎Ž‘ÖÏ!ŽŽŸN8“±qŸÿ®0Ž‘|s±qŸÿ®1ŽŽŽŽŽ‘;Ý«.Ž¦·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘ ³/Ïslop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“x‘‰ffŽ“yŽ‘Rö”«=–Ç(Ïdelta‘‰ffŽ–®x‘‰ffŽ“qŽ›)xã·6«=“0Ž‘Ç)“?“Ïdelta‘‰ffŽ–®y‘‰ffŽ“qŽ‘)°Y±=Ïdelta‘‰ffŽ–®x‘‰ffŽ“qŽ˜«:“ÝINVALID_REALŽ‘BM\«;Ž¡‘ -ÂrealŽ‘ ³/Ïslop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“x‘‰ffŽ“zŽ‘RŠ«=–Ç(Ïdelta‘‰ffŽ–®x‘‰ffŽ“qŽ›)xã·6«=“0Ž‘Ç)“?“Ïdelta‘‰ffŽ–®z‘‰ffŽ“qŽ‘(ì±=Ïdelta‘‰ffŽ–®x‘‰ffŽ“qŽ˜«:“ÝINVALID_REALŽ‘BM\«;Ž¡‘ -ÂrealŽ‘ ³/Ïslop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“z‘‰ffŽ“yŽ‘RiÇ«=–Ç(Ïdelta‘‰ffŽ–®z‘‰ffŽ“qŽ›(ì·6«=“0Ž‘Ç)“?“Ïdelta‘‰ffŽ–®y‘‰ffŽ“qŽ‘)°Y±=Ïdelta‘‰ffŽ–®z‘‰ffŽ“qŽ˜«:“ÝINVALID_REALŽ‘BM\«;Ž¦‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ErrorÈ ÝafterÈ ÝhereÈ Ý4.Ž‘kÆÜ\n"Ž‘~ÔS·‘ÇÏ ushŽ‘€«;ŽŸÂ535.‘ ü«The–½traces“on“the“x-y“plane.‘]?Ïx‘‰ffŽ‘®iŽ‘G£«,‘$Ïy‘‰ffŽ‘®iŽ‘Eé«,‘$Ïz‘‰ffŽ‘®iŽ‘¦«,‘$Ïy‘‰ffŽ–®int‘‰ffŽ“pŽ‘!ží«,‘$and“Ïy‘‰ffŽ–®int‘‰ffŽ“qŽ‘$hd«are“set“to“ÝINVALID_REALŽ‘Eµ¾«so“that“I‘®canŽ¡test–UUfor“whether“the“routines“bGelo¸ãw“succeed“in“setting“them“correctly‘ÿ*ª.Ž¦·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘ 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-ÂifŽ‘´ù«(Ïslop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“x‘‰ffŽ“yŽ‘2Ce·6«=‘ÇÝINVALID_REALŽ‘BM\«)‘±=·‘ÿý«±xŸÿ´qŽ‘1­·6«=‘Ç0.‘o·±=Ž¡‘ -·fŽ¡‘Ïy‘‰ffŽ–®int‘‰ffŽ“qŽ‘5«=‘ÇÏq0‘‰ffŽ‘®yŽ‘¤l·–8à«(Ïslop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“x‘‰ffŽ“yŽ‘1µ-·“Ïq0‘‰ffŽ‘®xŽ‘÷¥«);Ž¡‘ -·gŽ¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ErrorÈ ÝafterÈ ÝhereÈ Ý6.Ž‘kÆÜ\n"Ž‘~ÔS·‘ÇÏ ushŽ‘€«;ŽŽŽŒ‹‘ê Šn ý‘ì·x«536›­3DLDFPR•ÃŽG’S†TRA“CE‘ÕXVERSION˜«145Ž €n ý•@PÂ536.Ž¤ ·Ž‘ -«If–vŒbGoth“of“the“traces“of‘‹±~Ž“pŽŽ‘ õ«and‘pU±~Ž“qŽŽ‘ ¿Â«in“the“x-y“plane“are“parallel“to“the“y-axis“(i.e.,›~Ù±x–þs«=“0),˜w¸ãe–vŒtest“whetherŽ¡‘ -±pŸÿ´xŽ‘9«=‘0±qŸÿ´xŽ‘ä«.›.ÔIf–”Ythey“are,‘¤then“w¸ãe“set“Ïx‘‰ffŽ‘®iŽ‘«to“that“v‘ÿqÇalue.˜If“they're“not,›¤the“lines“don't“in¸ãtersect,˜so“w¸ãe“returnŽ¡‘ -ÝINVALID_POINTŽ‘NÆB«.Ž¡·Ž‘ -«If–òOthe“trace“of‘ñ~Ž“pŽŽ‘ -ìž«or“the“trace“of‘ì±~Ž“qŽŽ‘ -·H«in“the“x-y“plane“is“parallel“to“the“y-axis,›w¸ãe“set“Ïx‘‰ffŽ‘®iŽ‘Ï«to“its“x-v‘ÿqÇalue,˜bGecauseŽ¡‘ -in–UUthis“case,“the“inš¸ãtersection“pGoin˜t“m˜ust“ha˜v˜e“this“x-v‘ÿqÇalue.Ž¡·Ž‘ -«If–UU±xŸÿ´pŽ‘fj·6«=›Ç0“and“±xŸÿ´qŽ‘1­·6«=˜0,“wš¸ãe“deriv˜e“Ïx‘‰ffŽ‘®iŽ‘•«using“the“slopGe“and“y-in˜tercept“of“the“lines.Ž©·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¡‘ -ÂifŽ‘´ù«(Ïy‘‰ffŽ–®int‘‰ffŽ“pŽ‘!Aö·‘ÇÝINVALID_REALŽ‘D†<·^‘8àÏy‘‰ffŽ–®int‘‰ffŽ“qŽ‘#8â·‘ÇÝINVALID_REALŽ‘BM\«)Ž¡‘±=·‘q±~Ž‘ÿýpŸÿ´xzŽŽŽ‘Ç«and‘O±~Ž‘UUqŸÿ´xzŽŽŽ‘Eð«are–UUbGoth“parallel“to“the“z-axis.‘o·±=Ž¡‘ -·fŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ErrorÈ ÝafterÈ ÝhereÈ Ý7.Ž‘kÆÜ\n"Ž‘~ÔS·‘ÇÏ ushŽ‘€«;Ž¡‘ÂifŽ‘´ú«(Ïp0‘‰ffŽ‘®xŽ‘¶·‘ÇÏq0‘‰ffŽ‘®xŽ‘…Ý«)‘±=·‘ÿý«They›UUha•¸ãv“e˜the˜same˜v‘ÿqÇalue˜for˜±x«.‘o·±=Ž¡‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ErrorÈ ÝafterÈ ÝhereÈ Ý8.Ž‘kÆÜ\n"Ž‘~ÔS·‘ÇÏ ushŽ‘€«;Ž¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"TracesÈ ÝonÈ Ýx-yÈ ÝplaneŽ‘kÆÜÈ ÝareÈ Ýcoincident.\n"Ž’ÒÔ#·‘ÇÏ ushŽ‘€«;Ž¡‘Ïx‘‰ffŽ‘®iŽ‘-±«=‘ÇÏp0‘‰ffŽ‘®xŽ‘¶«;Ž¦‘ÂrealŽ‘4³1Ïy‘‰ffŽ–®int‘‰ffŽ“p‘‰ffŽ“zŽ‘^S «=‘ÇÝINVALID_REALŽ‘BM\«;Ž¡‘ÂrealŽ‘4³1Ïy‘‰ffŽ–®int‘‰ffŽ“q‘‰ffŽ“zŽ‘]Ð4«=‘ÇÝINVALID_REALŽ‘BM\«;Ž¦‘ÂifŽ‘)´û«(Ïslop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“z‘‰ffŽ“yŽ‘29q·6«=‘ÇÝINVALID_REALŽ‘BM\«)‘Ïy‘‰ffŽ–®int‘‰ffŽ“p‘‰ffŽ“zŽ‘.ŸÜ«=‘ÇÏp0‘‰ffŽ‘®yŽ‘'E·‘8àÏslop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“z‘‰ffŽ“yŽ‘3ä·‘8àÏp0‘‰ffŽ‘®zŽ‘ô«;Ž¡‘ÂifŽ‘)´û«(Ïslop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“z‘‰ffŽ“yŽ‘1¶˜·6«=‘ÇÝINVALID_REALŽ‘BM\«)‘Ïy‘‰ffŽ–®int‘‰ffŽ“q‘‰ffŽ“zŽ‘.«=‘ÇÏq0‘‰ffŽ‘®yŽ‘¤l·‘8àÏslop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“z‘‰ffŽ“yŽ‘3a@·‘8àÏq0‘‰ffŽ‘®zŽ‘q?«;Ž¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ErrorÈ ÝafterÈ ÝhereÈ Ý9.Ž‘kÆÜ\n"Ž‘~ÔS·‘ÇÏ ushŽ‘€«;Ž¡‘ÂifŽ‘)´û«(Ïslop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“z‘‰ffŽ“yŽ‘29q·‘ÇÝINVALID_REALŽ‘D†<·^‘8àÏslop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“z‘‰ffŽ“yŽ‘3ïx·‘ÇÝINVALID_REALŽ‘BM\«)‘·fŽ¡‘(ÂifŽ‘3´ü«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"BothÈ ÝtracesÈ ÝonÈ Ýz-yÈ Ž‘kÆÜÝplaneÈ ÝareÈ Ývertical\nŽ’ÔÆ "Ž’ÝT·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂifŽ‘3´ü«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ErrorÈ ÝafterÈ ÝhereÈ Ý10Ž‘kÆÜ.\n"Ž’„P·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂifŽ‘3´ü«(Ïp0‘‰ffŽ‘®zŽ‘‚P·‘ÇÏq0‘‰ffŽ‘®zŽ‘ÿw«)‘Ïc‘ÿ}'errŽ‘|¾·‘ÇÝ"LinesÈ ÝareÈ 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/¬;Ž¡‘­returnŽ‘Aæ½´INVALID_REALŽ’m¬;Ž¡‘°gŽ¡‘µrŽ‘‘.¬+=ŽŽ‘-悱tempŽ‘D@ö¬;Ž¡‘±tempŽ‘-!Ž¬=‘ǵaŽ‘H:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ›Mþ¬[2Ž‘]–8à°“µaŽ‘‚:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ˜¬[2Ž‘];Ž¡‘­ifŽ‘´ú¬(´MAX_REALŽ‘,¿0°‘8àµrŽ‘ Ê <‘DZtempŽ‘!Œ¬)‘°fŽ¡‘±c‘ÿ}'errŽ‘3|Á°‘Ç´"In® ´magnitude().\n"Ž‘g G¬;Ž¡‘±c‘ÿ}'errŽ‘3ço°‘1Æ´"Point® ´has® ´too® ´greatŽ‘l1Š® ´a® ´magnitude!\n"Ž’À·Â¬;‘µ=°‘?ÿ¬!!›1ÎThis‘•W±showŽ‘ V¬(‘ª®)–•Woutputs“to“±stdoutŽ‘]{¬.˜ItŽ¡‘2w¸ãould–UUbGe“nice“to“output“it“to“±stderrŽ‘!Ï=¬instead.‘qÇMust“write“function“for“this.‘o°µ=Ž¡‘±c‘ÿ}'errŽ‘3|Á°‘Ç´"Returning® ´INVALID_RŽ‘kÆÜEAL.\n"Ž’‘ /¬;Ž¡‘­returnŽ‘Aæ½´INVALID_REALŽ’m¬;Ž¡‘°gŽ¡‘µrŽ‘‘.¬+=ŽŽ‘-悱tempŽ‘D@ö¬;Ž¡‘­returnŽ‘7æ¼±sqrtŽ‘I–µ¬(µrŽ‘ʬ);Ž¡‘ +°gŽŸ­548.‘ üAngle›ÕTbQÇet•®9w“een˜t“w“o˜v“ectors.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.10.27.¬]Ž‘Y;Made–UUthis“function“­constŽ‘*¢¬.Ž¡‘ +[²LDF‘T2003.07.27.¬]Ž‘Y;Made–UUthe“argumenš¸ãt“µpŽ‘ ²ª¬a“­constŽ‘!÷P•®9oin“tŽ‘@o”¬&Ž‘H6².‘qÇNo“longer“cop˜ying“°Ž‘UV±thisŽ‘A ¬.‘qÇNo˜w“usingŽ¡±dot‘‰ffŽ‘®pr–ÿ}'o“ductŽ‘2€!¬(‘ª®)–UUinstead“of“calculating“the“angle“\b¸ãy“hand".‘qÇSimpli ed“the“coGde“of“the“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­realŽ‘ ³/±angleŽ‘8s‚¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié]¬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹’ Qß Šn ý‘ì¬146›¯ANGLE–ÕXBETWEEN“TWÃŽO“VECTORS’Çyž3DLDF-1.1.5.1˜°x¬549Ž €n ý•@P­549.Ž©°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¤ ‘ +­realŽ‘ ³/P•®9oin“tŽ‘=M{¬::‘±angleŽ‘ÀW¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié]¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­b•QÇo“olŽ‘-¡h´DEBUGŽ‘K.Ù¬=‘DZfalseŽ‘v\¬;‘µ=°–ÿý¬true“°µ=Ž¡‘­realŽ‘*³0±magŽ‘@Ã&¬=‘DZmagnitudeŽ‘1Š¬(‘ª¨);Ž¡‘­realŽ‘*³0±p‘‰ffŽ‘®magŽ‘I©¬=‘ǵpŽ‘Ï:±magnitudeŽ‘.=r¬(‘ª¨);Ž¦‘­ifŽ‘´ú¬(±magŽ‘ö°‘Ç´INVALID_REALŽ‘BM\¬)‘°fŽ¡‘±c‘ÿ}'errŽ‘3|Á°‘Ç´"WARNING!® ´In® ´angle()Ž‘kÆÜ.® ´magnitude()® ´failedŽ’ÔÆ ."Ž’â”°‘Ç´"® ´Returning® ´INVALID_Ž‘kÆÜREAL.\n"Ž’–M,¬;Ž¡‘­returnŽ‘Aæ½´INVALID_REALŽ’m¬;Ž¡‘°gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±magŽ‘ö°‘Ǭ0Ž‘Ç)‘°fŽ¡‘­ifŽ‘*›2¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'errŽ‘ül°‘FÆ´"WARNING!® ´In® ´angle()Ž‘mFŠ.\n"Ž’‡¬°‘FÆ´"*this® ´has® ´magnitudeŽ‘mFŠ® ´0.\n"Ž’‘“¦°Ž¡‘<´"Returning® ´INVALID_RŽ’¤ÿÊEAL.\n"Ž’ÊF¬;Ž¡‘­returnŽ‘Aæ½´INVALID_REALŽ’m¬;Ž¡‘°gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±p‘‰ffŽ‘®magŽ‘Úy°‘Ç´INVALID_REALŽ‘BM\¬)‘°fŽ¡‘±c‘ÿ}'errŽ‘3|Á°‘Ç´"WARNING!® ´In® ´angle()Ž‘kÆÜ.® ´p.magnitude()® ´failŽ’ÔÆ ed."Ž’í°‘Ç´"® ´Returning® ´INVALID_Ž‘kÆÜREAL.\n"Ž’–M,¬;Ž¡‘­returnŽ‘Aæ½´INVALID_REALŽ’m¬;Ž¡‘°gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±p‘‰ffŽ‘®magŽ‘Úy°‘Ǭ0Ž‘Ç)‘°fŽ¡‘­ifŽ‘*軬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'errŽ‘}¦°‘È´"WARNING!® ´In® ´angle()Ž‘mÇÄ.\n"Ž’ˆ °‘È´"p® ´has® ´magnitude® ´0.\Ž‘mÇÄn"Ž‘}–&°Ž¡‘<´"Returning® ´INVALID_RŽ’¤ÿÊEAL.\n"Ž’ÊF¬;Ž¡‘­returnŽ‘Aæ½´INVALID_REALŽ’m¬;Ž¡‘°gŽ¡‘­elseŽ‘+ØáreturnŽ‘O¿›¬(180ŽŽ‘µ=´PIŽ‘ ?B°‘8à±ac‘ÿ}'osŽ‘ô9¬(±dot‘‰ffŽ‘®pr–ÿ}'o“ductŽ‘2€!¬(µpŽ‘¬)µ=¬(±magŽ‘¾°‘8à±p‘‰ffŽ‘®magŽ‘LA¬)));Ž¡‘ +°gŽŸ­550.‘ üUnit‘ÕTv®9ector.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.10.27.¬]Ž‘Y·ùAdded–a“second“vš¸ãersion.‘If“±assignŽ‘#åB¬is“not“used,‘1±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘4Æx¬(‘ª®)“can“bGe“­constŽ‘Ú`¬,‘1so“I‘æno˜wŽ¡ha•¸ãv“e–<ça“­constŽ‘!O¬vš¸ãersion“with“no“argumen˜t“and“a“non-­constŽ‘4¬one“for“assignmen˜t“that“should“bGe“called“with“theŽ¡argumen¸ãt‘UU±trueŽ‘í¬.Ž¦ŸüÈ„`ÕÁGŽŽŸ­551.– üWith‘zÖassignmen®9t.“¬This–¤vš¸ãersion“should“only“ev˜er“bGe“called“with“±trueŽ‘Ñà¬as“its“argumen˜t.‘WŒUsing“±falseŽŽ¡¬will–UUwš¸ãork,“unless“°Ž‘UV±thisŽ‘–a¬is“­constŽ‘*¢¬,“in“whic˜h“case“it“will“cause“an“compilation“error.‘qÇ[²LDF‘T2002.10.27.¬]ŽŽ¡‘ +If–˜Óthe“optional“±silentŽ‘躬argumenš¸ãt“is“±trueŽ‘]k¬,‘¾‡w˜arning“messages“will“bšGe“suppressed,–¾‡otherwise,“they–˜Ówill“b˜e“issued.Ž¡The‘ýI­constŽ‘"Ï߬v•¸ãersion›ýIbGelo“w˜can't˜ha“v“e˜an˜optional˜±silentŽ‘ ±¦¬argumen“t,‘'EbGecause˜that˜w“ould˜mak“e˜a˜call˜to˜thisŽ¡function–UUwith“one“argumenš¸ãt“am˜biguous.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.10.27.¬]Ž‘Y;If‘UU±magnitudeŽ‘1’Ǭ(›ª®)–UUfails,“±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘3êʬ(˜)“no¸ãw“returns“´INVALID_POINTŽ‘Kpë¬instead“of“±originŽ‘Kv¬.Ž¡‘ +[²LDF‘T2003.07.01.¬]Ž‘XŽ'Added–ÛAthe“±silentŽ‘m–¬argumenš¸ãt“to“suppress“w˜arning“messages.‘II‘Û"k˜ept“getting“w˜arnings“whenŽ¡this–˜/function“wš¸ãas“called“from“in˜tersection“functions,‘¾in“cases“where“it“w˜asn't“a“problem,‘¾that“a“­P•®9oin“tŽ‘ ʦ¬(v˜ector)Ž¡had–UU0“magnitude.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­P•®9oin“tŽ‘(ïž±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘Y…¬(­constŽ‘*¢b•QÇo“olŽ‘7̱assignŽ‘S§$µ;‘ª¨­constŽ‘ÕJb•QÇo“olŽ‘9v°±silentŽ‘Tôܬ=‘DZfalseŽ‘v\¬);ŽŽŽŒ‹“ _† Šn ý‘ì°x¬552–¯3DLDF-1.1.5.1’4ÞWITH‘ÕXASSIGNMENT“¬147Ž €n ý•@P­552.Ž©°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¤ ‘ +­P•®9oin“tŽ‘(ïžP•®9oin“tŽ‘E‰ê¬::‘±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘1•y¬(­constŽ‘*¢b•QÇo“olŽ‘7̱assignŽ‘S§$µ;‘ª¨­constŽ‘ÕJb•QÇo“olŽ‘9v°±silentŽ‘R-Ĭ)Ž¡‘ +°fŽ¡‘­ifŽ‘´ú¬(±assignŽ‘¢4°‘DZfalseŽ‘v\¬)‘°fŽ¡‘­ifŽ‘)´û¬(°:±silentŽ‘·¬)‘°fŽ¡‘(±c‘ÿ}'errŽ‘BNa°‘˜·´"WARNING!® ´In® ´Point::Ž‘p˜{unit_vector():\n"Ž’Ñ÷g°Ž¡‘<´"Don't® ´call® ´this® ´funŽ’¤ÿÊction® ´with® ´false® ´as® Ž’ ÿŽ´its® ´argument.\n"Ž’hº°Ž¡‘<´"Use® ´unit_vector()® ´wŽ’¤ÿÊithout® ´an® ´argument® ´iŽ’ ÿŽnstead.\n"Ž’Ik¼°Ž¡‘<´"Calling® ´unit_vectorŽ’¤ÿÊ()® ´without® ´an® ´argumeŽ’ ÿŽnt.\n\n"Ž’;Lö°‘DZ ushŽ‘€¬;Ž¡‘°gŽ¡‘­returnŽ‘Aæ½±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘r|2¬(‘ª®);Ž¡‘°gŽ¡‘±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Zá¬(‘ª®);Ž¦‘­realŽ‘*³0µmŽ‘6Aÿ¬=‘DZmagnitudeŽ‘1Š¬(‘ª¨);Ž¦‘­ifŽ‘´ú¬(µmŽ‘ ŽÏ°‘Ǭ0Ž‘Ç)Ž¡‘µ=°‘ÿý¬LDF–UU2002.04.10.‘qÇAdded“this“error“handling“coGde“for“the“case“where“*this“has“no“magnitude.‘o°µ=Ž¡‘°fŽ¡‘­ifŽ‘)´û¬(°:±silentŽ‘·¬)‘°fŽ¡‘(±c‘ÿ}'errŽ‘BNa°‘˜·´"WARNING!® ´In® ´Point::Ž‘p˜{unit_vector().\n"Ž’Ñ÷g°Ž¡‘<´"Point® ´(vector)® ´has® Ž’¤ÿÊ´no® ´magnitude.® ´ReturnŽ’ ÿŽing® ´INVALID_POINT.\nŽ’vÿR\n"Ž’Š É°‘DZ ushŽ‘€¬;Ž¡‘°gŽ¡‘­returnŽ‘Aæ½´INVALID_POINTŽ’†¬þ¬;Ž¡‘°gŽ¡‘­forŽ‘%般(­in®9tŽ‘¤÷µiŽ‘Þ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ3Ž“;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)‘±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Rþ¬[µiŽ‘qô¬]‘ǵ=¬=ŽŽ‘UOµmŽ‘¬;Ž¡‘±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘a¬[3Ž‘]–Ç=“1Ž‘Ç;‘µ=°‘ÿý¬[²LDF‘T2002.10.27.¬]Ž‘T7Setting–UUthe“w-cošGordinate“to“1,“just“to“b˜e“sure.‘o°µ=Ž¡‘­returnŽ‘7æ¼°Ž‘<æ½±thisŽ‘MÒs¬;Ž¡‘ +°gŽŸ­553.‘ üconst–ÕT(no“assignmen®9t).Ž¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­P•®9oin“tŽ‘(ïž±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘Y…¬(‘ª®)‘UU­constŽ‘*¢¬;ŽŸ­554.Ž¦°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¡‘ +­P•®9oin“tŽ‘(ïžP•®9oin“tŽ‘E‰ê¬::‘±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘1•y¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­P•®9oin“tŽ‘2aŽ‘88Ϭ(°Ž‘±thisŽ‘ë·¬);Ž¦‘­returnŽ‘7æ¼µaŽ‘=/ì:±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u¬(±trueŽ‘ʬ);Ž¡‘ +°gŽŸ­555.‘ üMediation.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.12.09.¬]Ž‘Y;Changed–UUfrom“a“non-memš¸ãbGer“to“a“­constŽ‘!÷¬mem˜bGer“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­P•®9oin“tŽ‘(ïž±me‘ÿ}'diateŽ‘K­¬(­P•®9oin“tŽ‘ïµpŽ‘#÷;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµrŽ‘>¤¬=‘ǵ:¬5ŽŽ‘ +Ž6)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹” n„ Šn ý‘ì¬148–¯MEDIA‘ÿJªTION’'\v3DLDF-1.1.5.1“°x¬556Ž €n ý•@P­556.Ž©°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¤ ‘ +­P•®9oin“tŽ‘(ïžP•®9oin“tŽ‘E‰ê¬::‘±me‘ÿ}'diateŽ‘#½y¬(­P•®9oin“tŽ‘ïµpŽ‘#÷;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµrŽ‘;RŒ¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­P•®9oin“tŽ‘2tŽ‘6Œ¬(°Ž‘±thisŽ‘ë·¬);Ž¦‘µtŽ‘cŒ°¬=ŽŽ‘)ñÃ(1Ž‘8á°‘8àµrŽ‘ô¬);Ž¡‘µpŽ‘Ï°¬=ŽŽ‘+]QµrŽ‘0'e¬;Ž¡‘­returnŽ‘7漬(µtŽ‘ÕR¬+‘8àµpŽ‘@à¬);Ž¡‘ +°gŽŸ­557.– üGet‘/normal.“±get‘‰ffŽ‘®normalŽ‘< +p¬(‘ª®)–ĵm¸ãust“bšGe“de ned“in“®paths.web¬,‘á¢b˜ecause“it“uses“a“­P®9athŽ‘άin“its“de nition,Ž¡whicš¸ãh–UUis“an“incompletely“de ned“t˜ypGe“in“this“ le.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.07.11.¬]Ž‘Y;Added–UUthis“declaration.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­P•®9oin“tŽ‘(ïž±get‘‰ffŽ‘®normalŽ‘Yz¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié];‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒµqŽ‘K^¯¬)‘UU­constŽ‘*¢¬;Ž¤­558.‘ üComparison.Ž¡559.– üEqualit®9y‘ÿ +«.“¬!!‘RˆI‘÷ma•¸ãy›÷™ha“v“e˜to˜adjust˜to˜v‘ÿqÇalue˜of˜±epsŽ‘[¬.‘RˆIt˜w“ould˜b•Ge˜nice˜to˜b“e˜able˜to˜use˜±epsilonŽ‘"f¬(‘ª®),‘ +XbutŽ¤ for– ,other“purpšGoses“±epsilonŽ‘"{0¬(‘ª®)“m¸ãust“b˜e“smaller.‘YdT‘ÿ*ªransformations“seem“to“cause“fairly“large“inaccuracies“in“theŽ¡v‘ÿqÇalues–UUof“the“coGordinates,“so“I“need“greater“tolerance“in“the“functions“testing“for“equalitš¸ãy“and“inequalit˜y‘ÿ*ª.Ž¡‘ +This–1Øfunction“could“bGe“formš¸ãulated“more“succinctly‘ÿ*ª,‘8ñbut“I‘1Ïhad“some“trouble“getting“it“to“w˜ork“propGerly‘ÿ*ª,‘8ñsoŽ¡I'm–UUleaš¸ãving“it“in“its“more“v˜erbGose“form,“in“case“I“ha˜v˜e“to“debug“it“some“more.ŽŸ­560.‘ üNon-const‘ÕTv®9ersion.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.10.27.¬]Ž‘Y1ãRevised–~ýthis“function.›î¾No¸ãw“using“­P•®9oin“tŽ‘"˜BµaŽ‘+`o¬and“­P•®9oin“tŽ‘"˜BµqŽ‘'jì¬.˜Added“±factorŽ‘"جand“using“it“asŽ¡the–,Rargumen¸ãt“to“±cle‘ÿ}'anŽ‘mÔ¬(‘ª®)“and“for“calculating“±epsŽ‘N¬.‘dSince“this“function“is“an“opšGerator,‘4†it's“not“p˜ossible“to“passŽ¡±factorŽ‘:[¬as–6}an“argumenš¸ãt,‘nÇunfortunately‘ÿ*ª.‘?Using“±cle‘ÿ}'anŽ‘wÿ¬(±factorŽ‘Þ¬)“mak˜es“it“pšGossible“to“compare“the“co˜ordinatesŽ¡with–¢0“directly“rather“than“using“±fabsŽ‘ÔÙ¬(‘ª®)“and“±epsŽ‘Ãɬ.‘WÝAlso,‘µ4­opQÇeratorŽ‘/Ké°Ž‘7¬(‘ª¨)“no¸ãw“uses“±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘TX ¬directlyŽ¡rather–UUthan“±get‘‰ffŽ‘®xŽ‘㼬(›ª®),“±get‘‰ffŽ‘®yŽ‘Ék¬(˜),“and“±get‘‰ffŽ‘®zŽ‘]V¬(˜).Ž¡‘ +[²LDF‘T2003.07.09.¬]Ž‘Y;Made–UUthis“function“non-­constŽ‘ÕM¬,“and“added“­constŽ‘!÷¬vš¸ãersion“bGelo˜w.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¡‘ +­b•QÇo“olŽ‘#¡gopQÇeratorŽ‘O8°Ž‘Vÿ:¬(­P•®9oin“tŽ‘ïµpŽ‘#÷¬);ŽŽŽŒ‹• yö Šn ý‘ì°x¬561–¯3DLDF-1.1.5.1’ñÎ?NON-­CONST‘ÕX¯VERSION“¬149Ž €n ý•@P­561.Ž¤°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž© ‘ +­b•QÇo“olŽ‘#¡gP•®9oin“tŽ‘@;³¬::Ž‘FÉñ­opQÇeratorŽ‘r`¦°Ž‘z'Ĭ(­P•®9oin“tŽ‘ïµpŽ‘#÷¬)°f‘UU­b•QÇo“olŽ‘ö»´DEBUGŽ‘:„,¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Entering® ´Point::opeŽ‘kÆÜrator==()"Ž’£”>°‘Ç´"\n"Ž‘Œ°‘DZ ushŽ‘€¬;Ž¡‘­unsignedŽ‘N7shortŽ‘l´±factorŽ’‰Ìª¬=‘Ç10ŽŽ‘ Ç;‘µ=°‘ÿý¬LDF‘UU2002.10.27.‘qÇAdded.‘o°µ=Ž¡‘±cle‘ÿ}'anŽ‘5A…¬(±factorŽ‘Þ¬);Ž¦‘µpŽ‘#:±cle‘ÿ}'anŽ‘A‚¬(±factorŽ‘Þ¬);Ž¡‘­realŽ‘4³1±epsŽ‘Fœ ¬=‘DZepsilonŽ‘"6¬(‘ª¨)–8à°“±factorŽ‘<¾¬;‘µ=°‘ÿý¬This–UUcurrenš¸ãtly“mak˜es“±epsŽ‘Ìl°‘ǵ:¬0001.‘o°µ=Ž¦‘­realŽ‘4³1±t‘‰ffŽ‘®xŽ‘DÕ‚¬=‘DZworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘OÛ¬[0Ž‘];Ž¦‘­realŽ‘4³1±t‘‰ffŽ‘®yŽ‘D»1¬=‘DZworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘OÛ¬[1Ž‘];Ž¦‘­realŽ‘4³1±t‘‰ffŽ‘®zŽ‘DO¬=‘DZworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘OÛ¬[2Ž‘];Ž¦‘­realŽ‘4³1±p‘‰ffŽ‘®xŽ‘FŸw¬=‘ǵpŽ‘Ï:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ¬[0Ž‘];Ž¦‘­realŽ‘4³1±p‘‰ffŽ‘®yŽ‘F…&¬=‘ǵpŽ‘Ï:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ¬[1Ž‘];Ž¦‘­realŽ‘4³1±p‘‰ffŽ‘®zŽ‘F¬=‘ǵpŽ‘Ï:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ¬[2Ž‘];ŽŸ­562.‘ üP•®9oin“tsŽ‘/À¬are–™frequen¸ãtly“compared“to“´INVALID_POINTŽ‘HâÚ¬,‘Njso“it's“bGest“to“suppress“debugging“output“forŽ¦these–UUcomparisons,“bGecause“they're“probably“not“the“ones“wš¸ãe're“in˜terested“in.Ž¡°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¦‘ +­ifŽ‘Û¬(±t‘‰ffŽ‘®xŽ‘aÊ°‘‘´INVALID_REALŽ–Dß°_‘RD±t‘‰ffŽ‘®yŽ‘™½°‘‘´INVALID_REALŽ“°_‘RD±t‘‰ffŽ‘®zŽ‘-¨°‘‘´INVALID_REALŽ“°_‘RD±p‘‰ffŽ‘®xŽ‘~°‘‘´INVALID_REALŽ“°_‘RD±p‘‰ffŽ‘®yŽ‘c²°Ž¦‘(´INVALID_REALŽ‘i¿(°_‘8à±p‘‰ffŽ‘®zŽ‘žÀ°‘Ç´INVALID_REALŽ‘BM\¬)‘´DEBUGŽ‘"q¬=‘DZfalseŽ‘v\¬;ŽŸ­563.‘ ü¬Debugging‘UUoutput.Ž¡°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¦‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽ¦‘±c‘ÿ}'outŽ‘* Q°‘Ç´"t_x® ´==® ´"Ž‘5T}°‘DZt‘‰ffŽ‘®xŽ‘éi°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¦‘±c‘ÿ}'outŽ‘* Q°‘Ç´"t_y® ´==® ´"Ž‘5T}°‘DZt‘‰ffŽ‘®yŽ‘Ï°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¦‘±c‘ÿ}'outŽ‘* Q°‘Ç´"t_z® ´==® ´"Ž‘5T}°‘DZt‘‰ffŽ‘®zŽ‘c°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¦‘±c‘ÿ}'outŽ‘* Q°‘Ç´"p_x® ´==® ´"Ž‘5T}°‘DZp‘‰ffŽ‘®xŽ‘³^°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¦‘±c‘ÿ}'outŽ‘* Q°‘Ç´"p_y® ´==® ´"Ž‘5T}°‘DZp‘‰ffŽ‘®yŽ‘™ °‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¦‘±c‘ÿ}'outŽ‘* Q°‘Ç´"p_z® ´==® ´"Ž‘5T}°‘DZp‘‰ffŽ‘®zŽ‘,ø°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¦‘ +°gŽŸ­564.‘ ü¬Chec¸ãk–UUwhether“the“cošGordinates“of“b˜oth“­P•®9oin“tsŽ‘&Î.¬are“all“0.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ +¬[²LDF‘T2002.10.27.¬]Ž‘XTNo¸ãw–¡6that“±cle‘ÿ}'anŽ‘⸬(10ŽŽ› +)“and“µpŽ‘©6:±cle‘ÿ}'anŽ‘A‚¬(10ŽŽ˜)“are“called“abGo•¸ãv“e,‘Åi³¬blo˜c¸ãks“where“calculations“are“p˜erformed“b˜elo¸ãw,Ž¡just–UUin“case“o•¸ãv“er o“w‘UUoGccurs.Ž¡‘ +!!‘>BUnder–D)Linš¸ãux,‘ÝbGoth“this“function“and“the“v˜ersion“of“±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘UѬ(‘ª®)“using“traces“ha˜v˜e“failed“inŽ¡the–cksame“cases,‘fñwhicš¸ãh“in˜v˜olv˜ed“coplanar“lines“whic˜h“had“bšGeen“rotated“ab˜out“the“z-axis“or“the“y“and“z-axes.Ž¡I‘€¥suspGect–€òit“has“to“do“with“the“routines“for“sine“and“cosine,‘ËÙsince“I'v¸ãe“had“trouble“with“rotation“in“theŽ¡constructors–UUfor“­P®9olyhedraŽ‘6Ö±¬.‘qÇ[²LDF‘T2003.06.29.¬]ŽŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.04.10.¬]Ž‘Y;Added–UUthis“function.‘qÇIt“replaces“the“old“vš¸ãersion,“bGelo˜w.Ž¡‘ +[²LDF‘T2002.04.12.¬]Ž‘YòÈRemo•¸ãv“ed–?âthe“de nition“of“this“function“to“®lines.web¬,‘z…bGecause“it“requires“the“use“ofŽ¡­LinesŽ‘Ῥ,–UUand“­LineŽ‘-¬is“an“incomplete“t¸ãypGe“here.Ž¡‘ +[²LDF‘T2003.06.29.¬]Ž‘YÝStarted–Ì÷using“this“vš¸ãersion“again.‘Ø®Bug“ xes“I'v˜e“made“elsewhere“seem“to“ha˜v˜e“made“itŽ¡function.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž¤ ‘ +­staticŽ‘(Þºb•QÇo“olu½‰™šs4Ž‘Ôwp“oin®9tŽ‘a5±interse–ÿ}'ction‘‰ffŽ‘®p“ointŽ’®³ ¬(­constŽ‘À‚P•®9oin“tŽ‘ŸÓVEŽ‘ãxXŽ‘l/section“forŽ¡the–UUvš¸ãector“v˜ersion,“abGo˜v˜e,“for“more“information.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯329“°i‘Ǭ+°Ž© ‘ +­staticŽ‘)HÚb•QÇo“olu½‰™šs4Ž‘Ôwp“oin®9tŽ‘aðu±interse–ÿ}'ction‘‰ffŽ‘®p“ointŽ’¯‡K¬(­P•®9oin“tŽ‘ï±p0Ž‘+]µ;‘ª¨­P•®9oin“tŽ‘ šE±p1Ž‘,±µ;‘ª¨­P•®9oin“tŽ‘ šE±q0Ž–,.,µ;‘ª¨­P•®9oin“tŽ‘ šE±q1Ž“µ;‘ª¨­constŽ‘ÕJb•QÇo“olŽ‘9v°±tr–ÿ}'ac“eŽ‘OÁ¬);ŽŸ­574.Ž¡°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¦‘ +­b•QÇo“olu½‰™šs4Ž‘Ôwp“oin®9tŽ‘BÑP•®9oin“tŽ‘_kL¬::‘±interse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘N–Ú¬(­P•®9oin“tŽ‘±p0Ž‘+/Áµ;‘ª¨­P•®9oin“tŽ‘ é±p1Ž‘,Úiµ;‘ª¨­P•®9oin“tŽ‘ é±q0Ž–,Wµ;‘ª¨­P•®9oin“tŽ‘ é±q1Ž“µ;‘ª¨­constŽ‘þ®b•QÇo“olŽ‘9Éx±tr–ÿ}'ac“eŽ‘Oà‰¬)°fŽ¦‘2­b•QÇo“olŽ‘K¡k´DEBUGŽ‘i.ܬ=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘°fŽ¦‘(±c‘ÿ}'outŽ‘> S°‘Ç´"Entering® ´Point::intŽ‘kÆÜersection_point().\nŽ’ÔÆ "Ž’ÝT°‘DZ ushŽ‘€¬;Ž¦‘(±p0Ž‘4ĵ:±showŽ‘Šÿ¬(´"p0"Ž‘†\¬);Ž¦‘(±p1Ž‘4ĵ:±showŽ‘Šÿ¬(´"p1"Ž‘†\¬);Ž¦‘(±q0Ž‘3“ëµ:±showŽ‘Šÿ¬(´"q0"Ž‘†\¬);Ž¦‘(±q1Ž‘3“ëµ:±showŽ‘Šÿ¬(´"q1"Ž‘†\¬);Ž¦‘°gŽ¡‘­b•QÇo“olu½‰™šs4Ž‘Ôwp“oin®9tŽ‘V§ž±bpŽ‘a‚¬;‘µ=°‘ÿý¬Return‘UUv‘ÿqÇalue.‘o°µ=Ž¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Error® ´after® ´here® ´0.Ž‘kÆÜ\n"Ž‘~ÔS°‘DZ ushŽ‘€¬;ŽŸ­575.‘ ü¬Apply–¦the“transformations,‘%–so“wš¸ãe“ha˜v˜e“the“correct“v‘ÿqÇalues“for“x,–%–y‘ÿ*ª,“and–¦z“in“eac˜h“of“the“­P•®9oin“tsŽ‘#=*¬.‘]âThenŽ¦assign–UUthem“to“v‘ÿqÇariables.Ž¡°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¦‘ +±p0Ž‘Áµ:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¦‘ +±p1Ž‘Áµ:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¦‘ +±q0Ž‘“èµ:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¦‘ +±q1Ž‘“èµ:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¡‘ +­realŽ‘ ³/±p0‘‰ffŽ‘®xŽ‘7»å¬=‘DZp0Ž‘Ýص:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ¬[0Ž‘];Ž¦‘ +­realŽ‘ ³/±p0‘‰ffŽ‘®yŽ‘7¡”¬=‘DZp0Ž‘Ýص:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ¬[1Ž‘];Ž¦‘ +­realŽ‘ ³/±p0‘‰ffŽ‘®zŽ‘75¬=‘DZp0Ž‘Ýص:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ¬[2Ž‘];Ž¦‘ +­realŽ‘ ³/±p1‘‰ffŽ‘®xŽ‘7»å¬=‘DZp1Ž‘Ýص:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ¬[0Ž‘];Ž¦‘ +­realŽ‘ ³/±p1‘‰ffŽ‘®yŽ‘7¡”¬=‘DZp1Ž‘Ýص:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ¬[1Ž‘];Ž¦‘ +­realŽ‘ ³/±p1‘‰ffŽ‘®zŽ‘75¬=‘DZp1Ž‘Ýص:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ¬[2Ž‘];Ž¦‘ +­realŽ‘ ³/±q0‘‰ffŽ‘®xŽ‘79 ¬=‘DZq0Ž‘Zÿµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ¬[0Ž‘];Ž¦‘ +­realŽ‘ ³/±q0‘‰ffŽ‘®yŽ‘7»¬=‘DZq0Ž‘Zÿµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ¬[1Ž‘];Ž¦‘ +­realŽ‘ ³/±q0‘‰ffŽ‘®zŽ‘6²¦¬=‘DZq0Ž‘Zÿµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ¬[2Ž‘];Ž¦‘ +­realŽ‘ ³/±q1‘‰ffŽ‘®xŽ‘79 ¬=‘DZq1Ž‘Zÿµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ¬[0Ž‘];Ž¦‘ +­realŽ‘ ³/±q1‘‰ffŽ‘®yŽ‘7»¬=‘DZq1Ž‘Zÿµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ¬[1Ž‘];Ž¦‘ +­realŽ‘ ³/±q1‘‰ffŽ‘®zŽ‘6²¦¬=‘DZq1Ž‘Zÿµ:±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘Mþ¬[2Ž‘];Ž¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Error® ´after® ´here® ´1.Ž‘kÆÜ\n"Ž‘~ÔS°‘DZ ushŽ‘€¬;ŽŽŽŒ‹š ÊH Šn ý‘ì¬154–¯TRAÃŽCE‘ÕXVERSION’ßð3DLDF-1.1.5.1“°x¬576Ž €n ý•@P­576.‘ ü¬Get‘UUdeltas.Ž©°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¤ ‘ +­realŽ‘ ³/±delta‘‰ffŽ–®x‘‰ffŽ“pŽ‘Jn¬=‘DZp1‘‰ffŽ‘®xŽ‘A–°‘8à±p0‘‰ffŽ‘®xŽ‘z~¬;Ž¡‘ +­realŽ‘ ³/±delta‘‰ffŽ–®y‘‰ffŽ“pŽ‘J¥|¬=‘DZp1‘‰ffŽ‘®yŽ‘'E°‘8à±p0‘‰ffŽ‘®yŽ‘`-¬;Ž¡‘ +­realŽ‘ ³/±delta‘‰ffŽ–®z‘‰ffŽ“pŽ‘Iá9¬=‘DZp1‘‰ffŽ‘®zŽ‘»0°‘8à±p0‘‰ffŽ‘®zŽ‘ô¬;Ž¡‘ +­realŽ‘ ³/±delta‘‰ffŽ–®x‘‰ffŽ“qŽ‘J,¬=‘DZq1‘‰ffŽ‘®xŽ‘¾½°‘8à±q0‘‰ffŽ‘®xŽ‘÷¥¬;Ž¡‘ +­realŽ‘ ³/±delta‘‰ffŽ–®y‘‰ffŽ“qŽ‘Jcˆ¬=‘DZq1‘‰ffŽ‘®yŽ‘¤l°‘8à±q0‘‰ffŽ‘®yŽ‘ÝT¬;Ž¡‘ +­realŽ‘ ³/±delta‘‰ffŽ–®z‘‰ffŽ“qŽ‘IŸE¬=‘DZq1‘‰ffŽ‘®zŽ‘8W°‘8à±q0‘‰ffŽ‘®zŽ‘q?¬;Ž¦‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Error® ´after® ´here® ´2.Ž‘kÆÜ\n"Ž‘~ÔS°‘DZ ushŽ‘€¬;ŽŸ­577.‘ ü¬SlopGes–UUfor“lineŸü±È“°ŽŽ‘ö<‘þ㎎Ž‘gþ!ŽŽŸN8“µpŸÿ³0Ž‘|sµpŸÿ³1ŽŽŽŽŽ‘^;¬.Ž¦°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¡‘ +­realŽ‘ ³/±slop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“x‘‰ffŽ“yŽ‘Sym¬=–Ç(±delta‘‰ffŽ–®x‘‰ffŽ“pŽ›)º×°6¬=“0Ž‘Ç)“?“±delta‘‰ffŽ–®y‘‰ffŽ“pŽ‘)òMµ=±delta‘‰ffŽ–®x‘‰ffŽ“pŽ˜¬:“´INVALID_REALŽ‘BM\¬;Ž¡‘ +­realŽ‘ ³/±slop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“x‘‰ffŽ“zŽ‘S X¬=–Ç(±delta‘‰ffŽ–®x‘‰ffŽ“pŽ›)º×°6¬=“0Ž‘Ç)“?“±delta‘‰ffŽ–®z‘‰ffŽ“pŽ‘). +µ=±delta‘‰ffŽ–®x‘‰ffŽ“pŽ˜¬:“´INVALID_REALŽ‘BM\¬;Ž¡‘ +­realŽ‘ ³/±slop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“z‘‰ffŽ“yŽ‘Rì ¬=–Ç(±delta‘‰ffŽ–®z‘‰ffŽ“pŽ›). +°6¬=“0Ž‘Ç)“?“±delta‘‰ffŽ–®y‘‰ffŽ“pŽ‘)òMµ=±delta‘‰ffŽ–®z‘‰ffŽ“pŽ˜¬:“´INVALID_REALŽ‘BM\¬;Ž¦‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Error® ´after® ´here® ´3.Ž‘kÆÜ\n"Ž‘~ÔS°‘DZ ushŽ‘€¬;ŽŸ­578.‘ ü¬SlopGes–UUfor“lineŸü±È“°ŽŽ‘e ‘þ㎎Ž‘ÖÏ!ŽŽŸN8“µqŸÿ³0Ž‘|sµqŸÿ³1ŽŽŽŽŽ‘;ݬ.Ž¦°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¡‘ +­realŽ‘ ³/±slop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“x‘‰ffŽ“yŽ‘Rö”¬=–Ç(±delta‘‰ffŽ–®x‘‰ffŽ“qŽ›)xã°6¬=“0Ž‘Ç)“?“±delta‘‰ffŽ–®y‘‰ffŽ“qŽ‘)°Yµ=±delta‘‰ffŽ–®x‘‰ffŽ“qŽ˜¬:“´INVALID_REALŽ‘BM\¬;Ž¡‘ +­realŽ‘ ³/±slop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“x‘‰ffŽ“zŽ‘RŠ¬=–Ç(±delta‘‰ffŽ–®x‘‰ffŽ“qŽ›)xã°6¬=“0Ž‘Ç)“?“±delta‘‰ffŽ–®z‘‰ffŽ“qŽ‘(ìµ=±delta‘‰ffŽ–®x‘‰ffŽ“qŽ˜¬:“´INVALID_REALŽ‘BM\¬;Ž¡‘ +­realŽ‘ ³/±slop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“z‘‰ffŽ“yŽ‘RiǬ=–Ç(±delta‘‰ffŽ–®z‘‰ffŽ“qŽ›(ì°6¬=“0Ž‘Ç)“?“±delta‘‰ffŽ–®y‘‰ffŽ“qŽ‘)°Yµ=±delta‘‰ffŽ–®z‘‰ffŽ“qŽ˜¬:“´INVALID_REALŽ‘BM\¬;Ž¦‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Error® ´after® ´here® ´4.Ž‘kÆÜ\n"Ž‘~ÔS°‘DZ ushŽ‘€¬;ŽŸ­579.‘ ü¬The–½traces“on“the“x-y“plane.‘]?±x‘‰ffŽ‘®iŽ‘G£¬,‘$±y‘‰ffŽ‘®iŽ‘Eé¬,‘$±z‘‰ffŽ‘®iŽ‘¦¬,‘$±y‘‰ffŽ–®int‘‰ffŽ“pŽ‘!ží¬,‘$and“±y‘‰ffŽ–®int‘‰ffŽ“qŽ‘$hd¬are“set“to“´INVALID_REALŽ‘Eµ¾¬so“that“I‘®canŽ¡test–UUfor“whether“the“routines“bGelo¸ãw“succeed“in“setting“them“correctly‘ÿ*ª.Ž¦°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¡‘ +­realŽ‘ ³/±x‘‰ffŽ‘®iŽ‘0d«¬=‘Ç´INVALID_REALŽ‘BM\¬;‘µ=°‘ÿý¬x-cošGordinate–UUof“the“in¸ãtersection“p˜oin¸ãt.‘o°µ=Ž¡‘ +­realŽ‘ ³/±y‘‰ffŽ‘®iŽ‘0œ!¬=‘Ç´INVALID_REALŽ‘BM\¬;‘µ=°‘ÿý¬y-cošGordinate–UUof“the“in¸ãtersection“p˜oin¸ãt.‘o°µ=Ž¡‘ +­realŽ‘ ³/±z‘‰ffŽ‘®iŽ‘/×Þ¬=‘Ç´INVALID_REALŽ‘BM\¬;‘µ=°‘ÿý¬z-cošGordinate–UUof“the“in¸ãtersection“p˜oin¸ãt.‘o°µ=Ž¡‘ +­realŽ‘ ³/±y‘‰ffŽ–®int‘‰ffŽ“pŽ‘Aõ%¬=‘Ç´INVALID_REALŽ‘BM\¬;‘µ=°‘ÿý¬y-in¸ãtercept–UUofŸü±È“°ŽŽ‘ö<‘þ㎎Ž‘gþ!ŽŽŸN8“µpŸÿ³0Ž‘|sµpŸÿ³1ŽŽŽŽŽ‘^;¬.‘o°µ=Ž¡‘ +­realŽ‘ ³/±y‘‰ffŽ–®int‘‰ffŽ“qŽ‘A³1¬=‘Ç´INVALID_REALŽ‘BM\¬;‘µ=°‘ÿý¬y-in¸ãtercept–UUofŸü±È“°ŽŽ‘e ‘þ㎎Ž‘ÖÏ!ŽŽŸN8“µqŸÿ³0Ž‘|sµqŸÿ³1ŽŽŽŽŽ‘;ݬ.‘o°µ=Ž¦‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Error® ´after® ´here® ´5.Ž‘kÆÜ\n"Ž‘~ÔS°‘DZ ushŽ‘€¬;Ž¡‘ +­ifŽ‘´ù¬(±slop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“x‘‰ffŽ“yŽ‘2Æ>°6¬=‘Ç´INVALID_REALŽ‘BM\¬)‘µ=°‘ÿý¬µxŸÿ·pŽ‘fj°6¬=‘Ç0.‘o°µ=Ž¡‘ +°fŽ¡‘±y‘‰ffŽ–®int‘‰ffŽ“pŽ‘5Aø¬=‘DZp0‘‰ffŽ‘®yŽ‘'E°–8à¬(±slop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“x‘‰ffŽ“yŽ‘28°“±p0‘‰ffŽ‘®xŽ‘z~¬);Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(±slop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“x‘‰ffŽ“yŽ‘2Ce°6¬=‘Ç´INVALID_REALŽ‘BM\¬)‘µ=°‘ÿý¬µxŸÿ·qŽ‘1­°6¬=‘Ç0.‘o°µ=Ž¡‘ +°fŽ¡‘±y‘‰ffŽ–®int‘‰ffŽ“qŽ‘5¬=‘DZq0‘‰ffŽ‘®yŽ‘¤l°–8à¬(±slop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“x‘‰ffŽ“yŽ‘1µ-°“±q0‘‰ffŽ‘®xŽ‘÷¥¬);Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Error® ´after® ´here® ´6.Ž‘kÆÜ\n"Ž‘~ÔS°‘DZ ushŽ‘€¬;ŽŽŽŒ‹› Úx Šn ý‘ì°x¬580–¯3DLDF-1.1.5.1’ßðTRAÃŽCE‘ÕXVERSION“¬155Ž €n ý•@P­580.Ž¤ °Ž‘ +¬If–vŒbGoth“of“the“traces“of‘‹µ~Ž“pŽŽ‘ õ¬and‘pUµ~Ž“qŽŽ‘ ¿Â¬in“the“x-y“plane“are“parallel“to“the“y-axis“(i.e.,›~Ùµx–þs¬=“0),˜w¸ãe–vŒtest“whetherŽ¡‘ +µpŸÿ·xŽ‘9¬=‘0µqŸÿ·xŽ‘ä¬.›.ÔIf–”Ythey“are,‘¤then“w¸ãe“set“±x‘‰ffŽ‘®iŽ‘¬to“that“v‘ÿqÇalue.˜If“they're“not,›¤the“lines“don't“in¸ãtersect,˜so“w¸ãe“returnŽ¡‘ +´INVALID_POINTŽ‘NÆB¬.Ž¡°Ž‘ +¬If–òOthe“trace“of‘õ~Ž“pŽŽ‘ +재or“the“trace“of‘ìµ~Ž“qŽŽ‘ +·H¬in“the“x-y“plane“is“parallel“to“the“y-axis,›w¸ãe“set“±x‘‰ffŽ‘®iŽ‘Ϭto“its“x-v‘ÿqÇalue,˜bGecauseŽ¡‘ +in–UUthis“case,“the“inš¸ãtersection“pGoin˜t“m˜ust“ha˜v˜e“this“x-v‘ÿqÇalue.Ž¡°Ž‘ +¬If–UUµxŸÿ·pŽ‘fj°6¬=›Ç0“and“µxŸÿ·qŽ‘1­°6¬=˜0,“wš¸ãe“deriv˜e“±x‘‰ffŽ‘®iŽ‘•¬using“the“slopGe“and“y-in˜tercept“of“the“lines.Ž©°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¡‘ +­ifŽ‘´ù¬(±y‘‰ffŽ–®int‘‰ffŽ“pŽ‘!Aö°‘Ç´INVALID_REALŽ‘D†<°^‘8à±y‘‰ffŽ–®int‘‰ffŽ“qŽ‘#8â°‘Ç´INVALID_REALŽ‘BM\¬)Ž¡‘µ=°‘qµ~Ž‘ÿýpŸÿ·xzŽŽŽ‘Ǭand‘Oµ~Ž‘UUqŸÿ·xzŽŽŽ‘Eð¬are–UUbGoth“parallel“to“the“z-axis.‘o°µ=Ž¡‘ +°fŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Error® ´after® ´here® ´7.Ž‘kÆÜ\n"Ž‘~ÔS°‘DZ ushŽ‘€¬;Ž¡‘­ifŽ‘´ú¬(±p0‘‰ffŽ‘®xŽ‘¶°‘DZq0‘‰ffŽ‘®xŽ‘…ݬ)‘µ=°‘ÿý¬They›UUha•¸ãv“e˜the˜same˜v‘ÿqÇalue˜for˜µx¬.‘o°µ=Ž¡‘°fŽ¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Error® ´after® ´here® ´8.Ž‘kÆÜ\n"Ž‘~ÔS°‘DZ ushŽ‘€¬;Ž¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Traces® ´on® ´x-y® ´planeŽ‘kÆÜ® ´are® ´coincident.\n"Ž’ÒÔ#°‘DZ ushŽ‘€¬;Ž¡‘±x‘‰ffŽ‘®iŽ‘-±¬=‘DZp0‘‰ffŽ‘®xŽ‘¶¬;Ž¦‘­realŽ‘4³1±y‘‰ffŽ–®int‘‰ffŽ“p‘‰ffŽ“zŽ‘^S ¬=‘Ç´INVALID_REALŽ‘BM\¬;Ž¡‘­realŽ‘4³1±y‘‰ffŽ–®int‘‰ffŽ“q‘‰ffŽ“zŽ‘]Ð4¬=‘Ç´INVALID_REALŽ‘BM\¬;Ž¦‘­ifŽ‘)´û¬(±slop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“z‘‰ffŽ“yŽ‘29q°6¬=‘Ç´INVALID_REALŽ‘BM\¬)‘±y‘‰ffŽ–®int‘‰ffŽ“p‘‰ffŽ“zŽ‘.ŸÜ¬=‘DZp0‘‰ffŽ‘®yŽ‘'E°‘8à±slop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“z‘‰ffŽ“yŽ‘3ä°‘8à±p0‘‰ffŽ‘®zŽ‘ô¬;Ž¡‘­ifŽ‘)´û¬(±slop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“z‘‰ffŽ“yŽ‘1¶˜°6¬=‘Ç´INVALID_REALŽ‘BM\¬)‘±y‘‰ffŽ–®int‘‰ffŽ“q‘‰ffŽ“zŽ‘.¬=‘DZq0‘‰ffŽ‘®yŽ‘¤l°‘8à±slop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“z‘‰ffŽ“yŽ‘3a@°‘8à±q0‘‰ffŽ‘®zŽ‘q?¬;Ž¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Error® ´after® ´here® ´9.Ž‘kÆÜ\n"Ž‘~ÔS°‘DZ ushŽ‘€¬;Ž¡‘­ifŽ‘)´û¬(±slop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“z‘‰ffŽ“yŽ‘29q°‘Ç´INVALID_REALŽ‘D†<°^‘8à±slop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“z‘‰ffŽ“yŽ‘3ïx°‘Ç´INVALID_REALŽ‘BM\¬)‘°fŽ¡‘(­ifŽ‘3´ü¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Both® ´traces® ´on® ´z-y® Ž‘kÆÜ´plane® ´are® ´vertical\nŽ’ÔÆ "Ž’ÝT°‘DZ ushŽ‘€¬;Ž¡‘(­ifŽ‘3´ü¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Error® ´after® ´here® ´10Ž‘kÆÜ.\n"Ž’„P°‘DZ ushŽ‘€¬;Ž¡‘(­ifŽ‘3´ü¬(±p0‘‰ffŽ‘®zŽ‘‚P°‘DZq0‘‰ffŽ‘®zŽ‘ÿw¬)‘±c‘ÿ}'errŽ‘|¾°‘Ç´"Lines® ´are® ´coincidenŽ‘kÆÜt.\n"Ž’†5¬;Ž¡‘(­elseŽ‘?Øã±c‘ÿ}'errŽ‘UU¡°‘Ç´"Lines® ´do® ´not® ´intersŽ‘kÆÜect.\n"Ž’‘ /¬;Ž¡‘(±c‘ÿ}'errŽ‘=|°‘Ç´"Returning® ´INVALID_BŽ‘kÆÜOOL_POINT.\n\n"Ž’½Ô/°‘DZ ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾´INVALID_BOOL_POINTŽ’ªìð¬;Ž¡‘°gŽ¡‘­elseŽ‘4.7ifŽ‘?ã/¬(±slop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“z‘‰ffŽ“yŽ‘29q°‘Ç´INVALID_REALŽ‘BM\¬)‘°fŽ¡‘(­ifŽ‘3´ü¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"The® ´p-trace® ´is® ´vertŽ‘kÆÜical\n"Ž’“ÔG°‘DZ ushŽ‘€¬;Ž¡‘(­ifŽ‘3´ü¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Error® ´after® ´here® ´11Ž‘kÆÜ.\n"Ž’„P°‘DZ ushŽ‘€¬;Ž¡‘(±z‘‰ffŽ‘®iŽ‘7$³¬=‘DZp0‘‰ffŽ‘®zŽ‘‚P¬;Ž¡‘(±y‘‰ffŽ‘®iŽ‘7èö¬=‘DZz‘‰ffŽ‘®iŽ‘]°‘8à±slop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“z‘‰ffŽ“yŽ‘3a@¬+‘8à±y‘‰ffŽ–®int‘‰ffŽ“q‘‰ffŽ“zŽ‘(ŽË¬;Ž¡‘(­ifŽ‘3´ü¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘2±c‘ÿ}'outŽ‘H T°‘Ç´"x_i® ´==® ´"Ž‘5T}°‘DZx‘‰ffŽ‘®iŽ‘x”°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘2±c‘ÿ}'outŽ‘H T°‘Ç´"y_i® ´==® ´"Ž‘5T}°‘DZy‘‰ffŽ‘®iŽ‘° +°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘2±c‘ÿ}'outŽ‘H T°‘Ç´"z_i® ´==® ´"Ž‘5T}°‘DZz‘‰ffŽ‘®iŽ‘ëÇ°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘2±c‘ÿ}'outŽ‘H T°‘Ç´"slope_q_z_y® ´==® ´"Ž‘_Te°‘DZslop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“z‘‰ffŽ“yŽ‘4}°°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘2±c‘ÿ}'outŽ‘H T°‘Ç´"y_int_q_z® ´==® ´"Ž‘TÔk°‘DZy‘‰ffŽ–®int‘‰ffŽ“q‘‰ffŽ“zŽ‘+䰑DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘(°gŽ¡‘gŽ¡‘­elseŽ‘4.7ifŽ‘?ã/¬(±slop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“z‘‰ffŽ“yŽ‘1¶˜°‘Ç´INVALID_REALŽ‘BM\¬)‘°fŽ¡‘(­ifŽ‘3´ü¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"The® ´q-trace® ´is® ´vertŽ‘kÆÜical\n"Ž’“ÔG°‘DZ ushŽ‘€¬;Ž¡‘(­ifŽ‘3´ü¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Error® ´after® ´here® ´12Ž‘kÆÜ.\n"Ž’„P°‘DZ ushŽ‘€¬;Ž¡‘(±z‘‰ffŽ‘®iŽ‘7$³¬=‘DZq0‘‰ffŽ‘®zŽ‘ÿw¬;Ž¡‘(±y‘‰ffŽ‘®iŽ‘7èö¬=‘DZz‘‰ffŽ‘®iŽ‘]°‘8à±slop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“z‘‰ffŽ“yŽ‘3ä¬+‘8à±y‘‰ffŽ–®int‘‰ffŽ“p‘‰ffŽ“zŽ‘)¤¬;Ž¡‘(­ifŽ‘3´ü¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘2±c‘ÿ}'outŽ‘H T°‘Ç´"x_i® ´==® ´"Ž‘5T}°‘DZx‘‰ffŽ‘®iŽ‘x”°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘2±c‘ÿ}'outŽ‘H T°‘Ç´"y_i® ´==® ´"Ž‘5T}°‘DZy‘‰ffŽ‘®iŽ‘° +°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;ŽŽŽŒ‹œ ñ Šn ý‘ì¬156–¯TRAÃŽCE‘ÕXVERSION’ßð3DLDF-1.1.5.1“°x¬580Ž €n ý•@P‘2±c‘ÿ}'outŽ‘H T°‘Ç´"z_i® ´==® ´"Ž‘5T}°‘DZz‘‰ffŽ‘®iŽ‘ëÇ°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¤ ‘2±c‘ÿ}'outŽ‘H 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³¾«;Ž¡‘ -·gŽŽŽŒ‹“> Šn ý‘ì·x«537›­3DLDFPR•ÃŽG’S†TRA“CE‘ÕXVERSION˜«147Ž €n ý•@PÂ537.‘ ü«[¬LDF‘T2002.11.12.«]Ž‘ZBÇ!!‘Z¢BUG:–æOccurred“when“I‘Ôtried“to“ nd“an“inš¸ãtersection“of“t˜w˜o“lines“in“the“x-z“plane.Ž¤ This–¶ñcošGde“shouldn't“b˜e“reacš¸ãhed.‘<ûRotating“the“ob‘Ž8jects“90Ÿü^ÿºŽ‘OÕ«around“the“x-axis,‘Öžputting“them“in˜to“the“x-y“plane,Ž¡ xed–UUthe“problem.‘qÇOb¸ãviously›ÿ*ª,“the“case“that“the“ob‘Ž8jects“are“in“the“x-z“plane“already“isn't“handled“propGerly˜.Ž©·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¡‘ -ÂelseŽ‘0Øá±=·‘ÿý«Neither‘÷±~Ž‘UUqŸÿ´xyŽŽŽ–xæ«nor‘O±~Ž‘UUqŸÿ´xyŽŽŽ“«is–UUparallel“to“the“y-axis.‘o·±=Ž¡‘ -·fŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘±=·‘ÿý«[¬LDF‘T2002.11.12.«]Ž‘T7Start–UUw¸ãorking“on“ nding“bug“here.‘o·±=Ž¡‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"ErrorÈ ÝafterÈ ÝhereÈ Ý17Ž‘kÆÜ.\n"Ž’„P·‘ÇÏ ushŽ‘€«;Ž¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"slope_p_x_yÈ Ý==È Ý"Ž‘_Te·‘ÇÏslop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“x‘‰ffŽ“yŽ‘5V·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"slope_q_x_yÈ Ý==È Ý"Ž‘_Te·‘ÇÏslop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“x‘‰ffŽ“yŽ‘5 -}·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(Ïslop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“x‘‰ffŽ“yŽ‘2Æ>·6«=‘ÇÏslop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“x‘‰ffŽ“yŽ‘2Ce«)‘·fŽ¡‘Ïx‘‰ffŽ‘®iŽ‘-±«=‘Ç(Ïy‘‰ffŽ–®int‘‰ffŽ“qŽ‘ qÊ·‘8àÏy‘‰ffŽ–®int‘‰ffŽ“pŽ‘ ³¾«)±=«(Ïslop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“x‘‰ffŽ“yŽ‘28·‘8àÏslop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“x‘‰ffŽ“yŽ‘1µ-«);Ž¡‘Ïy‘‰ffŽ‘®iŽ‘-èõ«=‘ÇÏslop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“x‘‰ffŽ“yŽ‘4ÿ·‘8àÏx‘‰ffŽ‘®iŽ‘\$«+‘8àÏy‘‰ffŽ–®int‘‰ffŽ“pŽ‘ ³¾«;Ž¡‘·gŽ¡‘ -gŽŸÂ538.‘ ü«The–|trace“on“the“x-z“plane.‘åËW‘ÿ*ªe“don't“need“to“do“this“if“w•¸ãe'v“e–|calculated“Ïz‘‰ffŽ‘®iŽ‘U™«abGo•¸ãv“e,‘…¬in–|the“case“thatŽ¡the–UUtraces“on“the“x-y“plane“are“coinciden¸ãt.Ž¦·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¡‘ -ÂifŽ‘´ù«(Ïz‘‰ffŽ‘®iŽ‘$¯·‘ÇÝINVALID_REALŽ‘BM\«)‘UU·fŽ¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ErrorÈ ÝafterÈ ÝhereÈ Ý18Ž‘kÆÜ.\n"Ž’„P·‘ÇÏ ushŽ‘€«;Ž¦‘ -ÂrealŽ‘ ³/Ïz‘‰ffŽ–®int‘‰ffŽ“pŽ‘A0â«=‘ÇÝINVALID_REALŽ‘BM\«;‘±=·‘ÿý«z-in¸ãtercept–UUofŸü±È“·ŽŽ‘ö<‘þ㎎Ž‘gþ!ŽŽŸN8“±pŸÿ®0Ž‘|s±pŸÿ®1ŽŽŽŽŽ‘^;«.‘o·±=Ž¡‘ -ÂrealŽ‘ ³/Ïz‘‰ffŽ–®int‘‰ffŽ“qŽ‘@îî«=‘ÇÝINVALID_REALŽ‘BM\«;‘±=·‘ÿý«z-in¸ãtercept–UUofŸü±È“·ŽŽ‘e ‘þ㎎Ž‘ÖÏ!ŽŽŸN8“±qŸÿ®0Ž‘|s±qŸÿ®1ŽŽŽŽŽ‘;Ý«.‘o·±=Ž¦‘ -ÂifŽ‘´ù«(Ïslop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“x‘‰ffŽ“zŽ‘2Z)·6«=‘ÇÝINVALID_REALŽ‘BM\«)‘±=·‘ÿý«±xŸÿ´pŽ‘fj·6«=‘Ç0.‘o·±=Ž¡‘ -·fŽ¡‘Ïz‘‰ffŽ–®int‘‰ffŽ“pŽ‘4}µ«=‘ÇÏp0‘‰ffŽ‘®zŽ‘»0·–8à«(Ïslop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“x‘‰ffŽ“zŽ‘1Ëñ·“Ïp0‘‰ffŽ‘®xŽ‘z~«);Ž¡‘ -·gŽ¡‘ -ÂifŽ‘´ù«(Ïslop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“x‘‰ffŽ“zŽ‘1×P·6«=‘ÇÝINVALID_REALŽ‘BM\«)‘±=·‘ÿý«±xŸÿ´qŽ‘1­·6«=‘Ç0.‘o·±=Ž¡‘ -·fŽ¡‘Ïz‘‰ffŽ–®int‘‰ffŽ“qŽ‘4;Á«=‘ÇÏq0‘‰ffŽ‘®zŽ‘8W·–8à«(Ïslop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“x‘‰ffŽ“zŽ‘1I·“Ïq0‘‰ffŽ‘®xŽ‘÷¥«);Ž¡‘ -·gŽ¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"z_int_pÈ Ý==È Ý"Ž‘JTq·‘ÇÏz‘‰ffŽ–®int‘‰ffŽ“pŽ‘#DË·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"z_int_qÈ Ý==È Ý"Ž‘JTq·‘ÇÏz‘‰ffŽ–®int‘‰ffŽ“qŽ‘#×·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ -·gŽŸÂ539.‘ ü«[¬LDF‘T2003.06.24.«]Ž‘Z‹”Ïx‘‰ffŽ‘®iŽ‘jΫ«will–X³bGe“equal“to“ÝINVALID_REALŽ‘BÞ÷«,‘Y‹if“the“traces“of“the“lines“on“the“x-y“plane“w¸ãereŽ¡colinear.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.06.24.«]Ž‘Y;Added–UUthis“conditional.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¡‘ -ÂifŽ‘´ù«(Ïx‘‰ffŽ‘®iŽ‘±|·‘ÇÝINVALID_REALŽ–D†<·^›8à:«(Ïz‘‰ffŽ–®int‘‰ffŽ“pŽ‘ }³·‘ÇÝINVALID_REALŽ“·_˜Ïz‘‰ffŽ–®int‘‰ffŽ“qŽ‘"tŸ·‘ÇÝINVALID_REALŽ‘BM\«))‘·fŽ¡‘Ïx‘‰ffŽ‘®iŽ‘#±~«=‘Ç(Ïz‘‰ffŽ–®int‘‰ffŽ“qŽ‘­‡·‘8àÏz‘‰ffŽ–®int‘‰ffŽ“pŽ‘ï{«)±=«(Ïslop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“x‘‰ffŽ“zŽ‘1Ëñ·‘8àÏslop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“x‘‰ffŽ“zŽ‘1I«);Ž¡‘Ïy‘‰ffŽ‘®iŽ‘#èô«=‘ÇÏp0‘‰ffŽ‘®yŽ‘îe«;Ž¡‘ -·gŽŽŽŒ‹”+ø Šn ý‘ì«148›­TRA•ÃŽCE‘ÕXVERSION’S†3DLDFPR“G˜·x«540Ž €n ý•@PÂ540.‘ ü«In–Ì“the“folloš¸ãwing“case,‘þÖ±~Ž‘êbpŸÿ´xzŽŽŽ‘ãj«and‘Æ\±~Ž“qŸÿ´xzŽŽŽ‘4l«are“bGoth“parallel“to“the“z-axis.‘×€They“ha˜v˜e“the“same“v‘ÿqÇalue“for“±x«.Ž¤ W‘ÿ*ªe'vš¸ãe–UUset“Ïx‘‰ffŽ‘®iŽ‘•«abGo˜v˜e,“so“there's“no“need“to“do“so“here“again.ŽŸ·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¡‘ -ÂifŽ‘´ù«(Ïz‘‰ffŽ–®int‘‰ffŽ“pŽ‘ }³·‘ÇÝINVALID_REALŽ‘D†<·^‘8àÏz‘‰ffŽ–®int‘‰ffŽ“qŽ‘"tŸ·‘ÇÝINVALID_REALŽ‘BM\«)‘·fŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ErrorÈ ÝafterÈ ÝhereÈ Ý19Ž‘kÆÜ.\n"Ž’„P·‘ÇÏ ushŽ‘€«;Ž¡‘ÂifŽ‘´ú«(Ïp0‘‰ffŽ‘®xŽ‘¶·6«=‘ÇÏq0‘‰ffŽ‘®xŽ‘…Ý«)‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ErrorÈ ÝafterÈ ÝhereÈ Ý20Ž‘kÆÜ.\n"Ž’„P·‘ÇÏ ushŽ‘€«;Ž¡‘Ïc‘ÿ}'errŽ‘4ûõ·‘FLÝ"LinesÈ ÝdoÈ ÝnotÈ ÝintersŽ‘mFect:\n"Ž’–Ò¯·‘FLÝ"("Ž‘Ò÷·‘FLÏp0‘‰ffŽ‘®xŽ‘Î6·‘FLÝ",È Ý"Ž–ô·‘FLÏp0‘‰ffŽ‘®zŽ‘Gз‘FLÝ",È Ý"Ž“·Ž¡‘2Ïp0‘‰ffŽ‘®zŽ‘I¿Ü·‘ŸÝ")È Ý--È Ý("Ž‘2Ž·‘ŸÏp1‘‰ffŽ‘®xŽ‘JÜ·‘ŸÝ",È Ý"Ž–š·‘ŸÏp1‘‰ffŽ‘®zŽ›Äv·‘ŸÝ",È Ý"Ž“·‘ŸÏp1‘‰ffŽ‘®zŽ˜·‘ŸÝ")\n("Ž‘(”·‘ŸÏq0‘‰ffŽ‘®xŽ‘È·Ž¡‘2Ý",È Ý"Ž‘KÊ ·‘C¿Ïq0‘‰ffŽ‘®zŽ–¿Ý·‘C¿Ý",È Ý"Ž› Ú·‘C¿Ïq0‘‰ffŽ‘®zŽ“·‘C¿Ý")È Ý--È Ý("Ž‘3 η‘C¿Ïq1‘‰ffŽ‘®xŽ‘FC·‘C¿Ý",È Ý"Ž˜·‘C¿Ïq1‘‰ffŽ‘®zŽ“·‘C¿Ïq1‘‰ffŽ‘®zŽ“·Ž¡‘2Ý")\nReturningÈ ÝINVALIŽ’šÿÉD_BOOL_POINT.\n"Ž’òM·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½ÝINVALID_BOOL_POINTŽ’ ìï«;Ž¡‘·gŽ¡‘ +­elseŽ‘ .5ifŽ‘+ã-¬(±y‘‰ffŽ–®int‘‰ffŽ“pŽ‘!Aö°‘Ç´INVALID_REALŽ‘BM\¬)‘µ=°‘qµ~Ž‘ÿýpŸÿ·xyŽŽŽ‘´½¬is–UUparallel“to“the“y-axis.‘o°µ=Ž¡‘ +°fŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Error® ´after® ´here® ´15Ž‘kÆÜ.\n"Ž’„P°‘DZ ushŽ‘€¬;Ž¡‘±x‘‰ffŽ‘®iŽ‘#±~¬=‘DZp0‘‰ffŽ‘®xŽ‘¶¬;Ž¡‘±y‘‰ffŽ‘®iŽ‘#èô¬=‘DZslop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“x‘‰ffŽ“yŽ‘4|E°‘8à±x‘‰ffŽ‘®iŽ‘\$¬+‘8à±y‘‰ffŽ–®int‘‰ffŽ“qŽ‘ qʬ;Ž¡‘ +°gŽ¡‘ +­elseŽ‘ .5ifŽ‘+ã-¬(±y‘‰ffŽ–®int‘‰ffŽ“qŽ‘!°‘Ç´INVALID_REALŽ‘BM\¬)‘µ=°‘ùƵ~Ž‘ÿýqŸÿ·xyŽŽŽ‘#Ž¬is–UUparallel“to“the“y-axis.‘o°µ=Ž¡‘ +°fŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Error® ´after® ´here® ´16Ž‘kÆÜ.\n"Ž’„P°‘DZ ushŽ‘€¬;Ž¡‘±x‘‰ffŽ‘®iŽ‘#±~¬=‘DZq0‘‰ffŽ‘®xŽ‘…ݬ;Ž¡‘±y‘‰ffŽ‘®iŽ‘#èô¬=‘DZslop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“x‘‰ffŽ“yŽ‘4ÿ°‘8à±x‘‰ffŽ‘®iŽ‘\$¬+‘8à±y‘‰ffŽ–®int‘‰ffŽ“pŽ‘ ³¾¬;Ž¡‘ +°gŽŽŽŒ‹ = Šn ý‘ì°x¬581–¯3DLDF-1.1.5.1’ßðTRAÃŽCE‘ÕXVERSION“¬157Ž €n ý•@P­581.‘ ü¬[²LDF‘T2002.11.12.¬]Ž‘ZBÇ!!‘Z¢BUG:–æOccurred“when“I‘Ôtried“to“ nd“an“inš¸ãtersection“of“t˜w˜o“lines“in“the“x-z“plane.Ž¤ This–¶ñcošGde“shouldn't“b˜e“reacš¸ãhed.‘<ûRotating“the“ob‘Ž8jects“90Ÿü^ÿ¶Ž‘OÕ¬around“the“x-axis,‘Öžputting“them“in˜to“the“x-y“plane,Ž¡ xed–UUthe“problem.‘qÇOb¸ãviously›ÿ*ª,“the“case“that“the“ob‘Ž8jects“are“in“the“x-z“plane“already“isn't“handled“propGerly˜.Ž©°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¡‘ +­elseŽ‘0Øáµ=°‘ÿý¬Neither‘÷µ~Ž‘UUqŸÿ·xyŽŽŽ–xæ¬nor‘Oµ~Ž‘UUqŸÿ·xyŽŽŽ“¬is–UUparallel“to“the“y-axis.‘o°µ=Ž¡‘ +°fŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘µ=°‘ÿý¬[²LDF‘T2002.11.12.¬]Ž‘T7Start–UUw¸ãorking“on“ nding“bug“here.‘o°µ=Ž¡‘°fŽ¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"Error® ´after® ´here® ´17Ž‘kÆÜ.\n"Ž’„P°‘DZ ushŽ‘€¬;Ž¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"slope_p_x_y® ´==® ´"Ž‘_Te°‘DZslop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“x‘‰ffŽ“yŽ‘5V°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"slope_q_x_y® ´==® ´"Ž‘_Te°‘DZslop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“x‘‰ffŽ“yŽ‘5 +}°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘°gŽ¡‘­ifŽ‘´ú¬(±slop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“x‘‰ffŽ“yŽ‘2Æ>°6¬=‘DZslop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“x‘‰ffŽ“yŽ‘2Ce¬)‘°fŽ¡‘±x‘‰ffŽ‘®iŽ‘-±¬=‘Ç(±y‘‰ffŽ–®int‘‰ffŽ“qŽ‘ qÊ°‘8à±y‘‰ffŽ–®int‘‰ffŽ“pŽ‘ ³¾¬)µ=¬(±slop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“x‘‰ffŽ“yŽ‘28°‘8à±slop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“x‘‰ffŽ“yŽ‘1µ-¬);Ž¡‘±y‘‰ffŽ‘®iŽ‘-èõ¬=‘DZslop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“x‘‰ffŽ“yŽ‘4ÿ°‘8à±x‘‰ffŽ‘®iŽ‘\$¬+‘8à±y‘‰ffŽ–®int‘‰ffŽ“pŽ‘ ³¾¬;Ž¡‘°gŽ¡‘ +gŽŸ­582.‘ ü¬The–|trace“on“the“x-z“plane.‘åËW‘ÿ*ªe“don't“need“to“do“this“if“w•¸ãe'v“e–|calculated“±z‘‰ffŽ‘®iŽ‘U™¬abGo•¸ãv“e,‘…¬in–|the“case“thatŽ¡the–UUtraces“on“the“x-y“plane“are“coinciden¸ãt.Ž¦°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¡‘ +­ifŽ‘´ù¬(±z‘‰ffŽ‘®iŽ‘$¯°‘Ç´INVALID_REALŽ‘BM\¬)‘UU°fŽ¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Error® ´after® ´here® ´18Ž‘kÆÜ.\n"Ž’„P°‘DZ ushŽ‘€¬;Ž¦‘ +­realŽ‘ ³/±z‘‰ffŽ–®int‘‰ffŽ“pŽ‘A0â¬=‘Ç´INVALID_REALŽ‘BM\¬;‘µ=°‘ÿý¬z-in¸ãtercept–UUofŸü±È“°ŽŽ‘ö<‘þ㎎Ž‘gþ!ŽŽŸN8“µpŸÿ³0Ž‘|sµpŸÿ³1ŽŽŽŽŽ‘^;¬.‘o°µ=Ž¡‘ +­realŽ‘ ³/±z‘‰ffŽ–®int‘‰ffŽ“qŽ‘@îî¬=‘Ç´INVALID_REALŽ‘BM\¬;‘µ=°‘ÿý¬z-in¸ãtercept–UUofŸü±È“°ŽŽ‘e ‘þ㎎Ž‘ÖÏ!ŽŽŸN8“µqŸÿ³0Ž‘|sµqŸÿ³1ŽŽŽŽŽ‘;ݬ.‘o°µ=Ž¦‘ +­ifŽ‘´ù¬(±slop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“x‘‰ffŽ“zŽ‘2Z)°6¬=‘Ç´INVALID_REALŽ‘BM\¬)‘µ=°‘ÿý¬µxŸÿ·pŽ‘fj°6¬=‘Ç0.‘o°µ=Ž¡‘ +°fŽ¡‘±z‘‰ffŽ–®int‘‰ffŽ“pŽ‘4}µ¬=‘DZp0‘‰ffŽ‘®zŽ‘»0°–8à¬(±slop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“x‘‰ffŽ“zŽ‘1Ëñ°“±p0‘‰ffŽ‘®xŽ‘z~¬);Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(±slop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“x‘‰ffŽ“zŽ‘1×P°6¬=‘Ç´INVALID_REALŽ‘BM\¬)‘µ=°‘ÿý¬µxŸÿ·qŽ‘1­°6¬=‘Ç0.‘o°µ=Ž¡‘ +°fŽ¡‘±z‘‰ffŽ–®int‘‰ffŽ“qŽ‘4;Á¬=‘DZq0‘‰ffŽ‘®zŽ‘8W°–8à¬(±slop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“x‘‰ffŽ“zŽ‘1I°“±q0‘‰ffŽ‘®xŽ‘÷¥¬);Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"z_int_p® ´==® ´"Ž‘JTq°‘DZz‘‰ffŽ–®int‘‰ffŽ“pŽ‘#DË°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"z_int_q® ´==® ´"Ž‘JTq°‘DZz‘‰ffŽ–®int‘‰ffŽ“qŽ‘#×°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘ +°gŽŸ­583.‘ ü¬[²LDF‘T2003.06.24.¬]Ž‘Z‹”±x‘‰ffŽ‘®iŽ‘jΫ¬will–X³bGe“equal“to“´INVALID_REALŽ‘BÞ÷¬,‘Y‹if“the“traces“of“the“lines“on“the“x-y“plane“w¸ãereŽ¡colinear.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.06.24.¬]Ž‘Y;Added–UUthis“conditional.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¡‘ +­ifŽ‘´ù¬(±x‘‰ffŽ‘®iŽ‘±|°‘Ç´INVALID_REALŽ–D†<°^›8à:¬(±z‘‰ffŽ–®int‘‰ffŽ“pŽ‘ }³°‘Ç´INVALID_REALŽ“°_˜±z‘‰ffŽ–®int‘‰ffŽ“qŽ‘"tŸ°‘Ç´INVALID_REALŽ‘BM\¬))‘°fŽ¡‘±x‘‰ffŽ‘®iŽ‘#±~¬=‘Ç(±z‘‰ffŽ–®int‘‰ffŽ“qŽ‘­‡°‘8à±z‘‰ffŽ–®int‘‰ffŽ“pŽ‘ï{¬)µ=¬(±slop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“x‘‰ffŽ“zŽ‘1Ëñ°‘8à±slop‘ÿ}'e‘‰ffŽ–®q‘‰ffŽ“x‘‰ffŽ“zŽ‘1I¬);Ž¡‘±y‘‰ffŽ‘®iŽ‘#èô¬=‘DZp0‘‰ffŽ‘®yŽ‘îe¬;Ž¡‘ +°gŽŽŽŒ‹ž û Šn ý‘ì¬158–¯TRAÃŽCE‘ÕXVERSION’ßð3DLDF-1.1.5.1“°x¬584Ž €n ý•@P­584.‘ ü¬In–Ì“the“folloš¸ãwing“case,‘þÖµ~Ž‘êbpŸÿ·xzŽŽŽ‘ãj¬and‘Æ\µ~Ž“qŸÿ·xzŽŽŽ‘4l¬are“bGoth“parallel“to“the“z-axis.‘×€They“ha˜v˜e“the“same“v‘ÿqÇalue“for“µx¬.Ž¤ W‘ÿ*ªe'vš¸ãe–UUset“±x‘‰ffŽ‘®iŽ‘•¬abGo˜v˜e,“so“there's“no“need“to“do“so“here“again.ŽŸ°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¡‘ +­ifŽ‘´ù¬(±z‘‰ffŽ–®int‘‰ffŽ“pŽ‘ }³°‘Ç´INVALID_REALŽ‘D†<°^‘8à±z‘‰ffŽ–®int‘‰ffŽ“qŽ‘"tŸ°‘Ç´INVALID_REALŽ‘BM\¬)‘°fŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Error® ´after® ´here® ´19Ž‘kÆÜ.\n"Ž’„P°‘DZ ushŽ‘€¬;Ž¡‘­ifŽ‘´ú¬(±p0‘‰ffŽ‘®xŽ‘¶°6¬=‘DZq0‘‰ffŽ‘®xŽ‘…ݬ)‘°fŽ¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Error® ´after® ´here® ´20Ž‘kÆÜ.\n"Ž’„P°‘DZ ushŽ‘€¬;Ž¡‘±c‘ÿ}'errŽ‘4ûõ°‘FL´"Lines® ´do® ´not® ´intersŽ‘mFect:\n"Ž’–Ò¯°‘FL´"("Ž‘Ò÷°‘FL±p0‘‰ffŽ‘®xŽ‘Î6°‘FL´",® ´"Ž–ô°‘FL±p0‘‰ffŽ‘®zŽ‘Gа‘FL´",® ´"Ž“°Ž¡‘2±p0‘‰ffŽ‘®zŽ‘I¿Ü°‘Ÿ´")® ´--® ´("Ž‘2Ž°‘Ÿ±p1‘‰ffŽ‘®xŽ‘JÜ°‘Ÿ´",® ´"Ž–š°‘Ÿ±p1‘‰ffŽ‘®zŽ›Äv°‘Ÿ´",® ´"Ž“°‘Ÿ±p1‘‰ffŽ‘®zŽ˜°‘Ÿ´")\n("Ž‘(”°‘Ÿ±q0‘‰ffŽ‘®xŽ‘È°Ž¡‘2´",® ´"Ž‘KÊ °‘C¿±q0‘‰ffŽ‘®zŽ–¿Ý°‘C¿´",® ´"Ž› Ú°‘C¿±q0‘‰ffŽ‘®zŽ“°‘C¿´")® ´--® ´("Ž‘3 ΰ‘C¿±q1‘‰ffŽ‘®xŽ‘FC°‘C¿´",® ´"Ž˜°‘C¿±q1‘‰ffŽ‘®zŽ“°‘C¿±q1‘‰ffŽ‘®zŽ“°Ž¡‘2´")\nReturning® ´INVALIŽ’šÿÉD_BOOL_POINT.\n"Ž’òM°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½´INVALID_BOOL_POINTŽ’ ìï¬;Ž¡‘°gŽ¡‘ gŽ¡‘ -ÂelseŽ‘ .5ifŽ‘+ã-«(Ïz‘‰ffŽ–®int‘‰ffŽ“pŽ‘ }³·‘ÇÝINVALID_REALŽ‘BM\«)‘·fŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ErrorÈ ÝafterÈ ÝhereÈ Ý21Ž‘kÆÜ.\n"Ž’„P·‘ÇÏ ushŽ‘€«;Ž¡‘Ïz‘‰ffŽ‘®iŽ‘#$±«=‘ÇÏp0‘‰ffŽ‘®zŽ‘‚P«;Ž¡‘ -·gŽ¡‘ -ÂelseŽ‘ .5ifŽ‘+ã-«(Ïz‘‰ffŽ–®int‘‰ffŽ“qŽ‘ ;¿·‘ÇÝINVALID_REALŽ‘BM\«)‘·fŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ErrorÈ ÝafterÈ ÝhereÈ Ý22Ž‘kÆÜ.\n"Ž’„P·‘ÇÏ ushŽ‘€«;Ž¡‘Ïz‘‰ffŽ‘®iŽ‘#$±«=‘ÇÏq0‘‰ffŽ‘®zŽ‘ÿw«;Ž¡‘ -·gŽ¡‘ -ÂelseŽ‘!Øà·fŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ErrorÈ ÝafterÈ ÝhereÈ Ý23Ž‘kÆÜ.\n"Ž’„P·‘ÇÏ ushŽ‘€«;Ž¡‘Ïz‘‰ffŽ‘®iŽ‘#$±«=‘ÇÏslop‘ÿ}'e‘‰ffŽ–®p‘‰ffŽ“x‘‰ffŽ“zŽ‘4“ ·‘8àÏx‘‰ffŽ‘®iŽ‘\$«+‘8àÏz‘‰ffŽ–®int‘‰ffŽ“pŽ‘ï{«;Ž¡‘ -·gŽ¡‘ -gŽŽŽŒ‹•?‰ Šn ý‘ì·x«541›­3DLDFPR•ÃŽG’S†TRA“CE‘ÕXVERSION˜«149Ž €n ý•@PÂ541.‘ ü«[¬LDF‘T2002.10.27.«]Ž‘ZÅuIf‘’”Ïx‘‰ffŽ‘®iŽ‘|ø«,‘¡äÏy‘‰ffŽ‘®iŽ‘þ«,›¡äand‘’”Ïz‘‰ffŽ‘®iŽ‘‚¿«are–’”all“v‘ÿqÇalid,˜set“ÏbpŽ‘m ±:ÏptŽ‘ w1«using“those“v‘ÿqÇalues.‘)…Otherwise,˜set“it“toŽ¤ ÝINVALID_POINTŽ‘DÆA«.‘mJIf–Gßthis“ÂP•®9oin“tŽ‘"*«is“on“bGoth“of“the“line“segmen¸ãtsŸü±È“·ŽŽ‘èÆ‘þ㎎Ž‘gþ!ŽŽŸN8“±pŸÿ®0Ž‘|s±pŸÿ®1ŽŽŽŽŽ‘˜¤«andŸü±È“·ŽŽ‘W—‘þ㎎Ž‘ÖÏ!ŽŽŸN8“±qŸÿ®0Ž‘|s±qŸÿ®1ŽŽŽŽŽ‘.g«,›Jset“ÏbpŽ‘"X±:bŽ‘’‰«to“ÏtrueŽ‘ w«,˜otherwise“setŽ¡it–UUto“ÏfalseŽ‘™«.ŽŸ·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"ErrorÈ ÝafterÈ ÝhereÈ Ý24Ž‘kÆÜ.\n"Ž’„P·‘ÇÏ ushŽ‘€«;Ž¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"x_iÈ Ý==È Ý"Ž‘5T}·‘ÇÏx‘‰ffŽ‘®iŽ‘x”·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"y_iÈ Ý==È Ý"Ž‘5T}·‘ÇÏy‘‰ffŽ‘®iŽ‘° -·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"z_iÈ Ý==È Ý"Ž‘5T}·‘ÇÏz‘‰ffŽ‘®iŽ‘ëÇ·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ -·gŽ¡‘ -ÂifŽ‘´ù«(Ïx‘‰ffŽ‘®iŽ‘±|·‘ÇÝINVALID_REALŽ–D†<·_‘8àÏy‘‰ffŽ‘®iŽ‘!Ò·‘ÇÝINVALID_REALŽ“·_‘8àÏz‘‰ffŽ‘®iŽ‘]·‘ÇÝINVALID_REALŽ‘BM\«)‘·fŽ¡‘ÂreturnŽ‘7æ¼ÝINVALID_BOOL_POINTŽ’–ìî«;Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ReturningÈ ÝINVALID_BŽ‘kÆÜOOL_POINT.\n"Ž’³T5·‘ÇÏ ushŽ‘€«;Ž¡‘ -·gŽ¡‘ -ÂelseŽ‘!Øà·fŽ¡‘ÏbpŽ‘Ú{±:ÏptŽ‘ ä±:ÏsetŽ‘ x„«(Ïx‘‰ffŽ‘®iŽ‘ êd±;‘ª¨Ïy‘‰ffŽ‘®iŽ‘Ì‚±;‘ª¨Ïz‘‰ffŽ‘®iŽ‘?«);Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘ÏbpŽ‘Úy±:ÏptŽ‘ ä±:ÏshowŽ‘Šÿ«(Ý"bp.pt"Ž‘%FS«);Ž¡‘ -·gŽ¡‘ -ÂifŽ‘´ù«(ÏbpŽ‘ -Úy±:ÏptŽ– ä±:Ïis‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ›=5O«(Ïp0Ž‘ À±;‘ª¨Ïp1Ž‘ Áh«)±:Ï rstŽ‘|·‘ÇÏfalseŽ‘¯<·_‘8àÏbpŽ‘ Y±:ÏptŽ“±:Ïis‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ˜«(Ïq0Ž‘ “ç±;‘ª¨Ïq1Ž‘ >«)±:Ï rstŽ‘|·‘ÇÏfalseŽ–v\«)‘ÏbpŽ‘Úy±:bŽ‘«=‘ÇÏfalseŽ“«;Ž¡‘ -ÂelseŽ‘!ØàÏbpŽ‘,³Y±:bŽ‘«=‘ÇÏtrueŽ‘‹°«;Ž¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"bp.bÈ Ý==È Ý"Ž‘:”z·‘ÇÏbpŽ‘ ¡‘±:bŽ‘·‘ÇÏend‘‚ØlŽ‘¸Ú«;Ž¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"ExitingÈ ÝPoint::inteŽ‘kÆÜrsection_point().\n"Ž’Ø ·‘ÇÏ ushŽ‘€«;Ž¡‘ -·gŽ¡‘ -ÂreturnŽ‘-æ»ÏbpŽ‘8Á4«;‘qÇ·gŽ©Â542.– üPicture‘Þmfunctions.“«These–ufunctions“m¸ãust“bšGe“de ned“here,‘‹½b˜ecause“they“use“t¸ãyp˜es“whic¸ãh“areŽ¡incompletely–UUde ned“in“Èpictures.web«.Ž¦Â543.– üAssignmen®9t‘ûøopQÇerator.“«!!›2ÇPOR‘ÿ*ªTING‘˜#[¬LDF‘T2002.12.05.«]Ž‘Pã[Mo•¸ãv“ed–˜Shere“from“Èpictures.web«.˜See“thatŽ¡ le–UUfor“explanation.Ž©·h–ª¨«De ne‘UUÂPictureŽ‘,F·«functions‘@­219“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙPictureŽ‘I™ê«::Ž‘P((ÂopQÇeratorŽ‘{¾Ý«=Ž’ƒ…û(ÂconstŽ‘*¢PictureŽ‘G«&Ž‘Nã"±pŽ‘Së"«)Ž¡‘ 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-ÂPictureŽ‘0œ«::‘ÂPictureŽ‘&œ«(ÂconstŽ‘*¢PictureŽ‘G«&Ž‘Nã"±pŽ‘Së"«)Ž¡‘ -:‘qÇÏdo‘‰ffŽ‘®lab‘ÿ}'elsŽ‘*­ª«(ÏtrueŽ‘Ę«)‘UU·fŽŽŽŒ‹–Jz Šn ý‘ì«150›­COPY‘ÕXCONSTR•ÃŽUCTOR’‡Z3DLDFPR“G˜·x«544Ž €n ý•@P‘·Ž‘ÏthisŽ‘,²Ñ«=‘DZpŽ‘Ï«;Ž¤ ‘ -·gŽ©Â545.– üCom®9bining‘ÕTPictures.“«[¬LDF‘T2002.04.17.«]Ž‘Zˆ6Added–UUthis“function.ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.10.29.«]Ž‘Y;Made‘UU±pŽ‘ ²ªÂconstŽ‘)ÝL«and–UU xed“bugs“that“cš¸ãhanged“±pŽ‘ ²ª«(see“bGelo˜w).Ž¡‘ -[¬LDF‘T2002.10.29.«]Ž‘Yi‘BUG‘¶’FIX:–¶«Noš¸ãw,‘ϱpŽ‘×:Ïtr‘ÿ}'ansformŽ‘/iì«is“applied“to“·Ž‘¶¬«(Ïshap‘ÿ}'esŽ‘:Ïb‘ÿ}'ackŽ‘üë(‘ª¨)),‘Ïpreviously“it“w˜as“appliedŽ¡to‘UU·Ž‘UVŽ‘ UWÏiterŽ‘ U«,–UUwhicš¸ãh“w˜as“not“what“I“w˜an˜ted.Ž¡‘ -[¬LDF‘T2002.10.29.«]Ž‘X¤BUG‘ñFIX:–ñ"Noš¸ãw,‘,±pŽ‘ ,:Ïtr‘ÿ}'ansformŽ‘.¤c«is“applied“to“·Ž‘ñ#«(Ïlab‘ÿ}'elsŽ‘Tð±:Ïb‘ÿ}'ackŽ‘üë(‘ª¨)‘þŸ±~ŽŽ‘ÏptŽ‘ äž«),‘,previously“it“w˜as“appliedŽ¡to‘UU·Ž‘UV«((·Ž‘ÏiterŽ‘Êÿ«)‘þŸ±~ŽŽ‘ÏptŽ‘ äž«),–UUwhicš¸ãh“is“not“what“I“w˜an˜ted.Ž¡‘ -[¬LDF‘T2002.10.29.«]Ž‘Y;BUG–UUFIX:“No¸ãw,“±pŽ‘]U:Ïtr‘ÿ}'ansformŽ‘+³A±:Ïr‘ÿ}'esetŽ‘Æ·«(‘ª¨)“is“no“longer“called.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«De ne‘UUÂPictureŽ‘,F·«functions‘@­219“·i‘Ç«+·Ž¤ ‘ -Âv®9oidŽ‘"ýÙPictureŽ‘I™ê«::Ž‘P((ÂopQÇeratorŽ‘{¾Ý«+=ŽŽŽ’‹M(ÂconstŽ‘*¢PictureŽ‘G«&Ž‘Nã"±pŽ‘Së"«)Ž¡‘ -·fŽ¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂShapQÇeŽ‘"Ab·Ž‘'Aci‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W«=‘DZpŽ–Ï:Ïshap‘ÿ}'esŽ›:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);‘ÿýÏiterŽ‘’·6«=‘DZpŽ“:Ïshap‘ÿ}'esŽ˜±:ÏendŽ‘ಫ(‘ª¨);‘ÿýÏiterŽ‘JûŸÿ®+‘ÿ+ŽŽ‘"«)‘·fŽ¡‘Ïshap‘ÿ}'esŽ‘::Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«((·Ž‘ÏiterŽ‘Êÿ«)‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®c‘ÿ}'opyŽ‘(õ«(‘ª¨));Ž¡¡‘(±=·‘Ü<«[¬LDF‘T2002.10.29.«]Ž‘SÀµNormally‘ÿ*ª,‘8ºÏtr‘ÿ}'ansformŽ‘2«in–1”a“ÂPictureŽ‘+ÿ5«is“applied“to“its“ÂShapQÇesŽ‘)Øq«when“it's“output,Ž¡‘2ho•¸ãw“ev“er,‘›µit›¢m“ust˜bGe˜done˜no“w˜for˜the˜copies˜of˜the˜ÂShapQÇesŽ‘*«from˜ÂPictureŽ‘,·Q±pŽ‘5Ló«that˜are˜copiedŽ¡‘2onš¸ãto‘=î·Ž‘=ïÏthisŽ‘)¥«,‘BœbGecause‘=î±pŽ‘Eî:Ïtr‘ÿ}'ansformŽ‘.ñ/«is–=îonly“kno˜wn“within“±pŽ‘Eî«;‘iúthe“ÂShapQÇesŽ‘)ñ%«don't“\kno˜w"“abGout“it.‘¢·±=Ž¡‘·Ž‘#«(Ïshap‘ÿ}'esŽ‘:Ïb‘ÿ}'ackŽ‘üë(‘ª¨))‘Ç·«=ŽŽ‘UO±pŽ‘]O:Ïtr‘ÿ}'ansformŽ‘+³A«;Ž¡‘·gŽ¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂLabQÇelŽ‘–¸·Ž‘$–¹i‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W«=‘DZpŽ–Ï:Ïlab‘ÿ}'elsŽ›Tð±:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);‘ÿýÏiterŽ‘’·6«=‘DZpŽ“:Ïlab‘ÿ}'elsŽ˜±:ÏendŽ‘ಫ(‘ª¨);‘ÿýÏiterŽ‘JûŸÿ®+‘ÿ+ŽŽ‘"«)‘·fŽ¡‘Ïlab‘ÿ}'elsŽ‘6Tó±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«((·Ž‘ÏiterŽ‘Êÿ«)‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®c‘ÿ}'opyŽ‘(õ«(‘ª¨));Ž¡¡‘·Ž‘#«(Ïlab‘ÿ}'elsŽ‘Tð±:Ïb‘ÿ}'ackŽ‘üë(‘ª¨)‘þŸ±~ŽŽ‘ÏptŽ‘ 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+[²LDF‘T2002.10.29.¬]Ž‘Y;BUG–UUFIX:“No¸ãw,“µpŽ‘]U:±tr‘ÿ}'ansformŽ‘+³Aµ:±r‘ÿ}'esetŽ‘Æ·¬(‘ª¨)“is“no“longer“called.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬De ne‘UU­PictureŽ‘,F·¬functions‘@¯264“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘"ýÙPictureŽ‘I™ê¬::Ž‘P((­opQÇeratorŽ‘{¾Ý¬+=ŽŽŽ’‹M(­constŽ‘*¢PictureŽ‘G¬&Ž‘Nã"µpŽ‘Së"¬)Ž¡‘ 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-[¬LDF‘T2003.05.16.«]Ž‘XCChanged‘e]Âb•QÇo“olŽ‘ËÏdo‘‰ffŽ‘®sortŽ‘=•í«to‘e]ÂconstŽ‘ unsignedŽ‘NçshortŽ‘kÁÈÏsort‘‰ffŽ‘®valueŽ’—«â«.‘!ÊAbGout–e]to“add“ÂnamespaceŽŽ¡SortingŽ‘(¿›«with–UUconstanš¸ãts“for“di eren˜t“w˜a˜ys“of“sorting,“i.e.,“\no“sort",“\nearest-last",“or“\furthest- rst".Ž¤ŸüÈ„`ÕÁGŽŽ¦Â548.‘ üF‘ÿ -«oQÇcus‘ÕTargumen®9t.Ž¡·h–ª¨«De ne‘UUÂPictureŽ‘,F·«functions‘@­219“·i‘Ç«+·Ž¤ ‘ -Âv®9oidŽ‘#ð9PictureŽ‘JŒJ«::‘ÏoutputŽ‘D«(ÂconstŽ‘F‘ÿ -«oQÇcusŽ‘@Z«&Ž‘H!!±fŽ‘N;‘ª¨ÂconstŽ‘ ǪunsignedŽ‘QñshortŽ‘p®Ïpr‘ÿ}'ojŽ’ƒ¡Þ±;‘ª¨ÂrealŽ‘P6ÏfactorŽ‘4T±;‘ª¨ÂconstŽŽ¡‘2unsignedŽ‘b“ÙshortŽ’€»BÏsort‘‰ffŽ‘®valueŽ’¬¥\±;‘ª¨ÂconstŽ‘ 2b•QÇo“olŽ‘:0<Ïdo‘‰ffŽ‘®warningsŽ‘pdþ±;‘ª¨ÂconstŽ‘ 2realŽ‘7BÏmin‘‰ffŽ–®x‘‰ffŽ“pr‘ÿ}'ojŽ‘gR±;‘ª¨ÂconstŽ‘ 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ushŽ‘€«;Ž¡‘·g‘±=·‘ÿý«Checš¸ãk–UUwhether“the“Âv®9ectorŽ‘&TòÏshap‘ÿ}'esŽ‘F˜Ð«has“an˜ything“in“it.‘qÇIf“it“doGesn't,“return.‘o·±=Ž¡‘ÂifŽ‘)´û«(Ïshap‘ÿ}'esŽ‘:ÏsizeŽ›\«(‘ª¨)–Ç·“«0Ž‘ ÿù·^‘8àÏlab‘ÿ}'elsŽ‘б:ÏsizeŽ˜«(‘ª¨)“·“«0Ž‘Ç)‘·fŽ¡‘(ÂifŽ‘3´ü«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"PictureÈ ÝisÈ Ýempty.È ÝRŽ‘kÆÜeturning.\n"Ž’®8·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘H‘i«;Ž¡‘·gŽŽŽŒ‹˜nè Šn ý‘ì«152›ÂF®9OCUS‘ÕX­AR•ÃŽGUMENT’XE3DLDFPR“G˜·x«549Ž €n ý•@PÂ549.‘ ü«[¬LDF‘T2002.09.17.«]Ž‘ZF1Some‘PÂShapQÇesŽ‘)›é«maš¸ãy–Pconsist“of“other“ÂShapQÇesŽ‘&ˆ™«,‘ „and“not“ha˜v˜e“an“ÏoutputŽ‘ "«(‘ª®)“function“ofŽ¤ their–Mªoš¸ãwn,‘O3so“w˜e“m˜ust“extract“their“con˜ten˜ts“recursiv˜ely“un˜til“w˜e“get“to“ÂShapQÇesŽ‘*«that“ha˜v˜e“one.‘o9So“far,‘O3onlyŽ¡ÂP•®9oin“tŽ‘šH«,‘UUÂP®9athŽ‘湫,–UUand“ÂSolidŽ‘ («ha•¸ãv“e‘UUÏoutputŽ‘ d•«(‘ª®)–UUfunctions,“and“all“other“ÂShapQÇesŽ‘*ó«reduce“to“ÂP®9athsŽ‘#ÅJ«or“ÂSolidsŽ‘!\h«.Ž¡‘ -[¬LDF‘T2002.09.17.«]Ž‘Y5~Ïextr‘ÿ}'actŽ‘w÷í«(‘ª®)›‚˜c•¸ãhec“ks˜that˜all˜of˜the˜ÂP•®9oin“tsŽ‘'(´«con“tained˜in˜the˜ÂShapQÇeŽ‘%ñ=«can˜bGe˜pro‘Ž8jected˜withŽ¡the‘ÆïÂF‘ÿ -«oQÇcusŽ‘"ƒ*«that–Æïis“bšGeing“used.‘BPIf“an¸ãy“of“them“cannot“b˜e,‘ãjthen“Ïextr‘ÿ}'actŽ‘!‰^«(‘ª®)“returns“an“empt¸ãy“Âv®9ectorŽ‘%8&«of“ÂShapQÇesŽ‘&<8«.Ž¡This– )means“that“anš¸ãy“ÂShapQÇeŽ‘$þ_«m˜ust“bGe“en˜tirely“pro‘Ž8jectable;‘"partial“ÂShapQÇesŽ‘)‡›«will“not“bšGe“output.‘Xcproblem,‘eto˜o.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.01.05.«]Ž‘Y;MošGdi ed–UUthe“T‘þU>ŸÓVEŽ‘ãxXŽ‘Gtext“ab˜o•¸ãv“e–UUto“accounš¸ãt“for“the“fact“that“I'v˜e“added“ÂSolidŽ‘Ó,«.Ž¡‘ -[¬LDF‘T2003.01.05.«]Ž‘Z_ BUG‘¬aFIX:›¬ºMo•¸ãv“ed˜the˜co•Gde˜that˜causes˜Ïtr‘ÿ}'ansformŽ‘5 µ«to˜b“e˜applied˜to˜the˜elemen¸ãts˜ofŽ¡Ïshap‘ÿ}'esŽ‘.›œõThis–cºis“no¸ãw“done“Ïb–ÿ}'efor“e‘$«the‘cºÏextr“emesŽ‘-Ø«are–cºset.˜The“w•¸ãa“y–cºit“wš¸ãas“bGefore“didn't“w˜ork“prop•Gerly‘ÿ*ª,‘gSb“ecauseŽ¡Ïextr‘ÿ}'actŽ‘Âo«(‘ª®)–W -used“the“unš¸ãtransformed“v‘ÿqÇalues“to“decide“whether“a“ÂShapQÇeŽ‘%š!«w˜as“pro‘Ž8jectable.‘våIn“order“to“do“this,‘WwIŽ¡had–UUto“mak¸ãe“Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Iu4«(‘ª®)“a“ÂShapQÇeŽ‘%–·«function.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«De ne‘UUÂPictureŽ‘,F·«functions‘@­219“·i‘Ç«+·Ž¤ ‘ -Âv®9ectorŽ‘)ªI·hÂShapQÇeŽ‘"Ab·Ž‘'Aci‘UU±vŽ‘Š«;Ž¡‘ -Âv®9ectorŽ‘)ªI·hÂShapQÇeŽ‘"Ab·Ž‘'Aci‘UUÏelementsŽ‘*;P«;Ž¤‘ -Âv®9ectorŽ‘)ªI·hÂShapQÇeŽ‘"Ab·Ž‘'Aci‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘:d5«;Ž¡‘ -Âb•QÇo“olŽ‘#¡gÏdo‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘`³«=‘Ç·:Ïtr‘ÿ}'ansformŽ‘+³A±:Ïis‘‰ffŽ‘®identityŽ‘-2¢«(‘ª¨);Ž¡‘ -ÝDEBUGŽ‘'r«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¤ ‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘ÂifŽ‘´ú«(Ïdo‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘9š4«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"ApplyingÈ Ýtransform.Ž‘kÆÜ\n"Ž‘| ;«;Ž¡‘Ïtr‘ÿ}'ansformŽ‘I³D±:ÏshowŽ‘Šÿ«(Ý"transform:"Ž‘?†D«);Ž¡‘·gŽ¡‘ÂelseŽ‘+ØáÏc‘ÿ}'outŽ‘Aù0·‘ÇÝ"NotÈ ÝapplyingÈ ÝtransfŽ‘kÆÜorm.\n"Ž’‘ /«;Ž¡‘ -·gŽ¡‘ -ÂforŽ‘臫(ÏiterŽ‘’«=‘ÇÏshap‘ÿ}'esŽ–µ¡±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏshap‘ÿ}'esŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘ÂifŽ‘´ú«(Ïdo‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘9š4«)‘·fŽ¡‘«(·Ž‘Ž‘ -ÏiterŽ‘Ë«)‘Ç·«=ŽŽ‘UOÏtr‘ÿ}'ansformŽ‘>«;Ž¡‘·gŽ¡‘±vŽ‘û׫=‘Ç(·Ž‘ÏiterŽ‘Êÿ«)‘þŸ±~ŽŽ‘Ïextr‘ÿ}'actŽ‘"Âp«(±fŽ‘øæ;‘ª¨Ïpr‘ÿ}'ojŽ‘žk±;‘ª¨ÏfactorŽ‘®†«);Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÿ9·^‘8à±vŽ‘m:ÏsizeŽ‘\«(‘ª¨)–Ç·“«0Ž‘Ç)Ž¡‘Ïc‘ÿ}'errŽ‘3|Á·‘ÇÝ"WARNING!È ÝInÈ ÝPictureŽ‘kÆÜ::output():\n"Ž’¸”2·‘ÇÝ"extract()È ÝreturnedÈ Ž‘kÆÜÝanÈ ÝemptyÈ Ývector.È Ý"Ž’Í”&·Ž¡‘2Ý"Continuing.\n"Ž’„ X·‘ÇÏ ushŽ‘€«;Ž¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂShapQÇeŽ‘"Ab·Ž‘'Aci‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7±iŽ‘/ÒC«=‘DZvŽ–ûÕ:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿý±iŽ‘ 9 ·6«=‘DZvŽ“:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘G±iŽ‘¹«)‘·fŽ¡‘ÏelementsŽ‘Dåþ±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(·Ž‘±iŽ‘qõ«);Ž¡‘·gŽ¡‘ +The–1†simple“painš¸ãter's“algorithm“implemen˜ted“here“for“surface“hiding“fails“for“­ShapQÇesŽ‘)ØU¬where“one“­ShapQÇeŽ‘%O¬isŽ¡partly–çÒin“fron¸ãt“of“and“partly“bšGehind“another.‘)?F‘ÿ*ªor“these“cases,‘ qit“will“b˜e“necessary“to“ nd“the“in¸ãtersectionŽ¡pGoinš¸ãts–u8and“divide“the“­ShapQÇesŽ‘*_¹¬in˜to“parts.‘ÑqTO‘u0DO:“Implemen˜t“a“routine“for“dividing“up“­ShapQÇesŽ‘&ê¬.‘ÑqThis“willŽ¡not–UUbšGe“done“so˜on!Ž¡‘ +±do‘‰ffŽ‘®warningsŽ‘@4ì:‘¬¢Sometimes–òÂwš¸ãe'll“w˜an˜t“use“the“±min‘‰ffŽ–®x‘‰ffŽ“pr‘ÿ}'ojŽ‘3Ĭ,‘±max‘‰ffŽ–®x‘‰ffŽ“pr‘ÿ}'ojŽ‘4û¬,–etc.,“argumen˜ts–òÂto“cut“o “parts“ofŽ¡the–Bÿimage,‘Fªor“wš¸ãe'll“delibGerately“place“the“­F‘ÿ +«oQÇcusŽ‘#{J¬where“it“w˜on't“bGe“able“to“\see"“part“of“the“image.‘kªIn“theseŽ¡cases,–UUit“will“bGe“annoš¸ãying“to“see“the“w˜arnings.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.09.21.¬]Ž‘Y;Added–UUthe“argumen¸ãts“±do‘‰ffŽ‘®sortŽ‘&Äo¬and“±do‘‰ffŽ‘®warningsŽ‘9Š¬.Ž¡‘ +[²LDF‘T2003.05.16.¬]Ž‘XCChanged‘e]­b•QÇo“olŽ‘˱do‘‰ffŽ‘®sortŽ‘=•í¬to‘e]­constŽ‘ unsignedŽ‘NçshortŽ‘kÁȱsort‘‰ffŽ‘®valueŽ’—«â¬.‘!ÊAbGout–e]to“add“­namespaceŽŽ¡SortingŽ‘(¿›¬with–UUconstanš¸ãts“for“di eren˜t“w˜a˜ys“of“sorting,“i.e.,“\no“sort",“\nearest-last",“or“\furthest- rst".Ž¤ŸüÈ„`ÕÁGŽŽ¦­592.‘ üF‘ÿ +«oQÇcus‘ÕTargumen®9t.Ž¡°h–ª¨¬De ne‘UU­PictureŽ‘,F·¬functions‘@¯264“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘#ð9PictureŽ‘JŒJ¬::‘±outputŽ‘D¬(­constŽ‘F‘ÿ +«oQÇcusŽ‘@Z¬&Ž‘H!!µfŽ‘N;‘ª¨­constŽ‘ ǪunsignedŽ‘QñshortŽ‘p®±pr‘ÿ}'ojŽ’ƒ¡Þµ;‘ª¨­realŽ‘P6±factorŽ‘4Tµ;‘ª¨­constŽŽ¡‘2unsignedŽ‘b“ÙshortŽ’€»B±sort‘‰ffŽ‘®valueŽ’¬¥\µ;‘ª¨­constŽ‘ 2b•QÇo“olŽ‘:0<±do‘‰ffŽ‘®warningsŽ‘pdþµ;‘ª¨­constŽ‘ 2realŽ‘7B±min‘‰ffŽ–®x‘‰ffŽ“pr‘ÿ}'ojŽ‘gRµ;‘ª¨­constŽ‘ 2realŽŽ¡‘2±max‘‰ffŽ–®x‘‰ffŽ“pr‘ÿ}'ojŽ‘bàøµ;‘ª¨­constŽ‘×vrealŽ‘6ŒÐ±min‘‰ffŽ–®y‘‰ffŽ“pr‘ÿ}'ojŽ‘f•”µ;‘ª¨­constŽ‘×vrealŽ‘6ŒÐ±max‘‰ffŽ–®y‘‰ffŽ“pr‘ÿ}'ojŽ‘g¥9µ;‘ª¨­constŽ‘×vrealŽ‘6ŒÐ±min‘‰ffŽ–®z‘‰ffŽ“pr‘ÿ}'ojŽ‘eÑQµ;‘ª¨­constŽ‘×vrealŽŽ¡‘2±max‘‰ffŽ–®z‘‰ffŽ“pr‘ÿ}'ojŽ‘bT+¬)°f‘UU­b•QÇo“olŽ‘ö»´DEBUGŽ‘:„,¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¡‘­usingŽ‘ S°‘Ç´"Entering® ´Picture::oŽ‘kÆÜutput(const® ´Focus&® ´.Ž’ÔÆ ..).\n"Ž’üÔ °‘DZ ushŽ‘€¬;Ž¡‘(±c‘ÿ}'outŽ‘> S°‘Ç´"min_x_proj® ´==® ´"Ž‘Zh°‘DZmin‘‰ffŽ–®x‘‰ffŽ“pr‘ÿ}'ojŽ‘5_~°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘(±c‘ÿ}'outŽ‘> S°‘Ç´"max_x_proj® ´==® ´"Ž‘Zh°‘DZmax‘‰ffŽ–®x‘‰ffŽ“pr‘ÿ}'ojŽ‘6o#°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘(±c‘ÿ}'outŽ‘> S°‘Ç´"min_y_proj® ´==® ´"Ž‘Zh°‘DZmin‘‰ffŽ–®y‘‰ffŽ“pr‘ÿ}'ojŽ‘5–ô°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘(±c‘ÿ}'outŽ‘> S°‘Ç´"max_y_proj® ´==® ´"Ž‘Zh°‘DZmax‘‰ffŽ–®y‘‰ffŽ“pr‘ÿ}'ojŽ‘6¦™°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘°g‘µ=°‘ÿý¬Checš¸ãk–UUwhether“the“­v®9ectorŽ‘&Tò±shap‘ÿ}'esŽ‘F˜Ð¬has“an˜ything“in“it.‘qÇIf“it“doGesn't,“return.‘o°µ=Ž¡‘­ifŽ‘)´û¬(±shap‘ÿ}'esŽ‘:±sizeŽ›\¬(‘ª¨)–Ç°“¬0Ž‘ ÿù°^‘8à±lab‘ÿ}'elsŽ‘е:±sizeŽ˜¬(‘ª¨)“°“¬0Ž‘Ç)‘°fŽ¡‘(­ifŽ‘3´ü¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Picture® ´is® ´empty.® ´RŽ‘kÆÜeturning.\n"Ž’®8°‘DZ ushŽ‘€¬;Ž¡‘(­returnŽ‘H‘i¬;Ž¡‘°gŽŽŽŒ‹¢ ^û Šn ý‘ì¬162–­F®9OCUS‘ÕX¯ARÃŽGUMENT’üä¯3DLDF-1.1.5.1“°x¬593Ž €n ý•@P­593.‘ ü¬[²LDF‘T2002.09.17.¬]Ž‘ZF1Some‘P­ShapQÇesŽ‘)›é¬maš¸ãy–Pconsist“of“other“­ShapQÇesŽ‘&ˆ™¬,‘ „and“not“ha˜v˜e“an“±outputŽ‘ "¬(‘ª®)“function“ofŽ¤ their–Mªoš¸ãwn,‘O3so“w˜e“m˜ust“extract“their“con˜ten˜ts“recursiv˜ely“un˜til“w˜e“get“to“­ShapQÇesŽ‘*¬that“ha˜v˜e“one.‘o9So“far,‘O3onlyŽ¡­P•®9oin“tŽ‘šH¬,‘UU­P®9athŽ‘湬,–UUand“­SolidŽ‘ (¬ha•¸ãv“e‘UU±outputŽ‘ d•¬(‘ª®)–UUfunctions,“and“all“other“­ShapQÇesŽ‘*ó¬reduce“to“­P®9athsŽ‘#ÅJ¬or“­SolidsŽ‘!\h¬.Ž¡‘ +[²LDF‘T2002.09.17.¬]Ž‘Y5~±extr‘ÿ}'actŽ‘w÷í¬(‘ª®)›‚˜c•¸ãhec“ks˜that˜all˜of˜the˜­P•®9oin“tsŽ‘'(´¬con“tained˜in˜the˜­ShapQÇeŽ‘%ñ=¬can˜bGe˜pro‘Ž8jected˜withŽ¡the‘Æï­F‘ÿ +«oQÇcusŽ‘"ƒ*¬that–Æïis“bšGeing“used.‘BPIf“an¸ãy“of“them“cannot“b˜e,‘ãjthen“±extr‘ÿ}'actŽ‘!‰^¬(‘ª®)“returns“an“empt¸ãy“­v®9ectorŽ‘%8&¬of“­ShapQÇesŽ‘&<8¬.Ž¡This– )means“that“anš¸ãy“­ShapQÇeŽ‘$þ_¬m˜ust“bGe“en˜tirely“pro‘Ž8jectable;‘"partial“­ShapQÇesŽ‘)‡›¬will“not“bšGe“output.‘Xcproblem,‘eto˜o.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.01.05.¬]Ž‘Y;MošGdi ed–UUthe“T‘þU>ŸÓVEŽ‘ãxXŽ‘Gtext“ab˜o•¸ãv“e–UUto“accounš¸ãt“for“the“fact“that“I'v˜e“added“­SolidŽ‘Ó,¬.Ž¡‘ 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Âc®9harŽ‘¬ËÏaxisŽ‘/j«data–—×memš¸ãbGer.‘9MIt“indicates“the“axis“to“whic˜h“Ïp‘ÿ}'ositionŽ‘*t«should“bGe“transformed“to“when“it's“put“inŽ¡standard–Ü’pGosition.‘~This“determines“whicš¸ãh“plane“the“image“is“pro‘Ž8jected“on˜to.‘~If“ÏaxisŽ‘Á×·‘¨}Ý'z'Ž‘Ën«(the“default),Ž¡the–UUimage“is“pro‘Ž8jected“on¸ãto“the“x-y“plane,“if“ÏaxisŽ‘Y5·‘ÇÝ'x'Ž‘ w«,“the“z-y“plane,“if“Ý'y'Ž‘›´«,“the“x-z“plane.Ž¡‘ -A¸ãt–nthis“time,›´JI'm“not“adding“the“routines“that“will“do“this,˜whicš¸ãh“will“en˜tail“c˜hanging“Ïtr‘ÿ}'ansformŽ‘4s«andŽ¡pGossibly‘z¨Ïp‘ÿ}'erspŽ‘<í«,‘ƒýI'm–z¨just“adding“ÏaxisŽ‘·p«.‘áÀI‘zžmš¸ãust“also“add“a“function“for“c˜hanging“axis“without“c˜hanging“an˜y“ofŽ¡the–UUother“data“mem¸ãbGers.‘qÇTO“DO:“Add“these“routines!!Ž¡‘ -[¬LDF‘T2002.09.14.«]Ž‘Y;Added‘UUÂT‘ÿ -«ransformŽ‘;'Ïp‘ÿ}'erspŽ‘Ràl«.‘qÇIt's–UUneeded“bGecause“I“need“to“get“the“±zŽ‘ ÁÈ«v‘ÿqÇalue“of“theŽ¡Ïworld‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘R e«after–øgthe“transformation“that“puts“the“ÂF‘ÿ -«oQÇcusŽ‘&æ«in¸ãto“standard“pšGosition,‘a+but“b˜efore“theŽ¡p•Gersp“ectiv¸ãe–Úütransformation“is“pšGerformed.‘¼This“±zŽ‘ Í«v‘ÿqÇalue“can“b˜e“used“in“an“algorithm“for“surfaces“hiding.‘¼IfŽ¡this–GHwš¸ãere“not“the“case,‘JI‘GDcould“com˜bine“the“transformations,‘JbGecause“matrix“m˜ultiplication“is“assoGciativ˜e“(itŽ¡is–UUnot,“ho•¸ãw“ev“er,›UUcomm“utativ“e,˜except˜with˜spGecial˜matrices).Ž¡‘ -[¬LDF‘T2002.09.11.«]Ž‘YÅzAdded‘”ÂclassŽ‘°$F‘ÿ -«oQÇcusŽ‘@¸«and–”the“follo¸ãwing“constructors:‘ìDThe“default“constructor“with“noŽ¡argumenš¸ãts,‘»’the–•!one“with“t˜w˜o“ÂP•®9oin“tŽ‘ ÄŠ«argumen˜ts“and“a“ÂrealŽ‘ˆÏar‘ÿ}'gumentŽ‘B&«,‘»’and“the“one“with“sev˜en“ÂrealŽ‘ˆ«argumen˜ts.Ž¦‘ -ÂformatŽ‘3c(ÏF‘ÿ;¼o‘ÿ}'cusŽ‘UxintŽŽ¦·h–ª¨«De ne‘UUÂclassŽ‘5¦F‘ÿ -«oQÇcusŽ‘?jö­556“·i‘ÇŽ¡‘ -ÂclassŽ‘$àRF‘ÿ -«oQÇcusŽ‘E*ó·fŽ¡‘ÂP•®9oin“tŽ‘2ïŸÏp‘ÿ}'ositionŽ‘V3ö«;Ž¡‘ÂP•®9oin“tŽ‘2ïŸÏdir–ÿ}'e“ctionŽ‘Yè«;Ž¡‘ÂP•®9oin“tŽ‘2ïŸÏupŽ‘>Ž]«;Ž¡‘ÂrealŽ‘*³0Ïdistanc‘ÿ}'eŽ‘Nù-«;Ž¡‘ÂrealŽ‘*³0ÏangleŽ‘Bsƒ«;Ž¡‘Âc®9harŽ‘-jKÏaxisŽ‘?§«;Ž¡‘ÂT‘ÿ -«ransformŽ‘KÈÔÏtr‘ÿ}'ansformŽ‘w|«;Ž¡‘ÂT‘ÿ -«ransformŽ‘KÈÔÏp‘ÿ}'erspŽ‘c‹«;Ž¦‘ -ÂpublicŽ‘)=Ö«:‘·h–ª¨«Declare‘UUÂF‘ÿ -«oQÇcusŽ‘#Ÿö«functions‘@­558“·iŽ¡‘ -g«;ŽŸ ­This–ÕXcoÈ ÝtoÈ ÝcŽ‘kÆÜontinue.\n\n"Ž’³T5·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¦‘ÂT‘ÿ -«ransformŽ‘KÜ/Ïunalign‘‰ffŽ‘®upŽ‘~«=‘çZÏtr‘ÿ}'ansformŽ‘.š›±:ÏinverseŽ‘ ‡«(‘ª¨);‘ª¯±=·‘X«Use–h°the“pGositiv¸ãe“y-axis“for“the“\up"“direction,Ž¡‘(if‘UUÏaxisŽ›Y5·‘ÇÝ'x'Ž‘bÌ«or‘UUÝ'z'Ž‘›´«,–UUand“the“pGositiv¸ãe“x-axis“if“ÏaxisŽ˜·‘ÇÝ'y'Ž‘ w«.‘o·±=Ž¦‘ÂifŽ‘´ú«(ÏaxisŽ‘à·‘ÇÝ'z'Ž‘FW·_‘8àÏaxisŽ‘<À·‘ÇÝ'x'Ž‘ w«)‘ÏupŽ‘ž¾±:ÏsetŽ‘ x„«(0Ž‘±;‘ª¨«1Ž–ª©±;‘ª¨«0Ž“);Ž¡‘ÂelseŽ‘+ØáÏupŽ‘7wŸ±:ÏsetŽ‘ x„«(1Ž‘±;‘ª¨«0Ž–ª©±;‘ª¨«0Ž“);Ž¡‘ÂifŽ‘´ú«(ÏangleŽ‘‡k·6«=‘Ç0Ž‘Ç)‘·fŽ¡‘ÂifŽ‘)´û«(ÏaxisŽ‘à·‘ÇÝ'z'Ž‘ w«)‘ÏupŽ‘eÖ·«=ŽŽ‘"ô Ïtr‘ÿ}'ansformŽ‘N§N±:Ïr‘ÿ}'otateŽ‘o>«(0Ž‘±;‘ª¨«0Ž‘ª©±;‘ª¨·Ž‘ qÆÏangleŽ‘!2«);Ž¡‘ÂelseŽ‘4.7ifŽ‘?ã/«(ÏaxisŽ‘à·‘ÇÝ'x'Ž‘ w«)‘ÏupŽ‘eÖ·«=ŽŽ‘"ô Ïtr‘ÿ}'ansformŽ‘N§N±:Ïr‘ÿ}'otateŽ‘o>«(·Ž‘ÇÏangleŽ‘‡q«);Ž¡‘ÂelseŽ‘4.7ifŽ‘?ã/«(ÏaxisŽ‘à·‘ÇÝ'y'Ž‘ w«)‘ÏupŽ‘eÖ·«=ŽŽ‘"ô Ïtr‘ÿ}'ansformŽ‘N§N±:Ïr‘ÿ}'otateŽ‘o>«(0Ž‘±;‘ª¨·Ž‘ qÆÏangleŽ‘!2«);Ž¡‘ÂelseŽ‘5Øâ·fŽ¡‘(Ïc‘ÿ}'errŽ‘@hú·‘³PÝ"ERROR!È ÝInÈ ÝFocus::FoŽ‘n³cus():\n"Ž’¤,±·‘³PÝ"ThisÈ Ýcan'tÈ Ýhappen!È Ž‘n³Ý\ŽŽ¡‘<È ÝaxisÈ ÝhasÈ ÝinvalidÈ ÝvaŽ’¤ÿÊlue:È Ý"Ž’È­·‘ŠÏaxisŽ‘Qâ·‘ŠÏend‘‚ØlŽ‘Ü·‘ŠÝ"RotatingÈ ÝaroundÈ Ýz-aŽ‘lŠQxis.\n"Ž’•[1·Ž¡‘<Ý"EnterÈ ÝÈ ÝtoÈ ÝtŽ’¤ÿÊryÈ ÝtoÈ Ýcontinue.\n"Ž’Í·‘ÇÏ ushŽ‘€«;Ž¡‘(ÏupŽ‘6eÚ·«=ŽŽ‘EôÏtr‘ÿ}'ansformŽ‘q§R±:Ïr‘ÿ}'otateŽ‘o>«(0Ž‘±;‘ª¨«0Ž‘ª©±;‘ª¨·Ž‘ qÆÏangleŽ‘!2«);Ž¡‘·gŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘ÏupŽ‘ž¾±:ÏshowŽ‘Šÿ«(Ý"upÈ ÝafterÈ Ýrotation"Ž‘dF/«);Ž¡‘·gŽ¡‘ÏupŽ‘"eØ·«=ŽŽ‘1ôÏunalign‘‰ffŽ‘®upŽ‘a2›«;Ž¡‘ÏupŽ‘žÀ±:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨);Ž¡‘Ïtr‘ÿ}'ansformŽ‘?³C±:ÏshiftŽ‘}«(0Ž‘±;‘ª¨«0Ž‘ª©±;‘ª¨·Ž‘ qÆÏdistanc‘ÿ}'eŽ‘-·Ã«);Ž¡‘Ïp‘ÿ}'erspŽ‘+ÂG±:Ïset‘‰ffŽ‘®elementŽ‘2 ×«(2Ž‘±;‘ª¨«2Ž–ª©±;‘ª¨«0Ž“);Ž¡‘Ïp‘ÿ}'erspŽ‘+ÂG±:Ïset‘‰ffŽ‘®elementŽ‘2 ×«(2Ž‘±;‘ª¨«3Ž–ª©±;‘ª¨«1Ž“±=Ïdistanc‘ÿ}'eŽ‘$Eý«);Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ExitingÈ ÝFocus()È Ý(7È Ž‘kÆÜÝrealÈ Ýarguments).\n"Ž’ÒÔ#·‘ÇÏ 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-«oQÇcusŽ‘#Ÿö«functions‘@­558“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"¬«ÏsetŽ‘0%/«(ÂconstŽ‘ÙtP•®9oin“tŽ‘"‹«&Ž‘Eé©ÏdirŽ‘Så±;‘ª¨ÂconstŽ‘„realŽ‘5æÏdistŽ‘Fò‰±;‘ª¨ÂconstŽ‘„realŽ‘5æÏangŽ‘IgÚ«=‘Ç0±:«0ŽŽ‘Ž7±;‘ª¨Âc®9harŽ‘ÃÃÏaxŽ‘)ö«=‘ÇÝ'z'Ž‘ w«);ŽŸÂ568.Ž¦·h–ª¨«De ne‘UUÂF‘ÿ -«oQÇcusŽ‘#Ÿö«functions‘@­561“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙF‘ÿ -«oQÇcusŽ‘@ó)«::‘ÏsetŽ‘xˆ«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]Ïp‘ÿ}'osŽ‘T±;‘ª¨ÂconstŽ‘ÕJP•®9oin“tŽ‘>Äç«&Ž‘FŒÏdirŽ‘T‡a±;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆxÏdistŽ‘G”å±;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆxÏangŽ‘GC±;‘ª¨Âc®9harŽ‘ñÏaxŽ‘&Œ «)Ž¡‘ -·fŽ¡‘ÂF‘ÿ -«oQÇcusŽ‘4J£±fŽ‘:C‰«(Ïp‘ÿ}'osŽ‘!±:Ïget‘‰ffŽ‘®xŽ‘Žg«(–ª¨)±;“Ïp‘ÿ}'osŽ›Ìj±:Ïget‘‰ffŽ‘®yŽ‘t«(“)±;“Ïp‘ÿ}'osŽ˜±:Ïget‘‰ffŽ‘®zŽ‘«(“)±;“ÏdirŽ›¦±:Ïget‘‰ffŽ‘®xŽ‘Žg«(“)±;“ÏdirŽ˜±:Ïget‘‰ffŽ‘®yŽ‘t«(“)±;“ÏdirŽ˜±:Ïget‘‰ffŽ‘®zŽ‘«(“)±;“ÏdistŽ‘·±;“ÏangŽ‘eN±;“ÏaxŽ‘ !ë);Ž¦‘·Ž‘ÏthisŽ‘,²Ñ«=‘DZfŽ‘¿þ«;Ž¡‘ -·gŽŸÂ569.– üAssignmen®9t.“«[¬LDF‘T2002.10.13.«]Ž‘Z­ŸAdded–z¾this“function.‘âNo¸ãw“using“it“in“all“but“the“ 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qÆÏangleŽ‘!2«);Ž¡‘·gŽ¡‘gŽ¡‘ÏupŽ‘"eØ·«=ŽŽ‘1ôÏunalign‘‰ffŽ‘®upŽ‘a2›«;Ž¡‘ÏupŽ‘žÀ±:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨);Ž¡‘Ïtr‘ÿ}'ansformŽ‘?³C±:ÏshiftŽ‘}«(0Ž‘±;‘ª¨«0Ž‘ª©±;‘ª¨·Ž‘ qÆÏdistanc‘ÿ}'eŽ‘-·Ã«);Ž¡‘Ïp‘ÿ}'erspŽ‘+ÂG±:Ïset‘‰ffŽ‘®elementŽ‘2 ×«(2Ž‘±;‘ª¨«2Ž–ª©±;‘ª¨«0Ž“);Ž¡‘Ïp‘ÿ}'erspŽ‘+ÂG±:Ïset‘‰ffŽ‘®elementŽ‘2 ×«(2Ž‘±;‘ª¨«3Ž–ª©±;‘ª¨«1Ž“±=Ïdistanc‘ÿ}'eŽ‘$Eý«);Ž¡‘ -·gŽŸÂ573.‘ üSho®9w.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.09.17.«]Ž‘Y;Added–UUthis“function.Ž¡‘ -[¬LDF‘T2003.07.09.«]Ž‘Y;Made–UUthe“argumen¸ãts“ÂconstŽ‘*¢«.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂF‘ÿ -«oQÇcusŽ‘#Ÿö«functions‘@­558“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙÏshowŽ‘9ˆØ«(ÂconstŽ‘*¢stringŽ‘?OïÏtext‘‰ffŽ‘®strŽ‘bÞK«=‘ÇÝ"Focus:"Ž‘-Mh±;‘ª¨ÂconstŽ‘ÕJb•QÇo“olŽ‘9v°Ïshow‘‰ffŽ‘®tr‘ÿ}'ansformsŽ’„¸2«=‘ÇÏfalseŽ‘v\«)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹¡¹ Šn ý‘ì·x«574›­3DLDFPR•ÃŽG’H’FSHO“W˜«161Ž €n ý•@PÂ574.ŽŸ·h–ª¨«De ne‘UUÂF‘ÿ -«oQÇcusŽ‘#Ÿö«functions‘@­561“·i‘Ç«+·Ž¤ ‘ -Âv®9oidŽ‘"ýÙF‘ÿ 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-:‘qÇÏp‘ÿ}'ositionŽ‘'¶«(±lŽ–.::Ïp‘ÿ}'ositionŽ‘#DW«)±;‘ÿýÏdir–ÿ}'e“ctionŽ‘+øî«(±lŽ“:Ïdir–ÿ}'e“ctionŽ‘&øñ«)‘UU·fŽ¡‘Ïp‘ÿ}'ositionŽ‘7DY±:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨);Ž¡‘Ïdir–ÿ}'e“ctionŽ‘:øó±:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨);Ž¡‘ -·gŽŸÂ599.‘ üAssignmen®9t.Ž¦·h–ª¨«Declare‘UUÂLineŽ‘-«functions‘@­599“·i‘ÇŽ¡‘ -Âv®9oidŽ‘"ýÙopQÇeratorŽ‘N”Ž«=Ž‘V[¬(ÂconstŽ‘*¢LineŽ‘7Øz«&Ž‘?Ÿ˜±lŽ‘BÍÒ«);Ž¤ ­See–ÕXalso“sections“602,“604,“and“608.Ž¡This–ÕXco‹Û«&Ž‘FRùÏpp0Ž‘W†)±;‘ª¨ÂconstŽ‘ ŽP•®9oin“tŽ‘@6ƒ«&Ž‘Gý¡Ïpp1Ž‘Y0ѱ;‘ª¨ÂconstŽ‘ ŽP•®9oin“tŽŽ¡‘2«&Ž‘9Ç#Ïqq0Ž‘Iô¡±;‘ª¨ÂconstŽ‘ÕJP•®9oin“tŽ‘>Äç«&Ž‘FŒÏqq1Ž‘V¹ƒ«)Ž¡‘ -·f‘±=·‘ÿý«ST–ÿ*ªAR“T–UUHERE.“DEBUGGING.“[¬LDF‘T2003.06.24.«]Ž‘P²â·±=Ž¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¤‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EnteringÈ ÝPoint::intŽ‘kÆÜersection_point()\n"Ž’ÕM«;Ž¡‘ÂLineŽ‘-­ÚÏl‘‰ffŽ‘®pŽ‘<ò«=‘ÇÏpp0Ž‘úH±:Ïget‘‰ffŽ‘®lineŽ‘!O«(Ïpp1Ž‘30«);Ž© 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ushŽ‘€«;ŽŽŽŒ‹ªp‘ Šn ý‘ì«170–­GET‘ÕXDIST‘ÿJªANCE’ üp3DLDFPRÃŽG“·x«606Ž €n ý•@PÂ606.‘ ü«Lines›UUha•¸ãv“e˜an˜in“tersection.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ -«[¬LDF‘T2003.08.27.«]Ž‘X¥ëCommen¸ãted-out–óthe“declarations“of“Ïv‘‰ffŽ‘®xŽ‘•Z«,‘®Ïv‘‰ffŽ‘®yŽ‘Ž²«,›®and“Ïv‘‰ffŽ‘®zŽ‘ô«,˜since“they“are“not“used.‘QI‘òìha•¸ãv“en'tŽ¡deleted–UUthem,“in“case“I“need“them“someda¸ãy‘ÿ*ª.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«De ne‘UUÂLineŽ‘-«functions‘@­600“·i‘Ç«+·Ž¤ ‘ -ÂifŽ‘´ù«(ÏbrpŽ‘î±:rŽ‘‘,<‘ÇÂP•®9oin“tŽ‘ad«::Ž‘%ï¢ÏepsilonŽ‘E^¦«(‘ª¨))‘·fŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"LinesÈ ÝhaveÈ ÝanÈ ÝinterŽ‘kÆÜsection.\n"Ž’¨Ô;·‘ÇÏ ushŽ‘€«;Ž¡‘ÏbrpŽ‘#ð±:rŽ‘‘,«=‘Ç0Ž‘Ç;Ž¡‘ÏbrpŽ‘#ð±:bŽ‘«=‘ÇÏtrueŽ‘‹°«;Ž©‘ÂrealŽ‘*³0Ïa‘‰ffŽ‘®xŽ‘<Ÿv«=‘ÇÏp‘ÿ}'ositionŽ‘& o±:Ïget‘‰ffŽ‘®xŽ‘Žg«(‘ª¨);Ž¡‘ÂrealŽ‘*³0Ïa‘‰ffŽ‘®yŽ‘<…%«=‘ÇÏp‘ÿ}'ositionŽ‘& o±:Ïget‘‰ffŽ‘®yŽ‘t«(‘ª¨);Ž¡‘ÂrealŽ‘*³0Ïa‘‰ffŽ‘®zŽ‘<«=‘ÇÏp‘ÿ}'ositionŽ‘& 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­«=‘DZlŽ‘õR:Ïdir–ÿ}'e“ctionŽ‘&øñ±:Ïget‘‰ffŽ‘®yŽ‘t«(‘ª¨);Ž¡‘ÂrealŽ‘*³0Ïw‘‰ffŽ‘®zŽ‘=¡˜«=‘DZlŽ‘õR:Ïdir–ÿ}'e“ctionŽ‘&øñ±:Ïget‘‰ffŽ‘®zŽ‘«(‘ª¨);Ž¡‘ÂrealŽ‘*³0Ïu‘‰ffŽ‘®xŽ‘<àâ«=‘ÇÏnormalŽ‘#б:Ïget‘‰ffŽ‘®xŽ‘Žg«(‘ª¨);Ž¡‘ÂrealŽ‘*³0Ïu‘‰ffŽ‘®yŽ‘<Æ‘«=‘ÇÏnormalŽ‘#б:Ïget‘‰ffŽ‘®yŽ‘t«(‘ª¨);Ž¡‘ÂrealŽ‘*³0Ïu‘‰ffŽ‘®zŽ‘aZ«&Ž‘F(x±pŽ‘K0x«);ŽŽŽŒ‹®¥) Šn ý‘ì«174›­COPY‘ÕXCONSTR•ÃŽUCTOR’‡Z3DLDFPR“G˜·x«622Ž €n ý•@PÂ622.Ž©·h–ª¨«De ne‘UUÂPlaneŽ‘#Œ «functions‘@­620“·i‘Ç«+·Ž¤ ‘ -ÂPlaneŽ‘'áh«::‘ÂPlaneŽ‘ág«(ÂconstŽ‘*¢PlaneŽ‘>aZ«&Ž‘F(x±pŽ‘K0x«)Ž¡‘ -·fŽ¡‘Ž‘ÏthisŽ‘,²Ñ«=‘DZpŽ‘Ï«;Ž¡‘ÂreturnŽ‘4‘g«;Ž¡‘ -·gŽŸÂ623.‘ üP•®9oin“t‘ÕTargumen“ts.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.06.03.«]Ž‘Y_¾Changed–¬Øthis“function.‘xPBUG‘¬ÁFIX:“Ïdistanc‘ÿ}'eŽ‘+Ÿ­«is“no¸ãw“calculated,‘¸instead“of“bGeing“passedŽ¡as–UUan“argumenš¸ãt.‘qÇÏnormalŽ‘(Ô«is“no˜w“made“a“unit“v˜ector.Ž¡‘ 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à«::Ž‘t˜ÂopQÇeratorŽ’ .Ó«=Ž’§õñ(ÂconstŽ‘*¢PlaneŽ‘>aZ«&Ž‘F(x±pŽ‘K0x«)Ž¡‘ -·fŽ¡‘ÂifŽ‘´ú«(ÏthisŽ‘²Î·‘Ç«&Ž‘ -Ž6±pŽ‘–6«)‘±=·‘ÿý«Makš¸ãe–UUsure“it's“not“self-assignmen˜t.‘qÇ[¬LDF‘T2003.06.06.«]Ž‘U$©·±=Ž¡‘ÂreturnŽ‘Aæ½·Ž‘Fæ¾ÏthisŽ‘WÒt«;Ž¡‘Ïp‘ÿ}'ointŽ‘-õ¦«=‘DZpŽ‘Ï:Ïp‘ÿ}'ointŽ‘.Œ«;Ž¡‘ÏnormalŽ‘7Ò«=‘DZpŽ‘Ï:ÏnormalŽ‘ V¸«;Ž¡‘Ïdistanc‘ÿ}'eŽ‘; «=‘DZpŽ‘Ï:Ïdistanc‘ÿ}'eŽ‘$Eý«;Ž¡‘ÂreturnŽ‘7æ¼±pŽ‘<;Ž¡‘ -·gŽŸÂ627.‘ üComparing‘ÕTPlanes.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.06.06.«]Ž‘Y;Added–UUthis“section.Ž¦ŸüÈ„`ÕÁGŽŽŸÂ628.‘ üEqualit®9y‘ÿ +[²LDF‘T2002.04.25.¬]Ž‘X,Added–kFfolloš¸ãwing“conditional.‘#ÂSometimes“it's“irritating“to“ha˜v˜e“the“labGels“when“a“­PictureŽŽ¡¬is–UUcopied“and“transformed,“and“bGoth“the“original“and“the“transformed“v¸ãersions“are“output.Ž¦°h–ª¨¬De ne‘UU­PictureŽ‘,F·¬functions‘@¯264“°i‘Ǭ+°Ž¡‘ +­ifŽ‘´ù¬(±do‘‰ffŽ‘®lab‘ÿ}'elsŽ‘)û°‘DZtrueŽ‘‹°¬)‘°fŽ¡‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­LabQÇelŽ‘–¸°Ž‘$–¹i‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7µiŽ‘/ÒC¬=‘DZlab‘ÿ}'elsŽ–µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿýµiŽ‘ 9 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+±tr‘ÿ}'ansformŽ‘5³Bµ:±r‘ÿ}'esetŽ‘Æ·¬(‘ª¨);Ž¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Exiting® ´Picture::ouŽ‘kÆÜtput(const® ´Focus&® ´..Ž’ÔÆ .).\n"Ž’÷”°‘DZ ushŽ‘€¬;Ž¡‘ +°gŽŽŽŒ‹¥ ”É Šn ý‘ì°x¬598›¯3DLDF-1.1.5.1’íûNO–ÕX­F®9OCUS“¯ARÃŽGUMENT˜¬165Ž €n ý•@P­598.‘ üNo–ÕTF‘ÿ +«oQÇcus“argumen®9t.Ž©°h–ª¨¬De ne‘UU­PictureŽ‘,F·¬functions‘@¯264“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘#úUPictureŽ‘J–f¬::‘±outputŽ‘D¬(­constŽ‘'unsignedŽ‘PZ¨shortŽ‘o!DZpr‘ÿ}'ojŽ’‚Šµ;‘ª¨­realŽ‘ZR±factorŽ‘4^0µ;‘ª¨­constŽ‘ ÑÆunsignedŽ‘RPshortŽŽ¡‘2±sort‘‰ffŽ‘®valueŽ‘]êµ;‘ª¨­constŽ‘ 3b•QÇo“olŽ‘:‚±do‘‰ffŽ‘®warningsŽ‘p=Dµ;‘ª¨­constŽ‘ 3realŽ‘7J±min‘‰ffŽ–®x‘‰ffŽ“pr‘ÿ}'ojŽ‘f똵;‘ª¨­constŽ‘ 3realŽ‘7J±max‘‰ffŽ–®x‘‰ffŽ“pr‘ÿ}'ojŽ‘gû=µ;‘ª¨­constŽŽ¡‘2realŽ‘H³3±min‘‰ffŽ–®y‘‰ffŽ“pr‘ÿ}'ojŽ‘x»÷µ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±max‘‰ffŽ–®y‘‰ffŽ“pr‘ÿ}'ojŽ‘g áµ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±min‘‰ffŽ–®z‘‰ffŽ“pr‘ÿ}'ojŽ‘eÌùµ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±max‘‰ffŽ–®z‘‰ffŽ“pr‘ÿ}'ojŽ‘fÜž¬)Ž¡‘ +°fŽ¡‘±outputŽ‘1B¬(±default‘‰ffŽ‘®fo‘ÿ}'cusŽ‘7Ýþµ;‘ª¨±pr‘ÿ}'ojŽ‘žkµ;‘ª¨±factorŽ‘®†µ;‘ª¨±sort‘‰ffŽ‘®valueŽ‘-”µ;‘ª¨±do‘‰ffŽ‘®warningsŽ‘7ßjµ;‘ª¨±min‘‰ffŽ–®x‘‰ffŽ“pr‘ÿ}'ojŽ‘1{öµ;‘ª¨±max‘‰ffŽ–®x‘‰ffŽ“pr‘ÿ}'ojŽ‘2‹›µ;‘ª¨±min‘‰ffŽ–®y‘‰ffŽ“pr‘ÿ}'ojŽ‘1³lµ;Ž¡‘(±max‘‰ffŽ–®y‘‰ffŽ“pr‘ÿ}'ojŽ‘Ymµ;‘ª¨±min‘‰ffŽ–®z‘‰ffŽ“pr‘ÿ}'ojŽ‘0ï)µ;‘ª¨±max‘‰ffŽ–®z‘‰ffŽ“pr‘ÿ}'ojŽ‘1þά);Ž¡‘ +°gŽ¤­599.‘ üF‘ÿ +«oQÇcus.Ž¡600.› üF‘ÿ +«oQÇcus–ôvclass“de nition.˜¬[²LDF‘T2002.09.18.¬]Ž‘YĬMade‘‘Ë­F‘ÿ +«oQÇcusŽ‘"â¬a‘‘Ë­classŽ‘®’¬(it–‘Ëw¸ãas“formerly“a“­structŽ‘ Üm¬).‘0™AddedŽ¤ ­c®9harŽ‘¬Ë±axisŽ‘/j¬data–—×memš¸ãbGer.‘9MIt“indicates“the“axis“to“whic˜h“±p‘ÿ}'ositionŽ‘*t¬should“bGe“transformed“to“when“it's“put“inŽ¡standard–Ü’pGosition.‘~This“determines“whicš¸ãh“plane“the“image“is“pro‘Ž8jected“on˜to.‘~If“±axisŽ‘Á×°‘¨}´'z'Ž‘Ën¬(the“default),Ž¡the–UUimage“is“pro‘Ž8jected“on¸ãto“the“x-y“plane,“if“±axisŽ‘Y5°‘Ç´'x'Ž‘ w¬,“the“z-y“plane,“if“´'y'Ž‘›´¬,“the“x-z“plane.Ž¡‘ +A¸ãt–nthis“time,›´JI'm“not“adding“the“routines“that“will“do“this,˜whicš¸ãh“will“en˜tail“c˜hanging“±tr‘ÿ}'ansformŽ‘4s¬andŽ¡pGossibly‘z¨±p‘ÿ}'erspŽ‘<í¬,‘ƒýI'm–z¨just“adding“±axisŽ‘·p¬.‘áÀI‘zžmš¸ãust“also“add“a“function“for“c˜hanging“axis“without“c˜hanging“an˜y“ofŽ¡the–UUother“data“mem¸ãbGers.‘qÇTO“DO:“Add“these“routines!!Ž¡‘ +[²LDF‘T2002.09.14.¬]Ž‘Y;Added‘UU­T‘ÿ +«ransformŽ‘;'±p‘ÿ}'erspŽ‘Ràl¬.‘qÇIt's–UUneeded“bGecause“I“need“to“get“the“µzŽ‘ ÁȬv‘ÿqÇalue“of“theŽ¡±world‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘R e¬after–øgthe“transformation“that“puts“the“­F‘ÿ +«oQÇcusŽ‘&æ¬in¸ãto“standard“pšGosition,‘a+but“b˜efore“theŽ¡p•Gersp“ectiv¸ãe–Úütransformation“is“pšGerformed.‘¼This“µzŽ‘ ͬv‘ÿqÇalue“can“b˜e“used“in“an“algorithm“for“surfaces“hiding.‘¼IfŽ¡this–GHwš¸ãere“not“the“case,‘JI‘GDcould“com˜bine“the“transformations,‘JbGecause“matrix“m˜ultiplication“is“assoGciativ˜e“(itŽ¡is–UUnot,“ho•¸ãw“ev“er,›UUcomm“utativ“e,˜except˜with˜spGecial˜matrices).Ž¡‘ +[²LDF‘T2002.09.11.¬]Ž‘YÅzAdded‘”­classŽ‘°$F‘ÿ +«oQÇcusŽ‘@¸¬and–”the“follo¸ãwing“constructors:‘ìDThe“default“constructor“with“noŽ¡argumenš¸ãts,‘»’the–•!one“with“t˜w˜o“­P•®9oin“tŽ‘ ÄŠ¬argumen˜ts“and“a“­realŽ‘ˆ±ar‘ÿ}'gumentŽ‘B&¬,‘»’and“the“one“with“sev˜en“­realŽ‘ˆ¬argumen˜ts.Ž¦‘ +­formatŽ‘3c(±F‘ÿ;¼o‘ÿ}'cusŽ‘UxintŽŽ¦°h–ª¨¬De ne‘UU­classŽ‘5¦F‘ÿ +«oQÇcusŽ‘?jö¯600“°i‘ÇŽ¡‘ +­classŽ‘$àRF‘ÿ +«oQÇcusŽ‘E*ó°fŽ¡‘­P•®9oin“tŽ‘2p‘ÿ}'ositionŽ‘V3ö¬;Ž¡‘­P•®9oin“tŽ‘2dir–ÿ}'e“ctionŽ‘Yè¬;Ž¡‘­P•®9oin“tŽ‘2upŽ‘>Ž]¬;Ž¡‘­realŽ‘*³0±distanc‘ÿ}'eŽ‘Nù-¬;Ž¡‘­realŽ‘*³0±angleŽ‘Bsƒ¬;Ž¡‘­c®9harŽ‘-jK±axisŽ‘?§¬;Ž¡‘­T‘ÿ +«ransformŽ‘KÈÔ±tr‘ÿ}'ansformŽ‘w|¬;Ž¡‘­T‘ÿ +«ransformŽ‘KÈÔ±p‘ÿ}'erspŽ‘c‹¬;Ž¦‘ +­publicŽ‘)=Ö¬:‘°h–ª¨¬Declare‘UU­F‘ÿ +«oQÇcusŽ‘#Ÿö¬functions‘@¯602“°iŽ¡‘ +g¬;ŽŸ ¯This–ÕXco® ´to® ´cŽ‘kÆÜontinue.\n\n"Ž’³T5°‘DZ ushŽ‘€¬;Ž¡‘°gŽ¦‘­T‘ÿ +«ransformŽ‘KÜ/±unalign‘‰ffŽ‘®upŽ‘~¬=‘çZ±tr‘ÿ}'ansformŽ‘.š›µ:±inverseŽ‘ ‡¬(‘ª¨);‘ª¯µ=°‘X¬Use–h°the“pGositiv¸ãe“y-axis“for“the“\up"“direction,Ž¡‘(if‘UU±axisŽ›Y5°‘Ç´'x'Ž‘b̬or‘UU´'z'Ž‘›´¬,–UUand“the“pGositiv¸ãe“x-axis“if“±axisŽ˜°‘Ç´'y'Ž‘ w¬.‘o°µ=Ž¦‘­ifŽ‘´ú¬(±axisŽ‘à°‘Ç´'z'Ž‘FW°_‘8à±axisŽ‘<À°‘Ç´'x'Ž‘ w¬)‘±upŽ‘ž¾µ:±setŽ‘ x„¬(0Ž‘µ;‘ª¨¬1Ž–ª©µ;‘ª¨¬0Ž“);Ž¡‘­elseŽ‘+Øá±upŽ‘7wŸµ:±setŽ‘ x„¬(1Ž‘µ;‘ª¨¬0Ž–ª©µ;‘ª¨¬0Ž“);Ž¡‘­ifŽ‘´ú¬(±angleŽ‘‡k°6¬=‘Ç0Ž‘Ç)‘°fŽ¡‘­ifŽ‘)´û¬(±axisŽ‘à°‘Ç´'z'Ž‘ w¬)‘±upŽ‘eÖ°¬=ŽŽ‘"ô ±tr‘ÿ}'ansformŽ‘N§Nµ:±r‘ÿ}'otateŽ‘o>¬(0Ž‘µ;‘ª¨¬0Ž‘ª©µ;‘ª¨°Ž‘ qƱangleŽ‘!2¬);Ž¡‘­elseŽ‘4.7ifŽ‘?ã/¬(±axisŽ‘à°‘Ç´'x'Ž‘ w¬)‘±upŽ‘eÖ°¬=ŽŽ‘"ô ±tr‘ÿ}'ansformŽ‘N§Nµ:±r‘ÿ}'otateŽ‘o>¬(°Ž‘DZangleŽ‘‡q¬);Ž¡‘­elseŽ‘4.7ifŽ‘?ã/¬(±axisŽ‘à°‘Ç´'y'Ž‘ w¬)‘±upŽ‘eÖ°¬=ŽŽ‘"ô ±tr‘ÿ}'ansformŽ‘N§Nµ:±r‘ÿ}'otateŽ‘o>¬(0Ž‘µ;‘ª¨°Ž‘ qƱangleŽ‘!2¬);Ž¡‘­elseŽ‘5Øâ°fŽ¡‘(±c‘ÿ}'errŽ‘@hú°‘³P´"ERROR!® ´In® ´Focus::FoŽ‘n³cus():\n"Ž’¤,±°‘³P´"This® ´can't® ´happen!® Ž‘n³´\ŽŽ¡‘<® ´axis® ´has® ´invalid® ´vaŽ’¤ÿÊlue:® ´"Ž’È­°‘Š±axisŽ‘Qâ°‘Š±end‘‚ØlŽ‘Ü°‘Š´"Rotating® ´around® ´z-aŽ‘lŠQxis.\n"Ž’•[1°Ž¡‘<´"Enter® ´® ´to® ´tŽ’¤ÿÊry® ´to® ´continue.\n"Ž’Í°‘DZ ushŽ‘€¬;Ž¡‘(±upŽ‘6eÚ°¬=ŽŽ‘Eô±tr‘ÿ}'ansformŽ‘q§Rµ:±r‘ÿ}'otateŽ‘o>¬(0Ž‘µ;‘ª¨¬0Ž‘ª©µ;‘ª¨°Ž‘ qƱangleŽ‘!2¬);Ž¡‘°gŽ¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±upŽ‘ž¾µ:±showŽ‘Šÿ¬(´"up® ´after® ´rotation"Ž‘dF/¬);Ž¡‘°gŽ¡‘±upŽ‘"eØ°¬=ŽŽ‘1ô±unalign‘‰ffŽ‘®upŽ‘a2›¬;Ž¡‘±upŽ‘žÀµ:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¡‘±tr‘ÿ}'ansformŽ‘?³Cµ:±shiftŽ‘}¬(0Ž‘µ;‘ª¨¬0Ž‘ª©µ;‘ª¨°Ž‘ qƱdistanc‘ÿ}'eŽ‘-·Ã¬);Ž¡‘±p‘ÿ}'erspŽ‘+ÂGµ:±set‘‰ffŽ‘®elementŽ‘2 ×¬(2Ž‘µ;‘ª¨¬2Ž–ª©µ;‘ª¨¬0Ž“);Ž¡‘±p‘ÿ}'erspŽ‘+ÂGµ:±set‘‰ffŽ‘®elementŽ‘2 ×¬(2Ž‘µ;‘ª¨¬3Ž–ª©µ;‘ª¨¬1Ž“µ=±distanc‘ÿ}'eŽ‘$Eý¬);Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Exiting® ´Focus()® ´(7® Ž‘kÆÜ´real® ´arguments).\n"Ž’ÒÔ#°‘DZ ushŽ‘€¬;Ž¡‘ +°gŽŸ ¯See–ÕXalso“sections“607,“610,“612,“614,“616,“618,“626,“and“629.ŽŽŽŒ‹¨ ÍV Šn ý‘ì¬168–¯CONSTRÃŽUCTOR’Îä3DLDF-1.1.5.1“°x¬605Ž €n ý•@P¯This–ÕXcoÄç¬&Ž‘FŒ±dirŽ‘T‡aµ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±distŽ‘G”åµ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±angŽ‘J +6¬=‘Ç0µ:¬0ŽŽ‘Ž7µ;‘ª¨­c®9harŽ‘ñ±axŽ‘)S$¬=‘Ç´'z'Ž‘ w¬);Ž¡­610.Ž¦°h–ª¨¬De ne‘UU­F‘ÿ +«oQÇcusŽ‘#Ÿö¬functions‘@¯605“°i‘Ǭ+°Ž¤ ‘ +­F‘ÿ +«oQÇcusŽ‘'õQ¬::‘­F‘ÿ +«oQÇcusŽ‘õP¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±p‘ÿ}'osŽ‘Tµ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±dirŽ‘T‡aµ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±distŽ‘G”åµ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±angŽ‘GCµ;‘ª¨­c®9harŽ‘ñ±axŽ‘&Œ ¬)Ž¡‘ +°fŽ¡‘­F‘ÿ +«oQÇcusŽ‘4J£µfŽ‘:C‰¬(±p‘ÿ}'osŽ‘!µ:±get‘‰ffŽ‘®xŽ‘Žg¬(–ª¨)µ;“±p‘ÿ}'osŽ›Ìjµ:±get‘‰ffŽ‘®yŽ‘t¬(“)µ;“±p‘ÿ}'osŽ˜µ:±get‘‰ffŽ‘®zŽ‘¬(“)µ;“±dirŽ›¦µ:±get‘‰ffŽ‘®xŽ‘Žg¬(“)µ;“±dirŽ˜µ:±get‘‰ffŽ‘®yŽ‘t¬(“)µ;“±dirŽ˜µ:±get‘‰ffŽ‘®zŽ‘¬(“)µ;“±distŽ‘·µ;“±angŽ‘eNµ;“±axŽ‘ !ì);Ž¦‘°Ž‘±thisŽ‘,²Ñ¬=‘ǵfŽ‘¿þ¬;Ž¡‘ +°gŽŸ­611.– üSetting‘ÕTfunction.“¬[²LDF‘T2002.09.17.¬]Ž‘Zˆ6Added–UUthis“function.Ž¦°h–ª¨¬Declare‘UU­F‘ÿ +«oQÇcusŽ‘#Ÿö¬functions‘@¯602“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"¬«±setŽ‘0%/¬(­constŽ‘ÙtP•®9oin“tŽ‘"‹¬&Ž‘E驱dirŽ‘Såµ;‘ª¨­constŽ‘„realŽ‘5æ±distŽ‘Fò‰µ;‘ª¨­constŽ‘„realŽ‘5æ±angŽ‘IgÚ¬=‘Ç0µ:¬0ŽŽ‘Ž7µ;‘ª¨­c®9harŽ‘ÃñaxŽ‘)ö¬=‘Ç´'z'Ž‘ w¬);ŽŸ­612.Ž¦°h–ª¨¬De ne‘UU­F‘ÿ +«oQÇcusŽ‘#Ÿö¬functions‘@¯605“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙF‘ÿ +«oQÇcusŽ‘@ó)¬::‘±setŽ‘xˆ¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±p‘ÿ}'osŽ‘Tµ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±dirŽ‘T‡aµ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±distŽ‘G”åµ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±angŽ‘GCµ;‘ª¨­c®9harŽ‘ñ±axŽ‘&Œ ¬)Ž¡‘ +°fŽ¡‘­F‘ÿ +«oQÇcusŽ‘4J£µfŽ‘:C‰¬(±p‘ÿ}'osŽ‘!µ:±get‘‰ffŽ‘®xŽ‘Žg¬(–ª¨)µ;“±p‘ÿ}'osŽ›Ìjµ:±get‘‰ffŽ‘®yŽ‘t¬(“)µ;“±p‘ÿ}'osŽ˜µ:±get‘‰ffŽ‘®zŽ‘¬(“)µ;“±dirŽ›¦µ:±get‘‰ffŽ‘®xŽ‘Žg¬(“)µ;“±dirŽ˜µ:±get‘‰ffŽ‘®yŽ‘t¬(“)µ;“±dirŽ˜µ:±get‘‰ffŽ‘®zŽ‘¬(“)µ;“±distŽ‘·µ;“±angŽ‘eNµ;“±axŽ‘ !ì);Ž¦‘°Ž‘±thisŽ‘,²Ñ¬=‘ǵfŽ‘¿þ¬;Ž¡‘ +°gŽŸ­613.– üAssignmen®9t.“¬[²LDF‘T2002.10.13.¬]Ž‘Z­ŸAdded–z¾this“function.‘âNo¸ãw“using“it“in“all“but“the“ rst“of“the“non-Ž¡default–ãžconstructors.‘¢This“sa•¸ãv“es–ãžon“duplicating“coGde“and“reduces“the“probabilitš¸ãy“of“bugs“that“migh˜t“ariseŽ¡from–UUinconsistencies“among“the“constructors“and“setting“functions.Ž¦°h–ª¨¬Declare‘UU­F‘ÿ +«oQÇcusŽ‘#Ÿö¬functions‘@¯602“°i‘Ǭ+°Ž¡‘ +­constŽ‘(*£F‘ÿ +«oQÇcusŽ‘HuD¬&Ž‘PuC¬&Ž‘FuC¬&Ž‘F¬(0Ž‘µ;‘ª¨¬0Ž‘ª©µ;‘ª¨°Ž‘ qƱangleŽ‘!2¬);Ž¡‘­elseŽ‘4.7ifŽ‘?ã/¬(±axisŽ‘à°‘Ç´'x'Ž‘ w¬)‘±upŽ‘eÖ°¬=ŽŽ‘"ô ±tr‘ÿ}'ansformŽ‘N§Nµ:±r‘ÿ}'otateŽ‘o>¬(°Ž‘DZangleŽ‘‡q¬);Ž¡‘­elseŽ‘4.7ifŽ‘?ã/¬(±axisŽ‘à°‘Ç´'y'Ž‘ w¬)‘±upŽ‘eÖ°¬=ŽŽ‘"ô ±tr‘ÿ}'ansformŽ‘N§Nµ:±r‘ÿ}'otateŽ‘o>¬(0Ž‘µ;‘ª¨°Ž‘ qƱangleŽ‘!2¬);Ž¡‘­elseŽ‘5Øâ°fŽ¡‘(±c‘ÿ}'errŽ‘@hú°‘³P´"ERROR!® ´In® ´Focus::FoŽ‘n³cus():\n"Ž’¤,±°‘³P´"This® ´can't® ´happen!® Ž‘n³´\ŽŽ¡‘<® ´axis® ´has® ´invalid® ´vaŽ’¤ÿÊlue:® ´"Ž’È­°‘Š±axisŽ‘Qâ°‘Š±end‘‚ØlŽ‘Ü°‘Š´"Rotating® ´around® ´z-aŽ‘lŠQxis.\n"Ž’•[1°Ž¡‘<´"Enter® ´® ´to® ´tŽ’¤ÿÊry® ´to® ´continue.\n"Ž’Í°‘DZ ushŽ‘€¬;Ž¡‘(±upŽ‘6eÚ°¬=ŽŽ‘Eô±tr‘ÿ}'ansformŽ‘q§Rµ:±r‘ÿ}'otateŽ‘o>¬(0Ž‘µ;‘ª¨¬0Ž‘ª©µ;‘ª¨°Ž‘ qƱangleŽ‘!2¬);Ž¡‘°gŽ¡‘gŽ¡‘±upŽ‘"eØ°¬=ŽŽ‘1ô±unalign‘‰ffŽ‘®upŽ‘a2›¬;Ž¡‘±upŽ‘žÀµ:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¡‘±tr‘ÿ}'ansformŽ‘?³Cµ:±shiftŽ‘}¬(0Ž‘µ;‘ª¨¬0Ž‘ª©µ;‘ª¨°Ž‘ qƱdistanc‘ÿ}'eŽ‘-·Ã¬);Ž¡‘±p‘ÿ}'erspŽ‘+ÂGµ:±set‘‰ffŽ‘®elementŽ‘2 ×¬(2Ž‘µ;‘ª¨¬2Ž–ª©µ;‘ª¨¬0Ž“);Ž¡‘±p‘ÿ}'erspŽ‘+ÂGµ:±set‘‰ffŽ‘®elementŽ‘2 ×¬(2Ž‘µ;‘ª¨¬3Ž–ª©µ;‘ª¨¬1Ž“µ=±distanc‘ÿ}'eŽ‘$Eý¬);Ž¡‘ +°gŽŸ­617.‘ üSho®9w.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.09.17.¬]Ž‘Y;Added–UUthis“function.Ž¡‘ +[²LDF‘T2003.07.09.¬]Ž‘Y;Made–UUthe“argumen¸ãts“­constŽ‘*¢¬.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­F‘ÿ +«oQÇcusŽ‘#Ÿö¬functions‘@¯602“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙ±showŽ‘9ˆØ¬(­constŽ‘*¢stringŽ‘?Oï±text‘‰ffŽ‘®strŽ‘bÞK¬=‘Ç´"Focus:"Ž‘-Mhµ;‘ª¨­constŽ‘ÕJb•QÇo“olŽ‘9v°±show‘‰ffŽ‘®tr‘ÿ}'ansformsŽ’„¸2¬=‘DZfalseŽ‘v\¬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹« ÷æ Šn ý‘ì°x¬618–¯3DLDF-1.1.5.1’@°SHOÃŽW“¬171Ž €n ý•@P­618.ŽŸ°h–ª¨¬De ne‘UU­F‘ÿ +«oQÇcusŽ‘#Ÿö¬functions‘@¯605“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘"ýÙF‘ÿ +«oQÇcusŽ‘@ó)¬::‘±showŽ‘‹¬(­constŽ‘*¢stringŽ‘?Oï±text‘‰ffŽ‘®strŽ‘`3µ;‘ª¨­constŽ‘ÕJb•QÇo“olŽ‘9v°±show‘‰ffŽ‘®tr‘ÿ}'ansformsŽ’ñ¬)‘UU­constŽŽ¡‘ +°fŽ¡‘±c‘ÿ}'outŽ‘* Q°‘DZtext‘‰ffŽ‘®strŽ‘&Ut°‘DZend‘‚ØlŽ‘¸Ú¬;Ž¡‘±p‘ÿ}'ositionŽ‘7DYµ:±showŽ‘Šÿ¬(´"position:"Ž‘:FG¬);Ž¡‘±dir–ÿ}'e“ctionŽ‘:øóµ:±showŽ‘Šÿ¬(´"direction:"Ž‘?†D¬);Ž¡‘±upŽ‘žÀµ:±showŽ‘Šÿ¬(´"up:"Ž‘ÆY¬);Ž¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"distance® ´==® ´"Ž‘O”n°‘DZdistanc‘ÿ}'eŽ‘)Ô-°‘Ç´".® ´"Ž‘Œ°‘Ç´"axis® ´==® ´"Ž‘:”z°‘DZaxisŽ‘Êø°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"angle® ´==® ´"Ž‘?Ôw°‘DZangleŽ‘Nƒ°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘­ifŽ‘´ú¬(±show‘‰ffŽ‘®tr‘ÿ}'ansformsŽ‘KA‚°‘DZtrueŽ‘‹°¬)‘°fŽ¡‘±tr‘ÿ}'ansformŽ‘I³Dµ:±showŽ‘Šÿ¬(´"transform:"Ž‘?†D¬);Ž¡‘±p‘ÿ}'erspŽ‘5ÂHµ:±showŽ‘Šÿ¬(´"persp:"Ž‘*†P¬);Ž¡‘°gŽ¡‘­returnŽ‘4‘g¬;Ž¡‘ +°gŽ©­619.› üReturning–Ö•elemen®9ts“and“information.˜¬[²LDF‘T2002.09.18.¬]Ž‘Z‰MAdded–Vlthis“section.‘u The“functions“inŽ¡this–Ensection“are“noš¸ãw“necessary‘ÿ*ª,‘tsince“I'v˜e“made“­F‘ÿ +«oQÇcusŽ‘%€(¬a“­classŽ‘ ج(it“w˜as“formerly“a“­structŽ‘"¬),‘tand“the“dataŽ¡mem¸ãbGers‘UU­priv‘ÿ\rateŽ‘&ýÓ¬.Ž¦­620.‘ üGet‘ÕTpQÇosition.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.09.18.¬]Ž‘Y;Added–UUthis“function.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­F‘ÿ +«oQÇcusŽ‘#Ÿö¬functions‘@¯602“°i‘Ǭ+°Ž¤ ‘ +­inlineŽ‘)ŠIconstŽ‘G´ëP•®9oin“tŽ‘f¤ˆ¬&Ž‘nk¦±get‘‰ffŽ‘®p‘ÿ}'ositionŽ’¡ã¹¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼±p‘ÿ}'ositionŽ‘[+¬;Ž¡‘ +°gŽ¦­621.‘ üGet‘ÕTdirection.ŽŸŸû9ŸüÈ„`Ö+U‘ 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ushŽ‘€¬;ŽŽŽŒ‹´ aƒ Šn ý‘ì¬180–¯GET‘ÕXDIST‘ÿJªANCE’ˆÚ3DLDF-1.1.5.1“°x¬650Ž €n ý•@P­650.‘ ü¬Lines›UUha•¸ãv“e˜an˜in“tersection.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ +¬[²LDF‘T2003.08.27.¬]Ž‘X¥ëCommen¸ãted-out–óthe“declarations“of“±v‘‰ffŽ‘®xŽ‘•Z¬,‘®±v‘‰ffŽ‘®yŽ‘Ž²¬,›®and“±v‘‰ffŽ‘®zŽ‘ô¬,˜since“they“are“not“used.‘QI‘òìha•¸ãv“en'tŽ¡deleted–UUthem,“in“case“I“need“them“someda¸ãy‘ÿ*ª.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬De ne‘UU­LineŽ‘-¬functions‘@¯644“°i‘Ǭ+°Ž¤ ‘ +­ifŽ‘´ù¬(±brpŽ‘îµ:rŽ‘‘,<‘Ç­P•®9oin“tŽ‘ad¬::Ž‘%epsilonŽ‘E^¦¬(‘ª¨))‘°fŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Lines® ´have® ´an® ´interŽ‘kÆÜsection.\n"Ž’¨Ô;°‘DZ ushŽ‘€¬;Ž¡‘±brpŽ‘#ðµ:rŽ‘‘,¬=‘Ç0Ž‘Ç;Ž¡‘±brpŽ‘#ðµ:bŽ‘¬=‘DZtrueŽ‘‹°¬;Ž©‘­realŽ‘*³0±a‘‰ffŽ‘®xŽ‘<Ÿv¬=‘DZp‘ÿ}'ositionŽ‘& oµ:±get‘‰ffŽ‘®xŽ‘Žg¬(‘ª¨);Ž¡‘­realŽ‘*³0±a‘‰ffŽ‘®yŽ‘<…%¬=‘DZp‘ÿ}'ositionŽ‘& oµ:±get‘‰ffŽ‘®yŽ‘t¬(‘ª¨);Ž¡‘­realŽ‘*³0±a‘‰ffŽ‘®zŽ‘<¬=‘DZp‘ÿ}'ositionŽ‘& 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– Šn ý‘ì¬184–¯COPY‘ÕXCONSTRÃŽUCTOR’ûÄ3DLDF-1.1.5.1“°x¬666Ž €n ý•@P­666.Ž©°h–ª¨¬De ne‘UU­PlaneŽ‘#Œ ¬functions‘@¯664“°i‘Ǭ+°Ž¤ ‘ +­PlaneŽ‘'áh¬::‘­PlaneŽ‘ág¬(­constŽ‘*¢PlaneŽ‘>aZ¬&Ž‘F(xµpŽ‘K0x¬)Ž¡‘ +°fŽ¡‘Ž‘±thisŽ‘,²Ñ¬=‘ǵpŽ‘Ϭ;Ž¡‘­returnŽ‘4‘g¬;Ž¡‘ +°gŽŸ­667.‘ üP•®9oin“t‘ÕTargumen“ts.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.06.03.¬]Ž‘Y_¾Changed–¬Øthis“function.‘xPBUG‘¬ÁFIX:“±distanc‘ÿ}'eŽ‘+Ÿ­¬is“no¸ãw“calculated,‘¸instead“of“bGeing“passedŽ¡as–UUan“argumenš¸ãt.‘qDZnormalŽ‘(Ô¬is“no˜w“made“a“unit“v˜ector.Ž¡‘ +[²LDF‘T2003.06.06.¬]Ž‘YpCChanged,›×_so–½]that“if“±p‘ÿ}'ointŽ‘©F¬or“±normalŽ‘'Ñr¬is“equal“to“´INVALID_POINTŽ‘Hƒž¬,˜the“other“one“is“alsoŽ¡set–UUto“´INVALID_POINTŽ‘H–¬,“and“±distanc‘ÿ}'eŽ‘*ð§¬is“set“to“´INVALID_REALŽ‘BÛ™¬.Ž¡‘ +[²LDF‘T2003.06.06.¬]Ž‘Y Argumenš¸ãts–a%are“no“longer“optional.‘•8I'v˜e“made“this“c˜hange,‘dbGecause“I'v˜e“added“a“defaultŽ¡constructor.Ž¡‘ +[²LDF‘T2003.06.06.¬]Ž‘XùÁAdded–FÛconditional“to“test“for“case“that“±p‘ÿ}'ointŽ‘ug°Ž‘"<…±normalŽ‘B“=¬.‘lôIn“this“case,‘IÀa“w¸ãarning“messageŽ¡is–UUprin¸ãted“to“standard“error,“they“are“bGoth“set“to“´INVALID_POINTŽ‘H–¬,“and“±distanc‘ÿ}'eŽ‘*ð§¬is“set“to“´INVALID_REALŽ‘BÛ™¬.Ž¡‘ +[²LDF‘T2003.06.24.¬]Ž‘Y^^BUG‘«bFIX:›«xF–ÿ*ªormerly“,‘Á´INVALID_PLANEŽ‘L2º¬w¸ãas˜returned,‘Áif˜±p‘ÿ}'ointŽ‘0¬°‘V¨±normalŽ‘#­`¬.‘t1This˜has˜bGeenŽ¡c¸ãhanged,›so–„Pthat“´INVALID_PLANEŽ‘KÎá¬is“returned,˜if“±normalŽ‘&ðl°‘d±originŽ‘ …¬.‘þ·There“is,˜of“course,˜no“reason“wh¸ãy“±p‘ÿ}'ointŽŽ¡¬shouldn't–UUbGe“equal“to“±normalŽ‘#¬ ¬.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­PlaneŽ‘#Œ ¬functions‘@¯663“°i‘Ǭ+°Ž¡‘ +­PlaneŽ‘&ád¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié];‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒµnŽ‘LŒŸ¬);ŽŽŽŒ‹¹ š· Šn ý‘ì°x¬668–¯3DLDF-1.1.5.1’ùh8­POINT‘ÕX¯ARÃŽGUMENTS“¬185Ž €n ý•@P­668.Ž©°h–ª¨¬De ne‘UU­PlaneŽ‘#Œ ¬functions‘@¯664“°i‘Ǭ+°Ž¤ ‘ +­PlaneŽ‘'áh¬::‘­PlaneŽ‘ág¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié];‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒµnŽ‘LŒŸ¬)Ž¡‘ +:‘qDZnormalŽ‘$Ȭ(µnŽ‘š¬)µ;‘ÿý±p‘ÿ}'ointŽ‘.‰¬(µpŽ‘¬)‘UU°fŽ¡‘±p‘ÿ}'ointŽ‘+.Žµ:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¡‘±normalŽ‘4Vºµ:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¡‘­ifŽ‘´ú¬(±p‘ÿ}'ointŽ‘õ¤°‘Ç´INVALID_POINTŽ‘GY¬)‘°fŽ¡‘±normalŽ‘AÓ¬=‘Ç´INVALID_POINTŽ‘GY¬;Ž¡‘±distanc‘ÿ}'eŽ‘E ¬=‘Ç´INVALID_REALŽ‘BM\¬;Ž¡‘­returnŽ‘>‘h¬;Ž¡‘°gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±normalŽ‘#а‘Ç´INVALID_POINTŽ‘GY¬)‘°fŽ¡‘±p‘ÿ}'ointŽ‘7õ§¬=‘Ç´INVALID_POINTŽ‘GY¬;Ž¡‘±distanc‘ÿ}'eŽ‘E ¬=‘Ç´INVALID_REALŽ‘BM\¬;Ž¡‘­returnŽ‘>‘h¬;Ž¡‘°gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±normalŽ‘#а‘DZoriginŽ‘½9¬)‘°fŽ¡‘±c‘ÿ}'errŽ‘3‘¼°‘Ü´"WARNING!® ´In® ´Plane()Ž‘kÛ×:\nnormal® ´==® ´origin.Ž’ÔÛ›® ´"Ž’â¾°‘Ü´"Plane® ´is® ´INVALID_PLŽ‘kÛ×ANE.\n\n"Ž’ž~7°Ž¡‘2± ushŽ‘G¹¬;Ž¡‘±p‘ÿ}'ointŽ‘7õ§¬=‘Ç´INVALID_POINTŽ‘GY¬;Ž¡‘±distanc‘ÿ}'eŽ‘E ¬=‘Ç´INVALID_REALŽ‘BM\¬;Ž¡‘­returnŽ‘>‘h¬;Ž¡‘°gŽ¡‘±normalŽ‘4Vºµ:±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u¬(±trueŽ‘ʬ);Ž¡‘±distanc‘ÿ}'eŽ‘; ¬=‘Ç°Ž‘ +Ž6±p‘ÿ}'ointŽ‘!¼Âµ:±dot‘‰ffŽ‘®pr–ÿ}'o“ductŽ‘2€!¬(±normalŽ‘ V¸¬);Ž¡‘­ifŽ‘´ú¬(±fabsŽ‘2Ò¬(±distanc‘ÿ}'eŽ‘$Eý¬)–ǵ<“­P•®9oin“tŽ‘ad¬::Ž‘%epsilonŽ‘E^¦¬(‘ª¨))‘±distanc‘ÿ}'eŽ‘, ¬=“0Ž‘Ç;Ž¡‘­returnŽ‘4‘g¬;Ž¡‘ +°gŽŸ­669.‘ üAssignmen®9t.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.06.06.¬]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­PlaneŽ‘#Œ ¬functions‘@¯663“°i‘Ǭ+°Ž¡‘ +­constŽ‘(*£PlaneŽ‘Ha[¬&Ž‘P(y­opQÇeratorŽ‘{¿.¬=Ž’ƒ†L(­constŽ‘*¢PlaneŽ‘>aZ¬&Ž‘F(xµpŽ‘K0x¬);ŽŽŽŒ‹º ¢C Šn ý‘ì¬186–¯ASSIGNMENT’ U®3DLDF-1.1.5.1“°x¬670Ž €n ý•@P­670.Ž©°h–ª¨¬De ne‘UU­PlaneŽ‘#Œ ¬functions‘@¯664“°i‘Ǭ+°Ž¤ ‘ +­constŽ‘(*£PlaneŽ‘Ha[¬&Ž‘P(y­PlaneŽ‘n à¬::Ž‘t˜­opQÇeratorŽ’ .Ó¬=Ž’§õñ(­constŽ‘*¢PlaneŽ‘>aZ¬&Ž‘F(xµpŽ‘K0x¬)Ž¡‘ +°fŽ¡‘­ifŽ‘´ú¬(±thisŽ‘²Î°‘Ǭ&Ž‘ +Ž6µpŽ‘–6¬)‘µ=°‘ÿý¬Makš¸ãe–UUsure“it's“not“self-assignmen˜t.‘qÇ[²LDF‘T2003.06.06.¬]Ž‘U$©°µ=Ž¡‘­returnŽ‘Aæ½°Ž‘Fæ¾±thisŽ‘WÒt¬;Ž¡‘±p‘ÿ}'ointŽ‘-õ¦¬=‘ǵpŽ‘Ï:±p‘ÿ}'ointŽ‘.Œ¬;Ž¡‘±normalŽ‘7Ò¬=‘ǵpŽ‘Ï:±normalŽ‘ V¸¬;Ž¡‘±distanc‘ÿ}'eŽ‘; ¬=‘ǵpŽ‘Ï:±distanc‘ÿ}'eŽ‘$Eý¬;Ž¡‘­returnŽ‘7æ¼µpŽ‘<;Ž¡‘ +°gŽŸ­671.‘ üComparing‘ÕTPlanes.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.06.06.¬]Ž‘Y;Added–UUthis“section.Ž¦ŸüÈ„`ÕÁGŽŽŸ­672.‘ üEqualit®9y‘ÿ «.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.06.06.«]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂPlaneŽ‘#Œ «functions‘@­619“·i‘Ç«+·Ž¡‘ -Âb•QÇo“olŽ‘#¡gopQÇeratorŽ‘O8·Ž‘Vÿ:«(ÂconstŽ‘*¢PlaneŽ‘>aZ«&Ž‘F(x±pŽ‘K0x«)‘UUÂconstŽ‘*¢«;ŽŸÂ629.Ž¦·h–ª¨«De ne‘UUÂPlaneŽ‘#Œ «functions‘@­620“·i‘Ç«+·Ž¡‘ -Âb•QÇo“olŽ‘#¡gPlaneŽ‘A‚Ϋ::Ž‘H ÂopQÇeratorŽ‘s§Á·Ž‘{nß«(ÂconstŽ‘*¢PlaneŽ‘>aZ«&Ž‘F(x±pŽ‘K0x«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7漫((Ïp‘ÿ}'ointŽ‘õ¤·‘DZpŽ›Ï:Ïp‘ÿ}'ointŽ‘.Œ«)–8à·^“«(ÏnormalŽ‘#з‘DZpŽ˜:ÏnormalŽ‘ V¸«)“·^“«(Ïdistanc‘ÿ}'eŽ‘' ·‘DZpŽ˜:Ïdistanc‘ÿ}'eŽ‘$Eý«));Ž¡‘ -·gŽŸÂ630.‘ üInequalit®9y‘ÿ +¬[²LDF‘T2003.06.06.¬]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­PlaneŽ‘#Œ ¬functions‘@¯663“°i‘Ǭ+°Ž¡‘ +­b•QÇo“olŽ‘#¡gopQÇeratorŽ‘O8°Ž‘Vÿ:¬(­constŽ‘*¢PlaneŽ‘>aZ¬&Ž‘F(xµpŽ‘K0x¬)‘UU­constŽ‘*¢¬;ŽŸ­673.Ž¦°h–ª¨¬De ne‘UU­PlaneŽ‘#Œ ¬functions‘@¯664“°i‘Ǭ+°Ž¡‘ +­b•QÇo“olŽ‘#¡gPlaneŽ‘A‚ά::Ž‘H ­opQÇeratorŽ‘s§Á°Ž‘{n߬(­constŽ‘*¢PlaneŽ‘>aZ¬&Ž‘F(xµpŽ‘K0x¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7漬((±p‘ÿ}'ointŽ‘õ¤°‘ǵpŽ›Ï:±p‘ÿ}'ointŽ‘.Œ¬)–8à°^“¬(±normalŽ‘#а‘ǵpŽ˜:±normalŽ‘ V¸¬)“°^“¬(±distanc‘ÿ}'eŽ‘' °‘ǵpŽ˜:±distanc‘ÿ}'eŽ‘$Eý¬));Ž¡‘ +°gŽŸ­674.‘ üInequalit®9y‘ÿ «.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.06.06.«]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂPlaneŽ‘#Œ «functions‘@­619“·i‘Ç«+·Ž¡‘ -Âb•QÇo“olŽ‘#¡gopQÇeratorŽ‘O8·6«=Ž‘Vÿ:(ÂconstŽ‘*¢PlaneŽ‘>aZ«&Ž‘F(x±pŽ‘K0x«)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹±¹@ Šn ý‘ì·x«631–­3DLDFPRÃŽG’+U¸INEQUALITY“«177Ž €n ý•@PÂ631.Ž©·h–ª¨«De ne‘UUÂPlaneŽ‘#Œ «functions‘@­620“·i‘Ç«+·Ž¤ ‘ -Âb•QÇo“olŽ‘#¡gPlaneŽ‘A‚Ϋ::Ž‘H ÂopQÇeratorŽ‘s§Á·6«=Ž‘{nß(ÂconstŽ‘*¢PlaneŽ‘>aZ«&Ž‘F(x±pŽ‘K0x«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼·:«(ÂopQÇeratorŽ‘+–µ·Ž‘3]Ó«(±pŽ‘«));Ž¡‘ -·gŽ¤Â632.‘ üGet‘ÕTdistance.Ž¡633.› üP•®9oin“t‘6Ôargumen“t.˜«[¬LDF‘T2003.06.03.«]Ž‘[»šThis–ˆ¹function“returns“a“Ârealu½‰™šs4Ž‘ÔwshortŽ‘;%Û±rŽ‘?ïï«,‘Õ’where“±rŽ‘ RÍ:Ï rstŽ‘>c«is“theŽ¤ distance–>ÿof“the“ÂP•®9oin“tŽ‘"F«from“the“ÂPlaneŽ‘ b«.‘jU±rŽ› 4i:Ï rstŽ‘ô©«is“alw•¸ãa“ys‘>ÿpGositiv“e.‘jU±rŽ˜:Ïse–ÿ}'c“ondŽ‘ æÆ«can›>ÿtak“e˜on˜the˜follo“wing˜v‘ÿqÇalues:Ž¡0Ž‘ -If–UUthe“ÂP•®9oin“tŽ‘"Dò«lies“in“the“ÂPlaneŽ‘ 6¸«.Ž¡1Ž‘ -If–,éit“lies“on“the“side“of“the“ÂPlaneŽ‘#;5«pGoinš¸ãted“at“b˜y“the“normal“to“the“ÂPlaneŽ‘ L«,‘4ÿconsidered“to“bGe“the“\outside".Ž¡‘üª«-1Ž‘ -If–Ÿ1it“lies“on“the“side“of“the“ÂPlaneŽ‘"ÅÏnot‘’ «pGoinš¸ãted“at“b˜y“the“normal“to“the“ÂPlaneŽ‘€”«,‘Þconsidered“to“bGe“the“\inside".ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.06.03.«]Ž‘Xô¹Changed–AÓthe“de nition“of“this“function.›kFThe“old“de nition“w¸ãas“incorrect.˜Also“c¸ãhangedŽ¡return–UUt¸ãypGe“from“ÂrealŽ‘ƒ«to“Ârealu½‰™šs4Ž‘ÔwshortŽ‘5i¾«.Ž¡‘ -[¬LDF‘T2003.06.04.«]Ž‘X1{BUG‘~^FIX:–~•In“the“case“that“Ïr‘‰ffŽ‘®fabsŽ‘^±<‘ÇÂP•®9oin“tŽ‘ad«::Ž‘%ï¢ÏepsilonŽ‘E^¦«(‘ª¨),‘©ˆno¸ãw“Ïr‘‰ffŽ‘®fabsŽ‘„«is“set“to“0.‘*2Previously‘ÿ*ª,Ž¡±rŽ‘Ü>«w•¸ãas,‘A_whic“h›*w“as˜wrong,–A_bGecause˜Ïr‘‰ffŽ‘®fabsŽ‘"<®«is˜returned,“not˜±rŽ‘Ü>«.‘¨FAlso,“I‘ùno¸ãw˜set˜Ïr‘‰ffŽ‘®fabsŽ‘"<®«and˜±sŽ‘ ÔT«to˜0˜separately‘ÿ*ª,Ž¡bGecause–ªthey“are“of“di erenš¸ãt“t˜ypšGes.‘oÛI‘©ðdon't“b˜elievš¸ãe“an˜y“compiler“w˜ould“ha˜v˜e“trouble“with“this,‘¿2but“I‘©ðthinkŽ¡it's–UUcleaner“if“they“are“assigned“to“separately‘ÿ*ª.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂPlaneŽ‘#Œ «functions‘@­619“·i‘Ç«+·Ž¡‘ -Ârealu½‰™šs4Ž‘ÔwshortŽ‘?i¿Ïget‘‰ffŽ‘®distanc‘ÿ}'eŽ‘sãx«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]±pŽ‘Ié]«)‘UUÂconstŽ‘*¢«;ŽŸÂ634.Ž¦·h–ª¨«De ne‘UUÂPlaneŽ‘#Œ «functions‘@­620“·i‘Ç«+·Ž¡‘ -Ârealu½‰™šs4Ž‘ÔwshortŽ‘?i¿PlaneŽ‘]K&«::‘Ïget‘‰ffŽ‘®distanc‘ÿ}'eŽ‘5y½«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]±pŽ‘Ié]«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂrealŽ‘*³0±rŽ‘2D\«=‘Ç(±pŽ‘@à·‘8àÏp‘ÿ}'ointŽ‘gl«)±:Ïdot‘‰ffŽ‘®pr–ÿ}'o“ductŽ‘2€!«(ÏnormalŽ‘ V¸«);Ž¡‘ÂrealŽ‘*³0Ïr‘‰ffŽ‘®fabsŽ‘G’¢«=‘ÇÏfabsŽ‘ùê«(±rŽ‘Ê«);Ž¡‘ÂsignedŽ‘7oøshortŽ‘U:›±sŽ‘Yꛫ;Ž¦‘ÂifŽ‘´ú«(Ïr‘‰ffŽ‘®fabsŽ‘ßr±<‘ÇÂP•®9oin“tŽ‘ad«::Ž‘%ï¢ÏepsilonŽ‘E^¦«(‘ª¨))‘·fŽ¡‘Ïr‘‰ffŽ‘®fabsŽ‘:ßu«=‘Ç0Ž‘Ç;Ž¡‘±sŽ‘%w«=‘Ç0Ž‘Ç;Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá±sŽ‘3Où«=‘ÇÂstaticu½‰™šs4Ž‘ÔwcastŽ‘7Dº·hÂsignedŽ‘#oöshortŽ‘=åD·i«(±rŽ‘Ê=Ïr‘‰ffŽ‘®fabsŽ‘Z«);Ž¡‘ÂreturnŽ‘7æ¼realu½‰™šs4Ž‘ÔwshortŽ‘iû%«(Ïr‘‰ffŽ‘®fabsŽ‘Z±;‘ª¨sŽ‘Z¨«);Ž¡‘ -·gŽŸÂ635.– üNo‘D]argumen®9t.“«[¬LDF‘T2003.06.03.«]Ž‘Z -'This–×Fvš¸ãersion“of“Ïget‘‰ffŽ‘®distanc‘ÿ}'eŽ‘7Pÿ«(‘ª®)“returns“the“data“mem˜bGer“Ïdistanc‘ÿ}'eŽŽ¡«and–JÁits“sign,–LÞi.e.,“the–JÁdistance“of“ÏoriginŽ‘!‹£«to“the“ÂPlaneŽ‘ ,$«,‘LÞand“whic¸ãh“side“of“the“ÂPlaneŽ‘#vå«it“lies“on.‘n@I'm“not“usingŽ¡ÏoriginŽ‘³T«as–½3the“default“for“an“optional“ÂP•®9oin“tŽ‘!®«argumenš¸ãt,‘Û bGecause“of“problems“that“ma˜y“arise,‘Û when“I‘½ implemen˜tŽ¡Ïuser‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘K v«and‘UUÏview‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘K¯«.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.06.03.«]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂPlaneŽ‘#Œ «functions‘@­619“·i‘Ç«+·Ž¡‘ -Ârealu½‰™šs4Ž‘ÔwshortŽ‘?i¿Ïget‘‰ffŽ‘®distanc‘ÿ}'eŽ‘sãx«(Âv®9oidŽ‘¨ƒ«)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹²ÀÓ Šn ý‘ì«178›­NO‘ÕXAR•ÃŽGUMENT’v¾3DLDFPR“G˜·x«636Ž €n ý•@PÂ636.Ž©·h–ª¨«De ne‘UUÂPlaneŽ‘#Œ «functions‘@­620“·i‘Ç«+·Ž¤ ‘ -Ârealu½‰™šs4Ž‘ÔwshortŽ‘?i¿PlaneŽ‘]K&«::‘Ïget‘‰ffŽ‘®distanc‘ÿ}'eŽ‘5y½«(Âv®9oidŽ‘¨ƒ«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂrealŽ‘*³0±fŽ‘3s.«=‘ÇÏfabsŽ‘ùê«(Ïdistanc‘ÿ}'eŽ‘$Eý«);Ž¡‘ÂsignedŽ‘7oøshortŽ‘U:›±sŽ‘\±³«=‘ÇÂstaticu½‰™šs4Ž‘ÔwcastŽ‘7Dº·hÂsignedŽ‘#oöshortŽ‘=åD·i«(Ïdistanc‘ÿ}'eŽ‘$Eý±=fŽ‘øæ«);Ž¦‘ÂreturnŽ‘7æ¼realu½‰™šs4Ž‘ÔwshortŽ‘iû%«(±fŽ‘øæ;‘ª¨sŽ‘Z¨«);Ž¡‘ -·gŽŸÂ637.› üP•®9oin“t–ðlis“on“Plane.˜«[¬LDF‘T2003.06.04.«]Ž‘ZŸÅThis–läfunction“returns“ÏtrueŽ‘1|«,‘rÈif“the“ÂP•®9oin“tŽ‘"t«lies“on“the“ÂPlaneŽŽ¡±pŽ‘«,‘Y‹otherwise‘X³ÏfalseŽ‘÷«.›{âDeclared–X³in“Èpoints.web«.˜Must“bšGe“de ned“here,‘Y‹b˜ecause“ÂPlaneŽ‘#’É«is“an“incomplete“t¸ãyp˜e“inŽ¡that‘UU le.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.06.04.«]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¡‘ -Âb•QÇo“olŽ‘#¡gP•®9oin“tŽ‘@;³«::‘Ïis‘‰ffŽ–®on‘‰ffŽ“planeŽ‘2‚Þ«(ÂconstŽ‘*¢PlaneŽ‘>aZ«&Ž‘F(x±pŽ‘K0x«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂifŽ‘´ú«(±pŽ‘:Ïget‘‰ffŽ‘®distanc‘ÿ}'eŽ‘4y¹«(·Ž‘ÏthisŽ‘ë·«)±:Ïse–ÿ}'c“ondŽ‘ nß·‘Ç«0Ž‘Ç)‘ÂreturnŽ‘(æºÏtrueŽ‘;«R«;Ž¡‘ÂelseŽ‘+ØáreturnŽ‘O¿›ÏfalseŽ‘dnß«;Ž¡‘ -·gŽ¤Â638.‘ üIn®9tersection.Ž¡639.‘ üIn®9tersection–ÕTwith“a“line.Ž¡640.‘ üP•®9oin“t‘ÕTargumen“ts.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ -«[¬LDF‘T2003.06.03.«]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂPlaneŽ‘#Œ «functions‘@­619“·i‘Ç«+·Ž¡‘ -Âb•QÇo“olu½‰™šs4Ž‘Ôwp“oin®9tŽ‘B§œÏinterse–ÿ}'ction‘‰ffŽ‘®p“ointŽ’>r«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]Ïp0Ž‘Pø±;‘ª¨ÂconstŽ‘ÕJP•®9oin“tŽ‘>Äç«&Ž‘FŒÏp1Ž‘R¢Å«)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹³Ðå Šn ý‘ì·x«641›­3DLDFPR•ÃŽG’ÛÎÂPOINT‘ÕX­AR“GUMENTS˜«179Ž €n ý•@PÂ641.Ž©·h–ª¨«De ne‘UUÂPlaneŽ‘#Œ «functions‘@­620“·i‘Ç«+·Ž¤ ‘ -Âb•QÇo“olu½‰™šs4Ž‘Ôwp“oin®9tŽ‘B§œPlaneŽ‘`‰«::‘Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘N–Ú«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]Ïp0Ž‘Pø±;‘ª¨ÂconstŽ‘ÕJP•®9oin“tŽ‘>Äç«&Ž‘FŒÏp1Ž‘R¢Å«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘Âb•QÇo“olu½‰™šs4Ž‘Ôwp“oin®9tŽ‘L§ÏbpŽ‘W‚«;Ž¡‘ÂrealŽ‘*³0ÏdenominatorŽ‘f#«=‘Ç(Ïp0Ž–O ·‘8àÏp1Ž“«)±:Ïdot‘‰ffŽ‘®pr–ÿ}'o“ductŽ‘2€!«(ÏnormalŽ‘ V¸«);Ž¦‘ÂifŽ‘Ý9«(ÏdenominatorŽ‘;²ú·‘ -,«0Ž‘ --)‘±=·‘(<«!!‘ê…TO‘}ŠDO:–}”Handle“cases:‘ÂEÂP®9athŽ‘ Ñ=«is“in“ÂPlaneŽ‘ ^÷«,‘‡¤and“ÂP®9athŽ‘ŒŒ«is“in“a“parallelŽ¡‘(ÂPlaneŽ‘Dág«.‘qÇ[¬LDF‘T2003.06.03.«]Ž‘U$©·±=Ž¡‘·fŽ¡‘Ïc‘ÿ}'errŽ‘4†4·‘ЋÝ"ERROR!È ÝInÈ ÝPlane::inŽ‘lÐOtersection_point(conŽ’ÕÐstÈ ÝPoint&,È ÝconstÈ ÝPoiŽ’>Ï×nt&,):"Ž’gæµ·Ž¡‘2Ý"denominatorÈ ÝisÈ Ý0.È Ž’šÿÉÝCan'tÈ Ýdivide.È Ý"Ž’í, ·‘æœÝ"PathÈ ÝisÈ ÝeitherÈ ÝinÈ ÝPŽ‘kæ`lane,È ÝorÈ ÝparallelÈ ÝtoŽ’Ôæ$\ŽŽ¡‘2È ÝPlane."Ž‘ar«(ÂconstŽ‘*¢P®9athŽ‘:[«&Ž‘AØy±pŽ‘Fày«)‘UUÂconstŽ‘*¢«;ŽŸÂ643.‘ üInš®9tersection–ÕTof“t˜w˜o“Planes.‘ ü«[¬LDF‘T2002.10.29.«]Ž‘Zˆ6TO–UUDO:“LoGok“up“and“explain!ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.06.04.«]Ž‘Y;Changed–UUto“ÂconstŽ‘*¢«.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂPlaneŽ‘#Œ «functions‘@­619“·i‘Ç«+·Ž¡‘ -ÂLineŽ‘#­ÙÏinterse‘ÿ}'ction‘‰ffŽ‘®lineŽ‘k1«(ÂconstŽ‘*¢PlaneŽ‘>aZ«&Ž‘F(xÏplŽ‘O^ƒ«)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹´ØÔ Šn ý‘ì«180‘­INTERSECTION–ÕXOF“TWšÃŽO“ÂPLANES’È^­3DLDFPR˜G‘·x«644Ž €n ý•@PÂ644.Ž©·h–ª¨«De ne‘UUÂPlaneŽ‘#Œ «functions‘@­620“·i‘Ç«+·Ž¤ ‘ -ÂLineŽ‘#­ÙPlaneŽ‘A@«::‘Ïinterse‘ÿ}'ction‘‰ffŽ‘®lineŽ‘Hƒª«(ÂconstŽ‘*¢PlaneŽ‘>aZ«&Ž‘F(xÏplŽ‘O^ƒ«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EnteringÈ ÝPlane::intŽ‘kÆÜersection_line()\n"Ž’Ð «;Ž¦‘ÂP•®9oin“tŽ‘2ïŸÏpl‘‰ffŽ‘®normalŽ‘^Ÿ«(ÏplŽ‘ 6 ±:ÏnormalŽ‘ V¸«);Ž¡‘ÂP•®9oin“tŽ‘2ïŸÏdir–ÿ}'e“ction‘‰ffŽ‘®ve“ctorŽ‘z1«=‘ÇÏnormalŽ‘#б:Ïcr–ÿ}'oss‘‰ffŽ‘®pr“o“ductŽ‘:Œé«(Ïpl‘‰ffŽ‘®normalŽ‘+¯s«);‘±=·‘ÿý«[¬LDF‘T2002.10.29.«]Ž‘T7Needed??‘o·±=Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïdir–ÿ}'e“ction‘‰ffŽ‘®ve“ctorŽ‘Iæz±:ÏshowŽ‘Šÿ«(Ý"direction_vector"Ž‘_2«);Ž¡‘ÂifŽ‘´ú«(Ïdir–ÿ}'e“ction‘‰ffŽ‘®ve“ctorŽ‘G­’·‘ÇÏoriginŽ‘½9«)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘3|Á·‘ÇÝ"InÈ ÝPlane::intersectŽ‘kÆÜion_line().\n"Ž’¸”2·‘ÇÝ"PlanesÈ ÝareÈ ÝparallelŽ‘kÆÜ\n"Ž‘| ;«;Ž¡‘ÂifŽ‘)´û«(Ïdistanc‘ÿ}'eŽ‘' ·‘ÇÏplŽ‘ ý#±:Ïdistanc‘ÿ}'eŽ‘$Eý«)‘·fŽ¡‘2±=·‘fÂEllipseŽ‘'÷C«::‘Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã«(ÂEllipseŽ‘%L—«&Ž‘-µ)–c¾calls“this“function“to“ nd“out“whether“t•¸ãw“o‘c¾ÂPlanesŽŽ¡‘<«are–†Écoincidenš¸ãt,‘“%so“sometimes“w˜e“don't“w˜an˜t“to“see“these“messages.‘"I‘†¼ma˜y“decide“to“add“anŽ¡‘<argumen¸ãt‘UUÂb•QÇo“olŽ‘ö»ÏsilentŽ‘9$«to–UUthis“function.–qÇ??“Add‘UUÂb•QÇo“olŽ‘ö»ÏsilentŽ‘5­Ï«??‘o·±=Ž¡‘(Ïc‘ÿ}'errŽ‘=”Ü·‘ß2Ý"PlanesÈ ÝareÈ ÝcoincideŽ‘kÞönt.\n"Ž’ŽÄ~·‘ß2Ý"ReturningÈ ÝLineÈ ÝwithŽ‘kÞöÈ ÝoriginÈ ÝasÈ ÝpositionÈ Ž’ÔÞºÝ\n"Ž’èK·Ž¡‘<Ý"andÈ ÝINVALID_POINTÈ ÝaŽ’¤ÿÊsÈ Ýdirection.\n\n"Ž’·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾ÝINVALID_LINEŽ’‹m«;Ž¡‘·gŽ¡‘ÂelseŽ‘5Øâ·fŽ¡‘(Ïc‘ÿ}'errŽ‘=|·‘ÇÝ"PlanesÈ ÝareÈ ÝnotÈ ÝcoinŽ‘kÆÜcident.\n"Ž’£”>·‘ÇÝ"ReturningÈ ÝINVALID_LŽ‘kÆÜINE.\n\n"Ž’žTA·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾ÝINVALID_LINEŽ’‹m«;Ž¡‘·gŽ¡‘g‘±=·‘ÿý«Outer‘UUÂifŽ‘ ´ø«.‘o·±=Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"PlanesÈ ÝareÈ ÝnotÈ ÝparaŽ‘kÆÜllel\n"Ž’“ÔG·‘ÇÏ ushŽ‘€«;Ž¡‘(±=·‘ u«Aš¸ãt–bÍleast“one“of“the“x,–f+y‘ÿ*ª,“or–bÍz“compGonen˜ts“of“Ïdir–ÿ}'e“ction‘‰ffŽ‘®ve“ctorŽ‘K¬«m˜ust“bGe“non-zero,–f+otherwise,“thisŽ¡‘2function–UUwš¸ãould“ha˜v˜e“exited“b˜y“no˜w.‘o·±=Ž¦‘ÂrealŽ‘*³0±xŽ‘0jL;‘ÿýyŽ‘ +¬[²LDF‘T2003.06.06.¬]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­PlaneŽ‘#Œ ¬functions‘@¯663“°i‘Ǭ+°Ž¡‘ +­b•QÇo“olŽ‘#¡gopQÇeratorŽ‘O8°6¬=Ž‘Vÿ:(­constŽ‘*¢PlaneŽ‘>aZ¬&Ž‘F(xµpŽ‘K0x¬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹» ªB Šn ý‘ì°x¬675–¯3DLDF-1.1.5.1’"â"INEQUALITY“¬187Ž €n ý•@P­675.Ž©°h–ª¨¬De ne‘UU­PlaneŽ‘#Œ ¬functions‘@¯664“°i‘Ǭ+°Ž¤ ‘ +­b•QÇo“olŽ‘#¡gPlaneŽ‘A‚ά::Ž‘H ­opQÇeratorŽ‘s§Á°6¬=Ž‘{nß(­constŽ‘*¢PlaneŽ‘>aZ¬&Ž‘F(xµpŽ‘K0x¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼°:¬(­opQÇeratorŽ‘+–µ°Ž‘3]Ó¬(µpŽ‘¬));Ž¡‘ +°gŽ¤­676.‘ üGet‘ÕTdistance.Ž¡677.› üP•®9oin“t‘6Ôargumen“t.˜¬[²LDF‘T2003.06.03.¬]Ž‘[»šThis–ˆ¹function“returns“a“­realu½‰™šs4Ž‘ÔwshortŽ‘;%ÛµrŽ‘?ïï¬,‘Õ’where“µrŽ‘ RÍ:± rstŽ‘>c¬is“theŽ¤ distance–>ÿof“the“­P•®9oin“tŽ‘"F¬from“the“­PlaneŽ‘ b¬.‘jUµrŽ› 4i:± rstŽ‘ô©¬is“alw•¸ãa“ys‘>ÿpGositiv“e.‘jUµrŽ˜:±se–ÿ}'c“ondŽ‘ æƬcan›>ÿtak“e˜on˜the˜follo“wing˜v‘ÿqÇalues:Ž¡0Ž‘ +If–UUthe“­P•®9oin“tŽ‘"Dò¬lies“in“the“­PlaneŽ‘ 6¸¬.Ž¡1Ž‘ +If–,éit“lies“on“the“side“of“the“­PlaneŽ‘#;5¬pGoinš¸ãted“at“b˜y“the“normal“to“the“­PlaneŽ‘ L¬,‘4ÿconsidered“to“bGe“the“\outside".Ž¡‘üª«-1Ž‘ +If–Ÿ1it“lies“on“the“side“of“the“­PlaneŽ‘"űnot‘’ ¬pGoinš¸ãted“at“b˜y“the“normal“to“the“­PlaneŽ‘€”¬,‘Þconsidered“to“bGe“the“\inside".ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.06.03.¬]Ž‘Xô¹Changed–AÓthe“de nition“of“this“function.›kFThe“old“de nition“w¸ãas“incorrect.˜Also“c¸ãhangedŽ¡return–UUt¸ãypGe“from“­realŽ‘ƒ¬to“­realu½‰™šs4Ž‘ÔwshortŽ‘5i¾¬.Ž¡‘ +[²LDF‘T2003.06.04.¬]Ž‘X1{BUG‘~^FIX:–~•In“the“case“that“±r‘‰ffŽ‘®fabsŽ‘^µ<‘Ç­P•®9oin“tŽ‘ad¬::Ž‘%epsilonŽ‘E^¦¬(‘ª¨),‘©ˆno¸ãw“±r‘‰ffŽ‘®fabsŽ‘„¬is“set“to“0.‘*2Previously‘ÿ*ª,Ž¡µrŽ‘Ü>¬w•¸ãas,‘A_whic“h›*w“as˜wrong,–A_bGecause˜±r‘‰ffŽ‘®fabsŽ‘"<®¬is˜returned,“not˜µrŽ‘Ü>¬.‘¨FAlso,“I‘ùno¸ãw˜set˜±r‘‰ffŽ‘®fabsŽ‘"<®¬and˜µsŽ‘ ÔT¬to˜0˜separately‘ÿ*ª,Ž¡bGecause–ªthey“are“of“di erenš¸ãt“t˜ypšGes.‘oÛI‘©ðdon't“b˜elievš¸ãe“an˜y“compiler“w˜ould“ha˜v˜e“trouble“with“this,‘¿2but“I‘©ðthinkŽ¡it's–UUcleaner“if“they“are“assigned“to“separately‘ÿ*ª.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­PlaneŽ‘#Œ ¬functions‘@¯663“°i‘Ǭ+°Ž¡‘ +­realu½‰™šs4Ž‘ÔwshortŽ‘?i¿±get‘‰ffŽ‘®distanc‘ÿ}'eŽ‘sãx¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié]¬)‘UU­constŽ‘*¢¬;ŽŸ­678.Ž¦°h–ª¨¬De ne‘UU­PlaneŽ‘#Œ ¬functions‘@¯664“°i‘Ǭ+°Ž¡‘ +­realu½‰™šs4Ž‘ÔwshortŽ‘?i¿PlaneŽ‘]K&¬::‘±get‘‰ffŽ‘®distanc‘ÿ}'eŽ‘5y½¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié]¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­realŽ‘*³0µrŽ‘2D\¬=‘Ç(µpŽ‘@à°‘8à±p‘ÿ}'ointŽ‘gl¬)µ:±dot‘‰ffŽ‘®pr–ÿ}'o“ductŽ‘2€!¬(±normalŽ‘ V¸¬);Ž¡‘­realŽ‘*³0±r‘‰ffŽ‘®fabsŽ‘G’¢¬=‘DZfabsŽ‘ùê¬(µrŽ‘ʬ);Ž¡‘­signedŽ‘7oøshortŽ‘U:›µsŽ‘Yꛬ;Ž¦‘­ifŽ‘´ú¬(±r‘‰ffŽ‘®fabsŽ‘ßrµ<‘Ç­P•®9oin“tŽ‘ad¬::Ž‘%epsilonŽ‘E^¦¬(‘ª¨))‘°fŽ¡‘±r‘‰ffŽ‘®fabsŽ‘:ßu¬=‘Ç0Ž‘Ç;Ž¡‘µsŽ‘%w¬=‘Ç0Ž‘Ç;Ž¡‘°gŽ¡‘­elseŽ‘+ØáµsŽ‘3Où¬=‘Ç­staticu½‰™šs4Ž‘ÔwcastŽ‘7Dº°h­signedŽ‘#oöshortŽ‘=åD°i¬(µrŽ‘Ê=±r‘‰ffŽ‘®fabsŽ‘Z¬);Ž¡‘­returnŽ‘7æ¼realu½‰™šs4Ž‘ÔwshortŽ‘iû%¬(±r‘‰ffŽ‘®fabsŽ‘Zµ;‘ª¨sŽ‘Z¨¬);Ž¡‘ +°gŽŸ­679.– üNo‘D]argumen®9t.“¬[²LDF‘T2003.06.03.¬]Ž‘Z +'This–×Fvš¸ãersion“of“±get‘‰ffŽ‘®distanc‘ÿ}'eŽ‘7Pÿ¬(‘ª®)“returns“the“data“mem˜bGer“±distanc‘ÿ}'eŽŽ¡¬and–JÁits“sign,–LÞi.e.,“the–JÁdistance“of“±originŽ‘!‹£¬to“the“­PlaneŽ‘ ,$¬,‘LÞand“whic¸ãh“side“of“the“­PlaneŽ‘#vå¬it“lies“on.‘n@I'm“not“usingŽ¡±originŽ‘³T¬as–½3the“default“for“an“optional“­P•®9oin“tŽ‘!®¬argumenš¸ãt,‘Û bGecause“of“problems“that“ma˜y“arise,‘Û when“I‘½ implemen˜tŽ¡±user‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘K 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Áë Šn ý‘ì°x¬685–¯3DLDF-1.1.5.1’ùh8­POINT‘ÕX¯ARÃŽGUMENTS“¬189Ž €n ý•@P­685.Ž©°h–ª¨¬De ne‘UU­PlaneŽ‘#Œ ¬functions‘@¯664“°i‘Ǭ+°Ž¤ ‘ +­b•QÇo“olu½‰™šs4Ž‘Ôwp“oin®9tŽ‘B§œPlaneŽ‘`‰¬::‘±interse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘N–Ú¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±p0Ž‘Pøµ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±p1Ž‘R¢Å¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­b•QÇo“olu½‰™šs4Ž‘Ôwp“oin®9tŽ‘L§±bpŽ‘W‚¬;Ž¡‘­realŽ‘*³0±denominatorŽ‘f#¬=‘Ç(±p0Ž–O °‘8à±p1Ž“¬)µ:±dot‘‰ffŽ‘®pr–ÿ}'o“ductŽ‘2€!¬(±normalŽ‘ V¸¬);Ž¦‘­ifŽ‘Ý9¬(±denominatorŽ‘;²ú°‘ +,¬0Ž‘ +-)‘µ=°‘(<¬!!‘ê…TO‘}ŠDO:–}”Handle“cases:‘ÂE­P®9athŽ‘ Ñ=¬is“in“­PlaneŽ‘ ^÷¬,‘‡¤and“­P®9athŽ‘ŒŒ¬is“in“a“parallelŽ¡‘(­PlaneŽ‘Dág¬.‘qÇ[²LDF‘T2003.06.03.¬]Ž‘U$©°µ=Ž¡‘°fŽ¡‘±c‘ÿ}'errŽ‘4†4°‘Ћ´"ERROR!® ´In® ´Plane::inŽ‘lÐOtersection_point(conŽ’ÕÐst® ´Point&,® ´const® ´PoiŽ’>Ï×nt&,):"Ž’gæµ°Ž¡‘2´"denominator® ´is® ´0.® Ž’šÿÉ´Can't® ´divide.® ´"Ž’í, °‘朴"Path® ´is® ´either® ´in® ´PŽ‘kæ`lane,® ´or® ´parallel® ´toŽ’Ôæ$\ŽŽ¡‘2® ´Plane."Ž‘ar¬(­constŽ‘*¢P®9athŽ‘:[¬&Ž‘AØyµpŽ‘Fày¬)‘UU­constŽ‘*¢¬;ŽŸ­687.‘ 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V¸¬);Ž¡‘­P•®9oin“tŽ‘2dir–ÿ}'e“ction‘‰ffŽ‘®ve“ctorŽ‘z1¬=‘DZnormalŽ‘#е:±cr–ÿ}'oss‘‰ffŽ‘®pr“o“ductŽ‘:Œé¬(±pl‘‰ffŽ‘®normalŽ‘+¯s¬);‘µ=°‘ÿý¬[²LDF‘T2002.10.29.¬]Ž‘T7Needed??‘o°µ=Ž¦‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±dir–ÿ}'e“ction‘‰ffŽ‘®ve“ctorŽ‘Iæzµ:±showŽ‘Šÿ¬(´"direction_vector"Ž‘_2¬);Ž¡‘­ifŽ‘´ú¬(±dir–ÿ}'e“ction‘‰ffŽ‘®ve“ctorŽ‘G­’°‘DZoriginŽ‘½9¬)‘°fŽ¡‘±c‘ÿ}'errŽ‘3|Á°‘Ç´"In® ´Plane::intersectŽ‘kÆÜion_line().\n"Ž’¸”2°‘Ç´"Planes® ´are® ´parallelŽ‘kÆÜ\n"Ž‘| ;¬;Ž¡‘­ifŽ‘)´û¬(±distanc‘ÿ}'eŽ‘' °‘DZplŽ‘ ý#µ:±distanc‘ÿ}'eŽ‘$Eý¬)‘°fŽ¡‘2µ=°‘f­EllipseŽ‘'÷C¬::‘±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã¬(­EllipseŽ‘%L—¬&Ž‘-µ)–c¾calls“this“function“to“ nd“out“whether“t•¸ãw“o‘c¾­PlanesŽŽ¡‘<¬are–†Écoincidenš¸ãt,‘“%so“sometimes“w˜e“don't“w˜an˜t“to“see“these“messages.‘"I‘†¼ma˜y“decide“to“add“anŽ¡‘<argumen¸ãt‘UU­b•QÇo“olŽ‘ö»±silentŽ‘9$¬to–UUthis“function.–qÇ??“Add‘UU­b•QÇo“olŽ‘ö»±silentŽ‘5­Ï¬??‘o°µ=Ž¡‘(±c‘ÿ}'errŽ‘=”Ü°‘ß2´"Planes® ´are® ´coincideŽ‘kÞönt.\n"Ž’ŽÄ~°‘ß2´"Returning® ´Line® ´withŽ‘kÞö® ´origin® ´as® ´position® Ž’ÔÞº´\n"Ž’èK°Ž¡‘<´"and® ´INVALID_POINT® ´aŽ’¤ÿÊs® ´direction.\n\n"Ž’°‘DZ ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾´INVALID_LINEŽ’‹m¬;Ž¡‘°gŽ¡‘­elseŽ‘5Øâ°fŽ¡‘(±c‘ÿ}'errŽ‘=|°‘Ç´"Planes® ´are® ´not® ´coinŽ‘kÆÜcident.\n"Ž’£”>°‘Ç´"Returning® ´INVALID_LŽ‘kÆÜINE.\n\n"Ž’žTA°‘DZ ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾´INVALID_LINEŽ’‹m¬;Ž¡‘°gŽ¡‘g‘µ=°‘ÿý¬Outer‘UU­ifŽ‘ ´ø¬.‘o°µ=Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Planes® ´are® ´not® ´paraŽ‘kÆÜllel\n"Ž’“ÔG°‘DZ ushŽ‘€¬;Ž¡‘(µ=°‘ u¬Aš¸ãt–bÍleast“one“of“the“x,–f+y‘ÿ*ª,“or–bÍz“compGonen˜ts“of“±dir–ÿ}'e“ction‘‰ffŽ‘®ve“ctorŽ‘K¬¬m˜ust“bGe“non-zero,–f+otherwise,“thisŽ¡‘2function–UUwš¸ãould“ha˜v˜e“exited“b˜y“no˜w.‘o°µ=Ž¦‘­realŽ‘*³0µxŽ‘0jL;‘ÿýyŽ‘ Bõ;‘ÿýzŽ‘ -«;Ž¡‘ÂrealŽ‘*³0±dŽ‘2®º«=‘ÇÏdistanc‘ÿ}'eŽ‘' «;Ž¡‘ÂrealŽ‘*³0±eŽ‘2"I«=‘ÇÏplŽ‘ ý#±:Ïdistanc‘ÿ}'eŽ‘$Eý«;Ž¡‘ÂrealŽ‘*³0ÏnxŽ‘9t;«=‘ÇÏnormalŽ‘#б:Ïget‘‰ffŽ‘®xŽ‘Žg«(‘ª¨);Ž¡‘ÂrealŽ‘*³0ÏnyŽ‘9Yê«=‘ÇÏnormalŽ‘#б:Ïget‘‰ffŽ‘®yŽ‘t«(‘ª¨);Ž¡‘ÂrealŽ‘*³0ÏnzŽ‘8íÕ«=‘ÇÏnormalŽ‘#б:Ïget‘‰ffŽ‘®zŽ‘«(‘ª¨);Ž¡‘ÂrealŽ‘*³0ÏmxŽ‘<s«=‘ÇÏplŽ‘ ý#±:ÏnormalŽ‘ V¸±:Ïget‘‰ffŽ‘®xŽ‘Žg«(‘ª¨);Ž¡‘ÂrealŽ‘*³0ÏmyŽ‘;è"«=‘ÇÏplŽ‘ ý#±:ÏnormalŽ‘ V¸±:Ïget‘‰ffŽ‘®yŽ‘t«(‘ª¨);Ž¡‘ÂrealŽ‘*³0ÏmzŽ‘;| «=‘ÇÏplŽ‘ ý#±:ÏnormalŽ‘ V¸±:Ïget‘‰ffŽ‘®zŽ‘«(‘ª¨);Ž¡‘ÂrealŽ‘*³0ÏvxŽ‘8nŠ«=‘ÇÏdir–ÿ}'e“ction‘‰ffŽ‘®ve“ctorŽ‘G­’±:Ïget‘‰ffŽ‘®xŽ‘Žg«(‘ª¨);Ž¡‘ÂrealŽ‘*³0ÏvyŽ‘8T9«=‘ÇÏdir–ÿ}'e“ction‘‰ffŽ‘®ve“ctorŽ‘G­’±:Ïget‘‰ffŽ‘®yŽ‘t«(‘ª¨);Ž¡‘ÂrealŽ‘*³0ÏvzŽ‘7è$«=‘ÇÏdir–ÿ}'e“ction‘‰ffŽ‘®ve“ctorŽ‘G­’±:Ïget‘‰ffŽ‘®zŽ‘«(‘ª¨);Ž¦‘ÂifŽ‘´ú«(Ïdir–ÿ}'e“ction‘‰ffŽ‘®ve“ctorŽ‘Dæz±:Ïget‘‰ffŽ‘®xŽ‘Žg«(‘ª¨)–Ç·6«=“0Ž‘Ç)‘·fŽ¡‘±xŽ‘&~7«=‘Ç0Ž‘Ç;Ž¡‘±yŽ‘& -«=‘Ç·Ž‘ -Ž6«1Ž‘Ç·–8à«((±dŽ‘mR·“ÏmzŽ‘s…·“±eŽ‘ Á·“ÏnzŽ‘ ¬m«)±=ÏvxŽ‘ -ôB«);Ž¡‘±zŽ‘%Þ9«=‘Ç(±dŽ‘mR·‘8àÏmyŽ‘ßš·‘8à±eŽ‘ Á·‘8àÏnyŽ‘‚«)±=ÏvxŽ‘ -ôB«;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(Ïdir–ÿ}'e“ction‘‰ffŽ‘®ve“ctorŽ‘Dæz±:Ïget‘‰ffŽ‘®yŽ‘t«(‘ª¨)–Ç·6«=“0Ž‘Ç)‘·fŽ¡‘±xŽ‘&~7«=‘Ç(±dŽ‘mR·‘8àÏmzŽ‘s…·‘8à±eŽ‘ Á·‘8àÏnzŽ‘ ¬m«)±=ÏvyŽ‘ -Ùñ«;Ž¡‘±yŽ‘& -«=‘Ç0Ž‘Ç;Ž¡‘±zŽ‘%Þ9«=‘Ç·Ž‘ -Ž6«1Ž‘Ç·–8à«((±dŽ‘mR·“ÏmxŽ‘ùë·“±eŽ‘ Á·“ÏnxŽ‘2Ó«)±=ÏvyŽ‘ -Ùñ«);Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘±xŽ‘&~7«=‘Ç·Ž‘ -Ž6«1Ž‘Ç·–8à«((±dŽ‘mR·“ÏmyŽ‘ßš·“±eŽ‘ Á·“ÏnyŽ‘‚«)±=ÏvzŽ‘ -mÜ«);ŽŽŽŒ‹µãÉ Šn ý‘ì·x«644‘­3DLDFPRšÃŽG’È^INTERSECTION–ÕXOF“TW˜O“ÂPLANES‘«181Ž €n ý•@P‘±yŽ‘& -«=‘Ç(±dŽ‘mR·‘8àÏmxŽ‘ùë·‘8à±eŽ‘ Á·‘8àÏnxŽ‘2Ó«)±=ÏvzŽ‘ -mÜ«;Ž¤ ‘±zŽ‘%Þ9«=‘Ç0Ž‘Ç;Ž¡‘·gŽ¤‘ÂP•®9oin“tŽ‘2ïŸÏp‘ÿ}'oint‘‰ffŽ–®on‘‰ffŽ“lineŽ‘kÛ³«(±xŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁÆ«);Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¤ ‘Ïp‘ÿ}'oint‘‰ffŽ–®on‘‰ffŽ“lineŽ‘Vì±:ÏshowŽ‘Šÿ«(Ý"point_on_line:"Ž‘T†8«);Ž¡‘Ïdir–ÿ}'e“ction‘‰ffŽ‘®ve“ctorŽ‘bæ}±:ÏshowŽ‘Šÿ«(Ý"direction_vector:"Ž‘dF/«);Ž¡‘ÏgetcharŽ‘?%ÿ«(‘ª®);Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"ExitingÈ ÝPlane::inteŽ‘kÆÜrsection_line()\n"Ž’ÊÍ«;Ž¡‘ÏgetcharŽ‘?%ÿ«(‘ª®);Ž¡‘·gŽ¡‘ÂreturnŽ‘7æ¼LineŽ‘N??«(Ïp‘ÿ}'oint‘‰ffŽ–®on‘‰ffŽ“lineŽ‘8ì±;‘ª¨Ïdir–ÿ}'e“ction‘‰ffŽ‘®ve“ctorŽ‘F‘"«);Ž¡‘ -·gŽ©Â645.‘ üSho®9w.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.06.06.«]Ž‘Y;Minor–UUc¸ãhange“to“the“conditional“that“handles“ÏtextŽ‘­!«.Ž¡‘ -[¬LDF‘T2003.06.06.«]Ž‘Y;Made‘UUÏshowŽ‘àT«(‘ª®)‘UUÂconstŽ‘*¢«.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂPlaneŽ‘#Œ «functions‘@­619“·i‘Ç«+·ŽŸ ‘ -Âv®9oidŽ‘"ýÙÏshowŽ‘9ˆØ«(ÂstringŽ‘!%MÏtextŽ‘5D1«=‘ÇÝ""Ž‘ Íz«)‘UUÂconstŽ‘*¢«;Ž¦Â646.Ž¡·h–ª¨«De ne‘UUÂPlaneŽ‘#Œ «functions‘@­620“·i‘Ç«+·Ž¤ ‘ -Âv®9oidŽ‘"ýÙPlaneŽ‘@ß@«::‘ÏshowŽ‘‹«(ÂstringŽ‘!%MÏtextŽ‘2}«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂifŽ‘´ú«(ÏtextŽ‘ä·‘ÇÝ""Ž‘ Íz«)‘ÏtextŽ‘ä«=‘ÇÝ"Plane:"Ž‘-Mh«;Ž¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÏtextŽ‘åü·‘ÇÏend‘‚ØlŽ‘¸Ú«;Ž¡‘ÂifŽ‘´ú«(·Ž‘ÏthisŽ‘²Ï·‘ÇÝINVALID_PLANEŽ‘GY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"INVALID_PLANE.È ÝCan'Ž‘kÆÜtÈ Ýshow."Ž’™D·‘ÇÏend‘‚ØlŽ–ò·‘ÇÏend‘‚ØlŽ“·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘>‘h«;Ž¡‘·gŽ¡‘ÏnormalŽ‘4Vº±:ÏshowŽ‘Šÿ«(Ý"normal:"Ž‘/ÆM«);Ž¡‘Ïp‘ÿ}'ointŽ‘+.Ž±:ÏshowŽ‘Šÿ«(Ý"point:"Ž‘*†P«);Ž¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"distanceÈ Ý==È Ý"Ž‘O”n·‘ÇÏdistanc‘ÿ}'eŽ‘)Ô-·‘ÇÏend‘‚ØlŽ–ò·‘ÇÏend‘‚ØlŽ“·‘ÇÏ ushŽ‘€«;Ž¡‘ -·gŽ¦Â647.‘ üGlobal–ÕTconstan®9ts“for“Plane.ŽŸ·h‘ª¨ÂPlaneŽ‘!á`«global‘UUconstan¸ãts‘@­647‘ª¨·i‘ÇŽ¡‘ -ÂexternŽ‘.×constŽ‘LHyPlaneŽ‘l1ÝINVALID_PLANEŽ’±Er«(ÝINVALID_POINTŽ‘DÆA±;‘ª¨ÝINVALID_POINTŽ‘Fpé«);ŽŸ ­This–ÕXcoNoš¸ãw– -Xall“of“the“data“mem˜bGers“of“ÂclassŽ‘Ÿ¬P®9athŽ‘<;h«are“assigned“to“except“for“Ïon‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘;¯J«.Ž¡This–Ÿyhas“bšGecome“necessary“b˜ecause“of“c¸ãhanges“in“ÂSolidŽ‘T«::‘ÏoutputŽ‘D«(‘ª®),‘òwhere“temp˜orary“ÂP®9athsŽ‘&Y’«ha•¸ãv“e–Ÿyto“b˜eŽ¡created–UUin“order“to“sort“them.Ž¡‘ -[¬LDF‘T2002.12.18.«]Ž‘XwMo•¸ãv“ed–`‘here.‘ 1With“the“DEC›`Scompiler“under“Compaq“T‘ÿ*ªru64“on“the“DEC˜Alpha“computer,Ž¡it›¬&w•¸ãork“ed˜to˜ha“v“e˜this˜follo“wing˜the˜constructors.‘9bWith˜the˜GNU–«û¬C‘€Ÿÿ®+‘ÿ+ŽŽ‘óF«compiler˜(GCC)“under˜GNU/Lin¸ãux˜onŽ¡the–ãInš¸ãtel“i686“computer,‘ùëit“didn't:‘8¥The“cop˜y“constructor“used“the“default“assignmen˜t“opGerator“instead“of“thisŽ¡function,‘Špresumably–óbGecause“this“function“wš¸ãasn't“kno˜wn“at“the“time“the“cop˜y“constructor“w˜as“compiled,Ž¡Ïalthough–säit“had“b–ÿ}'e“en›säde“clar“e“d˜pr“eviously‘â}«!‘f.UR•¸ãGENT:›2‰Mo“v“e˜assignmen“t˜op•Gerators˜for˜the˜other˜ÏclassesŽ‘$Ü#«b“eforeŽ¡the‘UUconstructors!Ž¡‘ -[¬LDF‘T2003.04.09.«]Ž‘Y;??‘qÇBUG–UUFIX:“No¸ãw“resizing“Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘WY¦«,“if“after“setting“it“toŽ¡±pŽ‘:Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ«,‘{Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘X̱:ÏsizeŽ‘\«(‘ª¨)–Íô·“«0Ž‘Íõ.‘JïThis›ó prev•¸ãen“ts˜a˜Memory˜F‘ÿ*ªault˜error˜at˜run-time.‘JïIŽ¡don't–:%knoš¸ãw“wh˜y“it“should“bGe“necessary‘ÿ*ª,–?•though,“since–:%all“of“the“constructors“of“ÂP®9athŽ‘®«and“its“deriv˜ed“classesŽ¡resize‘UUÏpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘WY¦«;–UUat“least,“I“though¸ãt“they“did.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘ÇŽ¡‘ -ÂvirtualŽ‘/ÔP®9athŽ‘Kt«&Ž‘S;«ÂopQÇeratorŽ‘~Ò`«=Ž’†™~(ÂconstŽ‘*¢P®9athŽ‘:[«&Ž‘AØy±pŽ‘Fày«);Ž© ­See–´?also“sections“660,–ºÝ663,“665,“668,“670,“673,“675,“677,“680,“682,“684,“686,“688,“690,“692,“695,“697,“700,“702,“704,“706,“708,“713,Ž¤ -‘719,–áú721,“723,“725,“728,“730,“733,“735,“738,“740,“742,“747,“749,“751,“754,“756,“758,“762,“767,“769,“775,“777,“784,“786,“793,Ž¡‘795,–áú801,“803,“806,“808,“812,“814,“820,“823,“825,“829,“831,“834,“836,“839,“841,“845,“846,“848,“850,“852,“854,“856,“866,“868,Ž¡‘871,–ÕX872,“874,“876,“877,“878,“879,“881,“888,“890,“892,“894,“896,“902,“908,“911,“915,“917,“920,“and“932.Ž¦This–ÕXco¬«;Ž¡‘Ïdr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘E³S«=‘DZpŽ‘Ï:Ïdr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘.ì9«;‘±=·‘éR«[¬LDF‘T2002.10.23.«]Ž‘SÚáÏdr–ÿ}'aw‘‰ffŽ‘®c“olorŽ’†Ä«and‘>ªÏ l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘,©«pGoin¸ãt–>ªto“the“same“ÂColorŽŽ¡‘(«as‘UU±pŽ–]U:Ïdr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘2AŽ«and‘UU±pŽ“:Ï l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘%˜U«.‘qÇNo–UUmemory“allošGcation“is“p˜erformed.‘o·±=Ž¡‘Ï l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘<_o«=‘DZpŽ‘Ï:Ï l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘%˜U«;Ž¡‘Ïdashe‘ÿ}'dŽ‘4ñ»«=‘DZpŽ‘Ï:Ïdashe‘ÿ}'dŽ‘*¡«;Ž¡‘Ïp‘ÿ}'enŽ‘&àÍ«=‘DZpŽ‘Ï:Ïp‘ÿ}'enŽ‘³«;Ž¡‘Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘jËk«=‘DZpŽ‘Ï:Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ«;‘±=·‘ÿý«LDF–UU2002.09.18.‘qÇAdded“this“line.‘o·±=Ž¡‘ÂifŽ‘´ú«(Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ±:ÏsizeŽ‘\«(‘ª¨)–Ç·“«0Ž‘Ç)‘±=·‘ÿý«LDF–UU2003.04.09.‘qÇAdded“this“conditional.‘o·±=Ž¡‘Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘rT±:Ïr‘ÿ}'esizeŽ‘i«(6Ž‘±;‘ª¨«0Ž‘ª©);Ž¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂP•®9oin“tŽ‘ï·Ž‘#ïži‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûp‘‰ffŽ‘®iterŽ‘_ß”«=‘DZpŽ–Ï:Ïp‘ÿ}'ointsŽ›$•±:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);‘ÿýÏp‘‰ffŽ‘®iterŽ‘!\–·6«=‘DZpŽ“:Ïp‘ÿ}'ointsŽ˜±:ÏendŽ‘ಫ(‘ª¨);‘ÿýÏp‘‰ffŽ‘®iterŽ‘~Ÿÿ®+‘ÿ+ŽŽ‘*Üž«)Ž¡‘Ïp‘ÿ}'ointsŽ‘9$˜±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂP•®9oin“tŽ‘šL«::Ž‘#(ŠÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“p‘ÿ}'ointŽ‘kþ†«(·Ž‘Ïp‘‰ffŽ‘®iterŽ‘•‚«));Ž¡‘ÂforŽ‘&Q(«(Âv®9ectorŽ‘ªH·hÂstringŽ‘Ïø·i‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûc‘‰ffŽ‘®iterŽ‘` «=‘ux±pŽ–}x:Ïc–ÿ}'onne“ctorsŽ›/4.±:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);‘hÏc‘‰ffŽ‘®iterŽ‘!ð½·6«=‘ux±pŽ“:Ïc–ÿ}'onne“ctorsŽ˜±:ÏendŽ‘ಫ(‘ª¨);Ž¡‘2Ïc‘‰ffŽ‘®iterŽ‘K’­Ÿÿ®+‘ÿ+ŽŽ‘WYÍ«)‘·fŽ¡‘Ïc–ÿ}'onne“ctorsŽ‘M41±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(·Ž‘Ïc‘‰ffŽ‘®iterŽ‘©«);Ž¡‘·gŽ¡‘ÂreturnŽ‘7æ¼·Ž‘<æ½ÏthisŽ‘MÒs«;Ž¡‘ -·gŽ© ­See–´?also“sections“661,–ºÝ664,“666,“669,“671,“674,“676,“678,“681,“683,“685,“687,“689,“693,“696,“698,“701,“703,“705,“707,“709,“714,“720,Ž¤ -‘722,–áú724,“726,“729,“731,“734,“736,“739,“741,“743,“748,“750,“752,“755,“757,“759,“763,“764,“765,“766,“768,“770,“771,“776,“778,Ž¡‘785,–áú787,“794,“796,“802,“804,“807,“809,“813,“815,“821,“824,“826,“830,“832,“835,“837,“840,“842,“843,“844,“847,“849,“851,“853,Ž¡‘855,–áú857,“858,“859,“860,“861,“862,“863,“867,“869,“873,“875,“880,“882,“883,“884,“885,“886,“889,“891,“893,“897,“898,“899,“900,Ž¡‘903,–ÕX909,“912,“913,“914,“916,“918,“921,“and“933.Ž¦This–ÕXco“«0Ž‘Ç)‘·fŽ¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂP•®9oin“tŽ‘ï·Ž‘#ïži‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘ÇÏp‘ÿ}'ointsŽ–ë­±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏp‘ÿ}'ointsŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘ÂdeleteŽ‘?ƽ·Ž‘DƾÏiterŽ‘U‘¼«;Ž¡‘·gŽ¡‘Ïp‘ÿ}'ointsŽ‘/$—±:Ïcle‘ÿ}'arŽ‘(Ù«(‘ª¨);Ž¡‘ -·gŽ¡‘ -ÂifŽ‘´ù«(Ïc–ÿ}'onne“ctorsŽ‘/4.±:ÏsizeŽ‘\«(›ª¨)–DZ>“«0Ž‘Ç)‘Ïc–ÿ}'onne“ctorsŽ‘44.±:Ïcle‘ÿ}'arŽ‘(Ù«(˜);ŽŽŽŒ‹º  Šn ý‘ì«186›­DISCARD–ÕXPOINTS“AND“CONNECTORS’Á¶ -3DLDFPRÃŽG˜·x«659Ž €n ý•@P­This–ÕXcoÄç«&Ž‘FŒÏp1Ž‘R¢Å«);ŽŽŽŒ‹» 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l‘‚Øl‘‰ffŽ–®dr‘ÿ}'aw‘‰ffŽ“valueŽ‘Us+«=‘Ç0Ž‘Ç;Ž¡‘Ïdr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘E³S«=‘Ç0Ž‘Ç;Ž¡‘Ï l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘<_o«=‘Ç0Ž‘Ç;Ž¡‘Ïdashe‘ÿ}'dŽ‘4ñ»«=‘ÇÝ""Ž‘ Íz«;‘±=·‘ÿý«LDF–UU2003.04.06.‘qÇAdded“these“three“lines.‘o·±=Ž¡‘Ïp‘ÿ}'enŽ‘&àÍ«=‘ÇÝ""Ž‘ Íz«;Ž¡‘Ïarr‘ÿ}'owŽ‘1'j«=‘ÇÏfalseŽ‘v\«;Ž¡‘·h–ª¨«Discard‘UUÏp‘ÿ}'ointsŽ‘!Ï?«and‘UUÏc–ÿ}'onne“ctorsŽ‘6ɇ­659“·iŽ¡‘Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘jËk«=‘Ç0Ž‘Ç;‘±=·‘ÿý«LDF–UU2002.09.18.‘qÇAdded“this“line.‘o·±=Ž¡‘Ïp‘ÿ}'ointsŽ‘/$—±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂP•®9oin“tŽ‘šL«::Ž‘#(ŠÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“p‘ÿ}'ointŽ‘kþ†«(Ïp0Ž‘ À«));Ž¡‘Ïp‘ÿ}'ointsŽ‘/$—±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂP•®9oin“tŽ‘šL«::Ž‘#(ŠÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“p‘ÿ}'ointŽ‘kþ†«(Ïp1Ž‘ À«));Ž¡‘Ïc–ÿ}'onne“ctorsŽ‘C40±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(Ý"--"Ž‘†\«);Ž¡‘Ïline‘‰ffŽ‘®switchŽ‘FiÛ«=‘ÇÏtrueŽ‘‹°«;Ž¡‘ -·gŽ©Â667.› üP•®9oin“ts–ñ|and“one“t®9ypQÇe“of“connector.˜«This–+ constructor“takš¸ães“a“v‘ÿqÇariable“n˜um˜bGer“of“ÂP•®9oin“tŽ‘%ðZ·ŽŽ¡«argumenš¸ãts,‘´'but–mýonly“allo˜ws“one“t˜ypGe“of“connector.‘»ÀThe“argumen˜t“list“m˜ust“end“with“0.‘»ÀIf“the“order“ofŽ¡the–?]named“argumenš¸ãts“is“rev˜ersed,‘yßthe“compiler“can't“resolv˜e“certain“calls“to“ÂP®9athŽ‘ÐÁ«(‘ª®).‘/ßIt“couldn't“resolv˜eŽ¡bGet•¸ãw“een‘ÚÂP®9athŽ‘’>«(Âb•QÇo“olŽ‘LëÏcycleŽ‘0Æ ±;‘ª¨ÂstringŽ‘z Ïc–ÿ}'onne“ctorŽ‘R/¤±:–ª¨:“:Ž‘_„ó«)–Úand“ÂP®9athŽ‘ “«(“ÂP•®9oin“tŽ‘#›ü·Ž‘(›ýÏ rst‘‰ffŽ–®p‘ÿ}'oint‘‰ffŽ“ptrŽ‘jÙ>±:–ª¨:“:Ž‘|/g«).‘tVI‘®don't“kno¸ãwŽ¡whš¸ãy–UUit“should“ha˜v˜e“had“trouble,“though,“since“pGoin˜ters“to“ÂP•®9oin“tsŽ‘&Î.«are“not“Âb•QÇo“olsŽ‘*¢«.Ž¡‘ -[¬LDF‘T2002.4.6.«]Ž‘O5âProbably–Âøit“couldn't“distinguish“bšGet•¸ãw“een–Âøa“p˜oin¸ãter“and“an“Âin®9tŽ‘Õ’«on“the“one“hand“and“a“Âb•QÇo“olŽŽ¡«and–UUan“Âin®9tŽ‘úL«on“the“other.‘qÇI“hopGe“that“Âb•QÇo“olsŽ‘!÷«are“more“ecienš¸ãtly“implemen˜ted“than“as“ÏintsŽ‘Ãã«,“though!Ž¡‘ -[¬LDF‘T2002.10.29.«]Ž‘Y.®??‘åI‘{¾don't–{Èknoš¸ãw“wh˜y“Ècweave“«needs“instructions“to“put“thin“spaces“after“the“\Âb•QÇo“olŽ‘L«"“inŽ¡the–UUdeclaration“and“de nition“bšGelo•¸ãw.‘qÇMa“yb˜e–UUit's“b˜ecause“of“the“\±:–ª¨:“:Ž‘ ª§«".Ž¦Â668.‘ üConstructor.ŽŸ·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·Ž¡‘ -ÂP®9athŽ‘"‘e«(ÂstringŽ‘!%MÏc–ÿ}'onne“ctorŽ‘L„'±;‘ª¨Âb•QÇo“olŽ‘LÏcycleŽ‘8oï±:–ª¨:“:Ž‘EÅ>«);ŽŽŽŒ‹½ EJ Šn ý‘ì·x«669›­3DLDFPR•ÃŽG’BzCONSTR“UCTOR˜«189Ž €n ý•@PÂ669.Ž©·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¤ ‘ -ÂP®9athŽ‘#‘i«::‘ÂP®9athŽ‘‘h«(ÂstringŽ‘!%MÏc–ÿ}'onne“ctorŽ‘L„'±;‘ª¨Âb•QÇo“olŽ‘LÏcycleŽ‘8oï±:–ª¨:“:Ž‘EÅ>«)Ž¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EnteringÈ ÝPath()È Ý(coŽ‘kÆÜnnector,È Ýcycle,È Ý...)Ž’ÔÆ .\n"Ž’í·‘ÇÏ ushŽ‘€«;Ž¡‘Ïon‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘Nl «=‘ÇÏfalseŽ‘v\«;Ž¡‘Ïline‘‰ffŽ‘®switchŽ‘FiÛ«=‘ÇÏfalseŽ‘v\«;Ž¡‘Ïcycle‘‰ffŽ‘®switchŽ‘KÇ´«=‘ÇÏcycleŽ‘@M«;Ž¡‘Ïc–ÿ}'onne“ctorsŽ‘C40±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(Ïc–ÿ}'onne“ctorŽ‘+^Ú«);Ž¡‘Ïdo‘‰ffŽ‘®outputŽ‘A½M«=‘ÇÏtrueŽ‘‹°«;‘±=·‘ÿý«LDF–UU2002.09.18.‘qÇAdded“this“line.‘o·±=Ž¡‘Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘hS±:Ïr‘ÿ}'esizeŽ‘i«(6Ž‘±;‘ª¨«0Ž‘ª©);‘±=·‘ÿý«LDF–UU2002.09.18.‘qÇAdded“this“line.‘o·±=Ž¡‘Ï l‘‚Øl‘‰ffŽ–®dr‘ÿ}'aw‘‰ffŽ“valueŽ‘Us+«=‘Ç0Ž‘Ç;Ž¡‘Ïdr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘E³S«=‘Ç0Ž‘Ç;Ž¡‘Ï l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘<_o«=‘Ç0Ž‘Ç;Ž¡‘Ïdashe‘ÿ}'dŽ‘4ñ»«=‘ÇÝ""Ž‘ Íz«;‘±=·‘ÿý«LDF–UU2003.04.06.‘qÇAdded“these“three“lines.‘o·±=Ž¡‘Ïp‘ÿ}'enŽ‘&àÍ«=‘ÇÝ""Ž‘ Íz«;Ž¡‘Ïarr‘ÿ}'owŽ‘1'j«=‘ÇÏfalseŽ‘v\«;Ž¦‘Âv‘ÿ\rau½‰™šs4Ž‘ÔwlistŽ‘7'ýÏapŽ‘B…O«;‘±=·‘ÿý«F‘ÿ*ªor–UUthe“v‘ÿqÇariable“length“argumen¸ãt“list.‘o·±=Ž¦‘Ïva‘‰ffŽ‘®startŽ‘6éi«(ÏapŽ‘ ]R±;‘ª¨ÏcycleŽ‘#Ý«);Ž¦‘ÂP•®9oin“tŽ‘2Ž‘7ï Ïar‘ÿ}'g‘‰ffŽ‘®ptrŽ‘WE«;Ž¦‘ÂwhileŽ‘2C.«((Ïar‘ÿ}'g‘‰ffŽ‘®ptrŽ‘"•«=‘ÇÏva‘‰ffŽ‘®ar‘ÿ}'gŽ‘û,«(ÏapŽ‘ ]R±;‘ª¨ÂP•®9oin“tŽ‘ 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üDestructor.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.08.27.«]Ž‘ZÖMade‘eðÂvirtualŽ‘&žn«,‘ªbGecause–eðGCC‘eªwith“the“\È-Wall«"“option“issued“the“folloš¸ãwing“w˜arning:Ž¡\`class–UUP¸ãath'“has“virtual“functions“but“non-virtual“destructor".Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/Ô·Ž‘7TòÂP®9athŽ‘OæV«(‘ª¨);ŽŽŽŒ‹Ã ‘] Šn ý‘ì·x«685›­3DLDFPR•ÃŽG’&dDESTR“UCTOR˜«195Ž €n ý•@PÂ685.‘ ü«!!‘qÇMakš¸ãe–UUsure“to“delete“an˜ything“else“that“I“alloGcate“dynamically!Ž©·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¤ ‘ -ÂP®9athŽ‘#‘i«::Ž‘*§·Ž‘1æÅÂP®9athŽ‘Jx)«(‘ª¨)Ž¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"EnteringÈ Ý~Path().\nŽ‘kÆÜ"Ž‘tTY·‘ÇÏ ushŽ‘€«;Ž¡‘ÏshowŽ‘4‹«(Ý"Path:"Ž‘%FS«);Ž¡‘ÏgetcharŽ‘?%ÿ«(‘ª®);Ž¡‘·gŽ¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂP•®9oin“tŽ‘ï·Ž‘#ïži‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘ÇÏp‘ÿ}'ointsŽ–ë­±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏp‘ÿ}'ointsŽ“±:ÏendŽ‘ಫ(˜);‘ÿýÏiterŽ‘JûŸÿ®+‘ÿ+ŽŽ‘"«)‘·fŽ¡‘ÂdeleteŽ‘?ƽ·Ž‘DƾÏiterŽ‘U‘¼«;Ž¡‘·gŽ¡‘Ïp‘ÿ}'ointsŽ‘/$—±:Ïcle‘ÿ}'arŽ‘(Ù«(‘ª¨);Ž¡‘±=·‘ÿý«[¬LDF‘T2002.11.03.«]Ž‘T7This–UUreplaces“a“ÂwhileŽ‘!˜«loGop“in“whicš¸ãh“Ïp–ÿ}'op‘‰ffŽ‘®b“ackŽ‘)Ò¢«(‘ª®)“w˜as“used“to“empt˜y“Ïp‘ÿ}'ointsŽ‘yê«.‘o·±=Ž¡‘Ïc–ÿ}'onne“ctorsŽ‘C40±:Ïcle‘ÿ}'arŽ‘(Ù«(‘ª¨);‘±=·‘ÿý«LDF‘UU2002.11.03.‘qÇAdded.‘o·±=Ž¡‘=·‘ÿý«LDF–UU2002.10.07.‘qÇAdded“coGde“for“handling“Ïdr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘5–ã«and“Ï l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘(íª«.‘o·±=Ž¡‘ÂifŽ‘´ú«(Ïdr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘1³Q·6«=‘Ç0Ž‘ ÿù·^‘8àÏdr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘/%Ÿ±~ŽŽ‘5%Ïis‘‰ffŽ–®on‘‰ffŽ“fr–ÿ}'e“e‘‰ffŽ‘®stor“eŽ‘wŸï«(‘ª¨)–Ç·“ÏtrueŽ‘‹°«)‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"DeletingÈ Ýdraw_colorŽ‘kÆÜ\n"Ž‘| ;«;Ž¡‘ÂdeleteŽ‘?ƽÏdr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘n²ö«;Ž¡‘Ïdr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘O³T«=‘Ç0Ž‘Ç;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"NotÈ ÝdeletingÈ Ýdraw_cŽ‘kÆÜolor\n"Ž’‘ /«;Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(Ï l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘(_m·6«=‘Ç0Ž‘ ÿù·^‘8àÏ l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘%Ñ5Ÿ±~ŽŽ‘+Ñ6Ïis‘‰ffŽ–®on‘‰ffŽ“fr–ÿ}'e“e‘‰ffŽ‘®stor“eŽ‘nL «(‘ª¨)–Ç·“ÏtrueŽ‘‹°«)‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"DeletingÈ Ýfill_colorŽ‘kÆÜ\n"Ž‘| ;«;Ž¡‘ÂdeleteŽ‘?Æ½Ï l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘e_«;Ž¡‘Ï l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘F_p«=‘Ç0Ž‘Ç;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"NotÈ ÝdeletingÈ Ýfill_cŽ‘kÆÜolor\n"Ž’‘ /«;Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"ExitingÈ Ý~Path().\n"Ž‘o\·‘ÇÏ ushŽ‘€«;Ž¡‘ÏgetcharŽ‘?%ÿ«(‘ª®);Ž¡‘·gŽ¡‘ -gŽŸÂ686.– üClear.“«LDF‘´Undated.‘VCThis–Éfunction“is“needed“bGecause“it's“a“pure“ÂvirtualŽ‘(>«function“in“ÂShapQÇeŽ‘!îÖ«,‘KandŽ¡for–UUgetting“rid“of“items“in“ÂPictureŽ‘)ñf«::‘Ïcle‘ÿ}'arŽ‘(Ý«(‘ª®).Ž¡‘ -[¬LDF‘T2002.10.07.«]Ž‘YlDÏcle‘ÿ}'arŽ‘o•«(‘ª®)–¹^is“needed“bGecause“it's“called“on“the“ÂShapQÇesŽ‘*è«that“are“stored“in“ÂPicturesŽ‘-Þ§«,‘Ò`andŽ¡I‘Omdon't–O®knoš¸ãw“of“a“w˜a˜y“of“o˜v˜erloading“destructors.‘`ÑThat“is,›ŽCin“ÂPictureŽ‘*ë¿«::‘Ïcle‘ÿ}'arŽ‘(Ý«(‘ª®),˜the“actual“t¸ãypGes“of“theŽ¡ÂShapQÇesŽ‘'ʾ«are–Uuunkno¸ãwn,›•}so“I‘U3can't“call“·Ž‘ “ÂP®9athŽ‘$­÷«(–ª¨),˜·Ž‘ \›ÂCircleŽ‘*¿Ç«(“),˜or–Uuother“destructors“directly‘ÿ*ª.‘r'But“a“namedŽ¡function–UUsucš¸ãh“as“Ïcle‘ÿ}'arŽ‘~.«(‘ª®)“can“serv˜e“the“same“purpGose.ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.10.07.«]Ž‘X Added–#cošGde“for“deallo˜cating“the“memory“allo˜cated“for“Ïdr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘5 -«and“Ï l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘(§x«,‘-if“an¸ãy‘ÿ*ª.Ž¦ŸüÈ„`ÕÁGŽŽ¡‘ -??‘€I›†1tried–†=calling“·Ž‘ M[ÂP®9athŽ‘#Þ¿«(‘ª¨)“inside“ÂP®9athŽ‘Þ«:‘Ó˜Ïcle‘ÿ}'arŽ‘üq«(‘ª®),‘’xbut“I˜got“a“memory“fault.‘€Don't“knoš¸ãw“wh˜y‘ÿ*ª.‘€TO‘†1DO:Ž¡T‘ÿ*ªry–UUto“ nd“out.‘qÇHo•¸ãw“ev“er,–UUthis“isn't“urgen¸ãt.ŽŽŽŒ‹Ä –Ï Šn ý‘ì«196–­CLEAR’Dêp3DLDFPRÃŽG“·x«686Ž €n ý•@P·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·Ž¤ ‘ -ÂvirtualŽ‘/Ôv®9oidŽ‘H‹¬Ïcle‘ÿ}'arŽ‘^´…«(‘ª®);ŽŸÂ687.Ž©·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙP®9athŽ‘‘h¬;Ž¡‘°gŽ¡‘±normalŽ‘4Vºµ:±showŽ‘Šÿ¬(´"normal:"Ž‘/ÆM¬);Ž¡‘±p‘ÿ}'ointŽ‘+.Žµ:±showŽ‘Šÿ¬(´"point:"Ž‘*†P¬);Ž¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"distance® ´==® ´"Ž‘O”n°‘DZdistanc‘ÿ}'eŽ‘)Ô-°‘DZend‘‚ØlŽ–ò°‘DZend‘‚ØlŽ“°‘DZ ushŽ‘€¬;Ž¡‘ +°gŽ¦­691.‘ üGlobal–ÕTconstan®9ts“for“Plane.ŽŸ°h‘ª¨­PlaneŽ‘!á`¬global‘UUconstan¸ãts‘@¯691‘ª¨°i‘ÇŽ¡‘ +­externŽ‘.×constŽ‘LHyPlaneŽ‘l1´INVALID_PLANEŽ’±Er¬(´INVALID_POINTŽ‘DÆAµ;‘ª¨´INVALID_POINTŽ‘Fpé¬);ŽŸ ¯This–ÕXcoNoš¸ãw– +Xall“of“the“data“mem˜bGers“of“­classŽ‘Ÿ¬P®9athŽ‘<;h¬are“assigned“to“except“for“±on‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘;¯J¬.Ž¡This–Ÿyhas“bšGecome“necessary“b˜ecause“of“c¸ãhanges“in“­SolidŽ‘T¬::‘±outputŽ‘D¬(‘ª®),‘òwhere“temp˜orary“­P®9athsŽ‘&Y’¬ha•¸ãv“e–Ÿyto“b˜eŽ¡created–UUin“order“to“sort“them.Ž¡‘ +[²LDF‘T2002.12.18.¬]Ž‘XwMo•¸ãv“ed–`‘here.‘ 1With“the“DEC›`Scompiler“under“Compaq“T‘ÿ*ªru64“on“the“DEC˜Alpha“computer,Ž¡it›¬&w•¸ãork“ed˜to˜ha“v“e˜this˜follo“wing˜the˜constructors.‘9bWith˜the˜GNU–«û²C‘€Ÿÿ³+‘ÿ+ŽŽ‘óF¬compiler˜(GCC)“under˜GNU/Lin¸ãux˜onŽ¡the–ãInš¸ãtel“i686“computer,‘ùëit“didn't:‘8¥The“cop˜y“constructor“used“the“default“assignmen˜t“opGerator“instead“of“thisŽ¡function,‘Špresumably–óbGecause“this“function“wš¸ãasn't“kno˜wn“at“the“time“the“cop˜y“constructor“w˜as“compiled,Ž¡±although–säit“had“b–ÿ}'e“en›säde“clar“e“d˜pr“eviously‘â}¬!‘f.UR•¸ãGENT:›2‰Mo“v“e˜assignmen“t˜op•Gerators˜for˜the˜other˜±classesŽ‘$Ü#¬b“eforeŽ¡the‘UUconstructors!Ž¡‘ +[²LDF‘T2003.04.09.¬]Ž‘Y;??‘qÇBUG–UUFIX:“No¸ãw“resizing“±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘WY¦¬,“if“after“setting“it“toŽ¡µpŽ‘:±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ¬,‘{±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘X̵:±sizeŽ‘\¬(‘ª¨)–Íô°“¬0Ž‘Íõ.‘JïThis›ó prev•¸ãen“ts˜a˜Memory˜F‘ÿ*ªault˜error˜at˜run-time.‘JïIŽ¡don't–:%knoš¸ãw“wh˜y“it“should“bGe“necessary‘ÿ*ª,–?•though,“since–:%all“of“the“constructors“of“­P®9athŽ‘®¬and“its“deriv˜ed“classesŽ¡resize‘UU±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘WY¦¬;–UUat“least,“I“though¸ãt“they“did.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘ÇŽ¡‘ +­virtualŽ‘/ÔP®9athŽ‘Kt¬&Ž‘S;«­opQÇeratorŽ‘~Ò`¬=Ž’†™~(­constŽ‘*¢P®9athŽ‘:[¬&Ž‘AØyµpŽ‘Fày¬);Ž© ¯See–´?also“sections“704,–ºÝ707,“709,“712,“714,“717,“719,“721,“726,“728,“730,“732,“735,“738,“740,“743,“745,“747,“749,“751,“756,“762,“764,Ž¤ +‘766,–áú768,“771,“773,“776,“778,“781,“783,“785,“790,“792,“794,“797,“799,“801,“805,“810,“812,“818,“820,“827,“829,“836,“838,“844,Ž¡‘846,–áú849,“851,“855,“857,“863,“866,“868,“872,“874,“877,“879,“882,“884,“888,“889,“891,“893,“895,“897,“899,“909,“911,“914,“916,Ž¡‘918,–ÕX920,“921,“922,“923,“925,“932,“934,“936,“938,“940,“946,“952,“955,“959,“961,“964,“and“976.Ž¦This–ÕXco¬¬;Ž¡‘±dr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘P+A¬=‘?µpŽ‘G:±dr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘.ì9¬;‘µ=°‘Gò¬[²LDF‘T2002.10.23.¬]Ž‘T˜!±dr–ÿ}'aw‘‰ffŽ‘®c“olorŽ’‡!¤¬and‘J± l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘,Òé¬pGoin¸ãt–Jto“the“sameŽ¡‘2­ColorŽ‘Q¤ø¬as‘UUµpŽ–]U:±dr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘2AŽ¬and‘UUµpŽ“:± l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘%˜U¬.‘qÇNo–UUmemory“allošGcation“is“p˜erformed.‘o°µ=Ž¡‘± l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘F_p¬=‘ǵpŽ‘Ï:± l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘%˜U¬;Ž¡‘±dashe‘ÿ}'dŽ‘>ñ¼¬=‘ǵpŽ‘Ï:±dashe‘ÿ}'dŽ‘*¡¬;Ž¡‘±p‘ÿ}'enŽ‘0àά=‘ǵpŽ‘Ï:±p‘ÿ}'enŽ‘³¬;Ž¡‘±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘tËl¬=‘ǵpŽ‘Ï:±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ¬;‘µ=°‘ÿý¬LDF–UU2002.09.18.‘qÇAdded“this“line.‘o°µ=Ž¡‘­ifŽ‘)´û¬(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQµ:±sizeŽ‘\¬(‘ª¨)–Ç°“¬0Ž‘Ç)‘µ=°‘ÿý¬LDF–UU2003.04.09.‘qÇAdded“this“conditional.‘o°µ=Ž¡‘(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘|Uµ:±r‘ÿ}'esizeŽ‘i¬(6Ž‘µ;‘ª¨¬0Ž‘ª©);Ž¡‘­forŽ‘/þ¬(­v®9ectorŽ‘ªH°h­P•®9oin“tŽ‘0°Ž‘$1i‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûp‘‰ffŽ‘®iterŽ‘`‰¬=‘ë µpŽ–ó :±p‘ÿ}'ointsŽ›$•µ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);‘±p‘‰ffŽ‘®iterŽ‘!–°6¬=‘ë µpŽ“:±p‘ÿ}'ointsŽ˜µ:±endŽ‘ಬ(‘ª¨);‘±p‘‰ffŽ‘®iterŽ‘+Ÿÿ³+‘ÿ+ŽŽ‘*ò1¬)Ž¡‘2±p‘ÿ}'ointsŽ‘M$šµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­P•®9oin“tŽ‘!¶µµ>‘Ǭ(°Ž‘±p‘‰ffŽ‘®iterŽ‘•‚¬)–UU)“;Ž¡‘­forŽ‘0+á¬(­v®9ectorŽ‘ªH°h­stringŽ‘Ïø°i‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûc‘‰ffŽ‘®iterŽ‘_Ìø¬=‘7UµpŽ–?U:±c–ÿ}'onne“ctorsŽ›/4.µ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);‘CU±c‘‰ffŽ‘®iterŽ‘!R°6¬=‘7UµpŽ“:±c–ÿ}'onne“ctorsŽ˜µ:±endŽ‘ಬ(‘ª¨);Ž¡‘<±c‘‰ffŽ‘®iterŽ‘U’®Ÿÿ³+‘ÿ+ŽŽ‘aYά)‘°fŽ¡‘(±c–ÿ}'onne“ctorsŽ‘W42µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(°Ž‘±c‘‰ffŽ‘®iterŽ‘©¬);Ž¡‘°gŽ¡‘­returnŽ‘Aæ½°Ž‘Fæ¾±thisŽ‘WÒt¬;‘UU°gŽ© ¯See–´?also“sections“705,–ºÝ708,“710,“713,“715,“718,“720,“722,“727,“729,“731,“733,“736,“739,“741,“744,“746,“748,“750,“752,“757,“763,“765,Ž¤ +‘767,–áú769,“772,“774,“777,“779,“782,“784,“786,“791,“793,“795,“798,“800,“802,“806,“807,“808,“809,“811,“813,“814,“819,“821,“828,Ž¡‘830,–áú837,“839,“845,“847,“850,“852,“856,“858,“864,“867,“869,“873,“875,“878,“880,“883,“885,“886,“887,“890,“892,“894,“896,“898,Ž¡‘900,–áú901,“902,“903,“904,“905,“906,“910,“912,“915,“917,“919,“924,“926,“927,“928,“929,“930,“933,“935,“937,“941,“942,“943,“944,Ž¡‘947,–ÕX953,“956,“957,“958,“960,“962,“965,“and“977.Ž¦This–ÕXco“¬0Ž‘Ç)‘°fŽ¡‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­P•®9oin“tŽ‘ï°Ž‘#ïži‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZp‘ÿ}'ointsŽ–ë­µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZp‘ÿ}'ointsŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘­deleteŽ‘?ƽ°Ž‘Dƾ±iterŽ‘U‘¼¬;Ž¡‘°gŽ¡‘±p‘ÿ}'ointsŽ‘/$—µ:±cle‘ÿ}'arŽ‘(Ù¬(‘ª¨);Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(±c–ÿ}'onne“ctorsŽ‘/4.µ:±sizeŽ‘\¬(›ª¨)–ǵ>“¬0Ž‘Ç)‘±c–ÿ}'onne“ctorsŽ‘44.µ:±cle‘ÿ}'arŽ‘(Ù¬(˜);ŽŸ ¯This–ÕXcoÄç¬&Ž‘FŒ±p1Ž‘R¢Å¬);ŽŽŽŒ‹Å$Á Šn ý‘ì°x¬708–¯3DLDF-1.1.5.1’ÎäCONSTRÃŽUCTOR“¬197Ž €n ý•@P­708.Ž¤°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž© ‘ +­P®9athŽ‘#‘i¬::‘­P®9athŽ‘‘h¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±p0Ž‘Pøµ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±p1Ž‘R¢Å¬)°f‘UU­b•QÇo“olŽ‘ö»´DEBUGŽ‘:„,¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Entering® ´Path()® ´(liŽ‘kÆÜne® ´version).\n"Ž’½Ô/°‘DZ ushŽ‘€¬;Ž¦‘±on‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘Xl ¬=‘DZfalseŽ‘v\¬;Ž¦‘±line‘‰ffŽ‘®switchŽ‘Piܬ=‘DZtrueŽ‘‹°¬;Ž¦‘±cycle‘‰ffŽ‘®switchŽ‘Uǵ¬=‘DZfalseŽ‘v\¬;Ž¦‘±do‘‰ffŽ‘®outputŽ‘K½N¬=‘DZtrueŽ‘‹°¬;‘µ=°‘ÿý¬LDF–UU2002.09.18.‘qÇAdded“this“line.‘o°µ=Ž¦‘±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘rTµ:±r‘ÿ}'esizeŽ‘i¬(6Ž‘µ;‘ª¨¬0Ž‘ª©);‘µ=°‘ÿý¬LDF–UU2002.09.18.‘qÇAdded“this“line.‘o°µ=Ž¦‘± l‘‚Øl‘‰ffŽ–®dr‘ÿ}'aw‘‰ffŽ“valueŽ‘_s,¬=‘Ç0Ž‘Ç;Ž¦‘±dr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘O³T¬=‘Ç0Ž‘Ç;Ž¦‘± l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘F_p¬=‘Ç0Ž‘Ç;Ž¦‘±dashe‘ÿ}'dŽ‘>ñ¼¬=‘Ç´""Ž‘ Íz¬;‘µ=°‘ÿý¬LDF–UU2003.04.06.‘qÇAdded“these“three“lines.‘o°µ=Ž¦‘±p‘ÿ}'enŽ‘0àά=‘Ç´""Ž‘ Íz¬;Ž¦‘±arr‘ÿ}'owŽ‘;Ij¬=‘é±falseŽ‘˜[¬;‘i»±p‘ÿ}'ointsŽ‘ŽPµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ›. ¬(‘i»±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6c:µ<‘i»­P•®9oin“tŽ‘!íµ>‘é¬(±p0Ž‘ À¬)–i»)“;‘®ú±p‘ÿ}'ointsŽ‘Óµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ˜¬(“±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6c:µ<Ž¦‘2­P•®9oin“tŽ‘Paeµ>‘Ǭ(±p1Ž‘ À¬)–UU)“;Ž¦‘±c–ÿ}'onne“ctorsŽ‘M41µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(´"--"Ž‘†\¬);Ž¦‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Exiting® ´Path()® ´(linŽ‘kÆÜe® ´version).\n"Ž’¸”2°‘DZ ushŽ‘€¬;Ž¦‘­returnŽ‘>‘h¬;‘qÇ°gŽŸ­709.‘ üSetting‘ÕTfunction.Ž¡°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¦‘ +­v®9oidŽ‘"ýÙ±setŽ‘0v]¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±p0Ž‘Pøµ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±p1Ž‘R¢Å¬);ŽŸ­710.Ž¡°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¦‘ +­v®9oidŽ‘"ýÙP®9athŽ‘Äç¬&Ž‘FŒ±p1Ž‘R¢Å¬)°f‘UU±line‘‰ffŽ‘®switchŽ‘5¿.¬=‘DZtrueŽ‘‹°¬;Ž¦‘±cycle‘‰ffŽ‘®switchŽ‘Uǵ¬=‘DZfalseŽ‘v\¬;Ž¦‘±do‘‰ffŽ‘®outputŽ‘K½N¬=‘DZtrueŽ‘‹°¬;‘µ=°‘ÿý¬LDF–UU2002.09.18.‘qÇAdded“this“line.‘o°µ=Ž¦‘± l‘‚Øl‘‰ffŽ–®dr‘ÿ}'aw‘‰ffŽ“valueŽ‘_s,¬=‘Ç0Ž‘Ç;Ž¦‘±dr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘O³T¬=‘Ç0Ž‘Ç;Ž¦‘± l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘F_p¬=‘Ç0Ž‘Ç;Ž¦‘±dashe‘ÿ}'dŽ‘>ñ¼¬=‘Ç´""Ž‘ Íz¬;‘µ=°‘ÿý¬LDF–UU2003.04.06.‘qÇAdded“these“three“lines.‘o°µ=Ž¦‘±p‘ÿ}'enŽ‘0àά=‘Ç´""Ž‘ Íz¬;Ž¦‘±arr‘ÿ}'owŽ‘;'k¬=‘DZfalseŽ‘v\¬;Ž¦‘°h–ª¨¬Discard‘UU±p‘ÿ}'ointsŽ‘!Ï?¬and‘UU±c–ÿ}'onne“ctorsŽ‘6ɇ¯703“°iŽ¦‘±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘tËl¬=‘Ç0Ž‘Ç;‘µ=°‘ÿý¬LDF–UU2002.09.18.‘qÇAdded“this“line.‘o°µ=Ž¦‘±p‘ÿ}'ointsŽ‘9$˜µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ›.vC¬(‘ñ±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘5˦µ<‘ñ­P•®9oin“tŽ‘!Qµ>‘Ǭ(±p0Ž‘ À¬)–ñ)“;‘_P±p‘ÿ}'ointsŽ‘ƒåµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ˜¬(“±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘5˦µ<“­P•®9oin“tŽ‘!Qµ>‘Ǭ(±p1Ž‘ À¬)“)“;Ž¦‘±c–ÿ}'onne“ctorsŽ‘M41µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(´"--"Ž‘†\¬);Ž¦‘±line‘‰ffŽ‘®switchŽ‘Piܬ=‘DZtrueŽ‘‹°¬;‘UU°gŽŸ­711.› üP•®9oin“ts–ñ|and“one“t®9ypQÇe“of“connector.˜¬This–+ 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¬=‘DZfalseŽ‘v\¬;Ž¦‘±line‘‰ffŽ‘®switchŽ‘Piܬ=‘DZfalseŽ‘v\¬;Ž¦‘±cycle‘‰ffŽ‘®switchŽ‘Uǵ¬=‘DZcycleŽ‘@M¬;Ž¦‘±c–ÿ}'onne“ctorsŽ‘M41µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(±c–ÿ}'onne“ctorŽ‘+^Ú¬);Ž¦‘±do‘‰ffŽ‘®outputŽ‘K½N¬=‘DZtrueŽ‘‹°¬;‘µ=°‘ÿý¬LDF–UU2002.09.18.‘qÇAdded“this“line.‘o°µ=Ž¦‘±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘rTµ:±r‘ÿ}'esizeŽ‘i¬(6Ž‘µ;‘ª¨¬0Ž‘ª©);‘µ=°‘ÿý¬LDF–UU2002.09.18.‘qÇAdded“this“line.‘o°µ=Ž¦‘± l‘‚Øl‘‰ffŽ–®dr‘ÿ}'aw‘‰ffŽ“valueŽ‘_s,¬=‘Ç0Ž‘Ç;Ž¦‘±dr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘O³T¬=‘Ç0Ž‘Ç;Ž¦‘± l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘F_p¬=‘Ç0Ž‘Ç;Ž¦‘±dashe‘ÿ}'dŽ‘>ñ¼¬=‘Ç´""Ž‘ Íz¬;‘µ=°‘ÿý¬LDF–UU2003.04.06.‘qÇAdded“these“three“lines.‘o°µ=Ž¦‘±p‘ÿ}'enŽ‘0àά=‘Ç´""Ž‘ Íz¬;Ž¦‘±arr‘ÿ}'owŽ‘;'k¬=‘DZfalseŽ‘v\¬;Ž¡‘­v‘ÿ\rau½‰™šs4Ž‘ÔwlistŽ‘A'þ±apŽ‘L…P¬;‘µ=°‘ÿý¬F‘ÿ*ªor–UUthe“v‘ÿqÇariable“length“argumen¸ãt“list.‘o°µ=Ž¡‘±va‘‰ffŽ‘®startŽ‘@éj¬(±apŽ‘ ]Rµ;‘ª¨±cycleŽ‘#ݬ);Ž¡‘­P•®9oin“tŽ‘=ÚÖ°Ž‘BÚ×±ar‘ÿ}'g‘‰ffŽ‘®ptrŽ‘b0T¬;‘@‹­whileŽ‘#ní¬((±ar‘ÿ}'g‘‰ffŽ‘®ptrŽ‘#¤˜¬=‘O±va‘‰ffŽ‘®ar‘ÿ}'gŽ‘ ƒ/¬(±apŽ‘ 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l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘F_p¬=‘Ç0Ž‘Ç;Ž¡‘±dashe‘ÿ}'dŽ‘>ñ¼¬=‘Ç´""Ž‘ Íz¬;‘µ=°‘ÿý¬LDF–UU2003.04.06.‘qÇAdded“these“three“lines.‘o°µ=Ž¡‘±p‘ÿ}'enŽ‘0àά=‘Ç´""Ž‘ Íz¬;Ž¡‘±arr‘ÿ}'owŽ‘;'k¬=‘DZfalseŽ‘v\¬;Ž¡‘±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘tËl¬=‘Ç0Ž‘Ç;‘µ=°‘ÿý¬LDF–UU2002.09.18.‘qÇAdded“this“line.‘o°µ=Ž¡‘±c–ÿ}'onne“ctorsŽ‘M41µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(±c–ÿ}'onne“ctorŽ‘+^Ú¬);Ž¦‘­v‘ÿ\rau½‰™šs4Ž‘ÔwlistŽ‘A'þ±apŽ‘L…P¬;‘µ=°‘ÿý¬F‘ÿ*ªor–UUthe“v‘ÿqÇariable“length“argumen¸ãt“list.‘o°µ=Ž¦‘±va‘‰ffŽ‘®startŽ‘@éj¬(±apŽ‘ ]Rµ;‘ª¨±cycleŽ‘#ݬ);Ž¦‘­P•®9oin“tŽ‘=ÚÖ°Ž‘BÚ×±ar‘ÿ}'g‘‰ffŽ‘®ptrŽ‘b0T¬;‘@‹­whileŽ‘#ní¬((±ar‘ÿ}'g‘‰ffŽ‘®ptrŽ‘#¤˜¬=‘O±va‘‰ffŽ‘®ar‘ÿ}'gŽ‘ ƒ/¬(±apŽ‘ ]Rµ;‘ª¨­P•®9oin“tŽ‘!…{°Ž‘&…|¬))–O°6¬=“­staticu½‰™šs4Ž‘ÔwcastŽ‘8̽°h­P•®9oin“tŽ‘ÚÓ°Ž‘$ÚÔi¬(0Ž‘))Ž¡‘2±p‘ÿ}'ointsŽ‘M$šµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­P•®9oin“tŽ‘!¶µµ>‘Ǭ(±ar‘ÿ}'g‘‰ffŽ‘®ptrŽ‘U}¬)–UU)“;Ž¡‘±va‘‰ffŽ‘®endŽ‘ñ¼¬=‘Ç´""Ž‘ Íz¬;‘µ=°‘ÿý¬LDF–UU2003.04.06.‘qÇAdded“these“three“lines.‘o°µ=Ž¦‘±p‘ÿ}'enŽ‘0àά=‘Ç´""Ž‘ Íz¬;Ž¦‘±arr‘ÿ}'owŽ‘;'k¬=‘DZfalseŽ‘v\¬;‘UU±p‘ÿ}'ointsŽ‘yêµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­P•®9oin“tŽ‘!¶µµ>‘Ǭ(± rst‘‰ffŽ–®p‘ÿ}'oint‘‰ffŽ“ptrŽ‘<‘¿¬)–UU)“;Ž¡‘­v‘ÿ\rau½‰™šs4Ž‘ÔwlistŽ‘A'þ±apŽ‘L…P¬;‘µ=°‘ÿý¬F‘ÿ*ªor–UUthe“v‘ÿqÇariable“length“argumen¸ãt“list.‘o°µ=Ž¡‘±va‘‰ffŽ‘®startŽ‘@éj¬(±apŽ‘ ]Rµ;‘ª¨± rst‘‰ffŽ–®p‘ÿ}'oint‘‰ffŽ“ptrŽ‘>‚Œ¬=‘Ï?±va‘‰ffŽ‘®ar‘ÿ}'gŽ‘S¬(±apŽ‘ ]Rµ;‘ª¨­c®9harŽ‘Õ°Ž‘ Ö¬))–Ï?°6¬=“­staticu½‰™šs4Ž‘ÔwcastŽ‘7Lá°h­c®9harŽ‘o-°Ž‘o.i¬(0Ž‘))‘Z9°fŽ¦‘2±c–ÿ}'onne“ctorsŽ‘a43µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬((±c–ÿ}'onne“ctor‘‰ffŽ‘®stringŽ‘J”¬=‘DZc–ÿ}'onne“ctor‘‰ffŽ‘®ptrŽ‘>ze¬));Ž¦‘­ifŽ‘)´û¬((±p‘ÿ}'oint‘‰ffŽ‘®ptrŽ‘*j̬=‘DZva‘‰ffŽ‘®ar‘ÿ}'gŽ‘û,¬(±apŽ‘ ]Rµ;‘ª¨­P•®9oin“tŽ‘ šE°Ž‘%šF¬))–Ç°“­staticu½‰™šs4Ž‘ÔwcastŽ‘7Dº°h­P•®9oin“tŽ‘ï°Ž‘#ïži¬(0Ž‘))‘°fŽ¦‘(±cycle‘‰ffŽ‘®switchŽ‘_Ƕ¬=‘DZtrueŽ‘‹°¬;Ž¦‘(­breakŽ‘D¡h¬;Ž¦‘°gŽ¦‘±p‘ÿ}'ointsŽ‘9$˜µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­P•®9oin“tŽ‘!¶µµ>‘Ǭ(±p‘ÿ}'oint‘‰ffŽ‘®ptrŽ‘'£´¬)–UU)“;‘qÇ°g“±va‘‰ffŽ‘®endŽ‘!š!¬(±apŽ‘ ]R¬);Ž¦‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Exiting® ´Path()® ´(PoiŽ‘kÆÜnt*® ´...).\n"Ž’®8°‘DZ ushŽ‘€¬;Ž¦‘°gŽŸ­719.‘ üSetting‘ÕTfunction.Ž¡°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¦‘ +­v®9oidŽ‘"ýÙ±setŽ‘3˲¬(‘UU­P•®9oin“tŽ‘"Dò°Ž‘'Dó± rst‘‰ffŽ–®p‘ÿ}'oint‘‰ffŽ“ptrŽ‘eZµ:–ª¨:“:Ž‘v+þ¬)‘UU;ŽŽŽŒ‹ÉXJ Šn ý‘ì°x¬720–¯3DLDF-1.1.5.1’¨SETTING‘ÕXFUNCTION“¬201Ž €n ý•@P­720.Ž©°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘"ýÙP®9athŽ‘ñ¼¬=‘Ç´""Ž‘ Íz¬;‘µ=°‘ÿý¬LDF–UU2003.04.06.‘qÇAdded“these“three“lines.‘o°µ=Ž¡‘±p‘ÿ}'enŽ‘0àά=‘Ç´""Ž‘ Íz¬;Ž¡‘±arr‘ÿ}'owŽ‘;'k¬=‘DZfalseŽ‘v\¬;‘UU±p‘ÿ}'ointsŽ‘yêµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­P•®9oin“tŽ‘!¶µµ>‘Ǭ(± rst‘‰ffŽ–®p‘ÿ}'oint‘‰ffŽ“ptrŽ‘<‘¿¬)–UU)“;Ž¦‘­v‘ÿ\rau½‰™šs4Ž‘ÔwlistŽ‘A'þ±apŽ‘L…P¬;‘µ=°‘ÿý¬F‘ÿ*ªor–UUthe“v‘ÿqÇariable“length“argumen¸ãt“list.‘o°µ=Ž¦‘±va‘‰ffŽ‘®startŽ‘@éj¬(±apŽ‘ ]Rµ;‘ª¨± rst‘‰ffŽ–®p‘ÿ}'oint‘‰ffŽ“ptrŽ‘>ze¬));Ž¡‘­ifŽ‘)´û¬((±p‘ÿ}'oint‘‰ffŽ‘®ptrŽ‘*j̬=‘DZva‘‰ffŽ‘®ar‘ÿ}'gŽ‘û,¬(±apŽ‘ ]Rµ;‘ª¨­P•®9oin“tŽ‘ šE°Ž‘%šF¬))–Ç°“­staticu½‰™šs4Ž‘ÔwcastŽ‘7Dº°h­P•®9oin“tŽ‘ï°Ž‘#ïži¬(0Ž‘))‘°fŽ¡‘(±cycle‘‰ffŽ‘®switchŽ‘_Ƕ¬=‘DZtrueŽ‘‹°¬;Ž¡‘(­breakŽ‘D¡h¬;Ž¡‘°gŽ¡‘±p‘ÿ}'ointsŽ‘9$˜µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­P•®9oin“tŽ‘!¶µµ>‘Ǭ(±p‘ÿ}'oint‘‰ffŽ‘®ptrŽ‘'£´¬)–UU)“;›qÇ°g“±va‘‰ffŽ‘®endŽ‘!š!¬(±apŽ‘ ]R¬);˜°gŽŸ­721.– üCop®9y‘…×constructor.“¬[²LDF‘T2003.04.06.¬]Ž‘[!³??–>>!!“BUG:–îÒGot“a“memory“fault“when“I‘îªtried“to“use“thisŽ¡function.›ƒHa•¸ãv“en't–[tested“it“y¸ãet.˜It“w•¸ãork“ed–[to“use“the“default“constructor“and“then“the“assignmen¸ãt“opGerator.Ž¡Maš¸ãybGe–UUit's“not“k˜osher“to“use“\°Ž‘±thisŽ‘²Ï¬=‘ǵpŽ‘Ϭ"“in“a“cop˜y“constructor.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.10.15.¬]Ž‘Y‚PRewrote–Ïjthis“function.‘àThe“old“v¸ãersion“caused“a“memory“fault“when“I‘ÏJtried“to“use“it.Ž¡I'v•¸ãe›×tak“en˜coGde˜from˜the˜default˜constructor˜and˜the˜assignmen“t˜op•Gerator˜and˜put˜it˜here˜without˜b“otheringŽ¡to–Ö see“what“wš¸ãas“causing“the“problem.‘G‹Probably“the“old“v˜ersion“didn't“accoun˜t“for“c˜hanges“I'v˜e“made“in“otherŽ¡places,–UUpGerhaps“in“the“class“de nition.Ž¡‘ +[²LDF‘T2002.11.03.¬]Ž‘Y;Rewrote–UUthis“function.‘qÇNoš¸ãw“just“using“the“assignmen˜t“opGerator.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¡‘ +­P®9athŽ‘"‘e¬(­constŽ‘*¢P®9athŽ‘:[¬&Ž‘AØyµpŽ‘Fày¬);ŽŽŽŒ‹Êe» Šn ý‘ì¬202–¯COPY‘ÕXCONSTRÃŽUCTOR’ûÄ3DLDF-1.1.5.1“°x¬722Ž €n ý•@P­722.Ž©°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¤ ‘ +­P®9athŽ‘#‘i¬::‘­P®9athŽ‘‘h¬(­constŽ‘*¢P®9athŽ‘:[¬&Ž‘AØyµpŽ‘Fày¬)Ž¡‘ +°fŽ¡‘­b•QÇo“olŽ‘-¡h´DEBUGŽ‘K.Ù¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¦‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Entering® ´Path® ´copy® Ž‘kÆÜ´constructor.\n"Ž’» ¬;Ž¡‘°Ž‘±thisŽ‘,²Ñ¬=‘ǵpŽ‘Ϭ;Ž¡‘±on‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘Nl ¬=‘DZfalseŽ‘v\¬;Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Exiting® ´Path()® ´(copŽ‘kÆÜy® ´constructor).\n"Ž’Í”&°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘4‘g¬;Ž¡‘ +°gŽ¤­723.‘ üPseudo-constructor–ÕTfor“dynamic“alloQÇcation.Ž¡724.‘ üP•®9oin“ter‘ÕTargumen“t.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ +¬[²LDF‘T2002.10.29.¬]Ž‘X~öAdded–Ìargumen¸ãt“­constŽ‘ mmP®9athŽ‘;Êá°Ž‘@ÊâµpŽ‘EÒâ¬.‘DIf“µpŽ‘ +›(°6¬=‘Ç0Ž‘Ç,‘ç„the“new“­P®9athŽ‘)„¬is“assigned“to“using“the“v‘ÿqÇaluesŽ¡from‘UUµpŽ‘]U¬.Ž¡‘ +[²LDF‘T2003.12.30.¬]Ž‘WëÉReplaced–8ãthis“v¸ãersion“of“­P®9athŽ‘ÊK¬::‘±cr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“p‘ÿ}'athŽ‘F£¬(‘ª®)“with“a“spGecialization“of“­templateŽ‘/ +A°h­classŽ‘ŠüŸ€„ +Ž¡µCŽ‘ÜÌ°i‘UUµCŽ‘ 2!°Ž‘2"±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘?Áæ¬(‘ª¨).Ž¡‘ +[²LDF‘T2003.12.30.¬]Ž‘Y;Changed–UUthe“argumenš¸ãt.‘qÇIt's“no˜w“a“­constŽ‘!÷P®9athŽ‘=f°°Ž‘Bf±¬.Ž¡‘ +[²LDF‘T2003.12.30.¬]Ž‘YÂÿRemo•¸ãv“ed–default“argumen¸ãt“\0",‘>ÊbGecause“this“caused“a“compiler“error“when“using“theŽ¡DEC–UU²C‘€Ÿÿ³+‘ÿ+ŽŽ‘œu¬compiler.‘qÇApparenš¸ãtly‘ÿ*ª,“it“suces“to“declare“a“default“argumen˜t“in“the“template“declaration.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h›ª¨¬Declare–UUnon-mem¸ãbGer“template“functions“for“­P®9athŽ‘ &½¯724˜°i‘ÇŽ¡‘ +­P®9athŽ‘%溰Ž‘*æ»±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘Zv¬(­constŽ‘*¢P®9athŽ‘:[°Ž‘?\µpŽ‘D\¬);Ž¤ ¯See–ÕXalso“section“725.Ž¡This–ÕXco¬function“in“­ShapQÇeŽ‘!îÖ¬,‘KandŽ¡for–UUgetting“rid“of“items“in“­PictureŽ‘)ñf¬::‘±cle‘ÿ}'arŽ‘(ݬ(‘ª®).Ž¡‘ +[²LDF‘T2002.10.07.¬]Ž‘YlD±cle‘ÿ}'arŽ‘o•¬(‘ª®)–¹^is“needed“bGecause“it's“called“on“the“­ShapQÇesŽ‘*è¬that“are“stored“in“­PicturesŽ‘-Þ§¬,‘Ò`andŽ¡I‘Omdon't–O®knoš¸ãw“of“a“w˜a˜y“of“o˜v˜erloading“destructors.‘`ÑThat“is,›ŽCin“­PictureŽ‘*뿬::‘±cle‘ÿ}'arŽ‘(ݬ(‘ª®),˜the“actual“t¸ãypGes“of“theŽ¡­ShapQÇesŽ‘'ʾ¬are–Uuunkno¸ãwn,›•}so“I‘U3can't“call“°Ž‘ “­P®9athŽ‘$­÷¬(–ª¨),˜°Ž‘ \›­CircleŽ‘*¿Ç¬(“),˜or–Uuother“destructors“directly‘ÿ*ª.‘r'But“a“namedŽ¡function–UUsucš¸ãh“as“±cle‘ÿ}'arŽ‘~.¬(‘ª®)“can“serv˜e“the“same“purpGose.ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.10.07.¬]Ž‘X Added–#cošGde“for“deallo˜cating“the“memory“allo˜cated“for“±dr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘5 +¬and“± l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘(§x¬,‘-if“an¸ãy‘ÿ*ª.Ž¦ŸüÈ„`ÕÁGŽŽ¡‘ +??‘€I›†1tried–†=calling“°Ž‘ M[­P®9athŽ‘#Þ¿¬(‘ª¨)“inside“­P®9athŽ‘Þ¬:‘Ó˜±cle‘ÿ}'arŽ‘üq¬(‘ª®),‘’xbut“I˜got“a“memory“fault.‘€Don't“knoš¸ãw“wh˜y‘ÿ*ª.‘€TO‘†1DO:Ž¡T‘ÿ*ªry–UUto“ nd“out.‘qÇHo•¸ãw“ev“er,–UUthis“isn't“urgen¸ãt.ŽŽŽŒ‹Ì‚Œ Šn ý‘ì¬204–¯CLEAR’«(ÂconstŽ‘*¢ColorŽ‘=Ï•«&Ž‘E–³±cŽ‘Iꎫ)Ž¡‘ -·fŽ¡‘Ï l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘<_o«=‘Ç&Ž‘ -Ž6±cŽ‘â«;Ž¡‘ÂreturnŽ‘4‘g«;Ž¡‘ -·gŽŸÂ702.‘ üColor–ÕTpQÇoinš®9ter“v˜ersion.Ž¦·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/Ôv®9oidŽ‘H‹¬Ïset‘‰ffŽ–® l‘‚Øl‘‰ffŽ“c‘ÿ}'olorŽ‘}Ôæ«(ÂconstŽ‘*¢ColorŽ‘=Ï•·Ž‘BÏ–±cŽ‘G#q«);ŽŸÂ703.Ž¦·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙP®9athŽ‘«(ÂconstŽ‘*¢ColorŽ‘=Ï•·Ž‘BÏ–±cŽ‘G#q«)Ž¡‘ -·fŽ¡‘ÂifŽ‘´ú«(Ï l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘(_m·6«=‘Ç0Ž‘ ÿù·^‘8àÏ l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘%Ñ5Ÿ±~ŽŽ‘+Ñ6Ïis‘‰ffŽ–®on‘‰ffŽ“fr–ÿ}'e“e‘‰ffŽ‘®stor“eŽ‘nL «(‘ª¨)–Ç·“ÏtrueŽ‘‹°«)‘·fŽ¡‘ÂdeleteŽ‘?Æ½Ï l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘e_«;Ž¡‘·gŽ¡‘Ï l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘<_o«=‘DZcŽ‘ó«;Ž¡‘ÂreturnŽ‘4‘g«;Ž¡‘ -·gŽŸÂ704.‘ üSet–ÕTdash“pattern.Ž¦·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/Ôv®9oidŽ‘H‹¬Ïset‘‰ffŽ–®dash‘‰ffŽ“p‘ÿ}'atternŽ’iB«(ÂconstŽ‘*¢stringŽ‘?Oï±sŽ‘FÇ«=‘ÇÝ""Ž‘ Íz«);ŽŽŽŒ‹Ç »[ Šn ý‘ì·x«705‘­3DLDFPR•ÃŽG’ VPSET›ÕXD“ASH˜P–ÿJªA“TTERN‘«199Ž €n ý•@PÂ705.Ž©·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¤ ‘ -Âv®9oidŽ‘"ýÙP®9athŽ‘’ˆ«=‘Ç0Ž–DZ;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±zŽ‘>f®«=‘Ç0Ž“);ŽŽŽŒ‹È Å' Šn ý‘ì«200‘­RšÃŽOT–ÿJªA“TION–ÕXAR˜OUND“THE“MAIN“AXES’Â7v3DLDFPR˜G‘·x«714Ž €n ý•@PÂ714.Ž©·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¤ ‘ -ÂT‘ÿ -«ransformŽ‘AÈÓP®9athŽ‘[Z;«::‘Ïr‘ÿ}'otateŽ‘oB«(ÂconstŽ‘*¢realŽ‘4ÝбxŽ‘:”ì;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±yŽ‘;Ëp;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±zŽ‘;Ÿ–«)Ž¡‘ -·fŽ¡‘ÂT‘ÿ -«ransformŽ‘KÈÔ±tŽ‘OeF«;Ž¦‘±tŽ‘œt:Ïr‘ÿ}'otateŽ‘o>«(±xŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁÆ«);Ž¡‘ÂreturnŽ‘7æ¼·Ž‘<æ½ÏthisŽ‘P™‹·«=ŽŽ‘`'±tŽ‘cÄ4«;Ž¡‘ -·gŽ¤Â715.‘ üRotatation–ÕTaround“an“arbitrary“axis.Ž¡716.– üT‘ÿ -«ransform‘í‘v®9ersion.“«Declared–' in“Ètransfor.web«.‘ è¨Must“bšGe“de ned“here,‘œ2b˜ecause“ÂP®9athŽ‘"फis“anŽ¤ incomplete–UUt¸ãypGe“there.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.05.02.«]Ž‘YËSChanged–mname“of“this“function“from“Ïr–ÿ}'otate‘‰ffŽ‘®ar“oundŽ‘@„ü«(›ª®)“to“Ïr‘ÿ}'otateŽ‘‡««(˜).‘»This“function“no¸ãwŽ¡o•¸ãv“erloads‘UUÏr‘ÿ}'otateŽ‘Ä“«(‘ª®)–UUwith“three“ÂrealŽ‘ƒ«argumen¸ãts.Ž¡‘ -[¬LDF‘T2003.07.06.«]Ž‘Y;Changed,–UUso“that“Ïis‘‰ffŽ‘®line‘ÿ}'arŽ‘(jÒ«(›ª®)“is“used,“instead“of“Ïget‘‰ffŽ–®line‘‰ffŽ“switchŽ‘C+Ò«(˜).Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«De ne‘UUÂT‘ÿ -«ransformŽ‘;'«functions‘@­125“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ 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+­virtualŽ‘/Ôb•QÇo“olŽ‘I/:±set‘‰ffŽ–®on‘‰ffŽ“fr–ÿ}'e“e‘‰ffŽ‘®stor“eŽ’…¬(­b•QÇo“olŽ‘¡fµbŽ‘ ³(¬=‘DZtrueŽ‘‹°¬);ŽŸ­733.Ž¡°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¦‘ +­b•QÇo“olŽ‘#¡gP®9athŽ‘=2Ϭ::‘±set‘‰ffŽ–®on‘‰ffŽ“fr–ÿ}'e“e‘‰ffŽ‘®stor“eŽ‘HUÛ¬(­b•QÇo“olŽ‘¡fµbŽ‘ì¬)Ž¦‘ +°fŽ¦‘±on‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘Nl ¬=‘ǵbŽ‘¬;Ž¦‘­returnŽ‘7æ¼µbŽ‘<1f¬;Ž¦‘ +°gŽ¤­734.‘ üSetting–ÕTdra®9wing“and“ lling“data.Ž¡735.‘ üSet‘ÕT ll‘°¡‰ffs4Ž–#Õdra®9w‘°¡‰ffs4Ž“v‘ÿ\ralue.ŽŸ°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¦‘ +­virtualŽ‘/Ôv®9oidŽ‘H‹¬±set‘‰ffŽ–® l‘‚Øl‘‰ffŽ“dr‘ÿ}'aw‘‰ffŽ“valueŽ’–袬(­constŽ‘*¢signedŽ‘Aš˜shortŽ‘_e;µsŽ‘d;¬);Ž¡­736.ŽŸ°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¦‘ +­v®9oidŽ‘"ýÙP®9athŽ‘¬(­constŽ‘*¢ColorŽ‘=Ï•¬&Ž‘E–³µcŽ‘Iꎬ)Ž¦‘ +°fŽ¦‘± l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘<_o¬=‘Ç&Ž‘ +Ž6µcŽ‘â¬;Ž¦‘­returnŽ‘4‘g¬;Ž¦‘ +°gŽ¡­745.‘ üColor–ÕTpQÇoinš®9ter“v˜ersion.ŽŸ°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¦‘ +­virtualŽ‘/Ôv®9oidŽ‘H‹¬±set‘‰ffŽ–® l‘‚Øl‘‰ffŽ“c‘ÿ}'olorŽ‘}Ôæ¬(­constŽ‘*¢ColorŽ‘=Ï•°Ž‘BÏ–µcŽ‘G#q¬);Ž¡­746.ŽŸ°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¦‘ +­v®9oidŽ‘"ýÙP®9athŽ‘¬(­constŽ‘*¢ColorŽ‘=Ï•°Ž‘BÏ–µcŽ‘G#q¬)Ž¦‘ +°fŽ¦‘­ifŽ‘´ú¬(± l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘(_m°6¬=‘Ç0Ž‘ ÿù°^‘8à± l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘%Ñ5Ÿµ~ŽŽ‘+Ñ6±is‘‰ffŽ–®on‘‰ffŽ“fr–ÿ}'e“e‘‰ffŽ‘®stor“eŽ‘nL ¬(‘ª¨)–Ç°“±trueŽ‘‹°¬)‘°fŽ¦‘­deleteŽ‘?ƽ± l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘e_¬;Ž¦‘°gŽ¦‘± l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘<_o¬=‘ǵcŽ‘ó¬;Ž¦‘­returnŽ‘4‘g¬;Ž¦‘ +°gŽ¡­747.‘ üSet–ÕTdash“pattern.ŽŸ°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¦‘ +­virtualŽ‘/Ôv®9oidŽ‘H‹¬±set‘‰ffŽ–®dash‘‰ffŽ“p‘ÿ}'atternŽ’iB¬(­constŽ‘*¢stringŽ‘?OïµsŽ‘FǬ=‘Ç´""Ž‘ Íz¬);ŽŽŽŒ‹Ï§œ Šn ý‘ì°x¬748›¯3DLDF-1.1.5.1’âºSET–ÕXDÃŽASH“P–ÿJªA“TTERN˜¬207Ž €n ý•@P­748.Ž©°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘"ýÙP®9athŽ‘’ˆ¬=‘Ç0Ž–ǵ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµzŽ‘>f®¬=‘Ç0Ž“);ŽŽŽŒ‹Ð²c Šn ý‘ì¬208‘¯RšÃŽOT–ÿJªA“TION–ÕXAR˜OUND“THE“MAIN“AXES’¹Ãà3DLDF-1.1.5.1‘°x¬757Ž €n ý•@P­757.Ž©°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¤ ‘ +­T‘ÿ +«ransformŽ‘AÈÓP®9athŽ‘[Z;¬::‘±r‘ÿ}'otateŽ‘oB¬(­constŽ‘*¢realŽ‘4ÝеxŽ‘:”ì;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµyŽ‘;Ëp;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµzŽ‘;Ÿ–¬)Ž¡‘ +°fŽ¡‘­T‘ÿ +«ransformŽ‘KÈÔµtŽ‘OeF¬;Ž¦‘µtŽ‘œt:±r‘ÿ}'otateŽ‘o>¬(µxŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁƬ);Ž¡‘­returnŽ‘7æ¼°Ž‘<æ½±thisŽ‘P™‹°¬=ŽŽ‘`'µtŽ‘cÄ4¬;Ž¡‘ +°gŽ¤­758.‘ üRotatation–ÕTaround“an“arbitrary“axis.Ž¡759.– üT‘ÿ +«ransform‘í‘v®9ersion.“¬Declared–' in“®transfor.web¬.‘ è¨Must“bšGe“de ned“here,‘œ2b˜ecause“­P®9athŽ‘"बis“anŽ¤ incomplete–UUt¸ãypGe“there.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.05.02.¬]Ž‘YËSChanged–mname“of“this“function“from“±r–ÿ}'otate‘‰ffŽ‘®ar“oundŽ‘@„ü¬(›ª®)“to“±r‘ÿ}'otateŽ‘‡«¬(˜).‘»This“function“no¸ãwŽ¡o•¸ãv“erloads‘UU±r‘ÿ}'otateŽ‘Ä“¬(‘ª®)–UUwith“three“­realŽ‘ƒ¬argumen¸ãts.Ž¡‘ +[²LDF‘T2003.07.06.¬]Ž‘Y;Changed,–UUso“that“±is‘‰ffŽ‘®line‘ÿ}'arŽ‘(jÒ¬(›ª®)“is“used,“instead“of“±get‘‰ffŽ–®line‘‰ffŽ“switchŽ‘C+Ò¬(˜).Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬De ne‘UU­T‘ÿ +«ransformŽ‘;'¬functions‘@¯169“°i‘Ǭ+°Ž¡‘ +­T‘ÿ «ransformŽ‘AÈÓT‘ÿ -«ransformŽ‘w«(±pŽ‘:Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH«(0Ž‘)±;‘ª¨pŽ‘²¨:Ïget‘‰ffŽ–®last‘‰ffŽ“p‘ÿ}'ointŽ‘:$>«(–ª¨)±;“ÏangleŽ‘jû«);Ž¡‘ÂreturnŽ‘7漫(·Ž‘ÏthisŽ‘²Ï·«=ŽŽ‘(A±tŽ‘+Ýx«);Ž¡‘ -·gŽŽŽŒ‹É Îb Šn ý‘ì·x«717–­3DLDFPRÃŽG’èPÂPOINT‘ÕX­VERSION“«201Ž €n ý•@PÂ717.› üP•®9oin“t‘‘lv“ersion.˜«Declared–øäin“Èpoints.web«.‘\uMust“bšGe“de ned“here,‘!Èb˜ecause“ÂP®9athŽ‘ ƒ,«is“an“incompleteŽ¤ t¸ãypGe‘UUthere.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.05.02.«]Ž‘YËSChanged–mname“of“this“function“from“Ïr–ÿ}'otate‘‰ffŽ‘®ar“oundŽ‘@„ü«(›ª®)“to“Ïr‘ÿ}'otateŽ‘‡««(˜).‘»This“function“no¸ãwŽ¡o•¸ãv“erloads‘UUÏr‘ÿ}'otateŽ‘Ä“«(‘ª®)–UUwith“three“ÂrealŽ‘ƒ«argumen¸ãts.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¤ ‘ -ÂT‘ÿ -«ransformŽ‘AÈÓP•®9oin“tŽ‘^c«::‘Ïr‘ÿ}'otateŽ‘oB«(ÂconstŽ‘*¢P®9athŽ‘:[«&Ž‘AØy±pŽ‘Fày;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆxÏangleŽ‘NHË«)Ž¡‘ -·fŽ¡‘ÂifŽ‘´ú«(·:±pŽ‘:Ïget‘‰ffŽ–®line‘‰ffŽ“switchŽ‘?Ö}«(‘ª¨))‘·fŽ¡‘Ïc‘ÿ}'errŽ‘8(¢·‘rùÝ"ERROR!È ÝInÈ ÝPoint::roŽ‘pr½tate(Path,È Ýreal).\n"Ž’ákâ·Ž¡‘2Ý"PathÈ ÝisÈ ÝnotÈ ÝaÈ Ýline.Ž’šÿÉÈ ÝReturningÈ ÝINVALID_Ž’ÿTRANSFORM.\n\n"Ž’SEÈ«;Ž¡‘ÂreturnŽ‘Aæ½ÝINVALID_TRANSFORMŽ’›¬ò«;Ž¡‘·gŽ©‘ÂP•®9oin“tŽ‘2ïŸÏpt0Ž‘Eò«=‘DZpŽ‘Ï:Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH«(0Ž‘);Ž¡‘ÂP•®9oin“tŽ‘2ïŸÏpt1Ž‘Eò«=‘DZpŽ‘Ï:Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH«(1Ž‘);Ž¦‘ÂreturnŽ‘7æ¼Ïr‘ÿ}'otateŽ‘RUú«(Ïpt0Ž‘i;±;‘ª¨Ïpt1Ž‘ã±;‘ª¨ÏangleŽ‘jû«);Ž¡‘ -·gŽ¤Â718.‘ üP•®9ath‘ÕTv“ersions.Ž¡719.‘ üP•®9oin“t‘ÕTargumen“ts.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ -«[¬LDF‘T2002.4.7.«]Ž‘OÈ?Added–UUdefault“v‘ÿqÇalue“for“ÏangleŽ‘jý·‘Ç«180.Ž¡‘ -[¬LDF‘T2003.05.02.«]Ž‘YËSChanged–mname“of“this“function“from“Ïr–ÿ}'otate‘‰ffŽ‘®ar“oundŽ‘@„ü«(›ª®)“to“Ïr‘ÿ}'otateŽ‘‡««(˜).‘»This“function“no¸ãwŽ¡o•¸ãv“erloads‘UUÏr‘ÿ}'otateŽ‘Ä“«(‘ª®)–UUwith“three“ÂrealŽ‘ƒ«argumen¸ãts.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/ÔT‘ÿ -«ransformŽ‘gV¦Ïr‘ÿ}'otateŽ’Åä«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]Ïp0Ž‘Pø±;‘ª¨ÂconstŽ‘ÕJP•®9oin“tŽ‘>Äç«&Ž‘FŒÏp1Ž‘R¢Å±;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆxÏangleŽ‘Qã«=‘Ç180ŽŽ‘Ç);ŽŸÂ720.‘ ü«TO›]¬DO:–]¯Change“this,‘_Åso“that“I˜use“ÂopQÇeratorŽ‘.ôd·«=ŽŽŽ‘;»ƒ(ÂT‘ÿ -«ransformŽ‘4s}«)“here“and“in“the“other“transformationŽ¡functions.Ž¦·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ -«ransformŽ‘AÈÓP®9athŽ‘[Z;«::‘Ïr‘ÿ}'otateŽ‘oB«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]Ïp0Ž‘Pø±;‘ª¨ÂconstŽ‘ÕJP•®9oin“tŽ‘>Äç«&Ž‘FŒÏp1Ž‘R¢Å±;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆxÏangleŽ‘NHË«)Ž¡‘ -·fŽ¡‘ÂT‘ÿ -«ransformŽ‘KÈÔ±tŽ‘OeF«;Ž¦‘±tŽ‘œt:Ïr‘ÿ}'otateŽ‘o>«(Ïp0Ž‘ À±;‘ª¨Ïp1Ž‘ Áh±;‘ª¨ÏangleŽ‘jû«);Ž¡‘ÂreturnŽ‘7漫(·Ž‘ÏthisŽ‘²Ï·«=ŽŽ‘(A±tŽ‘+Ýx«);Ž¡‘ -·gŽŽŽŒ‹Ê ÖÞ Šn ý‘ì«202›ÂP–ÿ -«A“TH‘ÕX­AR•ÃŽGUMENTS’¯3DLDFPR“G˜·x«721Ž €n ý•@PÂ721.‘ üP•®9ath‘ÕTargumen“ts.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ -«[¬LDF‘T2002.4.7.«]Ž‘OÈ?Added–UUdefault“v‘ÿqÇalue“for“ÏangleŽ‘jý·‘Ç«180.Ž¡‘ -[¬LDF‘T2002.11.03.«]Ž‘Y;Got–UUrid“of“loGcal“ÂP•®9oin“tsŽ‘&Î.Ïp0Ž‘6:C«and“Ïp1Ž‘l«.Ž¡‘ -[¬LDF‘T2003.05.02.«]Ž‘YËSChanged–mname“of“this“function“from“Ïr–ÿ}'otate‘‰ffŽ‘®ar“oundŽ‘@„ü«(›ª®)“to“Ïr‘ÿ}'otateŽ‘‡««(˜).‘»This“function“no¸ãwŽ¡o•¸ãv“erloads‘UUÏr‘ÿ}'otateŽ‘Ä“«(‘ª®)–UUwith“three“ÂrealŽ‘ƒ«argumen¸ãts.Ž¡‘ -[¬LDF‘T2003.07.13.«]Ž‘Y;Changed,–UUso“that“Ïis‘‰ffŽ‘®line‘ÿ}'arŽ‘(jÒ«(‘ª®)“is“used“instead“of“c•¸ãhec“king–UUthe“return“v‘ÿqÇalue“ofŽ¡Ïget‘‰ffŽ–®line‘‰ffŽ“switchŽ‘?Ö}«(–ª®).‘MyAlso,‘þ3Ïget‘‰ffŽ–®last‘‰ffŽ“p‘ÿ}'ointŽ‘="q«(“)–èjpassed“as“the“second“argumen¸ãt“to“Ïr‘ÿ}'otateŽ‘W¨«(‘ª®),‘þ3instead“of“Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘*J²«(1Ž‘).Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·Ž© ‘ -ÂT‘ÿ -«ransformŽ‘AÈÓÏr‘ÿ}'otateŽ‘\8«(ÂconstŽ‘*¢P®9athŽ‘:[«&Ž‘AØy±pŽ‘Fày;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆxÏangleŽ‘Qã«=‘Ç180ŽŽ‘Ç);ŽŸÂ722.Ž¡·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¦‘ -ÂT‘ÿ -«ransformŽ‘AÈÓP®9athŽ‘[Z;«::‘Ïr‘ÿ}'otateŽ‘oB«(ÂconstŽ‘*¢P®9athŽ‘:[«&Ž‘AØy±pŽ‘Fày;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆxÏangleŽ‘NHË«)Ž¦‘ -·fŽ¦‘ÂifŽ‘´ú«(·:±pŽ‘:Ïis‘‰ffŽ‘®line‘ÿ}'arŽ‘%}«(‘ª¨))‘·fŽ¦‘Ïc‘ÿ}'errŽ‘8K·‘•oÝ"ERROR!È ÝInÈ ÝPath::rotŽ‘p•3ate(Path,È Ýreal).\n"Ž’ÜpÑ·Ž¦‘2Ý"PathÈ ÝisÈ ÝnotÈ ÝaÈ Ýline.Ž’šÿÉÈ ÝReturningÈ ÝINVALID_Ž’ÿTRANSFORM.\n\n"Ž’SEÈ«;Ž¦‘ÂreturnŽ‘Aæ½ÝINVALID_TRANSFORMŽ’›¬ò«;Ž¦‘·gŽ¦‘ÂreturnŽ‘7æ¼Ïr‘ÿ}'otateŽ‘RUú«(±pŽ‘:Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH«(0Ž‘)±;‘ª¨pŽ‘²¨:Ïget‘‰ffŽ–®last‘‰ffŽ“p‘ÿ}'ointŽ‘:$>«(–ª¨)±;“ÏangleŽ‘jû«);Ž¦‘ -·gŽŸÂ723.– üScale.“«[¬LDF‘T2002.12.20.«]Ž‘Zˆ6TO–UUDO:“Mak¸ãe“all“of“the“transformations“ÂvirtualŽ‘%Ó«!Ž¡·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·Ž¦‘ -ÂT‘ÿ -«ransformŽ‘AÈÓÏsc‘ÿ}'aleŽ‘W}Å«(ÂrealŽ‘³.±xŽ‘jJ;‘ª¨ÂrealŽ‘]Ö±yŽ‘ gæ«=‘Ç1Ž–DZ;‘ª¨ÂrealŽ‘]Ö±zŽ‘ < «=‘Ç1Ž“);ŽŸÂ724.Ž¡·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¦‘ -ÂT‘ÿ -«ransformŽ‘AÈÓP®9athŽ‘[Z;«::‘Ïsc‘ÿ}'aleŽ‘´ö«(ÂrealŽ‘³.±xŽ‘jJ;‘ª¨ÂrealŽ‘]Ö±yŽ‘ Î;‘ª¨ÂrealŽ‘]Ö±zŽ‘tô«)Ž¦‘ -·fŽ¦‘ÂT‘ÿ -«ransformŽ‘KÈÔ±tŽ‘OeF«;Ž¡‘±tŽ‘œt:Ïsc‘ÿ}'aleŽ‘´ò«(±xŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁÆ«);Ž¦‘ÂreturnŽ‘7漫(·Ž‘ÏthisŽ‘²Ï·«=ŽŽ‘(A±tŽ‘+Ýx«);Ž¦‘ -·gŽŸÂ725.‘ üShear.Ž¡·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·Ž¦‘ -ÂT‘ÿ -«ransformŽ‘AÈÓÏshe‘ÿ}'arŽ‘Yý «(ÂrealŽ‘³.ÏxyŽ‘!—±;‘ª¨ÂrealŽ‘]ÖÏxzŽ‘%œÀ«=‘Ç0Ž–DZ;‘ª¨ÂrealŽ‘]ÖÏyxŽ‘&Zœ«=‘Ç0Ž“±;‘ª¨ÂrealŽ‘]ÖÏyzŽ‘%Ô6«=‘Ç0Ž“±;‘ª¨ÂrealŽ‘]ÖÏzxŽ‘%–Y«=‘Ç0Ž“±;‘ª¨ÂrealŽ‘]ÖÏzyŽ‘%|«=‘Ç0Ž“);ŽŽŽŒ‹Ë â Šn ý‘ì·x«726–­3DLDFPRÃŽG’EF,SHEAR“«203Ž €n ý•@PÂ726.Ž©·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¤ ‘ -ÂT‘ÿ -«ransformŽ‘AÈÓP®9athŽ‘[Z;«::‘Ïshe‘ÿ}'arŽ‘4>«(ÂrealŽ‘³.ÏxyŽ‘!—±;‘ª¨ÂrealŽ‘]ÖÏxzŽ‘"Õ¨±;‘ª¨ÂrealŽ‘]ÖÏyxŽ‘#“„±;‘ª¨ÂrealŽ‘]ÖÏyzŽ‘# ±;‘ª¨ÂrealŽ‘]ÖÏzxŽ‘"ÏA±;‘ª¨ÂrealŽ‘]ÖÏzyŽ‘"´ð«)Ž¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EnteringÈ ÝPath::sheaŽ‘kÆÜr().\n"Ž’‘ /«;Ž¦‘ÂT‘ÿ -«ransformŽ‘KÈÔ±tŽ‘OeF«;Ž¦‘±tŽ‘œt:Ïshe‘ÿ}'arŽ‘4:«(ÏxyŽ‘ -ãç±;‘ª¨ÏxzŽ‘ "z±;‘ª¨ÏyxŽ‘ àV±;‘ª¨ÏyzŽ‘ Yð±;‘ª¨ÏzxŽ‘ ±;‘ª¨ÏzyŽ‘ «);Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ExitingÈ ÝPath::shearŽ‘kÆÜ().\n"Ž’‹Í2«;Ž¡‘ÂreturnŽ‘7漫(·Ž‘ÏthisŽ‘²Ï·«=ŽŽ‘(A±tŽ‘+Ýx«);Ž¡‘ -·gŽ¤Â727.‘ üShift.Ž¡728.‘ üreal‘ÕTargumen®9ts.Ž¦·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·ŽŸ ‘ -ÂT‘ÿ -«ransformŽ‘AÈÓÏshiftŽ‘UæP«(ÂrealŽ‘³.±xŽ‘jJ;‘ª¨ÂrealŽ‘]Ö±yŽ‘ gæ«=‘Ç0Ž–DZ;‘ª¨ÂrealŽ‘]Ö±zŽ‘ < «=‘Ç0Ž“);Ž¡Â729.Ž¦·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¤ ‘ -ÂT‘ÿ -«ransformŽ‘AÈÓP®9athŽ‘[Z;«::‘ÏshiftŽ‘«(ÂrealŽ‘³.±xŽ‘jJ;‘ª¨ÂrealŽ‘]Ö±yŽ‘ Î;‘ª¨ÂrealŽ‘]Ö±zŽ‘tô«)Ž¡‘ -·fŽ¡‘ÂT‘ÿ -«ransformŽ‘KÈÔ±tŽ‘OeF«;Ž¦‘±tŽ‘œt:ÏshiftŽ‘}«(±xŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁÆ«);Ž¡‘ÂreturnŽ‘7漫(·Ž‘ÏthisŽ‘²Ï·«=ŽŽ‘(A±tŽ‘+Ýx«);Ž¡‘ -·gŽŸÂ730.‘ üP•®9oin“t‘ÕTargumen“t.Ž¦·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ -«ransformŽ‘AÈÓÏshiftŽ‘UæP«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]±pŽ‘Ié]«);ŽŸÂ731.Ž¦·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ -«ransformŽ‘AÈÓP®9athŽ‘[Z;«::‘ÏshiftŽ‘«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]±pŽ‘Ié]«)Ž¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼ÏshiftŽ‘L9«(±pŽ‘:Ïget‘‰ffŽ‘®xŽ‘Žg«(–ª¨)±;“pŽ›²¨:Ïget‘‰ffŽ‘®yŽ‘t«(“)±;“pŽ˜:Ïget‘‰ffŽ‘®zŽ‘«(“));Ž¡‘ -·gŽŸÂ732.‘ üShift‘ÕTtimes.Ž¡‘ -«[¬LDF‘T2003.01.19.«]Ž‘Z}Ïshift‘‰ffŽ‘®timesŽ’ˆô¸«(‘ª®)–U—returns“Âv®9oidŽ‘þ«,‘•§bšGecause“ÂP®9athŽ‘!<’«do˜esn't“ha•¸ãv“e–U—a“ÂT‘ÿ -«ransformŽ‘=««data“mem¸ãb˜er,Ž¡and–UUthere's“no“guaranš¸ãtee“that“all“of“the“ÂP•®9oin“tsŽ‘&Î.«on“Ïp‘ÿ}'ointsŽ‘!Ï?«will“ha˜v˜e“iden˜tical“Ïtr‘ÿ}'ansformsŽ‘3-«.Ž¡‘ -[¬LDF‘T2003.01.19.«]Ž‘Y;ÓNote–ˆíthat“Ïshift‘‰ffŽ‘®timesŽ‘2u(«(‘ª®)“will“only“ha•¸ãv“e–ˆían“e ect“on“the“ÂP•®9oin“tsŽ‘'5^«on“a“ÂP®9athŽ‘£>«if“it's“calledŽ¡Ïafter‘6j«a–"Ýcall“to“ÏshiftŽ‘@Z«(›ª®)“and“Ïb–ÿ}'efor“e‘ã8«an–"ÝopGeration“is“applied“that“causes“ÂP•®9oin“tŽ‘½)«::‘Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Gã«(˜)“to“bGe“called.ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.01.19.«]Ž‘Y;Added–UUthis“section.Ž¦ŸüÈ„`ÕÁGŽŽŽŽŒ‹Ì îG Šn ý‘ì«204›ÂREAL‘ÕX­AR•ÃŽGUMENTS’í“3DLDFPR“G˜·x«733Ž €n ý•@PÂ733.‘ üreal‘ÕTargumen®9ts.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ© ‘ -«[¬LDF‘T2003.01.19.«]Ž‘Y;Added–UUthis“function.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·Ž¦‘ -ÂvirtualŽ‘/Ôv®9oidŽ‘H‹¬Ïshift‘‰ffŽ‘®timesŽ‘wwç«(ÂrealŽ‘³.±xŽ‘jJ;‘ª¨ÂrealŽ‘]Ö±yŽ‘ gæ«=‘Ç1Ž–DZ;‘ª¨ÂrealŽ‘]Ö±zŽ‘ < «=‘Ç1Ž“);ŽŸÂ734.Ž¡·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¦‘ -Âv®9oidŽ‘"ýÙP®9athŽ‘uC«&Ž‘FuC«&Ž‘FÄç«&Ž‘FŒÏp1Ž‘R¢Å±;‘ª¨ÂconstŽ‘ÕJc®9harŽ‘9?“ÏaxisŽ‘K|[«);ŽŸÂ752.Ž¡·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¦‘ -ÂT‘ÿ -«ransformŽ‘AÈÓP®9athŽ‘[Z;«::‘Ïalign‘‰ffŽ–®with‘‰ffŽ“axisŽ‘A²|«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]Ïp0Ž‘Pø±;‘ª¨ÂconstŽ‘ÕJP•®9oin“tŽ‘>Äç«&Ž‘FŒÏp1Ž‘R¢Å±;‘ª¨ÂconstŽ‘ÕJc®9harŽ‘9?“ÏaxisŽ‘NCs«=‘ÇÝ'z'Ž‘ w«)Ž¦‘ -·fŽ¦‘ÂT‘ÿ -«ransformŽ‘KÈÔ±tŽ‘OeF«;Ž¡‘±tŽ‘œt:Ïalign‘‰ffŽ–®with‘‰ffŽ“axisŽ‘@²x«(Ïp0Ž‘ À±;‘ª¨Ïp1Ž‘ Áh±;‘ª¨ÏaxisŽ‘çp«);Ž¦‘ÂreturnŽ‘7漫(·Ž‘ÏthisŽ‘²Ï·«=ŽŽ‘(A±tŽ‘+Ýx«);Ž¦‘ -·gŽ¤Â753.‘ üAdding›ÕTP•®9oin“ts˜to˜P“aths.Ž¡754.‘ üWith‘ÕTassignmen®9t.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ -«[¬LDF‘T2002.4.6.«]Ž‘O›çAdded–(ýthis“function.›bÿCurren¸ãtly‘ÿ*ª,‘1Ûit“doGesn't“return“a“ÂP®9athŽ‘ºa«.˜If“it“turns“out“that“it“w¸ãould“bGeŽ¦useful–UUto“return“·Ž‘UVÏthisŽ‘A 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-«[¬LDF‘T2002.11.03.«]Ž‘Y;No¸ãw–UUusing“·Ž‘UV«(Ïp‘ÿ}'ointsŽ›$•±:Ïb‘ÿ}'ackŽ‘üë(‘ª¨))“instead“of“Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘*·«(Ïp‘ÿ}'ointsŽ˜±:ÏsizeŽ‘\«(‘ª¨)–8à·“«1Ž‘8á).Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¡‘ -ÂifŽ‘´ù«(·Ž›«(Ïp‘ÿ}'ointsŽ‘$•±:Ïb‘ÿ}'ackŽ‘üë(‘ª¨))–Ç·6«=“Ïp‘ÿ}'aŽ‘ Ä\±:Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH«(0Ž˜))‘·fŽ¡‘Ïc‘ÿ}'errŽ‘+›·‘ålÝ"ERROR!È ÝInÈ ÝPath::opeŽ‘må0rator&(Path&)."Ž’Â×·‘ålÝ"PathsÈ Ýdon'tÈ Ýtouch.\Ž‘må0n"Ž‘}Ðþ·Ž¡‘(Ý"UsingÈ Ý\"..\"È ÝtoÈ ÝjoiŽ’ÿÈnÈ ÝthemÈ ÝinsteadÈ ÝofÈ Ý\"Ž’ùÿŒ&\".\n"Ž’" ÷·‘ÇÏ ushŽ‘€«;Ž¡‘Ïc–ÿ}'onne“ctorsŽ‘C40±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(Ý".."Ž‘†\«);Ž¡‘ -·gŽ¡‘ -ÂelseŽ‘!ØàÏc–ÿ}'onne“ctorsŽ‘Q ±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(Ý"&"Ž‘F_«);Ž¡‘ -ÂforŽ‘臫(Âv®9ectorŽ‘ªH·hÂP•®9oin“tŽ‘ï·Ž‘#ïži‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W«=‘ÇÏp‘ÿ}'aŽ‘ Ä\±:Ïp‘ÿ}'ointsŽ‘$•±:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¡‘±=·‘ÿý«[¬LDF‘T2002.4.6.«]Ž‘JÈ;Copš¸ãy–UUthe“ÂP•®9oin“tsŽ‘&Î.«in“Ïp‘ÿ}'aŽ‘§î«and“put“the“copies“on˜to“Ïp‘ÿ}'ointsŽ‘yê«.‘o·±=Ž¡‘ -ÏiterŽ‘’·6«=‘ÇÏp‘ÿ}'aŽ‘ 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)ÂColorŽ‘@#-«&Ž‘GêKÏl‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘p´f±;‘ª¨ÂstringŽ‘#$mÏddashe‘ÿ}'dŽ‘Fk~±;‘ª¨ÂstringŽŽ¡‘2Ïpp‘ÿ}'enŽ‘G6(±;‘ª¨ÂPictureŽ‘*œ -«&Ž‘2c(Ïpictur‘ÿ}'eŽ‘Qkþ«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EnteringÈ ÝPath::fillŽ‘kÆÜdraw().\n"Ž’£”>·‘ÇÏ ushŽ‘€«;Ž¡‘ÂifŽ‘´ú«(Ïp‘ÿ}'ointsŽ‘$•±:ÏsizeŽ‘\«(‘ª¨)–Ç·“«0Ž‘Ç)Ž¡‘±=·‘ÿý«LDF–UU2002.09.27.›qÇAdded“this“error“handling“coGde.˜If“the“ÂP®9athŽ‘<«is“emptš¸ãy‘ÿ*ª,“don't“ lldra˜w“it.‘o·±=Ž¡‘·fŽ¡‘Ïc‘ÿ}'errŽ‘3ÓK·‘¢Ý"WARNING!È ÝInÈ ÝPath::fŽ‘lfilldraw():\n"Ž’´I·‘¢Ý"PathÈ Ýdoesn'tÈ ÝcontaiŽ‘lfnÈ ÝanyÈ ÝPoints.\n"Ž’ÃÁ@·Ž¡‘2Ý"NotÈ ÝdoingÈ Ýanything.Ž’šÿÉ\n\n"Ž’¸:·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘>‘h«;Ž¡‘·gŽ¦‘ÂP®9athŽ‘/æ»·Ž‘4æ¼±pŽ‘<µÔ«=‘ÇÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“p‘ÿ}'athŽ‘GÚ·«(ÏthisŽ‘붫);Ž¦‘±pŽ‘Ÿ~ŽŽ‘Ï l‘‚Øl‘‰ffŽ–®dr‘ÿ}'aw‘‰ffŽ“valueŽ‘^{,«=‘ÇÝFILLDRAWŽ‘-Mh«;Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)Ž¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"ddraw_color.get_useŽ‘kÆÜ_name()È Ý==È 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+¬[²LDF‘T2003.05.02.¬]Ž‘YËSChanged–mname“of“this“function“from“±r–ÿ}'otate‘‰ffŽ‘®ar“oundŽ‘@„ü¬(›ª®)“to“±r‘ÿ}'otateŽ‘‡«¬(˜).‘»This“function“no¸ãwŽ¡o•¸ãv“erloads‘UU±r‘ÿ}'otateŽ‘Ä“¬(‘ª®)–UUwith“three“­realŽ‘ƒ¬argumen¸ãts.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¤ ‘ +­T‘ÿ +«ransformŽ‘AÈÓP•®9oin“tŽ‘^c¬::‘±r‘ÿ}'otateŽ‘oB¬(­constŽ‘*¢P®9athŽ‘:[¬&Ž‘AØyµpŽ‘Fày;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±angleŽ‘NHˬ)Ž¡‘ +°fŽ¡‘­ifŽ‘´ú¬(°:µpŽ‘:±get‘‰ffŽ–®line‘‰ffŽ“switchŽ‘?Ö}¬(‘ª¨))‘°fŽ¡‘±c‘ÿ}'errŽ‘8(¢°‘rù´"ERROR!® ´In® ´Point::roŽ‘pr½tate(Path,® ´real).\n"Ž’ákâ°Ž¡‘2´"Path® ´is® ´not® ´a® ´line.Ž’šÿÉ® ´Returning® ´INVALID_Ž’ÿTRANSFORM.\n\n"Ž’SEȬ;Ž¡‘­returnŽ‘Aæ½´INVALID_TRANSFORMŽ’›¬ò¬;Ž¡‘°gŽ©‘­P•®9oin“tŽ‘2pt0Ž‘Eò¬=‘ǵpŽ‘Ï:±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(0Ž‘);Ž¡‘­P•®9oin“tŽ‘2pt1Ž‘Eò¬=‘ǵpŽ‘Ï:±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(1Ž‘);Ž¦‘­returnŽ‘7æ¼±r‘ÿ}'otateŽ‘RUú¬(±pt0Ž‘i;µ;‘ª¨±pt1Ž‘ãµ;‘ª¨±angleŽ‘jû¬);Ž¡‘ +°gŽ¤­761.‘ üP•®9ath‘ÕTv“ersions.Ž¡762.‘ üP•®9oin“t‘ÕTargumen“ts.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ +¬[²LDF‘T2002.4.7.¬]Ž‘OÈ?Added–UUdefault“v‘ÿqÇalue“for“±angleŽ‘jý°‘Ǭ180.Ž¡‘ +[²LDF‘T2003.05.02.¬]Ž‘YËSChanged–mname“of“this“function“from“±r–ÿ}'otate‘‰ffŽ‘®ar“oundŽ‘@„ü¬(›ª®)“to“±r‘ÿ}'otateŽ‘‡«¬(˜).‘»This“function“no¸ãwŽ¡o•¸ãv“erloads‘UU±r‘ÿ}'otateŽ‘Ä“¬(‘ª®)–UUwith“three“­realŽ‘ƒ¬argumen¸ãts.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔT‘ÿ +«ransformŽ‘gV¦±r‘ÿ}'otateŽ’Åä¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±p0Ž‘Pøµ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±p1Ž‘R¢Åµ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±angleŽ‘Qã¬=‘Ç180ŽŽ‘Ç);ŽŸ­763.‘ ü¬TO›]¬DO:–]¯Change“this,‘_Åso“that“I˜use“­opQÇeratorŽ‘.ôd°¬=ŽŽŽ‘;»ƒ(­T‘ÿ +«ransformŽ‘4s}¬)“here“and“in“the“other“transformationŽ¡functions.Ž¦°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓP®9athŽ‘[Z;¬::‘±r‘ÿ}'otateŽ‘oB¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±p0Ž‘Pøµ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±p1Ž‘R¢Åµ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±angleŽ‘NHˬ)Ž¡‘ +°fŽ¡‘­T‘ÿ +«ransformŽ‘KÈÔµtŽ‘OeF¬;Ž¦‘µtŽ‘œt:±r‘ÿ}'otateŽ‘o>¬(±p0Ž‘ Àµ;‘ª¨±p1Ž‘ Áhµ;‘ª¨±angleŽ‘jû¬);Ž¡‘­returnŽ‘7漬(°Ž‘±thisŽ‘²Ï°¬=ŽŽ‘(AµtŽ‘+Ýx¬);Ž¡‘ +°gŽŽŽŒ‹ÒÄ Šn ý‘ì¬210›­P–ÿ +«A“TH‘ÕX¯ARÃŽGUMENTS’ÿ¡3DLDF-1.1.5.1˜°x¬764Ž €n ý•@P­764.‘ üP•®9ath‘ÕTargumen“ts.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ +¬[²LDF‘T2002.4.7.¬]Ž‘OÈ?Added–UUdefault“v‘ÿqÇalue“for“±angleŽ‘jý°‘Ǭ180.Ž¡‘ +[²LDF‘T2002.11.03.¬]Ž‘Y;Got–UUrid“of“loGcal“­P•®9oin“tsŽ‘&Î.±p0Ž‘6:C¬and“±p1Ž‘l¬.Ž¡‘ +[²LDF‘T2003.05.02.¬]Ž‘YËSChanged–mname“of“this“function“from“±r–ÿ}'otate‘‰ffŽ‘®ar“oundŽ‘@„ü¬(›ª®)“to“±r‘ÿ}'otateŽ‘‡«¬(˜).‘»This“function“no¸ãwŽ¡o•¸ãv“erloads‘UU±r‘ÿ}'otateŽ‘Ä“¬(‘ª®)–UUwith“three“­realŽ‘ƒ¬argumen¸ãts.Ž¡‘ +[²LDF‘T2003.07.13.¬]Ž‘Y;Changed,–UUso“that“±is‘‰ffŽ‘®line‘ÿ}'arŽ‘(jÒ¬(‘ª®)“is“used“instead“of“c•¸ãhec“king–UUthe“return“v‘ÿqÇalue“ofŽ¡±get‘‰ffŽ–®line‘‰ffŽ“switchŽ‘?Ö}¬(–ª®).‘MyAlso,‘þ3±get‘‰ffŽ–®last‘‰ffŽ“p‘ÿ}'ointŽ‘="q¬(“)–èjpassed“as“the“second“argumen¸ãt“to“±r‘ÿ}'otateŽ‘W¨¬(‘ª®),‘þ3instead“of“±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘*J²¬(1Ž‘).Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž© ‘ +­T‘ÿ +«ransformŽ‘AÈÓ±r‘ÿ}'otateŽ‘\8¬(­constŽ‘*¢P®9athŽ‘:[¬&Ž‘AØyµpŽ‘Fày;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±angleŽ‘Qã¬=‘Ç180ŽŽ‘Ç);ŽŸ­765.Ž¡°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¦‘ +­T‘ÿ +«ransformŽ‘AÈÓP®9athŽ‘[Z;¬::‘±r‘ÿ}'otateŽ‘oB¬(­constŽ‘*¢P®9athŽ‘:[¬&Ž‘AØyµpŽ‘Fày;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±angleŽ‘NHˬ)Ž¦‘ +°fŽ¦‘­ifŽ‘´ú¬(°:µpŽ‘:±is‘‰ffŽ‘®line‘ÿ}'arŽ‘%}¬(‘ª¨))‘°fŽ¦‘±c‘ÿ}'errŽ‘8K°‘•o´"ERROR!® ´In® ´Path::rotŽ‘p•3ate(Path,® ´real).\n"Ž’ÜpÑ°Ž¦‘2´"Path® ´is® ´not® ´a® ´line.Ž’šÿÉ® ´Returning® ´INVALID_Ž’ÿTRANSFORM.\n\n"Ž’SEȬ;Ž¦‘­returnŽ‘Aæ½´INVALID_TRANSFORMŽ’›¬ò¬;Ž¦‘°gŽ¦‘­returnŽ‘7æ¼±r‘ÿ}'otateŽ‘RUú¬(µpŽ‘:±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(0Ž‘)µ;‘ª¨pŽ‘²¨:±get‘‰ffŽ–®last‘‰ffŽ“p‘ÿ}'ointŽ‘:$>¬(–ª¨)µ;“±angleŽ‘jû¬);Ž¦‘ +°gŽŸ­766.– üScale.“¬[²LDF‘T2002.12.20.¬]Ž‘Zˆ6TO–UUDO:“Mak¸ãe“all“of“the“transformations“­virtualŽ‘%Ó¬!Ž¡°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¦‘ +­T‘ÿ +«ransformŽ‘AÈÓ±sc‘ÿ}'aleŽ‘W}Ŭ(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ gæ¬=‘Ç1Ž–ǵ;‘ª¨­realŽ‘]ÖµzŽ‘ < ¬=‘Ç1Ž“);ŽŸ­767.Ž¡°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¦‘ +­T‘ÿ +«ransformŽ‘AÈÓP®9athŽ‘[Z;¬::‘±sc‘ÿ}'aleŽ‘´ö¬(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ Î;‘ª¨­realŽ‘]ÖµzŽ‘tô¬)Ž¦‘ +°fŽ¦‘­T‘ÿ +«ransformŽ‘KÈÔµtŽ‘OeF¬;Ž¡‘µtŽ‘œt:±sc‘ÿ}'aleŽ‘´ò¬(µxŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁƬ);Ž¦‘­returnŽ‘7漬(°Ž‘±thisŽ‘²Ï°¬=ŽŽ‘(AµtŽ‘+Ýx¬);Ž¦‘ +°gŽŸ­768.‘ üShear.Ž¡°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¦‘ +­T‘ÿ +«ransformŽ‘AÈÓ±she‘ÿ}'arŽ‘Yý ¬(­realŽ‘³.±xyŽ‘!—µ;‘ª¨­realŽ‘]Ö±xzŽ‘%œÀ¬=‘Ç0Ž–ǵ;‘ª¨­realŽ‘]Ö±yxŽ‘&Zœ¬=‘Ç0Ž“µ;‘ª¨­realŽ‘]Ö±yzŽ‘%Ô6¬=‘Ç0Ž“µ;‘ª¨­realŽ‘]Ö±zxŽ‘%–Y¬=‘Ç0Ž“µ;‘ª¨­realŽ‘]Ö±zyŽ‘%|¬=‘Ç0Ž“);ŽŽŽŒ‹ÓÏV Šn ý‘ì°x¬769–¯3DLDF-1.1.5.1’<Ò–SHEAR“¬211Ž €n ý•@P­769.Ž©°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¤ ‘ +­T‘ÿ +«ransformŽ‘AÈÓP®9athŽ‘[Z;¬::‘±she‘ÿ}'arŽ‘4>¬(­realŽ‘³.±xyŽ‘!—µ;‘ª¨­realŽ‘]Ö±xzŽ‘"Õ¨µ;‘ª¨­realŽ‘]Ö±yxŽ‘#“„µ;‘ª¨­realŽ‘]Ö±yzŽ‘# µ;‘ª¨­realŽ‘]Ö±zxŽ‘"ÏAµ;‘ª¨­realŽ‘]Ö±zyŽ‘"´ð¬)Ž¡‘ +°fŽ¡‘­b•QÇo“olŽ‘-¡h´DEBUGŽ‘K.Ù¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¦‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Entering® ´Path::sheaŽ‘kÆÜr().\n"Ž’‘ /¬;Ž¦‘­T‘ÿ +«ransformŽ‘KÈÔµtŽ‘OeF¬;Ž¦‘µtŽ‘œt:±she‘ÿ}'arŽ‘4:¬(±xyŽ‘ +ãçµ;‘ª¨±xzŽ‘ "zµ;‘ª¨±yxŽ‘ àVµ;‘ª¨±yzŽ‘ Yðµ;‘ª¨±zxŽ‘ µ;‘ª¨±zyŽ‘ ¬);Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Exiting® ´Path::shearŽ‘kÆÜ().\n"Ž’‹Í2¬;Ž¡‘­returnŽ‘7漬(°Ž‘±thisŽ‘²Ï°¬=ŽŽ‘(AµtŽ‘+Ýx¬);Ž¡‘ +°gŽ¤­770.‘ üShift.Ž¡771.‘ üreal‘ÕTargumen®9ts.Ž¦°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°ŽŸ ‘ +­T‘ÿ +«ransformŽ‘AÈÓ±shiftŽ‘UæP¬(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ gæ¬=‘Ç0Ž–ǵ;‘ª¨­realŽ‘]ÖµzŽ‘ < ¬=‘Ç0Ž“);Ž¡­772.Ž¦°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¤ ‘ +­T‘ÿ +«ransformŽ‘AÈÓP®9athŽ‘[Z;¬::‘±shiftŽ‘¬(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ Î;‘ª¨­realŽ‘]ÖµzŽ‘tô¬)Ž¡‘ +°fŽ¡‘­T‘ÿ +«ransformŽ‘KÈÔµtŽ‘OeF¬;Ž¦‘µtŽ‘œt:±shiftŽ‘}¬(µxŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁƬ);Ž¡‘­returnŽ‘7漬(°Ž‘±thisŽ‘²Ï°¬=ŽŽ‘(AµtŽ‘+Ýx¬);Ž¡‘ +°gŽŸ­773.‘ üP•®9oin“t‘ÕTargumen“t.Ž¦°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓ±shiftŽ‘UæP¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié]¬);ŽŸ­774.Ž¦°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓP®9athŽ‘[Z;¬::‘±shiftŽ‘¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié]¬)Ž¡‘ +°fŽ¡‘­returnŽ‘7æ¼±shiftŽ‘L9¬(µpŽ‘:±get‘‰ffŽ‘®xŽ‘Žg¬(–ª¨)µ;“pŽ›²¨:±get‘‰ffŽ‘®yŽ‘t¬(“)µ;“pŽ˜:±get‘‰ffŽ‘®zŽ‘¬(“));Ž¡‘ +°gŽŸ­775.‘ üShift‘ÕTtimes.Ž¡‘ +¬[²LDF‘T2003.01.19.¬]Ž‘Z}±shift‘‰ffŽ‘®timesŽ’ˆô¸¬(‘ª®)–U—returns“­v®9oidŽ‘þ¬,‘•§bšGecause“­P®9athŽ‘!<’¬do˜esn't“ha•¸ãv“e–U—a“­T‘ÿ +«ransformŽ‘=«¬data“mem¸ãb˜er,Ž¡and–UUthere's“no“guaranš¸ãtee“that“all“of“the“­P•®9oin“tsŽ‘&Î.¬on“±p‘ÿ}'ointsŽ‘!Ï?¬will“ha˜v˜e“iden˜tical“±tr‘ÿ}'ansformsŽ‘3-¬.Ž¡‘ +[²LDF‘T2003.01.19.¬]Ž‘Y;ÓNote–ˆíthat“±shift‘‰ffŽ‘®timesŽ‘2u(¬(‘ª®)“will“only“ha•¸ãv“e–ˆían“e ect“on“the“­P•®9oin“tsŽ‘'5^¬on“a“­P®9athŽ‘£>¬if“it's“calledŽ¡±after‘6j¬a–"Ýcall“to“±shiftŽ‘@Z¬(›ª®)“and“±b–ÿ}'efor“e‘ã8¬an–"ÝopGeration“is“applied“that“causes“­P•®9oin“tŽ‘½)¬::‘±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Gã¬(˜)“to“bGe“called.ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.01.19.¬]Ž‘Y;Added–UUthis“section.Ž¦ŸüÈ„`ÕÁGŽŽŽŽŒ‹ÔÛŽ Šn ý‘ì¬212–­REAL‘ÕX¯ARÃŽGUMENTS’ÿyý3DLDF-1.1.5.1“°x¬776Ž €n ý•@P­776.‘ üreal‘ÕTargumen®9ts.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ© ‘ +¬[²LDF‘T2003.01.19.¬]Ž‘Y;Added–UUthis“function.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¦‘ +­virtualŽ‘/Ôv®9oidŽ‘H‹¬±shift‘‰ffŽ‘®timesŽ‘wwç¬(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ gæ¬=‘Ç1Ž–ǵ;‘ª¨­realŽ‘]ÖµzŽ‘ < ¬=‘Ç1Ž“);ŽŸ­777.Ž¡°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¦‘ +­v®9oidŽ‘"ýÙP®9athŽ‘uC¬&Ž‘FuC¬&Ž‘FÄç¬&Ž‘FŒ±p1Ž‘R¢Åµ;‘ª¨­constŽ‘ÕJc®9harŽ‘9?“±axisŽ‘K|[¬);ŽŸ­795.Ž¡°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¦‘ +­T‘ÿ +«ransformŽ‘AÈÓP®9athŽ‘[Z;¬::‘±align‘‰ffŽ–®with‘‰ffŽ“axisŽ‘A²|¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±p0Ž‘Pøµ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±p1Ž‘R¢Åµ;‘ª¨­constŽ‘ÕJc®9harŽ‘9?“±axisŽ‘NCs¬=‘Ç´'z'Ž‘ w¬)Ž¦‘ +°fŽ¦‘­T‘ÿ +«ransformŽ‘KÈÔµtŽ‘OeF¬;Ž¡‘µtŽ‘œt:±align‘‰ffŽ–®with‘‰ffŽ“axisŽ‘@²x¬(±p0Ž‘ Àµ;‘ª¨±p1Ž‘ Áhµ;‘ª¨±axisŽ‘çp¬);Ž¦‘­returnŽ‘7漬(°Ž‘±thisŽ‘²Ï°¬=ŽŽ‘(AµtŽ‘+Ýx¬);Ž¦‘ +°gŽ¤­796.‘ üAdding›ÕTP•®9oin“ts˜to˜P“aths.Ž¡797.‘ üWith‘ÕTassignmen®9t.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ +¬[²LDF‘T2002.4.6.¬]Ž‘O›çAdded–(ýthis“function.›bÿCurren¸ãtly‘ÿ*ª,‘1Ûit“doGesn't“return“a“­P®9athŽ‘ºa¬.˜If“it“turns“out“that“it“w¸ãould“bGeŽ¦useful–UUto“return“°Ž‘UV±thisŽ‘A ¬,“I“can“c¸ãhange“it.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¦‘ +­v®9oidŽ‘"ýÙopQÇeratorŽ‘N”Ž¬+=ŽŽŽ‘^"Ê(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±ptŽ‘NÅú¬);ŽŸ­798.Ž¡°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¦‘ +­v®9oidŽ‘"ýÙP®9athŽ‘‘Ǭ(±ptŽ‘ ä¬)–UU)“;Ž¦‘­returnŽ‘>‘h¬;‘qÇ°gŽŸ­799.‘ üWithout‘ÕTassignmen®9t.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ +¬[²LDF‘T2002.4.6.¬]Ž‘OÈ?Added–UUthis“function.Ž¡ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¦‘ +­P®9athŽ‘%æºopQÇeratorŽ‘Q}o¬+Ž‘YD(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±ptŽ‘NÅú¬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹Ø 1 Šn ý‘ì¬216–¯WITHOUT‘ÕXASSIGNMENT’òî3DLDF-1.1.5.1“°x¬800Ž €n ý•@P­800.Ž©°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¤ ‘ +­P®9athŽ‘%ó“P®9athŽ‘?„û¬::Ž‘F9­opQÇeratorŽ‘q©î¬+Ž‘yq (­constŽ‘7{P•®9oin“tŽ‘=3ñ¬&Ž‘Dû±ptŽ‘N߬¬)‘b.­constŽ‘7{°f‘b.­P®9athŽ‘UÀ±p‘ÿ}'aŽ‘*S¬(°Ž‘±thisŽ‘ë·¬);‘b.±p‘ÿ}'aŽ‘_rµ:±p‘ÿ}'ointsŽ‘$•µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.º€¬(‘b.±cr–ÿ}'e“ate‘‰ffŽ‘®newŽŽ¡‘2µ<‘UU­P•®9oin“tŽ‘!¶µµ>‘Ǭ(±ptŽ‘ ä¬)–UU)“;Ž¡‘­returnŽ‘Aæ½±p‘ÿ}'aŽ‘Lä¬;‘qÇ°gŽŸ­801.‘ üAdding–ÕTconnectors“to“P®9aths.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.02.09.¬]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙopQÇeratorŽ‘N”Ž¬+=ŽŽŽ‘^"Ê(­constŽ‘*¢stringŽ‘?OïµsŽ‘Cÿï¬);ŽŸ­802.Ž¦°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙP®9athŽ‘¬;Ž¡‘(­returnŽ‘H‘i¬;Ž¡‘°gŽ¦‘­stringŽ‘?%P±last‘‰ffŽ‘®c–ÿ}'onne“ctorŽ‘}F ¬;ŽŽŽŒ‹Ùœ Šn ý‘ì°x¬807–¯3DLDF-1.1.5.1’4ÞWITH‘ÕXASSIGNMENT“¬217Ž €n ý•@P­807.‘ ü¬[²LDF‘T2002.4.6.¬]Ž‘Q±If–¾there“isn't“an“explicit“connector“for“evš¸ãery“pair“of“­P•®9oin“tsŽ‘'ŸÂ¬in“±thisŽ‘©ÕŸµ~ŽŽ‘©Ö±p‘ÿ}'ointsŽ‘3Îk¬,‘ØRthen“w˜eŽ¤ ha•¸ãv“e–to“ ll“up“±c–ÿ}'onne“ctorsŽ‘7P4¬so“that“there“are“enough.››ÒOtherwise,‘ Ь);ŽŸ­808.‘ ü¬[²LDF‘T2002.4.6.¬]Ž‘PõÆIf–áthe“­P®9athsŽ‘# b¬don't“touc¸ãh,‘_they“are“joined“using“\.."›VKinstead“of“\&".˜This“mimics“theŽ¡bGehaš¸ãvior–UUof“MET‘ÿ*ªAF˜ONT.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.11.03.¬]Ž‘Y;No¸ãw–UUusing“°Ž‘UV¬(±p‘ÿ}'ointsŽ›$•µ:±b‘ÿ}'ackŽ‘üì(‘ª¨))“instead“of“±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘*·¬(±p‘ÿ}'ointsŽ˜µ:±sizeŽ‘\¬(‘ª¨)–8à°“¬1Ž‘8á).Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¡‘ +­ifŽ‘´ù¬(°Ž›¬(±p‘ÿ}'ointsŽ‘$•µ:±b‘ÿ}'ackŽ‘üì(‘ª¨))–Ç°6¬=“±p‘ÿ}'aŽ‘ Ä\µ:±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(0Ž˜))‘°fŽ¡‘±c‘ÿ}'errŽ‘+›°‘ål´"ERROR!® ´In® ´Path::opeŽ‘må0rator&(Path&)."Ž’Â×°‘ål´"Paths® ´don't® ´touch.\Ž‘må0n"Ž‘}Ðþ°Ž¡‘(´"Using® ´\"..\"® ´to® ´joiŽ’ÿÈn® ´them® ´instead® ´of® ´\"Ž’ùÿŒ&\".\n"Ž’" ÷°‘DZ ushŽ‘€¬;Ž¡‘±c–ÿ}'onne“ctorsŽ‘C40µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(´".."Ž‘†\¬);Ž¡‘ +°gŽ¡‘ +­elseŽ‘!Øà±c–ÿ}'onne“ctorsŽ‘Q µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(´"&"Ž‘F_¬);Ž¡‘ +­forŽ‘臬(­v®9ectorŽ‘ªH°h­P•®9oin“tŽ‘ï°Ž‘#ïži‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘DZp‘ÿ}'aŽ‘ Ä\µ:±p‘ÿ}'ointsŽ‘$•µ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¡‘µ=°‘ÿý¬[²LDF‘T2002.4.6.¬]Ž‘JÈ;Copš¸ãy–UUthe“­P•®9oin“tsŽ‘&Î.¬in“±p‘ÿ}'aŽ‘§î¬and“put“the“copies“on˜to“±p‘ÿ}'ointsŽ‘yê¬.‘o°µ=Ž¡‘ +±iterŽ‘’°6¬=‘DZp‘ÿ}'aŽ‘ Ä\µ:±p‘ÿ}'ointsŽ‘$•µ:±endŽ‘ಬ(‘ª¨);‘ÿý±iterŽ‘JûŸÿ³+‘ÿ+ŽŽ‘"¬)‘UU±p‘ÿ}'ointsŽ‘yêµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­P•®9oin“tŽ‘!¶µµ>‘Ǭ(°Ž‘±iterŽ‘Êÿ¬)–UU)“;ŽŸ­809.‘ ü¬[²LDF‘T2002.4.6.¬]Ž‘R_}Put–l˜the“connectors“from“±p‘ÿ}'aŽ‘Öt¬on¸ãto“the“new“­P®9athŽ‘ýü¬.‘·Since“they're“­stringsŽ‘&œè¬,‘²hand“notŽ¡pGoin•¸ãters,‘íöw“e–Ïpdon't“ha•¸ãv“e–Ïpto“copš¸ãy“them.‘àI‘ÏPtested“this“to“mak˜e“sure“it's“true.‘àI‘ÏPdon't“kno˜w“ho˜w“­stringsŽ‘)Ï0¬areŽ¡implemenš¸ãted,–UUbut“they“seem“to“bGe“handled“lik˜e“string“literals.Ž¦°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¡‘ +­forŽ‘œ +¬(­v®9ectorŽ‘ªH°h­stringŽ‘Ïø°i‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘DZp‘ÿ}'aŽ– Ä\µ:±c–ÿ}'onne“ctorsŽ›/4.µ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);‘³€±iterŽ‘E–°6¬=‘DZp‘ÿ}'aŽ“µ:±c–ÿ}'onne“ctorsŽ˜µ:±endŽ‘ಬ(‘ª¨);‘³€±iterŽ‘þ~Ÿÿ³+‘ÿ+ŽŽ‘!Åž¬)‘°fŽ¡‘±c–ÿ}'onne“ctorsŽ‘C40µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(°Ž‘±iterŽ‘Êÿ¬);Ž¡‘ +°gŽ¡‘ +­returnŽ‘*‘f¬;‘qÇ°gŽŸ­810.‘ üWithout‘ÕTassignmen®9t.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.4.6.¬]Ž‘OÈ?Added–UUthis“function.‘qÇIt“bšGeha•¸ãv“es–UUthe“w•¸ãa“y–UUthe“op˜erator“\&"“do˜es“in“MET‘ÿ*ªAF¸ãONT.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¡‘ +­P®9athŽ‘%æºopQÇeratorŽ‘Q}o¬&Ž‘YD(­constŽ‘*¢P®9athŽ‘:[¬&Ž‘AØy±p‘ÿ}'aŽ‘LÕ½¬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹Ú € Šn ý‘ì¬218–¯WITHOUT‘ÕXASSIGNMENT’òî3DLDF-1.1.5.1“°x¬811Ž €n ý•@P­811.Ž©°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¤ ‘ +­P®9athŽ‘%æºP®9athŽ‘?x"¬::Ž‘F`­opQÇeratorŽ‘q¬&Ž‘yd3(­constŽ‘*¢P®9athŽ‘:[¬&Ž‘AØy±p‘ÿ}'aŽ‘LÕ½¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­P®9athŽ‘/滵rŽ‘4°Ï¬(°Ž‘±thisŽ‘ë·¬);Ž¦‘µrŽ‘‘.¬&=ŽŽ‘-悱p‘ÿ}'aŽ‘8ãƬ;Ž¡‘­returnŽ‘7æ¼µrŽ‘<°Ð¬;Ž¡‘ +°gŽŸ­812.› üAppQÇending–‰Qwith“a“connector“argumen®9t.˜¬[²LDF‘T2002.4.7.¬]Ž‘Qä½It–ñØwš¸ãould“not“ha˜v˜e“bšGeen“p˜ossible“toŽ¡spšGecify–d}a“connector“if“I'd“de ned“this“function“as“a“binary“op˜erator,–hGe.g.,“­opQÇeratorŽ‘.þü¬+=ŽŽŽ‘>8(‘ª¨),“so–d}I'v¸ãe“made“it“aŽ¡named–&function.‘b It“can“bGe“useful“when,›/Žfor“instance,˜rotation“causes“t•¸ãw“o‘&­P•®9oin“tsŽ‘#I ¬,˜whic“h–&should“bGe“iden¸ãtical,Ž¡to–0di er“bš¸ãy“a“small“amoun˜t,‘7{lik˜e“1µ=¬10µ;‘ª¨¬000“in“one“cošGordinate.‘eWThis“has“actually“happ˜ened,‘7{whicš¸ãh“is“wh˜y“I'v˜eŽ¡added–þ»this“function.‘TéMET‘ÿ*ªAPOST‘þ¥can“reco•¸ãv“er–þ»gracefully“b¸ãy“using“\´..Ž‘ b¬"“instead“of“\&"“to“connect“the“paths,Ž¡but–Œúit“issues“an“error“message“and“stops“to“wš¸ãait“for“a“respGonse.‘·Using“this“function“can“help“to“a˜v˜oid“suc˜hŽ¡problems.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.4.7.¬]Ž‘OÈ?Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¡‘ +­P®9athŽ‘%溱app‘ÿ}'endŽ‘E™ã¬(­constŽ‘*¢P®9athŽ‘:[¬&Ž‘AØy±p‘ÿ}'aŽ‘LÕ½µ;‘ª¨­stringŽ‘"Ïõ±c–ÿ}'onne“ctorŽ‘Põç¬=‘Ç´"--"Ž‘Mtµ;‘ª¨­b•QÇo“olŽ‘L±assignŽ‘9îB¬=‘DZtrueŽ‘‹°¬);ŽŸ­813.Ž¦°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¡‘ +­P®9athŽ‘%æºP®9athŽ‘?x"¬::‘±app‘ÿ}'endŽ‘ ³-¬(­constŽ‘*¢P®9athŽ‘:[¬&Ž‘AØy±p‘ÿ}'aŽ‘LÕ½µ;‘ª¨­stringŽ‘"Ïõ±c–ÿ}'onne“ctorŽ‘N.ϵ;‘ª¨­b•QÇo“olŽ‘L±assignŽ‘7'*¬)°f‘UU­P®9athŽ‘<µrŽ‘$"¬(°Ž‘±thisŽ‘ë·¬);Ž¡‘­stringŽ‘?Vè±last‘‰ffŽ‘®c–ÿ}'onne“ctorŽ‘}w¸¬;‘µ=°‘1•¬[²LDF‘T2002.4.6.¬]Ž‘K+kIf–†íthere“isn't“an“explicit“connector“for“ev¸ãery“pair“ofŽ¡‘2­P•®9oin“tsŽ‘U‰6¬in‘e­±thisŽ‘QcŸµ~ŽŽ‘Qd±p‘ÿ}'ointsŽ‘3uù¬,‘iÃthen–e­wš¸ãe“ha˜v˜e“to“ ll“up“±c–ÿ}'onne“ctorsŽ‘5ÿˆ¬so“that“there“are“enough.‘¢ÎOtherwise,Ž¡‘2the–UU\&"“will“bšGe“at“the“wrong“place.‘qÇW‘ÿ*ªe“don't“ha•¸ãv“e–UUto“w¸ãorry“ab˜out“the“connectors“for“±p‘ÿ}'aŽ‘R™¬.‘o°µ=Ž¦‘­ifŽ‘)´û¬(µrŽ‘Ê:±c–ÿ}'onne“ctorsŽ‘/4.µ:±sizeŽ‘\¬(‘ª¨)–Ç°“¬0Ž‘Ç)‘±last‘‰ffŽ‘®c–ÿ}'onne“ctorŽ‘Eçè¬=“´"--"Ž‘Mt¬;Ž¡‘­elseŽ‘5Øâ±last‘‰ffŽ‘®c–ÿ}'onne“ctorŽ‘vÀʬ=‘ǵrŽ‘‘,:±c–ÿ}'onne“ctorsŽ‘/4.µ:±b‘ÿ}'ackŽ‘üì(‘ª¨);Ž¡‘­whileŽ‘ 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ned“andŽ¡used‘B1´MIN_REALŽ‘3[¬=‘QÚ­n®9umericu½‰™šs4Ž‘ÔwlimitsŽ‘N@æ°h­realŽ‘]Ù°i‘¬::Ž‘ŽB±minŽ‘³W¬(‘ª¨).‘8[Ho•¸ãw“ev“er,‘}hthis–B1isn't“the“negativ¸ãe“­realŽ‘â;¬with“the“largestŽ¡magnitude,–UUbut“the“smallest“pGositiv¸ãe“­realŽ‘³.¬.ŽŸ°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¡‘ +±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘^R¬[0Ž‘]–Ç=“´MAX_REALŽ‘-Mh¬;‘µ=°‘ÿý¬Minima.‘o°µ=Ž¡‘ +±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘^R¬[2Ž‘]–Ç=“´MAX_REALŽ‘-Mh¬;Ž¡‘ +±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘^R¬[4Ž‘]–Ç=“´MAX_REALŽ‘-Mh¬;Ž¡‘ +±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘^R¬[1Ž‘]–Ç=“°Ž‘ +Ž6´MAX_REALŽ‘5†¬;‘µ=°‘ÿý¬Maxima.‘o°µ=Ž¡‘ +±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘^R¬[3Ž‘]–Ç=“°Ž‘ +Ž6´MAX_REALŽ‘5†¬;Ž¡‘ +±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘^R¬[5Ž‘]–Ç=“°Ž‘ +Ž6´MAX_REALŽ‘5†¬;Ž¡‘ +­forŽ‘臬(­v®9ectorŽ‘ªH°h­P•®9oin“tŽ‘ï°Ž‘#ïži‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZp‘ÿ}'ointsŽ–ë­µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZp‘ÿ}'ointsŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"min® ´x® ´==® 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´"Ž‘?Ôw°‘DZpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘VËi¬[4Ž‘]–Ç°“±end‘‚ØlŽ‘¸Ú¬;Ž¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"max® ´z® ´==® ´"Ž‘?Ôw°‘DZpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘VËi¬[5Ž‘]–Ç°“±end‘‚ØlŽ‘¸Ú¬;Ž¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"z® ´world® ´==® ´"Ž‘JTq°–Ǭ(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±get‘‰ffŽ‘®zŽ‘¬(‘ª¨)“°“±end‘‚ØlŽ‘¸Ú¬;Ž¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"z® ´persp® ´==® ´"Ž‘JTq°›Ç¬(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±get‘‰ffŽ‘®zŽ‘¬(´'p'Ž‘F_µ;‘ª¨±falseŽ–Yìµ;‘ª¨±falseŽ“¬)˜°˜±end‘‚ØlŽ‘¸Ú¬;Ž¡‘°gŽ¡‘±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘hS¬[0Ž›]–Ç=“±minŽ‘ì-¬(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ¬[0Ž˜]µ;–ª¨¬(°Ž˜Ž‘ +±iterŽ‘ˬ)µ:±get‘‰ffŽ‘®xŽ‘Žg¬(´'p'Ž‘F_µ;“±falseŽ›Yìµ;“±falseŽ˜¬));‘µ=°–ÿý¬Min‘UUx“°µ=Ž¡‘±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘hS¬[2Ž›]–Ç=“±minŽ‘ì-¬(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ¬[2Ž˜]µ;–ª¨¬(°Ž˜Ž‘ +±iterŽ‘ˬ)µ:±get‘‰ffŽ‘®yŽ‘t¬(´'p'Ž‘F_µ;“±falseŽ›Yìµ;“±falseŽ˜¬));‘µ=°–ÿý¬Min‘UUy“°µ=Ž¡‘±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘hS¬[4Ž›]–Ç=“±minŽ‘ì-¬(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ¬[4Ž˜]µ;–ª¨¬(°Ž˜Ž‘ +±iterŽ‘ˬ)µ:±get‘‰ffŽ‘®zŽ‘¬(´'p'Ž‘F_µ;“±falseŽ›Yìµ;“±falseŽ˜¬));‘µ=°–ÿý¬Min‘UUz“°µ=Ž¡‘±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘hS¬[1Ž›]–Ç=“±maxŽ‘k³¬(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ¬[1Ž˜]µ;–ª¨¬(°Ž˜Ž‘ +±iterŽ‘ˬ)µ:±get‘‰ffŽ‘®xŽ‘Žg¬(´'p'Ž‘F_µ;“±falseŽ›Yìµ;“±falseŽ˜¬));‘µ=°–ÿý¬Max‘UUx“°µ=Ž¡‘±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘hS¬[3Ž›]–Ç=“±maxŽ‘k³¬(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ¬[3Ž˜]µ;–ª¨¬(°Ž˜Ž‘ +±iterŽ‘ˬ)µ:±get‘‰ffŽ‘®yŽ‘t¬(´'p'Ž‘F_µ;“±falseŽ›Yìµ;“±falseŽ˜¬));‘µ=°–ÿý¬Max‘UUy“°µ=Ž¡‘±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘hS¬[5Ž›]–Ç=“±maxŽ‘k³¬(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ¬[5Ž˜]µ;–ª¨¬(°Ž˜Ž‘ +±iterŽ‘ˬ)µ:±get‘‰ffŽ‘®zŽ‘¬(´'p'Ž‘F_µ;“±falseŽ›Yìµ;“±falseŽ˜¬));‘µ=°–ÿý¬Max‘UUz“°µ=Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘­forŽ‘%般(­in®9tŽ‘¤÷µiŽ‘Þ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ6Ž“;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)Ž¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"projective_extremesŽ‘kÆÜ["Ž‘y”V°‘ǵiŽ‘ $°‘Ç´"]® ´==® ´"Ž‘*Ôƒ°‘DZpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘VËi¬[µiŽ‘qô¬]–Ç°“±end‘‚ØlŽ‘ò°“± ushŽ‘€¬;Ž¡‘ +°gŽŽŽŒ‹ì» Šn ý‘ì¬236–¯SET‘ÕXEXTREMES’:ú3DLDF-1.1.5.1“°x¬887Ž €n ý•@P­887.‘ ü¬[²LDF‘T2002.09.18.¬]Ž‘[Å=Added–’\this“error“handling“coGde.‘(ÝThere“is“a“remote“c¸ãhance“that“a“v‘ÿqÇalid“­P•®9oin“tŽŽ¤ ¬could›Bha•¸ãv“e˜a˜coGordinate˜°˜´MAX_REALŽ‘3 +„¬or˜°Ž‘ 8´MIN_REALŽ‘6ˆ¬,›}Kho“w“ev“er,˜it–Bis“virtually“impšGossible“that“it“w¸ãould“b˜eŽ¡pro‘Ž8jectable.‘Õ®If–v¢it's“the“x“or“y-coGordinate,‘~õit“wš¸ãould“probably“lie“outside“the“limits“de ned“for“the“in˜v˜oGcationŽ¡of‘7¬­PictureŽ‘*Ó½¬::‘±outputŽ‘D¬(‘ª®),›pAand–7¬if“it“w¸ãas“the“µzŽ‘ Nʬ,˜it“w¸ãould“either“bšGe“b˜ehind“the“­F‘ÿ +«oQÇcusŽ‘%d¤¬or“so“far“a•¸ãw“a“y–7¬as“to“b˜eŽ¡practically›‹.in•¸ãvisible.‘SI‘ŠÞbGeliev“e˜that˜this˜is˜the˜case,‘ؤev“en˜though˜the˜z-coGordinates˜are˜made˜smaller˜b“yŽ¡applying–UUthe“equation“µzŸÿ·pŽ‘fj¬=‘ǵzp—=¬(µz‘©w¬+‘8àµp¬).Ž©°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¡‘ +­forŽ‘臬(­in®9tŽ‘¤÷µiŽ‘Þ¬=‘Ç0Ž–Ç;‘ÿýµiŽ› 9 <‘Ǭ6Ž“;‘ÿýµiŽ˜¬+=ŽŽ‘Ž]2Ž‘"Ž^)‘°fŽ¡‘­ifŽ‘´ú¬(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ¬[µiŽ‘qô¬]–Ç°“´MAX_REALŽ‘AMiµ=°–ÿý¬Minima“°µ=Ž¡‘8â°_‘8à±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘V=1¬[µiŽ‘ªÔ¬+‘8à1Ž‘8á]–Ç°“Ž‘ +Ž6´MAX_REALŽ‘5†¬)‘µ=°–ÿý¬Maxima“°µ=Ž¡‘°fŽ¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘(±c‘ÿ}'outŽ‘> S°‘Ç´"i® ´==® ´"Ž‘*Ôƒ°‘ǵiŽ‘ $°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘(±c‘ÿ}'outŽ‘> S°‘Ç´"projective_extremesŽ‘kÆÜ["Ž‘y”V°‘ǵiŽ‘ $°‘Ç´"]® ´==® ´"Ž‘*Ôƒ°‘DZpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘VËi¬[µiŽ‘qô¬]–Ç°“±end‘‚ØlŽ‘ò°“± ushŽ‘€¬;Ž¡‘°gŽ¡‘±c‘ÿ}'errŽ‘3|Á°‘Ç´"ERROR!® ´In® ´Path::setŽ‘kÆÜ_extremes():\n"Ž’½Ô/°‘Ç´"maxima® ´and® ´minima® ´cŽ‘kÆÜould® ´not® ´be® ´set® ´propŽ’ÔÆ \ŽŽ¡‘2erly.® ´"Ž‘Z p°‘Ç´"Setting® ´them® ´all® ´toŽ‘kÆÜ® ´INVALID_REAL® ´and® ´reŽ’ÔÆ turning® ´false.\n"Ž’1Sí°‘Ç± ushŽ‘€¬;Ž¡‘±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘tËl¬=‘Ç´INVALID_REALŽ‘BM\¬;Ž¡‘­returnŽ‘Aæ½±falseŽ‘V–¬;Ž¡‘­breakŽ‘:¡g¬;Ž¡‘°gŽ¡‘ gŽ¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ExitingÈ ÝPath::set_eŽ‘kÆÜxtremes()"Ž’£”>·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ -ÂreturnŽ‘-æ»ÏtrueŽ‘@«S«;‘qÇ·gŽŸÂ845.– üGet‘3Lextremes.“«[¬LDF‘T2002.09.18.«]Ž‘ZÙìAdded–§ this“function.‘fêAnš¸ãy“coGde“that“calls“Ïget‘‰ffŽ‘®extr‘ÿ}'emesŽ‘:ëk«(‘ª®)“m˜ustŽ¡ensure–UUthat“Ïpr–ÿ}'oje“ctŽ‘!Ìc«(‘ª®)“has“bGeen“in•¸ãv“ok“ed‘UU rst.Ž¦·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/ÔinlineŽ‘OconstŽ‘mB¾v‘ÿ\ralarra®9yŽ’–œÿ·hÂrealŽ‘]Ù·i‘UUÏget‘‰ffŽ‘®extr‘ÿ}'emesŽ‘:™µ«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ’‹ë «;Ž¡‘ -·gŽŸÂ846.› üGet–ÕTminim®9um“z.˜«[¬LDF‘T2003.05.16.«]Ž‘Zˆ6Added–UUthis“function.Ž¦·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/ÔrealŽ‘FAÏget‘‰ffŽ–®minimum‘‰ffŽ“zŽ’‰žÚ«(‘ª®)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹å D' Šn ý‘ì·x«847›­3DLDFPRÃŽG’´GET–ÕXMINIMUM“Z˜«229Ž €n ý•@PÂ847.Ž©·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¤ ‘ -ÂrealŽ‘ ³/P®9athŽ‘:D—«::‘Ïget‘‰ffŽ–®minimum‘‰ffŽ“zŽ‘D]Ü«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"EnteringÈ ÝPath::get_Ž‘kÆÜminimum_z()"Ž’®8·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"projective_extremesŽ‘kÆÜ[4]È Ý==È Ý"Ž’™D·‘ÇÏpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘VËi«[4Ž‘]–Ç·“Ïend‘‚ØlŽ‘ò·“Ï ushŽ‘€«;Ž¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"ExitingÈ ÝPath::get_mŽ‘kÆÜinimum_z()"Ž’¨Ô;·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¡‘ÂreturnŽ‘7æ¼Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ’‹ë «[4Ž‘];Ž¡‘ -·gŽŸÂ848.› üGet–ÕTmaxim®9um“z.˜«[¬LDF‘T2002.09.17.«]Ž‘Zˆ6Added–UUthis“function.Ž¦·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/ÔrealŽ‘FAÏget‘‰ffŽ–®maximum‘‰ffŽ“zŽ’Š®«(‘ª®)‘UUÂconstŽ‘*¢«;ŽŸÂ849.Ž¦·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘ ³/P®9athŽ‘:D—«::‘Ïget‘‰ffŽ–®maximum‘‰ffŽ“zŽ‘Em«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"EnteringÈ ÝPath::get_Ž‘kÆÜmaximum_z()"Ž’®8·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"projective_extremesŽ‘kÆÜ[5]È Ý==È Ý"Ž’™D·‘ÇÏpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘VËi«[5Ž‘]–Ç·“Ïend‘‚ØlŽ‘ò·“Ï ushŽ‘€«;Ž¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"ExitingÈ ÝPath::get_mŽ‘kÆÜaximum_z()"Ž’¨Ô;·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¡‘ÂreturnŽ‘7æ¼Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ’‹ë «[5Ž‘];Ž¡‘ -·gŽŸÂ850.› üGet–ÕTmean“z.˜«[¬LDF‘T2003.05.16.«]Ž‘Zˆ6Added–UUthis“function.Ž¦·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/ÔrealŽ‘FAÏget‘‰ffŽ–®me‘ÿ}'an‘‰ffŽ“zŽ‘v÷ «(‘ª®)‘UUÂconstŽ‘*¢«;ŽŸÂ851.Ž¦·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘ ³/P®9athŽ‘:D—«::‘Ïget‘‰ffŽ–®me‘ÿ}'an‘‰ffŽ“zŽ‘1¶«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7漫((Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ«[4Ž›]–8à+“Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘V=1«[5Ž˜])±=«2Ž˜);Ž¡‘ -·gŽŸÂ852.– üSuppress‘xÿoutput.“«[¬LDF‘T2002.09.18.«]Ž‘[ˆAdded–ã§this“function.‘½It's“needed“bGecause“trying“to“erase“aŽ¡ÂShapQÇeŽ‘"Ab·Ž‘*–¸«from‘UUÏelementsŽ‘-¥«in‘UUÂPictureŽ‘)ñf«::‘ÏoutputŽ‘D«(‘ª®)–UUcauses“a“memory“fault.Ž¦·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/Ôv®9oidŽ‘H‹¬Ïsuppr‘ÿ}'ess‘‰ffŽ‘®outputŽ’r.«(‘ª®);ŽŽŽŒ‹æ P” Šn ý‘ì«230–­SUPPRESS‘ÕXOUTPUT’eø3DLDFPRÃŽG“·x«853Ž €n ý•@PÂ853.Ž©·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¤ ‘ -Âv®9oidŽ‘"ýÙP®9athŽ‘È ÝtoÈ ÝcoŽ’ÿÈntinue.\n"Ž’ÈÍ*·‘ÇÏ ushŽ‘€«;Ž¡‘ÏgetcharŽ‘5%þ«(‘ª®);Ž¡‘Ïc‘ÿ}'errŽ‘*SI·‘¡Ý"WARNING!È ÝInÈ ÝPath::oŽ‘leutput():\n"Ž’ªM·‘¡Ý"PathÈ Ýdoesn'tÈ ÝcontaiŽ‘lenÈ ÝanyÈ ÝPoints.\n"Ž’ÄÁ>·Ž¡‘(Ý"NotÈ ÝdoingÈ Ýanything.Ž’ÿÈ\n\n"Ž’®9·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘4‘g«;Ž¡‘ -·gŽŽŽŒ‹è f´ Šn ý‘ì«232–­OUTPUT’=\03DLDFPRÃŽG“·x«859Ž €n ý•@PÂ859.Ž©·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¤ ‘ -Âv®9ectorŽ‘)ªI·hÂP•®9oin“tŽ‘ï·Ž‘#ïži‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7p‘ÿ}'oint‘‰ffŽ‘®iterŽ‘V’:«=‘ÇÏp‘ÿ}'ointsŽ‘ë­±:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¡‘ -Âv®9ectorŽ‘)ªI·hÂstringŽ‘Ïø·i‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7c–ÿ}'onne“ctor‘‰ffŽ‘®iterŽ‘j¡Ó«=‘ÇÏc–ÿ}'onne“ctorsŽ‘1ûF±:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¦‘ -ÂstringŽ‘+%NÏc–ÿ}'onne“ctor‘‰ffŽ‘®stringŽ‘rëÊ«;Ž¦‘ -ÂifŽ‘´ù«(Ïc–ÿ}'onne“ctorsŽ‘/4.±:ÏsizeŽ‘\«(‘ª¨)–DZ>“«0Ž›Ç)‘Ïc–ÿ}'onne“ctor‘‰ffŽ‘®stringŽ‘O”«=“·Ž˜Ïc–ÿ}'onne“ctor‘‰ffŽ‘®iterŽ‘FˆŸÿ®+‘ÿ+ŽŽ‘RO½«;Ž¡‘ -ÂelseŽ‘!ØàÏc–ÿ}'onne“ctor‘‰ffŽ‘®stringŽ‘lft«=‘ÇÝ"--"Ž‘Mt«;Ž¡‘ -ÂifŽ‘´ù«(Ï l‘‚Øl‘‰ffŽ–®dr‘ÿ}'aw‘‰ffŽ“valueŽ‘As)·‘ÇÝDRAWŽ‘Mt«)‘·fŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"Drawing.\n"Ž‘Et·‘ÇÏ ushŽ‘€«;Ž¡‘ÂifŽ‘´ú«(Ïarr‘ÿ}'owŽ‘'h·‘ÇÏtrueŽ‘‹°«)‘Ïout‘‰ffŽ‘®str–ÿ}'e“amŽ‘7´·‘ÇÝ"drawarrowÈ Ý"Ž‘Et·‘ÇŽ‘ÇŽ‘ ÇÏp‘ÿ}'oint‘‰ffŽ‘®iterŽ‘7yŸÿ®+‘ÿ+ŽŽ‘C@%«;Ž¡‘ÂelseŽ‘+ØáÏout‘‰ffŽ‘®str–ÿ}'e“amŽ‘]à•·‘ÇÝ"drawÈ Ý"Ž‘*Ôƒ·‘ÇŽ‘ÇŽ‘ ÇÏp‘ÿ}'oint‘‰ffŽ‘®iterŽ‘7yŸÿ®+‘ÿ+ŽŽ‘C@%«;Ž¡‘·h–ª¨«Output‘²ÎÂP®9athŽ‘ „6­864“·i‘±=·‘]v«[¬LDF‘T2002.09.26.«]Ž‘TÃ)Comparing–²ÎpGoinš¸ãters“seems“to“w˜ork“here.‘Š2I‘²¶think“itŽ¡‘(should,–UUbut“I“wš¸ãasn't“sure“that“it“really“w˜ould.‘o·±=Ž¡‘ÂifŽ‘´ú«(Ïdr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘1³Q·6«=‘ÇÂColorsŽ‘$Ÿö«::Ž‘+.4Ïdefault‘‰ffŽ‘®c‘ÿ}'olorŽ‘bª«)‘·fŽ¡‘Ïout‘‰ffŽ‘®str–ÿ}'e“amŽ‘P··‘ÇÝ"È ÝwithcolorÈ Ý"Ž‘JTq·‘ÇŽ‘ÇÏdr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘6³R«;Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(Ïdashe‘ÿ}'dŽ– ñ¹·6«=‘ÇÝ""Ž‘ Íz«)‘Ïout‘‰ffŽ‘®str–ÿ}'e“amŽ‘7´·‘ÇÝ"È ÝdashedÈ Ý"Ž‘:”z·‘ÇÏdashe‘ÿ}'dŽ“«;Ž¡‘ÂifŽ‘´ú«(Ïp‘ÿ}'enŽ–àË·6«=‘ÇÝ""Ž‘ Íz«)‘Ïout‘‰ffŽ‘®str–ÿ}'e“amŽ‘7´·‘ÇÝ"È ÝwithpenÈ Ý"Ž‘?Ôw·‘ÇÏp‘ÿ}'enŽ“«;Ž¡‘Ïout‘‰ffŽ‘®str–ÿ}'e“amŽ‘F¶·‘ÇÝ";\n"Ž‘ T‰·‘ÇÏ ushŽ‘€«;Ž¡‘ -·gŽ¡‘ -ÂelseŽ‘ .5ifŽ‘+ã-«(Ï l‘‚Øl‘‰ffŽ–®dr‘ÿ}'aw‘‰ffŽ“valueŽ‘As)·‘ÇÝFILLŽ‘Mt«)‘·fŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"Filling.\n"Ž‘Et·‘ÇÏ ushŽ‘€«;Ž¡‘Ïout‘‰ffŽ‘®str–ÿ}'e“amŽ‘F¶·‘ÇÝ"fillÈ Ý"Ž‘*Ôƒ·‘ÇŽ‘ÇŽ‘ ÇÏp‘ÿ}'oint‘‰ffŽ‘®iterŽ‘7yŸÿ®+‘ÿ+ŽŽ‘C@%«;Ž¡‘·h–ª¨«Output‘UUÂP®9athŽ‘ &½­864“·iŽ¡‘ÂifŽ‘´ú«(Ï l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘(_m·6«=‘ÇÂColorsŽ‘$Ÿö«::Ž‘+.4Ïdefault‘‰ffŽ‘®c‘ÿ}'olorŽ‘bª«)‘Ïout‘‰ffŽ‘®str–ÿ}'e“amŽ‘7´·‘ÇÝ"È ÝwithcolorÈ Ý"Ž‘JTq·‘ÇŽ‘ÇÏ l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘-_n«;Ž¡‘Ïout‘‰ffŽ‘®str–ÿ}'e“amŽ‘F¶·‘ÇÝ";\n"Ž‘ T‰·‘ÇÏ ushŽ‘€«;Ž¡‘ -·gŽ¡‘ -ÂelseŽ‘ .5ifŽ‘+ã-«(Ï l‘‚Øl‘‰ffŽ–®dr‘ÿ}'aw‘‰ffŽ“valueŽ‘As)·‘ÇÝFILLDRAWŽ‘-Mh«)‘UU·fŽ¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"Filldrawing.\n"Ž‘Zh·‘ÇÏ ushŽ‘€«;Ž¡‘ -ÂifŽ‘´ù«(Ïdr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘1³Q·‘ÇÏ l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘(_m«)‘·fŽ¡‘Ïout‘‰ffŽ‘®str–ÿ}'e“amŽ‘F¶·‘ÇÝ"filldrawÈ Ý"Ž‘?Ôw·‘ÇŽ‘ÇŽ‘ ÇÏp‘ÿ}'oint‘‰ffŽ‘®iterŽ‘7yŸÿ®+‘ÿ+ŽŽ‘C@%«;Ž¡‘·h–ª¨«Output‘UUÂP®9athŽ‘ &½­864“·iŽ¡‘ÂifŽ‘´ú«(Ïdr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘1³Q·6«=‘ÇÂColorsŽ‘$Ÿö«::Ž‘+.4Ïdefault‘‰ffŽ‘®c‘ÿ}'olorŽ‘bª«)‘Ïout‘‰ffŽ‘®str–ÿ}'e“amŽ‘7´·‘ÇÝ"È ÝwithcolorÈ Ý"Ž‘JTq·‘ÇŽ‘ÇÏdr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘6³R«;Ž¡‘ÂifŽ‘´ú«(Ïdashe‘ÿ}'dŽ– ñ¹·6«=‘ÇÝ""Ž‘ Íz«)‘Ïout‘‰ffŽ‘®str–ÿ}'e“amŽ‘7´·‘ÇÝ"È ÝdashedÈ Ý"Ž‘:”z·‘ÇÏdashe‘ÿ}'dŽ“«;Ž¡‘ÂifŽ‘´ú«(Ïp‘ÿ}'enŽ–àË·6«=‘ÇÝ""Ž‘ Íz«)‘Ïout‘‰ffŽ‘®str–ÿ}'e“amŽ‘7´·‘ÇÝ"È ÝwithpenÈ Ý"Ž‘?Ôw·‘ÇÏp‘ÿ}'enŽ“«;Ž¡‘Ïout‘‰ffŽ‘®str–ÿ}'e“amŽ‘F¶·‘ÇÝ";\n"Ž‘ T‰·‘ÇÏ ushŽ‘€«;Ž¡‘ -·gŽ¡‘ -ÂelseŽ‘0Øá±=·‘ÿý«W‘ÿ*ªe›UUha•¸ãv“e˜t“w“o˜di eren“t˜colors,˜so˜w“e˜ha“v“e˜to˜ ll˜once˜and˜dra“w˜once.‘o·±=Ž¡‘ -·f‘UUÏout‘‰ffŽ‘®str–ÿ}'e“amŽ‘5] ·‘ÇÝ"fillÈ Ý"Ž‘*Ôƒ·‘ÇŽ‘ÇŽ‘ ÇÏp‘ÿ}'oint‘‰ffŽ‘®iterŽ‘7yŸÿ®+‘ÿ+ŽŽ‘C@%«;Ž¡‘ -·h–ª¨«Output‘UUÂP®9athŽ‘ &½­864“·iŽ¡‘ -Ïout‘‰ffŽ‘®str–ÿ}'e“amŽ‘<µ·‘ÇÝ"È ÝwithcolorÈ Ý"Ž‘JTq·‘ÇŽ‘ÇÏ l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘-_n«;Ž¡‘ -Ïout‘‰ffŽ‘®str–ÿ}'e“amŽ‘<µ·‘ÇÝ";\n"Ž‘ T‰·‘ÇÏ ushŽ‘€«;Ž¡‘ -Ïp‘ÿ}'oint‘‰ffŽ‘®iterŽ‘6ù«=‘ÇÏp‘ÿ}'ointsŽ‘ë­±:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);ŽŽŽŒ‹é lL Šn ý‘ì·x«860–­3DLDFPRÃŽG’=\0OUTPUT“«233Ž €n ý•@PÂ860.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ -«[¬LDF‘T2002.05.10.«]Ž‘X_Added–`ythe“coGde“in“this“section.› )It“ xes“a“bug.˜If“it's“not“done,‘‘rthen“the“correct“connectorsŽ¡are–UUnot“used“when“the“ÂP®9athŽ‘<«is“output“the“second“time.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¤ ‘ -Ïc–ÿ}'onne“ctor‘‰ffŽ‘®iterŽ‘K«=‘ÇÏc–ÿ}'onne“ctorsŽ‘1ûF±:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¡‘ -ÂifŽ‘´ù«(Ïc–ÿ}'onne“ctorsŽ‘/4.±:ÏsizeŽ‘\«(‘ª¨)–DZ>“«0Ž›Ç)‘Ïc–ÿ}'onne“ctor‘‰ffŽ‘®stringŽ‘O”«=“·Ž˜Ïc–ÿ}'onne“ctor‘‰ffŽ‘®iterŽ‘FˆŸÿ®+‘ÿ+ŽŽ‘RO½«;Ž¡‘ -ÂelseŽ‘!ØàÏc–ÿ}'onne“ctor‘‰ffŽ‘®stringŽ‘lft«=‘ÇÝ"--"Ž‘Mt«;ŽŸÂ861.ŽŸ·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¡‘ 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-ÂvirtualŽ‘/Ôb•QÇo“olŽ‘I/:Ïis‘‰ffŽ‘®planarŽ‘qUÉ«(Âb•QÇo“olŽ‘¡fÏverb‘ÿ}'oseŽ‘<ùÛ«=‘ÇÏfalseŽ‘v\±;‘ª¨ÂstringŽ‘"ÏõÏtextŽ‘6îÙ«=‘ÇÝ""Ž‘ Íz«)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹ï Ä< Šn ý‘ì·x«873–­3DLDFPRÃŽG’3´TIS‘ÕXPLANAR“«239Ž €n ý•@PÂ873.Ž©·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¤ ‘ -Âb•QÇo“olŽ‘#¡gP®9athŽ‘=2Ï«::‘Ïis‘‰ffŽ‘®planarŽ‘)&“«(Âb•QÇo“olŽ‘¡fÏverb‘ÿ}'oseŽ‘:2ñ;‘ª¨ÂstringŽ‘"ÏõÏtextŽ‘4'Á«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂifŽ‘´ú«(ÝVERBOSE_GLOBALŽ‘J>«)‘Ïverb‘ÿ}'oseŽ‘(Xu«=‘ÇÏtrueŽ‘‹°«;Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÿ9·_‘8àÏverb‘ÿ}'oseŽ‘"Ê=«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EnteringÈ ÝPath::is_pŽ‘kÆÜlanar().\n"Ž’¦ #«;Ž¦‘ÂP•®9oin“tŽ‘2pŽ‘7÷Ÿ«(Ïget‘‰ffŽ‘®normalŽ‘0Št«(‘ª®));Ž¦‘ÂifŽ‘´ú«(±pŽ‘Ï·‘ÇÝINVALID_POINTŽ‘GY«)‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ExitingÈ ÝPath::is_plŽ‘kÆÜanar().È ÝReturningÈ ÝfaŽ’ÔÆ lse.\n\n"Ž’T·‘ÇÏ ushŽ‘€«;Ž¡‘ÂifŽ‘)´û«(Ïverb‘ÿ}'oseŽ‘ ‘]«)‘·fŽ¡‘(ÂifŽ‘3´ü«(ÏtextŽ‘ä·‘ÇÝ""Ž‘ Íz«)‘ÏtextŽ‘ä«=‘ÇÝ"Path"Ž‘"Ín«;Ž¡‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÏtextŽ‘åü·‘ÇÝ"È ÝisÈ Ýnon-planar.\n\nŽ‘kÆÜ"Ž‘qA«;Ž¡‘·gŽ¡‘ÂreturnŽ‘Aæ½ÏfalseŽ‘V–«;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(±pŽ‘Ï·‘ÇÏoriginŽ‘½9«)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘3|Á·‘ÇÝ"WARNING!È ÝInÈ ÝPath::iŽ‘kÆÜs_planar():\n"Ž’¸”2·‘ÇÝ"PathÈ ÝisÈ Ýlinear.È ÝReŽ‘kÆÜturningÈ Ýtrue.\n\n"Ž’Í”&·Ž¡‘2Ï ushŽ‘G¹«;Ž¡‘ÂifŽ‘)´û«(Ïverb‘ÿ}'oseŽ‘ ‘]«)‘·fŽ¡‘(ÂifŽ‘3´ü«(ÏtextŽ‘ä·‘ÇÝ""Ž‘ Íz«)‘ÏtextŽ‘ä«=‘ÇÝ"Path"Ž‘"Ín«;Ž¡‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÏtextŽ‘åü·‘ÇÝ"È ÝisÈ Ýplanar.\n\n"Ž‘\M«;Ž¡‘·gŽ¡‘ÂreturnŽ‘Aæ½ÏtrueŽ‘T«U«;Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘ÂifŽ‘)´û«(Ïverb‘ÿ}'oseŽ‘ ‘]«)‘·fŽ¡‘(ÂifŽ‘3´ü«(ÏtextŽ‘ä·‘ÇÝ""Ž‘ Íz«)‘ÏtextŽ‘ä«=‘ÇÝ"Path"Ž‘"Ín«;Ž¡‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÏtextŽ‘åü·‘ÇÝ"È ÝisÈ Ýplanar.\n\n"Ž‘\M«;Ž¡‘·gŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ExitingÈ ÝPath::is_plŽ‘kÆÜanar().È ÝReturningÈ ÝtrŽ’ÔÆ ue.\n\n"Ž’·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½ÏtrueŽ‘T«U«;Ž¡‘·gŽ¡‘ -gŽŸÂ874.– üIs‘þ“linear.“«[¬LDF‘T2003.04.09.«]Ž‘Z¬Ïis‘‰ffŽ‘®line‘ÿ}'arŽ‘Á‘«(‘ª®)–y3 rst“c•¸ãhec“ks–y3whether“Ïline‘‰ffŽ‘®switchŽ‘6•'«is“ÏtrueŽ‘=Ë«.‘ÝaIf“it“is,‘‚+it“returnsŽ¡ÏtrueŽ‘Á«righ•¸ãt›<)a“w“a“y‘ÿ*ª.‘icOtherwise,‘A2it˜uses˜the˜return˜v‘ÿqÇalue˜of˜Ïget‘‰ffŽ‘®normalŽ‘3Æ«(‘ª®)˜to˜determine˜whether˜·Ž‘<*ÏthisŽ‘d «is˜linear˜orŽ¡not.‘qÇIf–UUit“is,“Ïis‘‰ffŽ‘®line‘ÿ}'arŽ‘(jÒ«(‘ª®)“returns“ÏtrueŽ‘í«,“otherwise,“it“returns“ÏfalseŽ‘™«.ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.11.05.«]Ž‘Y;Added–UUthis“function.Ž¡‘ -[¬LDF‘T2002.11.06.«]Ž‘YCvAdded–optional“ÂconstŽ‘!ömb•QÇo“olŽ‘;ÓÏverb‘ÿ}'oseŽ‘_ôû«and“ÂstringŽ‘$ñÏtextŽ‘9Ùt«argumen¸ãts“for“writing“a“messageŽ¡to–UUthe“standard“output.Ž¡‘ -[¬LDF‘T2003.04.09.«]Ž‘YþØNo•¸ãw›Kòc“hec“king˜whether˜Ïline‘‰ffŽ‘®switchŽ‘8:¥«is˜ÏtrueŽ‘\|«bGefore˜calling˜Ïget‘‰ffŽ‘®normalŽ‘4Öf«(‘ª®).–Už!!“If˜a˜ÂP®9athŽŽ¡«whose‘ûÏline‘‰ffŽ‘®switchŽ‘9+·‘êÔÏtrueŽ‘Mg«is–ûmoGdi ed“sucš¸ãh“that“it's“no“longer“linear,‘ð$the“programmer“m˜ust“ensure“thatŽ¡Ïline‘‰ffŽ‘®switchŽ‘2ø«is–UUset“to“ÏfalseŽ‘™«!Ž¡‘ -[¬LDF‘T2003.08.14.«]Ž‘Y;Made‘UUÏverb‘ÿ}'oseŽ‘'<«non-ÂconstŽ‘ÕM«.‘qÇSetting–UUit“to“ÏtrueŽ‘oB«if“ÝVERBOSE_GLOBALŽ‘P°è«is“ÏtrueŽ‘í«.Ž¡Added‘UUÝVERBOSE_GLOBALŽ‘P°è«to–UUÈpspglb.web“«toGda¸ãy‘ÿ*ª.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·Ž¡‘ -Âb•QÇo“olŽ‘#¡gÏis‘‰ffŽ‘®line‘ÿ}'arŽ‘H¶ä«(Âb•QÇo“olŽ‘¡fÏverb‘ÿ}'oseŽ‘<ùÛ«=‘ÇÏfalseŽ‘v\±;‘ª¨ÂstringŽ‘"ÏõÏtextŽ‘6îÙ«=‘ÇÝ""Ž‘ Íz«)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹ð РŠn ý‘ì«240–­IS‘ÕXLINEAR’73DLDFPRÃŽG“·x«875Ž €n ý•@PÂ875.Ž©·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¤ ‘ -Âb•QÇo“olŽ‘#¡gP®9athŽ‘=2Ï«::‘Ïis‘‰ffŽ‘®line‘ÿ}'arŽ‘&«(Âb•QÇo“olŽ‘¡fÏverb‘ÿ}'oseŽ‘:2ñ;‘ª¨ÂstringŽ‘"ÏõÏtextŽ‘4'Á«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂifŽ‘´ú«(ÝVERBOSE_GLOBALŽ‘J>«)‘Ïverb‘ÿ}'oseŽ‘(Xu«=‘ÇÏtrueŽ‘‹°«;Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÿ9·_‘8àÏverb‘ÿ}'oseŽ‘"Ê=«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EnteringÈ ÝPath::is_lŽ‘kÆÜinear().\n"Ž’¦ #«;Ž¡‘ÂifŽ‘´ú«(Ïline‘‰ffŽ‘®switchŽ‘/¢Á«)‘±=·‘ÿý«LDF–UU2003.04.09.‘qÇAdded“this“conditional.‘o·±=Ž¡‘ÂreturnŽ‘Aæ½ÏtrueŽ‘T«U«;Ž¦‘ÂP•®9oin“tŽ‘2pŽ‘7÷Ÿ«(Ïget‘‰ffŽ‘®normalŽ‘0Št«(‘ª®));Ž¦‘ÂifŽ‘´ú«(±pŽ‘Ï·‘ÇÏoriginŽ‘½9«)‘·fŽ¡‘ÂifŽ‘)´û«(Ïverb‘ÿ}'oseŽ‘ ‘]«)‘·fŽ¡‘(ÂifŽ‘3´ü«(ÏtextŽ‘ä·‘ÇÝ""Ž‘ Íz«)‘ÏtextŽ‘ä«=‘ÇÝ"Path"Ž‘"Ín«;Ž¡‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÏtextŽ‘åü·‘ÇÝ"È ÝisÈ Ýlinear.\n\n"Ž‘\M«;Ž¡‘·gŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ExitingÈ ÝPath::is_liŽ‘kÆÜnear().È Ý"Ž’žTA·‘ÇÝ"ReturningÈ Ýtrue.\n\nŽ‘kÆÜ"Ž‘tTY·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½ÏtrueŽ‘T«U«;Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘ÂifŽ‘)´û«(Ïverb‘ÿ}'oseŽ‘ ‘]«)‘·fŽ¡‘(ÂifŽ‘3´ü«(ÏtextŽ‘ä·‘ÇÝ""Ž‘ Íz«)‘ÏtextŽ‘ä«=‘ÇÝ"Path"Ž‘"Ín«;Ž¡‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÏtextŽ‘åü·‘ÇÝ"È ÝisÈ Ýnon-linear.\n\nŽ‘kÆÜ"Ž‘qA«;Ž¡‘·gŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ExitingÈ ÝPath::is_liŽ‘kÆÜnear().È Ý"Ž’žTA·‘ÇÝ"ReturningÈ Ýfalse.\n\Ž‘kÆÜn"Ž‘y”V·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½ÏfalseŽ‘V–«;Ž¡‘·gŽ¡‘ -gŽŸÂ876.› üGet–$line“switc®9h.˜«[¬LDF‘T2002.11.03.«]Ž‘ZÍThis–š9function“returns“ÏtrueŽ‘ù -«for“ÂP®9athsŽ‘$O«that“are“created“or“setŽ¡using›UUt•¸ãw“o˜ÂP•®9oin“tsŽ‘&Î.«only‘ÿ*ª,˜and˜no˜connectors,˜as˜argumen“ts.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.11.03.«]Ž‘XIúRenamed–—this“function“Ïget‘‰ffŽ–®line‘‰ffŽ“switchŽ‘Bm‘«(›ª®)“from“Ïis‘‰ffŽ‘®lineŽ‘ˆS«(˜).‘2\AbGout“to“add“Ïis‘‰ffŽ‘®line‘ÿ}'arŽ‘'¬‘«(˜),‘½!whic¸ãhŽ¡will–UUtest“whether“all“the“ÂP•®9oin“tsŽ‘&Î.«are“colinear“or“not.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·Ž¡‘ -ÂinlineŽ‘)ŠIb•QÇo“olŽ‘C+¯Ïget‘‰ffŽ–®line‘‰ffŽ“switchŽ’ƒ,«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼Ïline‘‰ffŽ‘®switchŽ‘g‰}«;Ž¡‘ -·gŽŸÂ877.‘ üT‘ÿ -«est–ÕTfor“cycles.Ž¦·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·Ž¡‘ -ÂinlineŽ‘)ŠIb•QÇo“olŽ‘C+¯Ïis‘‰ffŽ‘®cycleŽ‘dzÇ«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼Ïcycle‘‰ffŽ‘®switchŽ‘lçV«;Ž¡‘ -·gŽŸÂ878.‘ üSize›ÕT(n•®9um“b•QÇer˜of˜p“oin®9ts).Ž¦·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·ŽŽŽŒ‹ñ ß - Šn ý‘ì·x«878›­3DLDFPRÃŽG’í}PSIZE–ÕX(NUMBER“OF“POINTS)˜«241Ž €n ý•@P‘ -ÂinlineŽ‘)ŠIin®9tŽ‘;/@ÏsizeŽ‘LJœ«(‘ª®)Ž¤ ‘ -·fŽ¡‘ÂreturnŽ‘7æ¼Ïp‘ÿ}'ointsŽ‘S Q±:ÏsizeŽ‘\«(‘ª¨);Ž¡‘ -·gŽ©Â879.– üSlopQÇe.“«[¬LDF‘T2002.11.05.«]Ž‘\OÊÏslop‘ÿ}'eŽ‘r‡•«(‘ª®)–écan“only“bGe“used“for“linear“ÂP®9athsŽ‘"7‰«.‘ ȃIt“returns“a“ÂrealŽ‘—««v‘ÿqÇalueŽ¡represenš¸ãting–ƒthe“slopGe“of“the“Ïtr–ÿ}'ac“e‘Cl«of–ƒa“line“on“the“ma‘Ž8jor“plane“represen˜ted“b˜y“the“Âc®9harŽ‘«argumen˜ts,‘ÎorŽ¡ÝINVALID_REALŽ‘?†D«,›B*if–=`the“ÂP®9athŽ‘ $«is“non-linear.‘iËF‘ÿ*ªor“example,˜ifŸü±È“·ŽŽ‘ÞG‘þ㎎Ž‘gþ!ŽŽŸN8“±pŸÿ®0Ž‘|s±pŸÿ®1ŽŽŽŽŽ‘ƒ¦«is“a“ÂP®9athŽ‘ $±pŽ‘'Q„«andŸü±È“·ŽŽ‘M‘þ㎎Ž‘ÖÏ!ŽŽŸN8“±qŸÿ®0Ž‘|s±qŸÿ®1ŽŽŽŽŽ‘aH«is“the“trace“of“±pŽ‘ ‚À«on“theŽ¡x-y–é.plane,‘$then“±pŽ‘ñ.:Ïslop‘ÿ}'eŽ‘7Ë«(Ý'x'Ž‘F_±;‘ª¨Ý'y'Ž‘ñ«)“returns“a“ÂrealŽ‘05±m“«sucš¸ãh“that“±m–½€«=“(±b–›p·“±y[Ù«)±=x–é.«where“±b“«is“the“y-in˜tercept“ofŽ¡Ÿü±È·ŽŽ‘¸‘þ㎎Ž‘ÖÏ!ŽŽŸN8±qŸÿ®0Ž‘|s±qŸÿ®1ŽŽŽŽŽ‘;Ý«and–UU±x“«and“±y‘±.«are“the“x“and“y-cošGordinates“of“p˜oin¸ãts“onŸü±È“·ŽŽ‘e ‘þ㎎Ž‘ÖÏ!ŽŽŸN8“±qŸÿ®0Ž‘|s±qŸÿ®1ŽŽŽŽŽ‘;Ý«.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.11.05.«]Ž‘X؃Changed–%this“function,‘/(so“that“Ïis‘‰ffŽ‘®line‘ÿ}'arŽ‘(;«(›ª®)“is“used“instead“of“Ïget‘‰ffŽ–®line‘‰ffŽ“switchŽ‘Bü«(˜)“(formerlyŽ¡\Ïis‘‰ffŽ‘®lineŽ‘ñ?«(‘ª®)").‘qµNo¸ãw,›U)it–Ucan“bGe“used“for“all“linear“ÂP®9athsŽ‘ o¾«,˜not“just“ones“created“using“the“constructor“for“lines.Ž¡Also,–UUit“wš¸ãas“commen˜ted-out.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·ŽŸ ‘ -ÂrealŽ‘ ³/Ïslop‘ÿ}'eŽ‘6êú«(Âc®9harŽ‘jI±aŽ‘!z‘«=‘ÇÝ'x'Ž– w±;‘ª¨Âc®9harŽ‘ñ±bŽ‘"&³«=‘ÇÝ'y'Ž“«);Ž¦Â880.Ž¡·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¤ ‘ -ÂrealŽ‘ ³/P®9athŽ‘:D—«::‘Ïslop‘ÿ}'eŽ‘7Ï«(Âc®9harŽ‘jI±aŽ‘³y;‘ª¨Âc®9harŽ‘ñ±bŽ‘_›«)Ž¡‘ -·fŽ¡‘ÂifŽ‘´ú«(·:Ïis‘‰ffŽ‘®line‘ÿ}'arŽ‘%}«(‘ª¨))‘·fŽ¡‘Ïc‘ÿ}'errŽ‘7ó·‘_JÝ"ERROR!È ÝInÈ ÝPath::sloŽ‘o_pe().È ÝPathÈ ÝisÈ ÝnotÈ ÝliŽ’Ø^Ònear!\n"Ž’ Dl·Ž¡‘2Ý"ReturningÈ ÝINVALID_RŽ’šÿÉEAL\n"Ž’½Í7·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½ÝINVALID_REALŽ’m«;Ž¡‘·gŽ¡‘ÂreturnŽ‘7æ¼Ïp‘ÿ}'ointsŽ‘S Q«[1Ž–]‘þŸ±~ŽŽ‘Ïslop‘ÿ}'eŽ‘7Ì«(·Ž“Ïp‘ÿ}'ointsŽ‘ $–«[0Ž“]±;‘ª¨aŽ‘óØ;‘ª¨bŽ‘õR«);Ž¡‘ -·gŽ¦Â881.– üSubpath.“«[¬LDF‘T2002.11.05.«]Ž‘Zˆ6Ïsubp‘ÿ}'athŽ‘|˜«(‘ª®)–UUreturns“a“new“ÂP®9athŽ‘<«using“Ïp‘ÿ}'ointsŽ‘yê«[ÏstartŽ‘…M«]“throughŽ¡Ïp‘ÿ}'ointsŽ‘$•«[ÏendŽ‘ª—·‘Éå«1Ž‘Éæ]–×from“·Ž‘ØÏthisŽ‘ Ž«.‘_HIf“the“optional“Âb•QÇo“olŽ‘‡¿«argumen¸ãt“ÏcycleŽ‘´ã«is“used,‘(ðthen“the“new“ÂP®9athŽ‘Í«will“bGe“a“cycle,Ž¡whether‘ý'·Ž‘ý(ÏthisŽ‘æ«is–ý'or“not.›TbOne“optional“connector“argumen¸ãt“can“bGe“used.˜If“it“is,‘Êit“will“bGe“the“only“connector.Ž¡Otherwise,–UUthe“connectors“from“·Ž‘UVÏthisŽ‘–a«are“used.Ž¡‘ -[¬LDF‘T2002.11.05.«]Ž‘Y;ÏstartŽ‘qâÝ«m¸ãust–UUbšGe“±<“ÏendŽ‘6«.‘qÇIt“is“not“p˜ossible“to“ha•¸ãv“e‘UUÏstartŽ‘/÷±>‘UUÏendŽ‘6«,›UUev“en˜if˜·Ž‘UVÏthisŽ‘–a«is˜a˜cycle.ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.11.05.«]Ž‘Y½Rewrote– -!this“function.›,Made“Ïsubp‘ÿ}'athŽ‘%„ƒ«(‘ª®)“itself“and“its“argumen¸ãts“ÂconstŽ‘ßn«.˜Added“errorŽ¡handling‘UUcoGde.Ž¡‘ -[¬LDF‘T2003.07.16.«]Ž‘Y;Please–UUnote“that“ÏstartŽ‘/÷«and“ÏendŽ‘‹\«cannot“bGe“made“ÂconstŽ‘*¢«.Ž¡‘ -[¬LDF‘T2003.08.27.«]Ž‘YE‹Changed‘’¥Âin®9tŽ‘tì±iŽ‘y…«to‘’¥Âsizeu½‰™šs4Ž‘ÔwtŽ‘#"ž±iŽ‘*'7«in–’¥the“ÂforŽ‘¸{«loGops“that“compare“±iŽ‘ -—>«to“ÏstartŽ‘ª—«and“ÏendŽ‘sW«.‘)¸The“w•¸ãa“yŽ¡it–UUwš¸ãas“bGefore“caused“GCC“with“the“\È-Wall«"“option“to“issue“a“w˜arning.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·ŽŸ ‘ -ÂP®9athŽ‘%åíÏsubp‘ÿ}'athŽ‘G`O«(Âsizeu½‰™šs4Ž‘ÔwtŽ‘QÜÏstartŽ‘4×)±;‘ª¨Âsizeu½‰™šs4Ž‘ÔwtŽ‘ ü„ÏendŽ‘1Ý6±;‘ª¨ÂconstŽ‘Ô}b•QÇo“olŽ‘9uÏcycleŽ‘Rµc«=‘ÇÏfalseŽ‘v\±;‘ª¨ÂconstŽ‘Ô}stringŽ‘@øýÏc–ÿ}'onne“ctorŽ‘oï«=‘ÇÝ""Ž‘ Íz«)‘TˆÂconstŽ‘)Õ«;ŽŽŽŒ‹ò ê÷ Šn ý‘ì«242›­SUBP–ÿJªA“TH’:kÒ3DLDFPRÃŽG˜·x«882Ž €n ý•@PÂ882.Ž©·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¤ ‘ -ÂP®9athŽ‘%Ï6P®9athŽ‘?`ž«::‘Ïsubp‘ÿ}'athŽ‘"zf«(Âsizeu½‰™šs4Ž‘ÔwtŽ‘;%ÏstartŽ‘4Àr±;‘ª¨Âsizeu½‰™šs4Ž‘ÔwtŽ‘ åÍÏendŽ‘1Ʊ;‘ª¨ÂconstŽ‘½Æb•QÇo“olŽ‘9G¨ÏcycleŽ‘OÀݱ;‘ª¨ÂconstŽ‘½ÆstringŽ‘@ËÏc–ÿ}'onne“ctorŽ‘l*i«)‘=ÑÂconstŽ‘·f‘=ÑÂb•QÇo“olŽŽ¡‘2ÝDEBUGŽ‘Ov«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂP®9athŽ‘9æ¼±pŽ‘>;ŽŸÂ883.‘ ü«[¬LDF‘T2002.11.05.«]Ž‘[˜There–e!is“no“\ÝINVALID_PATHŽ‘?†D«",›©so“I‘dÛreturn“an“empt¸ãy“one,˜if“ÏstartŽ‘vƒ·‘ŒÏendŽ‘lÇ«.‘¡+SinceŽ¡ÂopQÇeratorŽ‘+–µ·Ž‘3]Ó«(‘ª¨)–=¬currenš¸ãtly“doGesn't“exist,‘wÂthere's“not“m˜uc˜h“pGoin˜t“in“de ning“ÝINVALID_PATHŽ‘CÃð«,‘wÂsince“there's“noŽ¡w•¸ãa“y–UUto“compare“another“ÂP®9athŽ‘<«to“it.Ž¦·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¡‘ -ÂifŽ‘´ù«(ÏstartŽ‘Le·‘ÇÏendŽ‘§Ê«)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘*'c·‘q»Ý"ERROR!È ÝInÈ ÝPath::subŽ‘lqpath():\n"Ž’¤é„·‘q»Ý"TheÈ Ý\"start\"È ÝargumŽ‘lqentÈ ÝisÈ Ý<È ÝtheÈ Ý\"end\"Ž’ÕqC\ŽŽ¡‘(È Ýargument.\n"Ž‘o]·‘ÇÝ"ReturningÈ ÝemptyÈ ÝPatŽ‘kÆÜh.\n\n"Ž’“ÔG·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘7æ¼±pŽ‘<;Ž¡‘ -·gŽŸÂ884.‘ ü«[¬LDF‘T2002.11.05.«]Ž‘Zˆ6More–UUerror“handling.‘qÇIn“these“cases,“it's“pGossible“to“reco•¸ãv“er.Ž¦·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¡‘ -ÂifŽ‘´ù«(ÏstartŽ‘Le±>‘ÇÏp‘ÿ}'ointsŽ‘ë­±:ÏsizeŽ‘\«(‘ª¨)–8à·“«1Ž‘8á)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘*'c·‘q»Ý"ERROR!È ÝInÈ ÝPath::subŽ‘lqpath():\n"Ž’¤é„·‘q»Ý"\"start\"È ÝargumentÈ Ž‘lqÝisÈ Ý>È Ýpoints.size()È Ý-Ž’ÕqC\ŽŽ¡‘(È Ý1.\n"Ž‘JÍr·‘ÇÝ"WillÈ ÝtryÈ ÝtoÈ ÝrecoverŽ‘kÆÜÈ ÝbyÈ ÝsettingÈ ÝstartÈ Ý=È Ž’ÔÆ Ý0.\n\n"Ž’üÔ ·‘ÇÏ ushŽ‘€«;Ž¡‘ÏstartŽ‘,Lg«=‘Ç0Ž‘Ç;Ž¡‘ -·gŽ¡‘ -ÂifŽ‘´ù«(ÏendŽ‘§Ê±>‘ÇÏp‘ÿ}'ointsŽ‘ë­±:ÏsizeŽ‘\«(‘ª¨))‘·fŽ¡‘Ïc‘ÿ}'errŽ‘)ðò·‘;JÝ"ERROR!È ÝInÈ ÝPath::subŽ‘l;path():\n"Ž’¤|¢·‘;JÝ"\"end\"È ÝargumentÈ ÝisŽ‘l;È Ý>È Ýpoints.size().\n"Ž’Øü„·Ž¡‘(Ý"WillÈ ÝtryÈ ÝtoÈ ÝrecoverŽ’ÿÈÈ ÝbyÈ ÝsettingÈ ÝendÈ Ý=È ÝpoŽ’ùÿŒints.size().\n\n"Ž’VŒÙ·‘ÇÏ ushŽ‘€«;Ž¡‘ÏendŽ‘'§Ì«=‘ÇÏp‘ÿ}'ointsŽ‘ë­±:ÏsizeŽ‘\«(‘ª¨);Ž¡‘ -·gŽŸÂ885.‘ ü«[¬LDF‘T2002.11.05.«]Ž‘Y«If–x4a“Ïc–ÿ}'onne“ctorŽ‘0OB«argumenš¸ãt“is“spGeci ed,‘¤nall“w˜e“ha˜v˜e“to“do“is“put“the“appropriate“ÂP•®9oin“tsŽŽ¡«from‘UUÏp‘ÿ}'ointsŽ‘!Ï?«onš¸ãto‘UU±pŽ‘]U:Ïp‘ÿ}'ointsŽ‘$•«,–UUput“Ïc–ÿ}'onne“ctorŽ‘2 „«on˜to“±pŽ›]U:Ïc–ÿ}'onne“ctorsŽ‘/4.«,“and“return“±pŽ˜«.Ž¦·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¡‘ -ÂifŽ‘´ù«(Ïc–ÿ}'onne“ctorŽ‘.%ò·6«=‘ÇÝ""Ž‘ Íz«)‘·fŽ¡‘ÂforŽ‘%舫(Âsizeu½‰™šs4Ž‘ÔwtŽ‘R©±iŽ‘%‹µ«=‘ÇÏstartŽ‘Le«;‘ÿý±iŽ‘ 9 <‘ÇÏendŽ‘§Ê«;‘ÿý±iŽ‘ññŸÿ®+‘ÿ+ŽŽ‘¹«)‘·fŽ¡‘ÂifŽ‘)´û«(±iŽ‘9 ·‘ÇÏp‘ÿ}'ointsŽ‘ë­±:ÏsizeŽ‘\«(‘ª¨))‘·fŽ¡‘(Ïc‘ÿ}'errŽ‘>Y‰·‘£ßÝ"ERROR!È ÝInÈ ÝPath::subŽ‘l££path():\n"Ž’¥MÌ·‘£ßÝ"endÈ ÝargumentÈ Ý>È ÝpoinŽ‘l££ts.size().\n"Ž’µ ÷Ž¡‘<Ý"BreakingÈ ÝoutÈ ÝofÈ ÝlooŽ’¤ÿÊp.\n\n"Ž’Í 5·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂbreakŽ‘D¡h«;Ž¡‘·gŽ¡‘±pŽ‘#:Ïp‘ÿ}'ointsŽ–$•±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂP•®9oin“tŽ‘šL«::Ž‘#(ŠÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“p‘ÿ}'ointŽ‘kþ†«(Ïp‘ÿ}'ointsŽ“«[±iŽ‘qô«]));Ž¡‘·gŽ¡‘±pŽ‘:Ïc–ÿ}'onne“ctorsŽ‘/4.±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(Ïc–ÿ}'onne“ctorŽ‘+^Ú«);Ž¡‘±pŽ‘:Ïset‘‰ffŽ‘®cycleŽ‘&*«(ÏcycleŽ‘y5«);Ž¡‘ÂreturnŽ‘7æ¼±pŽ‘<;Ž¡‘ -·gŽŽŽŒ‹ó ü Šn ý‘ì·x«886›­3DLDFPRÃŽG’:kÒSUBP–ÿJªA“TH˜«243Ž €n ý•@PÂ886.‘ ü«[¬LDF‘T2002.11.05.«]Ž‘ZNTIf–sno“Ïc–ÿ}'onne“ctorŽ‘1•À«argumenš¸ãt“is“spGeci ed,‘'then“w˜e“ha˜v˜e“to“get“the“appropriate“connec-Ž¤ tors– Pfrom“·Ž‘ QÏthisŽ‘ø«.‘YpThis“is“slighš¸ãtly“tric˜ky‘ÿ*ª,‘ëbšGecause“Ïc–ÿ}'onne“ctorsŽ‘5LΫdo˜esn't“ha•¸ãv“e– Pto“conš¸ãtain“a“Ïc–ÿ}'onne“ctorŽ‘1wz«for“eac˜h“pairŽ¡of‘fjÂP•®9oin“tsŽ‘&ðX«that–fjis“joined“in“a“ÂP®9athŽ‘÷Ϋ.‘¥So,‘j° rst“wš¸ãe“m˜ust“ ll“up“±pŽ‘nj:Ïc–ÿ}'onne“ctorsŽ‘2š˜«so“that“w˜e“can“tell“whic˜h“ones“toŽ¡use.Ž¡‘ -[¬LDF‘T2002.11.05.«]Ž‘YEµActually‘ÿ*ª,›¢-with–’Ïthe“constructors“that“exist,˜there“will“either“bGe“only“one“connector“or“aŽ¡connector–0$for“eacš¸ãh“pair“of“ÂP•®9oin“tsŽ‘&ƒÌ«that“need“to“bGe“joined.‘eaHo˜w˜ev˜er,‘7”it“w˜ould“bGe“easy“to“write“functions“thatŽ¡add–UUor“remo•¸ãv“e–UUconnectors,“so“it's“bGest“to“ha•¸ãv“e–UUthis“routine.Ž©·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¡‘ -±pŽ‘Ï«=‘Ç·Ž‘ÇÏthisŽ‘²Ï«;Ž¦‘ -ÂunsignedŽ‘:7shortŽ‘X²±aŽ‘`ú«=‘ÇÏp‘ÿ}'ointsŽ‘ë­±:ÏsizeŽ‘\«(‘ª¨);Ž¦‘ -ÂifŽ‘´ù«(·:ÏcycleŽ‘y5«)‘±aŽ‘ H·«=ŽŽ‘eœ1Ž‘$e;Ž¦‘ -Âin®9tŽ‘¤ø±iŽ‘ì«;Ž¡‘ -ÂstringŽ‘+%N±sŽ‘2œf«=‘ÇÏc–ÿ}'onne“ctorsŽ‘1ûF±:Ïb‘ÿ}'ackŽ‘üë(‘ª¨);Ž¦‘ -ÂforŽ‘臫(±iŽ‘9 «=‘ÇÏc–ÿ}'onne“ctorsŽ‘1ûF±:ÏsizeŽ‘\«(‘ª¨);‘ÿý±iŽ‘ 9 <‘ÇaŽ‘H«;‘ÿý±iŽ‘ññŸÿ®+‘ÿ+ŽŽ‘¹«)‘·fŽ¡‘±pŽ‘:Ïc–ÿ}'onne“ctorsŽ‘/4.±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(±sŽ‘°«);Ž¡‘ -·gŽ¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"p.connectors.size()Ž‘kÆÜÈ Ý==È Ý"Ž’‰TM·‘DZpŽ‘Ï:Ïc–ÿ}'onne“ctorsŽ‘/4.±:ÏsizeŽ‘\«(‘ª¨)–Ç·“Ïend‘‚ØlŽ‘ò·“Ï ushŽ‘€«;Ž¦‘ -ÂP®9athŽ‘%溱qŽ‘*¹d«;Ž¦‘ -ÂforŽ‘臫(Âsizeu½‰™šs4Ž‘ÔwtŽ‘R©±iŽ‘%‹µ«=‘ÇÏstartŽ‘Le«;‘ÿý±iŽ‘ 9 <‘ÇÏendŽ‘§Ê«;‘ÿý±iŽ‘ññŸÿ®+‘ÿ+ŽŽ‘¹«)‘·fŽ¡‘±qŽ‘Ò¬:Ïp‘ÿ}'ointsŽ–$•±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂP•®9oin“tŽ‘šL«::Ž‘#(ŠÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“p‘ÿ}'ointŽ‘kþ†«(±pŽ‘:Ïp‘ÿ}'ointsŽ“«[±iŽ‘qô«]));Ž¡‘ÂifŽ‘´ú«(±iŽ‘9 <‘ÇpŽ‘Ï:Ïc–ÿ}'onne“ctorsŽ–/4.±:ÏsizeŽ‘\«(‘ª¨))‘±qŽ‘ Òª:Ïc–ÿ}'onne“ctorsŽ“±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(±pŽ‘:Ïc–ÿ}'onne“ctorsŽ“«[±iŽ‘qô«]);Ž¡‘ -·gŽ¡‘ -±qŽ‘Ò«:Ïset‘‰ffŽ‘®cycleŽ‘&*«(ÏcycleŽ‘y5«);Ž¡‘ -ÂreturnŽ‘-æ»±qŽ‘2¹e«;‘qÇ·gŽ¤Â887.‘ üGet‘ÕTpQÇoin®9t.Ž¡888.‘ ünon-const‘ÕTv®9ersion.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ -«[¬LDF‘T2002.11.05.«]Ž‘Y;Made–UUnon-ÂinlineŽ‘4ó«.‘qÇChanged“return“v‘ÿqÇalue“to“ÂconstŽ‘!÷P•®9oin“tŽ‘@o”«&Ž‘H6².Ž¡‘ -[¬LDF‘T2003.11.28.«]Ž‘Y˜{BUG‘åpFIX:–å•Changed,‘ ¥so“that“Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Jt«(‘ª®)“is“called“on“the“ÂP•®9oin“tŽ‘Ý«.‘"†This“en¸ãtailedŽ¡making–ÅÃthis“function“non-ÂconstŽ‘ÕM«.‘ÃAdded“ÂconstŽ‘"`Ó«vš¸ãersion“bGelo˜w.‘ÃThis“ma˜y“actually“bGe“a“bug,‘áÞrather“than“aŽ¡bug–s x,‘mdepGending“on“hoš¸ãw“this“function“is“used“elsewhere.‘U|Ho˜w˜ev˜er,‘mI‘]really“think“Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘I R«(‘ª®)“shouldŽ¡bGe‘UUcalled.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·Ž¡‘ -ÂconstŽ‘(*£P•®9oin“tŽ‘G@«&Ž‘Ná^Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘vC¦«(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±aŽ‘quƒ«);ŽŽŽŒ‹ô -\ Šn ý‘ì«244–­NON-ÂCONST‘ÕX­VERSION’úAÕ3DLDFPRÃŽG“·x«889Ž €n ý•@PÂ889.Ž©·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¤ ‘ -ÂconstŽ‘(*£P•®9oin“tŽ‘G@«&Ž‘Ná^ÂP®9athŽ‘hrÆ«::‘Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘(bL«(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±aŽ‘quƒ«)Ž¡‘ -·fŽ¡‘ÂifŽ‘´ú«(±aŽ‘H<‘ÇÏp‘ÿ}'ointsŽ‘ë­±:ÏsizeŽ‘\«(‘ª¨))‘·fŽ¡‘«(Ïp‘ÿ}'ointsŽ‘$•«[±aŽ‘I0«])‘þŸ±~ŽŽ‘Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Jà«(‘ª¨);Ž¡‘ÂreturnŽ‘Aæ½·Ž‘Fæ¾Ïp‘ÿ}'ointsŽ‘b S«[±aŽ‘I0«];Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘Ïc‘ÿ}'errŽ‘4w0·‘Á‡Ý"ERROR!È ÝInÈ ÝPath::getŽ‘lÁK_point():\n"Ž—° ·‘Á‡Ý"ArgumentÈ ÝisÈ Ý>=È ÝsizeŽ‘lÁKÈ ÝofÈ ÝPath.\n"Ž“·Ž¡‘2Ý"ReturningÈ ÝINVALID_PŽ’šÿÉOINT.\n\n"Ž’ÒÍ+·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½ÝINVALID_POINTŽ’†¬þ«;Ž¡‘·gŽ¡‘ -gŽŸÂ890.‘ üconst‘ÕTv®9ersion.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.11.28.«]Ž‘Y;Added–UUthis“v¸ãersion.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·Ž¡‘ -ÂP•®9oin“tŽ‘(ïžÏget‘‰ffŽ‘®p‘ÿ}'ointŽ‘PQæ«(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±aŽ‘quƒ«)‘UUÂconstŽ‘*¢«;ŽŸÂ891.Ž¦·h–ª¨«De ne‘UUÂP®9athŽ‘<«functions‘@­657“·i‘Ç«+·Ž¡‘ -ÂP•®9oin“tŽ‘(ïžP®9athŽ‘B«::‘Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘(bL«(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±aŽ‘quƒ«)‘UUÂconstŽŽ¡‘ 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-ÂconstŽ‘(*£P•®9oin“tŽ‘G@«&Ž‘Ná^ÂP®9athŽ‘hrÆ«::‘Ïget‘‰ffŽ–®last‘‰ffŽ“p‘ÿ}'ointŽ‘;$B«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂifŽ‘´ú«(Ïp‘ÿ}'ointsŽ›$•±:ÏsizeŽ‘\«(‘ª¨)–Ç·6«=“0Ž‘Ç)‘ÂreturnŽ‘(溷Ž‘-æ»Ïp‘ÿ}'ointsŽ‘I P«[Ïp‘ÿ}'ointsŽ˜±:ÏsizeŽ‘\«(‘ª¨)–8à·“«1Ž‘8á];Ž¡‘ÂelseŽ‘+Øá·fŽ¡‘Ïc‘ÿ}'errŽ‘5ž4·‘è‹Ý"ERROR!È ÝInÈ ÝPath::getŽ‘mèO_last_point():\n"Ž’Ì—·‘è‹Ý"PathÈ ÝisÈ Ýempty.\n"Ž‘h×H·Ž¡‘2Ý"ReturningÈ ÝINVALID_PŽ’šÿÉOINT.\n\n"Ž’ÒÍ+·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½ÝINVALID_POINTŽ’†¬þ«;Ž¡‘·gŽ¡‘ -gŽŸÂ894.‘ üGet‘ÕTsize.Ž¦·h–ª¨«Declare‘UUÂP®9athŽ‘<«functions‘@­656“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/ÔinlineŽ‘Osizeu½‰™šs4Ž‘ÔwtŽ‘njÅÏget‘‰ffŽ‘®sizeŽ’¹Ý«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼Ïp‘ÿ}'ointsŽ‘S Q±:ÏsizeŽ‘\«(‘ª¨);Ž¡‘ -·gŽŸÂ895.‘ üGet‘ÕTnormal.ŽŽŽŒ‹ö !¹ Šn ý‘ì«246›ÂP–ÿ -«A“TH‘ÕX­VERSION’!13DLDFPRÃŽG˜·x«896Ž €n ý•@PÂ896.› üP•®9ath‘õÓv“ersion.˜«[¬LDF‘T2002.11.05.«]Ž‘YÅÛÏget‘‰ffŽ‘®normalŽ’ŠPO«(‘ª®)–’úreturns“a“unit“vš¸ãector“represen˜ting“the“normal“to“theŽ¤ plane–f -of“the“ÂP®9athŽ‘]x·Ž‘$]yÏthisŽ‘5I/«,‘j8if“·Ž‘f 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-«Then–èit“c•¸ãhec“ks–èwhether“the“ÂP®9athŽ‘­4«has“only“t•¸ãw“o‘èÂP•®9oin“tsŽ‘"±l«.‘/NIf–èit“doGes,‘µËÏget‘‰ffŽ‘®normalŽ‘3@?«(‘ª®)“returns“the“ÂP•®9oin“tŽ‘ ¶«(0±;–ª¨«0±;“«0),Ž¡‘ -bšGecause–UUthe“ÂP®9athŽ‘<«will“b˜e“linear.Ž¦·Ž‘ -«Then–¨ it“gets“the“cross“proGduct“±bŸÿ®0Ž›$“«ofŸü±È“·ŽŽ‘ I‘þ㎎Ž‘gþ!ŽŽŸN8“±pŸÿ®0Ž‘|s±pŸÿ®1ŽŽŽŽŽ‘Y&«andŸü±È“·ŽŽ‘ I‘þ㎎Ž‘gþ!ŽŽŸN8“±pŸÿ®0Ž‘|s±pŸÿ®2ŽŽŽŽŽ‘±«,‘¼Ówhere“±pŸÿ®0Ž˜«and“±pŸÿ®1Ž˜«are“the“ rst“and“second“ÂP•®9oin“tsŽ‘'sÄ«onŽ¡‘ -the‘‡ÂP®9athŽ‘’ë«,‘Jand–‡±pŸÿ®2Ž‘}ú«is“the“next“ÂP•®9oin“tŽ‘!V«on“the“ÂP®9athŽ›”r«suc¸ãh“that“±bŸÿ®0Ž‘C‹·6«=‘Ç(0±;–ª¨«0±;“«0).‘UØIf–‡no“ÂP•®9oin“tsŽ‘&&’«on“the“ÂP®9athŽ˜«ful llŽ¡‘ -this–UUcondition,“then“all“of“the“ÂP•®9oin“tsŽ‘&Î.«are“colinear,“so“Ïget‘‰ffŽ‘®normalŽ‘3ßÉ«(‘ª®)“returns“ÏoriginŽ‘Kv«.Ž¦·Ž‘ -«If,›Ñho•¸ãw“ev“er,˜±bŸÿ®0Ž‘C‹·6«=‘Ç(0±;–ª¨«0±;“«0)–pexists,˜then“cross“proGducts“±bŸÿ´xŽ‘ T«are“calculated“usingŸü±È“·ŽŽ‘¤W‘þ㎎Ž‘gþ!ŽŽŸN8“±pŸÿ®0Ž‘|s±pŸÿ®1ŽŽŽŽŽ‘Æ«and“the“direction“v¸ãectorsŽ¡Ÿü±È‘ -·ŽŽ‘ç!‘þ㎎Ž‘®6!ŽŽŸN8‘ -±pŸÿ®0Ž‘|s±pŸÿ´xŽŽŽŽŽ‘! ‡«for–‹/the“rest“of“the“ÂP•®9oin“tsŽ‘'9â±pŸÿ´xŽ‘”«on“the“ÂP®9athŽ‘“«.‘TIf“and“only“if“±bŸÿ´xŽ›)¼«=‘ رbŸÿ®0Ž‘|s«,‘˜¥or“±bŸÿ´xŽ˜«=‘ Ø·±bŸÿ®0Ž‘|s«,‘˜¥or“±bŸÿ´xŽ˜«=‘ Ø(0±;–ª¨«0±;“«0)‘‹/forŽ¡‘ -all–òþ±bŸÿ´xŽ‘ä«,›©then“the“ÂP®9athŽ‘w`«is“planar,˜and“Ïget‘‰ffŽ‘®normalŽ‘3}r«(‘ª®)“returns“·±bŸÿ®0Ž‘oq«(see“explanation“of“sign“bGelo¸ãw).‘QOtherwise,Ž¡‘ -the‘UUÂP®9athŽ‘<«is–UUnon-planar,“and“Ïget‘‰ffŽ‘®normalŽ‘3ßÉ«(‘ª®)“returns“ÝINVALID_POINTŽ‘H–«.Ž¦‘ -[¬LDF‘T2003.06.04.«]Ž‘XP™Revš¸ãersing–³the“sign“of“±bŸÿ®0Ž‘&«ensures“that“the“normal“will“pGoin˜t“in“the“direction“of“the“pGositiv˜eŽ¡y-axis,›Ï‚when–® a“plane“ gure“is“created“in“the“x-z“plane,˜using“one“of“the“constructors“taking“a“ÂP•®9oin“tŽ‘ öb«argumen¸ãtŽ¡for–˜¾the“cen•¸ãter,‘¾vÂrealŽ‘µ «argumen“ts–˜¾for“the“dimensions,‘¾vand“three“ÂrealŽ‘U«argumen¸ãts“for“the“rotation“abGout“the“ma‘Ž8jorŽ¡axes.›iIf–ýnon-zero“argumen¸ãts“are“used“for“rotation,‘' 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üGet–ÕTmean“z.˜¬[²LDF‘T2003.05.16.¬]Ž‘Zˆ6Added–UUthis“function.Ž¦°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔrealŽ‘FA±get‘‰ffŽ–®me‘ÿ}'an‘‰ffŽ“zŽ‘v÷ ¬(‘ª®)‘UU­constŽ‘*¢¬;ŽŸ­894.Ž¦°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¡‘ +­realŽ‘ ³/P®9athŽ‘:D—¬::‘±get‘‰ffŽ–®me‘ÿ}'an‘‰ffŽ“zŽ‘1¶¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7漬((±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ¬[4Ž›]–8à+“±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘V=1¬[5Ž˜])µ=¬2Ž˜);Ž¡‘ +°gŽŸ­895.– üSuppress‘xÿoutput.“¬[²LDF‘T2002.09.18.¬]Ž‘[ˆAdded–ã§this“function.‘½It's“needed“bGecause“trying“to“erase“aŽ¡­ShapQÇeŽ‘"Ab°Ž‘*–¸¬from‘UU±elementsŽ‘-¥¬in‘UU­PictureŽ‘)ñf¬::‘±outputŽ‘D¬(‘ª®)–UUcauses“a“memory“fault.Ž¦°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/Ôv®9oidŽ‘H‹¬±suppr‘ÿ}'ess‘‰ffŽ‘®outputŽ’r.¬(‘ª®);ŽŽŽŒ‹î=“ Šn ý‘ì¬238–¯SUPPRESS‘ÕXOUTPUT’òb3DLDF-1.1.5.1“°x¬896Ž €n ý•@P­896.Ž©°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘"ýÙP®9athŽ‘® ´to® ´coŽ’ÿÈntinue.\n"Ž’ÈÍ*°‘DZ 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O°‘Ç´"Drawing.\n"Ž‘Et°‘DZ ushŽ‘€¬;Ž¡‘­ifŽ‘´ú¬(±arr‘ÿ}'owŽ‘'h°‘DZtrueŽ‘‹°¬)‘±out‘‰ffŽ‘®str–ÿ}'e“amŽ‘7´°‘Ç´"drawarrow® ´"Ž‘Et°‘ÇŽ‘ÇŽ‘ DZp‘ÿ}'oint‘‰ffŽ‘®iterŽ‘7yŸÿ³+‘ÿ+ŽŽ‘C@%¬;Ž¡‘­elseŽ‘+Øá±out‘‰ffŽ‘®str–ÿ}'e“amŽ‘]à•°‘Ç´"draw® ´"Ž‘*Ôƒ°‘ÇŽ‘ÇŽ‘ DZp‘ÿ}'oint‘‰ffŽ‘®iterŽ‘7yŸÿ³+‘ÿ+ŽŽ‘C@%¬;Ž¡‘°h–ª¨¬Output‘²Î­P®9athŽ‘ „6¯907“°i‘µ=°‘]v¬[²LDF‘T2002.09.26.¬]Ž‘TÃ)Comparing–²ÎpGoinš¸ãters“seems“to“w˜ork“here.‘Š2I‘²¶think“itŽ¡‘(should,–UUbut“I“wš¸ãasn't“sure“that“it“really“w˜ould.‘o°µ=Ž¡‘­ifŽ‘´ú¬(±dr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘1³Q°6¬=‘Ç­ColorsŽ‘$Ÿö¬::Ž‘+.4±default‘‰ffŽ‘®c‘ÿ}'olorŽ‘bª¬)‘°fŽ¡‘±out‘‰ffŽ‘®str–ÿ}'e“amŽ‘P·°‘Ç´"® ´withcolor® ´"Ž‘JTq°‘ÇŽ‘DZdr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘6³R¬;Ž¡‘°gŽ¡‘­ifŽ‘´ú¬(±dashe‘ÿ}'dŽ– ñ¹°6¬=‘Ç´""Ž‘ Íz¬)‘±out‘‰ffŽ‘®str–ÿ}'e“amŽ‘7´°‘Ç´"® ´dashed® ´"Ž‘:”z°‘DZdashe‘ÿ}'dŽ“¬;Ž¡‘­ifŽ‘´ú¬(±p‘ÿ}'enŽ–àË°6¬=‘Ç´""Ž‘ Íz¬)‘±out‘‰ffŽ‘®str–ÿ}'e“amŽ‘7´°‘Ç´"® ´withpen® ´"Ž‘?Ôw°‘DZp‘ÿ}'enŽ“¬;Ž¡‘±out‘‰ffŽ‘®str–ÿ}'e“amŽ‘F¶°‘Ç´";\n"Ž‘ T‰°‘DZ ushŽ‘€¬;Ž¡‘ +°gŽ¡‘ +­elseŽ‘ .5ifŽ‘+ã-¬(± l‘‚Øl‘‰ffŽ–®dr‘ÿ}'aw‘‰ffŽ“valueŽ‘As)°‘Ç´FILLŽ‘Mt¬)‘°fŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Filling.\n"Ž‘Et°‘DZ ushŽ‘€¬;Ž¡‘±out‘‰ffŽ‘®str–ÿ}'e“amŽ‘F¶°‘Ç´"fill® ´"Ž‘*Ôƒ°‘ÇŽ‘ÇŽ‘ DZp‘ÿ}'oint‘‰ffŽ‘®iterŽ‘7yŸÿ³+‘ÿ+ŽŽ‘C@%¬;Ž¡‘°h–ª¨¬Output‘UU­P®9athŽ‘ &½¯907“°iŽ¡‘­ifŽ‘´ú¬(± l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘(_m°6¬=‘Ç­ColorsŽ‘$Ÿö¬::Ž‘+.4±default‘‰ffŽ‘®c‘ÿ}'olorŽ‘bª¬)‘±out‘‰ffŽ‘®str–ÿ}'e“amŽ‘7´°‘Ç´"® ´withcolor® ´"Ž‘JTq°‘ÇŽ‘DZ l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘-_n¬;Ž¡‘±out‘‰ffŽ‘®str–ÿ}'e“amŽ‘F¶°‘Ç´";\n"Ž‘ T‰°‘DZ ushŽ‘€¬;Ž¡‘ +°gŽ¡‘ +­elseŽ‘ .5ifŽ‘+ã-¬(± l‘‚Øl‘‰ffŽ–®dr‘ÿ}'aw‘‰ffŽ“valueŽ‘As)°‘Ç´FILLDRAWŽ‘-Mh¬)‘UU°fŽ¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Filldrawing.\n"Ž‘Zh°‘DZ ushŽ‘€¬;Ž¡‘ +­ifŽ‘´ù¬(±dr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘1³Q°‘DZ l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘(_m¬)‘°fŽ¡‘±out‘‰ffŽ‘®str–ÿ}'e“amŽ‘F¶°‘Ç´"filldraw® ´"Ž‘?Ôw°‘ÇŽ‘ÇŽ‘ DZp‘ÿ}'oint‘‰ffŽ‘®iterŽ‘7yŸÿ³+‘ÿ+ŽŽ‘C@%¬;Ž¡‘°h–ª¨¬Output‘UU­P®9athŽ‘ 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+±p‘ÿ}'oint‘‰ffŽ‘®iterŽ‘6ù¬=‘DZp‘ÿ}'ointsŽ‘ë­µ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);ŽŽŽŒ‹ñYQ Šn ý‘ì°x¬903–¯3DLDF-1.1.5.1’4èšOUTPUT“¬241Ž €n ý•@P­903.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ +¬[²LDF‘T2002.05.10.¬]Ž‘X_Added–`ythe“coGde“in“this“section.› )It“ xes“a“bug.˜If“it's“not“done,‘‘rthen“the“correct“connectorsŽ¡are–UUnot“used“when“the“­P®9athŽ‘<¬is“output“the“second“time.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¤ ‘ +±c–ÿ}'onne“ctor‘‰ffŽ‘®iterŽ‘K¬=‘DZc–ÿ}'onne“ctorsŽ‘1ûFµ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¡‘ +­ifŽ‘´ù¬(±c–ÿ}'onne“ctorsŽ‘/4.µ:±sizeŽ‘\¬(‘ª¨)–ǵ>“¬0Ž›Ç)‘±c–ÿ}'onne“ctor‘‰ffŽ‘®stringŽ‘O”¬=“°Ž˜±c–ÿ}'onne“ctor‘‰ffŽ‘®iterŽ‘FˆŸÿ³+‘ÿ+ŽŽ‘RO½¬;Ž¡‘ +­elseŽ‘!Øà±c–ÿ}'onne“ctor‘‰ffŽ‘®stringŽ‘lft¬=‘Ç´"--"Ž‘Mt¬;ŽŸ­904.ŽŸ°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¡‘ +­ifŽ‘´ù¬(±arr‘ÿ}'owŽ‘'h°‘DZtrueŽ‘‹°¬)‘±out‘‰ffŽ‘®str–ÿ}'e“amŽ‘7´°‘Ç´"drawarrow® ´"Ž‘Et°‘ÇŽ‘ÇŽ‘ DZp‘ÿ}'oint‘‰ffŽ‘®iterŽ‘7yŸÿ³+‘ÿ+ŽŽ‘C@%¬;Ž¡‘ +­elseŽ‘!Øà±out‘‰ffŽ‘®str–ÿ}'e“amŽ‘Sà”°‘Ç´"draw® ´"Ž‘*Ôƒ°‘ÇŽ‘ÇŽ‘ 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rst“c•¸ãhec“ks–y3whether“±line‘‰ffŽ‘®switchŽ‘6•'¬is“±trueŽ‘=ˬ.‘ÝaIf“it“is,‘‚+it“returnsŽ¡±trueŽ‘Á¬righ•¸ãt›<)a“w“a“y‘ÿ*ª.‘icOtherwise,‘A2it˜uses˜the˜return˜v‘ÿqÇalue˜of˜±get‘‰ffŽ‘®normalŽ‘3Ƭ(‘ª®)˜to˜determine˜whether˜°Ž‘<*±thisŽ‘d ¬is˜linear˜orŽ¡not.‘qÇIf–UUit“is,“±is‘‰ffŽ‘®line‘ÿ}'arŽ‘(jÒ¬(‘ª®)“returns“±trueŽ‘í¬,“otherwise,“it“returns“±falseŽ‘™¬.ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.11.05.¬]Ž‘Y;Added–UUthis“function.Ž¡‘ +[²LDF‘T2002.11.06.¬]Ž‘YCvAdded–optional“­constŽ‘!ömb•QÇo“olŽ‘;Ó±verb‘ÿ}'oseŽ‘_ôû¬and“­stringŽ‘$ñ±textŽ‘9Ùt¬argumen¸ãts“for“writing“a“messageŽ¡to–UUthe“standard“output.Ž¡‘ +[²LDF‘T2003.04.09.¬]Ž‘YþØNo•¸ãw›Kòc“hec“king˜whether˜±line‘‰ffŽ‘®switchŽ‘8:¥¬is˜±trueŽ‘\|¬bGefore˜calling˜±get‘‰ffŽ‘®normalŽ‘4Öf¬(‘ª®).–Už!!“If˜a˜­P®9athŽŽ¡¬whose‘û±line‘‰ffŽ‘®switchŽ‘9+°‘êÔ±trueŽ‘Mg¬is–ûmoGdi ed“sucš¸ãh“that“it's“no“longer“linear,‘ð$the“programmer“m˜ust“ensure“thatŽ¡±line‘‰ffŽ‘®switchŽ‘2ø¬is–UUset“to“±falseŽ‘™¬!Ž¡‘ +[²LDF‘T2003.08.14.¬]Ž‘Y;Made‘UU±verb‘ÿ}'oseŽ‘'<¬non-­constŽ‘ÕM¬.‘qÇSetting–UUit“to“±trueŽ‘oB¬if“´VERBOSE_GLOBALŽ‘P°è¬is“±trueŽ‘í¬.Ž¡Added‘UU´VERBOSE_GLOBALŽ‘P°è¬to–UU®pspglb.web“¬toGda¸ãy‘ÿ*ª.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¡‘ +­b•QÇo“olŽ‘#¡g±is‘‰ffŽ‘®line‘ÿ}'arŽ‘H¶ä¬(­b•QÇo“olŽ‘¡f±verb‘ÿ}'oseŽ‘<ùÛ¬=‘DZfalseŽ‘v\µ;‘ª¨­stringŽ‘"Ïõ±textŽ‘6îÙ¬=‘Ç´""Ž‘ Íz¬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹ø¾i Šn ý‘ì¬248–¯IS‘ÕXLINEAR’.Žú3DLDF-1.1.5.1“°x¬919Ž €n ý•@P­919.Ž©°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¤ ‘ +­b•QÇo“olŽ‘#¡gP®9athŽ‘=2Ϭ::‘±is‘‰ffŽ‘®line‘ÿ}'arŽ‘&¬(­b•QÇo“olŽ‘¡f±verb‘ÿ}'oseŽ‘:2õ;‘ª¨­stringŽ‘"Ïõ±textŽ‘4'Á¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­b•QÇo“olŽ‘-¡h´DEBUGŽ‘K.Ù¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¦‘­ifŽ‘´ú¬(´VERBOSE_GLOBALŽ‘J>¬)‘±verb‘ÿ}'oseŽ‘(Xu¬=‘DZtrueŽ‘‹°¬;Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÿ9°_‘8à±verb‘ÿ}'oseŽ‘"Ê=¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Entering® ´Path::is_lŽ‘kÆÜinear().\n"Ž’¦ #¬;Ž¡‘­ifŽ‘´ú¬(±line‘‰ffŽ‘®switchŽ‘/¢Á¬)‘µ=°‘ÿý¬LDF–UU2003.04.09.‘qÇAdded“this“conditional.‘o°µ=Ž¡‘­returnŽ‘Aæ½±trueŽ‘T«U¬;Ž¦‘­P•®9oin“tŽ‘2pŽ‘7÷Ÿ¬(±get‘‰ffŽ‘®normalŽ‘0Št¬(‘ª®));Ž¦‘­ifŽ‘´ú¬(µpŽ‘Ï°‘DZoriginŽ‘½9¬)‘°fŽ¡‘­ifŽ‘)´û¬(±verb‘ÿ}'oseŽ‘ ‘]¬)‘°fŽ¡‘(­ifŽ‘3´ü¬(±textŽ‘ä°‘Ç´""Ž‘ Íz¬)‘±textŽ‘ä¬=‘Ç´"Path"Ž‘"Ín¬;Ž¡‘(±c‘ÿ}'outŽ‘> S°‘DZtextŽ‘åü°‘Ç´"® ´is® ´linear.\n\n"Ž‘\M¬;Ž¡‘°gŽ¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Exiting® ´Path::is_liŽ‘kÆÜnear().® ´"Ž’žTA°‘Ç´"Returning® ´true.\n\nŽ‘kÆÜ"Ž‘tTY°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½±trueŽ‘T«U¬;Ž¡‘°gŽ¡‘­elseŽ‘+Øá°fŽ¡‘­ifŽ‘)´û¬(±verb‘ÿ}'oseŽ‘ ‘]¬)‘°fŽ¡‘(­ifŽ‘3´ü¬(±textŽ‘ä°‘Ç´""Ž‘ Íz¬)‘±textŽ‘ä¬=‘Ç´"Path"Ž‘"Ín¬;Ž¡‘(±c‘ÿ}'outŽ‘> S°‘DZtextŽ‘åü°‘Ç´"® ´is® ´non-linear.\n\nŽ‘kÆÜ"Ž‘qA¬;Ž¡‘°gŽ¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Exiting® ´Path::is_liŽ‘kÆÜnear().® ´"Ž’žTA°‘Ç´"Returning® ´false.\n\Ž‘kÆÜn"Ž‘y”V°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½±falseŽ‘V–¬;Ž¡‘°gŽ¡‘ +gŽŸ­920.› üGet–$line“switc®9h.˜¬[²LDF‘T2002.11.03.¬]Ž‘ZÍThis–š9function“returns“±trueŽ‘ù +¬for“­P®9athsŽ‘$O¬that“are“created“or“setŽ¡using›UUt•¸ãw“o˜­P•®9oin“tsŽ‘&Î.¬only‘ÿ*ª,˜and˜no˜connectors,˜as˜argumen“ts.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.11.03.¬]Ž‘XIúRenamed–—this“function“±get‘‰ffŽ–®line‘‰ffŽ“switchŽ‘Bm‘¬(›ª®)“from“±is‘‰ffŽ‘®lineŽ‘ˆS¬(˜).‘2\AbGout“to“add“±is‘‰ffŽ‘®line‘ÿ}'arŽ‘'¬‘¬(˜),‘½!whic¸ãhŽ¡will–UUtest“whether“all“the“­P•®9oin“tsŽ‘&Î.¬are“colinear“or“not.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¡‘ +­inlineŽ‘)ŠIb•QÇo“olŽ‘C+¯±get‘‰ffŽ–®line‘‰ffŽ“switchŽ’ƒ,¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼±line‘‰ffŽ‘®switchŽ‘g‰}¬;Ž¡‘ +°gŽŸ­921.‘ üT‘ÿ +«est–ÕTfor“cycles.Ž¦°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¡‘ +­inlineŽ‘)ŠIb•QÇo“olŽ‘C+¯±is‘‰ffŽ‘®cycleŽ‘dzǬ(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼±cycle‘‰ffŽ‘®switchŽ‘lçV¬;Ž¡‘ +°gŽŸ­922.‘ üSize›ÕT(n•®9um“b•QÇer˜of˜p“oin®9ts).Ž¦°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°ŽŽŽŒ‹ùÍs Šn ý‘ì°x¬922›¯3DLDF-1.1.5.1’å ºSIZE–ÕX(NUMBER“OF“POINTS)˜¬249Ž €n ý•@P‘ 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+°gŽ¦­925.– üSubpath.“¬[²LDF‘T2002.11.05.¬]Ž‘Zˆ6±subp‘ÿ}'athŽ‘|˜¬(‘ª®)–UUreturns“a“new“­P®9athŽ‘<¬using“±p‘ÿ}'ointsŽ‘yê¬[±startŽ‘…M¬]“throughŽ¡±p‘ÿ}'ointsŽ‘$•¬[±endŽ‘ª—°‘Éå¬1Ž‘Éæ]–×from“°Ž‘رthisŽ‘ Ž¬.‘_HIf“the“optional“­b•QÇo“olŽ‘‡¿¬argumen¸ãt“±cycleŽ‘´ã¬is“used,‘(ðthen“the“new“­P®9athŽ‘ͬwill“bGe“a“cycle,Ž¡whether‘ý'°Ž‘ý(±thisŽ‘æ¬is–ý'or“not.›TbOne“optional“connector“argumen¸ãt“can“bGe“used.˜If“it“is,‘Êit“will“bGe“the“only“connector.Ž¡Otherwise,–UUthe“connectors“from“°Ž‘UV±thisŽ‘–a¬are“used.Ž¡‘ +[²LDF‘T2002.11.05.¬]Ž‘Y;±startŽ‘qâݬm¸ãust–UUbšGe“µ<“±endŽ‘6¬.‘qÇIt“is“not“p˜ossible“to“ha•¸ãv“e‘UU±startŽ‘/÷µ>‘UU±endŽ‘6¬,›UUev“en˜if˜°Ž‘UV±thisŽ‘–a¬is˜a˜cycle.ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.11.05.¬]Ž‘Y½Rewrote– +!this“function.›,Made“±subp‘ÿ}'athŽ‘%„ƒ¬(‘ª®)“itself“and“its“argumen¸ãts“­constŽ‘ßn¬.˜Added“errorŽ¡handling‘UUcoGde.Ž¡‘ +[²LDF‘T2003.07.16.¬]Ž‘Y;Please–UUnote“that“±startŽ‘/÷¬and“±endŽ‘‹\¬cannot“bGe“made“­constŽ‘*¢¬.Ž¡‘ +[²LDF‘T2003.08.27.¬]Ž‘YE‹Changed‘’¥­in®9tŽ‘tìµiŽ‘y…¬to‘’¥­sizeu½‰™šs4Ž‘ÔwtŽ‘#"žµiŽ‘*'7¬in–’¥the“­forŽ‘¸{¬loGops“that“compare“µiŽ‘ +—>¬to“±startŽ‘ª—¬and“±endŽ‘sW¬.‘)¸The“w•¸ãa“yŽ¡it–UUwš¸ãas“bGefore“caused“GCC“with“the“\®-Wall¬"“option“to“issue“a“w˜arning.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°ŽŸ ‘ +­P®9athŽ‘%åí±subp‘ÿ}'athŽ‘G`O¬(­sizeu½‰™šs4Ž‘ÔwtŽ‘QܱstartŽ‘4×)µ;‘ª¨­sizeu½‰™šs4Ž‘ÔwtŽ‘ ü„±endŽ‘1Ý6µ;‘ª¨­constŽ‘Ô}b•QÇo“olŽ‘9u±cycleŽ‘Rµc¬=‘DZfalseŽ‘v\µ;‘ª¨­constŽ‘Ô}stringŽ‘@øý±c–ÿ}'onne“ctorŽ‘oï¬=‘Ç´""Ž‘ Íz¬)‘Tˆ­constŽ‘)Õ¬;ŽŽŽŒ‹úÙb Šn ý‘ì¬250›¯SUBP–ÿJªA“TH’1ø<3DLDF-1.1.5.1˜°x¬926Ž €n ý•@P­926.Ž©°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¤ ‘ +­P®9athŽ‘%Ï6P®9athŽ‘?`ž¬::‘±subp‘ÿ}'athŽ‘"zf¬(­sizeu½‰™šs4Ž‘ÔwtŽ‘;%±startŽ‘4Àrµ;‘ª¨­sizeu½‰™šs4Ž‘ÔwtŽ‘ åͱendŽ‘1Ƶ;‘ª¨­constŽ‘½Æb•QÇo“olŽ‘9G¨±cycleŽ‘OÀݵ;‘ª¨­constŽ‘½ÆstringŽ‘@˱c–ÿ}'onne“ctorŽ‘l*i¬)‘=Ñ­constŽ‘°f‘=Ñ­b•QÇo“olŽŽ¡‘2´DEBUGŽ‘Ov¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¦‘­P®9athŽ‘9æ¼µpŽ‘>;ŽŸ­927.‘ ü¬[²LDF‘T2002.11.05.¬]Ž‘[˜There–e!is“no“\´INVALID_PATHŽ‘?†D¬",›©so“I‘dÛreturn“an“empt¸ãy“one,˜if“±startŽ‘vƒ°‘Œ±endŽ‘lǬ.‘¡+SinceŽ¡­opQÇeratorŽ‘+–µ°Ž‘3]Ó¬(‘ª¨)–=¬currenš¸ãtly“doGesn't“exist,‘wÂthere's“not“m˜uc˜h“pGoin˜t“in“de ning“´INVALID_PATHŽ‘CÃð¬,‘wÂsince“there's“noŽ¡w•¸ãa“y–UUto“compare“another“­P®9athŽ‘<¬to“it.Ž¦°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¡‘ +­ifŽ‘´ù¬(±startŽ‘Le°‘DZendŽ‘§Ê¬)‘°fŽ¡‘±c‘ÿ}'errŽ‘*'c°‘q»´"ERROR!® ´In® ´Path::subŽ‘lqpath():\n"Ž’¤é„°‘q»´"The® ´\"start\"® ´argumŽ‘lqent® ´is® ´<® ´the® ´\"end\"Ž’ÕqC\ŽŽ¡‘(® ´argument.\n"Ž‘o]°‘Ç´"Returning® ´empty® ´PatŽ‘kÆÜh.\n\n"Ž’“ÔG°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘7æ¼µpŽ‘<;Ž¡‘ +°gŽŸ­928.‘ ü¬[²LDF‘T2002.11.05.¬]Ž‘Zˆ6More–UUerror“handling.‘qÇIn“these“cases,“it's“pGossible“to“reco•¸ãv“er.Ž¦°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¡‘ +­ifŽ‘´ù¬(±startŽ‘Leµ>‘DZp‘ÿ}'ointsŽ‘ë­µ:±sizeŽ‘\¬(‘ª¨)–8à°“¬1Ž‘8á)‘°fŽ¡‘±c‘ÿ}'errŽ‘*'c°‘q»´"ERROR!® ´In® ´Path::subŽ‘lqpath():\n"Ž’¤é„°‘q»´"\"start\"® ´argument® Ž‘lq´is® ´>® ´points.size()® ´-Ž’ÕqC\ŽŽ¡‘(® ´1.\n"Ž‘JÍr°‘Ç´"Will® ´try® ´to® ´recoverŽ‘kÆÜ® ´by® ´setting® ´start® ´=® Ž’ÔÆ ´0.\n\n"Ž’üÔ °‘DZ ushŽ‘€¬;Ž¡‘±startŽ‘,Lg¬=‘Ç0Ž‘Ç;Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(±endŽ‘§Êµ>‘DZp‘ÿ}'ointsŽ‘ë­µ:±sizeŽ‘\¬(‘ª¨))‘°fŽ¡‘±c‘ÿ}'errŽ‘)ðò°‘;J´"ERROR!® ´In® ´Path::subŽ‘l;path():\n"Ž’¤|¢°‘;J´"\"end\"® ´argument® ´isŽ‘l;® ´>® ´points.size().\n"Ž’Øü„°Ž¡‘(´"Will® ´try® ´to® ´recoverŽ’ÿÈ® ´by® ´setting® ´end® ´=® ´poŽ’ùÿŒints.size().\n\n"Ž’VŒÙ°‘DZ ushŽ‘€¬;Ž¡‘±endŽ‘'§Ì¬=‘DZp‘ÿ}'ointsŽ‘ë­µ:±sizeŽ‘\¬(‘ª¨);Ž¡‘ +°gŽŸ­929.‘ ü¬[²LDF‘T2002.11.05.¬]Ž‘Y«If–x4a“±c–ÿ}'onne“ctorŽ‘0OB¬argumenš¸ãt“is“spGeci ed,‘¤nall“w˜e“ha˜v˜e“to“do“is“put“the“appropriate“­P•®9oin“tsŽŽ¡¬from‘UU±p‘ÿ}'ointsŽ‘!Ï?¬onš¸ãto‘UUµpŽ‘]U:±p‘ÿ}'ointsŽ‘$•¬,–UUput“±c–ÿ}'onne“ctorŽ‘2 „¬on˜to“µpŽ›]U:±c–ÿ}'onne“ctorsŽ‘/4.¬,“and“return“µpŽ˜¬.Ž¦°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¡‘ +­ifŽ‘´ù¬(±c–ÿ}'onne“ctorŽ‘.%ò°6¬=‘Ç´""Ž‘ Íz¬)–UU°f“­forŽ‘=Û¬(­sizeu½‰™šs4Ž‘ÔwtŽ‘R©µiŽ‘%‹µ¬=‘DZstartŽ‘Le¬;‘ÿýµiŽ‘ 9 <‘DZendŽ‘§Ê¬;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)“°fŽ¡‘ +­ifŽ‘´ù¬(µiŽ‘9 °‘DZp‘ÿ}'ointsŽ‘ë­µ:±sizeŽ‘\¬(‘ª¨))‘°fŽ¡‘±c‘ÿ}'errŽ‘*Ög°‘ ¿´"ERROR!® ´In® ´Path::subŽ‘m ƒpath():\n"Ž’¦GŒ°‘ ¿´"end® ´argument® ´>® ´poinŽ‘m ƒts.size().\n"Ž’¶ƒ°Ž¡‘(´"Breaking® ´out® ´of® ´looŽ’ÿÈp.\n\n"Ž’¹ 3°‘DZ ushŽ‘€¬;Ž¡‘­breakŽ‘0¡f¬;Ž¡‘ +°gŽ¡‘ +µpŽ‘:±p‘ÿ}'ointsŽ–$•µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­P•®9oin“tŽ‘!¶µµ>‘Ǭ(±p‘ÿ}'ointsŽ“¬[µiŽ‘qô¬])–UU)“;‘qÇ°g“µpŽ‘]U:±c–ÿ}'onne“ctorsŽ‘/4.µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(±c–ÿ}'onne“ctorŽ‘+^Ú¬);Ž¡‘ +µpŽ‘:±set‘‰ffŽ‘®cycleŽ‘&*¬(±cycleŽ‘y5¬);Ž¡‘ +­returnŽ‘-滵pŽ‘2;‘qÇ°gŽŽŽŒ‹ûêo Šn ý‘ì°x¬930›¯3DLDF-1.1.5.1’1ø‘ÐC¬(µpŽ‘:±p‘ÿ}'ointsŽ˜¬[µiŽ‘qô¬])Ž¡‘)‘UU;Ž¡‘ +­ifŽ‘´ù¬(µiŽ‘9 <‘ÇpŽ‘Ï:±c–ÿ}'onne“ctorsŽ–/4.µ:±sizeŽ‘\¬(‘ª¨))‘µqŽ‘ Òª:±c–ÿ}'onne“ctorsŽ“µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(µpŽ‘:±c–ÿ}'onne“ctorsŽ“¬[µiŽ‘qô¬]);Ž¡‘ +°g‘UUµqŽ‘'ÿ:±set‘‰ffŽ‘®cycleŽ‘&*¬(±cycleŽ‘y5¬);Ž¡‘ +­returnŽ‘-滵qŽ‘2¹e¬;‘qÇ°gŽ¤­931.‘ üGet‘ÕTpQÇoin®9t.Ž¡932.‘ ünon-const‘ÕTv®9ersion.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ +¬[²LDF‘T2002.11.05.¬]Ž‘Y;Made–UUnon-­inlineŽ‘4ó¬.‘qÇChanged“return“v‘ÿqÇalue“to“­constŽ‘!÷P•®9oin“tŽ‘@o”¬&Ž‘H6².Ž¡‘ +[²LDF‘T2003.11.28.¬]Ž‘Y˜{BUG‘åpFIX:–å•Changed,‘ ¥so“that“±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Jt¬(‘ª®)“is“called“on“the“­P•®9oin“tŽ‘ݬ.‘"†This“en¸ãtailedŽ¡making–ÅÃthis“function“non-­constŽ‘ÕM¬.‘ÃAdded“­constŽ‘"`Ó¬vš¸ãersion“bGelo˜w.‘ÃThis“ma˜y“actually“bGe“a“bug,‘áÞrather“than“aŽ¡bug–s x,‘mdepGending“on“hoš¸ãw“this“function“is“used“elsewhere.‘U|Ho˜w˜ev˜er,‘mI‘]really“think“±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘I R¬(‘ª®)“shouldŽ¡bGe‘UUcalled.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¡‘ +­constŽ‘(*£P•®9oin“tŽ‘G@¬&Ž‘Ná^±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘vC¦¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµaŽ‘quƒ¬);ŽŽŽŒ‹üø© Šn ý‘ì¬252–¯NON-­CONST‘ÕX¯VERSION’ñÎ?3DLDF-1.1.5.1“°x¬933Ž €n ý•@P­933.Ž©°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¤ ‘ +­constŽ‘(*£P•®9oin“tŽ‘G@¬&Ž‘Ná^­P®9athŽ‘hrƬ::‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘(bL¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµaŽ‘quƒ¬)Ž¡‘ +°fŽ¡‘­ifŽ‘´ú¬(µaŽ‘H<‘DZp‘ÿ}'ointsŽ‘ë­µ:±sizeŽ‘\¬(‘ª¨))‘°fŽ¡‘¬(±p‘ÿ}'ointsŽ‘$•¬[µaŽ‘I0¬])‘þŸµ~ŽŽ‘±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Jà¬(‘ª¨);Ž¡‘­returnŽ‘Aæ½°Ž‘Fæ¾±p‘ÿ}'ointsŽ‘b S¬[µaŽ‘I0¬];Ž¡‘°gŽ¡‘­elseŽ‘+Øá°fŽ¡‘±c‘ÿ}'errŽ‘4w0°‘Á‡´"ERROR!® ´In® ´Path::getŽ‘lÁK_point():\n"Ž—° °‘Á‡´"Argument® ´is® ´>=® ´sizeŽ‘lÁK® ´of® ´Path.\n"Ž“°Ž¡‘2´"Returning® ´INVALID_PŽ’šÿÉOINT.\n\n"Ž’ÒÍ+°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½´INVALID_POINTŽ’†¬þ¬;Ž¡‘°gŽ¡‘ +gŽŸ­934.‘ üconst‘ÕTv®9ersion.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.11.28.¬]Ž‘Y;Added–UUthis“v¸ãersion.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¡‘ +­P•®9oin“tŽ‘(ïž±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘PQæ¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµaŽ‘quƒ¬)‘UU­constŽ‘*¢¬;ŽŸ­935.Ž¦°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¡‘ +­P•®9oin“tŽ‘(ïžP®9athŽ‘B¬::‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘(bL¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµaŽ‘quƒ¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­ifŽ‘´ú¬(µaŽ‘H<‘DZp‘ÿ}'ointsŽ‘ë­µ:±sizeŽ‘\¬(‘ª¨))‘°fŽ¡‘­P•®9oin“tŽ‘<ï µpŽ‘D¾¸¬=‘Ç°Ž‘Ǭ(±p‘ÿ}'ointsŽ‘$•¬[µaŽ‘I0¬]);Ž¦‘µpŽ‘#:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¡‘­returnŽ‘Aæ½µpŽ‘F;Ž¡‘°gŽ¡‘­elseŽ‘+Øá°fŽ¡‘±c‘ÿ}'errŽ‘4w0°‘Á‡´"ERROR!® ´In® ´Path::getŽ‘lÁK_point():\n"Ž—° °‘Á‡´"Argument® ´is® ´>=® ´sizeŽ‘lÁK® ´of® ´Path.\n"Ž“°Ž¡‘2´"Returning® ´INVALID_PŽ’šÿÉOINT.\n\n"Ž’ÒÍ+°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½´INVALID_POINTŽ’†¬þ¬;Ž¡‘°gŽ¡‘ +gŽŸ­936.‘ üGet–ÕTlast“pQÇoin®9t.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.05.10.¬]Ž‘Y;Added–UUthis“function.Ž¡‘ +[²LDF‘T2002.11.05.¬]Ž‘Y;Made–UUnon-­inlineŽ‘4ó¬.‘qÇChanged“return“v‘ÿqÇalue“to“­constŽ‘!÷P•®9oin“tŽ‘@o”¬&Ž‘H6².Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¡‘ +­constŽ‘(*£P•®9oin“tŽ‘G@¬&Ž‘Ná^±get‘‰ffŽ–®last‘‰ffŽ“p‘ÿ}'ointŽ’‰œ¬(‘ª®)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹ý Šn ý‘ì°x¬937›¯3DLDF-1.1.5.1’îGET–ÕXLAST“POINT˜¬253Ž €n ý•@P­937.Ž©°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¤ ‘ +­constŽ‘(*£P•®9oin“tŽ‘G@¬&Ž‘Ná^­P®9athŽ‘hrƬ::‘±get‘‰ffŽ–®last‘‰ffŽ“p‘ÿ}'ointŽ‘;$B¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­ifŽ‘´ú¬(±p‘ÿ}'ointsŽ›$•µ:±sizeŽ‘\¬(‘ª¨)–Ç°6¬=“0Ž‘Ç)‘­returnŽ‘(溰Ž‘-æ»±p‘ÿ}'ointsŽ‘I P¬[±p‘ÿ}'ointsŽ˜µ:±sizeŽ‘\¬(‘ª¨)–8à°“¬1Ž‘8á];Ž¡‘­elseŽ‘+Øá°fŽ¡‘±c‘ÿ}'errŽ‘5ž4°‘è‹´"ERROR!® ´In® ´Path::getŽ‘mèO_last_point():\n"Ž’Ì—°‘è‹´"Path® ´is® ´empty.\n"Ž‘h×H°Ž¡‘2´"Returning® ´INVALID_PŽ’šÿÉOINT.\n\n"Ž’ÒÍ+°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½´INVALID_POINTŽ’†¬þ¬;Ž¡‘°gŽ¡‘ +gŽŸ­938.‘ üGet‘ÕTsize.Ž¦°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔinlineŽ‘Osizeu½‰™šs4Ž‘ÔwtŽ‘njűget‘‰ffŽ‘®sizeŽ’¹Ý¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼±p‘ÿ}'ointsŽ‘S Qµ:±sizeŽ‘\¬(‘ª¨);Ž¡‘ +°gŽŸ­939.‘ üGet‘ÕTnormal.ŽŽŽŒ‹þñ Šn ý‘ì¬254›­P–ÿ +«A“TH‘ÕX¯VERSION’­›3DLDF-1.1.5.1˜°x¬940Ž €n ý•@P­940.› üP•®9ath‘õÓv“ersion.˜¬[²LDF‘T2002.11.05.¬]Ž‘YÅÛ±get‘‰ffŽ‘®normalŽ’ŠPO¬(‘ª®)–’úreturns“a“unit“vš¸ãector“represen˜ting“the“normal“to“theŽ¤ plane–f +of“the“­P®9athŽ‘]x°Ž‘$]y±thisŽ‘5I/¬,‘j8if“°Ž‘f ±thisŽ›·Ë¬is“planar.‘£çIf“the“­P•®9oin“tsŽ‘&on“°Ž‘f ±thisŽ˜¬are“colinear“and“there“are“no“connectorsŽ¡that–˜pcould“mak¸ãe“the“­P®9athŽ›ÂD¬non-linear,‘©6then“±originŽ‘"'¬((0µ;–ª¨¬0µ;“¬0))–˜pis“returned.‘;If“the“­P®9athŽ˜¬is“neither“planar“norŽ¡linear,‘UU±get‘‰ffŽ‘®normalŽ‘3ßɬ(‘ª®)–UUreturns“´INVALID_POINTŽ‘H–¬.Ž¡‘ +[²LDF‘T2002.11.05.¬]ŽŽ¡°Ž‘ +±get‘‰ffŽ‘®normalŽ‘:Šu¬(›ª®)–> rst“c•¸ãhec“ks–>whether“a“­P®9athŽ‘ Çà¬con¸ãtains“no“­P•®9oin“tsŽ‘(Z¬or“only“one“­P•®9oin“tŽ‘µ†¬.‘ÂIf“so,‘L¸±get‘‰ffŽ‘®normalŽ‘4×,¬(˜)Ž¡‘ +returns‘UU´INVALID_POINTŽ‘H–¬.Ž©°Ž‘ +¬Then–KÒit“c•¸ãhec“ks–KÒwhether“the“­P®9athŽ‘!)¬has“connnectors“that“mighš¸ãt“mak˜e“the“­P®9athŽ‘!)¬non-planar,‘‰qev˜en“if“theŽ¡‘ +­P•®9oin“tsŽ‘.DÙ¬lie–!Tin“a“plane.›ÕÄIf“it“doGes,‘TTit“returns“´INVALID_POINTŽ‘H畬.˜Note“that“there“is“no“guaran¸ãtee“that“theŽ¡‘ +connectors–UUactually“±wil‘‚Øl‘]Þ¬mak¸ãe“the“­P®9athŽ‘<¬non-planar.Ž¦°Ž‘ +¬Then–èit“c•¸ãhec“ks–èwhether“the“­P®9athŽ‘­4¬has“only“t•¸ãw“o‘è­P•®9oin“tsŽ‘"±l¬.‘/NIf–èit“doGes,‘µË±get‘‰ffŽ‘®normalŽ‘3@?¬(‘ª®)“returns“the“­P•®9oin“tŽ‘ ¶¬(0µ;–ª¨¬0µ;“¬0),Ž¡‘ +bšGecause–UUthe“­P®9athŽ‘<¬will“b˜e“linear.Ž¦°Ž‘ +¬Then–¨ it“gets“the“cross“proGduct“µbŸÿ³0Ž›$“¬ofŸü±È“°ŽŽ‘ I‘þ㎎Ž‘gþ!ŽŽŸN8“µpŸÿ³0Ž‘|sµpŸÿ³1ŽŽŽŽŽ‘Y&¬andŸü±È“°ŽŽ‘ I‘þ㎎Ž‘gþ!ŽŽŸN8“µpŸÿ³0Ž‘|sµpŸÿ³2ŽŽŽŽŽ‘±¬,‘¼Ówhere“µpŸÿ³0Ž˜¬and“µpŸÿ³1Ž˜¬are“the“ rst“and“second“­P•®9oin“tsŽ‘'sĬonŽ¡‘ +the‘‡­P®9athŽ‘’ë¬,‘Jand–‡µpŸÿ³2Ž‘}ú¬is“the“next“­P•®9oin“tŽ‘!V¬on“the“­P®9athŽ›”r¬suc¸ãh“that“µbŸÿ³0Ž‘C‹°6¬=‘Ç(0µ;–ª¨¬0µ;“¬0).‘UØIf–‡no“­P•®9oin“tsŽ‘&&’¬on“the“­P®9athŽ˜¬ful llŽ¡‘ +this–UUcondition,“then“all“of“the“­P•®9oin“tsŽ‘&Î.¬are“colinear,“so“±get‘‰ffŽ‘®normalŽ‘3ßɬ(‘ª®)“returns“±originŽ‘Kv¬.Ž¦°Ž‘ +¬If,›Ñho•¸ãw“ev“er,˜µbŸÿ³0Ž‘C‹°6¬=‘Ç(0µ;–ª¨¬0µ;“¬0)–pexists,˜then“cross“proGducts“µbŸÿ·xŽ‘ T¬are“calculated“usingŸü±È“°ŽŽ‘¤W‘þ㎎Ž‘gþ!ŽŽŸN8“µpŸÿ³0Ž‘|sµpŸÿ³1ŽŽŽŽŽ‘Ƭand“the“direction“v¸ãectorsŽ¡Ÿü±È‘ +°ŽŽ‘ç!‘þ㎎Ž‘®6!ŽŽŸN8‘ +µpŸÿ³0Ž‘|sµpŸÿ·xŽŽŽŽŽ‘! ‡¬for–‹/the“rest“of“the“­P•®9oin“tsŽ‘'9âµpŸÿ·xŽ‘”¬on“the“­P®9athŽ‘“¬.‘TIf“and“only“if“µbŸÿ·xŽ›)¼¬=‘ صbŸÿ³0Ž‘|s¬,‘˜¥or“µbŸÿ·xŽ˜¬=‘ Ø°µbŸÿ³0Ž‘|s¬,‘˜¥or“µbŸÿ·xŽ˜¬=‘ Ø(0µ;–ª¨¬0µ;“¬0)‘‹/forŽ¡‘ +all–òþµbŸÿ·xŽ‘ä¬,›©then“the“­P®9athŽ‘w`¬is“planar,˜and“±get‘‰ffŽ‘®normalŽ‘3}r¬(‘ª®)“returns“°µbŸÿ³0Ž‘oq¬(see“explanation“of“sign“bGelo¸ãw).‘QOtherwise,Ž¡‘ +the‘UU­P®9athŽ‘<¬is–UUnon-planar,“and“±get‘‰ffŽ‘®normalŽ‘3ßɬ(‘ª®)“returns“´INVALID_POINTŽ‘H–¬.Ž¦‘ +[²LDF‘T2003.06.04.¬]Ž‘XP™Revš¸ãersing–³the“sign“of“µbŸÿ³0Ž‘&¬ensures“that“the“normal“will“pGoin˜t“in“the“direction“of“the“pGositiv˜eŽ¡y-axis,›Ï‚when–® a“plane“ gure“is“created“in“the“x-z“plane,˜using“one“of“the“constructors“taking“a“­P•®9oin“tŽ‘ öb¬argumen¸ãtŽ¡for–˜¾the“cen•¸ãter,‘¾v­realŽ‘µ ¬argumen“ts–˜¾for“the“dimensions,‘¾vand“three“­realŽ‘U¬argumen¸ãts“for“the“rotation“abGout“the“ma‘Ž8jorŽ¡axes.›iIf–ýnon-zero“argumen¸ãts“are“used“for“rotation,‘' 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´coliŽ‘l}±near.\n"Ž’šî°Ž¦‘2´"Returning® ´origin.\nŽ’šÿÉ\n"Ž’® @°‘DZ ushŽ‘€¬;Ž¦‘­returnŽ‘7æ¼±originŽ‘RÜݬ;Ž¦‘ +°gŽ¦‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±b0Ž‘“çµ:±showŽ‘Šÿ¬(´"b0"Ž‘†\¬);Ž¦‘ +±b0Ž‘“èµ:±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u¬(±trueŽ‘ʬ);Ž¦‘ +­ifŽ‘´ù¬(±iterŽ‘’°‘DZp‘ÿ}'ointsŽ‘ë­µ:±endŽ‘ಬ(‘ª¨)–8à°^“±b0Ž‘“ß°6¬=‘DZoriginŽ‘½9¬)‘°fŽ¦‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘°fŽ¦‘±c‘ÿ}'outŽ‘4 R°‘Ç´"Exiting® ´Path::get_nŽ‘kÆÜormal().® ´"Ž’£”>°‘Ç´"Points® ´are® ´all® ´coliŽ‘kÆÜnear® ´except® ´for® ´one.Ž’ÔÆ \n"Ž’çÔ°Ž¦‘2´"Returning® ´normal.\nŽ’šÿÉ\n"Ž’® @°‘DZ ushŽ‘€¬;Ž¦‘°gŽ¦‘­returnŽ‘7æ¼°Ž‘?­Ú±b0Ž‘KAÁ¬;Ž¦‘ +°gŽ¡‘ +­P•®9oin“tŽ‘(ïž±b1Ž‘4ƒ…¬;Ž¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Entering® ´second® ´whiŽ‘kÆÜle.\n"Ž’Ž”J°‘DZ ushŽ‘€¬;Ž¦‘ +­whileŽ‘(C-¬(±iterŽ‘’°6¬=‘DZp‘ÿ}'ointsŽ‘ë­µ:±endŽ‘ಬ(‘ª¨))‘°fŽ¦‘±p2Ž‘"ÝÚ¬=‘Ç°Ž‘ÇŽ‘ DZiterŽ‘Ÿÿ³+‘ÿ+ŽŽ‘)Ù8¬;Ž¦‘±a1Ž‘"ÝÚ¬=‘DZp2Ž‘¸°‘8à±p0Ž‘O ¬;Ž¦‘±b1Ž‘"[¬=‘DZa0Ž‘Ýص:±cr–ÿ}'oss‘‰ffŽ‘®pr“o“ductŽ‘:Œé¬(±a1Ž‘ À¬);Ž¦‘­ifŽ‘´ú¬(±b1Ž‘Zÿ°6¬=‘DZoriginŽ‘½9¬)Ž¦‘(µ=°‘ÿý¬[²LDF‘T2002.11.03.¬]Ž‘T7This‘UU­ifŽ‘ 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-«[¬LDF‘T2003.07.11.«]Ž‘Y;Added–UUthis“function.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¤ ‘ -ÂP•®9oin“tŽ‘(ïžP•®9oin“tŽ‘E‰ê«::‘Ïget‘‰ffŽ‘®normalŽ‘1Šx«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]±pŽ‘Ié];‘ª¨ÂconstŽ‘ÕJP•®9oin“tŽ‘>Äç«&Ž‘FŒ±qŽ‘K^¯«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂP®9athŽ‘/æ»±rŽ‘4°Ï«;Ž©‘±rŽ‘Ê:Ïset‘‰ffŽ‘®c–ÿ}'onne“ctorsŽ‘>å«(Ý"--"Ž‘†\«);Ž¡‘±rŽ‘‘.«+=ŽŽ‘-æ‚·Ž‘2æƒÏthisŽ‘CÒ9«;Ž¡‘±rŽ‘‘.«+=ŽŽ‘-悱pŽ‘2î‚«;Ž¡‘±rŽ‘‘.«+=ŽŽ‘-悱qŽ‘2¹,«;Ž¡‘ÂifŽ‘´ú«(·:±rŽ‘Ê:Ïis‘‰ffŽ‘®planarŽ‘(&«(‘ª¨))‘·fŽ¡‘Ïc‘ÿ}'errŽ‘8÷f·‘A½Ý"ERROR!È ÝInÈ ÝPoint::geŽ‘qAt_normal():\n"Ž’É|·Ž¡‘2Ý"TheÈ ÝPointsÈ ÝdoÈ ÝnotÈ ÝdŽ’šÿÉetermineÈ ÝaÈ Ýplane.\n"Ž’M ·‘ÇÝ"ReturningÈ ÝINVALID_PŽ‘kÆÜOINT.\n\n"Ž’£”>·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½ÝINVALID_POINTŽ’†¬þ«;Ž¡‘·gŽ¡‘ÂelseŽ‘+ØáreturnŽ‘O¿›±rŽ‘T‰¯:Ïget‘‰ffŽ‘®normalŽ‘0Št«(‘ª¨);Ž¡‘ -·gŽŸÂ902.‘ üGet‘ÕTplane.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.11.05.«]Ž‘Y;Rewrote–UUthis“function“to“correspGond“to“the“new“de 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‘FÝ"*thisÈ Ýdoesn'tÈ ÝlieÈ ÝiŽ’®ÿËnÈ ÝtheÈ ÝplaneÈ ÝdeterminŽ’ÿedÈ Ý"Ž’1 /·‘†DÝ"byÈ ÝtheÈ Ýarguments.\nŽ‘l†"Ž‘uÒ±·Ž¡‘FÝ"ReturningÈ Ýfalse.\n\Ž’®ÿËn"Ž’¼ÍE·‘ÇÏ ushŽ‘€«;Ž¡‘(·gŽ¡‘(ÂreturnŽ‘Kæ¾ÏfalseŽ‘`–«;Ž¡‘·gŽ©‘ÂP•®9oin“tŽ‘<ï ±tŽ‘@Œ«(·Ž‘ÏthisŽ‘ë·«);Ž¡‘ÂP•®9oin“tŽ‘<ï ±cŽ‘AC{«(Ïp0Ž‘ À«);Ž¡‘ÂP•®9oin“tŽ‘<ï ±dŽ‘B$«(Ïp1Ž‘ À«);Ž¡‘ÂP•®9oin“tŽ‘<ï ±eŽ‘A—¡«(Ïp2Ž‘ 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-M«(Ïlamb‘ÿ}'da‘‰ffŽ‘®denominatorŽ‘]E¿·‘Ç«0Ž‘ ÿù·_‘8àÏmu‘‰ffŽ‘®denominatorŽ‘Nâ5·‘Ç«0Ž‘Ç)‘UU·fŽ¡‘ÂifŽ‘+Hˆ«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘Àá·‘gªÝ"lambda_denominatorÈ Ž‘ngnÝorÈ Ýmu_denominatorÈ Ý==Ž’×g2È Ý0.È Ý"Ž’÷•5·Ž¡‘<Ý"ExchangingÈ ÝyÈ ÝandÈ Ýz-Ž’¤ÿÊcoordinates.\n"Ž’÷ ·‘ÇÏ ushŽ‘€«;Ž¦‘ÂrealŽ‘4³1ÏtempŽ‘K ¥«;Ž¦‘ÏtempŽ‘7!«=‘ÇÏt‘‰ffŽ‘®yŽ‘«;Ž¡‘Ït‘‰ffŽ‘®yŽ‘.«=‘ÇÏt‘‰ffŽ‘®zŽ‘›ë«;Ž¡‘Ït‘‰ffŽ‘®zŽ‘-›î«=‘ÇÏtempŽ‘!Œ«;Ž¡‘ÏtempŽ‘7!«=‘ÇÏc‘‰ffŽ‘®yŽ‘O«;Ž¡‘Ïc‘‰ffŽ‘®yŽ‘/O«=‘ÇÏc‘‰ffŽ‘®zŽ‘ã«;Ž¡‘Ïc‘‰ffŽ‘®zŽ‘.ã -«=‘ÇÏtempŽ‘!Œ«;Ž¡‘ÏtempŽ‘7!«=‘ÇÏd‘‰ffŽ‘®yŽ‘Ñõ«;Ž¡‘Ïd‘‰ffŽ‘®yŽ‘/Ñø«=‘ÇÏd‘‰ffŽ‘®zŽ‘eà«;Ž¡‘Ïd‘‰ffŽ‘®zŽ‘/eã«=‘ÇÏtempŽ‘!Œ«;Ž¡‘ÏtempŽ‘7!«=‘ÇÏe‘‰ffŽ‘®yŽ‘O«;Ž¡‘Ïe‘‰ffŽ‘®yŽ‘/O«=‘ÇÏe‘‰ffŽ‘®zŽ‘ã«;Ž¡‘Ïe‘‰ffŽ‘®zŽ‘.ã -«=‘ÇÏtempŽ‘!Œ«;ŽŽŽŒ‹ü f’ Šn ý‘ì«252›ÂPOINT–ÕX­LIES“WITHIN“TRIANGLE’ÑÝ 3DLDFPRÃŽG˜·x«904Ž €n ý•@P‘Ïlamb‘ÿ}'da‘‰ffŽ‘®denominatorŽ‘{E«=‘Ç(((Ïe‘‰ffŽ‘®xŽ–Û5·‘8àÏc‘‰ffŽ‘®xŽ“«)–8à·“«(Ïd‘‰ffŽ‘®yŽ‘C½·“Ïc‘‰ffŽ‘®yŽ›Àä«))“·“«((Ïe‘‰ffŽ‘®yŽ˜·“Ïc‘‰ffŽ‘®yŽ˜«)“·“«(Ïd‘‰ffŽ‘®xŽ‘^·“Ïc‘‰ffŽ‘®xŽ‘Û5«)));Ž¤ ‘Ïmu‘‰ffŽ‘®denominatorŽ‘j©X«=‘Ç((Ïe‘‰ffŽ‘®xŽ–Û5·‘8àÏc‘‰ffŽ‘®xŽ“«)–8à·“«(Ïd‘‰ffŽ‘®yŽ‘C½·“Ïc‘‰ffŽ‘®yŽ›Àä«))“·“«((Ïe‘‰ffŽ‘®yŽ˜·“Ïc‘‰ffŽ‘®yŽ˜«)“·“«(Ïd‘‰ffŽ‘®xŽ‘^·“Ïc‘‰ffŽ‘®xŽ‘Û5«));Ž¡‘ÂifŽ‘)´û«(·:«(Ïlamb‘ÿ}'da‘‰ffŽ‘®denominatorŽ‘]E¿·‘Ç«0Ž‘ ÿù·_‘8àÏmu‘‰ffŽ‘®denominatorŽ‘Nâ5·‘Ç«0Ž‘Ç))‘·fŽ¡‘(ÂifŽ‘5^Ö«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘æ ·‘ŒÖÝ"ExchangingÈ ÝyÈ ÝandÈ Ýz-Ž‘nŒšcoordinatesÈ Ýworked.\Ž’׌^n"Ž’è–·Ž¡‘FÝ"lambda_denominatorÈ Ž’®ÿËÝandÈ Ýmu_denominatorÈ ÝaŽ’ÿreÈ ÝnoÈ ÝlongerÈ Ý0.\n"Ž’yÌÙ·‘ÇÏ ushŽ‘€«;Ž¡‘(Ïexchange‘‰ffŽ–®y‘‰ffŽ“zŽ‘c´›«=‘ÇÏtrueŽ‘‹°«;Ž¡‘·gŽ¡‘ÂelseŽ‘4.7·fŽ¡‘ÂifŽ‘+Ϋ(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘}·‘#ÊÝ"ExchangingÈ ÝyÈ ÝandÈ Ýz-Ž‘n#ŽcoordinatesÈ Ýdidn'tÈ ÝwŽ’×#Rork.\n"Ž’o·Ž¡‘<Ý"ExchangingÈ ÝxÈ ÝandÈ Ýz-Ž’¤ÿÊcoordinates.\n"Ž’÷ ·‘ÇÏ ushŽ‘€«;ŽŸÂ905.‘ ü«First,–UUput“things“bacš¸ãk“the“w˜a˜y“they“w˜ere.‘qÇIt's“w˜asteful,“but“less“confusing.‘qÇ[¬LDF‘T2003.06.24.«]ŽŽŸ·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¡‘ -ÏtempŽ‘#!«=‘ÇÏt‘‰ffŽ‘®yŽ‘«;Ž¡‘ -Ït‘‰ffŽ‘®yŽ‘«=‘ÇÏt‘‰ffŽ‘®zŽ‘›ë«;Ž¡‘ -Ït‘‰ffŽ‘®zŽ‘›ì«=‘ÇÏtempŽ‘!Œ«;Ž¡‘ -ÏtempŽ‘#!«=‘ÇÏc‘‰ffŽ‘®yŽ‘O«;Ž¡‘ -Ïc‘‰ffŽ‘®yŽ‘O«=‘ÇÏc‘‰ffŽ‘®zŽ‘ã«;Ž¡‘ -Ïc‘‰ffŽ‘®zŽ‘ã«=‘ÇÏtempŽ‘!Œ«;Ž¡‘ -ÏtempŽ‘#!«=‘ÇÏd‘‰ffŽ‘®yŽ‘Ñõ«;Ž¡‘ -Ïd‘‰ffŽ‘®yŽ‘Ñö«=‘ÇÏd‘‰ffŽ‘®zŽ‘eà«;Ž¡‘ -Ïd‘‰ffŽ‘®zŽ‘eá«=‘ÇÏtempŽ‘!Œ«;Ž¡‘ -ÏtempŽ‘#!«=‘ÇÏe‘‰ffŽ‘®yŽ‘O«;Ž¡‘ -Ïe‘‰ffŽ‘®yŽ‘O«=‘ÇÏe‘‰ffŽ‘®zŽ‘ã«;Ž¡‘ -Ïe‘‰ffŽ‘®zŽ‘ã«=‘ÇÏtempŽ‘!Œ«;ŽŽŽŒ‹ý xZ Šn ý‘ì·x«906›­3DLDFPRÃŽG’ÑÝ ÂPOINT–ÕX­LIES“WITHIN“TRIANGLE˜«253Ž €n ý•@PÂ906.‘ ü«No•¸ãw,›UUexc“hange˜the˜x˜and˜z-coGordinates.‘qÇ[¬LDF‘T2003.06.24.«]ŽŽ©ª·h–ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«functions‘@­285“·i‘Ç«+·Ž¤ ‘ -ÏtempŽ‘#!«=‘ÇÏt‘‰ffŽ‘®xŽ‘"Q«;Ž¡‘ -Ït‘‰ffŽ‘®xŽ‘"R«=‘ÇÏt‘‰ffŽ‘®zŽ‘›ë«;Ž¡‘ -Ït‘‰ffŽ‘®zŽ‘›ì«=‘ÇÏtempŽ‘!Œ«;Ž¡‘ -ÏtempŽ‘#!«=‘ÇÏc‘‰ffŽ‘®xŽ‘im«;Ž¡‘ -Ïc‘‰ffŽ‘®xŽ‘in«=‘ÇÏc‘‰ffŽ‘®zŽ‘ã«;Ž¡‘ -Ïc‘‰ffŽ‘®zŽ‘ã«=‘ÇÏtempŽ‘!Œ«;Ž¡‘ -ÏtempŽ‘#!«=‘ÇÏd‘‰ffŽ‘®xŽ‘ìF«;Ž¡‘ -Ïd‘‰ffŽ‘®xŽ‘ìG«=‘ÇÏd‘‰ffŽ‘®zŽ‘eà«;Ž¡‘ -Ïd‘‰ffŽ‘®zŽ‘eá«=‘ÇÏtempŽ‘!Œ«;Ž¡‘ -ÏtempŽ‘#!«=‘ÇÏe‘‰ffŽ‘®xŽ‘im«;Ž¡‘ -Ïe‘‰ffŽ‘®xŽ‘in«=‘ÇÏe‘‰ffŽ‘®zŽ‘ã«;Ž¡‘ -Ïe‘‰ffŽ‘®zŽ‘ã«=‘ÇÏtempŽ‘!Œ«;Ž¡‘ -Ïlamb‘ÿ}'da‘‰ffŽ‘®denominatorŽ‘gEÀ«=‘Ç(((Ïe‘‰ffŽ‘®xŽ–Û5·‘8àÏc‘‰ffŽ‘®xŽ“«)–8à·“«(Ïd‘‰ffŽ‘®yŽ‘C½·“Ïc‘‰ffŽ‘®yŽ›Àä«))“·“«((Ïe‘‰ffŽ‘®yŽ˜·“Ïc‘‰ffŽ‘®yŽ˜«)“·“«(Ïd‘‰ffŽ‘®xŽ‘^·“Ïc‘‰ffŽ‘®xŽ‘Û5«)));Ž¡‘ -Ïmu‘‰ffŽ‘®denominatorŽ‘V©V«=‘Ç((Ïe‘‰ffŽ‘®xŽ–Û5·‘8àÏc‘‰ffŽ‘®xŽ“«)–8à·“«(Ïd‘‰ffŽ‘®yŽ‘C½·“Ïc‘‰ffŽ‘®yŽ›Àä«))“·“«((Ïe‘‰ffŽ‘®yŽ˜·“Ïc‘‰ffŽ‘®yŽ˜«)“·“«(Ïd‘‰ffŽ‘®xŽ‘^·“Ïc‘‰ffŽ‘®xŽ‘Û5«));Ž¡‘ -ÂifŽ‘´ù«(·:«(Ïlamb‘ÿ}'da‘‰ffŽ‘®denominatorŽ‘]E¿·‘Ç«0Ž‘ ÿù·_‘8àÏmu‘‰ffŽ‘®denominatorŽ‘Nâ5·‘Ç«0Ž‘Ç))‘·fŽ¡‘ÂifŽ‘!¬h«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘gW·‘ Ý"ExchangingÈ ÝxÈ ÝandÈ Ýz-Ž‘o äcoordinatesÈ Ýworked.\Ž’Ø ¨n"Ž’é"*·Ž¡‘2Ý"lambda_denominatorÈ Ž’šÿÉÝandÈ Ýmu_denominatorÈ ÝaŽ’ÿreÈ ÝnoÈ ÝlongerÈ Ý0.\n"Ž’eÌ×·‘ÇÏ ushŽ‘€«;Ž¡‘Ïexchange‘‰ffŽ–®x‘‰ffŽ“zŽ‘O}#«=‘ÇÏtrueŽ‘‹°«;Ž¡‘ -·gŽ¡‘ -ÂelseŽ‘!Øà·fŽ¡‘ÂifŽ‘´ú«(Ïverb‘ÿ}'oseŽ‘"Ê=·_‘8àÝDEBUGŽ‘ÿ9«)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘8(¢·‘rùÝ"WARNING!È ÝInÈ ÝPoint::Ž‘pr½is_in_triangle():\n"Ž’ákâ·Ž¡‘2Ý"lambda_denominatorÈ Ž’šÿÉÝorÈ Ýmu_denominatorÈ ÝisŽ’ÿÈ Ý0.\n"Ž’&Ìû·‘ÇÝ"ReturningÈ Ýfalse.\n\Ž‘kÆÜn"Ž‘y”V·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¡‘ÂreturnŽ‘7æ¼ÏfalseŽ‘L–«;Ž¡‘ -·gŽ¡‘ -g–UUg“ÂrealŽ‘ƒÏlamb‘ÿ}'daŽ‘<>ž«=‘Ç(((Ït‘‰ffŽ‘®xŽ‘”·‘8àÏc‘‰ffŽ‘®xŽ‘Û5«)–8à·“«(Ïd‘‰ffŽ‘®yŽ‘C½·“Ïc‘‰ffŽ‘®yŽ›Àä«))“·“«((Ït‘‰ffŽ‘®yŽ‘yÈ·“Ïc‘‰ffŽ‘®yŽ˜«)“·“«(Ïd‘‰ffŽ‘®xŽ‘^·“Ïc‘‰ffŽ‘®xŽ‘Û5«)))±=Ïlamb‘ÿ}'da‘‰ffŽ‘®denominatorŽ‘Z~§«;Ž¡‘ -ÂrealŽ‘ ³/ÏmuŽ‘2Là«=‘Ç·Ž‘ -Ž6«((((Ït‘‰ffŽ‘®xŽ‘”·‘8àÏc‘‰ffŽ‘®xŽ‘Û5«)–8à·“«(Ïe‘‰ffŽ‘®yŽ›Àä·“Ïc‘‰ffŽ‘®yŽ˜«))“·“«((Ït‘‰ffŽ‘®yŽ‘yÈ·“Ïc‘‰ffŽ‘®yŽ˜«)“·“«(Ïe‘‰ffŽ‘®xŽ›Û5·“Ïc‘‰ffŽ‘®xŽ˜«)))±=Ïmu‘‰ffŽ‘®denominatorŽ‘Iâ=«);Ž¦‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"lambdaÈ Ý==È Ý"Ž‘Et·‘ÇÏlamb‘ÿ}'daŽ‘$ý3·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"muÈ Ý==È Ý"Ž‘0€·‘ÇÏmuŽ‘`É·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"lambdaÈ Ý+È ÝmuÈ Ý==È Ý"Ž‘_Te·‘ÇÏlamb‘ÿ}'daŽ‘$nû«+‘8àÏmuŽ‘Ò‘·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘Ïc‘ÿ}'outŽ‘*³.·‘YõÝ"(lambdaÈ Ý>=È Ý0È Ý&&È ÝmuÈ Ž‘lY¹Ý>=È Ý0È Ý&&È Ý((lambdaÈ Ý+È ÝmŽ’ÕY}u)È Ý<=È Ý1))È Ý==È Ý"Ž’"¹°·–Yõ«(Ïlamb‘ÿ}'daŽ‘"Èø·“«0Ž‘ -Í•·^‘sŸÏmuŽ‘ -·Ž¡‘(«0Ž‘/8å·^–8à«((Ïlamb‘ÿ}'daŽ‘!§ã«+“ÏmuŽ‘ 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nedŽ¡here,–UUbšGecause“ÂP®9athŽ‘<«is“an“incomplete“t¸ãyp˜e“in“Èplanes.web«.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.06.03.«]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«De ne‘UUÂPlaneŽ‘#Œ «functions‘@­620“·i‘Ç«+·Ž¡‘ -Âb•QÇo“olu½‰™šs4Ž‘Ôwp“oin®9tŽ‘B§œPlaneŽ‘`‰«::‘Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘N–Ú«(ÂconstŽ‘*¢P®9athŽ‘:[«&Ž‘AØy±pŽ‘Fày«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂifŽ‘´ú«(±pŽ–:Ïis‘‰ffŽ‘®line‘ÿ}'arŽ‘%}«(›ª¨))‘ÂreturnŽ‘(æºÏinterse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘v}«(±pŽ“:Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH«(0Ž‘)±;˜pŽ‘²¨:Ïget‘‰ffŽ–®last‘‰ffŽ“p‘ÿ}'ointŽ‘:$>«(˜));Ž¡‘ÂelseŽ‘+Øá·fŽ¡‘Ïc‘ÿ}'errŽ‘5¨·‘òjÝ"ERROR!È ÝInÈ ÝPlane::inŽ‘mò.tersection_point(conŽ’ÖñòstÈ ÝPath&):"Ž’*£·‘òjÏend‘‚ØlŽ‘Ö–·Ž¡‘2Ý"PathÈ ÝisÈ ÝnotÈ Ýlinear!Ž’šÿÉÈ ÝReturningÈ ÝINVALID_Ž’ÿBOOL_POINT."Ž’FLé·‘ÇÏend‘‚ØlŽ–ò·‘ÇÏend‘‚ØlŽ“·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½ÝINVALID_BOOL_POINTŽ’ ìï«;Ž¡‘·gŽ¡‘ -gŽŸÂ923.– 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ÏRearranged“order“ofŽ¡argumenš¸ãts.‘HyAlso,‘tgot–ò;rid“of“the“argumen˜ts“Ïsuppr‘ÿ}'ess‘‰ffŽ‘®xŽ‘2$(«,‘tÏsuppr‘ÿ}'ess‘‰ffŽ‘®yŽ‘21«,‘tand“Ïsuppr‘ÿ}'ess‘‰ffŽ‘®zŽ‘1«.‘HyNo˜w“using“the“empt˜yŽ¡string–hö(Ý""Ž‘ b«)“in“the“argumen¸ãts“Ïp‘ÿ}'os‘‰ffŽ‘®xŽ‘>{«,‘íÝÏp‘ÿ}'os‘‰ffŽ‘®yŽ‘©«,‘íÝand“Ïp‘ÿ}'os‘‰ffŽ‘®zŽ‘"! «to“indicate“that“the“correspGonding“axes“shouldŽ¡bšGe–èsuppressed.‘ ‰Added“error“handling“co˜de“that“prinš¸ãts“a“w˜arning“to“ÏstderrŽ‘%4c«if“all“axes“are“suppressed.Ž¡([¬LDF‘T2003.05.06.«]Ž‘P†Note–a¡that“Ý""Ž‘ɤ«will“nev¸ãer“bšGe“needed“for“lab˜elling“an“axis,‘¤´b˜ecause“putting“the“lab˜el“onŽ¡top–UUof“the“ÂP•®9oin“tŽ‘"Dò«wš¸ãould“in˜terfere“with“the“arro˜w.)Ž¡‘ -[¬LDF‘T2003.04.01.«]Ž‘Y¶ Added–:argumen¸ãts“Ïshift‘‰ffŽ‘®xŽ‘ ³Ã«,‘.³Ïshift‘‰ffŽ‘®yŽ‘ Äë«,‘.³and“Ïshift‘‰ffŽ‘®zŽ‘$0—«for“adjusting“the“pšGosition“of“the“lab˜els.Ž¡Note–1that“the“adjustmen¸ãt“a ects“the“pGosition“of“the“three-dimensional“ÂP•®9oin“tŽ‘#üP«within“the“ÂLabQÇelŽ‘ rg«,‘gïÏnot‘#Ü«theŽ¡t•¸ãw“o-dimensional–¯vpro‘Ž8jected“pšGoin¸ãt.‘€)Therefore,‘Åþit's“not“p˜ossible“to“adjust“the“p˜osition“of“the“ÂLabQÇelŽ‘# O«preciselyŽŽŽŒ‹ ·³ Šn ý‘ì«258–­DRA‘ÿ8WING‘ÕXAXES’´š3DLDFPRÃŽG“·x«923Ž €n ý•@Pwithout–Yc¸ãhanging“the“MetapšGost“co˜de.‘[TO‘HDO:“Change“Ïlab‘ÿ}'elŽ‘…ñ«(‘ª®),‘òso“that“it's“p˜ossible“to“adjust“the“p˜osition“ofŽ¤ the–yºpGoinš¸ãts“in“the“pro‘Ž8jection!‘ÞõThis“ma˜y“opGen“a“can“of“w˜orms,–‚Óthough,“espšGecially–yºif“the“same“co˜de“is“used“toŽ¡generate–UUdraš¸ãwings“using“di eren˜t“pro‘Ž8jections“and/or“di eren˜t“ÏF‘ÿ;¼o‘ÿ}'cusesŽ‘%ÅF«.Ž¡‘ -[¬LDF‘T2003.07.13.«]Ž‘Y;Made‘UUÏddashe‘ÿ}'dŽ‘)ñ»«and‘UUÏpp‘ÿ}'enŽ‘àÍÂconstŽ‘: o«in–UUbGoth“v¸ãersions.Ž¤ŸüÈ„`ÕÁGŽŽ©Â924.‘ üLength–ÕTargumen®9t“ rst.Ž¡·h–ª¨«Declare‘UUÏdr‘ÿ}'aw‘‰ffŽ‘®axesŽ‘/[+«(‘ª®)‘@­924“·i‘ÇŽ¤ ‘ -Âv®9oidŽ‘$©Ïdr‘ÿ}'aw‘‰ffŽ‘®axesŽ‘P%«(ÂrealŽ‘ÔþÏdistŽ‘-‹†«=‘ª2±:«5ŽŽ‘q:±;‘ª¨ÂstringŽ‘#ñÅÏp‘ÿ}'os‘‰ffŽ‘®xŽ‘@qe«=‘ªÝ"bot"Ž–pt±;‘ª¨ÂstringŽ‘#ñÅÏp‘ÿ}'os‘‰ffŽ‘®yŽ‘@W«=‘ªÝ"lft"Ž“±;‘ª¨ÂstringŽŽ¡‘Ïp‘ÿ}'os‘‰ffŽ‘®zŽ‘9Ìå«=‘}ÃÝ"bot"Ž‘D±;‘ª¨ÂconstŽ‘ ÜColorŽ‘Aˆ§«&Ž‘IOÅÏddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ’Ö1«=‘}÷Ž‘ }ÄÂColorsŽ‘+V¢«::Ž‘1äàÏdefault‘‰ffŽ‘®c‘ÿ}'olorŽ‘i`»±;‘ª¨ÂconstŽ‘ ÜstringŽŽ¡‘Ïddashe‘ÿ}'dŽ‘Epj«=‘)VÝ""Ž–/¸±;‘ª¨ÂconstŽ‘ ©ÖstringŽ‘B£¯Ïpp‘ÿ}'enŽ‘\(«=‘)VÝ""Ž“±;‘ª¨ÂconstŽ‘ ©ÖP•®9oin“tŽ‘@mÿ«&Ž‘H5Ïshift‘‰ffŽ‘®xŽ‘iü«=‘)VÏoriginŽ‘w±;‘ª¨ÂconstŽ‘ ©ÖP•®9oin“tŽŽ¡‘«&Ž‘%Ç!Ïshift‘‰ffŽ‘®yŽ‘E$q«=‘ÇÏoriginŽ–½9±;‘ª¨ÂconstŽ‘ÕJP•®9oin“tŽ‘>Äç«&Ž‘FŒÏshift‘‰ffŽ‘®zŽ‘e}@«=‘ÇÏoriginŽ“±;‘ª¨ÂPictureŽ‘*œ -«&Ž‘2c(Ïpictur‘ÿ}'eŽ‘T3«=‘ÇÏcurr–ÿ}'ent‘‰ffŽ‘®pictur“eŽ‘Dìß«);Ž¤ ­See–ÕXalso“section“929.Ž¡This–ÕXcoS-«&Ž‘FKÏshift‘‰ffŽ‘®xŽ‘bÊÔ±;‘ª¨ÂconstŽ‘œmP•®9oin“tŽ‘>S-«&Ž‘FKÏshift‘‰ffŽ‘®yŽ‘b°ƒ±;‘ª¨ÂconstŽ‘œmP•®9oin“tŽŽ¡‘2«&Ž‘9Ç#Ïshift‘‰ffŽ‘®zŽ‘UñF±;‘ª¨ÂPictureŽ‘*œ -«&Ž‘2c(Ïpictur‘ÿ}'eŽ‘Qkþ«)·fŽ¤ 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-[¬LDF‘T2003.06.14.«]Ž‘Y;Added–UUerror“handling“coGde“for“the“case“that“Ïget‘‰ffŽ‘®planeŽ‘+Ì=«(‘ª®)“fails.Ž¦‘ -[¬LDF‘T2003.06.14.«]Ž‘X^§No–«Álonger“taking“absolute“v›ÿqÇalue“of“the“ÂrealŽ‘µ[«v˜alue“Ïr0Ž‘‰G«returned“b¸ãy“ÂPlaneŽ‘ («::‘Ïget‘‰ffŽ‘®distanc‘ÿ}'eŽ‘5y½«(‘ª®),Ž¦since–UUit“will“alw•¸ãa“ys–UUbšGe“p˜ositivš¸ãe,“an˜yw˜a˜y‘ÿ*ª.‘qÇCommen˜t“at“place“bGelo˜w,“where“I“made“this“c˜hange.Ž¦‘ -[¬LDF‘T2003.07.01.«]Ž‘Y;Added–UUargumen¸ãt“Ïsuppr‘ÿ}'ess‘‰ffŽ‘®warningsŽ‘Szf«.Ž¦‘ -[¬LDF‘T2003.07.16.«]Ž‘YÖChanged–kðname“of“Ïc‘ÿ}'enterŽ‘"ák«argumenš¸ãt“to“Ïr‘ÿ}'ef‘‰ffŽ‘®ptŽ‘]ã«,‘q–bGecause“I'v˜e“made“Ïc‘ÿ}'enterŽ‘"ák«a“data“mem˜bGerŽ¦of‘UUÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘lLí«.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘o¢B«functions‘@­943“·i‘Ç«+·Ž¦‘ -ÂvirtualŽ‘/ÔsignedŽ‘RýÊshortŽ‘pÈmÏlo–ÿ}'c“ationŽ’“‰ê«(ÂP•®9oin“tŽ‘ïÏr‘ÿ}'ef‘‰ffŽ‘®ptŽ‘7á±;‘ª¨ÂP•®9oin“tŽ‘ 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ÿ«;Ž¡‘Ïr‘ÿ}'ef‘‰ffŽ‘®ptŽ‘6ñö±:ÏshowŽ‘Šÿ«(Ý"ref_pt"Ž‘*†P«);Ž¡‘Ïpt0Ž‘-i>±:ÏshowŽ‘Šÿ«(Ý"pt0"Ž‘ÆY«);Ž¡‘·gŽ¦‘ÂunsignedŽ‘D7shortŽ‘b³ÏorientationŽ’“tò«;Ž¡‘ÂconstŽ‘2*¤unsignedŽ‘ba²shortŽ’€,UÝX_YŽ’“9Ì«=‘Ç0Ž‘Ç;Ž¡‘ÂconstŽ‘2*¤unsignedŽ‘ba²shortŽ’€,UÝX_ZŽ’“9Ì«=‘Ç1Ž‘Ç;Ž¡‘ÂconstŽ‘2*¤unsignedŽ‘ba²shortŽ’€,UÝZ_YŽ’“9Ì«=‘Ç2Ž‘Ç;Ž¡‘ÂPlaneŽ‘46ºÏplŽ‘=lÅ«(Ïget‘‰ffŽ‘®planeŽ‘(vè«(‘ª®));Ž¦‘ÂifŽ‘´ú«(ÏplŽ‘ ý#·‘ÇÝINVALID_PLANEŽ‘GY«)‘±=·‘ÿý«LDF–UU2003.06.14.‘qÇAdded“this“error“handling“coGde.‘o·±=Ž¡‘·fŽ¡‘Ïc‘ÿ}'errŽ‘7ÁA·‘ ˜Ý"ERROR!È ÝInÈ ÝReg_Cl_PlŽ‘p \ane_Curve::location(Ž’Ù ):"Ž’ð]·Ž¡‘2Ý"TheÈ ÝReg_Cl_Plane_CuŽ’šÿÉrveÈ ÝisÈ Ýnon-planar.\nŽ’ÿ"Ž’ -·‘ÇÝ"ReturningÈ Ý-6\n\n"Ž‘d”b·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½·Ž‘I­Û«6Ž‘N­Ü;Ž¡‘·gŽ¦‘ÂrealŽ‘*³0Ïr0Ž‘8¬ «=‘ÇÏplŽ‘ ý#±:Ïget‘‰ffŽ‘®distanc‘ÿ}'eŽ‘4y¹«(Ïpt0Ž‘i;«)±:Ï rstŽ‘µª«;Ž¦‘ÂifŽ‘´ú«(Ïr0Ž‘ øݱ>‘ÇÂP•®9oin“tŽ‘ad«::Ž‘%ï¢ÏepsilonŽ‘E^¦«(‘ª¨))Ž¡‘±=·‘âÁ«LDF‘82003.06.14.–h Changed.“Ïr0Ž‘Ñç«will›8alw•¸ãa“ys˜b•Ge˜p“ositiv•¸ãe,‘=òso˜I‘8no“w˜longer˜tak“e˜its˜absolute˜v‘ÿqÇalue.‘±·±=Ž¡‘·fŽ¡‘ÂifŽ‘*9j«(·:Ïsuppr‘ÿ}'ess‘‰ffŽ‘®warningsŽ‘P%«)‘Ïc‘ÿ}'errŽ‘Yv·‘£ÐÝ"WARNING!È ÝInÈ ÝReg_Cl_Ž‘l£”Plane_Curve::locatioŽ’Õ£Xn().\n"Ž’þ{·Ž¡‘<Ý"PointÈ ÝisÈ ÝnotÈ ÝinÈ ÝplaŽ’¤ÿÊneÈ ÝofÈ ÝregularÈ ÝclosedŽ’ ÿŽÈ ÝplaneÈ Ýcurve.\n"Ž’hº·Ž¡‘<Ý"ReturningÈ Ý-2.\n\n"Ž’£ M·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½·Ž‘I­Û«2Ž‘N­Ü;Ž¡‘·gŽ¦‘ÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ’€LïÏc‘ÿ}'opyŽ’”Üç«(·Ž‘ÏthisŽ‘ë·«);Ž¦‘ÂifŽ‘´ú«(Ïr‘ÿ}'ef‘‰ffŽ‘®ptŽ‘¹ ·6«=‘ÇÏoriginŽ‘½9«)‘Ïpt0Ž‘0S·«=ŽŽ‘&¾ŠÏr‘ÿ}'ef‘‰ffŽ‘®ptŽ‘Bw•·«=ŽŽ‘RÌÏc‘ÿ}'opyŽ‘f•Ä±:ÏshiftŽ‘}«(·Ž‘ÇÏr‘ÿ}'ef‘‰ffŽ‘®ptŽ‘ ¹«);‘±=·‘ÿý«LDF‘UU2002.11.05.‘qÇSimpli ed.‘o·±=Ž¦‘ÂP•®9oin“tŽ‘2ïŸÏc‘ÿ}'opy‘‰ffŽ‘®normalŽ‘læ#«=‘ÇÏc‘ÿ}'opyŽ‘W±:Ïget‘‰ffŽ‘®normalŽ‘0Št«(‘ª¨);Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'opy‘‰ffŽ‘®normalŽ‘±:Ïdotlab‘ÿ}'elŽ‘!ÿó«(Ý"pt0"Ž‘ÆY«);Ž¦‘Ïpt0Ž‘-i>±:ÏshowŽ‘Šÿ«(Ý"pt0"Ž‘ÆY«);Ž¦‘·gŽ¡‘ÂT‘ÿ -«ransformŽ‘KÈÔÏt3Ž‘VŸ«;Ž¦‘ÂP•®9oin“tŽ‘2ïŸÏpt1Ž‘Eò«=‘ÇÏc‘ÿ}'opyŽ‘W±:Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH«(0Ž‘);Ž¡‘Ïpt1Ž‘&0U·«=ŽŽ‘8…©Ïr‘ÿ}'ef‘‰ffŽ‘®ptŽ‘Qwœ«;Ž¦‘Ïpt1Ž‘#i=±:Ïunit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u«(ÏtrueŽ‘Ę«);Ž¡‘ÂP•®9oin“tŽ‘2ïŸÏx‘‰ffŽ‘®axisŽ‘M~«(1Ž‘±;‘ª¨«0Ž–ª©±;‘ª¨«0Ž“);Ž¦‘ÂP•®9oin“tŽ‘2ïŸÏz‘‰ffŽ‘®axisŽ‘Lñ:«(0Ž‘±;‘ª¨«0Ž–ª©±;‘ª¨«1Ž“);Ž¡‘ÂifŽ‘´ú«(ÏorientationŽ‘4:W·‘ÇÝX_YŽ‘FW·_‘8àÏorientationŽ‘6s7·‘ÇÝX_ZŽ‘ w«)‘·fŽ¦‘ÂifŽ‘)´û«(Ïpt1Ž‘0S·6«=‘ÇÏx‘‰ffŽ‘®axisŽ‘Ž`·^‘8àÏpt1Ž‘i3·6«=‘Ç·Ž‘ -Ž6Ïx‘‰ffŽ‘®axisŽ‘%ž«)‘·fŽ¦‘(Ït3Ž‘2Lϱ:Ïalign‘‰ffŽ–®with‘‰ffŽ“axisŽ‘@²x«(Ïr‘ÿ}'ef‘‰ffŽ‘®ptŽ‘ñó±;‘ª¨Ïpt1Ž‘ã±;‘ª¨Ý'x'Ž‘ñ«);Ž¦‘(Ïc‘ÿ}'opyŽ‘?W·«=ŽŽ‘NåKÏr‘ÿ}'ef‘‰ffŽ‘®ptŽ‘jžV·«=ŽŽ‘z,Ïpt0Ž’Œ\à·«=ŽŽ’›ëÏt3Ž’¦7â«;Ž¦‘·gŽ¦‘gŽ¦‘ÂelseŽ‘*.6ifŽ‘5ã.«(ÏorientationŽ‘4:W·‘ÇÝZ_YŽ‘ w«)‘·fŽ¦‘ÂifŽ‘)´û«(Ïpt1Ž‘0S·6«=‘ÇÏz‘‰ffŽ‘®axisŽ‘“·^‘8àÏpt1Ž‘i3·6«=‘Ç·Ž‘ -Ž6Ïz‘‰ffŽ‘®axisŽ‘$Ñ«)‘·fŽ¦‘(Ït3Ž‘2Lϱ:Ïalign‘‰ffŽ–®with‘‰ffŽ“axisŽ‘@²x«(Ïr‘ÿ}'ef‘‰ffŽ‘®ptŽ‘ñó±;‘ª¨Ïpt1Ž‘ã±;‘ª¨Ý'z'Ž‘ñ«);Ž¦‘(Ïc‘ÿ}'opyŽ‘?W·«=ŽŽ‘NåKÏt3Ž‘Y2«;Ž¦‘(Ïr‘ÿ}'ef‘‰ffŽ‘®ptŽ‘C¹·«=ŽŽ‘SGFÏt3Ž‘]”«;Ž¦‘(Ïpt0Ž‘:0W·«=ŽŽ‘I¾ŽÏt3Ž‘T Y«;Ž¦‘·gŽ¦‘gŽ¡‘Ârealu½‰™šs4Ž‘ÔwpairŽ‘CpƒÏrrŽ‘MuÔ«;Ž¦‘ÂrealŽ‘*³0Ïpt0‘‰ffŽ‘®vŽ‘Bœ«;‘±=·‘ÿý«[¬LDF‘T2002.11.05.«]Ž‘T7V‘ÿ*ªertical.‘o·±=Ž¦‘ÂrealŽ‘*³0Ïpt0‘‰ffŽ‘®hŽ‘BPK«;‘±=·‘ÿý«[¬LDF‘T2002.11.05.«]Ž‘T7Horizon¸ãtal.‘o·±=Ž¡‘ÂifŽ‘´ú«(ÏorientationŽ‘4:W·‘ÇÝX_YŽ‘ w«)‘·fŽ¦‘Ïpt0‘‰ffŽ‘®hŽ‘8d6«=‘ÇÏpt0Ž‘0S±:Ïget‘‰ffŽ‘®xŽ‘Žg«(‘ª¨);Ž¦‘Ïpt0‘‰ffŽ‘®vŽ‘80‡«=‘ÇÏpt0Ž‘0S±:Ïget‘‰ffŽ‘®yŽ‘t«(‘ª¨);ŽŽŽŒ‹ ;Ä Šn ý‘ì·x«949›­3DLDFPRÃŽG’ýãLOCA‘ÿJªTION–ÕXOF“A“POINT˜«267Ž €n ý•@P‘·gŽ¤ ‘ÂelseŽ‘*.6ifŽ‘5ã.«(ÏorientationŽ‘4:W·‘ÇÝX_ZŽ‘ w«)‘·fŽ¡‘Ïpt0‘‰ffŽ‘®hŽ‘8d6«=‘ÇÏpt0Ž‘0S±:Ïget‘‰ffŽ‘®xŽ‘Žg«(‘ª¨);Ž¡‘Ïpt0‘‰ffŽ‘®vŽ‘80‡«=‘ÇÏpt0Ž‘0S±:Ïget‘‰ffŽ‘®zŽ‘«(‘ª¨);Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(ÏorientationŽ‘4:W·‘ÇÝZ_YŽ‘ w«)‘·fŽ¡‘Ïpt0‘‰ffŽ‘®hŽ‘8d6«=‘ÇÏpt0Ž‘0S±:Ïget‘‰ffŽ‘®zŽ‘«(‘ª¨);Ž¡‘Ïpt0‘‰ffŽ‘®vŽ‘80‡«=‘ÇÏpt0Ž‘0S±:Ïget‘‰ffŽ‘®yŽ‘t«(‘ª¨);Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘Ïc‘ÿ}'errŽ‘7|U·‘ƬÝ"ERROR!È ÝInÈ ÝReg_Cl_PlŽ‘oÆpane_Curve::location(Ž’ØÆ4).\n"Ž’úS9·Ž¡‘2Ý"orientationÈ ÝhasÈ ÝinvŽ’šÿÉalidÈ Ývalue:È Ý"Ž’â"·‘ÇÏorientationŽ‘7o·‘ÇÝ"\nReturningÈ Ý-5\n\n"Ž‘o\·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½·Ž‘I­Û«5Ž‘N­Ü;Ž¡‘·gŽ¡‘ÏrrŽ‘ Ìk«=‘ÇÏsolveŽ‘þã«(Ý'v'Ž‘F_±;‘ª¨Ïpt0‘‰ffŽ‘®hŽ‘Gë);‘±=·‘ÿý«[¬LDF‘T2002.11.05.«]Ž‘T7TO–UUDO:“Explain.‘o·±=Ž¡‘ÂifŽ‘´ú«(ÏrrŽ‘ -Q±:Ï rstŽ‘|·‘ÇÝINVALID_REALŽ‘D†<·^‘8àÏrrŽ‘ >1±:Ïse–ÿ}'c“ondŽ‘ nß·‘ÇÝINVALID_REALŽ‘BM\«)‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÝ"PointÈ ÝisÈ ÝoutsideÈ ÝreŽ‘kÆÜgularÈ ÝclosedÈ ÝplaneÈ ÝcŽ’ÔÆ urve.È Ý"Ž’üÔ ·‘ÇÝ"ReturningÈ Ý-1.\n"Ž‘\M«;Ž¡‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÝ"ExitingÈ ÝReg_Cl_PlanŽ‘kÆÜe_Curve::location()\Ž’ÔÆ n"Ž’ßÍ«;Ž¡‘·gŽ¡‘ÂreturnŽ‘Aæ½·Ž‘I­Û«1Ž‘N­Ü;Ž¡‘·gŽ¡‘ÂelseŽ‘)ª¼ifŽ‘4Ü:«((ÏfabsŽ–2Ò«(ÏfabsŽ“«(Ïpt0‘‰ffŽ‘®vŽ›il«)–1î·“ÏfabsŽ‘dÀ«(ÏrrŽ‘ -Q±:Ï rstŽ‘µª«))–DZ<“ÂP•®9oin“tŽ‘ad«::Ž‘%ï¢ÏepsilonŽ‘E^¦«(‘ª¨))–1î·_“«(ÏfabsŽ–2Ò«(ÏfabsŽ“«(Ïpt0‘‰ffŽ‘®vŽ˜«)–1î·“ÏfabsŽ‘dÀ«(ÏrrŽ‘ -Q±:Ïse–ÿ}'c“ondŽ‘§Ç«))‘DZ<Ž¡‘2ÂP•®9oin“tŽ‘NšQ«::Ž‘U(ÏepsilonŽ‘t—“«(‘ª¨)))‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘(Ïc‘ÿ}'outŽ‘?·‘CÇÝ"PointÈ ÝisÈ ÝonÈ ÝregularŽ‘mC‹È ÝclosedÈ ÝplaneÈ Ýcurve.Ž’ÖCOÈ Ý"Ž’åx·‘CÇÝ"ReturningÈ Ý0.\n"Ž‘] Æ·Ž¡‘<Ý"ExitingÈ ÝReg_Cl_PlanŽ’¤ÿÊe_Curve::location()\Ž’ ÿŽn"Ž’ð«;Ž¡‘(ÏgetcharŽ‘I&«(‘ª®);Ž¡‘·gŽ¡‘ÂreturnŽ‘A潫0Ž‘Fæ¾;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(ÏfabsŽ‘2Ò«(Ïpt0‘‰ffŽ‘®vŽ‘il«)–DZ<“ÏfabsŽ‘ùê«(ÏrrŽ‘ -Q±:Ï rstŽ‘µª«))‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÝ"PointÈ ÝisÈ ÝinsideÈ ÝregŽ‘kÆÜularÈ ÝclosedÈ ÝplaneÈ ÝcuŽ’ÔÆ rve.È Ý"Ž’÷”·‘ÇÝ"ReturningÈ Ý1.\n"Ž‘WMP«;Ž¡‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÝ"ExitingÈ ÝReg_Cl_PlanŽ‘kÆÜe_Curve::location()\Ž’ÔÆ n"Ž’ßÍ«;Ž¡‘(ÏgetcharŽ‘I&«(‘ª®);Ž¡‘·gŽ¡‘ÂreturnŽ‘A潫1Ž‘Fæ¾;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(ÏfabsŽ‘2Ò«(Ïpt0‘‰ffŽ‘®vŽ‘il«)–DZ>“ÏfabsŽ‘ùê«(ÏrrŽ‘ -Q±:Ï rstŽ‘µª«))Ž¡‘±=·‘ÿý«This–UUcase“should“nev¸ãer“ošGccur,“I“b˜eliev•¸ãe.‘qÇ[¬LDF‘T2002.11.05.«]Ž‘SzWh“y‘UUnot??‘o·±=Ž¡‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘(Ïc‘ÿ}'outŽ‘>ØU·‘Ý"PointÈ ÝisÈ ÝoutsideÈ ÝreŽ‘l~ÞgularÈ ÝclosedÈ ÝplaneÈ ÝcŽ’Õ~¢urve.È Ý"Ž’þD·‘Ý"ReturningÈ Ý-1.\n"Ž‘`Äi·Ž¡‘<Ý"ExitingÈ ÝReg_Cl_PlanŽ’¤ÿÊe_Curve::location()\Ž’ ÿŽn"Ž’ð«;Ž¡‘(ÏgetcharŽ‘I&«(‘ª®);Ž¡‘·gŽ¡‘ÂreturnŽ‘Aæ½·Ž‘I­Û«1Ž‘N­Ü;Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘Ïc‘ÿ}'errŽ‘7|U·‘ƬÝ"ERROR!È ÝInÈ ÝReg_Cl_PlŽ‘oÆpane_Curve::location(Ž’ØÆ4).\n"Ž’úS9·Ž¡‘2Ý"ThisÈ Ýcan'tÈ Ýhappen!È Ž’šÿÉÝReturningÈ Ý-3.\n"Ž’òM·‘ÇÏ ushŽ‘€«;ŽŽŽŒ‹ L] Šn ý‘ì«268›­LOCA‘ÿJªTION–ÕXOF“A“POINT’ýã3DLDFPRÃŽG˜·x«949Ž €n ý•@P‘ÏgetcharŽ‘?%ÿ«(‘ª®);Ž¤ ‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ExitingÈ ÝReg_Cl_PlanŽ‘kÆÜe_Curve::location()\Ž’ÔÆ n"Ž’ßÍ«;Ž¡‘ÂreturnŽ‘Aæ½·Ž‘I­Û«3Ž‘N­Ü;Ž¡‘·gŽ¡‘ -gŽ¤ ­See–ÕXalso“sections“951,“954,“955,“956,“957,“958,“959,“960,“961,“962,“963,“965,“and“968.Ž¡This–ÕXco S·‘ÇÝ"È Ý***È ÝEnteringÈ ÝReg_CŽ‘kÆÜl_Plane_Curve::"Ž’Ã,·‘ÇÝ"intersection_pointsŽ‘kÆÜ()\n"Ž’‰TM·‘ÇÏ ushŽ‘€«;Ž¦‘Âb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘odñÏbppŽ’‚"ò«=‘ÇÝINVALID_BOOL_POINT_PAIRŽ‘| ;«;Ž¡‘ÂPlaneŽ‘>6»ÏplŽ‘J3Þ«=‘ÇÏget‘‰ffŽ‘®planeŽ‘+>«(‘ª¨);Ž¦‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘ÏplŽ‘6 ±:ÏnormalŽ‘ 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ne‘UUÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘o¢B«functions‘@­949“·i‘Ç«+·Ž¡‘ -ÂifŽ‘qv«(Ïpt‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘*jÉ·‘ÇÝINVALID_POINTŽ–I?5·_‘±ÜÏplŽ› -çç±:ÏnormalŽ‘#з‘ÇÝINVALID_POINTŽ“·_‘±ÜÏpt‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘,¥·‘ÇÏoriginŽ‘o·_‘±ÜÏplŽ˜±:ÏnormalŽ‘#з‘ÇÏoriginŽ‘½9«)Ž¡‘·fŽ¡‘Ïc‘ÿ}'errŽ‘,e]·‘¯µÝ"ERROR!È ÝInÈ ÝReg_Cl_PlŽ‘n¯yane_Curve:intersectiŽ’ׯ=on_points():\n"Ž’,¥-·Ž¡‘(Ý"SomethingÈ ÝisÈ ÝwrongÈ Ž’ÿÈÝwithÈ ÝtheÈ Ýnormals:\n"Ž’ú…ô«;Ž¡‘Ïpt‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘;£³±:ÏshowŽ‘Šÿ«(Ý"pt_vector:"Ž‘?†D«);Ž¡‘ÏplŽ‘6 ±:ÏnormalŽ‘ V¸±:ÏshowŽ‘Šÿ«(Ý"pl.normal"Ž‘:FG«);Ž¡‘Ïc‘ÿ}'errŽ‘)|À·‘ÇÝ"ReturningÈ ÝINVALID_BŽ‘kÆÜOOL_POINT_PAIR.\n\n"Ž’Ø ·‘ÇÏ ushŽ‘€«;Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ExitingÈ ÝPolygon::inŽ‘kÆÜtersection_points().Ž’ÔÆ \n\n"Ž’òT·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘7æ¼ÝINVALID_BOOL_POINT_PAIRŽ’±,ß«;Ž¡‘ -·gŽŸÂ956.‘ üP®9arallel–ÕTand“coplanar“cases.Ž¦·h–ª¨«De ne‘UUÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘o¢B«functions‘@­949“·i‘Ç«+·Ž¡‘ -ÂelseŽ‘?ìifŽ‘*›«(Ïsurfac–ÿ}'e‘‰ffŽ‘®ve“ctorŽ‘@…Ä·‘ÇÏpt‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘*Ç·_\RÏsurfac–ÿ}'e‘‰ffŽ‘®ve“ctorŽ‘@â·‘ÇŽ‘ -Ž6Ïpt‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘2Ž9·_\RÏcr‘ÿ}'ossŽ–ˆ·‘ÇÏplŽ‘ ý#±:ÏnormalŽ‘ ³ -·_\RÏcr‘ÿ}'ossŽ“·‘ÇŽ‘ -Ž6ÏplŽ‘ÄA±:ÏnormalŽ‘ V¸«)Ž¡‘·fŽŽŽŒ‹ u€ Šn ý‘ì·x«957–­3DLDFPRÃŽG’º COPLANAR‘ÕXCASE“«271Ž €n ý•@PÂ957.‘ üCoplanar‘ÕTcase.Ž©·h–ª¨«De ne‘UUÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘o¢B«functions‘@­949“·i‘Ç«+·Ž¤ ‘ -ÂifŽ‘´ù«(Ïdistanc‘ÿ}'eŽ‘' ·‘Ç«0Ž‘Ç)‘UU·fŽ¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"LineÈ ÝandÈ ÝReg_Cl_PlaŽ‘kÆÜne_CurveÈ ÝareÈ ÝcoplanaŽ’ÔÆ r.\n"Ž’ïŒù«;Ž¦‘ -ÂT‘ÿ -«ransformŽ‘AÈÓÏt0Ž‘Lž«;Ž¡‘ -ÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘vLîÏc‘ÿ}'opyŽ’ŠÜæ«(·Ž‘ÏthisŽ‘ë·«);Ž¡‘ -ÂP•®9oin“tŽ‘(ïžÏcurve‘‰ffŽ‘®0Ž‘MÁ/«=‘ÇÏc‘ÿ}'opyŽ‘W±:Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH«(0Ž‘);Ž¦‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"AfterÈ Ýcopying:"Ž‘Zh·‘ÇÏend‘‚ØlŽ‘¸Ú«;Ž¡‘ÏshowŽ‘*‹«(Ý"this:"Ž‘%FS«);Ž¡‘Ïc‘ÿ}'opyŽ‘(ú±:ÏshowŽ‘Šÿ«(Ý"copy:"Ž‘%FS«);Ž¡‘Ïcurve‘‰ffŽ‘®0Ž‘6 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-ÂP•®9oin“tŽ‘(ïžÏtr–ÿ}'ac“e‘‰ffŽ–®x‘‰ffŽ“z‘‰ffŽ“0Ž‘[Ih«=‘ÇÏcurve‘‰ffŽ‘®0Ž‘$Ñ‘«;Ž¦‘ -Ïtr–ÿ}'ac“e‘‰ffŽ–®x‘‰ffŽ“z‘‰ffŽ“0Ž‘9’³±:ÏshiftŽ‘}«(0Ž‘±;‘ª¨·Ž‘ qÆ«(Ïcurve‘‰ffŽ‘®0Ž‘" -y±:Ïget‘‰ffŽ‘®yŽ‘t«(‘ª¨)));Ž¦‘ -ÂP•®9oin“tŽ‘(ïžÏx‘‰ffŽ–®axis‘‰ffŽ“ptŽ‘O»»«(1Ž‘);Ž¡‘ -ÂrealŽ‘ ³/ÏangŽ‘44í«=‘ÇÏtr–ÿ}'ac“e‘‰ffŽ–®x‘‰ffŽ“z‘‰ffŽ“0Ž‘2Yʱ:ÏangleŽ‘ÀS«(Ïx‘‰ffŽ–®axis‘‰ffŽ“ptŽ‘&Ì«);Ž¦‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"angÈ Ý==È Ý"Ž‘5T}·‘ÇÏangŽ‘HÖ·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ -·gŽ¡‘ -ÂifŽ‘´ù«(ÏangŽ‘¾·6«=‘Ç0Ž‘Ç)‘·fŽ¡‘ÂifŽ‘´ú«(Ïcurve‘‰ffŽ‘®0Ž‘" -y±:Ïget‘‰ffŽ‘®zŽ‘«(‘ª¨)–DZ>“«0Ž‘Ç)‘ÏangŽ‘¾·«=ŽŽ‘(õ·Ž‘/׫1Ž‘4×;Ž¡‘Ït0Ž‘!å·«=ŽŽ‘0¢Ïcurve‘‰ffŽ‘®0Ž‘Us­·«=ŽŽ‘eäÏpt0Ž‘w27·«=ŽŽ’†ÀnÏpt1Ž’˜ðÁ·«=ŽŽ’¨~øÏc‘ÿ}'opyŽ’½ð±:Ïr‘ÿ}'otateŽ‘o>«(0Ž‘±;‘ª¨ÏangŽ‘eN«);Ž¡‘ -·gŽ¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"AfterÈ ÝrotatingÈ ÝsoÈ ÝtŽ‘kÆÜheÈ ÝtraceÈ ÝofÈ Ýcurve_0È Ž’ÔÆ ÝisÈ ÝonÈ Ýx-axis:"Ž’!“ö·‘ÇÏend‘‚ØlŽ‘¸Ú«;Ž¡‘Ïc‘ÿ}'opyŽ‘(ú±:ÏshowŽ‘Šÿ«(Ý"copy:"Ž‘%FS«);Ž¡‘Ïcurve‘‰ffŽ‘®0Ž‘6 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rstŽ‘|«=‘ÇÏfalseŽ‘v\«;Ž¦‘Ïon‘‰ffŽ‘®se‘ÿ}'gmentŽ‘F_n±:Ïse–ÿ}'c“ondŽ‘ nß«=‘ÇÝINVALID_REALŽ‘BM\«;Ž¦‘ -·gŽ¦‘ -ÂelseŽ‘!ØàÏon‘‰ffŽ‘®se‘ÿ}'gmentŽ‘Vÿd«=‘ÇÏbppŽ‘¾±:Ïse–ÿ}'c“ondŽ‘§Ç±:ÏptŽ‘ ä±:Ïis‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘=5O«(Ïpt0Ž‘i;±;‘ª¨Ïpt1Ž‘ã«);Ž¦‘ -ÂifŽ‘´ù«(Ïon‘‰ffŽ‘®se‘ÿ}'gmentŽ‘2_l±:Ï rstŽ‘|·‘ÇÏtrueŽ–‹°«)‘ÏbppŽ‘öé±:Ïse–ÿ}'c“ondŽ‘§Ç±:bŽ‘«=‘ÇÏtrueŽ“«;Ž¦‘ -ÂelseŽ‘!ØàÏbppŽ‘1Ïɱ:Ïse–ÿ}'c“ondŽ‘§Ç±:bŽ‘«=‘ÇÏfalseŽ‘v\«;Ž¦‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘·fŽ¦‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"on_segment.firstÈ Ý==Ž‘kÆÜÈ Ý"Ž‘y”V·‘ÇÏon‘‰ffŽ‘®se‘ÿ}'gmentŽ‘5&„±:Ï rstŽ‘|·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¦‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"on_segment.secondÈ Ý=Ž‘kÆÜ=È Ý"Ž‘~ÔS·‘ÇÏon‘‰ffŽ‘®se‘ÿ}'gmentŽ‘5&„±:Ïse–ÿ}'c“ondŽ‘ nß·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¦‘ -·gŽ¦‘ -ÂifŽ‘´ù«(ÏbppŽ‘öé±:Ïse–ÿ}'c“ondŽ‘§Ç±:ÏptŽ‘ «µ·6«=‘ÇÝINVALID_POINTŽ‘GY«)‘·fŽ¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"TransformingÈ Ýbpp.seŽ‘kÆÜcond.pt\n"Ž’£”>·‘ÇÏ ushŽ‘€«;Ž¦‘ÏbppŽ‘#öë±:Ïse–ÿ}'c“ondŽ‘§Ç±:ÏptŽ‘ «µ·«=ŽŽ‘9ìÏt‘‰ffŽ‘®inverseŽ‘CI«;Ž¦‘ -·gŽ¦‘ -ÂelseŽ‘!Øà·fŽ¦‘ÏbppŽ‘#öë±:Ïse–ÿ}'c“ondŽ‘§Ç±:ÏptŽ‘ «µ«=‘ÇÝINVALID_POINTŽ‘GY«;Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"bpp.second.ptÈ ÝisÈ ÝinŽ‘kÆÜvalid\n"Ž’™D·‘ÇÏ ushŽ‘€«;Ž¦‘ -·gŽ¦‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘·fŽ¦‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"rr.firstÈ Ý==È Ý"Ž‘O”n·‘ÇÏrrŽ‘ Ìi±:Ï rstŽ‘|·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¦‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"rr.secondÈ Ý==È Ý"Ž‘TÔk·‘ÇÏrrŽ‘ Ìi±:Ïse–ÿ}'c“ondŽ‘ nß·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¦‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"bpp.first.bÈ Ý==È Ý"Ž‘_Te·‘ÇÏbppŽ‘¾±:Ï rstŽ‘µª±:bŽ‘·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¦‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"bpp.second.bÈ Ý==È Ý"Ž‘d”b·‘ÇÏbppŽ‘¾±:Ïse–ÿ}'c“ondŽ‘§Ç±:bŽ‘·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¦‘ÏbppŽ‘#öë±:Ï rstŽ‘µª±:ÏptŽ‘ ä±:ÏshowŽ‘Šÿ«(Ý"bpp.first.pt"Ž‘J>«);Ž¦‘ÏbppŽ‘#öë±:Ïse–ÿ}'c“ondŽ‘§Ç±:ÏptŽ‘ ä±:ÏshowŽ‘Šÿ«(Ý"bpp.second.pt"Ž‘OF;«);Ž¦‘ -·gŽ¦‘ -ÂreturnŽ‘-æ»ÏbppŽ‘=ݤ«;‘qÇ·g‘±=·‘ÿý«End–UUof“coplanar“case.‘o·±=ŽŽŽŒ‹ ¸§ Šn ý‘ì«276–­P‘ÿJªARALLEL‘ÕXCASE’(&3DLDFPRÃŽG“·x«962Ž €n ý•@PÂ962.‘ üP®9arallel‘ÕTcase.Ž©·h–ª¨«De ne‘UUÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘o¢B«functions‘@­949“·i‘Ç«+·Ž¤ ‘ -ÂelseŽ‘!Øà·fŽ¡‘Ïc‘ÿ}'errŽ‘+ýû·‘HSÝ"WARNING!È ÝInÈ ÝReg_Cl_Ž‘nHPlane_Curve::interseŽ’×GÛction_points():\n"Ž’;–`·Ž¡‘(Ý"LineÈ ÝandÈ ÝReg_Cl_PlaŽ’ÿÈne_CurveÈ ÝareÈ ÝinÈ ÝparaŽ’ùÿŒllelÈ Ýplanes.\n"Ž’O€n·Ž¡‘(Ý"NoÈ Ýintersections.È ÝRŽ’ÿÈeturningÈ ÝINVALID_BOOŽ’ùÿŒL_POINT_PAIR."Ž’FÌâ·‘ÇÏend‘‚ØlŽ–ò·‘ÇÏend‘‚ØlŽ“·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘7æ¼ÝINVALID_BOOL_POINT_PAIRŽ’±,ß«;Ž¡‘ -·gŽ¡‘ -g‘±=·‘ÿý«End–UUof“parallel“and“coplanar“cases.‘o·±=ŽŸÂ963.› üP®9erpQÇendicular–õand“non-coplanar“cases.˜«[¬LDF‘T2003.06.13.«]Ž‘ZÄÂThese–‘ácases“are“handled“in“exactlyŽ¡the–UUsame“w•¸ãa“y‘ÿ*ª.Ž¦·h–ª¨«De ne‘UUÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘o¢B«functions‘@­949“·i‘Ç«+·Ž¡‘ -ÂelseŽ‘!Øà·fŽ¡‘ÂifŽ‘´ú«(ÏplŽ‘ 6 ±:ÏnormalŽ–#з‘ÇÏpt‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘,£©·_‘8àÏplŽ‘ në±:ÏnormalŽ“·‘ÇŽ‘ -Ž6Ïpt‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘21ç«)‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)Ž¡‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÝ"TheÈ ÝlineÈ ÝisÈ ÝperpendŽ‘kÆÜicularÈ ÝtoÈ ÝtheÈ Ý"Ž’½Ô/·‘ÇÝ"Reg_Cl_Plane_Curve.Ž‘kÆÜ\n"Ž‘~ÔS·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)Ž¡‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÝ"TheÈ ÝlineÈ ÝandÈ ÝtheÈ ÝReŽ‘kÆÜg_Cl_Plane_CurveÈ Ý"Ž’Í”&·‘ÇÝ"areÈ Ýnon-coplanar.\nŽ‘kÆÜ"Ž‘tTY·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¦‘Âb•QÇo“olu½‰™šs4Ž‘Ôwp“oin®9tŽ‘L§ÏbpŽ‘ZI.«=‘ÇÏplŽ‘ ý#±:Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘M–Ö«(Ïpt0Ž‘i;±;‘ª¨Ïpt1Ž‘ã«);Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘ÏbpŽ‘(Ú|±:ÏptŽ‘ ä±:ÏshowŽ‘Šÿ«(Ý"bp.pt"Ž‘%FS«);Ž¡‘·gŽ¦‘ÂshortŽ‘1Ê¥±sŽ‘9A½«=‘ÇÏlo–ÿ}'c“ationŽ‘%ˆ•«(Ïr‘ÿ}'ef‘‰ffŽ‘®ptŽ‘ñó±;‘ª¨ÏbpŽ‘ …!±:ÏptŽ‘ ä«);Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"location:È ÝsÈ Ý==È Ý"Ž‘_Te·‘DZsŽ‘ ->0·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ÂifŽ‘´ú«(±sŽ‘w>‘Ç·Ž‘ -Ž6«1Ž‘Ž7)‘·fŽ¡‘ÏbppŽ‘-öì±:Ï rstŽ‘µª±:ÏptŽ‘ «µ«=‘ÇÏbpŽ‘ ¡‘±:ÏptŽ‘ ä«;Ž¡‘ÏbppŽ‘-öì±:Ï rstŽ–µª±:bŽ‘«=‘ÇÏbpŽ‘ ¡‘±:ÏptŽ‘ ä±:Ïis‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘=5O«(Ïpt0Ž‘i;±;‘ª¨Ïpt1Ž‘ã«)±:Ï rstŽ“«;Ž¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"OnÈ Ýsegment:È Ý==È Ý"Ž‘_Te·‘ÇÏbppŽ‘¾±:Ï rstŽ‘µª±:bŽ‘·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½ÏbppŽ‘Qݦ«;Ž¡‘·gŽ¡‘ÂelseŽ‘+ØáreturnŽ‘O¿›ÝINVALID_BOOL_POINT_PAIRŽ’ɾ«;Ž¡‘ -·g‘±=·‘ÿý«End–UUof“\P¸ãerpGendicular“and“non-coplanar“cases".‘o·±=Ž¡‘ -·gŽŸÂ964.‘ üP•®9ath‘ÕTargumen“ts.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.06.20.«]Ž‘Y;Added–UUthis“function.Ž¡‘ -[¬LDF‘T2003.07.16.«]Ž‘YÖChanged–kðname“of“Ïc‘ÿ}'enterŽ‘"ák«argumenš¸ãt“to“Ïr‘ÿ}'ef‘‰ffŽ‘®ptŽ‘]ã«,‘q–bGecause“I'v˜e“made“Ïc‘ÿ}'enterŽ‘"ák«a“data“mem˜bGerŽ¡of‘UUÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘lLí«.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘o¢B«functions‘@­943“·i‘Ç«+·Ž¡‘ -Âb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘[dïÏinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ’¬ñΫ(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]Ïr‘ÿ}'ef‘‰ffŽ‘®ptŽ‘]ÓP±;‘ª¨ÂconstŽ‘ÕJP®9athŽ‘;¼«&Ž‘Cƒ!±pŽ‘H‹!«)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹ Ê. Šn ý‘ì·x«965‘­3DLDFPRšÃŽG’¯ÂP–ÿ -«A“TH‘ÕX­AR˜GUMENTS‘«277Ž €n ý•@PÂ965.Ž©·h–ª¨«De ne‘UUÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘o¢B«functions‘@­949“·i‘Ç«+·Ž¤ ‘ -Âb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘[ïRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ’Åy‹«::‘Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã«(ÂconstŽ‘G¢P•®9oin“tŽ‘=T?«&Ž‘E]Ïr‘ÿ}'ef‘‰ffŽ‘®ptŽ‘^ P±;‘ª¨ÂconstŽ‘òJP®9athŽ‘;ö«&Ž‘C½!±pŽ‘HÅ!«)Ž¡‘2ÂconstŽŽ¡‘ -·fŽ¡‘ÂifŽ‘´ú«(·:±pŽ‘:Ïis‘‰ffŽ‘®line‘ÿ}'arŽ‘%}«(‘ª¨))‘·fŽ¡‘Ïc‘ÿ}'errŽ‘6D·‘K›Ý"ERROR!È ÝInÈ ÝReg_Cl_PlŽ‘nK_ane_Curve::intersectŽ’×K#ion_points():\n"Ž’1ö·Ž¡‘2Ý"PathÈ ÝargumentÈ ÝpÈ ÝisÈ Ž’šÿÉÝnon-linear.È Ý"Ž’â»ç·‘õÝÝ"ReturningÈ ÝINVALID_BŽ‘kõ¡OOL_POINT_PAIR.\n\n"Ž’Øqª·Ž¡‘2Ï ushŽ‘G¹«;Ž¡‘ÂreturnŽ‘Aæ½ÝINVALID_BOOL_POINT_PAIRŽ’»,à«;Ž¡‘·gŽ¡‘ÂreturnŽ‘7æ¼Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ’‰s›«(Ïr‘ÿ}'ef‘‰ffŽ‘®ptŽ‘ñó±;‘ª¨pŽ–²¨:Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH«(0Ž‘)±;‘ª¨pŽ“:Ïget‘‰ffŽ–®last‘‰ffŽ“p‘ÿ}'ointŽ‘:$>«(‘ª¨));Ž¡‘ -·gŽŸÂ966.› üReg‘°¡‰ffs4Ž–#ÕCl‘°¡‰ffs4Ž“Plane‘°¡‰ffs4Ž“Curv•®9e‘ÕTsegmen“ts.˜«The–UUfunctions“in“this“section“require“that“theŽ¡ÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘m°;«ha•¸ãv“e–¸£a“meaningful“Ïc‘ÿ}'enterŽ‘ Â.«,‘win“order“to“makš¸ãe“it“pGossible“to“rotate“the“segmen˜ts.Ž¡[¬LDF‘T2003.07.16.«]ŽŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.07.16.«]Ž‘ZFìAdded–”this“section“and“its“subsections,‘ã²including“the“declarations“and“de nitions“ofŽ¡Ïse‘ÿ}'gmentŽ‘#õ¡«(–ª®),‘UUÏhalfŽ‘Îë«(“),–UUand“ÏquarterŽ‘$Z›«(‘ª®).‘qÇThey“wš¸ãere“formerly“mem˜bGers“of“ÂCircleŽ‘!¸«.Ž¦ŸüÈ„`ÕÁGŽŽŸÂ967.– üSegmenš®9t.“«[¬LDF‘T2002.11.10.«]Ž‘[ŸëÏse‘ÿ}'gmentŽ‘•Œ«(‘ª®)–m -returns“a“subpath“of“the“ÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv˜eŽ‘qѬ«repre-Ž¡senš¸ãting–UUa“segmen˜t“of“·Ž‘UVÏthisŽ‘A «.Ž©Âin®9tŽ‘¤÷ÏfactorŽŽ‘Lºö«Determines–²›hoš¸ãw“large“a“segmen˜t“of“the“ÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘p\Ϋis“returned.‘‰˜ÏfactorŽ‘$@«m˜ustŽ¡‘LºöbšGe–UU±>‘Ç«1“and“less“than“or“equal“to“the“n•¸ãum“b˜er–UUof“p˜oin¸ãts“on“the“ÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘lLí«.Ž¦ÂrealŽ‘³.ÏangleŽŽ‘Lºö«Optional,›with–ã|0“as“the“default.‘=IfÏangleŽ‘£Ï«is“·6«=‘´0,˜a“ÂP•®9oin“tŽ‘#a@«is“found“in“the“direction“of“theŽ¡‘Lºönormal–Ñrto“the“ÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘nš|«from“the“cen¸ãter“of“the“ÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘kÉ -«,‘ëÒandŽ¡‘Lºöthe–UUsegmenš¸ãt“is“rotated“around“the“cen˜ter“and“this“ÂP•®9oin“tŽ‘ï«.Ž¦Âb•QÇo“olŽ‘¡fÏclose‘ÿ}'dŽŽ‘Lºö«If‘F¨ÏtrueŽ‘ @«,‘|Ëthe‘F¨ÂP®9athŽ‘´«is–F¨made“a“\Âcycle«"“and“the“ends“of“the“segmenš¸ãt“are“joined“b˜y“concatenatingŽ¡‘Lºöthe–Á6curvš¸ãed“ÂP®9athŽ‘ Ыwith“the“straigh˜t“line“segmen˜t“from“its“last“to“its“ rst“ÂP•®9oin“tŽ‘#´«using“theŽ¡‘Lºöconnector‘UUÝ"&"Ž‘›´«.Ž¦‘ 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«µ«=‘ÇÏbpŽ‘ ¡‘±:ÏptŽ‘ ä«;Ž¡‘2ÏfoundŽ‘N™”«=‘ÇÏtrueŽ‘‹°«;Ž¡‘2ÂifŽ‘=´ý«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"FoundÈ ÝfirstÈ ÝinterseŽ‘kÆÜction.\n"Ž’›)«;Ž¡‘(·gŽ¡‘(ÂelseŽ‘?Øã·fŽ¡‘2ÏbppŽ‘Aöî±:Ïse–ÿ}'c“ondŽ‘§Ç±:bŽ‘«=‘ÇÏtrueŽ‘‹°«;Ž¡‘2ÏbppŽ‘Aöî±:Ïse–ÿ}'c“ondŽ‘§Ç±:ÏptŽ‘ «µ«=‘ÇÏbpŽ‘ ¡‘±:ÏptŽ‘ ä«;Ž¡‘2ÂifŽ‘=´ý«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"FoundÈ ÝsecondÈ ÝintersŽ‘kÆÜection.È ÝReturning.\nŽ’ÔÆ "Ž’Ú«;Ž¡‘2ÂreturnŽ‘Uæ¿ÏbppŽ‘eݨ«;Ž¡‘(·gŽ¡‘gŽ¡‘ÂelseŽ‘4.7ifŽ‘?ã/«(ÏbpŽ‘ -Úy±:ÏptŽ‘ «µ·6«=‘ÇÝINVALID_POINTŽ‘IÆ9·^‘8àÏbpŽ‘ Y±:ÏptŽ‘ ä±:Ïis‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘=5O«(Ïq0Ž‘ “ç±;‘ª¨Ïq1Ž‘ >«)±:Ï rstŽ‘µª«)‘·fŽ¡‘(ÂifŽ‘3´ü«(·:ÏfoundŽ‘Òw«)‘·fŽ¡‘2ÏbppŽ‘Aöî±:Ï rstŽ‘µª±:bŽ‘«=‘ÇÏfalseŽ‘v\«;Ž¡‘2ÏbppŽ‘Aöî±:Ï rstŽ‘µª±:ÏptŽ‘ «µ«=‘ÇÏbpŽ‘ ¡‘±:ÏptŽ‘ ä«;Ž¡‘2ÏfoundŽ‘N™”«=‘ÇÏtrueŽ‘‹°«;Ž¡‘2ÂifŽ‘=´ý«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"FoundÈ ÝfirstÈ ÝinterseŽ‘kÆÜction.\n"Ž’›)«;Ž¡‘(·gŽ¡‘(ÂelseŽ‘?Øã·fŽ¡‘2ÏbppŽ‘Aöî±:Ïse–ÿ}'c“ondŽ‘§Ç±:bŽ‘«=‘ÇÏfalseŽ‘v\«;Ž¡‘2ÏbppŽ‘Aöî±:Ïse–ÿ}'c“ondŽ‘§Ç±:ÏptŽ‘ «µ«=‘ÇÏbpŽ‘ ¡‘±:ÏptŽ‘ ä«;ŽŽŽŒ‹0R Šn ý‘ì·x«988–­3DLDFPRÃŽG’º COPLANAR‘ÕXCASE“«285Ž €n ý•@P‘2ÂifŽ‘=´ý«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"FoundÈ ÝsecondÈ ÝintersŽ‘kÆÜection.È ÝReturning.\nŽ’ÔÆ "Ž’Ú«;Ž¤ ‘2ÂreturnŽ‘Uæ¿ÏbppŽ‘eݨ«;Ž¡‘(·gŽ¡‘gŽ¡‘ÂelseŽ‘5Øâcon•®9tin“ueŽ‘`¿—«;Ž¡‘·g‘±=·‘ÿýÂforŽ‘“+·±=Ž¡‘ÂreturnŽ‘7æ¼ÏbppŽ‘GÝ¥«;Ž¡‘ -·g‘±=·‘ÿý«End–UUof“coplanar“case.‘o·±=ŽŸÂ989.‘ üP®9arallel‘ÕTcase.ŽŸ·h–ª¨«De ne‘UUÂP®9olygonŽ‘/¯˜«functions‘@­979“·i‘Ç«+·Ž¡‘ -ÂelseŽ‘!Øà·fŽ¡‘Ïc‘ÿ}'errŽ‘-y ·‘ÃdÝ"WARNING!È ÝInÈ ÝPolygonŽ‘oÃ(::intersection_pointŽ’ØÂìs():\n"Ž’Ì£·Ž¡‘(Ý"LineÈ ÝandÈ ÝPolygonÈ ÝarŽ’ÿÈeÈ ÝinÈ ÝparallelÈ ÝplanesŽ’ùÿŒ.\n"Ž’P·Ž¡‘(Ý"NoÈ Ýintersections.È ÝRŽ’ÿÈeturningÈ ÝINVALID_BOOŽ’ùÿŒL_POINT_PAIR."Ž’FÌâ·‘ÇÏend‘‚ØlŽ–ò·‘ÇÏend‘‚ØlŽ“·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘7æ¼ÝINVALID_BOOL_POINT_PAIRŽ’±,ß«;Ž¡‘ -·gŽ¡‘ -g‘±=·‘ÿý«End–UUof“parallel“and“coplanar“cases.‘o·±=ŽŽŽŒ‹@. Šn ý‘ì«286›­PERPENDICULAR–ÕXAND“NON-COPLANAR“CASES’˜6˜3DLDFPRÃŽG˜·x«990Ž €n ý•@PÂ990.› üP®9erpQÇendicular–õand“non-coplanar“cases.˜«[¬LDF‘T2003.06.13.«]Ž‘ZÄÂThese–‘ácases“are“handled“in“exactlyŽ¤ the–UUsame“w•¸ãa“y‘ÿ*ª.Ž©·h–ª¨«De ne‘UUÂP®9olygonŽ‘/¯˜«functions‘@­979“·i‘Ç«+·Ž¡‘ -ÂelseŽ‘ .5·fŽ¡‘ -ÂifŽ‘´ù«(ÏplŽ‘ 6 ±:ÏnormalŽ–#з‘ÇÏpt‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘,£©·_‘8àÏplŽ‘ në±:ÏnormalŽ“·‘ÇŽ‘ -Ž6Ïpt‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘21ç«)‘·fŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"TheÈ ÝlineÈ ÝisÈ ÝperpendŽ‘kÆÜicularÈ ÝtoÈ ÝtheÈ ÝPolygoŽ’ÔÆ n.\n"Ž’òT·‘ÇÏ ushŽ‘€«;Ž¡‘ -·gŽ¡‘ -ÂelseŽ‘!Øà·fŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"TheÈ ÝlineÈ ÝandÈ ÝtheÈ ÝPoŽ‘kÆÜlygonÈ ÝareÈ Ýnon-coplanŽ’ÔÆ ar.\n"Ž’÷”·‘ÇÏ ushŽ‘€«;Ž¡‘ -·gŽ¦‘ -Âb•QÇo“olu½‰™šs4Ž‘Ôwp“oin®9tŽ‘B§œÏbpŽ‘PI-«=‘ÇÏplŽ‘ ý#±:Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘M–Ö«(Ïpt0Ž‘i;±;‘ª¨Ïpt1Ž‘ã«);Ž¦‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘ÏbpŽ‘Ú{±:ÏptŽ‘ ä±:ÏshowŽ‘Šÿ«(Ý"bp.pt"Ž‘%FS«);Ž¡‘ -·gŽ¡‘ -ÂifŽ‘´ù«(ÏbpŽ‘ -Úy±:ÏptŽ‘ «µ·‘ÇÏc‘ÿ}'enterŽ‘У«)‘·fŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"bp.ptÈ Ý==È Ýcenter."Ž‘d”b·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¡‘ÏbppŽ‘#öë±:Ï rstŽ‘µª±:ÏptŽ‘ «µ«=‘ÇÏbpŽ‘ ¡‘±:ÏptŽ‘ ä«;Ž¡‘ÏbppŽ‘#öë±:Ï rstŽ–µª±:bŽ‘«=‘ÇÏbpŽ‘ ¡‘±:ÏptŽ‘ ä±:Ïis‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘=5O«(Ïpt0Ž‘i;±;‘ª¨Ïpt1Ž‘ã«)±:Ï rstŽ“«;Ž¡‘ÂreturnŽ‘7æ¼ÏbppŽ‘GÝ¥«;Ž¡‘ -·gŽ¦‘ -ÂP•®9oin“tŽ‘(ïžÏr0Ž‘4!c«;Ž¡‘ -ÂP•®9oin“tŽ‘(ïžÏr1Ž‘4!c«;Ž¦‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘ÏshowŽ‘*‹«(Ý"this:"Ž‘%FS«);Ž¡‘Ïc‘ÿ}'enterŽ‘0 ±:ÏshowŽ‘Šÿ«(Ý"center"Ž‘*†P«);Ž¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"points.size()È Ý==È Ý"Ž‘iÔ_·‘ÇÏp‘ÿ}'ointsŽ‘ë­±:ÏsizeŽ‘\«(‘ª¨)–Ç·“Ïend‘‚ØlŽ‘ò·“Ï ushŽ‘€«;Ž¡‘ -·gŽ¡‘ -ÂforŽ‘臫(Âv®9ectorŽ‘ªH·hÂP•®9oin“tŽ‘ï·Ž‘#ïži‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W«=‘ÇÏp‘ÿ}'ointsŽ–ë­±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏp‘ÿ}'ointsŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘UU·fŽ¡‘ -ÂifŽ‘´ù«((ÏiterŽ‘Þ«+‘8à1Ž‘8á)–Ç·“Ïp‘ÿ}'ointsŽ‘ë­±:ÏendŽ‘ಫ(‘ª¨))‘·fŽ¡‘Ïr0Ž‘!øß«=‘Ç·Ž‘Ç«(Ïp‘ÿ}'ointsŽ‘$•±:Ïb‘ÿ}'ackŽ‘üë(‘ª¨));Ž¡‘Ïr1Ž‘!øß«=‘Ç·Ž‘Ç«(Ïp‘ÿ}'ointsŽ‘$•±:Ïfr‘ÿ}'ontŽ‘I‘«(‘ª¨));Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïr0Ž‘)1ȱ:ÏshowŽ‘Šÿ«(Ý"r0"Ž‘†\«);Ž¡‘Ïr1Ž‘)1ȱ:ÏshowŽ‘Šÿ«(Ý"r1"Ž‘†\«);Ž¡‘·gŽ¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Exiting® ´Path::get_nŽ‘kÆÜormal().® ´"Ž’£”>°‘Ç´"Returning® ´normal.\nŽ‘kÆÜ\n"Ž‘~ÔS°‘DZ ushŽ‘€¬;Ž¦‘ +­returnŽ‘-æ»°Ž‘5­Ù±b0Ž‘AAÀ¬;‘UU°gŽŽŽŒ‹0Ù Šn ý‘ì°x¬945–¯3DLDF-1.1.5.1’ +tº­POINT‘ÕX¯VERSION“¬257Ž €n ý•@P­945.› üP•®9oin“t‘  v“ersion.˜P“oin“tŽ‘(H¬::‘±get‘‰ffŽ‘®normalŽ‘1Šx¬(‘ª®)–§­is“declared“®points.web¬,›Êibut“it“m¸ãust“bGe“de ned“here,˜bGecauseŽ¤ it–UUcalls“­P®9athŽ‘潬::‘±get‘‰ffŽ‘®normalŽ‘1Šx¬(‘ª®).‘qÇ[²LDF‘T2003.07.11.¬]ŽŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.07.11.¬]Ž‘Y;Added–UUthis“function.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬functions‘@¯330“°i‘Ǭ+°Ž¤ ‘ +­P•®9oin“tŽ‘(ïžP•®9oin“tŽ‘E‰ê¬::‘±get‘‰ffŽ‘®normalŽ‘1Šx¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié];‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒµqŽ‘K^¯¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­P®9athŽ‘/滵rŽ‘4°Ï¬;Ž©‘µrŽ‘Ê:±set‘‰ffŽ‘®c–ÿ}'onne“ctorsŽ‘>å¬(´"--"Ž‘†\¬);Ž¡‘µrŽ‘‘.¬+=ŽŽ‘-æ‚°Ž‘2惱thisŽ‘CÒ9¬;Ž¡‘µrŽ‘‘.¬+=ŽŽ‘-悵pŽ‘2;Ž¡‘µrŽ‘‘.¬+=ŽŽ‘-悵qŽ‘2¹,¬;Ž¡‘­ifŽ‘´ú¬(°:µrŽ‘Ê:±is‘‰ffŽ‘®planarŽ‘(&¬(‘ª¨))‘°fŽ¡‘±c‘ÿ}'errŽ‘8÷f°‘A½´"ERROR!® ´In® ´Point::geŽ‘qAt_normal():\n"Ž’É|°Ž¡‘2´"The® ´Points® ´do® ´not® ´dŽ’šÿÉetermine® ´a® ´plane.\n"Ž’M °‘Ç´"Returning® ´INVALID_PŽ‘kÆÜOINT.\n\n"Ž’£”>°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½´INVALID_POINTŽ’†¬þ¬;Ž¡‘°gŽ¡‘­elseŽ‘+ØáreturnŽ‘O¿›µrŽ‘T‰¯:±get‘‰ffŽ‘®normalŽ‘0Št¬(‘ª¨);Ž¡‘ +°gŽŸ­946.‘ üGet‘ÕTplane.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.11.05.¬]Ž‘Y;Rewrote–UUthis“function“to“correspGond“to“the“new“de nition“of“±get‘‰ffŽ‘®normalŽ‘3ßɬ(‘ª®).Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P®9athŽ‘<¬functions‘@¯700“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔPlaneŽ‘OÄŒ±get‘‰ffŽ‘®planeŽ‘x;t¬(‘ª®)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹> Šn ý‘ì¬258–¯GET‘ÕXPLANE’'Iž3DLDF-1.1.5.1“°x¬947Ž €n ý•@P­947.Ž©°h–ª¨¬De ne‘UU­P®9athŽ‘<¬functions‘@¯701“°i‘Ǭ+°Ž¤ ‘ 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+[²LDF‘T2003.06.24.¬]Ž‘Y;BUG–UUFIX:“When“the“­P•®9oin“tsŽ‘&Î.¬all“la¸ãy“in“the“x-z“plane,“or“a“plane“parallel“to“it,Ž¡±lamb‘ÿ}'da‘‰ffŽ‘®denominatorŽ‘^ð+¬wš¸ãas–q„0.‘ÆSThis“caused“±is‘‰ffŽ–®in‘‰ffŽ“triangleŽ‘>%¬(‘ª®)“to“return“±falseŽ‘ Ȭ,‘¸ev˜en“when“°Ž‘ q…±thisŽ‘ο¬did“lie“in“theŽ¡triangle.‘ +:áNo¸ãw,›¾uif‘C±lamb‘ÿ}'da‘‰ffŽ‘®denominatorŽ‘e·¬or‘C±mu‘‰ffŽ‘®denominatorŽ‘ThM¬is–Cequal“to“0,˜the“y“and“z-coGordinates“areŽ¡exc¸ãhanged,‘,Ùand‘"º±lamb‘ÿ}'da‘‰ffŽ‘®denominatorŽ‘`Ĭand‘"º±mu‘‰ffŽ‘®denominatorŽ‘P'±¬are–"ºrecalculated.‘`éIf“either“of“the“new“v‘ÿqÇalues“is“0,Ž¡the–¢Cx“and“z-cošGordinates“are“exc¸ãhanged“(based“on“the“original“co˜ordinate“v‘ÿqÇalues),‘µand“±lamb‘ÿ}'da‘‰ffŽ‘®denominatorŽŽ¡¬and‘4±mu‘‰ffŽ‘®denominatorŽ‘PK]¬are–4again“recalculated.‘fÛOnly“one“excš¸ãhange“has“bGeen“needed“in“the“cases“I'v˜e“tested“soŽ¡far.Ž¡‘ 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+­b•QÇo“olu½‰™šs4Ž‘Ôwp“oin®9tŽ‘B§œPlaneŽ‘`‰¬::‘±interse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘N–Ú¬(­constŽ‘*¢P®9athŽ‘:[¬&Ž‘AØyµpŽ‘Fày¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­ifŽ‘´ú¬(µpŽ–:±is‘‰ffŽ‘®line‘ÿ}'arŽ‘%}¬(›ª¨))‘­returnŽ‘(溱interse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘v}¬(µpŽ“:±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(0Ž‘)µ;˜pŽ‘²¨:±get‘‰ffŽ–®last‘‰ffŽ“p‘ÿ}'ointŽ‘:$>¬(˜));Ž¡‘­elseŽ‘+Øá°fŽ¡‘±c‘ÿ}'errŽ‘5¨°‘òj´"ERROR!® ´In® ´Plane::inŽ‘mò.tersection_point(conŽ’Öñòst® ´Path&):"Ž’*£°‘òj±end‘‚ØlŽ‘Ö–°Ž¡‘2´"Path® ´is® ´not® ´linear!Ž’šÿÉ® ´Returning® ´INVALID_Ž’ÿBOOL_POINT."Ž’FL鰑DZend‘‚ØlŽ–ò°‘DZend‘‚ØlŽ“°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½´INVALID_BOOL_POINTŽ’ ìï¬;Ž¡‘°gŽ¡‘ +gŽŸ­967.– üDra®9wing‘Zaxes.“¬This–“function“draš¸ãws“and“labGels“arro˜ws“for“the“main“axes“at“the“origin.‘+It“can“bGeŽ¡helpful–UUfor“determining“whether“the“\±upŽ‘ ž¾¬"“direction“is“correct“for“a“­F‘ÿ +«oQÇcusŽ‘ J¡¬.Ž¡‘ +[²LDF‘T2003.04.01.¬]Ž‘Yþ®Sometimes–KÈplaceholders“are“needed“for“the“±distŽ›£ý¬and“pGosition“argumen¸ãts.‘UIf“±distŽ˜¬is“aŽ¡n•¸ãum“bGer›Š5µx–8°“¬0,–—mthen˜it's˜set˜to˜the˜default,“curren•¸ãtly˜2.5.‘gIf˜a˜pGosition˜argumen“t˜(±p‘ÿ}'os‘‰ffŽ‘®xŽ‘Õ…¬,‘—m±p‘ÿ}'os‘‰ffŽ‘®yŽ‘R¡¬,‘—mor˜±p‘ÿ}'os‘‰ffŽ‘®zŽ‘ÙT¬)˜isŽ¡´"d"Ž‘F_¬,–UUit's“set“to“the“default.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.02.05.¬]Ž‘Z±Mo•¸ãv“ed–jËthis“function“from“®main.web“¬to“here,‘°(so“I‘jƒcan“use“it“in“m¸ãy“examples“for“theŽ¡T‘ÿ*ªexinfo–ü¤doGcumenš¸ãtation.‘T7Also,‘aadded“additional“argumen˜ts“spšGecifying“the“p˜ositions“of“lab˜els“and“suppressingŽ¡dra¸ãwing–UUthe“axes“(and“their“labGels).Ž¡‘ +[²LDF‘T2003.04.01.¬]Ž‘Z<>Added–‰Xargumen¸ãts“for“dash“pattern“(±ddashe‘ÿ}'dŽ‘#G¬)“and“pGen“(±pp‘ÿ}'enŽ‘6#¬).‘ ÏRearranged“order“ofŽ¡argumenš¸ãts.‘HyAlso,‘tgot–ò;rid“of“the“argumen˜ts“±suppr‘ÿ}'ess‘‰ffŽ‘®xŽ‘2$(¬,‘t±suppr‘ÿ}'ess‘‰ffŽ‘®yŽ‘21¬,‘tand“±suppr‘ÿ}'ess‘‰ffŽ‘®zŽ‘1¬.‘HyNo˜w“using“the“empt˜yŽ¡string–hö(´""Ž‘ 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+¦ Šn ý‘ì¬266–¯DRA‘ÿ8WING‘ÕXAXES’A3DLDF-1.1.5.1“°x¬967Ž €n ý•@Pwithout–Yc¸ãhanging“the“MetapšGost“co˜de.‘[TO‘HDO:“Change“±lab‘ÿ}'elŽ‘…ñ¬(‘ª®),‘òso“that“it's“p˜ossible“to“adjust“the“p˜osition“ofŽ¤ the–yºpGoinš¸ãts“in“the“pro‘Ž8jection!‘ÞõThis“ma˜y“opGen“a“can“of“w˜orms,–‚Óthough,“espšGecially–yºif“the“same“co˜de“is“used“toŽ¡generate–UUdraš¸ãwings“using“di eren˜t“pro‘Ž8jections“and/or“di eren˜t“±F‘ÿ;¼o‘ÿ}'cusesŽ‘%ÅF¬.Ž¡‘ +[²LDF‘T2003.07.13.¬]Ž‘Y;Made‘UU±ddashe‘ÿ}'dŽ‘)ñ»¬and‘UU±pp‘ÿ}'enŽ‘àÍ­constŽ‘: o¬in–UUbGoth“v¸ãersions.Ž¤ŸüÈ„`ÕÁGŽŽ©­968.‘ üLength–ÕTargumen®9t“ rst.Ž¡°h–ª¨¬Declare‘UU±dr‘ÿ}'aw‘‰ffŽ‘®axesŽ‘/[+¬(‘ª®)‘@¯968“°i‘ÇŽ¤ ‘ +­v®9oidŽ‘$©±dr‘ÿ}'aw‘‰ffŽ‘®axesŽ‘P%¬(­realŽ‘Ôþ±distŽ‘-‹†¬=‘ª2µ:¬5ŽŽ‘q:µ;‘ª¨­stringŽ‘#ñűp‘ÿ}'os‘‰ffŽ‘®xŽ‘@qe¬=‘ª´"bot"Ž–ptµ;‘ª¨­stringŽ‘#ñűp‘ÿ}'os‘‰ffŽ‘®yŽ‘@W¬=‘ª´"lft"Ž“µ;‘ª¨­stringŽŽ¡‘±p‘ÿ}'os‘‰ffŽ‘®zŽ‘9Ìå¬=‘}ô"bot"Ž‘Dµ;‘ª¨­constŽ‘ ÜColorŽ‘Aˆ§¬&Ž‘IOűddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ’Ö1¬=‘}ðŽ‘ }Ä­ColorsŽ‘+V¢¬::Ž‘1äà±default‘‰ffŽ‘®c‘ÿ}'olorŽ‘i`»µ;‘ª¨­constŽ‘ 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ne‘UU­Regu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘o¢B¬functions‘@¯993“°i‘Ǭ+°Ž¡‘ +­ifŽ‘qv¬(±pt‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘*jÉ°‘Ç´INVALID_POINTŽ–I?5°_‘±Ü±plŽ› +ççµ:±normalŽ‘#а‘Ç´INVALID_POINTŽ“°_‘±Ü±pt‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘,¥°‘DZoriginŽ‘o°_‘±Ü±plŽ˜µ:±normalŽ‘#а‘DZoriginŽ‘½9¬)Ž¡‘°fŽ¡‘±c‘ÿ}'errŽ‘,e]°‘¯µ´"ERROR!® ´In® ´Reg_Cl_PlŽ‘n¯yane_Curve:intersectiŽ’ׯ=on_points():\n"Ž’,¥-°Ž¡‘(´"Something® ´is® ´wrong® Ž’ÿÈ´with® ´the® ´normals:\n"Ž’ú…ô¬;Ž¡‘±pt‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘;£³µ:±showŽ‘Šÿ¬(´"pt_vector:"Ž‘?†D¬);Ž¡‘±plŽ‘6 µ:±normalŽ‘ V¸µ:±showŽ‘Šÿ¬(´"pl.normal"Ž‘:FG¬);Ž¡‘±c‘ÿ}'errŽ‘)|À°‘Ç´"Returning® ´INVALID_BŽ‘kÆÜOOL_POINT_PAIR.\n\n"Ž’Ø °‘DZ ushŽ‘€¬;Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Exiting® ´Polygon::inŽ‘kÆÜtersection_points().Ž’ÔÆ \n\n"Ž’òT°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘7æ¼´INVALID_BOOL_POINT_PAIRŽ’±,߬;Ž¡‘ +°gŽŸ­1000.‘ üP®9arallel–ÕTand“coplanar“cases.Ž¦°h–ª¨¬De ne‘UU­Regu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘o¢B¬functions‘@¯993“°i‘Ǭ+°Ž¡‘ +­elseŽ‘?ìifŽ‘*›¬(±surfac–ÿ}'e‘‰ffŽ‘®ve“ctorŽ‘@…Ä°‘DZpt‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘*Ç°_\R±surfac–ÿ}'e‘‰ffŽ‘®ve“ctorŽ‘@â°‘ÇŽ‘ +Ž6±pt‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘2Ž9°_\R±cr‘ÿ}'ossŽ–ˆ°‘DZplŽ‘ ý#µ:±normalŽ‘ ³ +°_\R±cr‘ÿ}'ossŽ“°‘ÇŽ‘ +Ž6±plŽ‘ÄAµ:±normalŽ‘ V¸¬)Ž¡‘°fŽŽŽŒ‹d© Šn ý‘ì°x¬1001–¯3DLDF-1.1.5.1’ +G COPLANAR‘ÕXCASE“¬279Ž €n ý•@P­1001.‘ üCoplanar‘ÕTcase.Ž©°h–ª¨¬De ne‘UU­Regu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘o¢B¬functions‘@¯993“°i‘Ǭ+°Ž¤ ‘ +­ifŽ‘´ù¬(±distanc‘ÿ}'eŽ‘' °‘Ǭ0Ž‘Ç)‘UU°fŽ¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Line® ´and® ´Reg_Cl_PlaŽ‘kÆÜne_Curve® ´are® ´coplanaŽ’ÔÆ r.\n"Ž’ïŒù¬;Ž¦‘ +­T‘ÿ +«ransformŽ‘AÈÓ±t0Ž‘Lž¬;Ž¡‘ +­Regu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘vLî±c‘ÿ}'opyŽ’ŠÜæ¬(°Ž‘±thisŽ‘ë·¬);Ž¡‘ +­P•®9oin“tŽ‘(ïž±curve‘‰ffŽ‘®0Ž‘MÁ/¬=‘DZc‘ÿ}'opyŽ‘Wµ:±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(0Ž‘);Ž¦‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"After® ´copying:"Ž‘Zh°‘DZend‘‚ØlŽ‘¸Ú¬;Ž¡‘±showŽ‘*‹¬(´"this:"Ž‘%FS¬);Ž¡‘±c‘ÿ}'opyŽ‘(úµ:±showŽ‘Šÿ¬(´"copy:"Ž‘%FS¬);Ž¡‘±curve‘‰ffŽ‘®0Ž‘6 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+­P•®9oin“tŽ‘(ïž±tr–ÿ}'ac“e‘‰ffŽ–®x‘‰ffŽ“z‘‰ffŽ“0Ž‘[Ih¬=‘DZcurve‘‰ffŽ‘®0Ž‘$Ñ‘¬;Ž¦‘ +±tr–ÿ}'ac“e‘‰ffŽ–®x‘‰ffŽ“z‘‰ffŽ“0Ž‘9’³µ:±shiftŽ‘}¬(0Ž‘µ;‘ª¨°Ž‘ qƬ(±curve‘‰ffŽ‘®0Ž‘" +yµ:±get‘‰ffŽ‘®yŽ‘t¬(‘ª¨)));Ž¦‘ +­P•®9oin“tŽ‘(ïž±x‘‰ffŽ–®axis‘‰ffŽ“ptŽ‘O»»¬(1Ž‘);Ž¡‘ +­realŽ‘ ³/±angŽ‘44í¬=‘DZtr–ÿ}'ac“e‘‰ffŽ–®x‘‰ffŽ“z‘‰ffŽ“0Ž‘2Yʵ:±angleŽ‘ÀS¬(±x‘‰ffŽ–®axis‘‰ffŽ“ptŽ‘&̬);Ž¦‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"ang® ´==® ´"Ž‘5T}°‘DZangŽ‘HÖ°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(±angŽ‘¾°6¬=‘Ç0Ž‘Ç)‘°fŽ¡‘­ifŽ‘´ú¬(±curve‘‰ffŽ‘®0Ž‘" +yµ:±get‘‰ffŽ‘®zŽ‘¬(‘ª¨)–ǵ>“¬0Ž‘Ç)‘±angŽ‘¾°¬=ŽŽ‘(õ°Ž‘/׬1Ž‘4×;Ž¡‘±t0Ž‘!å°¬=ŽŽ‘0¢±curve‘‰ffŽ‘®0Ž‘Us­°¬=ŽŽ‘eä±pt0Ž‘w27°¬=ŽŽ’†Àn±pt1Ž’˜ðÁ°¬=ŽŽ’¨~ø±c‘ÿ}'opyŽ’½ðµ:±r‘ÿ}'otateŽ‘o>¬(0Ž‘µ;‘ª¨±angŽ‘eN¬);Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"After® ´rotating® ´so® ´tŽ‘kÆÜhe® ´trace® ´of® ´curve_0® Ž’ÔÆ ´is® ´on® ´x-axis:"Ž’!“ö°‘DZend‘‚ØlŽ‘¸Ú¬;Ž¡‘±c‘ÿ}'opyŽ‘(úµ:±showŽ‘Šÿ¬(´"copy:"Ž‘%FS¬);Ž¡‘±curve‘‰ffŽ‘®0Ž‘6 +{µ:±showŽ‘Šÿ¬(´"curve_0"Ž‘/ÆM¬);Ž¡‘±pt0Ž‘#i=µ:±showŽ‘Šÿ¬(´"pt0"Ž‘ÆY¬);Ž¡‘±pt1Ž‘#i=µ:±showŽ‘Šÿ¬(´"pt1"Ž‘ÆY¬);Ž¡‘ +°gŽ¡‘ +±angŽ‘¿¬=‘DZcurve‘‰ffŽ‘®0Ž‘$Ñ‘µ:±angleŽ‘ÀS¬(±x‘‰ffŽ–®axis‘‰ffŽ“ptŽ‘&̬);ŽŽŽŒ‹u  Šn ý‘ì¬280–¯COPLANAR‘ÕXCASE’ +G 3DLDF-1.1.5.1“°x¬1001Ž €n ý•@P‘ +­ifŽ‘´ù¬(±angŽ‘¾°6¬=‘Ç0Ž‘Ç)‘°fŽ¤ ‘­ifŽ‘´ú¬(±curve‘‰ffŽ‘®0Ž‘" +yµ:±get‘‰ffŽ‘®yŽ‘t¬(‘ª¨)–ǵ>“¬0Ž‘Ç)‘±angŽ‘¾°¬=ŽŽ‘(õ°Ž‘/׬1Ž‘4×;Ž¡‘±t0Ž‘!å°¬=ŽŽ‘0¢±curve‘‰ffŽ‘®0Ž‘Us­°¬=ŽŽ‘eä±pt0Ž‘w27°¬=ŽŽ’†Àn±pt1Ž’˜ðÁ°¬=ŽŽ’¨~ø±c‘ÿ}'opyŽ’½ðµ:±r‘ÿ}'otateŽ‘o>¬(0Ž‘µ;‘ª¨¬0Ž‘ª©µ;‘ª¨±angŽ‘eN¬);Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"After® ´rotating® ´so® ´cŽ‘kÆÜurve_0® ´is® ´on® ´x-axis:Ž’ÔÆ "Ž’ÝT°‘DZend‘‚ØlŽ‘¸Ú¬;Ž¡‘±c‘ÿ}'opyŽ‘(úµ:±showŽ‘Šÿ¬(´"copy:"Ž‘%FS¬);Ž¡‘±pt0Ž‘#i=µ:±showŽ‘Šÿ¬(´"pt0"Ž‘ÆY¬);Ž¡‘±pt1Ž‘#i=µ:±showŽ‘Šÿ¬(´"pt1"Ž‘ÆY¬);Ž¡‘ +°gŽ©‘ +­P•®9oin“tŽ‘(ïž±curve‘‰ffŽ‘®4Ž‘MÁ/¬=‘DZc‘ÿ}'opyŽ‘Wµ:±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(±numb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜ointsŽ‘JÀ©µ=¬4Ž‘);Ž¡‘ 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ne‘UU­Regu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘o¢B¬functions‘@¯993“°i‘Ǭ+°Ž¤ ‘ +­elseŽ‘!Øà°fŽ¡‘±c‘ÿ}'errŽ‘+ýû°‘HS´"WARNING!® ´In® ´Reg_Cl_Ž‘nHPlane_Curve::interseŽ’×GÛction_points():\n"Ž’;–`°Ž¡‘(´"Line® ´and® ´Reg_Cl_PlaŽ’ÿÈne_Curve® ´are® ´in® ´paraŽ’ùÿŒllel® ´planes.\n"Ž’O€n°Ž¡‘(´"No® ´intersections.® ´RŽ’ÿÈeturning® ´INVALID_BOOŽ’ùÿŒL_POINT_PAIR."Ž’FÌⰑDZend‘‚ØlŽ–ò°‘DZend‘‚ØlŽ“°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘7æ¼´INVALID_BOOL_POINT_PAIRŽ’±,߬;Ž¡‘ +°gŽ¡‘ +g‘µ=°‘ÿý¬End–UUof“parallel“and“coplanar“cases.‘o°µ=ŽŸ­1007.› üP®9erpQÇendicular–gÔand“non-coplanar“cases.˜¬[²LDF‘T2003.06.13.¬]Ž‘Z(þThese–öcases“are“handled“in“exactlyŽ¡the–UUsame“w•¸ãa“y‘ÿ*ª.Ž¦°h–ª¨¬De ne‘UU­Regu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘o¢B¬functions‘@¯993“°i‘Ǭ+°Ž¡‘ +­elseŽ‘!Øà°fŽ¡‘­ifŽ‘´ú¬(±plŽ‘ 6 µ:±normalŽ–#а‘DZpt‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘,£©°_‘8à±plŽ‘ nëµ:±normalŽ“°‘ÇŽ‘ +Ž6±pt‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘21ç¬)‘°fŽ¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)Ž¡‘(±c‘ÿ}'outŽ‘> S°‘Ç´"The® ´line® ´is® ´perpendŽ‘kÆÜicular® ´to® ´the® ´"Ž’½Ô/°‘Ç´"Reg_Cl_Plane_Curve.Ž‘kÆÜ\n"Ž‘~ÔS°‘DZ ushŽ‘€¬;Ž¡‘°gŽ¡‘­elseŽ‘+Øá°fŽ¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)Ž¡‘(±c‘ÿ}'outŽ‘> S°‘Ç´"The® ´line® ´and® ´the® ´ReŽ‘kÆÜg_Cl_Plane_Curve® ´"Ž’Í”&°‘Ç´"are® ´non-coplanar.\nŽ‘kÆÜ"Ž‘tTY°‘DZ ushŽ‘€¬;Ž¡‘°gŽ¦‘­b•QÇo“olu½‰™šs4Ž‘Ôwp“oin®9tŽ‘L§±bpŽ‘ZI.¬=‘DZplŽ‘ ý#µ:±interse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘M–Ö¬(±pt0Ž‘i;µ;‘ª¨±pt1Ž‘ã¬);Ž¦‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±bpŽ‘(Ú|µ:±ptŽ‘ äµ:±showŽ‘Šÿ¬(´"bp.pt"Ž‘%FS¬);Ž¡‘°gŽ¦‘­shortŽ‘1Ê¥µsŽ‘9A½¬=‘DZlo–ÿ}'c“ationŽ‘%ˆ•¬(±r‘ÿ}'ef‘‰ffŽ‘®ptŽ‘ñóµ;‘ª¨±bpŽ‘ …!µ:±ptŽ‘ ä¬);Ž¦‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"location:® ´s® ´==® ´"Ž‘_Te°‘ǵsŽ‘ +>0°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘­ifŽ‘´ú¬(µsŽ‘w>‘Ç°Ž‘ +Ž6¬1Ž‘Ž7)‘°fŽ¡‘±bppŽ‘-öìµ:± rstŽ‘µªµ:±ptŽ‘ «µ¬=‘DZbpŽ‘ ¡‘µ:±ptŽ‘ ä¬;Ž¡‘±bppŽ‘-öìµ:± rstŽ–µªµ:bŽ‘¬=‘DZbpŽ‘ ¡‘µ:±ptŽ‘ äµ:±is‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘=5O¬(±pt0Ž‘i;µ;‘ª¨±pt1Ž‘ã¬)µ:± rstŽ“¬;Ž¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"On® ´segment:® ´==® ´"Ž‘_Te°‘DZbppŽ‘¾µ:± rstŽ‘µªµ:bŽ‘°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½±bppŽ‘Qݦ¬;Ž¡‘°gŽ¡‘­elseŽ‘+ØáreturnŽ‘O¿›´INVALID_BOOL_POINT_PAIRŽ’ɾ¬;Ž¡‘ +°g‘µ=°‘ÿý¬End–UUof“\P¸ãerpGendicular“and“non-coplanar“cases".‘o°µ=Ž¡‘ +°gŽŸ­1008.‘ üP•®9ath‘ÕTargumen“ts.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.06.20.¬]Ž‘Y;Added–UUthis“function.Ž¡‘ +[²LDF‘T2003.07.16.¬]Ž‘YÖChanged–kðname“of“±c‘ÿ}'enterŽ‘"ák¬argumenš¸ãt“to“±r‘ÿ}'ef‘‰ffŽ‘®ptŽ‘]ã¬,‘q–bGecause“I'v˜e“made“±c‘ÿ}'enterŽ‘"ák¬a“data“mem˜bGerŽ¡of‘UU­Regu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘lLí¬.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­Regu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘o¢B¬functions‘@¯987“°i‘Ǭ+°Ž¡‘ +­b•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘[dï±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ’¬ñά(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±r‘ÿ}'ef‘‰ffŽ‘®ptŽ‘]ÓPµ;‘ª¨­constŽ‘ÕJP®9athŽ‘;¼¬&Ž‘Cƒ!µpŽ‘H‹!¬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹¹p Šn ý‘ì°x¬1009›¯3DLDF-1.1.5.1’ú¡­P–ÿ +«A“TH‘ÕX¯ARÃŽGUMENTS˜¬285Ž €n ý•@P­1009.Ž©°h–ª¨¬De ne‘UU­Regu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘o¢B¬functions‘@¯993“°i‘Ǭ+°Ž¤ ‘ +­b•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘[ïRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ’Åy‹¬::‘±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã¬(­constŽ‘G¢P•®9oin“tŽ‘=T?¬&Ž‘E]±r‘ÿ}'ef‘‰ffŽ‘®ptŽ‘^ Pµ;‘ª¨­constŽ‘òJP®9athŽ‘;ö¬&Ž‘C½!µpŽ‘HÅ!¬)Ž¡‘2­constŽŽ¡‘ +°fŽ¡‘­ifŽ‘´ú¬(°:µpŽ‘:±is‘‰ffŽ‘®line‘ÿ}'arŽ‘%}¬(‘ª¨))‘°fŽ¡‘±c‘ÿ}'errŽ‘6D°‘K›´"ERROR!® ´In® ´Reg_Cl_PlŽ‘nK_ane_Curve::intersectŽ’×K#ion_points():\n"Ž’1ö°Ž¡‘2´"Path® ´argument® ´p® ´is® Ž’šÿÉ´non-linear.® ´"Ž’â»ç°‘õÝ´"Returning® ´INVALID_BŽ‘kõ¡OOL_POINT_PAIR.\n\n"Ž’Øqª°Ž¡‘2± ushŽ‘G¹¬;Ž¡‘­returnŽ‘Aæ½´INVALID_BOOL_POINT_PAIRŽ’»,à¬;Ž¡‘°gŽ¡‘­returnŽ‘7æ¼±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ’‰s›¬(±r‘ÿ}'ef‘‰ffŽ‘®ptŽ‘ñóµ;‘ª¨pŽ–²¨:±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(0Ž‘)µ;‘ª¨pŽ“:±get‘‰ffŽ–®last‘‰ffŽ“p‘ÿ}'ointŽ‘:$>¬(‘ª¨));Ž¡‘ +°gŽŸ­1010.› üReg‘°¡‰ffs4Ž–#ÕCl‘°¡‰ffs4Ž“Plane‘°¡‰ffs4Ž“Curv•®9e‘ÕTsegmen“ts.˜¬The–UUfunctions“in“this“section“require“that“theŽ¡­Regu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘m°;¬ha•¸ãv“e–¸£a“meaningful“±c‘ÿ}'enterŽ‘ 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¬.Ž©­in®9tŽ‘¤÷±factorŽŽ‘Lºö¬Determines–²›hoš¸ãw“large“a“segmen˜t“of“the“­Regu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘p\άis“returned.‘‰˜±factorŽ‘$@¬m˜ustŽ¡‘LºöbšGe–UUµ>‘Ǭ1“and“less“than“or“equal“to“the“n•¸ãum“b˜er–UUof“p˜oin¸ãts“on“the“­Regu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘lLí¬.Ž¦­realŽ‘³.±angleŽŽ‘Lºö¬Optional,›with–ã|0“as“the“default.‘=If±angleŽ‘£Ï¬is“°6¬=‘´0,˜a“­P•®9oin“tŽ‘#a@¬is“found“in“the“direction“of“theŽ¡‘Lºönormal–Ñrto“the“­Regu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘nš|¬from“the“cen¸ãter“of“the“­Regu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘kÉ +¬,‘ëÒandŽ¡‘Lºöthe–UUsegmenš¸ãt“is“rotated“around“the“cen˜ter“and“this“­P•®9oin“tŽ‘ï¬.Ž¦­b•QÇo“olŽ‘¡f±close‘ÿ}'dŽŽ‘Lºö¬If‘F¨±trueŽ‘ @¬,‘|Ëthe‘F¨­P®9athŽ‘´¬is–F¨made“a“\­cycle¬"“and“the“ends“of“the“segmenš¸ãt“are“joined“b˜y“concatenatingŽ¡‘Lºöthe–Á6curvš¸ãed“­P®9athŽ‘ Ьwith“the“straigh˜t“line“segmen˜t“from“its“last“to“its“ rst“­P•®9oin“tŽ‘#´¬using“theŽ¡‘Lºöconnector‘UU´"&"Ž‘›´¬.Ž¦‘ 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neŽ¡inš¸ãtersection–UUfunctions“that“will“w˜ork“for“bGoth“­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘H)^¬and“­RectangleŽ‘5”ê¬.ŽŸ±¹Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.06.06.¬]Ž‘Y;Added‘UU­classŽ‘5¦P®9olygonŽ‘G:”¬.ŽŸŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬De ne‘UU­classŽ‘5¦P®9olygonŽ‘Kz˜¯1019“°i‘ÇŽ¡‘ +­classŽ‘$àRP®9olygonŽ‘Q:•¬:‘qÇ­publicŽ‘'ñP®9athŽ‘B몰fŽ¡‘ +­protectedŽ‘:o™¬:‘­P•®9oin“tŽ‘#ï±c‘ÿ}'enterŽ‘?ù(¬;Ž¦‘ +­publicŽ‘)=Ö¬:‘°h–ª¨¬Declare‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1022“°iŽ¡‘ +g¬;ŽŸ øܯThis–ÕXco¬to“­P®9olygonŽ‘,³¬.‘Y—Also“remo•¸ãv“ed– Åthe“­RectangleŽŽ¡¬vš¸ãersions,–UUsince“­RectangleŽ‘8ê?¬inherits“the“­P®9olygonŽ‘/¯˜¬v˜ersions.ŽŸŸüÈ„`ÕÁGŽŽ¦­1022.‘ ünon-const‘ÕTv®9ersion.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.04.24.¬]Ž‘Y;Added–UUthis“function.Ž¡‘ +[²LDF‘T2003.05.09.¬]Ž‘Y;Changed–UUreturn“v‘ÿqÇalue“from“­P•®9oin“tŽ‘"Dò¬&Ž‘-aeto“­constŽ‘!÷P•®9oin“tŽ‘@o”¬&Ž‘H6².Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1022“°i‘ÇŽŸ ‘ 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´Polygon::iŽ‘kÆÜntersection_points()Ž’ÔÆ .\n"Ž’í°‘Ç± ushŽ‘€¬;Ž¡‘´DEBUGŽ‘;t¬=‘DZfalseŽ‘v\¬;Ž¦‘­b•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘oHȱbppŽ’‚ɬ=‘Ç´INVALID_BOOL_POINT_PAIRŽ‘| ;¬;‘µ=°‘ãÔ¬The–9,return“v‘ÿqÇalue.‘hd[²LDF‘T2003.06.13.¬]Ž‘Tÿ°µ=Ž¡‘­PlaneŽ‘>6»±plŽ‘J3Þ¬=‘DZget‘‰ffŽ‘®planeŽ‘+>¬(‘ª¨);Ž¡‘­P•®9oin“tŽ‘<ï ±pt‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘d“Q¬(±pt1Ž–¢°‘8à±pt0Ž“¬);Ž¡‘­P•®9oin“tŽ‘<ï ±surfac–ÿ}'e‘‰ffŽ‘®ve“ctorŽ‘z®L¬(±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(0Ž‘)–8à°“±c‘ÿ}'enterŽ‘Bk¬);Ž¦‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘(±plŽ‘16µ:±p‘ÿ}'ointŽ‘.Œµ:±showŽ‘Šÿ¬(´"pl.point"Ž‘5J¬);Ž¡‘(±plŽ‘16µ:±normalŽ‘ 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¡‘µ:±ptŽ‘ ä¬;Ž¡‘2±foundŽ‘N™”¬=‘DZtrueŽ‘‹°¬;Ž¡‘2­ifŽ‘=´ý¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Found® ´first® ´interseŽ‘kÆÜction.\n"Ž’›)¬;Ž¡‘(°gŽ¡‘(­elseŽ‘?Øã°fŽ¡‘2±bppŽ‘Aöîµ:±se–ÿ}'c“ondŽ‘§Çµ:bŽ‘¬=‘DZtrueŽ‘‹°¬;Ž¡‘2±bppŽ‘Aöîµ:±se–ÿ}'c“ondŽ‘§Çµ:±ptŽ‘ «µ¬=‘DZbpŽ‘ ¡‘µ:±ptŽ‘ ä¬;Ž¡‘2­ifŽ‘=´ý¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Found® ´second® ´intersŽ‘kÆÜection.® ´Returning.\nŽ’ÔÆ "Ž’Ú¬;Ž¡‘2­returnŽ‘U濱bppŽ‘eݨ¬;Ž¡‘(°gŽ¡‘gŽ¡‘­elseŽ‘4.7ifŽ‘?ã/¬(±bpŽ‘ +Úyµ:±ptŽ‘ «µ°6¬=‘Ç´INVALID_POINTŽ‘IÆ9°^‘8à±bpŽ‘ Yµ:±ptŽ‘ äµ:±is‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘=5O¬(±q0Ž‘ “çµ;‘ª¨±q1Ž‘ >¬)µ:± rstŽ‘µª¬)‘°fŽ¡‘(­ifŽ‘3´ü¬(°:±foundŽ‘Òw¬)‘°fŽ¡‘2±bppŽ‘Aöîµ:± rstŽ‘µªµ:bŽ‘¬=‘DZfalseŽ‘v\¬;Ž¡‘2±bppŽ‘Aöîµ:± rstŽ‘µªµ:±ptŽ‘ «µ¬=‘DZbpŽ‘ ¡‘µ:±ptŽ‘ ä¬;Ž¡‘2±foundŽ‘N™”¬=‘DZtrueŽ‘‹°¬;Ž¡‘2­ifŽ‘=´ý¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Found® ´first® ´interseŽ‘kÆÜction.\n"Ž’›)¬;Ž¡‘(°gŽ¡‘(­elseŽ‘?Øã°fŽ¡‘2±bppŽ‘Aöîµ:±se–ÿ}'c“ondŽ‘§Çµ:bŽ‘¬=‘DZfalseŽ‘v\¬;Ž¡‘2±bppŽ‘Aöîµ:±se–ÿ}'c“ondŽ‘§Çµ:±ptŽ‘ «µ¬=‘DZbpŽ‘ ¡‘µ:±ptŽ‘ ä¬;ŽŽŽŒ‹%  Šn ý‘ì°x¬1032–¯3DLDF-1.1.5.1’ +G COPLANAR‘ÕXCASE“¬293Ž €n ý•@P‘2­ifŽ‘=´ý¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Found® ´second® ´intersŽ‘kÆÜection.® ´Returning.\nŽ’ÔÆ "Ž’Ú¬;Ž¤ ‘2­returnŽ‘U濱bppŽ‘eݨ¬;Ž¡‘(°gŽ¡‘gŽ¡‘­elseŽ‘5Øâcon•®9tin“ueŽ‘`¿—¬;Ž¡‘°g‘µ=°‘ÿý­forŽ‘“+°µ=Ž¡‘­returnŽ‘7æ¼±bppŽ‘GÝ¥¬;Ž¡‘ +°g‘µ=°‘ÿý¬End–UUof“coplanar“case.‘o°µ=ŽŸ­1033.‘ üP®9arallel‘ÕTcase.ŽŸ°h–ª¨¬De ne‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1023“°i‘Ǭ+°Ž¡‘ +­elseŽ‘!Øà°fŽ¡‘±c‘ÿ}'errŽ‘-y °‘Ãd´"WARNING!® ´In® ´PolygonŽ‘oÃ(::intersection_pointŽ’ØÂìs():\n"Ž’Ì£°Ž¡‘(´"Line® ´and® ´Polygon® ´arŽ’ÿÈe® ´in® ´parallel® ´planesŽ’ùÿŒ.\n"Ž’P°Ž¡‘(´"No® ´intersections.® ´RŽ’ÿÈeturning® ´INVALID_BOOŽ’ùÿŒL_POINT_PAIR."Ž’FÌⰑDZend‘‚ØlŽ–ò°‘DZend‘‚ØlŽ“°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘7æ¼´INVALID_BOOL_POINT_PAIRŽ’±,߬;Ž¡‘ +°gŽ¡‘ +g‘µ=°‘ÿý¬End–UUof“parallel“and“coplanar“cases.‘o°µ=ŽŽŽŒ‹&/ä Šn ý‘ì¬294›¯PERPENDICULAR–ÕXAND“NON-COPLANAR“CASES’ŠÃ3DLDF-1.1.5.1˜°x¬1034Ž €n ý•@P­1034.› üP®9erpQÇendicular–gÔand“non-coplanar“cases.˜¬[²LDF‘T2003.06.13.¬]Ž‘Z(þThese–öcases“are“handled“in“exactlyŽ¤ the–UUsame“w•¸ãa“y‘ÿ*ª.Ž©°h–ª¨¬De ne‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1023“°i‘Ǭ+°Ž¡‘ +­elseŽ‘ .5°fŽ¡‘ +­ifŽ‘´ù¬(±plŽ‘ 6 µ:±normalŽ–#а‘DZpt‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘,£©°_‘8à±plŽ‘ nëµ:±normalŽ“°‘ÇŽ‘ +Ž6±pt‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘21ç¬)‘°fŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"The® ´line® ´is® ´perpendŽ‘kÆÜicular® ´to® ´the® ´PolygoŽ’ÔÆ n.\n"Ž’òT°‘DZ ushŽ‘€¬;Ž¡‘ +°gŽ¡‘ +­elseŽ‘!Øà°fŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"The® ´line® ´and® ´the® ´PoŽ‘kÆÜlygon® ´are® ´non-coplanŽ’ÔÆ ar.\n"Ž’÷”°‘DZ ushŽ‘€¬;Ž¡‘ +°gŽ¦‘ +­b•QÇo“olu½‰™šs4Ž‘Ôwp“oin®9tŽ‘B§œ±bpŽ‘PI-¬=‘DZplŽ‘ ý#µ:±interse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘M–Ö¬(±pt0Ž‘i;µ;‘ª¨±pt1Ž‘ã¬);Ž¦‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±bpŽ‘Ú{µ:±ptŽ‘ äµ:±showŽ‘Šÿ¬(´"bp.pt"Ž‘%FS¬);Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(±bpŽ‘ +Úyµ:±ptŽ‘ «µ°‘DZc‘ÿ}'enterŽ‘У¬)‘°fŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"bp.pt® ´==® ´center."Ž‘d”b°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘°gŽ¡‘±bppŽ‘#öëµ:± rstŽ‘µªµ:±ptŽ‘ «µ¬=‘DZbpŽ‘ ¡‘µ:±ptŽ‘ ä¬;Ž¡‘±bppŽ‘#öëµ:± rstŽ–µªµ:bŽ‘¬=‘DZbpŽ‘ ¡‘µ:±ptŽ‘ äµ:±is‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘=5O¬(±pt0Ž‘i;µ;‘ª¨±pt1Ž‘ã¬)µ:± rstŽ“¬;Ž¡‘­returnŽ‘7æ¼±bppŽ‘GÝ¥¬;Ž¡‘ +°gŽ¦‘ +­P•®9oin“tŽ‘(ïž±r0Ž‘4!c¬;Ž¡‘ +­P•®9oin“tŽ‘(ïž±r1Ž‘4!c¬;Ž¦‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±showŽ‘*‹¬(´"this:"Ž‘%FS¬);Ž¡‘±c‘ÿ}'enterŽ‘0 µ:±showŽ‘Šÿ¬(´"center"Ž‘*†P¬);Ž¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"points.size()® ´==® ´"Ž‘iÔ_°‘DZp‘ÿ}'ointsŽ‘ë­µ:±sizeŽ‘\¬(‘ª¨)–Ç°“±end‘‚ØlŽ‘ò°“± ushŽ‘€¬;Ž¡‘ +°gŽ¡‘ +­forŽ‘臬(­v®9ectorŽ‘ªH°h­P•®9oin“tŽ‘ï°Ž‘#ïži‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘DZp‘ÿ}'ointsŽ–ë­µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZp‘ÿ}'ointsŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘UU°fŽ¡‘ +­ifŽ‘´ù¬((±iterŽ‘Þ¬+‘8à1Ž‘8á)–Ç°“±p‘ÿ}'ointsŽ‘ë­µ:±endŽ‘ಬ(‘ª¨))‘°fŽ¡‘±r0Ž‘!ø߬=‘Ç°Ž‘Ǭ(±p‘ÿ}'ointsŽ‘$•µ:±b‘ÿ}'ackŽ‘üì(‘ª¨));Ž¡‘±r1Ž‘!ø߬=‘Ç°Ž‘Ǭ(±p‘ÿ}'ointsŽ‘$•µ:±fr‘ÿ}'ontŽ‘I‘¬(‘ª¨));Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±r0Ž‘)1ȵ:±showŽ‘Šÿ¬(´"r0"Ž‘†\¬);Ž¡‘±r1Ž‘)1ȵ:±showŽ‘Šÿ¬(´"r1"Ž‘†\¬);Ž¡‘°gŽ¡‘ gŽ¡‘ -ÂelseŽ‘!Øà·fŽ¡‘Ïr0Ž‘!øß«=‘Ç·Ž‘ÇŽ‘ ÇÏiterŽ‘’«;Ž¡‘Ïr1Ž‘!øß«=‘Ç·Ž‘ÇŽ‘ Ç«(ÏiterŽ‘Þ«+‘8à1Ž‘8á);Ž¡‘ -·gŽ¡‘ -ÂifŽ‘´ù«(ÏbpŽ‘ -Úy±:ÏptŽ– «µ·‘ÇÏr0Ž‘1½·_‘8àÏbpŽ‘ Y±:ÏptŽ“·‘ÇÏr1Ž‘ øÝ«)‘·fŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘ÂifŽ‘)´û«(ÏbpŽ‘ -Úy±:ÏptŽ‘ «µ·‘ÇÏr0Ž‘ øÝ«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"bp.ptÈ Ý==È Ýr0."Ž‘O”n·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ÂelseŽ‘4.7ifŽ‘?ã/«(ÏbpŽ‘ -Úy±:ÏptŽ‘ «µ·‘ÇÏr1Ž‘ øÝ«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"bp.ptÈ Ý==È Ýr1."Ž‘O”n·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¡‘ÏbppŽ‘#öë±:Ï rstŽ‘µª±:ÏptŽ‘ «µ«=‘ÇÏbpŽ‘ ¡‘±:ÏptŽ‘ ä«;Ž¡‘ÏbppŽ‘#öë±:Ï rstŽ–µª±:bŽ‘«=‘ÇÏbpŽ‘ ¡‘±:ÏptŽ‘ ä±:Ïis‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘=5O«(Ïpt0Ž‘i;±;‘ª¨Ïpt1Ž‘ã«)±:Ï rstŽ“«;Ž¡‘ÂreturnŽ‘7æ¼ÏbppŽ‘GÝ¥«;Ž¡‘ -·gŽŽŽŒ‹DC Šn ý‘ì·x«991›­3DLDFPRÃŽG’˜6˜PERPENDICULAR–ÕXAND“NON-COPLANAR“CASES˜«287Ž €n ý•@PÂ991.‘ ü«[¬LDF‘T2003.06.24.«]Ž‘Zˆ6ÝDEBUGŽ‘x£ä«is–UUpassed“as“the“Ïverb‘ÿ}'oseŽ‘'<«argumen¸ãt“to“Ïis‘‰ffŽ–®in‘‰ffŽ“triangleŽ‘<äö«(‘ª®).‘qÇSo,“ifŽ¤ Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘QŒß«(›ª®)–Dis“bGeing“debugged,‘ÆÏis‘‰ffŽ–®in‘‰ffŽ“triangleŽ‘>g«(˜)“will“prinš¸ãt“more“information.‘> Ho˜w˜ev˜er,‘ÆÝDEBUGŽ‘#Š5«inŽ¡Ïis‘‰ffŽ–®in‘‰ffŽ“triangleŽ‘9¡«(‘ª®)–UUwill“not“bGe“set“to“ÏtrueŽ‘í«.Ž©·h–ª¨«De ne‘UUÂP®9olygonŽ‘/¯˜«functions‘@­979“·i‘Ç«+·Ž¡‘ -ÂelseŽŽ¡‘ifŽ‘´ú«(ÏbpŽ‘ -Úy±:ÏptŽ‘ ä±:Ïis‘‰ffŽ–®in‘‰ffŽ“triangleŽ‘9¡«(Ïc‘ÿ}'enterŽ‘ ‹±;‘ª¨Ïr0Ž– Üm±;‘ª¨Ïr1Ž“±;‘ª¨ÝDEBUGŽ‘q«))‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"IntersectionÈ ÝpointÈ Ž‘kÆÜÝisÈ ÝwithinÈ Ýtriangle.\Ž’ÔÆ n"Ž’ßÍ«;Ž¡‘ÏbppŽ‘-öì±:Ï rstŽ‘µª±:ÏptŽ‘ «µ«=‘ÇÏbpŽ‘ ¡‘±:ÏptŽ‘ ä«;Ž¡‘ÏbppŽ‘-öì±:Ï rstŽ–µª±:bŽ‘«=‘ÇÏbpŽ‘ ¡‘±:ÏptŽ‘ ä±:Ïis‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘=5O«(Ïpt0Ž‘i;±;‘ª¨Ïpt1Ž‘ã«)±:Ï rstŽ“«;Ž¡‘ÂreturnŽ‘Aæ½ÏbppŽ‘Qݦ«;Ž¡‘·gŽ¡‘ -g–UUg‘±=·‘ÿý«End“of“\P¸ãerpGendicular“and“non-coplanar“cases".‘o·±=ŽŸÂ992.‘ üEnd–ÕTof“de nition.Ž¦·h–ª¨«De ne‘UUÂP®9olygonŽ‘/¯˜«functions‘@­979“·i‘Ç«+·Ž¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ExitingÈ ÝPolygon::inŽ‘kÆÜtersection_points().Ž’ÔÆ \n\n"Ž’òT·‘ÇÏ ushŽ‘€«;Ž¡‘ -ÂreturnŽ‘-æ»ÏbppŽ‘=ݤ«;‘qÇ·gŽŸÂ993.‘ üP•®9ath‘ÕTv“ersion.Ž¦·h–ª¨«Declare‘UUÂP®9olygonŽ‘/¯˜«functions‘@­978“·i‘Ç«+·Ž¡‘ -Âb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘[dïÏinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ’¬ñΫ(ÂconstŽ‘*¢P®9athŽ‘:[«&Ž‘AØy±pŽ‘Fày«)‘UUÂconstŽ‘*¢«;ŽŸÂ994.Ž¦·h–ª¨«De ne‘UUÂP®9olygonŽ‘/¯˜«functions‘@­979“·i‘Ç«+·Ž¡‘ -Âb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘[dïP®9olygonŽ’…iá«::‘Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã«(ÂconstŽ‘*¢P®9athŽ‘:[«&Ž‘AØy±pŽ‘Fày«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂifŽ‘´ú«(·:±pŽ‘:Ïis‘‰ffŽ‘®line‘ÿ}'arŽ‘%}«(‘ª¨))‘·fŽ¡‘Ïc‘ÿ}'errŽ‘5¼Y·‘°Ý"ERROR!È ÝInÈ ÝPolygon::Ž‘ntintersection_points(Ž’×8constÈ ÝPath&È Ýp):\n"Ž’;·Ž¡‘2Ý"PathÈ ÝpÈ ÝisÈ Ýnon-lineaŽ’šÿÉr.È ÝReturningÈ ÝINVALIŽ’ÿD_BOOL_POINT_PAIR.\nŽ’lÿQ\n"Ž’€ È·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½ÝINVALID_BOOL_POINT_PAIRŽ’»,à«;Ž¡‘·gŽ¡‘ÂreturnŽ‘7æ¼Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ’‰s›«(±pŽ‘:Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH«(0Ž‘)±;‘ª¨pŽ‘²¨:Ïget‘‰ffŽ–®last‘‰ffŽ“p‘ÿ}'ointŽ‘:$>«(‘ª¨));Ž¡‘ -·gŽŸÂ995.‘ üInš®9tersection–ê˜with“another“P˜olygon.‘ ü«TO‘‰DO:–‰7Explain“what“this“function“doGes“and“hoš¸ãw“it“w˜orks.Ž¡[¬LDF‘T2003.06.29.«]ŽŽ¡‘ -TO‘KDO:–ZFind“out“where“Ïunit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘3­Ï«(‘ª®)“gets“called,›$Œwhen“this“function“is“called,˜and“try“to“pass“ÏtrueŽ‘õL«as“itsŽ¡ÏsilentŽ‘ i«argumen¸ãt.‘qÇ[¬LDF‘T2003.07.16.«]ŽŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.06.29.«]Ž‘Y;Replaced–UUthe“dumm¸ãy“de nition“of“this“function“with“a“real“one.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂP®9olygonŽ‘/¯˜«functions‘@­978“·i‘Ç«+·Ž¡‘ -Âv®9ectorŽ‘)ªI·hÂP•®9oin“tŽ‘šH·i‘UUÏinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘Tâ4«(ÂconstŽ‘*¢P®9olygonŽ‘J„å«&Ž‘RL±rŽ‘W«)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹ R Šn ý‘ì«288›­INTERSECTION–ÕXWITH“ANOTHER“ÂPOL‘ÿ -«YGON’™ÔÄ­3DLDFPRÃŽG˜·x«996Ž €n ý•@PÂ996.Ž©·h–ª¨«De ne‘UUÂP®9olygonŽ‘/¯˜«functions‘@­979“·i‘Ç«+·Ž¤ ‘ -Âv®9ectorŽ‘)ªI·hÂP•®9oin“tŽ‘šH·i‘UUÂP®9olygonŽ‘-ZG«::‘Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã«(ÂconstŽ‘*¢P®9olygonŽ‘J„å«&Ž‘RL±rŽ‘W«)‘UUÂconstŽ‘*¢·f‘UUÂb•QÇo“olŽ‘ö»ÝDEBUGŽ‘:„,«=‘ÇÏfalseŽ‘v\«;Ž¡‘(±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¡‘Âv®9ectorŽ‘=ªK·hÂP•®9oin“tŽ‘šH·i‘UU±vŽ‘Š«;Ž¡‘ÂPlaneŽ‘>6»ÏplŽ‘J3Þ«=‘ÇÏget‘‰ffŽ‘®planeŽ‘+>«(‘ª¨);Ž¡‘ÂPlaneŽ‘>6»Ïr‘‰ffŽ‘®plŽ‘Rf«=‘DZrŽ‘‘,:Ïget‘‰ffŽ‘®planeŽ‘(vè«(‘ª¨);Ž¦‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘(ÏplŽ‘16±:ÏnormalŽ‘ V¸±:ÏshowŽ‘Šÿ«(Ý"pl.normal"Ž‘:FG«);Ž¡‘(Ïr‘‰ffŽ‘®plŽ‘9—±:ÏnormalŽ‘ V¸±:ÏshowŽ‘Šÿ«(Ý"r_pl.normal"Ž‘DÆA«);Ž¡‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÝ"pl.distanceÈ Ý==È Ý"Ž‘_Te·‘ÇÏplŽ‘ ý#±:Ïdistanc‘ÿ}'eŽ‘' ·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÝ"r_pl.distanceÈ Ý==È Ý"Ž‘iÔ_·‘ÇÏr‘‰ffŽ‘®plŽ‘⫱:Ïdistanc‘ÿ}'eŽ‘' ·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¦‘ÂrealŽ‘4³1Ïdistanc‘ÿ}'eŽ‘[ÀF«=‘ÇÏfabsŽ‘ùê«(ÏfabsŽ‘2Ò«(ÏplŽ‘ 6 ±:Ïdistanc‘ÿ}'eŽ›$Eý«)–8à·“ÏfabsŽ‘k²«(Ïr‘‰ffŽ‘®plŽ‘“±:Ïdistanc‘ÿ}'eŽ˜«));Ž¦‘ÂifŽ‘)´û«(Ïdistanc‘ÿ}'eŽ‘' ±<‘ÇÂP•®9oin“tŽ‘ad«::Ž‘%ï¢ÏepsilonŽ‘E^¦«(‘ª¨))‘Ïdistanc‘ÿ}'eŽ‘, «=‘Ç0Ž‘Ç;Ž¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"distanceÈ Ý==È Ý"Ž‘O”n·‘ÇÏdistanc‘ÿ}'eŽ‘)Ô-·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ÂifŽ‘)´û«(ÏplŽ‘ 6 ±:ÏnormalŽ‘#з‘ÇÏr‘‰ffŽ‘®plŽ‘⫱:ÏnormalŽ‘ V¸«)‘UU·fŽŸÂ997.‘ üCoplanar‘ÕTcase.Ž¦·h–ª¨«De ne‘UUÂP®9olygonŽ‘/¯˜«functions‘@­979“·i‘Ç«+·Ž¡‘ -ÂifŽ‘´ù«(Ïdistanc‘ÿ}'eŽ‘' ·‘Ç«0Ž‘Ç)‘·fŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"Coplanar.\n"Ž‘GY«;Ž¦‘Âb•QÇo“olu½‰™šs4Ž‘Ôwp“oin®9tŽ‘L§ÏbpŽ‘W‚«;Ž¡‘ÂP•®9oin“tŽ‘2Ž‘7ï ÏptrŽ‘F,g«;Ž¡‘ÂP•®9oin“tŽ‘2Ž‘7ï Ïr‘‰ffŽ‘®ptrŽ‘Nï«;Ž¦‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂP•®9oin“tŽ‘ï·Ž‘#ïži‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W«=‘ÇÏp‘ÿ}'ointsŽ–ë­±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏp‘ÿ}'ointsŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘ÂifŽ‘)´û«((ÏiterŽ‘Þ«+‘8à1Ž‘8á)–Ç·“Ïp‘ÿ}'ointsŽ›ë­±:ÏendŽ‘ಫ(‘ª¨))‘ÏptrŽ‘ß«=“Ïp‘ÿ}'ointsŽ˜±:Ïfr‘ÿ}'ontŽ‘I‘«(‘ª¨);Ž¡‘ÂelseŽ‘5ØâÏptrŽ‘FÜÁ«=‘Ç·Ž‘Ç«(ÏiterŽ‘Þ«+‘8à1Ž‘8á);Ž¡‘ÂforŽ‘/×C«(Âv®9ectorŽ‘ªH·hÂP•®9oin“tŽ‘ÞW·Ž‘#ÞXi‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûr‘‰ffŽ‘®iterŽ‘^ú™«=‘DZrŽ–‘,:Ïp‘ÿ}'ointsŽ›$•±:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);‘î·Ïr‘‰ffŽ‘®iterŽ‘ fU·6«=‘DZrŽ“:Ïp‘ÿ}'ointsŽ˜±:ÏendŽ‘ಫ(‘ª¨);‘n·Ÿÿ®+‘ÿ+ŽŽ‘5×Ïr‘‰ffŽ‘®iterŽ‘)æ]«)‘·fŽ¡‘(ÂifŽ‘3´ü«((Ïr‘‰ffŽ‘®iterŽ‘éf«+‘8à1Ž‘8á)–Ç·“±rŽ›‘,:Ïp‘ÿ}'ointsŽ‘$•±:ÏendŽ‘ಫ(‘ª¨))‘Ïr‘‰ffŽ‘®ptrŽ‘ég«=“±rŽ˜:Ïp‘ÿ}'ointsŽ‘$•±:Ïfr‘ÿ}'ontŽ‘I‘«(‘ª¨);Ž¡‘(ÂelseŽ‘?ØãÏr‘‰ffŽ‘®ptrŽ‘XÂJ«=‘Ç·Ž‘Ç«(Ïr‘‰ffŽ‘®iterŽ‘éf«+‘8à1Ž‘8á);Ž¡‘(ÏbpŽ‘5¡•«=‘ÇÂP•®9oin“tŽ‘ad«::Ž‘%ï¢Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘s†x«(·Ž‘Ž‘ -ÏiterŽ‘˱;‘ª¨·Ž‘ª©ÏptrŽ‘çp±;‘ª¨·Ž‘ª©Ž‘ ªªÏr‘‰ffŽ‘®iterŽ‘$[0±;‘ª¨·Ž‘ª©Ïr‘‰ffŽ‘®ptrŽ‘Ìø«);Ž¡‘(ÂifŽ‘3´ü«(ÏbpŽ– -Úy±:bŽ‘Jª«)‘±vŽ‘ -4½:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÏbpŽ“±:ÏptŽ‘ ä«);Ž¡‘·g‘±=·‘ÿý«Inner‘UUÂforŽ‘胷±=Ž¡‘·g‘±=·‘ÿý«Outer‘UUÂforŽ‘胷±=Ž¡‘ÂreturnŽ‘7æ¼±vŽ‘=y«;Ž¡‘ -·gŽŸÂ998.‘ üP®9arallel‘ÕTcase.Ž¦·h–ª¨«De ne‘UUÂP®9olygonŽ‘/¯˜«functions‘@­979“·i‘Ç«+·Ž¡‘ -ÂelseŽ‘0Øá±=·‘ÿý«P¸ãarallel.‘o·±=Ž¡‘ -·fŽ¡‘Ïc‘ÿ}'errŽ‘-V–·‘ îÝ"WARNING!È ÝInÈ ÝPolygoŽ‘o ²n::intersection_poinŽ’Ø vts():\n"Ž’ Ç´·Ž¡‘(Ý"TheÈ ÝPolygonsÈ ÝlieÈ ÝinŽ’ÿÈÈ ÝparallelÈ Ýplanes.È Ý"Ž’ø8Œ·‘ò•Ý"ReturningÈ ÝemptyÈ ÝvecŽ‘kòYtor.\n\n"Ž’Ãk&·Ž¡‘(Ï ushŽ‘=¹«;Ž¡‘ÂreturnŽ‘7æ¼±vŽ‘=y«;Ž¡‘ -·gŽ¡‘ -gŽŽŽŒ‹!`0 Šn ý‘ì·x«999›­3DLDFPRÃŽG’¸iêNON-P‘ÿJªARALLEL,–ÕXNON-COPLANAR“CASE˜«289Ž €n ý•@PÂ999.– üNon-parallel,‘non-coplanar‘kþcase.“±vŽ‘®u«will–ù¼conš¸ãtain“the“in˜tersection“pGoin˜ts“of“the“ÂLineŽ‘Kû±lŽ‘"sñ«with“·Ž‘ù½ÏthisŽŽ¤ «and‘µ‚±rŽ‘–«,‘Íif–µ‚anš¸ãy‘ÿ*ª.‘’M±vŽ‘|Œ«can“con˜tain“a“maxim˜um“of“four“ÂP•®9oin“tsŽ‘'Žˆ«in“this“case.‘’M±vŽ‘ -Ç -«[0Ž›]“and“±vŽ‘ê?«[1Ž˜]“will“bGe“the“in¸ãtersectionŽ¡pGoin¸ãts–Ücof“the“ÂLineŽ‘ I±lŽ‘(æ«with“·Ž‘ ÜdÏthisŽ‘È«,‘>&and“±vŽ› - «[2Ž‘]“and“±vŽ˜«[3Ž‘]“the“inš¸ãtersection“pGoin˜ts“of“±lŽ‘ ç«and“±rŽ‘ ¦w«,‘>&if“they“exist.‘ ðIfŽ¡an•¸ãy›Эin“tersection˜pGoin“t˜do•Gesn't˜exist,‘ïƒÝINVALID_POINTŽ‘L†q«will˜b“e˜stored˜in˜the˜corresp“onding˜elemen¸ãt˜of˜±vŽ‘ Ö«as˜aŽ¡placeholder.‘qÇ[¬LDF‘T2003.06.29.«]ŽŽ¡‘ -The–Ölv‘ÿqÇalues“in“±vŽ‘ -á•«proš¸ãvide“information“abGout“the“relativ˜e“pGositions“of“the“ÏPolygonsŽ‘*姫,–ïÎe.g.,“whether–Ölthey“touc˜h,Ž¡whether–EÇlies“within“the“pGerimeter“of“the“other,›Häetc.‘l˜Ho•¸ãw“ev“er,˜it's–EÇnot“pGossible“to“include“this“information“inŽ¡the–ϸreturn“v‘ÿqÇalue,‘îQsince“the“latter“is“merely“a“Âv®9ectorŽ‘#z·hÂP•®9oin“tŽ‘šH·i«.‘àðThe“routine“bGeloš¸ãw“ma˜y“need“to“bGe“put“in˜toŽ¡another–ýbfunction“in“order“to“use“this“information.‘iíIt“ma¸ãy“bšGe“of“imp˜ortance“in“breaking“up“ÏPolygonsŽ‘0 ÿ«andŽ¡ÂSolidsŽ‘!\h«for–UUan“impro•¸ãv“ed–UUsurface“hiding“routine.‘qÇ[¬LDF‘T2003.06.29.«]ŽŽ©·h–ª¨«De ne‘UUÂP®9olygonŽ‘/¯˜«functions‘@­979“·i‘Ç«+·Ž¡‘ -ÂelseŽ‘!Øà·fŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"Non-coplanar,È Ýnon-pŽ‘kÆÜarallel.\n"Ž’¦ #«;Ž¦‘ÂLineŽ‘-­Ú±lŽ‘3£,«=‘ÇÏplŽ‘ ý#±:Ïinterse‘ÿ}'ction‘‰ffŽ‘®lineŽ‘Gƒ¦«(Ïr‘‰ffŽ‘®plŽ‘“«);Ž¡‘Âb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘edðÏbppŽ‘x"ñ«=‘ÇÏinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘TS÷«(±lŽ–.::Ïp‘ÿ}'ositionŽ‘#DW±;‘ª¨«(±lŽ“:Ïp‘ÿ}'ositionŽ‘%}7«+‘8à±lŽ‘g:Ïdir–ÿ}'e“ctionŽ‘&øñ«));Ž¦‘±vŽ‘4¿:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÏbppŽ‘öé±:Ï rstŽ‘µª±:ÏptŽ‘ ä«);Ž¡‘ÂifŽ‘´ú«(ÏbppŽ‘öé±:Ï rstŽ‘µª±:ÏptŽ‘ «µ·‘ÇÏbppŽ‘¾±:Ïse–ÿ}'c“ondŽ‘§Ç±:ÏptŽ‘ ä«)‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"bpp.first.ptÈ ÝandÈ ÝbpŽ‘kÆÜp.second.ptÈ ÝareÈ ÝequaŽ’ÔÆ lÈ ÝforÈ Ý*this.\n"Ž’$ Û«;Ž¡‘±vŽ‘#4À:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÝINVALID_POINTŽ‘DÆA«);Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá±vŽ‘1 ž:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÏbppŽ‘öé±:Ïse–ÿ}'c“ondŽ‘§Ç±:ÏptŽ‘ ä«);Ž¡‘ÏbppŽ‘&¾«=‘DZrŽ‘‘,:Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘QŒß«(±lŽ–.::Ïp‘ÿ}'ositionŽ‘#DW±;‘ª¨«(±lŽ“:Ïp‘ÿ}'ositionŽ‘%}7«+‘8à±lŽ‘g:Ïdir–ÿ}'e“ctionŽ‘&øñ«));Ž¡‘±vŽ‘4¿:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÏbppŽ‘öé±:Ï rstŽ‘µª±:ÏptŽ‘ ä«);Ž¡‘ÂifŽ‘´ú«(ÏbppŽ‘öé±:Ï rstŽ‘µª±:ÏptŽ‘ «µ·‘ÇÏbppŽ‘¾±:Ïse–ÿ}'c“ondŽ‘§Ç±:ÏptŽ‘ ä«)‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"bpp.first.ptÈ ÝandÈ ÝbpŽ‘kÆÜp.second.ptÈ ÝareÈ ÝequaŽ’ÔÆ lÈ ÝforÈ Ýr.\n"Ž’ ç«;Ž¡‘±vŽ‘#4À:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÝINVALID_POINTŽ‘DÆA«);Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá±vŽ‘1 ž:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÏbppŽ‘öé±:Ïse–ÿ}'c“ondŽ‘§Ç±:ÏptŽ‘ ä«);Ž¡‘ÂifŽ‘Ln«(·:«(±vŽ‘4½«[0Ž›]–Ç·6«=“ÝINVALID_POINTŽ‘Hõ#·_‘gʱvŽ‘œ‡«[1Ž˜]“·6«=“ÝINVALID_POINTŽ‘Hõ#·_‘gʱvŽ‘œ‡«[2Ž˜]“·6«=“ÝINVALID_POINTŽ‘Hõ#·_‘gʱvŽ‘œ‡«[3Ž˜]“·6«=“ÝINVALID_POINTŽ‘GY«))Ž¡‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)Ž¡‘(Ïc‘ÿ}'outŽ‘>U7·‘ûüÝ"NoÈ ÝintersectionÈ ÝpoiŽ‘kûÀntsÈ Ýfound.È Ý"Ž’³½ý·‘ûüÝ"ReturningÈ ÝemptyÈ ÝvecŽ‘kûÀtor\n\n"Ž’¾=÷·Ž¡‘<Ï ushŽ‘Q¹«;Ž¡‘±vŽ‘#4À:Ïcle‘ÿ}'arŽ‘(Ù«(‘ª¨);Ž¡‘ÂreturnŽ‘Aæ½±vŽ‘Gz«;Ž¡‘·gŽ¦‘Âb•QÇo“olu½‰™šs4Ž‘ÔwrealŽ‘E@ƒÏbrŽ‘O§ö«[4Ž‘];Ž¦‘ÂifŽ‘´ú«(·:«(±vŽ‘4½«[2Ž›]–Ç·“ÝINVALID_POINTŽ‘IÆ9·_‘8à±vŽ‘m«[3Ž˜]“·“ÝINVALID_POINTŽ‘GY«))‘·fŽ¡‘ÂifŽ‘)´û«(±vŽ‘4½«[0Ž›]–Ç·6«=“ÝINVALID_POINTŽ‘GY«)‘ÏbrŽ‘gs«[0Ž˜]“=“±vŽ‘ûÕ«[0Ž˜]±:Ïis‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘=5O«(±vŽ‘4½«[2Ž˜]±;‘ª¨vŽ‘ße«[3Ž˜]);Ž¡‘ÂelseŽ‘5Øâ·fŽ¡‘(ÏbrŽ‘2gw«[0Ž‘]±:Ï rstŽ‘|«=‘ÇÏfalseŽ‘v\«;Ž¡‘(ÏbrŽ‘2gw«[0Ž‘]±:Ïse–ÿ}'c“ondŽ‘ nß«=‘Ç0Ž‘Ç;Ž¡‘·gŽ¡‘ÂifŽ‘)´û«(±vŽ‘4½«[1Ž›]–Ç·6«=“ÝINVALID_POINTŽ‘GY«)‘ÏbrŽ‘gs«[1Ž˜]“=“±vŽ‘ûÕ«[1Ž˜]±:Ïis‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘=5O«(±vŽ‘4½«[2Ž˜]±;‘ª¨vŽ‘ße«[3Ž˜]);Ž¡‘ÂelseŽ‘5Øâ·fŽ¡‘(ÏbrŽ‘2gw«[1Ž‘]±:Ï rstŽ‘|«=‘ÇÏfalseŽ‘v\«;Ž¡‘(ÏbrŽ‘2gw«[1Ž‘]±:Ïse–ÿ}'c“ondŽ‘ nß«=‘Ç0Ž‘Ç;Ž¡‘·gŽ¡‘gŽ¡‘ÂifŽ‘´ú«(·:«(±vŽ‘4½«[0Ž›]–Ç·“ÝINVALID_POINTŽ‘IÆ9·_‘8à±vŽ‘m«[1Ž˜]“·“ÝINVALID_POINTŽ‘GY«))‘·fŽ¡‘ÂifŽ‘)´û«(±vŽ‘4½«[2Ž›]–Ç·6«=“ÝINVALID_POINTŽ‘GY«)‘ÏbrŽ‘gs«[2Ž˜]“=“±vŽ‘ûÕ«[2Ž˜]±:Ïis‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘=5O«(±vŽ‘4½«[0Ž˜]±;‘ª¨vŽ‘ße«[1Ž˜]);ŽŽŽŒ‹"pÛ Šn ý‘ì«290›­NON-P‘ÿJªARALLEL,–ÕXNON-COPLANAR“CASE’¸iê3DLDFPRÃŽG˜·x«999Ž €n ý•@P‘ÂelseŽ‘5Øâ·fŽ¤ ‘(ÏbrŽ‘2gw«[2Ž‘]±:Ï rstŽ‘|«=‘ÇÏfalseŽ‘v\«;Ž¡‘(ÏbrŽ‘2gw«[2Ž‘]±:Ïse–ÿ}'c“ondŽ‘ nß«=‘Ç0Ž‘Ç;Ž¡‘·gŽ¡‘ÂifŽ‘)´û«(±vŽ‘4½«[3Ž›]–Ç·6«=“ÝINVALID_POINTŽ‘GY«)‘ÏbrŽ‘gs«[3Ž˜]“=“±vŽ‘ûÕ«[3Ž˜]±:Ïis‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘=5O«(±vŽ‘4½«[0Ž˜]±;‘ª¨vŽ‘ße«[1Ž˜]);Ž¡‘ÂelseŽ‘5Øâ·fŽ¡‘(ÏbrŽ‘2gw«[3Ž‘]±:Ï rstŽ‘|«=‘ÇÏfalseŽ‘v\«;Ž¡‘(ÏbrŽ‘2gw«[3Ž‘]±:Ïse–ÿ}'c“ondŽ‘ nß«=‘Ç0Ž‘Ç;Ž¡‘·gŽ¡‘gŽ¡‘ÂifŽ‘´ú«(ÏbrŽ‘ -gs«[0Ž–]±:Ï rstŽ‘^‘8àÏbrŽ‘  S«[1Ž“]±:Ï rstŽ‘µª«)‘·fŽ¡‘ÂifŽ‘+Ϋ(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘}·‘#ÊÝ"TheÈ ÝintersectionÈ ÝofŽ‘n#ŽÈ Ý*thisÈ ÝwithÈ ÝlÈ ÝliesÈ ÝwŽ’×#RithinÈ Ý"Ž’o·Ž¡‘<Ý"theÈ ÝintersectionÈ ÝofŽ’¤ÿÊÈ ÝrÈ ÝwithÈ Ýl.\n"Ž’éÆ «;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(ÏbrŽ‘ -gs«[2Ž–]±:Ï rstŽ‘^‘8àÏbrŽ‘  S«[3Ž“]±:Ï rstŽ‘µª«)‘·fŽ¡‘ÂifŽ‘+qB«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘·‘«‹Ý"TheÈ ÝintersectionÈ ÝofŽ‘n«OÈ ÝrÈ ÝwithÈ ÝlÈ ÝliesÈ ÝwithiŽ’׫nÈ Ý"Ž’íœý·Ž¡‘<Ý"theÈ ÝintersectionÈ ÝofŽ’¤ÿÊÈ Ý*thisÈ ÝwithÈ Ýl.\n"Ž’þÅÿ«;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(ÏbrŽ‘ -gs«[0Ž–]±:Ï rstŽ›_‘8àÏbrŽ‘  S«[1Ž“]±:Ï rstŽ˜·_‘8àÏbrŽ‘  S«[2Ž“]±:Ï rstŽ˜·_‘8àÏbrŽ‘  S«[3Ž“]±:Ï rstŽ‘µª«)‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"TheÈ ÝintersectionsÈ ÝoŽ‘kÆÜfÈ Ý*thisÈ ÝandÈ ÝrÈ ÝwithÈ ÝlŽ’ÔÆ È ÝoverlapÈ Ýpartially.\Ž’=Ædn"Ž’HÌÆ«;Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"TheÈ ÝintersectionsÈ ÝoŽ‘kÆÜfÈ Ý*thisÈ ÝandÈ ÝrÈ ÝwithÈ ÝlŽ’ÔÆ È Ýdon'tÈ ÝoverlapÈ ÝatÈ ÝalŽ’=Ædl.\n"Ž’XŒ½«;Ž¡‘·gŽ¡‘ÂreturnŽ‘7æ¼±vŽ‘=y«;Ž¡‘ -·g‘±=·‘ÿýÂelseŽ‘ØÜ«.‘qÇEnd–UUof“non-parallel,“non-coplanar“case.‘o·±=Ž¡‘ -·gŽ©Â1000.‘ üT‘ÿ +­elseŽ‘!Øà°fŽ¡‘±r0Ž‘!ø߬=‘Ç°Ž‘ÇŽ‘ DZiterŽ‘’¬;Ž¡‘±r1Ž‘!ø߬=‘Ç°Ž‘ÇŽ‘ Ǭ(±iterŽ‘Þ¬+‘8à1Ž‘8á);Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(±bpŽ‘ +Úyµ:±ptŽ– «µ°‘DZr0Ž‘1½°_‘8à±bpŽ‘ Yµ:±ptŽ“°‘DZr1Ž‘ øݬ)‘°fŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘­ifŽ‘)´û¬(±bpŽ‘ +Úyµ:±ptŽ‘ «µ°‘DZr0Ž‘ øݬ)‘±c‘ÿ}'outŽ‘ O°‘Ç´"bp.pt® ´==® ´r0."Ž‘O”n°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘­elseŽ‘4.7ifŽ‘?ã/¬(±bpŽ‘ +Úyµ:±ptŽ‘ «µ°‘DZr1Ž‘ øݬ)‘±c‘ÿ}'outŽ‘ O°‘Ç´"bp.pt® ´==® ´r1."Ž‘O”n°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘°gŽ¡‘±bppŽ‘#öëµ:± rstŽ‘µªµ:±ptŽ‘ «µ¬=‘DZbpŽ‘ ¡‘µ:±ptŽ‘ ä¬;Ž¡‘±bppŽ‘#öëµ:± rstŽ–µªµ:bŽ‘¬=‘DZbpŽ‘ ¡‘µ:±ptŽ‘ äµ:±is‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘=5O¬(±pt0Ž‘i;µ;‘ª¨±pt1Ž‘ã¬)µ:± rstŽ“¬;Ž¡‘­returnŽ‘7æ¼±bppŽ‘GÝ¥¬;Ž¡‘ +°gŽŽŽŒ‹'3þ Šn ý‘ì°x¬1035›¯3DLDF-1.1.5.1’ŠÃPERPENDICULAR–ÕXAND“NON-COPLANAR“CASES˜¬295Ž €n ý•@P­1035.‘ ü¬[²LDF‘T2003.06.24.¬]Ž‘Zˆ6´DEBUGŽ‘x£ä¬is–UUpassed“as“the“±verb‘ÿ}'oseŽ‘'<¬argumen¸ãt“to“±is‘‰ffŽ–®in‘‰ffŽ“triangleŽ‘<äö¬(‘ª®).‘qÇSo,“ifŽ¤ ±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘QŒß¬(›ª®)–Dis“bGeing“debugged,‘Ʊis‘‰ffŽ–®in‘‰ffŽ“triangleŽ‘>g¬(˜)“will“prinš¸ãt“more“information.‘> Ho˜w˜ev˜er,‘Æ´DEBUGŽ‘#Š5¬inŽ¡±is‘‰ffŽ–®in‘‰ffŽ“triangleŽ‘9¡¬(‘ª®)–UUwill“not“bGe“set“to“±trueŽ‘í¬.Ž©°h–ª¨¬De ne‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1023“°i‘Ǭ+°Ž¡‘ +­elseŽŽ¡‘ifŽ‘´ú¬(±bpŽ‘ +Úyµ:±ptŽ‘ äµ:±is‘‰ffŽ–®in‘‰ffŽ“triangleŽ‘9¡¬(±c‘ÿ}'enterŽ‘ ‹µ;‘ª¨±r0Ž– Ümµ;‘ª¨±r1Ž“µ;‘ª¨´DEBUGŽ‘q¬))‘°fŽ¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Intersection® ´point® Ž‘kÆÜ´is® ´within® ´triangle.\Ž’ÔÆ n"Ž’ßͬ;Ž¡‘±bppŽ‘-öìµ:± rstŽ‘µªµ:±ptŽ‘ «µ¬=‘DZbpŽ‘ ¡‘µ:±ptŽ‘ ä¬;Ž¡‘±bppŽ‘-öìµ:± rstŽ–µªµ:bŽ‘¬=‘DZbpŽ‘ ¡‘µ:±ptŽ‘ äµ:±is‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘=5O¬(±pt0Ž‘i;µ;‘ª¨±pt1Ž‘ã¬)µ:± rstŽ“¬;Ž¡‘­returnŽ‘Aæ½±bppŽ‘Qݦ¬;Ž¡‘°gŽ¡‘ +g–UUg‘µ=°‘ÿý¬End“of“\P¸ãerpGendicular“and“non-coplanar“cases".‘o°µ=ŽŸ­1036.‘ üEnd–ÕTof“de nition.Ž¦°h–ª¨¬De ne‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1023“°i‘Ǭ+°Ž¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Exiting® ´Polygon::inŽ‘kÆÜtersection_points().Ž’ÔÆ \n\n"Ž’òT°‘DZ ushŽ‘€¬;Ž¡‘ +­returnŽ‘-æ»±bppŽ‘=ݤ¬;‘qÇ°gŽŸ­1037.‘ üP•®9ath‘ÕTv“ersion.Ž¦°h–ª¨¬Declare‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1022“°i‘Ǭ+°Ž¡‘ +­b•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘[dï±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ’¬ñά(­constŽ‘*¢P®9athŽ‘:[¬&Ž‘AØyµpŽ‘Fày¬)‘UU­constŽ‘*¢¬;ŽŸ­1038.Ž¦°h–ª¨¬De ne‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1023“°i‘Ǭ+°Ž¡‘ +­b•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘[dïP®9olygonŽ’…iá¬::‘±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã¬(­constŽ‘*¢P®9athŽ‘:[¬&Ž‘AØyµpŽ‘Fày¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­ifŽ‘´ú¬(°:µpŽ‘:±is‘‰ffŽ‘®line‘ÿ}'arŽ‘%}¬(‘ª¨))‘°fŽ¡‘±c‘ÿ}'errŽ‘5¼Y°‘°´"ERROR!® ´In® ´Polygon::Ž‘ntintersection_points(Ž’×8const® ´Path&® ´p):\n"Ž’;°Ž¡‘2´"Path® ´p® ´is® ´non-lineaŽ’šÿÉr.® ´Returning® ´INVALIŽ’ÿD_BOOL_POINT_PAIR.\nŽ’lÿQ\n"Ž’€ È°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½´INVALID_BOOL_POINT_PAIRŽ’»,à¬;Ž¡‘°gŽ¡‘­returnŽ‘7æ¼±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ’‰s›¬(µpŽ‘:±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(0Ž‘)µ;‘ª¨pŽ‘²¨:±get‘‰ffŽ–®last‘‰ffŽ“p‘ÿ}'ointŽ‘:$>¬(‘ª¨));Ž¡‘ +°gŽŸ­1039.‘ üInš®9tersection–1mwith“another“P˜olygon.‘ ü¬TO‘ƒ¸DO:–„Explain“what“this“function“doGes“and“ho¸ãw“itŽ¡w¸ãorks.‘qÇ[²LDF‘T2003.06.29.¬]ŽŽ¡‘ +TO‘KDO:–ZFind“out“where“±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘3­Ï¬(‘ª®)“gets“called,›$Œwhen“this“function“is“called,˜and“try“to“pass“±trueŽ‘õL¬as“itsŽ¡±silentŽ‘ i¬argumen¸ãt.‘qÇ[²LDF‘T2003.07.16.¬]ŽŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.06.29.¬]Ž‘Y;Replaced–UUthe“dumm¸ãy“de nition“of“this“function“with“a“real“one.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1022“°i‘Ǭ+°Ž¡‘ +­v®9ectorŽ‘)ªI°h­P•®9oin“tŽ‘šH°i‘UU±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘Tâ4¬(­constŽ‘*¢P®9olygonŽ‘J„å¬&Ž‘RLµrŽ‘W¬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹(AÏ Šn ý‘ì¬296›¯INTERSECTION–ÕXWITH“ANOTHER“­POL‘ÿ +«YGON’Œa-¯3DLDF-1.1.5.1˜°x¬1040Ž €n ý•@P­1040.Ž©°h–ª¨¬De ne‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1023“°i‘Ǭ+°Ž¤ ‘ +­v®9ectorŽ‘)ªI°h­P•®9oin“tŽ‘šH°i‘UU­P®9olygonŽ‘-ZG¬::‘±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã¬(­constŽ‘*¢P®9olygonŽ‘J„å¬&Ž‘RLµrŽ‘W¬)‘UU­constŽ‘*¢°f‘UU­b•QÇo“olŽ‘ö»´DEBUGŽ‘:„,¬=‘DZfalseŽ‘v\¬;Ž¡‘(µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¡‘­v®9ectorŽ‘=ªK°h­P•®9oin“tŽ‘šH°i‘UUµvŽ‘Š¬;Ž¡‘­PlaneŽ‘>6»±plŽ‘J3Þ¬=‘DZget‘‰ffŽ‘®planeŽ‘+>¬(‘ª¨);Ž¡‘­PlaneŽ‘>6»±r‘‰ffŽ‘®plŽ‘Rf¬=‘ǵrŽ‘‘,:±get‘‰ffŽ‘®planeŽ‘(vè¬(‘ª¨);Ž¦‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘(±plŽ‘16µ:±normalŽ‘ V¸µ:±showŽ‘Šÿ¬(´"pl.normal"Ž‘:FG¬);Ž¡‘(±r‘‰ffŽ‘®plŽ‘9—µ:±normalŽ‘ V¸µ:±showŽ‘Šÿ¬(´"r_pl.normal"Ž‘DÆA¬);Ž¡‘(±c‘ÿ}'outŽ‘> S°‘Ç´"pl.distance® ´==® ´"Ž‘_Te°‘DZplŽ‘ ý#µ:±distanc‘ÿ}'eŽ‘' °‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘(±c‘ÿ}'outŽ‘> S°‘Ç´"r_pl.distance® ´==® ´"Ž‘iÔ_°‘DZr‘‰ffŽ‘®plŽ‘⫵:±distanc‘ÿ}'eŽ‘' °‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘°gŽ¦‘­realŽ‘4³1±distanc‘ÿ}'eŽ‘[ÀF¬=‘DZfabsŽ‘ùê¬(±fabsŽ‘2Ò¬(±plŽ‘ 6 µ:±distanc‘ÿ}'eŽ›$Eý¬)–8à°“±fabsŽ‘k²¬(±r‘‰ffŽ‘®plŽ‘“µ:±distanc‘ÿ}'eŽ˜¬));Ž¦‘­ifŽ‘)´û¬(±distanc‘ÿ}'eŽ‘' µ<‘Ç­P•®9oin“tŽ‘ad¬::Ž‘%epsilonŽ‘E^¦¬(‘ª¨))‘±distanc‘ÿ}'eŽ‘, ¬=‘Ç0Ž‘Ç;Ž¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"distance® ´==® ´"Ž‘O”n°‘DZdistanc‘ÿ}'eŽ‘)Ô-°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘­ifŽ‘)´û¬(±plŽ‘ 6 µ:±normalŽ‘#а‘DZr‘‰ffŽ‘®plŽ‘⫵:±normalŽ‘ V¸¬)‘UU°fŽŸ­1041.‘ üCoplanar‘ÕTcase.Ž¦°h–ª¨¬De ne‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1023“°i‘Ǭ+°Ž¡‘ +­ifŽ‘´ù¬(±distanc‘ÿ}'eŽ‘' °‘Ǭ0Ž‘Ç)‘°fŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Coplanar.\n"Ž‘GY¬;Ž¦‘­b•QÇo“olu½‰™šs4Ž‘Ôwp“oin®9tŽ‘L§±bpŽ‘W‚¬;Ž¡‘­P•®9oin“tŽ‘2Ž‘7ï ±ptrŽ‘F,g¬;Ž¡‘­P•®9oin“tŽ‘2Ž‘7ï ±r‘‰ffŽ‘®ptrŽ‘Nï¬;Ž¦‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­P•®9oin“tŽ‘ï°Ž‘#ïži‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘DZp‘ÿ}'ointsŽ–ë­µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZp‘ÿ}'ointsŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘­ifŽ‘)´û¬((±iterŽ‘Þ¬+‘8à1Ž‘8á)–Ç°“±p‘ÿ}'ointsŽ›ë­µ:±endŽ‘ಬ(‘ª¨))‘±ptrŽ‘߬=“±p‘ÿ}'ointsŽ˜µ:±fr‘ÿ}'ontŽ‘I‘¬(‘ª¨);Ž¡‘­elseŽ‘5Øâ±ptrŽ‘FÜÁ¬=‘Ç°Ž‘Ǭ(±iterŽ‘Þ¬+‘8à1Ž‘8á);Ž¡‘­forŽ‘/×C¬(­v®9ectorŽ‘ªH°h­P•®9oin“tŽ‘ÞW°Ž‘#ÞXi‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûr‘‰ffŽ‘®iterŽ‘^ú™¬=‘ǵrŽ–‘,:±p‘ÿ}'ointsŽ›$•µ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);‘î·±r‘‰ffŽ‘®iterŽ‘ fU°6¬=‘ǵrŽ“:±p‘ÿ}'ointsŽ˜µ:±endŽ‘ಬ(‘ª¨);‘n·Ÿÿ³+‘ÿ+ŽŽ‘5×±r‘‰ffŽ‘®iterŽ‘)æ]¬)‘°fŽ¡‘(­ifŽ‘3´ü¬((±r‘‰ffŽ‘®iterŽ‘éf¬+‘8à1Ž‘8á)–Ç°“µrŽ›‘,:±p‘ÿ}'ointsŽ‘$•µ:±endŽ‘ಬ(‘ª¨))‘±r‘‰ffŽ‘®ptrŽ‘ég¬=“µrŽ˜:±p‘ÿ}'ointsŽ‘$•µ:±fr‘ÿ}'ontŽ‘I‘¬(‘ª¨);Ž¡‘(­elseŽ‘?Øã±r‘‰ffŽ‘®ptrŽ‘XÂJ¬=‘Ç°Ž‘Ǭ(±r‘‰ffŽ‘®iterŽ‘éf¬+‘8à1Ž‘8á);Ž¡‘(±bpŽ‘5¡•¬=‘Ç­P•®9oin“tŽ‘ad¬::Ž‘%interse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘s†x¬(°Ž‘Ž‘ +±iterŽ‘˵;‘ª¨°Ž‘ª©±ptrŽ‘çpµ;‘ª¨°Ž‘ª©Ž‘ ªª±r‘‰ffŽ‘®iterŽ‘$[0µ;‘ª¨°Ž‘ª©±r‘‰ffŽ‘®ptrŽ‘Ìø¬);Ž¡‘(­ifŽ‘3´ü¬(±bpŽ– +Úyµ:bŽ‘Jª¬)‘µvŽ‘ +4½:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(±bpŽ“µ:±ptŽ‘ ä¬);Ž¡‘°g‘µ=°‘ÿý¬Inner‘UU­forŽ‘胰µ=Ž¡‘°g‘µ=°‘ÿý¬Outer‘UU­forŽ‘胰µ=Ž¡‘­returnŽ‘7æ¼µvŽ‘=y¬;Ž¡‘ +°gŽŸ­1042.‘ üP®9arallel‘ÕTcase.Ž¦°h–ª¨¬De ne‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1023“°i‘Ǭ+°Ž¡‘ +­elseŽ‘0Øáµ=°‘ÿý¬P¸ãarallel.‘o°µ=Ž¡‘ +°fŽ¡‘±c‘ÿ}'errŽ‘-V–°‘ î´"WARNING!® ´In® ´PolygoŽ‘o ²n::intersection_poinŽ’Ø vts():\n"Ž’ Ç´°Ž¡‘(´"The® ´Polygons® ´lie® ´inŽ’ÿÈ® ´parallel® ´planes.® ´"Ž’ø8Œ°‘ò•´"Returning® ´empty® ´vecŽ‘kòYtor.\n\n"Ž’Ãk&°Ž¡‘(± ushŽ‘=¹¬;Ž¡‘­returnŽ‘7æ¼µvŽ‘=y¬;Ž¡‘ +°gŽ¡‘ +gŽŽŽŒ‹)P Šn ý‘ì°x¬1043›¯3DLDF-1.1.5.1’ªöSNON-P‘ÿJªARALLEL,–ÕXNON-COPLANAR“CASE˜¬297Ž €n ý•@P­1043.– üNon-parallel,‘†Ònon-coplanar‘0case.“µvŽ‘7¬will–‚äconš¸ãtain“the“in˜tersection“pGoin˜ts“of“the“­LineŽ‘^KµlŽ‘'i¬withŽ¤ °Ž‘±thisŽ‘Á‘¬and‘ÕÚµrŽ‘ Ÿî¬,‘5ûif–ÕÚanš¸ãy‘ÿ*ª.‘óWµvŽ‘ýî¬can“con˜tain“a“maxim˜um“of“four“­P•®9oin“tsŽ‘)Ï8¬in“this“case.‘óWµvŽ‘(¬[0Ž›]“and“µvŽ‘ + +—¬[1Ž˜]“will“bGe“theŽ¡in•¸ãtersection›?pGoin“ts˜of˜the˜­LineŽ‘]µlŽ‘"z¬with˜°Ž‘@±thisŽ‘íö¬,‘Ýand˜µvŽ–6ü¬[2Ž‘]˜and˜µvŽ“¬[3Ž‘]˜the˜in•¸ãtersection˜pGoin“ts˜of˜µlŽ‘ 2¸¬and˜µrŽ‘ÌS¬,‘Ýif˜they˜exist.Ž¡If–4Banš¸ãy“in˜tersection“pGoin˜t“došGesn't“exist,‘:ß´INVALID_POINTŽ‘K5b¬will“b˜e“stored“in“the“corresp˜onding“elemen¸ãt“of“µvŽ‘ A¬as“aŽ¡placeholder.‘qÇ[²LDF‘T2003.06.29.¬]ŽŽ¡‘ +The–Ölv‘ÿqÇalues“in“µvŽ‘ +ᕬproš¸ãvide“information“abGout“the“relativ˜e“pGositions“of“the“±PolygonsŽ‘*姬,–ïÎe.g.,“whether–Ölthey“touc˜h,Ž¡whether–EÇlies“within“the“pGerimeter“of“the“other,›Häetc.‘l˜Ho•¸ãw“ev“er,˜it's–EÇnot“pGossible“to“include“this“information“inŽ¡the–ϸreturn“v‘ÿqÇalue,‘îQsince“the“latter“is“merely“a“­v®9ectorŽ‘#z°h­P•®9oin“tŽ‘šH°i¬.‘àðThe“routine“bGeloš¸ãw“ma˜y“need“to“bGe“put“in˜toŽ¡another–ýbfunction“in“order“to“use“this“information.‘iíIt“ma¸ãy“bšGe“of“imp˜ortance“in“breaking“up“±PolygonsŽ‘0 ÿ¬andŽ¡­SolidsŽ‘!\h¬for–UUan“impro•¸ãv“ed–UUsurface“hiding“routine.‘qÇ[²LDF‘T2003.06.29.¬]ŽŽ©°h–ª¨¬De ne‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1023“°i‘Ǭ+°Ž¡‘ +­elseŽ‘!Øà°fŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Non-coplanar,® ´non-pŽ‘kÆÜarallel.\n"Ž’¦ #¬;Ž¦‘­LineŽ‘-­ÚµlŽ‘3£,¬=‘DZplŽ‘ ý#µ:±interse‘ÿ}'ction‘‰ffŽ‘®lineŽ‘Gƒ¦¬(±r‘‰ffŽ‘®plŽ‘“¬);Ž¡‘­b•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘edð±bppŽ‘x"ñ¬=‘DZinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘TS÷¬(µlŽ–.::±p‘ÿ}'ositionŽ‘#DWµ;‘ª¨¬(µlŽ“:±p‘ÿ}'ositionŽ‘%}7¬+‘8àµlŽ‘g:±dir–ÿ}'e“ctionŽ‘&øñ¬));Ž¦‘µvŽ‘4¿:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(±bppŽ‘öéµ:± rstŽ‘µªµ:±ptŽ‘ ä¬);Ž¡‘­ifŽ‘´ú¬(±bppŽ‘öéµ:± rstŽ‘µªµ:±ptŽ‘ «µ°‘DZbppŽ‘¾µ:±se–ÿ}'c“ondŽ‘§Çµ:±ptŽ‘ ä¬)‘°fŽ¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"bpp.first.pt® ´and® ´bpŽ‘kÆÜp.second.pt® ´are® ´equaŽ’ÔÆ l® ´for® ´*this.\n"Ž’$ Û¬;Ž¡‘µvŽ‘#4À:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(´INVALID_POINTŽ‘DÆA¬);Ž¡‘°gŽ¡‘­elseŽ‘+ØáµvŽ‘1 ž:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(±bppŽ‘öéµ:±se–ÿ}'c“ondŽ‘§Çµ:±ptŽ‘ ä¬);Ž¡‘±bppŽ‘&¾¬=‘ǵrŽ‘‘,:±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘QŒß¬(µlŽ–.::±p‘ÿ}'ositionŽ‘#DWµ;‘ª¨¬(µlŽ“:±p‘ÿ}'ositionŽ‘%}7¬+‘8àµlŽ‘g:±dir–ÿ}'e“ctionŽ‘&øñ¬));Ž¡‘µvŽ‘4¿:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(±bppŽ‘öéµ:± rstŽ‘µªµ:±ptŽ‘ ä¬);Ž¡‘­ifŽ‘´ú¬(±bppŽ‘öéµ:± rstŽ‘µªµ:±ptŽ‘ «µ°‘DZbppŽ‘¾µ:±se–ÿ}'c“ondŽ‘§Çµ:±ptŽ‘ ä¬)‘°fŽ¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"bpp.first.pt® ´and® ´bpŽ‘kÆÜp.second.pt® ´are® ´equaŽ’ÔÆ l® ´for® ´r.\n"Ž’ ç¬;Ž¡‘µvŽ‘#4À:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(´INVALID_POINTŽ‘DÆA¬);Ž¡‘°gŽ¡‘­elseŽ‘+ØáµvŽ‘1 ž:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(±bppŽ‘öéµ:±se–ÿ}'c“ondŽ‘§Çµ:±ptŽ‘ ä¬);Ž¡‘­ifŽ‘Ln¬(°:¬(µvŽ‘4½¬[0Ž›]–Ç°6¬=“´INVALID_POINTŽ‘Hõ#°_‘gʵvŽ‘œ‡¬[1Ž˜]“°6¬=“´INVALID_POINTŽ‘Hõ#°_‘gʵvŽ‘œ‡¬[2Ž˜]“°6¬=“´INVALID_POINTŽ‘Hõ#°_‘gʵvŽ‘œ‡¬[3Ž˜]“°6¬=“´INVALID_POINTŽ‘GY¬))Ž¡‘°fŽ¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)Ž¡‘(±c‘ÿ}'outŽ‘>U7°‘ûü´"No® ´intersection® ´poiŽ‘kûÀnts® ´found.® ´"Ž’³½ý°‘ûü´"Returning® ´empty® ´vecŽ‘kûÀtor\n\n"Ž’¾=÷°Ž¡‘<± 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n߬=‘Ç0Ž‘Ç;Ž¡‘°gŽ¡‘gŽ¡‘­ifŽ‘´ú¬(°:¬(µvŽ‘4½¬[0Ž›]–Ç°“´INVALID_POINTŽ‘IÆ9°_‘8àµvŽ‘m¬[1Ž˜]“°“´INVALID_POINTŽ‘GY¬))‘°fŽ¡‘­ifŽ‘)´û¬(µvŽ‘4½¬[2Ž›]–Ç°6¬=“´INVALID_POINTŽ‘GY¬)‘±brŽ‘gs¬[2Ž˜]“=“µvŽ‘ûÕ¬[2Ž˜]µ:±is‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘=5O¬(µvŽ‘4½¬[0Ž˜]µ;‘ª¨vŽ‘ße¬[1Ž˜]);ŽŽŽŒ‹*`¶ Šn ý‘ì¬298›¯NON-P‘ÿJªARALLEL,–ÕXNON-COPLANAR“CASE’ªöS3DLDF-1.1.5.1˜°x¬1043Ž €n ý•@P‘­elseŽ‘5Øâ°fŽ¤ ‘(±brŽ‘2gw¬[2Ž‘]µ:± rstŽ‘|¬=‘DZfalseŽ‘v\¬;Ž¡‘(±brŽ‘2gw¬[2Ž‘]µ:±se–ÿ}'c“ondŽ‘ n߬=‘Ç0Ž‘Ç;Ž¡‘°gŽ¡‘­ifŽ‘)´û¬(µvŽ‘4½¬[3Ž›]–Ç°6¬=“´INVALID_POINTŽ‘GY¬)‘±brŽ‘gs¬[3Ž˜]“=“µvŽ‘ûÕ¬[3Ž˜]µ:±is‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘=5O¬(µvŽ‘4½¬[0Ž˜]µ;‘ª¨vŽ‘ße¬[1Ž˜]);Ž¡‘­elseŽ‘5Øâ°fŽ¡‘(±brŽ‘2gw¬[3Ž‘]µ:± rstŽ‘|¬=‘DZfalseŽ‘v\¬;Ž¡‘(±brŽ‘2gw¬[3Ž‘]µ:±se–ÿ}'c“ondŽ‘ n߬=‘Ç0Ž‘Ç;Ž¡‘°gŽ¡‘gŽ¡‘­ifŽ‘´ú¬(±brŽ‘ +gs¬[0Ž–]µ:± rstŽ‘^‘8à±brŽ‘  S¬[1Ž“]µ:± rstŽ‘µª¬)‘°fŽ¡‘­ifŽ‘+ά(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘}°‘#Ê´"The® ´intersection® ´ofŽ‘n#Ž® ´*this® ´with® ´l® ´lies® ´wŽ’×#Rithin® ´"Ž’o°Ž¡‘<´"the® ´intersection® ´ofŽ’¤ÿÊ® ´r® ´with® ´l.\n"Ž’éÆ 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-«[¬LDF‘T2002.08.07.«]Ž‘Y3Copied–€©the“en¸ãtire“\T‘ÿ*ªransformations"“section“from“Èellipses.web“«and“made“the“appro-Ž¡priate‘UUc¸ãhanges.Ž¡‘ -[¬LDF‘T2003.04.27.«]Ž‘YReThe–Ÿprevious“commenš¸ãt“w˜as“out-of-date.‘PDI‘Ÿlma˜y“ha˜v˜e“remo˜v˜ed“the“transformation“func-Ž¡tions.‘PëA•¸ãt›Ÿ¶an“y˜rate,‘²Othere˜w“ere˜only˜a˜couple˜here.‘PëI‘Ÿ£ha“v“e˜no“w˜copied˜the˜rest˜of˜them˜from˜Èellipses.webŽ¡«and–UUmade“the“appropriate“c¸ãhanges.Ž¡‘ -[¬LDF‘T2003.07.18.«]Ž‘Y;[¬LDF‘T2003.07.18.«]Ž’¨uMo•¸ãv“ed–UU\T‘ÿ*ªransformations"“section,“includingŽ¡ÂopQÇeratorŽ‘+–µ·«=ŽŽŽ‘8]Ô(ÂconstŽ‘T‘ÿ -«ransformŽ‘VØl«&Ž‘^ŸŠ)–ÇÑfrom“ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘IV«to“ÂP®9olygonŽ‘,Ì¿«.‘É:Also“remo•¸ãv“ed–ÇÑthe“ÂRectangleŽ‘9Ï7«v¸ãer-Ž¡sions–UUin“Èrectangs.web«.‘qÇThe“ÂP®9olygonŽ‘/¯˜«vš¸ãersions“are“no˜w“inherited“b˜y“ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘H)^«and“ÂRectangleŽ‘5”ê«.ŽŸŸüÈ„`ÕÁGŽŽ¦Â1001.‘ üApplying–ÕTa“transformation.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.11.06.«]Ž‘ZÛNoš¸ãw–Mõcalling“ÂP®9athŽ‘ß]«::Ž‘$m›ÂopQÇeratorŽ‘PP·«=ŽŽŽ‘\Ëo(‘ª¨)“instead“of“loGoping“through“Ïp‘ÿ}'ointsŽ‘rŠ«.‘[¦This“w˜a˜y‘ÿ*ª,‘Œif“IŽ¡cš¸ãhange‘UUÂP®9athŽ‘潫::Ž‘#tûÂopQÇeratorŽ‘O °·«=ŽŽŽ‘[ÒÏ(‘ª¨),–UUthe“c˜hange“will“automatically“bGe“re ected“here.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂP®9olygonŽ‘/¯˜«functions‘@­978“·i‘Ç«+·ŽŸ ‘ -ÂvirtualŽ‘/ÔT‘ÿ -«ransformŽ‘gV¦opQÇeratorŽ’’í[·«=ŽŽŽ’Ÿ´z(ÂconstŽ‘*¢T‘ÿ -«ransformŽ‘Uót«&Ž‘]º’±tŽ‘aW«);ŽŽŽŒ‹#„³ Šn ý‘ì·x«1002‘­3DLDFPRšÃŽG’ÑOAPPL‘ÿJªYING–ÕXA“TRANSF˜ORMA‘ÿJªTION‘«291Ž €n ý•@PÂ1002.Ž©·h–ª¨«De ne‘UUÂP®9olygonŽ‘/¯˜«functions‘@­979“·i‘Ç«+·Ž¤ ‘ -ÂT‘ÿ -«ransformŽ‘AÈÓP®9olygonŽ‘kÍÅ«::Ž‘r\ÂopQÇeratorŽ’ò¸·«=ŽŽŽ’ª¹×(ÂconstŽ‘*¢T‘ÿ -«ransformŽ‘Uót«&Ž‘]º’±tŽ‘aW«)Ž¡‘ -·fŽ¡‘ÂP®9athŽ‘-‘j«::Ž‘4¨ÂopQÇeratorŽ‘_¶]·«=ŽŽŽ‘l}|(±tŽ‘œr«);Ž¡‘ÂreturnŽ‘7漫(Ïc‘ÿ}'enterŽ‘У·«=ŽŽ‘.^Ú±tŽ‘1ûL«);Ž¡‘ -·gŽŸÂ1003.‘ üRotatation–ÕTaround“the“main“axes.Ž¦·h–ª¨«Declare‘UUÂP®9olygonŽ‘/¯˜«functions‘@­978“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/ÔT‘ÿ -«ransformŽ‘gV¦Ïr‘ÿ}'otateŽ’Åä«(ÂconstŽ‘*¢realŽ‘4ÝбxŽ‘:”ì;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±yŽ‘>’ˆ«=‘Ç0Ž–DZ;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±zŽ‘>f®«=‘Ç0Ž“);ŽŸÂ1004.Ž¦·h–ª¨«De ne‘UUÂP®9olygonŽ‘/¯˜«functions‘@­979“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ -«ransformŽ‘AÈÓP®9olygonŽ‘kÍÅ«::‘Ïr‘ÿ}'otateŽ‘oB«(ÂconstŽ‘*¢realŽ‘4ÝбxŽ‘:”ì;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±yŽ‘;Ëp;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±zŽ‘;Ÿ–«)Ž¡‘ -·fŽ¡‘ÂT‘ÿ -«ransformŽ‘KÈÔ±tŽ‘OeF«;Ž¦‘±tŽ‘œt:Ïr‘ÿ}'otateŽ‘o>«(±xŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁÆ«);Ž¡‘ÂreturnŽ‘7漫(·Ž‘ÏthisŽ‘²Ï·«=ŽŽ‘(A±tŽ‘+Ýx«);Ž¡‘ -·gŽ¤Â1005.‘ üRotate–ÕTaround“an“arbitrary“axis.Ž¡1006.‘ üP•®9oin“t‘ÕTargumen“ts.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ -«[¬LDF‘T2003.05.02.«]Ž‘YËSChanged–mname“of“this“function“from“Ïr–ÿ}'otate‘‰ffŽ‘®ar“oundŽ‘@„ü«(›ª®)“to“Ïr‘ÿ}'otateŽ‘‡««(˜).‘»This“function“no¸ãwŽ¡o•¸ãv“erloads‘UUÏr‘ÿ}'otateŽ‘Ä“«(‘ª®)–UUwith“three“ÂrealŽ‘ƒ«argumen¸ãts.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂP®9olygonŽ‘/¯˜«functions‘@­978“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/ÔT‘ÿ -«ransformŽ‘gV¦Ïr‘ÿ}'otateŽ’Åä«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]Ïp0Ž‘Pø±;‘ª¨ÂconstŽ‘ÕJP•®9oin“tŽ‘>Äç«&Ž‘FŒÏp1Ž‘R¢Å±;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆxÏangleŽ‘Qã«=‘Ç180ŽŽ‘Ç);ŽŸÂ1007.Ž¦·h–ª¨«De ne‘UUÂP®9olygonŽ‘/¯˜«functions‘@­979“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ -«ransformŽ‘AÈÓP®9olygonŽ‘kÍÅ«::‘Ïr‘ÿ}'otateŽ‘oB«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]Ïp0Ž‘Pø±;‘ª¨ÂconstŽ‘ÕJP•®9oin“tŽ‘>Äç«&Ž‘FŒÏp1Ž‘R¢Å±;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆxÏangleŽ‘NHË«)Ž¡‘ -·fŽ¡‘ÂT‘ÿ -«ransformŽ‘KÈÔ±tŽ‘OeF«;Ž¦‘±tŽ‘œt:Ïr‘ÿ}'otateŽ‘o>«(Ïp0Ž‘ À±;‘ª¨Ïp1Ž‘ Áh±;‘ª¨ÏangleŽ‘jû«);Ž¡‘ÂreturnŽ‘7漫(·Ž‘ÏthisŽ‘²Ï·«=ŽŽ‘(A±tŽ‘+Ýx«);Ž¡‘ -·gŽŸÂ1008.‘ üP•®9ath‘ÕTargumen“t.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.05.02.«]Ž‘YËSChanged–mname“of“this“function“from“Ïr–ÿ}'otate‘‰ffŽ‘®ar“oundŽ‘@„ü«(›ª®)“to“Ïr‘ÿ}'otateŽ‘‡««(˜).‘»This“function“no¸ãwŽ¡o•¸ãv“erloads‘UUÏr‘ÿ}'otateŽ‘Ä“«(‘ª®)–UUwith“three“ÂrealŽ‘ƒ«argumen¸ãts.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂP®9olygonŽ‘/¯˜«functions‘@­978“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/ÔT‘ÿ 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«=‘Ç1Ž“);ŽŸÂ1011.Ž¦·h–ª¨«De ne‘UUÂP®9olygonŽ‘/¯˜«functions‘@­979“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ -«ransformŽ‘AÈÓP®9olygonŽ‘kÍÅ«::‘Ïsc‘ÿ}'aleŽ‘´ö«(ÂrealŽ‘³.±xŽ‘jJ;‘ª¨ÂrealŽ‘]Ö±yŽ‘ Î;‘ª¨ÂrealŽ‘]Ö±zŽ‘tô«)Ž¡‘ -·fŽ¡‘ÂT‘ÿ -«ransformŽ‘KÈÔ±tŽ‘OeF«;Ž¦‘±tŽ‘œt:Ïsc‘ÿ}'aleŽ‘´ò«(±xŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁÆ«);Ž¡‘ÂreturnŽ‘7漫(·Ž‘ÏthisŽ‘²Ï·«=ŽŽ‘(A±tŽ‘+Ýx«);Ž¡‘ -·gŽŸÂ1012.‘ üShear.Ž¦·h–ª¨«Declare‘UUÂP®9olygonŽ‘/¯˜«functions‘@­978“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/ÔT‘ÿ -«ransformŽ‘gV¦Ïshe‘ÿ}'arŽ‘Šà«(ÂrealŽ‘³.ÏxyŽ‘!—±;‘ª¨ÂrealŽ‘]ÖÏxzŽ‘%œÀ«=‘Ç0Ž–DZ;‘ª¨ÂrealŽ‘]ÖÏyxŽ‘&Zœ«=‘Ç0Ž“±;‘ª¨ÂrealŽ‘]ÖÏyzŽ‘%Ô6«=‘Ç0Ž“±;‘ª¨ÂrealŽ‘]ÖÏzxŽ‘%–Y«=‘Ç0Ž“±;‘ª¨ÂrealŽ‘]ÖÏzyŽ‘%|«=‘Ç0Ž“);ŽŸÂ1013.Ž¦·h–ª¨«De ne‘UUÂP®9olygonŽ‘/¯˜«functions‘@­979“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ -«ransformŽ‘AÈÓP®9olygonŽ‘kÍÅ«::‘Ïshe‘ÿ}'arŽ‘4>«(ÂrealŽ‘³.ÏxyŽ‘!—±;‘ª¨ÂrealŽ‘]ÖÏxzŽ‘"Õ¨±;‘ª¨ÂrealŽ‘]ÖÏyxŽ‘#“„±;‘ª¨ÂrealŽ‘]ÖÏyzŽ‘# ±;‘ª¨ÂrealŽ‘]ÖÏzxŽ‘"ÏA±;‘ª¨ÂrealŽ‘]ÖÏzyŽ‘"´ð«)Ž¡‘ -·fŽ¡‘ÂT‘ÿ -«ransformŽ‘KÈÔ±tŽ‘OeF«;Ž¦‘±tŽ‘œt:Ïshe‘ÿ}'arŽ‘4:«(ÏxyŽ‘ -ãç±;‘ª¨ÏxzŽ‘ "z±;‘ª¨ÏyxŽ‘ àV±;‘ª¨ÏyzŽ‘ Yð±;‘ª¨ÏzxŽ‘ ±;‘ª¨ÏzyŽ‘ «);Ž¡‘ÂreturnŽ‘7漫(·Ž‘ÏthisŽ‘²Ï·«=ŽŽ‘(A±tŽ‘+Ýx«);Ž¡‘ -·gŽ¤Â1014.‘ üShift.Ž¡1015.‘ üreal‘ÕTargumen®9ts.Ž¦·h–ª¨«Declare‘UUÂP®9olygonŽ‘/¯˜«functions‘@­978“·i‘Ç«+·ŽŸ ‘ -ÂvirtualŽ‘/ÔT‘ÿ -«ransformŽ‘gV¦ÏshiftŽ‘{t#«(ÂrealŽ‘³.±xŽ‘jJ;‘ª¨ÂrealŽ‘]Ö±yŽ‘ gæ«=‘Ç0Ž–DZ;‘ª¨ÂrealŽ‘]Ö±zŽ‘ < «=‘Ç0Ž“);ŽŽŽŒ‹%ž´ Šn ý‘ì·x«1016›­3DLDFPR•ÃŽG’í’ÂREAL‘ÕX­AR“GUMENTS˜«293Ž €n ý•@PÂ1016.Ž©·h–ª¨«De ne‘UUÂP®9olygonŽ‘/¯˜«functions‘@­979“·i‘Ç«+·Ž¤ ‘ -ÂT‘ÿ -«ransformŽ‘AÈÓP®9olygonŽ‘kÍÅ«::‘ÏshiftŽ‘«(ÂrealŽ‘³.±xŽ‘jJ;‘ª¨ÂrealŽ‘]Ö±yŽ‘ Î;‘ª¨ÂrealŽ‘]Ö±zŽ‘tô«)Ž¡‘ -·fŽ¡‘ÂT‘ÿ -«ransformŽ‘KÈÔ±tŽ‘OeF«;Ž¦‘±tŽ‘œt:ÏshiftŽ‘}«(±xŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁÆ«);Ž¡‘ÂreturnŽ‘7漫(·Ž‘ÏthisŽ‘²Ï·«=ŽŽ‘(A±tŽ‘+Ýx«);Ž¡‘ -·gŽŸÂ1017.‘ üP•®9oin“t‘ÕTargumen“t.Ž¦·h–ª¨«Declare‘UUÂP®9olygonŽ‘/¯˜«functions‘@­978“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/ÔT‘ÿ -«ransformŽ‘gV¦ÏshiftŽ‘{t#«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]±pŽ‘Ié]«);ŽŸÂ1018.Ž¦·h–ª¨«De ne‘UUÂP®9olygonŽ‘/¯˜«functions‘@­979“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ -«ransformŽ‘AÈÓP®9olygonŽ‘kÍÅ«::‘ÏshiftŽ‘«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]±pŽ‘Ié]«)Ž¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼ÏshiftŽ‘L9«(±pŽ‘:Ïget‘‰ffŽ‘®xŽ‘Žg«(–ª¨)±;“pŽ›²¨:Ïget‘‰ffŽ‘®yŽ‘t«(“)±;“pŽ˜:Ïget‘‰ffŽ‘®zŽ‘«(“));Ž¡‘ -·gŽ¤Â1019.‘ üShift‘ÕTtimes.Ž¡1020.‘ üreal‘ÕTargumen®9ts.Ž¦·h–ª¨«Declare‘UUÂP®9olygonŽ‘/¯˜«functions‘@­978“·i‘Ç«+·ŽŸ ‘ -ÂvirtualŽ‘/Ôv®9oidŽ‘H‹¬Ïshift‘‰ffŽ‘®timesŽ‘wwç«(ÂrealŽ‘³.±xŽ‘jJ;‘ª¨ÂrealŽ‘]Ö±yŽ‘ gæ«=‘Ç1Ž–DZ;‘ª¨ÂrealŽ‘]Ö±zŽ‘ < «=‘Ç1Ž“);Ž¡Â1021.Ž¦·h–ª¨«De ne‘UUÂP®9olygonŽ‘/¯˜«functions‘@­979“·i‘Ç«+·Ž¤ ‘ -Âv®9oidŽ‘"ýÙP®9olygonŽ‘MË«::‘Ïshift‘‰ffŽ‘®timesŽ‘/ì?«(ÂrealŽ‘³.±xŽ‘jJ;‘ª¨ÂrealŽ‘]Ö±yŽ‘ Î;‘ª¨ÂrealŽ‘]Ö±zŽ‘tô«)Ž¡‘ -·fŽ¡‘ÂP®9athŽ‘-‘j«::Ž‘4¨Ïshift‘‰ffŽ‘®timesŽ‘c ã«(±xŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁÆ«);Ž¡‘Ïc‘ÿ}'enterŽ‘0 ±:Ïshift‘‰ffŽ‘®timesŽ‘.ì;«(±xŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁÆ«);Ž¡‘ÂreturnŽ‘4‘g«;Ž¡‘ -·gŽŸÂ1022.‘ üP•®9oin“t‘ÕTargumen“t.Ž¦·h–ª¨«Declare‘UUÂP®9olygonŽ‘/¯˜«functions‘@­978“·i‘Ç«+·Ž¡‘ 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-[¬LDF‘T2003.04.15.«]Ž‘Y¹TO‘DO:–3Add“Ïin‘‰ffŽ‘®cir‘ÿ}'cleŽ‘(È|«(–ª®),‘2kÏout‘‰ffŽ‘®cir‘ÿ}'cleŽ‘.#«(“).‘„bAlign–3a“line“from“Ïc‘ÿ}'enterŽ‘$ñ«in“the“direction“of“aŽ¡normal–UUwith“the“y-axis.‘qÇUse“the“in•¸ãv“erse–UUof“the“ÂT‘ÿ -«ransformŽ‘;'«to“transform“the“ÂCircleŽ‘!¸«.Ž¦‘ -ÂformatŽ‘3c(ÏR–ÿ}'e“g‘‰ffŽ‘®PolygonŽ‘rÊ'PolygonŽŽŸÂ1025.› üReg‘°¡‰ffs4Ž‘#ÕP®9olygon–ÕTclass“de nition.˜Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘PT«is–UUderiv¸ãed“from“ÂP®9olygonŽ‘,ZC«.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.04.15.«]Ž‘XÐChanged,›(fso–*that“ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘G¹«is“deriv¸ãed“from“ÂP®9athŽ‘®Ž«.‘_Previously‘ÿ*ª,˜it“wš¸ãas“deriv˜ed“fromŽ¡ÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘h÷˜«.Ž¡‘ -[¬LDF‘T2003.04.27.«]Ž‘XÉWChanged‘qÂprotectedŽ‘6œz«data–qmem¸ãbšGers“to“Âpriv‘ÿ\rateŽ‘&¾ï«.‘\ÑThey“no“longer“need“to“b˜e“ÂprotectedŽ‘3† «,Ž¡bGecause‘UUÂRectangleŽ‘8ê?«is–UUno“longer“deriv¸ãed“from“ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘DÔ «.Ž¡‘ 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-«(±eŽ‘¨:Ïp‘ÿ}'ointsŽ‘$•«[0Ž‘])“lies“on“the“x-axis.Ž¡Then,›a!it–^Åplugs“the“x“and“z-coGordinates“of“the“ÂP•®9oin“tsŽ‘&á«on“±eŽ‘ e‹«in¸ãto“the“ellipse“equation,˜i.e.,˜±xŸü^ÿ®2Ž‘|s±=aŸü^ÿ®2Ž‘»ž«+‘?+±zp—Ÿü^ÿ®2Ž‘í -±=bŸü^ÿ®2Ž‘SE«=‘ÖÒ1,Ž¡where–t±a“«is“half“of“the“horizonš¸ãtal“axis“of“the“ellipse,‘{±and“±b“«is“half“of“the“v˜ertical“axis.‘ÍØLet“±r‘AZ«=‘ú=±xŸü^ÿ®2Ž‘|s±=aŸü^ÿ®2Ž‘ÉÈ«+‘MU±zp—Ÿü^ÿ®2Ž‘í -±=bŸü^ÿ®2ŽŽ¡«and–ù’±“«stand“for“the“return“v‘ÿqÇalue“of“ÂP•®9oin“tŽ‘“Þ«::‘ÏepsilonŽ‘ o«(›ª®).‘S1If“·j±r‘Èx·‘[«1·j–DZ>“–ù’«for“an¸ãy“of“the“ÂP•®9oin“tsŽ‘&¨«on“±eŽ‘¡“«,‘ ìÏis‘‰ffŽ‘®el‘‚Øliptic‘ÿ}'alŽ‘3ø‚«(˜)Ž¡returns‘UUÏfalseŽ‘™«,–UUotherwise“it“returns“ÏtrueŽ‘í«.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.07.20.«]Ž‘Y;Added–UUthis“function.Ž¡‘ -[¬LDF‘T2003.07.25.«]Ž‘Y;No•¸ãw›UUc“hec“king˜ÏnormalŽ‘&s%·‘ÇÝINVALID_POINTŽ‘GY«.‘qÇIf˜it˜is,˜Ïis‘‰ffŽ‘®el‘‚Øliptic‘ÿ}'alŽ‘4Aë«(‘ª®)˜returns˜ÏfalseŽ‘™«.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·Ž¡‘ -Âb•QÇo“olŽ‘#¡gÏis‘‰ffŽ‘®el‘‚Øliptic‘ÿ}'alŽ‘Tý«(‘ª®)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹=Áã Šn ý‘ì·x«1127–­3DLDFPRÃŽG’äŸIS‘ÕXELLIPTICAL“«317Ž €n ý•@PÂ1127.Ž©·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¤ ‘ -Âb•QÇo“olŽ‘#¡gEllipseŽ‘FŠD«::‘Ïis‘‰ffŽ‘®el‘‚Øliptic‘ÿ}'alŽ‘1ìš«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·–ÿý«true“·±=Ž¡‘ÂP•®9oin“tŽ‘2ïŸÏnormalŽ‘V o«=‘ÇÏget‘‰ffŽ‘®normalŽ‘3QŒ«(‘ª¨);Ž¦‘ÂifŽ‘´ú«(ÏnormalŽ‘#з‘ÇÝINVALID_POINTŽ‘GY«)‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)Ž¡‘(Ïc‘ÿ}'errŽ‘=”Ü·‘ß2Ý"InÈ ÝEllipse::is_elliŽ‘kÞöptical():È Ý"Ž’©o·‘ß2Ý"get_normal()È ÝreturnŽ‘kÞöedÈ ÝINVALID_POINT."Ž’ÍÄZ·Ž¡‘<Ïend‘‚ØlŽ‘R¸à·‘ÇÝ"*thisÈ ÝisÈ Ýnon-planarŽ‘kÆÜ.È ÝReturningÈ Ýfalse."Ž’ÒÔ#·‘ÇÏend‘‚ØlŽ–ò·‘ÇÏend‘‚ØlŽ“·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½ÏfalseŽ‘V–«;Ž¡‘·gŽ¦‘ÂEllipseŽ‘9>0±eŽ‘@­I«=‘Ç·Ž‘ÇÏthisŽ‘²Ï«;Ž¦‘ÏnormalŽ‘4Vº±:ÏshiftŽ‘}«(Ïc‘ÿ}'enterŽ‘ ‹«);Ž¦‘ÂT‘ÿ -«ransformŽ‘KÈÔ±tŽ‘OeF«;Ž¦‘±tŽ‘œt:Ïalign‘‰ffŽ–®with‘‰ffŽ“axisŽ‘@²x«(Ïc‘ÿ}'enterŽ‘ ‹±;‘ª¨ÏnormalŽ‘"`±;‘ª¨Ý'y'Ž‘ñ«);Ž¡‘±eŽ‘¨:Ïdo‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘9š4«(±tŽ‘œr«);Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘±eŽ‘ ¨:ÏshowŽ‘Šÿ«(Ý"eÈ ÝafterÈ Ýalignment:"Ž‘i†,«);Ž¦‘ÂP•®9oin“tŽ‘2ïŸÏx‘‰ffŽ–®axis‘‰ffŽ“ptŽ‘Y»¼«(1Ž‘);Ž¡‘ÂP•®9oin“tŽ‘2ïŸÏp0Ž‘AÍw«=‘DZeŽ‘o:Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH«(0Ž‘);Ž¡‘ÂrealŽ‘*³0ÏangŽ‘>4î«=‘ÇÏp0Ž‘Ýر:ÏangleŽ‘ÀS«(Ïx‘‰ffŽ–®axis‘‰ffŽ“ptŽ‘&Ì«);Ž¦‘±tŽ‘œt:Ïr‘ÿ}'esetŽ‘Æ·«(‘ª¨);Ž¡‘±tŽ‘œt:Ïr‘ÿ}'otateŽ‘o>«(0Ž‘±;‘ª¨ÏangŽ‘eN«);Ž¡‘Ïp0Ž‘"ÝÚ·«=ŽŽ‘2l±eŽ‘7:Ïdo‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘9š4«(±tŽ‘œr«);Ž¡‘Ïp0Ž‘ ±:Ïunit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u«(ÏtrueŽ‘Ę«);Ž¡‘ÂifŽ‘´ú«(Ïp0Ž‘ÝØ·6«=‘ÇÏx‘‰ffŽ–®axis‘‰ffŽ“ptŽ‘)“5«)‘·fŽ¡‘±tŽ‘!œu:Ïr‘ÿ}'esetŽ‘Æ·«(‘ª¨);Ž¡‘±tŽ‘!œu:Ïr‘ÿ}'otateŽ‘o>«(0Ž‘±;‘ª¨·Ž‘ qÆ«2Ž‘ª§·‘8àÏangŽ‘ó†«);Ž¡‘±eŽ‘"¨:Ïdo‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘9š4«(±tŽ‘œr«);Ž¡‘·gŽ¡‘Ïp0Ž‘"ÝÚ«=‘DZeŽ‘o:Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH«(0Ž‘);Ž¡‘Ïp0Ž‘ ±:Ïunit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u«(ÏtrueŽ‘Ę«);Ž¡‘ÂifŽ‘´ú«(Ïp0Ž‘ÝØ·6«=‘ÇÏx‘‰ffŽ–®axis‘‰ffŽ“ptŽ‘)“5«)‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)Ž¡‘(Ïc‘ÿ}'errŽ‘=”Ü·‘ß2Ý"ERROR!È ÝInÈ Ýis_elliptŽ‘kÞöical():\n"Ž’£Är·‘ß2Ý"RotationÈ Ýfailed.\nRŽ‘kÞöeturningÈ Ýfalse\n\n"Ž’ÓW·Ž¡‘<Ï ushŽ‘Q¹«;Ž¡‘ÂreturnŽ‘Aæ½ÏfalseŽ‘V–«;Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘±eŽ‘ ¨:ÏshowŽ‘Šÿ«(Ý"eÈ ÝafterÈ ÝrotationÈ ÝinŽ‘hÿÄÈ Ýx-zÈ Ýplane:"Ž’¨†«);Ž¦‘ÂrealŽ‘*³0±xŽ‘0jL«;Ž¡‘ÂrealŽ‘*³0±zŽ‘/ÊN«;Ž¡‘ÂrealŽ‘*³0±aŽ‘2Ãx«=‘Ç(±eŽ‘¨:Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH«(0Ž‘)–8à·“±eŽ‘àá:Ïget‘‰ffŽ‘®c‘ÿ}'enterŽ‘,=G«(–ª¨))±:ÏmagnitudeŽ‘.=r«(“);Ž¡‘ÂrealŽ‘*³0±bŽ‘1Äò«=‘Ç(±eŽ‘¨:Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH«(Ïnumb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜ointsŽ‘JÀ©±=«4Ž‘)–8à·“±eŽ‘àá:Ïget‘‰ffŽ‘®c‘ÿ}'enterŽ‘,=G«(–ª¨))±:ÏmagnitudeŽ‘.=r«(“);Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"aÈ Ý==È Ý"Ž‘*Ôƒ·‘DZaŽ‘ -×`·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"bÈ Ý==È Ý"Ž‘*Ôƒ·‘DZbŽ‘ ØÚ·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¦‘ÂrealŽ‘*³0±rŽ‘/}D«;Ž¡‘Âin®9tŽ‘%¤ù±iŽ‘+Þ«=‘Ç0Ž‘Ç;ŽŽŽŒ‹>ÏÆ Šn ý‘ì«318–­IS‘ÕXELLIPTICAL’äŸ3DLDFPRÃŽG“·x«1127Ž €n ý•@P‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂP•®9oin“tŽ‘ï·Ž‘#ïži‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W«=‘DZeŽ–o:Ïp‘ÿ}'ointsŽ›$•±:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);‘ÿýÏiterŽ‘’·6«=‘DZeŽ“:Ïp‘ÿ}'ointsŽ˜±:ÏendŽ‘ಫ(‘ª¨);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¤ ‘±xŽ‘&~7«=‘Ç(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïget‘‰ffŽ‘®xŽ‘Žg«(‘ª¨);Ž¡‘±zŽ‘%Þ9«=‘Ç(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïget‘‰ffŽ‘®zŽ‘«(‘ª¨);Ž¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÝ"PointÈ Ý"Ž‘0€·‘DZiŽ‘ $·‘ÇÝ":È Ý"Ž‘Œ·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘((·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:ÏshowŽ‘Šÿ«(Ý"iter:"Ž‘%FS«);Ž¡‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÝ"xÈ Ý==È Ý"Ž‘*Ôƒ·‘DZxŽ‘ EL·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÝ"zÈ Ý==È Ý"Ž‘*Ôƒ·‘DZzŽ‘ -¥N·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¡‘±rŽ‘%‘/«=‘Ç((±xŽ–ïü·‘8à±xŽ“«)±=«(±aŽ–‚·‘8à±aŽ“«))–8à+“((±zŽ›Oþ·“±zŽ˜«)±=«(±bŽ›ƒŠ·“±bŽ˜«));Ž¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"rÈ Ý==È Ý"Ž‘*Ôƒ·‘DZrŽ‘ -XD·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ÂifŽ‘)´û«(ÏfabsŽ‘2Ò«(±rŽ‘ô·‘8à«1Ž‘8á)–DZ>“ÂP•®9oin“tŽ‘ad«::Ž‘%ï¢ÏepsilonŽ‘E^¦«(‘ª¨))‘·fŽ¡‘(ÂifŽ‘4r3«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘[ª·‘sÝ"PointÈ Ý"Ž‘2‹6·‘s±iŽ‘ vÚ·‘sÝ"È Ýdoesn'tÈ ÝsatisfyÈ ÝelŽ‘m7lipseÈ Ýequation.\n"Ž’Ð -Ü·Ž¡‘FÝ"ReturningÈ Ýfalse.\n\Ž’®ÿËn"Ž’¼ÍE·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾ÏfalseŽ‘`–«;Ž¡‘·gŽ¡‘€Ÿÿ®+‘ÿ+ŽŽ‘*G#±iŽ‘-¹«;Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)Ž¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"ExitingÈ ÝEllipse::isŽ‘kÆÜ_elliptical().È ÝRetuŽ’ÔÆ rningÈ Ýtrue."Ž’ü·‘ÇÏend‘‚ØlŽ–ò·‘ÇÏend‘‚ØlŽ“·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘7æ¼ÏtrueŽ‘J«T«;Ž¡‘ -·gŽ©Â1128.‘ üIs‘ÕTquadratic.ŽŸ·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·Ž¡‘ -ÂinlineŽ‘)ŠIb•QÇo“olŽ‘C+¯Ïis‘‰ffŽ‘®quadr‘ÿ}'aticŽ‘w£«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼ÏtrueŽ‘J«T«;Ž¡‘ -·gŽ¦Â1129.‘ üIs‘ÕTcubic.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.07.27.«]Ž‘Y;Made‘UUÂvirtualŽ‘(ã(«and‘UUnon-inline.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·ŽŸ ‘ -ÂvirtualŽ‘/Ôb•QÇo“olŽ‘I/:Ïis‘‰ffŽ‘®cubicŽ‘kT^«(‘ª®)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹?Ý Šn ý‘ì·x«1130–­3DLDFPRÃŽG’7l‰IS‘ÕXCUBIC“«319Ž €n ý•@PÂ1130.Ž©·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¤ ‘ -Âb•QÇo“olŽ‘#¡gEllipseŽ‘FŠD«::‘Ïis‘‰ffŽ‘®cubicŽ‘#%(«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼ÏfalseŽ‘L–«;Ž¡‘ -·gŽŸÂ1131.‘ üIs‘ÕTquartic.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.07.27.«]Ž‘Y;Made‘UUÂvirtualŽ‘(ã(«and‘UUnon-inline.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/Ôb•QÇo“olŽ‘I/:Ïis‘‰ffŽ‘®quarticŽ‘sa'«(‘ª®)‘UUÂconstŽ‘*¢«;ŽŸÂ1132.Ž¦·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¡‘ -Âb•QÇo“olŽ‘#¡gEllipseŽ‘FŠD«::‘Ïis‘‰ffŽ‘®quarticŽ‘+1ñ«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼ÏfalseŽ‘L–«;Ž¡‘ -·gŽŸÂ1133.– üSolv®9e.“«[¬LDF‘T2002.11.06.«]Ž‘ZÌÏsolveŽ‘pO—«(‘ª®)–äëassumes“that“the“ÂEllipseŽ‘'²¯«lies“in“a“ma‘Ž8jor“plane“with“its“cen¸ãter“atŽ¡the–ãÿorigin.›LCoGde“that“calls“it“m¸ãust“ensure“that“these“conditions“are“ful lled.˜ÏsolveŽ‘ƒË«(‘ª®)“returns“the“t•¸ãw“o‘ãÿpGossibleŽ¡v‘ÿqÇalues–UUfor“either“the“horizonš¸ãtal“or“the“v˜ertical“coGordinate.Ž¡‘ -TO–UUDO:“Read“through,“and“then“explain“this“function.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.07.20.«]Ž‘XŠ No¸ãw–×'using“Ïget‘‰ffŽ–®axis‘‰ffŽ“vŽ‘-ÐÁ«(›ª®)“and“Ïget‘‰ffŽ–®axis‘‰ffŽ“hŽ‘.p«(˜),‘ðcinstead“of“accessing“Ïaxis‘‰ffŽ‘®hŽ‘ §Û«and“Ïaxis‘‰ffŽ‘®vŽ‘ t,«directly‘ÿ*ª.Ž¡‘ -[¬LDF‘T2003.07.25.«]Ž‘Y;Remo•¸ãv“ed–UUsome“commenš¸ãted-out“coGde,“and“an“explanatory“commen˜t.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·Ž¡‘ -Ârealu½‰™šs4Ž‘ÔwpairŽ‘9p‚ÏsolveŽ‘O¨M«(Âc®9harŽ‘jIÏaxis‘‰ffŽ‘®unknownŽ‘UÞ±;‘ª¨ÂrealŽ‘]ÖÏknownŽ‘5>¢«)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹@眠Šn ý‘ì«320–­SOL‘ÿ8VE’Aë'3DLDFPRÃŽG“·x«1134Ž €n ý•@PÂ1134.Ž©·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¤ ‘ -Ârealu½‰™šs4Ž‘ÔwpairŽ‘9p‚EllipseŽ‘\Y_«::‘ÏsolveŽ‘7Ï«(Âc®9harŽ‘jIÏaxis‘‰ffŽ‘®unknownŽ‘UÞ±;‘ª¨ÂrealŽ‘]ÖÏknownŽ‘5>¢«)‘UUÂconstŽ‘*¢·f‘UUÂrealŽ‘ƒÏr‘ÿ}'adius‘‰ffŽ‘®knownŽ‘U -Š«;Ž¡‘ÂrealŽ‘4³1Ïr‘ÿ}'adius‘‰ffŽ‘®unknownŽ‘z²\«;Ž¦‘Ïaxis‘‰ffŽ‘®unknownŽ‘]:ë«=‘ÇÏtolowerŽ‘#í«(Ïaxis‘‰ffŽ‘®unknownŽ‘“Ïr‘ÿ}'adius‘‰ffŽ‘®knownŽ‘=É«)‘·fŽ¡‘(ÂreturnŽ‘Kæ¾ÝINVALID_REAL_PAIRŽ’¥¬ó«;Ž¡‘·gŽŽŽŒ‹Aï Šn ý‘ì·x«1135–­3DLDFPRÃŽG’Aë'SOL‘ÿ8VE“«321Ž €n ý•@PÂ1135.‘ ü«The–UUequation“for“an“ellipse“in“the“x-y“plane“with“its“cen¸ãter“at“the“origin“isŽ¤’ÃY¯±xŸûÞÿ®2Ž‘|s±=aŸûÞÿ®2Ž‘µS«+‘8à±y[ÙŸûÞÿ®2Ž‘ØL±=bŸûÞÿ®2Ž‘C‹«=‘Ç1Ž¡where–UU±a“«is“half“the“horizonš¸ãtal“axis“and“±b“«is“half“the“v˜ertical“axis.‘qÇTherefore,Ž¡’¹ë±y‘"ñ«=‘ÇŸöö5½pŽ‘ ÇŸöö5‰feFù+Ÿ Ë«(1–8à·“±xŸýr®2Ž–|s±=aŸýr®2Ž“«)–8à·“±bŸýr®2ŽŽŽŽŽ¡«andŽ¤ ’·´\±x–Ç«=“Ÿöö5½pŽ‘ ÇŸöö5‰feF…Ÿ Ë«(1–8à·“±y[ÙŸýr®2Ž‘ØL±=bŸýr®2Ž‘|s«)“·“±aŸýr®2ŽŽŽŽ‘SL ±:ŽŸ·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¡‘ -±rŽ‘Ê:Ï rstŽ‘|«=‘ÇÏsqrtŽ‘w«((1Ž‘‰Ä·–‰Ã«((ÏknownŽ›j·“ÏknownŽ˜«)±=«(Ïr‘ÿ}'adius‘‰ffŽ‘®knownŽ›;‹Ê·“Ïr‘ÿ}'adius‘‰ffŽ‘®knownŽ˜«)))“·“«(Ïr‘ÿ}'adius‘‰ffŽ‘®unknownŽ›Fˆî·“Ïr‘ÿ}'adius‘‰ffŽ‘®unknownŽ˜«));Ž¡‘ -±rŽ‘Ê:Ïse–ÿ}'c“ondŽ‘ nß«=‘Ç·Ž‘ -Ž6±rŽ‘XJ:Ï rstŽ‘µª«;Ž¡‘ -ÂreturnŽ‘-æ»±rŽ‘2°Ï«;‘qÇ·gŽŸÂ1136.– üGet‘ôcoQÇecien®9ts.“«This–Dis“used“for“getting“the“coGecien¸ãts“of“the“quadratic“equation“that“resultsŽ¡from–0ÿreplacing“±y‘ŒØ«with“±mx–ËQ«+“±b–0ÿ«from“the“line“equation,‘géwhere“±m“«is“the“slopGe“and“±b“«the“in¸ãtercept“with“theŽ¡v•¸ãertical›B#axis,‘Eú(whic“hev“er˜that˜migh“t˜b•Ge˜in˜a˜particular˜case;‘H‰it˜needn't˜b“e˜the˜y-axis)˜in˜the˜equation˜for˜theŽ¡ellipseŽ¡’ÁÔ€±xŸûÞÿ®2Ž‘|s±= zŸûÞÿ®2Ž‘¾Í«+‘8à±y[ÙŸûÞÿ®2Ž‘ØL±= ‘‡ŸûÞÿ®2Ž‘ʧ«=‘Ç1Ž©namely›UU!!‘qÇST–ÿ*ªAR“T˜HERE.˜Chec•¸ãk˜this.‘qÇI˜think˜the˜±x˜«in˜the˜coGecien“t˜for˜±xŸü^ÿ®2Ž‘ÑÈ«is˜wrong.Ž¡¡‘7 ²±xŸûÞÿ®2Ž›|s±= zŸûÞÿ®2Ž‘¾Í«+–8à(±mx“«+“±b«)ŸûÞÿ®2Ž˜±= ‘‡ŸûÞÿ®2Ž‘ý:get_focus()|:\n"Ž’ÉDk·‘?9Ý"InvalidÈ Ýargument:È Ý"Ž‘pž·‘?9±sŽ‘ .r·‘?9Ïend‘‚ØlŽ‘p4·Ž¡‘2Ý"ValidÈ ÝargumentsÈ ÝareŽ’šÿÉÈ Ý0È ÝandÈ Ý1.\n"Ž’ÝM%·‘ÇÝ"ReturningÈ ÝINVALID_PŽ‘kÆÜOINT.\n\n"Ž’£”>·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½ÝINVALID_POINTŽ’†¬þ«;Ž¡‘·gŽ¡‘ -gŽŸÂ1146.‘ üconst‘ÕTv®9ersion.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.07.25.«]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·Ž¡‘ -ÂP•®9oin“tŽ‘(ïžÏget‘‰ffŽ‘®fo‘ÿ}'cusŽ‘P1/«(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±sŽ‘pÜS«)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹Dƒ Šn ý‘ì«324–ÂCONST‘ÕX­VERSION’ ol3DLDFPRÃŽG“·x«1147Ž €n ý•@PÂ1147.Ž©·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¤ ‘ -ÂP•®9oin“tŽ‘(ïžEllipseŽ‘KØ{«::‘Ïget‘‰ffŽ‘®fo‘ÿ}'cusŽ‘(A•«(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±sŽ‘pÜS«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂP•®9oin“tŽ‘2pŽ‘7÷Ÿ«;Ž¦‘ÂifŽ‘´ú«(±sŽ‘w·‘Ç«0Ž‘Ç)‘·fŽ¡‘±pŽ‘%Ï«=‘ÇÏfo‘ÿ}'cus0Ž‘zB«;Ž¡‘±pŽ‘#:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨);Ž¡‘ÂreturnŽ‘Aæ½±pŽ‘F;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(±sŽ‘w·‘Ç«1Ž‘Ç)‘·fŽ¡‘±pŽ‘%Ï«=‘ÇÏfo‘ÿ}'cus1Ž‘zB«;Ž¡‘±pŽ‘#:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨);Ž¡‘ÂreturnŽ‘Aæ½±pŽ‘F;Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘Ïc‘ÿ}'errŽ‘3ôâ·‘?9Ý"ERROR!È ÝInÈ Ý|Ellipse:Ž‘l>ý:get_focus()|:\n"Ž’ÉDk·‘?9Ý"InvalidÈ Ýargument:È Ý"Ž‘pž·‘?9±sŽ‘ .r·‘?9Ïend‘‚ØlŽ‘p4·Ž¡‘2Ý"ValidÈ ÝargumentsÈ ÝareŽ’šÿÉÈ Ý0È ÝandÈ Ý1.\n"Ž’ÝM%·‘ÇÝ"ReturningÈ ÝINVALID_PŽ‘kÆÜOINT.\n\n"Ž’£”>·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½ÝINVALID_POINTŽ’†¬þ«;Ž¡‘·gŽ¡‘ -gŽŸÂ1148.‘ üGet–ÕTlinear“eccen•®9tricit“y‘ÿ +¬[²LDF‘T2002.08.07.¬]Ž‘Y3Copied–€©the“en¸ãtire“\T‘ÿ*ªransformations"“section“from“®ellipses.web“¬and“made“the“appro-Ž¡priate‘UUc¸ãhanges.Ž¡‘ +[²LDF‘T2003.04.27.¬]Ž‘YReThe–Ÿprevious“commenš¸ãt“w˜as“out-of-date.‘PDI‘Ÿlma˜y“ha˜v˜e“remo˜v˜ed“the“transformation“func-Ž¡tions.‘PëA•¸ãt›Ÿ¶an“y˜rate,‘²Othere˜w“ere˜only˜a˜couple˜here.‘PëI‘Ÿ£ha“v“e˜no“w˜copied˜the˜rest˜of˜them˜from˜®ellipses.webŽ¡¬and–UUmade“the“appropriate“c¸ãhanges.Ž¡‘ +[²LDF‘T2003.07.18.¬]Ž‘Y;[²LDF‘T2003.07.18.¬]Ž’¨uMo•¸ãv“ed–UU\T‘ÿ*ªransformations"“section,“includingŽ¡­opQÇeratorŽ‘+–µ°¬=ŽŽŽ‘8]Ô(­constŽ‘T‘ÿ +«ransformŽ‘VØl¬&Ž‘^ŸŠ)–ÇÑfrom“­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘IV¬to“­P®9olygonŽ‘,Ì¿¬.‘É:Also“remo•¸ãv“ed–ÇÑthe“­RectangleŽ‘9Ï7¬v¸ãer-Ž¡sions–UUin“®rectangs.web¬.‘qÇThe“­P®9olygonŽ‘/¯˜¬vš¸ãersions“are“no˜w“inherited“b˜y“­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘H)^¬and“­RectangleŽ‘5”ê¬.ŽŸŸüÈ„`ÕÁGŽŽ¦­1045.‘ üApplying–ÕTa“transformation.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.11.06.¬]Ž‘ZÛNoš¸ãw–Mõcalling“­P®9athŽ‘ß]¬::Ž‘$m›­opQÇeratorŽ‘PP°¬=ŽŽŽ‘\Ëo(‘ª¨)“instead“of“loGoping“through“±p‘ÿ}'ointsŽ‘rŠ¬.‘[¦This“w˜a˜y‘ÿ*ª,‘Œif“IŽ¡cš¸ãhange‘UU­P®9athŽ‘潬::Ž‘#tû­opQÇeratorŽ‘O °°¬=ŽŽŽ‘[ÒÏ(‘ª¨),–UUthe“c˜hange“will“automatically“bGe“re ected“here.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1022“°i‘Ǭ+°ŽŸ ‘ +­virtualŽ‘/ÔT‘ÿ +«ransformŽ‘gV¦opQÇeratorŽ’’í[°¬=ŽŽŽ’Ÿ´z(­constŽ‘*¢T‘ÿ +«ransformŽ‘Uót¬&Ž‘]º’µtŽ‘aW¬);ŽŽŽŒ‹+t‘ Šn ý‘ì°x¬1046‘¯3DLDF-1.1.5.1’È¥¹APPL›ÿJªYING–ÕXA“TRANSFÃŽORMA˜TION‘¬299Ž €n ý•@P­1046.Ž©°h–ª¨¬De ne‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1023“°i‘Ǭ+°Ž¤ ‘ +­T‘ÿ +«ransformŽ‘AÈÓP®9olygonŽ‘kÍŬ::Ž‘r\­opQÇeratorŽ’ò¸°¬=ŽŽŽ’ª¹×(­constŽ‘*¢T‘ÿ +«ransformŽ‘Uót¬&Ž‘]º’µtŽ‘aW¬)Ž¡‘ +°fŽ¡‘­P®9athŽ‘-‘j¬::Ž‘4¨­opQÇeratorŽ‘_¶]°¬=ŽŽŽ‘l}|(µtŽ‘œr¬);Ž¡‘­returnŽ‘7漬(±c‘ÿ}'enterŽ‘У°¬=ŽŽ‘.^ÚµtŽ‘1ûL¬);Ž¡‘ +°gŽŸ­1047.‘ üRotatation–ÕTaround“the“main“axes.Ž¦°h–ª¨¬Declare‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1022“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔT‘ÿ +«ransformŽ‘gV¦±r‘ÿ}'otateŽ’Åä¬(­constŽ‘*¢realŽ‘4ÝеxŽ‘:”ì;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµyŽ‘>’ˆ¬=‘Ç0Ž–ǵ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµzŽ‘>f®¬=‘Ç0Ž“);ŽŸ­1048.Ž¦°h–ª¨¬De ne‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1023“°i‘Ǭ+°Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓP®9olygonŽ‘kÍŬ::‘±r‘ÿ}'otateŽ‘oB¬(­constŽ‘*¢realŽ‘4ÝеxŽ‘:”ì;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµyŽ‘;Ëp;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµzŽ‘;Ÿ–¬)Ž¡‘ +°fŽ¡‘­T‘ÿ +«ransformŽ‘KÈÔµtŽ‘OeF¬;Ž¦‘µtŽ‘œt:±r‘ÿ}'otateŽ‘o>¬(µxŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁƬ);Ž¡‘­returnŽ‘7漬(°Ž‘±thisŽ‘²Ï°¬=ŽŽ‘(AµtŽ‘+Ýx¬);Ž¡‘ +°gŽ¤­1049.‘ üRotate–ÕTaround“an“arbitrary“axis.Ž¡1050.‘ üP•®9oin“t‘ÕTargumen“ts.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ +¬[²LDF‘T2003.05.02.¬]Ž‘YËSChanged–mname“of“this“function“from“±r–ÿ}'otate‘‰ffŽ‘®ar“oundŽ‘@„ü¬(›ª®)“to“±r‘ÿ}'otateŽ‘‡«¬(˜).‘»This“function“no¸ãwŽ¡o•¸ãv“erloads‘UU±r‘ÿ}'otateŽ‘Ä“¬(‘ª®)–UUwith“three“­realŽ‘ƒ¬argumen¸ãts.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1022“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔT‘ÿ +«ransformŽ‘gV¦±r‘ÿ}'otateŽ’Åä¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±p0Ž‘Pøµ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±p1Ž‘R¢Åµ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±angleŽ‘Qã¬=‘Ç180ŽŽ‘Ç);ŽŸ­1051.Ž¦°h–ª¨¬De ne‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1023“°i‘Ǭ+°Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓP®9olygonŽ‘kÍŬ::‘±r‘ÿ}'otateŽ‘oB¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±p0Ž‘Pøµ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±p1Ž‘R¢Åµ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±angleŽ‘NHˬ)Ž¡‘ +°fŽ¡‘­T‘ÿ +«ransformŽ‘KÈÔµtŽ‘OeF¬;Ž¦‘µtŽ‘œt:±r‘ÿ}'otateŽ‘o>¬(±p0Ž‘ Àµ;‘ª¨±p1Ž‘ Áhµ;‘ª¨±angleŽ‘jû¬);Ž¡‘­returnŽ‘7漬(°Ž‘±thisŽ‘²Ï°¬=ŽŽ‘(AµtŽ‘+Ýx¬);Ž¡‘ +°gŽŸ­1052.‘ üP•®9ath‘ÕTargumen“t.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.05.02.¬]Ž‘YËSChanged–mname“of“this“function“from“±r–ÿ}'otate‘‰ffŽ‘®ar“oundŽ‘@„ü¬(›ª®)“to“±r‘ÿ}'otateŽ‘‡«¬(˜).‘»This“function“no¸ãwŽ¡o•¸ãv“erloads‘UU±r‘ÿ}'otateŽ‘Ä“¬(‘ª®)–UUwith“three“­realŽ‘ƒ¬argumen¸ãts.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1022“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔT‘ÿ +«ransformŽ‘gV¦±r‘ÿ}'otateŽ’Åä¬(­constŽ‘*¢P®9athŽ‘:[¬&Ž‘AØyµpŽ‘Fày;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±angleŽ‘Qã¬=‘Ç180ŽŽ‘Ç);ŽŽŽŒ‹,‚àŠn ý‘ì¬300›­P–ÿ +«A“TH‘ÕX¯ARÃŽGUMENT’ÿZ3DLDF-1.1.5.1˜°x¬1053Ž €n ý•@P­1053.Ž©°h–ª¨¬De ne‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1023“°i‘Ǭ+°Ž¤ ‘ +­T‘ÿ +«ransformŽ‘AÈÓP®9olygonŽ‘kÍŬ::‘±r‘ÿ}'otateŽ‘oB¬(­constŽ‘*¢P®9athŽ‘:[¬&Ž‘AØyµpŽ‘Fày;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±angleŽ‘NHˬ)Ž¡‘ +°fŽ¡‘­ifŽ‘´ú¬(°:µpŽ‘:±is‘‰ffŽ‘®line‘ÿ}'arŽ‘%}¬(‘ª¨))‘°fŽ¡‘±c‘ÿ}'errŽ‘7ã·°‘.´"ERROR!® ´In® ´Ellipse::Ž‘p-Òrotate(Path,® ´real).\Ž’Ù-–n"Ž’ëb°Ž¡‘2´"Path® ´is® ´not® ´a® ´line.Ž’šÿÉ® ´Returning® ´INVALID_Ž’ÿTRANSFORM.\n\n"Ž’SEȬ;Ž¡‘­returnŽ‘Aæ½´INVALID_TRANSFORMŽ’›¬ò¬;Ž¡‘°gŽ¡‘­returnŽ‘7æ¼±r‘ÿ}'otateŽ‘RUú¬(µpŽ‘:±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(0Ž‘)µ;‘ª¨pŽ‘²¨:±get‘‰ffŽ–®last‘‰ffŽ“p‘ÿ}'ointŽ‘:$>¬(–ª¨)µ;“±angleŽ‘jû¬);Ž¡‘ +°gŽŸ­1054.‘ üScale.Ž¦°h–ª¨¬Declare‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1022“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔT‘ÿ +«ransformŽ‘gV¦±sc‘ÿ}'aleŽ‘} ˜¬(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ gæ¬=‘Ç1Ž–ǵ;‘ª¨­realŽ‘]ÖµzŽ‘ < ¬=‘Ç1Ž“);ŽŸ­1055.Ž¦°h–ª¨¬De ne‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1023“°i‘Ǭ+°Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓP®9olygonŽ‘kÍŬ::‘±sc‘ÿ}'aleŽ‘´ö¬(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ Î;‘ª¨­realŽ‘]ÖµzŽ‘tô¬)Ž¡‘ +°fŽ¡‘­T‘ÿ +«ransformŽ‘KÈÔµtŽ‘OeF¬;Ž¦‘µtŽ‘œt:±sc‘ÿ}'aleŽ‘´ò¬(µxŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁƬ);Ž¡‘­returnŽ‘7漬(°Ž‘±thisŽ‘²Ï°¬=ŽŽ‘(AµtŽ‘+Ýx¬);Ž¡‘ +°gŽŸ­1056.‘ üShear.Ž¦°h–ª¨¬Declare‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1022“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔT‘ÿ +«ransformŽ‘gV¦±she‘ÿ}'arŽ‘Šà¬(­realŽ‘³.±xyŽ‘!—µ;‘ª¨­realŽ‘]Ö±xzŽ‘%œÀ¬=‘Ç0Ž–ǵ;‘ª¨­realŽ‘]Ö±yxŽ‘&Zœ¬=‘Ç0Ž“µ;‘ª¨­realŽ‘]Ö±yzŽ‘%Ô6¬=‘Ç0Ž“µ;‘ª¨­realŽ‘]Ö±zxŽ‘%–Y¬=‘Ç0Ž“µ;‘ª¨­realŽ‘]Ö±zyŽ‘%|¬=‘Ç0Ž“);ŽŸ­1057.Ž¦°h–ª¨¬De ne‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1023“°i‘Ǭ+°Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓP®9olygonŽ‘kÍŬ::‘±she‘ÿ}'arŽ‘4>¬(­realŽ‘³.±xyŽ‘!—µ;‘ª¨­realŽ‘]Ö±xzŽ‘"Õ¨µ;‘ª¨­realŽ‘]Ö±yxŽ‘#“„µ;‘ª¨­realŽ‘]Ö±yzŽ‘# µ;‘ª¨­realŽ‘]Ö±zxŽ‘"ÏAµ;‘ª¨­realŽ‘]Ö±zyŽ‘"´ð¬)Ž¡‘ +°fŽ¡‘­T‘ÿ +«ransformŽ‘KÈÔµtŽ‘OeF¬;Ž¦‘µtŽ‘œt:±she‘ÿ}'arŽ‘4:¬(±xyŽ‘ +ãçµ;‘ª¨±xzŽ‘ "zµ;‘ª¨±yxŽ‘ àVµ;‘ª¨±yzŽ‘ Yðµ;‘ª¨±zxŽ‘ µ;‘ª¨±zyŽ‘ ¬);Ž¡‘­returnŽ‘7漬(°Ž‘±thisŽ‘²Ï°¬=ŽŽ‘(AµtŽ‘+Ýx¬);Ž¡‘ +°gŽ¤­1058.‘ üShift.Ž¡1059.‘ üreal‘ÕTargumen®9ts.Ž¦°h–ª¨¬Declare‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1022“°i‘Ǭ+°ŽŸ ‘ +­virtualŽ‘/ÔT‘ÿ +«ransformŽ‘gV¦±shiftŽ‘{t#¬(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ gæ¬=‘Ç0Ž–ǵ;‘ª¨­realŽ‘]ÖµzŽ‘ < ¬=‘Ç0Ž“);ŽŽŽŒ‹-Ž Šn ý‘ì°x¬1060–¯3DLDF-1.1.5.1’úyü­REAL‘ÕX¯ARÃŽGUMENTS“¬301Ž €n ý•@P­1060.Ž©°h–ª¨¬De ne‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1023“°i‘Ǭ+°Ž¤ ‘ +­T‘ÿ +«ransformŽ‘AÈÓP®9olygonŽ‘kÍŬ::‘±shiftŽ‘¬(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ Î;‘ª¨­realŽ‘]ÖµzŽ‘tô¬)Ž¡‘ +°fŽ¡‘­T‘ÿ +«ransformŽ‘KÈÔµtŽ‘OeF¬;Ž¦‘µtŽ‘œt:±shiftŽ‘}¬(µxŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁƬ);Ž¡‘­returnŽ‘7漬(°Ž‘±thisŽ‘²Ï°¬=ŽŽ‘(AµtŽ‘+Ýx¬);Ž¡‘ +°gŽŸ­1061.‘ üP•®9oin“t‘ÕTargumen“t.Ž¦°h–ª¨¬Declare‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1022“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔT‘ÿ +«ransformŽ‘gV¦±shiftŽ‘{t#¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié]¬);ŽŸ­1062.Ž¦°h–ª¨¬De ne‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1023“°i‘Ǭ+°Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓP®9olygonŽ‘kÍŬ::‘±shiftŽ‘¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié]¬)Ž¡‘ +°fŽ¡‘­returnŽ‘7æ¼±shiftŽ‘L9¬(µpŽ‘:±get‘‰ffŽ‘®xŽ‘Žg¬(–ª¨)µ;“pŽ›²¨:±get‘‰ffŽ‘®yŽ‘t¬(“)µ;“pŽ˜:±get‘‰ffŽ‘®zŽ‘¬(“));Ž¡‘ +°gŽ¤­1063.‘ üShift‘ÕTtimes.Ž¡1064.‘ üreal‘ÕTargumen®9ts.Ž¦°h–ª¨¬Declare‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1022“°i‘Ǭ+°ŽŸ ‘ +­virtualŽ‘/Ôv®9oidŽ‘H‹¬±shift‘‰ffŽ‘®timesŽ‘wwç¬(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ gæ¬=‘Ç1Ž–ǵ;‘ª¨­realŽ‘]ÖµzŽ‘ < ¬=‘Ç1Ž“);Ž¡­1065.Ž¦°h–ª¨¬De ne‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1023“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘"ýÙP®9olygonŽ‘Mˬ::‘±shift‘‰ffŽ‘®timesŽ‘/ì?¬(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ Î;‘ª¨­realŽ‘]ÖµzŽ‘tô¬)Ž¡‘ +°fŽ¡‘­P®9athŽ‘-‘j¬::Ž‘4¨±shift‘‰ffŽ‘®timesŽ‘c ã¬(µxŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁƬ);Ž¡‘±c‘ÿ}'enterŽ‘0 µ:±shift‘‰ffŽ‘®timesŽ‘.ì;¬(µxŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁƬ);Ž¡‘­returnŽ‘4‘g¬;Ž¡‘ +°gŽŸ­1066.‘ üP•®9oin“t‘ÕTargumen“t.Ž¦°h–ª¨¬Declare‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1022“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/Ôv®9oidŽ‘H‹¬±shift‘‰ffŽ‘®timesŽ‘wwç¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié]¬);ŽŽŽŒ‹.™9 Šn ý‘ì¬302–­POINT‘ÕX¯ARÃŽGUMENT’ù!3DLDF-1.1.5.1“°x¬1067Ž €n ý•@P­1067.Ž©°h–ª¨¬De ne‘UU­P®9olygonŽ‘/¯˜¬functions‘@¯1023“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘"ýÙP®9olygonŽ‘Mˬ::‘±shift‘‰ffŽ‘®timesŽ‘/ì?¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié]¬)Ž¡‘ +°fŽ¡‘­returnŽ‘7æ¼±shift‘‰ffŽ‘®timesŽ‘fÒ÷¬(µpŽ‘:±get‘‰ffŽ‘®xŽ‘Žg¬(–ª¨)µ;“pŽ›²¨:±get‘‰ffŽ‘®yŽ‘t¬(“)µ;“pŽ˜:±get‘‰ffŽ‘®zŽ‘¬(“));Ž¡‘ +°gŽŸ­1068.– üReg‘°¡‰ffs4Ž‘#ÕP®9olygon“(®polygons.web­).‘AÅy¬[²LDF‘T2003.04.15.¬]Ž’ͳTO–UUDO:“It“will“bGe“necessary“toŽ¡supply‘Ÿ/­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘H½¬with–Ÿ/a“complete“set“of“transformation“functions,‘±¦so“that“±c‘ÿ}'enterŽ‘#Gé¬will“bGe“transformedŽ¡along–UUwith“the“­P•®9oin“tsŽ‘&Î.¬pGoinš¸ãted“to“b˜y“the“pGoin˜ters“on“±p‘ÿ}'ointsŽ‘yê¬.‘qÇSome“are“presen˜t“already‘ÿ*ª,“but“not“all.Ž¡‘ +[²LDF‘T2003.04.15.¬]Ž‘Y¹TO‘DO:–3Add“±in‘‰ffŽ‘®cir‘ÿ}'cleŽ‘(È|¬(–ª®),‘2k±out‘‰ffŽ‘®cir‘ÿ}'cleŽ‘.#¬(“).‘„bAlign–3a“line“from“±c‘ÿ}'enterŽ‘$ñ¬in“the“direction“of“aŽ¡normal–UUwith“the“y-axis.‘qÇUse“the“in•¸ãv“erse–UUof“the“­T‘ÿ +«ransformŽ‘;'¬to“transform“the“­CircleŽ‘!¸¬.Ž¦‘ +­formatŽ‘3c(±R–ÿ}'e“g‘‰ffŽ‘®PolygonŽ‘rÊ'PolygonŽŽŸ­1069.› üReg‘°¡‰ffs4Ž‘#ÕP®9olygon–ÕTclass“de nition.˜Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘PT¬is–UUderiv¸ãed“from“­P®9olygonŽ‘,ZC¬.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.04.15.¬]Ž‘XÐChanged,›(fso–*that“­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘G¹¬is“deriv¸ãed“from“­P®9athŽ‘®Ž¬.‘_Previously‘ÿ*ª,˜it“wš¸ãas“deriv˜ed“fromŽ¡­Regu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘h÷˜¬.Ž¡‘ +[²LDF‘T2003.04.27.¬]Ž‘XÉWChanged‘q­protectedŽ‘6œz¬data–qmem¸ãbšGers“to“­priv‘ÿ\rateŽ‘&¾ï¬.‘\ÑThey“no“longer“need“to“b˜e“­protectedŽ‘3† ¬,Ž¡bGecause‘UU­RectangleŽ‘8ê?¬is–UUno“longer“deriv¸ãed“from“­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘DÔ ¬.Ž¡‘ +[²LDF‘T2003.06.06.¬]Ž‘X#9Changed,›ž!so–pSthat“­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘F_Z¬is“deriv¸ãed“from“­P®9olygonŽ‘+uA¬,˜whicš¸ãh“I'v˜e“just“added“abGo˜v˜e.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬De ne‘UU­classŽ‘5¦Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘cô^¯1069“°i‘ÇŽ¡‘ +­classŽ‘$àRRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘i´[¬:‘qÇ­publicŽ‘'ñP®9olygonŽ‘S_4°fŽ¡‘­realŽ‘*³0±internal‘‰ffŽ‘®angleŽ‘h?e¬;Ž¡‘­realŽ‘*³0±r‘ÿ}'adiusŽ‘F{S¬;Ž¡‘­unsignedŽ‘D7shortŽ‘b³±sidesŽ‘xKE¬;Ž¡‘­b•QÇo“olŽ‘-¡h±on‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘eFZ¬;Ž¦‘ +­publicŽ‘)=Ö¬:‘°h–ª¨¬Declare‘UU­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘H)^¬functions‘@¯1070“°iŽ¡‘ +g¬;ŽŸ ¯This–ÕXco Šn ý‘ì¬304–¯CONSTRÃŽUCTOR’Îã3DLDF-1.1.5.1“°x¬1077Ž €n ý•@P­1077.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ +¬[²LDF‘T2003.08.27.¬]Ž‘Xï„Revš¸ãersed–<žthe“order“of“the“initializations“follo˜wing“\:",‘AbGecause“GCC‘<˜with“the“\®--Wall¬"Ž¡option–UUissued“the“folloš¸ãwing“w˜arning:Ž¡\`­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘B~¸¬::‘±sidesŽ‘I–¬'–UUwill“bGe“initialized“after“`­realŽ‘³.Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘Y1æ¬::‘±r‘ÿ}'adiusŽ‘È'¬'".Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬De ne‘UU­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘H)^¬functions‘@¯1071“°i‘Ǭ+°Ž¤ ‘ +­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘L~¹¬::‘­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘B~¸¬(­constŽ‘…,P•®9oin“tŽ‘=ÏS¬&Ž‘E–q±c–ÿ}'c“enterŽ‘e¶ºµ;‘ª¨­constŽ‘ /ÔunsignedŽ‘PÁlshortŽ‘næ™±ssidesŽ’‰Fëµ;‘ª¨­constŽ‘ /ÔrealŽŽ¡‘2±ddiameterŽ‘^çjµ;‘ª¨­constŽ‘Ô›realŽ‘6‡±angle‘‰ffŽ‘®xŽ‘W öµ;‘ª¨­constŽ‘Ô›realŽ‘6‡±angle‘‰ffŽ‘®yŽ‘Vò¥µ;‘ª¨­constŽ‘Ô›realŽ‘6‡±angle‘‰ffŽ‘®zŽ‘V†¬):‘qo±r‘ÿ}'adiusŽ‘ 9’¬(±ddiameterŽ‘,çeµ=¬2Ž‘)µ;Ž¡‘2±sidesŽ‘HI—¬(±ssidesŽ‘`R¬)–UU°f“­b•QÇo“olŽ‘ö»´DEBUGŽ‘:„,¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý±trueŽ‘Ä’°µ=Ž©‘­ifŽ‘+׬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘®s°‘U<´"Entering® ´Reg_PolygoŽ‘oUn::Reg_Polygon()® ´"Ž’Ô°n°Ž¡‘<´"(center,® ´sides,® ´diaŽ’¤ÿÊmeter,® ´angles).\n"Ž’Í°‘DZ ushŽ‘€¬;Ž¡‘±c‘ÿ}'enterŽ‘<Ц¬=‘DZc–ÿ}'c“enterŽ‘"çaµ;‘ª¨±on‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘<²¬=‘DZfalseŽ‘v\¬;Ž¡‘±internal‘‰ffŽ‘®angleŽ‘^SP¬=‘Ç360µ:¬0ŽŽ‘Ž9µ=±sidesŽ‘I’¬;Ž¡‘±cycle‘‰ffŽ‘®switchŽ‘Uǵ¬=‘DZtrueŽ‘‹°¬;Ž¡‘±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘rTµ:±r‘ÿ}'esizeŽ‘i¬(6Ž‘µ;‘ª¨¬0Ž‘ª©);‘µ=°‘ÿý¬LDF–UU2003.04.09.‘qÇAdded“this“line.‘o°µ=Ž¡‘±c‘ÿ}'enterŽ‘: Žµ:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);ŽŸ­1078.‘ ü¬F‘ÿ*ªor–Ûÿregular“pGolygons“with“an“evš¸ãen“n˜um˜bGer“of“sides,‘ôDw˜e“rotate“them“so“that“a“ at“side“is“at“the“\top"Ž¡(in–UUthe“direction“of“the“pGositiv¸ãe“z-axis,“if“±angle‘‰ffŽ‘®xŽ‘#Û1¬,“±angle‘‰ffŽ‘®yŽ‘#Àà¬,“and“±angle‘‰ffŽ‘®zŽ‘&ª ¬are“all“0).Ž¦°h–ª¨¬De ne‘UU­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘H)^¬functions‘@¯1071“°i‘Ǭ+°Ž¡‘ +­forŽ‘臬(­in®9tŽ‘¤÷µiŽ‘Þ¬=‘Ç0Ž‘Ç;‘ÿýµiŽ‘ 9 <‘DZsidesŽ‘ª¬;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)–UU°f“­P•®9oin“tŽ‘"Dò°Ž‘'Dó±vertexŽ‘FK¨¬=“±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<“­P•®9oin“tŽ‘!¶µµ>‘Ǭ(0Ž‘);Ž¦‘ +±vertexŽ‘#±aŸµ~ŽŽ‘)±b±setŽ‘7)æ¬(0Ž‘µ;‘ª¨¬0Ž‘ª©µ;‘ª¨±r‘ÿ}'adiusŽ‘rˬ);Ž¡‘ +­ifŽ‘´ù¬(±sidesŽ‘‚r¯%Ž‘!Ю¬2Ž‘)—Ç°‘Ǭ0Ž‘Ç)‘±vertexŽ‘±`Ÿµ~ŽŽ‘$±a±r‘ÿ}'otateŽ‘? Ÿ¬(0Ž–µ;‘ª¨±internal‘‰ffŽ‘®angleŽ‘?6ݵ=¬2Ž“µ;‘ª¨¬0Ž‘ª©);Ž¡‘ +­ifŽ‘´ù¬(µiŽ‘9 >‘Ǭ0Ž‘Ç)‘µ=°‘ÿý¬[²LDF‘T2002.11.06.¬]Ž‘T7Only–UUrotate“if“the“angle“°6¬=‘Ç0,“i.e.,“don't“rotate“the“ rst“time.‘o°µ=Ž¡‘±vertexŽ‘-±bŸµ~ŽŽ‘3±c±r‘ÿ}'otateŽ‘N ¡¬(0Ž‘µ;‘ª¨iŽ‘U|°‘8à±internal‘‰ffŽ‘®angleŽ‘?ŵ;‘ª¨¬0Ž‘ª©);Ž¡‘ +­ifŽ‘´ù¬(±angle‘‰ffŽ‘®xŽ‘#Lô°6¬=‘Ç0Ž– ÿù°_‘8à±angle‘‰ffŽ‘®yŽ‘%kƒ°6¬=‘Ç0Ž“°_‘8à±angle‘‰ffŽ‘®zŽ‘$ÿn°6¬=‘Ç0Ž‘Ç)Ž¡‘µ=°‘ÿý¬Rotation–UUaround“the“x-axis,“y-axis,“and“z-axis,“if“applicable.‘o°µ=Ž¡‘±vertexŽ‘-±bŸµ~ŽŽ‘3±c±r‘ÿ}'otateŽ‘N ¡¬(±angle‘‰ffŽ‘®xŽ‘ …ܵ;‘ª¨±angle‘‰ffŽ‘®yŽ‘"3µ;‘ª¨±angle‘‰ffŽ‘®zŽ‘!ª¬);Ž¡‘ +±vertexŽ‘#±aŸµ~ŽŽ‘)±b±shiftŽ‘=Î߬(±c‘ÿ}'enterŽ‘ ‹¬);‘µ=°‘ÿý¬Put–UUin“pGosition“around“±c‘ÿ}'enterŽ‘^à¬.‘o°µ=Ž¡‘ +±p‘ÿ}'ointsŽ‘%$–µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(±vertexŽ‘±`¬);‘UU°gŽ¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)Ž¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"Exiting® ´Reg_PolygonŽ‘kÆÜ::Reg_Polygon()® ´"Ž’ÈT)°‘Ç´"(center,® ´sides,® ´diaŽ‘kÆÜmeter,® ´angles).\n"Ž’Í”&°Ž¡‘(± ushŽ‘=¹¬;Ž¡‘ +­returnŽ‘*‘f¬;‘qÇ°gŽŸ­1079.‘ 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nition.˜¬[²LDF‘T2003.07.18.¬]Ž‘ZïITO‘¼MDO:‘¼h±axis‘‰ffŽ‘®hŽ‘"r]¬and‘¼h±axis‘‰ffŽ‘®vŽ‘">®¬are–¼hnot“recalculatedŽ¡when–UUa“­RectangleŽ‘8ê?¬is“transformed.‘qÇI“should“do“something“abGout“this.Ž¦°h–ª¨¬De ne‘UU­classŽ‘5¦RectangleŽ‘Tµ?¯1101“°i‘ÇŽ¡‘ +­classŽ‘$àRRectangleŽ‘Zu<¬:‘qÇ­publicŽ‘'ñP®9olygonŽ‘S_4°fŽ¡‘­realŽ‘*³0±axis‘‰ffŽ‘®hŽ‘E¬½¬;Ž¡‘­realŽ‘*³0±axis‘‰ffŽ‘®vŽ‘Ey¬;Ž¡‘­b•QÇo“olŽ‘-¡h±on‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘eFZ¬;Ž¦‘ +­publicŽ‘)=Ö¬:‘°h–ª¨¬Declare‘UU­RectangleŽ‘8ê?¬functions‘@¯1103“°iŽ¡‘ +g¬;ŽŸ ð*¯This–ÕXco8ˬ&Ž‘Eÿé±c–ÿ}'c“enterŽ‘f 2µ;‘ª¨­constŽ‘ drealŽ‘7§±aaxis‘‰ffŽ‘®hŽ‘W½µ;‘ª¨­constŽ‘ drealŽ‘7§±aaxis‘‰ffŽ‘®vŽ‘W‰Rµ;‘ª¨­constŽŽ¡‘2realŽ‘Iñ±angle‘‰ffŽ‘®xŽ‘i•Íµ;‘ª¨­constŽ‘ 2realŽ‘7Aô±angle‘‰ffŽ‘®yŽ‘W­µ;‘ª¨­constŽ‘ 2realŽ‘7Aô±angle‘‰ffŽ‘®zŽ‘WAj¬):‘+C±axis‘‰ffŽ‘®hŽ‘ $Ь(±aaxis‘‰ffŽ‘®hŽ‘ ý¬)µ;‘\»±axis‘‰ffŽ‘®vŽ‘ 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S¢°_‘Œ‰±angle‘‰ffŽ‘®yŽ‘$¿,°6¬=‘Ç0Ž“°_‘Œ‰±angle‘‰ffŽ‘®zŽ‘$S°6¬=‘Ç0Ž‘Ç)‘µ=°‘©Ñ¬Rotation–ÿ)around“the“x-axis,–ey-axis,“and‘ÿ)z-axis.‘ÿ¶°µ=Ž¡‘°fŽ¡‘(±b‘ÿ}'ot‘‰ffŽ‘®lftŽ‘B›5µ:±r‘ÿ}'otateŽ‘o>¬(±angle‘‰ffŽ‘®xŽ‘ …ܵ;‘ª¨±angle‘‰ffŽ‘®yŽ‘"3µ;‘ª¨±angle‘‰ffŽ‘®zŽ‘!ª¬);Ž¡‘(±b‘ÿ}'ot‘‰ffŽ‘®rtŽ‘A3bµ:±r‘ÿ}'otateŽ‘o>¬(±angle‘‰ffŽ‘®xŽ‘ …ܵ;‘ª¨±angle‘‰ffŽ‘®yŽ‘"3µ;‘ª¨±angle‘‰ffŽ‘®zŽ‘!ª¬);Ž¡‘(±top‘‰ffŽ‘®lftŽ‘C çµ:±r‘ÿ}'otateŽ‘o>¬(±angle‘‰ffŽ‘®xŽ‘ …ܵ;‘ª¨±angle‘‰ffŽ‘®yŽ‘"3µ;‘ª¨±angle‘‰ffŽ‘®zŽ‘!ª¬);Ž¡‘(±top‘‰ffŽ‘®rtŽ‘B9µ:±r‘ÿ}'otateŽ‘o>¬(±angle‘‰ffŽ‘®xŽ‘ …ܵ;‘ª¨±angle‘‰ffŽ‘®yŽ‘"3µ;‘ª¨±angle‘‰ffŽ‘®zŽ‘!ª¬);Ž¡‘°g‘µ=°‘ÿý¬Put–UUaround“±c‘ÿ}'enterŽ‘^à¬.‘o°µ=Ž¡‘±b‘ÿ}'ot‘‰ffŽ‘®lftŽ‘8›4µ:±shiftŽ‘}¬(±c‘ÿ}'enterŽ‘ ‹¬);Ž¡‘±b‘ÿ}'ot‘‰ffŽ‘®rtŽ‘73aµ:±shiftŽ‘}¬(±c‘ÿ}'enterŽ‘ ‹¬);Ž¡‘±top‘‰ffŽ‘®lftŽ‘9 æµ:±shiftŽ‘}¬(±c‘ÿ}'enterŽ‘ ‹¬);Ž¡‘±top‘‰ffŽ‘®rtŽ‘89µ:±shiftŽ‘}¬(±c‘ÿ}'enterŽ‘ ‹¬);‘UU­forŽ‘=Û¬(­in®9tŽ‘¤÷µiŽ‘Þ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ4Ž“;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)‘UU±p‘ÿ}'ointsŽ‘yêµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­P•®9oin“tŽ‘!¶µµ>‘Ǭ(0Ž‘)–UU)“;Ž¡‘°Ž‘#±p‘ÿ}'ointsŽ‘>$™¬[0Ž‘]–Ç=“±b‘ÿ}'ot‘‰ffŽ‘®lftŽ‘bI¬;Ž¡‘°Ž‘#±p‘ÿ}'ointsŽ‘>$™¬[1Ž‘]–Ç=“±b‘ÿ}'ot‘‰ffŽ‘®rtŽ‘úv¬;Ž¡‘°Ž‘#±p‘ÿ}'ointsŽ‘>$™¬[2Ž‘]–Ç=“±top‘‰ffŽ‘®rtŽ‘(¬;Ž¡‘°Ž‘#±p‘ÿ}'ointsŽ‘>$™¬[3Ž‘]–Ç=“±top‘‰ffŽ‘®lftŽ‘gû¬;‘UU°gŽŸÌ ­1108.‘ üSetting‘ÕTfunction.ŽŸjŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.11.06.¬]Ž‘Y;Made‘UU­realŽ‘ƒ¬argumen¸ãts‘UU­constŽ‘*¢¬.ŽŸŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­RectangleŽ‘8ê?¬functions‘@¯1103“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"抱setŽ‘0_¬(­constŽ‘SP•®9oin“tŽ‘<롬&Ž‘D²¿±c–ÿ}'c“enterŽ‘dÓµ;‘ª¨­constŽ‘½ûrealŽ‘6YÚ±aaxis‘‰ffŽ‘®hŽ‘Vo×µ;‘ª¨­constŽ‘½ûrealŽ‘6YÚ±aaxis‘‰ffŽ‘®vŽ‘V<(µ;‘ª¨­constŽ‘½ûrealŽ‘6YÚ±angle‘‰ffŽ‘®xŽ‘Y¦Î¬=‘Ç0Ž‘ǵ;‘ª¨­constŽŽ¡‘realŽ‘4³1±angle‘‰ffŽ‘®yŽ‘WåÔ¬=‘Ç0Ž–ǵ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±angle‘‰ffŽ‘®zŽ‘YO¬=‘Ç0Ž“);ŽŸÌ ­1109.Ž¦°h–ª¨¬De ne‘UU­RectangleŽ‘8ê?¬functions‘@¯1104“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘#_ÒRectangleŽ‘VŸk¬::‘±setŽ‘xˆ¬(­constŽ‘Œ›P•®9oin“tŽ‘=Þ1¬&Ž‘E¥O±c–ÿ}'c“enterŽ‘eص;‘ª¨­constŽ‘ 7CrealŽ‘7Lj±aaxis‘‰ffŽ‘®hŽ‘Wbgµ;‘ª¨­constŽ‘ 7CrealŽ‘7Lj±aaxis‘‰ffŽ‘®vŽ‘W.¸µ;‘ª¨­constŽ‘ 7CrealŽŽ¡‘2±angle‘‰ffŽ‘®xŽ‘R…áµ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±angle‘‰ffŽ‘®yŽ‘Vôµ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±angle‘‰ffŽ‘®zŽ‘V‡î¬)Ž¡‘ +°fŽ¡‘­RectangleŽ‘I”ìµrŽ‘N_¬(±c–ÿ}'c“enterŽ‘ Iµ;‘ª¨±aaxis‘‰ffŽ‘®hŽ‘!À¥µ;‘ª¨±aaxis‘‰ffŽ‘®vŽ‘!Œöµ;‘ª¨±angle‘‰ffŽ‘®xŽ‘"0„µ;‘ª¨±angle‘‰ffŽ‘®yŽ‘"3µ;‘ª¨±angle‘‰ffŽ‘®zŽ‘!ª¬);Ž¦‘°Ž‘±thisŽ‘,²Ñ¬=‘ǵrŽ‘‘,¬;Ž¡‘ +°gŽŸ­1110.› üF‘ÿ +«our‘$±P•®9oin“ts.˜¬The‘»¼­P“oin“tŽ‘!À¬argumen•¸ãts›»¼m“ust˜bGe˜so˜ordered,‘Útthat˜they˜are˜con“tiguous˜in˜the˜resultingŽ¡­RectangleŽ‘2?•¬.ŽŽŽŒ‹7˜ Šn ý‘ì°x¬1111–¯3DLDF-1.1.5.1’ÎãCONSTRÃŽUCTOR“¬311Ž €n ý•@P­1111.‘ üConstructor.Ž¤°h–ª¨¬Declare‘UU­RectangleŽ‘8ê?¬functions‘@¯1103“°i‘Ǭ+°Ž© ‘ +­RectangleŽ‘Äç¬&Ž‘FŒ±pt1Ž–Uõ@µ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±pt2Ž“µ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±pt3Ž“¬);ŽŸ­1112.Ž¡°h–ª¨¬De ne‘UU­RectangleŽ‘8ê?¬functions‘@¯1104“°i‘Ǭ+°Ž¦‘ +­RectangleŽ‘=?š¬::‘­RectangleŽ‘3?™¬(­constŽ‘…¶P•®9oin“tŽ‘=Ðg¬&Ž‘E—…±pt0Ž‘UÀµ;‘ª¨­constŽ‘ 0^P•®9oin“tŽ‘?{¬&Ž‘GB-±pt1Ž–V«hµ;‘ª¨­constŽ‘ 0^P•®9oin“tŽ‘?{¬&Ž‘GB-±pt2Ž“µ;‘ª¨­constŽ‘ 0^P•®9oin“tŽŽ¦‘2¬&Ž‘9Ç#±pt3Ž‘I0^¬)°f‘UU­P•®9oin“tŽ‘"Dò±pt4Ž‘4uE¬=‘DZpt1Ž‘i3°‘8à±pt0Ž‘¢¬;‘µ=°‘ÿý¬Checš¸ãk–UUthat“the“­P•®9oin“tŽ‘"Dò¬argumen˜ts“are“coplanar.‘o°µ=Ž¦‘­P•®9oin“tŽ‘<ï ±pt5Ž‘Oó¬=‘DZpt2Ž‘i3°‘8à±pt0Ž‘¢¬;Ž¦‘­P•®9oin“tŽ‘<ï ±pt6Ž‘Oó¬=‘DZpt3Ž‘i3°‘8à±pt0Ž‘¢¬;Ž¦‘­P•®9oin“tŽ‘<ï ±pt7Ž‘Oó¬=‘DZpt4Ž‘0Sµ:±cr–ÿ}'oss‘‰ffŽ‘®pr“o“ductŽ‘:Œé¬(±pt5Ž‘i;¬);Ž¡‘±pt7Ž‘-i>µ:±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u¬(±trueŽ‘ʬ);Ž¡‘­P•®9oin“tŽ‘<ï ±pt8Ž‘Oó¬=‘DZpt4Ž‘0Sµ:±cr–ÿ}'oss‘‰ffŽ‘®pr“o“ductŽ‘:Œé¬(±pt6Ž‘i;¬);Ž¡‘±pt8Ž‘-i>µ:±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u¬(±trueŽ‘ʬ);‘UU­ifŽ‘ +M¬(±pt7Ž‘0S°‘DZpt8Ž–i3°_‘8à±pt7Ž“°‘ÇŽ‘ +Ž6±pt8Ž‘÷q¬)‘µ=°‘ÿý¬If–UUthey“are,“create“a“­RectangleŽ‘5”ê¬.‘o°µ=Ž¦‘°f‘UU±on‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘=Á_¬=‘DZfalseŽ‘v\¬;Ž¦‘±line‘‰ffŽ‘®switchŽ‘Piܬ=‘DZfalseŽ‘v\¬;Ž¦‘±cycle‘‰ffŽ‘®switchŽ‘Uǵ¬=‘DZtrueŽ‘‹°¬;Ž¦‘±c‘ÿ}'enterŽ‘<Ц¬=‘DZpt0Ž‘0Sµ:±me‘ÿ}'diateŽ‘"½u¬(±pt2Ž‘i;¬);Ž¦‘±axis‘‰ffŽ‘®hŽ‘;À¨¬=‘Ç(±pt1Ž–¢°‘8à±pt0Ž“¬)µ:±magnitudeŽ‘.=r¬(‘ª¨);Ž¦‘±axis‘‰ffŽ‘®vŽ‘<çά=›!í(±pt2Ž–,×°‘Ãœ±pt1Ž“¬)µ:±magnitudeŽ‘.=r¬(‘ª¨);‘%p±p‘ÿ}'ointsŽ‘Jµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘/}¬(‘%p±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘7Ú¤µ<‘%p­P•®9oin“tŽ‘#᥵>˜¬(±pt0Ž‘i;¬)–%p)“;Ž¦‘2±p‘ÿ}'ointsŽ‘M$šµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ›/Uø¬(‘ý¦±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘7‹µ<‘ý¦­P•®9oin“tŽ‘#wŒµ>‘ßž¬(±pt1Ž‘i;¬)–ý¦)“;‘j»±p‘ÿ}'ointsŽ‘!Pµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ˜¬(“±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘7‹µ<Ž¦‘2­P•®9oin“tŽ‘Paeµ>›Ç¬(±pt2Ž‘i;¬)–UU)“;‘qDZp‘ÿ}'ointsŽ‘–\µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(“±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<“­P•®9oin“tŽ‘!¶µµ>˜¬(±pt3Ž‘i;¬)“)“;Ž¦‘±c–ÿ}'onne“ctorsŽ‘M41µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(´"--"Ž‘†\¬);‘UU°gŽ¦‘­elseŽ‘5Øâ°fŽ¦‘(±c‘ÿ}'errŽ‘@Iy°‘“Ï´"ERROR!® ´In® ´RectangleŽ‘n““()® ´with® ´four® ´Point® ´aŽ’דWrguments.\n"Ž’­j°Ž¦‘<´"Points® ´are® ´not® ´coplŽ’¤ÿÊanar.® ´Returning.\n\Ž’ ÿŽn"Ž’Í°‘DZ ushŽ‘€¬;Ž¦‘°gŽ¦‘­returnŽ‘>‘h¬;‘qÇ°gŽŸ­1113.‘ üSetting‘ÕTfunction.Ž¡°h–ª¨¬Declare‘UU­RectangleŽ‘8ê?¬functions‘@¯1103“°i‘Ǭ+°Ž¦‘ +­v®9oidŽ‘"ýÙ±setŽ‘0v]¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±pt0Ž‘TJ˜µ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±pt1Ž–Uõ@µ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±pt2Ž“µ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±pt3Ž“¬);ŽŽŽŒ‹8¼ Šn ý‘ì¬312–¯SETTING‘ÕXFUNCTION’ý§3DLDF-1.1.5.1“°x¬1114Ž €n ý•@P­1114.Ž©°h–ª¨¬De ne‘UU­RectangleŽ‘8ê?¬functions‘@¯1104“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘"ýÙRectangleŽ‘V=r¬::‘±setŽ‘xˆ¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±pt0Ž‘TJ˜µ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±pt1Ž–Uõ@µ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±pt2Ž“µ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±pt3Ž“¬)Ž¡‘ +°fŽ¡‘­RectangleŽ‘I”ìµrŽ‘N_¬(±pt0Ž‘i;µ;‘ª¨±pt1Ž–ãµ;‘ª¨±pt2Ž“µ;‘ª¨±pt3Ž“¬);Ž¦‘°Ž‘±thisŽ‘,²Ñ¬=‘ǵrŽ‘‘,¬;Ž¡‘ +°gŽ¤­1115.‘ üPseudo-constructor–ÕTfor“dynamic“alloQÇcation.Ž¡1116.‘ üP•®9oin“ter‘ÕTargumen“t.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ +¬[²LDF‘T2003.12.30.¬]Ž‘Y9²Replaced‘†Ì­RectangleŽ‘6Æe¬::‘±cr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“r–ÿ}'e“ctangleŽ‘Z3¬(‘ª®)–†Ìwith“a“spGecialization“of“­templateŽ‘0X*°h­classŽŽ¡µCŽ‘ÜÌ°i‘UUµCŽ‘ 2!°Ž‘2"±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘?Áæ¬(‘ª¨)–UUfor“­RectangleŽ‘5”ê¬.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h›ª¨¬Declare–UUnon-mem¸ãbGer“template“functions“for“­RectangleŽ‘9Ôî¯1116˜°i‘ÇŽ¡‘ +­RectangleŽ‘?”ë°Ž‘D”ì±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘t$°¬(­constŽ‘*¢RectangleŽ‘S¿Œ°Ž‘X¿µcŽ‘]h¬);Ž¤ ¯See–ÕXalso“section“1117.Ž¡This–ÕXco‘Ǭ3Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘8²z°‘üÑ´"ERROR:® ´Rectangles® ´hŽ‘pü•ave® ´4® ´corners,® ´"Ž’Íž°Ž¡‘2´"numbered® ´0® ´through® Ž’šÿÉ´3.\nReturning® ´INVALIŽ’ÿD_POINT.\n"Ž’A 찑DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½´INVALID_POINTŽ’†¬þ¬;Ž¡‘°gŽ¡‘­returnŽ‘7æ¼°Ž‘<æ½±p‘ÿ}'ointsŽ‘X R¬[µcŽ‘SÛ¬];Ž¡‘ +°gŽŸ­1127.– üGet‘ÕTMid-pQÇoin®9t.“¬The–UUargumen¸ãt“µcŽ‘ +þ…¬should“bGe“in“the“range“0–ǵ<¬=“µc“<¬=“3.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.11.06.¬]Ž‘Y;Changed–UUthis“function“so“that“it“uses“±me‘ÿ}'diateŽ‘&ʬ(‘ª®).Ž¡‘ +[²LDF‘T2003.05.09.¬]Ž‘Y;Renamed–UUthis“function“±get‘‰ffŽ–®mid‘‰ffŽ“p‘ÿ}'ointŽ‘>À°¬(›ª®).‘qÇF–ÿ*ªormerly“,–UUit“w¸ãas“called“±mid‘‰ffŽ‘®p‘ÿ}'ointŽ‘.Œô¬(˜).Ž¡‘ +[²LDF‘T2003.07.18.¬]Ž‘Y;Made‘UU­constŽ‘*¢¬.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­RectangleŽ‘8ê?¬functions‘@¯1103“°i‘Ǭ+°Ž¡‘ +­P•®9oin“tŽ‘(ïž±get‘‰ffŽ–®mid‘‰ffŽ“p‘ÿ}'ointŽ‘dZù¬(­unsignedŽ‘07shortŽ‘N±µcŽ‘RUŒ¬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹;@5 Šn ý‘ì°x¬1128–¯3DLDF-1.1.5.1’ÃÛGET‘ÕXMID-POINT“¬315Ž €n ý•@P­1128.Ž©°h–ª¨¬De ne‘UU­RectangleŽ‘8ê?¬functions‘@¯1104“°i‘Ǭ+°Ž¤ ‘ +­P•®9oin“tŽ‘(ïžRectangleŽ‘\/7¬::‘±get‘‰ffŽ–®mid‘‰ffŽ“p‘ÿ}'ointŽ‘‘Ǭ3Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘8K°‘•o´"ERROR:® ´Rectangles® ´hŽ‘p•3ave® ´4® ´mid_points,® ´"Ž’ÜpÑ°Ž¡‘2´"numbered® ´0® ´through® Ž’šÿÉ´3.\nReturning® ´INVALIŽ’ÿD_POINT.\n"Ž’A 찑DZ 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les‘@¯6“°i‘Ǭ+°Ž¡¬#­includeŽ‘'Ø~´"loader.h"ŽŽ¡¬#­includeŽ‘'Ø~´"pspglb.h"ŽŽ¡¬#­includeŽ‘'Ø~´"creatnew.h"ŽŽ¡¬#­includeŽ‘'Ø~´"io.h"ŽŽ¡¬#­includeŽ‘'Ø~´"colors.h"ŽŽ¡¬#­includeŽ‘'Ø~´"transfor.h"ŽŽ¡¬#­includeŽ‘'Ø~´"shapes.h"ŽŽ¡¬#­includeŽ‘'Ø~´"pictures.h"ŽŽ¡¬#­includeŽ‘'Ø~´"points.h"ŽŽ¡¬#­includeŽ‘'Ø~´"lines.h"ŽŽ¡¬#­includeŽ‘'Ø~´"planes.h"ŽŽ¡¬#­includeŽ‘'Ø~´"paths.h"ŽŽ¡¬#­includeŽ‘'Ø~´"curves.h"ŽŽ¡¬#­includeŽ‘'Ø~´"polygons.h"ŽŽ¡¬#­includeŽ‘'Ø~´"rectangs.h"ŽŽŸ­1143.‘ üEllipse–ÕTclass“de nition.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.07.25.¬]Ž‘Y;Added‘UU±fo‘ÿ}'cus0Ž– ¬,‘UU±fo‘ÿ}'cus1Ž“¬,–UUand“±line–ÿ}'ar‘‰ffŽ‘®e“c“c“entricityŽ‘R0¬.Ž¡‘ +[²LDF‘T2003.07.27.¬]Ž‘Y;Added‘UU±numeric–ÿ}'al‘‰ffŽ‘®e“c“c“entricityŽ‘d'#¬.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬De ne‘UU­classŽ‘5¦EllipseŽ‘D^ƒ¯1143“°i‘ÇŽ¡‘ +­classŽ‘$àREllipseŽ‘J€¬:‘qÇ­publicŽ‘'ñRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ’“QÞ°fŽ¡‘ 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+¬[²LDF‘T2002.11.06.¬]Ž‘Y}ÉChanged–Êãthis“function“so“that“it“just“calls“­EllipseŽ‘&³À¬::‘±lab‘ÿ}'elŽ‘tœ¬(‘ª®)“with“±dotŽ‘Vô¬=‘‹±trueŽ‘Oœ¬.‘ÒqMade“itŽ¡­inlineŽ‘4ó¬.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¡‘ +­inlineŽ‘)ŠIv®9oidŽ‘Bˆ!±dotlab‘ÿ}'elŽ‘dˆ¬(­stringŽ‘!%M±p‘ÿ}'osŽ‘3'¬=‘Ç´"top"Ž‘qµ;‘ª¨­PictureŽ‘*œ +¬&Ž‘2c(±pictur‘ÿ}'eŽ‘T3¬=‘DZcurr–ÿ}'ent‘‰ffŽ‘®pictur“eŽ‘Dì߬)‘UU­constŽŽ¡‘ +°fŽ¡‘±lab‘ÿ}'elŽ‘(tš¬(±p‘ÿ}'osŽ‘!µ;‘ª¨±trueŽ‘o@µ;‘ª¨±pictur‘ÿ}'eŽ‘ ³~¬);Ž¡‘ +°gŽ¤­1163.‘ üReturning–ÕTelemen®9ts“and“information.Ž¡1164.– üIs‘ÕTelliptical.“¬[²LDF‘T2003.07.20.¬]Ž‘Zˆ6±is‘‰ffŽ‘®el‘‚Øliptic‘ÿ}'alŽ’‹t̬(‘ª®)–UU rst“c•¸ãhec“ks–UUwhether“°Ž‘UV±thisŽ‘–a¬is“planar“b¸ãy“callingŽ¤ ±get‘‰ffŽ‘®normalŽ‘0Št¬(›ª®).‘_HIf–Ùthe“latter“function“returns“´INVALID_POINTŽ‘Gä¬,‘(òthen“±is‘‰ffŽ‘®el‘‚Øliptic‘ÿ}'alŽ‘4 +o¬(˜)“returns“±falseŽ‘ͬ.‘_HOtherwise,‘(òitŽ¡makš¸ães–s a“cop˜y“of“°Ž‘s +±thisŽ‘Ñɬcalled“µeŽ‘ +¬,‘ Lputs“µeŽ‘ Ž¬in˜to“the“x-z“plane,› Land“rotates“it,˜so“that“°Ž‘s +¬(µeŽ‘¨:±p‘ÿ}'ointsŽ‘$•¬[0Ž‘])“lies“on“the“x-axis.Ž¡Then,›a!it–^Åplugs“the“x“and“z-coGordinates“of“the“­P•®9oin“tsŽ‘&á¬on“µeŽ‘ e‹¬in¸ãto“the“ellipse“equation,˜i.e.,˜µxŸü^ÿ³2Ž‘|sµ=aŸü^ÿ³2Ž‘»ž¬+‘?+µzp—Ÿü^ÿ³2Ž‘í +µ=bŸü^ÿ³2Ž‘SE¬=‘ÖÒ1,Ž¡where–tµa“¬is“half“of“the“horizonš¸ãtal“axis“of“the“ellipse,‘{±and“µb“¬is“half“of“the“v˜ertical“axis.‘ÍØLet“µr‘AZ¬=‘ú=µxŸü^ÿ³2Ž‘|sµ=aŸü^ÿ³2Ž‘ÉȬ+‘MUµzp—Ÿü^ÿ³2Ž‘í +µ=bŸü^ÿ³2ŽŽ¡¬and–ù’µ“¬stand“for“the“return“v‘ÿqÇalue“of“­P•®9oin“tŽ‘“Þ¬::‘±epsilonŽ‘ o¬(›ª®).‘S1If“°jµr‘Èx°‘[¬1°j–ǵ>“–ù’¬for“an¸ãy“of“the“­P•®9oin“tsŽ‘&¨¬on“µeŽ‘¡“¬,‘ ì±is‘‰ffŽ‘®el‘‚Øliptic‘ÿ}'alŽ‘3ø‚¬(˜)Ž¡returns‘UU±falseŽ‘™¬,–UUotherwise“it“returns“±trueŽ‘í¬.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.07.20.¬]Ž‘Y;Added–UUthis“function.Ž¡‘ +[²LDF‘T2003.07.25.¬]Ž‘Y;No•¸ãw›UUc“hec“king˜±normalŽ‘&s%°‘Ç´INVALID_POINTŽ‘GY¬.‘qÇIf˜it˜is,˜±is‘‰ffŽ‘®el‘‚Øliptic‘ÿ}'alŽ‘4Aë¬(‘ª®)˜returns˜±falseŽ‘™¬.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¡‘ +­b•QÇo“olŽ‘#¡g±is‘‰ffŽ‘®el‘‚Øliptic‘ÿ}'alŽ‘Tý¬(‘ª®)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹D©v Šn ý‘ì¬324–¯IS‘ÕXELLIPTICAL’q 3DLDF-1.1.5.1“°x¬1165Ž €n ý•@P­1165.Ž©°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¤ ‘ +­b•QÇo“olŽ‘#¡gEllipseŽ‘FŠD¬::‘±is‘‰ffŽ‘®el‘‚Øliptic‘ÿ}'alŽ‘1욬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­b•QÇo“olŽ‘-¡h´DEBUGŽ‘K.Ù¬=‘DZfalseŽ‘v\¬;‘µ=°–ÿý¬true“°µ=Ž¡‘­P•®9oin“tŽ‘2normalŽ‘V o¬=‘DZget‘‰ffŽ‘®normalŽ‘3QŒ¬(‘ª¨);Ž¦‘­ifŽ‘´ú¬(±normalŽ‘#а‘Ç´INVALID_POINTŽ‘GY¬)‘°fŽ¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)Ž¡‘(±c‘ÿ}'errŽ‘=”Ü°‘ß2´"In® ´Ellipse::is_elliŽ‘kÞöptical():® ´"Ž’©o°‘ß2´"get_normal()® ´returnŽ‘kÞöed® ´INVALID_POINT."Ž’ÍÄZ°Ž¡‘<±end‘‚ØlŽ‘R¸à°‘Ç´"*this® ´is® ´non-planarŽ‘kÆÜ.® ´Returning® ´false."Ž’ÒÔ#°‘DZend‘‚ØlŽ–ò°‘DZend‘‚ØlŽ“°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½±falseŽ‘V–¬;Ž¡‘°gŽ¦‘­EllipseŽ‘9>0µeŽ‘@­I¬=‘Ç°Ž‘DZthisŽ‘²Ï¬;Ž¦‘±normalŽ‘4Vºµ:±shiftŽ‘}¬(±c‘ÿ}'enterŽ‘ ‹¬);Ž¦‘­T‘ÿ +«ransformŽ‘KÈÔµtŽ‘OeF¬;Ž¦‘µtŽ‘œt:±align‘‰ffŽ–®with‘‰ffŽ“axisŽ‘@²x¬(±c‘ÿ}'enterŽ‘ ‹µ;‘ª¨±normalŽ‘"`µ;‘ª¨´'y'Ž‘ñ¬);Ž¡‘µeŽ‘¨:±do‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘9š4¬(µtŽ‘œr¬);Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘µeŽ‘ ¨:±showŽ‘Šÿ¬(´"e® ´after® ´alignment:"Ž‘i†,¬);Ž¦‘­P•®9oin“tŽ‘2x‘‰ffŽ–®axis‘‰ffŽ“ptŽ‘Y»¼¬(1Ž‘);Ž¡‘­P•®9oin“tŽ‘2p0Ž‘AÍw¬=‘ǵeŽ‘o:±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(0Ž‘);Ž¡‘­realŽ‘*³0±angŽ‘>4î¬=‘DZp0Ž‘Ýص:±angleŽ‘ÀS¬(±x‘‰ffŽ–®axis‘‰ffŽ“ptŽ‘&̬);Ž¦‘µtŽ‘œt:±r‘ÿ}'esetŽ‘Æ·¬(‘ª¨);Ž¡‘µtŽ‘œt:±r‘ÿ}'otateŽ‘o>¬(0Ž‘µ;‘ª¨±angŽ‘eN¬);Ž¡‘±p0Ž‘"ÝÚ°¬=ŽŽ‘2lµeŽ‘7:±do‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘9š4¬(µtŽ‘œr¬);Ž¡‘±p0Ž‘ µ:±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u¬(±trueŽ‘ʬ);Ž¡‘­ifŽ‘´ú¬(±p0Ž‘ÝØ°6¬=‘DZx‘‰ffŽ–®axis‘‰ffŽ“ptŽ‘)“5¬)‘°fŽ¡‘µtŽ‘!œu:±r‘ÿ}'esetŽ‘Æ·¬(‘ª¨);Ž¡‘µtŽ‘!œu:±r‘ÿ}'otateŽ‘o>¬(0Ž‘µ;‘ª¨°Ž‘ qƬ2Ž‘ª§°‘8à±angŽ‘ó†¬);Ž¡‘µeŽ‘"¨:±do‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘9š4¬(µtŽ‘œr¬);Ž¡‘°gŽ¡‘±p0Ž‘"ÝÚ¬=‘ǵeŽ‘o:±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(0Ž‘);Ž¡‘±p0Ž‘ µ:±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u¬(±trueŽ‘ʬ);Ž¡‘­ifŽ‘´ú¬(±p0Ž‘ÝØ°6¬=‘DZx‘‰ffŽ–®axis‘‰ffŽ“ptŽ‘)“5¬)‘°fŽ¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)Ž¡‘(±c‘ÿ}'errŽ‘=”Ü°‘ß2´"ERROR!® ´In® 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IS‘ÕXELLIPTICAL“¬325Ž €n ý•@P‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­P•®9oin“tŽ‘ï°Ž‘#ïži‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘ǵeŽ–o:±p‘ÿ}'ointsŽ›$•µ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);‘ÿý±iterŽ‘’°6¬=‘ǵeŽ“:±p‘ÿ}'ointsŽ˜µ:±endŽ‘ಬ(‘ª¨);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¤ ‘µxŽ‘&~7¬=‘Ç(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±get‘‰ffŽ‘®xŽ‘Žg¬(‘ª¨);Ž¡‘µzŽ‘%Þ9¬=‘Ç(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±get‘‰ffŽ‘®zŽ‘¬(‘ª¨);Ž¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘(±c‘ÿ}'outŽ‘> S°‘Ç´"Point® ´"Ž‘0€°‘ǵiŽ‘ $°‘Ç´":® ´"Ž‘Œ°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘((°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±showŽ‘Šÿ¬(´"iter:"Ž‘%FS¬);Ž¡‘(±c‘ÿ}'outŽ‘> S°‘Ç´"x® ´==® ´"Ž‘*Ôƒ°‘ǵxŽ‘ EL°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘(±c‘ÿ}'outŽ‘> S°‘Ç´"z® ´==® ´"Ž‘*Ôƒ°‘ǵzŽ‘ +¥N°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘°gŽ¡‘µrŽ‘%‘/¬=‘Ç((µxŽ–ïü°‘8àµxŽ“¬)µ=¬(µaŽ–‚°‘8àµaŽ“¬))–8à+“((µzŽ›Oþ°“µzŽ˜¬)µ=¬(µbŽ›ƒŠ°“µbŽ˜¬));Ž¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"r® ´==® ´"Ž‘*Ôƒ°‘ǵrŽ‘ +XD°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘­ifŽ‘)´û¬(±fabsŽ‘2Ò¬(µrŽ‘ô°‘8à¬1Ž‘8á)–ǵ>“­P•®9oin“tŽ‘ad¬::Ž‘%epsilonŽ‘E^¦¬(‘ª¨))‘°fŽ¡‘(­ifŽ‘4r3¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘[ª°‘s´"Point® ´"Ž‘2‹6°‘sµiŽ‘ vÚ°‘s´"® ´doesn't® ´satisfy® ´elŽ‘m7lipse® ´equation.\n"Ž’Ð +Ü°Ž¡‘F´"Returning® ´false.\n\Ž’®ÿËn"Ž’¼ÍE°‘DZ ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾±falseŽ‘`–¬;Ž¡‘°gŽ¡‘€Ÿÿ³+‘ÿ+ŽŽ‘*G#µiŽ‘-¹¬;Ž¡‘°gŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)Ž¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"Exiting® ´Ellipse::isŽ‘kÆÜ_elliptical().® ´RetuŽ’ÔÆ rning® ´true."Ž’ü°‘DZend‘‚ØlŽ–ò°‘DZend‘‚ØlŽ“°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘7æ¼±trueŽ‘J«T¬;Ž¡‘ +°gŽ©­1166.‘ üIs‘ÕTquadratic.ŽŸ°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¡‘ +­inlineŽ‘)ŠIb•QÇo“olŽ‘C+¯±is‘‰ffŽ‘®quadr‘ÿ}'aticŽ‘w£¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼±trueŽ‘J«T¬;Ž¡‘ +°gŽ¦­1167.‘ üIs‘ÕTcubic.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.07.27.¬]Ž‘Y;Made‘UU­virtualŽ‘(ã(¬and‘UUnon-inline.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°ŽŸ ‘ +­virtualŽ‘/Ôb•QÇo“olŽ‘I/:±is‘‰ffŽ‘®cubicŽ‘kT^¬(‘ª®)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹FÅY Šn ý‘ì¬326–¯IS‘ÕXCUBIC’.øó3DLDF-1.1.5.1“°x¬1168Ž €n ý•@P­1168.Ž©°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¤ ‘ +­b•QÇo“olŽ‘#¡gEllipseŽ‘FŠD¬::‘±is‘‰ffŽ‘®cubicŽ‘#%(¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼±falseŽ‘L–¬;Ž¡‘ +°gŽŸ­1169.‘ üIs‘ÕTquartic.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.07.27.¬]Ž‘Y;Made‘UU­virtualŽ‘(ã(¬and‘UUnon-inline.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/Ôb•QÇo“olŽ‘I/:±is‘‰ffŽ‘®quarticŽ‘sa'¬(‘ª®)‘UU­constŽ‘*¢¬;ŽŸ­1170.Ž¦°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¡‘ +­b•QÇo“olŽ‘#¡gEllipseŽ‘FŠD¬::‘±is‘‰ffŽ‘®quarticŽ‘+1ñ¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼±falseŽ‘L–¬;Ž¡‘ +°gŽŸ­1171.– üSolv®9e.“¬[²LDF‘T2002.11.06.¬]Ž‘ẔsolveŽ‘pO—¬(‘ª®)–äëassumes“that“the“­EllipseŽ‘'²¯¬lies“in“a“ma‘Ž8jor“plane“with“its“cen¸ãter“atŽ¡the–ãÿorigin.›LCoGde“that“calls“it“m¸ãust“ensure“that“these“conditions“are“ful lled.˜±solveŽ‘ƒË¬(‘ª®)“returns“the“t•¸ãw“o‘ãÿpGossibleŽ¡v‘ÿqÇalues–UUfor“either“the“horizonš¸ãtal“or“the“v˜ertical“coGordinate.Ž¡‘ +TO–UUDO:“Read“through,“and“then“explain“this“function.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.07.20.¬]Ž‘XŠ No¸ãw–×'using“±get‘‰ffŽ–®axis‘‰ffŽ“vŽ‘-ÐÁ¬(›ª®)“and“±get‘‰ffŽ–®axis‘‰ffŽ“hŽ‘.p¬(˜),‘ðcinstead“of“accessing“±axis‘‰ffŽ‘®hŽ‘ §Û¬and“±axis‘‰ffŽ‘®vŽ‘ t,¬directly‘ÿ*ª.Ž¡‘ +[²LDF‘T2003.07.25.¬]Ž‘Y;Remo•¸ãv“ed–UUsome“commenš¸ãted-out“coGde,“and“an“explanatory“commen˜t.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¡‘ +­realu½‰™šs4Ž‘ÔwpairŽ‘9p‚±solveŽ‘O¨M¬(­c®9harŽ‘jI±axis‘‰ffŽ‘®unknownŽ‘UÞµ;‘ª¨­realŽ‘]Ö±knownŽ‘5>¢¬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹GÏ5 Šn ý‘ì°x¬1172–¯3DLDF-1.1.5.1’9w‘SOL‘ÿ8VE“¬327Ž €n ý•@P­1172.Ž©°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¤ ‘ +­realu½‰™šs4Ž‘ÔwpairŽ‘9p‚EllipseŽ‘\Y_¬::‘±solveŽ‘7Ϭ(­c®9harŽ‘jI±axis‘‰ffŽ‘®unknownŽ‘UÞµ;‘ª¨­realŽ‘]Ö±knownŽ‘5>¢¬)‘UU­constŽ‘*¢°f‘UU­realŽ‘ƒ±r‘ÿ}'adius‘‰ffŽ‘®knownŽ‘U +Š¬;Ž¡‘­realŽ‘4³1±r‘ÿ}'adius‘‰ffŽ‘®unknownŽ‘z²\¬;Ž¦‘±axis‘‰ffŽ‘®unknownŽ‘]:ë¬=‘DZtolowerŽ‘#í¬(±axis‘‰ffŽ‘®unknownŽ‘“±r‘ÿ}'adius‘‰ffŽ‘®knownŽ‘=ɬ)‘°fŽ¡‘(­returnŽ‘Kæ¾´INVALID_REAL_PAIRŽ’¥¬ó¬;Ž¡‘°gŽŽŽŒ‹H× Šn ý‘ì¬328–¯SOL‘ÿ8VE’9w‘3DLDF-1.1.5.1“°x¬1173Ž €n ý•@P­1173.‘ ü¬The–UUequation“for“an“ellipse“in“the“x-y“plane“with“its“cen¸ãter“at“the“origin“isŽ¤’ÃY¯µxŸûÞÿ³2Ž‘|sµ=aŸûÞÿ³2Ž‘µS¬+‘8àµy[ÙŸûÞÿ³2Ž‘ØLµ=bŸûÞÿ³2Ž‘C‹¬=‘Ç1Ž¡where–UUµa“¬is“half“the“horizonš¸ãtal“axis“and“µb“¬is“half“the“v˜ertical“axis.‘qÇTherefore,Ž¡’¹ëµy‘"ñ¬=‘ÇŸöö5¸pŽ‘ ÇŸöö5‰feFù+Ÿ ˬ(1–8à°“µxŸýr³2Ž–|sµ=aŸýr³2Ž“¬)–8à°“µbŸýr³2ŽŽŽŽŽ¡¬andŽ¤ ’·´\µx–Ǭ=“Ÿöö5¸pŽ‘ ÇŸöö5‰feF…Ÿ ˬ(1–8à°“µy[ÙŸýr³2Ž‘ØLµ=bŸýr³2Ž‘|s¬)“°“µaŸýr³2ŽŽŽŽ‘SL µ:ŽŸ°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¡‘ +µrŽ‘Ê:± rstŽ‘|¬=‘DZsqrtŽ‘w¬((1Ž‘‰Ä°–‰Ã¬((±knownŽ›j°“±knownŽ˜¬)µ=¬(±r‘ÿ}'adius‘‰ffŽ‘®knownŽ›;‹Ê°“±r‘ÿ}'adius‘‰ffŽ‘®knownŽ˜¬)))“°“¬(±r‘ÿ}'adius‘‰ffŽ‘®unknownŽ›Fˆî°“±r‘ÿ}'adius‘‰ffŽ‘®unknownŽ˜¬));Ž¡‘ +µrŽ‘Ê:±se–ÿ}'c“ondŽ‘ n߬=‘Ç°Ž‘ +Ž6µrŽ‘XJ:± rstŽ‘µª¬;Ž¡‘ +­returnŽ‘-滵rŽ‘2°Ï¬;‘qÇ°gŽŸ­1174.– üGet‘ôcoQÇecien®9ts.“¬This–Dis“used“for“getting“the“coGecien¸ãts“of“the“quadratic“equation“that“resultsŽ¡from–0ÿreplacing“µy‘ŒØ¬with“µmx–ËQ¬+“µb–0ÿ¬from“the“line“equation,‘géwhere“µm“¬is“the“slopGe“and“µb“¬the“in¸ãtercept“with“theŽ¡v•¸ãertical›B#axis,‘Eú(whic“hev“er˜that˜migh“t˜b•Ge˜in˜a˜particular˜case;‘H‰it˜needn't˜b“e˜the˜y-axis)˜in˜the˜equation˜for˜theŽ¡ellipseŽ¡’ÁÔ€µxŸûÞÿ³2Ž‘|sµ= zŸûÞÿ³2Ž‘¾Í¬+‘8àµy[ÙŸûÞÿ³2Ž‘ØLµ= ‘‡ŸûÞÿ³2Ž‘ʧ¬=‘Ç1Ž©namely›UU!!‘qÇST–ÿ*ªAR“T˜HERE.˜Chec•¸ãk˜this.‘qÇI˜think˜the˜µx˜¬in˜the˜coGecien“t˜for˜µxŸü^ÿ³2Ž‘ÑȬis˜wrong.Ž¡¡‘7 ²µxŸûÞÿ³2Ž›|sµ= zŸûÞÿ³2Ž‘¾Í¬+–8à(µmx“¬+“µb¬)ŸûÞÿ³2Ž˜µ= ‘‡ŸûÞÿ³2Ž‘NON-­CONST‘ÕX¯VERSION“¬329Ž €n ý•@P­1177.‘ üNon-const‘ÕTv®9ersion.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ +¬[²LDF‘T2002.11.10.¬]Ž‘Y;Made–UUthis“function“­virtualŽ‘(ã(¬and“non-­inlineŽ‘4ó¬.Ž¡‘ +[²LDF‘T2003.05.09.¬]Ž‘Y;Changed–UUreturn“v‘ÿqÇalue“from“­P•®9oin“tŽ‘"Dò¬&Ž‘-aeto“­constŽ‘!÷P•®9oin“tŽ‘@o”¬&Ž‘H6².Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž© ‘ +­virtualŽ‘/ÔconstŽ‘M¸vP•®9oin“tŽ‘l¨¬&Ž‘to1±get‘‰ffŽ‘®c‘ÿ}'enterŽ’ ¬x¬(‘ª¨);ŽŸ­1178.Ž¡°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¦‘ +­constŽ‘(*£P•®9oin“tŽ‘G@¬&Ž‘Ná^­EllipseŽ‘qÊ;¬::Ž‘xXy±get‘‰ffŽ‘®c‘ÿ}'enterŽ’¤•À¬(‘ª¨)Ž¦‘ +°fŽ¦‘±c‘ÿ}'enterŽ‘0 µ:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¦‘­returnŽ‘7æ¼±c‘ÿ}'enterŽ‘SðG¬;Ž¦‘ +°gŽŸ­1179.‘ üconst‘ÕTv®9ersion.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ +¬[²LDF‘T2002.11.10.¬]Ž‘Y;Made–UUthis“function“­virtualŽ‘(ã(¬and“non-­inlineŽ‘4ó¬.Ž¡ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¦‘ +­virtualŽ‘/ÔP•®9oin“tŽ‘N}q±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘zº¸¬(‘ª®)‘UU­constŽ‘*¢¬;ŽŸ­1180.Ž¡°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¦‘ +­P•®9oin“tŽ‘(ïžEllipseŽ‘KØ{¬::‘±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘-=K¬(‘ª®)‘UU­constŽŽ¦‘ +°fŽ¦‘­P•®9oin“tŽ‘2pŽ‘7÷Ÿ¬(±c‘ÿ}'enterŽ‘ ‹¬);Ž¡‘µpŽ‘:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¦‘­returnŽ‘7æ¼µpŽ‘<;Ž¦‘ +°gŽ¤­1181.‘ üGet‘ÕTfoQÇcus.Ž¡1182.‘ üNon-const‘ÕTv®9ersion.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ +¬[²LDF‘T2003.07.25.¬]Ž‘Y;Added–UUthis“function.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¦‘ +­constŽ‘(*£P•®9oin“tŽ‘G@¬&Ž‘Ná^±get‘‰ffŽ‘®fo‘ÿ}'cusŽ‘v"ï¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµsŽ‘pÜS¬);ŽŽŽŒ‹Jð  Šn ý‘ì¬330–¯NON-­CONST‘ÕX¯VERSION’ìÎ>3DLDF-1.1.5.1“°x¬1183Ž €n ý•@P­1183.Ž©°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¤ ‘ +­constŽ‘(*£P•®9oin“tŽ‘G@¬&Ž‘Ná^­EllipseŽ‘qÊ;¬::‘±get‘‰ffŽ‘®fo‘ÿ}'cusŽ‘(A•¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµsŽ‘pÜS¬)Ž¡‘ +°fŽ¡‘­ifŽ‘´ú¬(µsŽ‘w°‘Ǭ0Ž‘Ç)‘°fŽ¡‘±fo‘ÿ}'cus0Ž‘:³-µ:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¡‘­returnŽ‘Aæ½±fo‘ÿ}'cus0Ž‘^™ç¬;Ž¡‘°gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(µsŽ‘w°‘Ǭ1Ž‘Ç)‘°fŽ¡‘±fo‘ÿ}'cus1Ž‘:³-µ:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¡‘­returnŽ‘Aæ½±fo‘ÿ}'cus1Ž‘^™ç¬;Ž¡‘°gŽ¡‘­elseŽ‘+Øá°fŽ¡‘±c‘ÿ}'errŽ‘3ôâ°‘?9´"ERROR!® ´In® ´|Ellipse:Ž‘l>ý:get_focus()|:\n"Ž’ÉDk°‘?9´"Invalid® ´argument:® ´"Ž‘pž°‘?9µsŽ‘ .r°‘?9±end‘‚ØlŽ‘p4°Ž¡‘2´"Valid® ´arguments® ´areŽ’šÿÉ® ´0® ´and® ´1.\n"Ž’ÝM%°‘Ç´"Returning® ´INVALID_PŽ‘kÆÜOINT.\n\n"Ž’£”>°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½´INVALID_POINTŽ’†¬þ¬;Ž¡‘°gŽ¡‘ +gŽŸ­1184.‘ üconst‘ÕTv®9ersion.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.07.25.¬]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¡‘ +­P•®9oin“tŽ‘(ïž±get‘‰ffŽ‘®fo‘ÿ}'cusŽ‘P1/¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµsŽ‘pÜS¬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹Kø$ Šn ý‘ì°x¬1185–¯3DLDF-1.1.5.1’ûÖ­CONST‘ÕX¯VERSION“¬331Ž €n ý•@P­1185.Ž©°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¤ ‘ +­P•®9oin“tŽ‘(ïžEllipseŽ‘KØ{¬::‘±get‘‰ffŽ‘®fo‘ÿ}'cusŽ‘(A•¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµsŽ‘pÜS¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­P•®9oin“tŽ‘2pŽ‘7÷Ÿ¬;Ž¦‘­ifŽ‘´ú¬(µsŽ‘w°‘Ǭ0Ž‘Ç)‘°fŽ¡‘µpŽ‘%Ϭ=‘DZfo‘ÿ}'cus0Ž‘zB¬;Ž¡‘µpŽ‘#:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¡‘­returnŽ‘Aæ½µpŽ‘F;Ž¡‘°gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(µsŽ‘w°‘Ǭ1Ž‘Ç)‘°fŽ¡‘µpŽ‘%Ϭ=‘DZfo‘ÿ}'cus1Ž‘zB¬;Ž¡‘µpŽ‘#:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¡‘­returnŽ‘Aæ½µpŽ‘F;Ž¡‘°gŽ¡‘­elseŽ‘+Øá°fŽ¡‘±c‘ÿ}'errŽ‘3ôâ°‘?9´"ERROR!® ´In® ´|Ellipse:Ž‘l>ý:get_focus()|:\n"Ž’ÉDk°‘?9´"Invalid® ´argument:® ´"Ž‘pž°‘?9µsŽ‘ .r°‘?9±end‘‚ØlŽ‘p4°Ž¡‘2´"Valid® ´arguments® ´areŽ’šÿÉ® ´0® ´and® ´1.\n"Ž’ÝM%°‘Ç´"Returning® ´INVALID_PŽ‘kÆÜOINT.\n\n"Ž’£”>°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½´INVALID_POINTŽ’†¬þ¬;Ž¡‘°gŽ¡‘ +gŽŸ­1186.‘ üGet–ÕTlinear“eccen•®9tricit“y‘ÿ «.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.07.25.«]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘ ³/Ïget‘‰ffŽ–®line›ÿ}'ar‘‰ffŽ“e˜c˜c˜entricityŽ‘“Æ«(‘ª®)‘UUÂconstŽ‘*¢«;ŽŸÂ1149.Ž¦·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘ ³/EllipseŽ‘Cœ «::‘Ïget‘‰ffŽ–®line›ÿ}'ar‘‰ffŽ“e˜c˜c˜entricityŽ‘_à›«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼Ïline–ÿ}'ar‘‰ffŽ‘®e“c“c“entricityŽ’†“—«;Ž¡‘ -·gŽŸÂ1150.‘ üGet–ÕTnš®9umerical“eccen˜tricit˜y‘ÿ +¬[²LDF‘T2003.07.25.¬]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¡‘ +­realŽ‘ ³/±get‘‰ffŽ–®line›ÿ}'ar‘‰ffŽ“e˜c˜c˜entricityŽ‘“Ƭ(‘ª®)‘UU­constŽ‘*¢¬;ŽŸ­1187.Ž¦°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¡‘ +­realŽ‘ ³/EllipseŽ‘Cœ ¬::‘±get‘‰ffŽ–®line›ÿ}'ar‘‰ffŽ“e˜c˜c˜entricityŽ‘_à›¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼±line–ÿ}'ar‘‰ffŽ‘®e“c“c“entricityŽ’†“—¬;Ž¡‘ +°gŽŸ­1188.‘ üGet–ÕTnš®9umerical“eccen˜tricit˜y‘ÿ «.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.07.27.«]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘ ³/Ïget‘‰ffŽ–®numeric›ÿ}'al‘‰ffŽ“e˜c˜c˜entricityŽ’‘¸¹«(‘ª®)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹E- Šn ý‘ì·x«1151›­3DLDFPRÃŽG’Ì·ßGET–ÕXNUMERICAL“ECCENTRICITY˜«325Ž €n ý•@PÂ1151.Ž©·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¤ ‘ -ÂrealŽ‘ ³/EllipseŽ‘Cœ «::‘Ïget‘‰ffŽ–®numeric›ÿ}'al‘‰ffŽ“e˜c˜c˜entricityŽ‘rŽ«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼Ïnumeric–ÿ}'al‘‰ffŽ‘®e“c“c“entricityŽ’˜¸Š«;Ž¡‘ -·gŽŸÂ1152.‘ üGet‘ÕTaxes.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.07.20.«]Ž‘Z©?Rewrote–öYthe“ÂconstŽ‘$Áÿ«v¸ãersions“of“the“functions“in“this“section,‘^™and“added“non-ÂconstŽŽ¡«vš¸ãersions.‘_All–Vof“them“no˜w“c˜hec˜k“whether“·Ž‘WÏthisŽ‘&c«is“still“elliptical“using“Ïis‘‰ffŽ‘®el‘‚ØlipseŽ‘*M$«(‘ª®).‘_If“it“is,‘(‰the“v‘ÿqÇalue“Ïaxis‘‰ffŽ‘®vŽ‘!Š«orŽ¡Ïaxis‘‰ffŽ‘®hŽ‘·«should›½òha•¸ãv“e˜is˜recalculated,‘Øand˜this˜v‘ÿqÇalue˜is˜returned.‘«In˜the˜non-ÂconstŽ‘“?«v“ersions,‘ØÏaxis‘‰ffŽ‘®vŽ‘"[é«or˜Ïaxis‘‰ffŽ‘®hŽŽ¡«is–‰ºreset“to“the“new“v‘ÿqÇalue.‘õIf“·Ž‘‰»ÏthisŽ‘ÿ+«is“no“longer“elliptical,›–Óthe“function“returns“ÝINVALID_REALŽ‘Cþ«,˜and“Ïaxis‘‰ffŽ‘®hŽ‘" «orŽ¡Ïaxis‘‰ffŽ‘®vŽ‘3«is–UUset“to“ÝINVALID_REALŽ‘F0î«in“the“non-ÂconstŽ‘*¢«v¸ãersions.Ž¡‘ -[¬LDF‘T2003.07.20.«]Ž‘X¸Ïaxis‘‰ffŽ‘®hŽ‘ul«and‘_ÒÏaxis‘‰ffŽ‘®vŽ‘…‚«are–_ÒupGdated“b¸ãy“the“transformation“functions,‘íand“these“are“presumablyŽ¡the–only“ones“that“could“cause“an“ÂEllipseŽ‘* -ý«to“bGecome“non-elliptical.‘¤ýSo,‘@c•¸ãhec“king–and“recalculating“themŽ¡here–UUis“probably“redundan•¸ãt.‘qÇHo“w“ev“er,–UUthis“maš¸ãy“c˜hange,“so“it's“safer“to“do“this“here.Ž¡‘ -[¬LDF‘T2003.07.25.«]Ž‘XUþBUG‘¢ëFIX:‘£Ïaxis‘‰ffŽ‘®hŽ‘ ?½«and‘£Ïaxis‘‰ffŽ‘®vŽ‘ «wš¸ãere–£toGo“small“b˜y“half.‘6^No˜w“m˜ultiplying“b˜y“2“in“all“v˜ersionsŽ¡of‘UUÏget‘‰ffŽ–®axis‘‰ffŽ“hŽ‘.‚ž«(›ª®)–UUand“Ïget‘‰ffŽ–®axis‘‰ffŽ“vŽ‘.Nï«(˜).Ž¦ŸüÈ„`ÕÁGŽŽ¤Â1153.‘ üGet–ÕTv®9ertical“axis.Ž¡1154.‘ üconst‘ÕTv®9ersion.Ž¦·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·ŽŸ ‘ -ÂrealŽ‘ ³/Ïget‘‰ffŽ–®axis‘‰ffŽ“vŽ‘K¬É«(‘ª®)‘UUÂconstŽ‘*¢«;Ž¡Â1155.Ž¦·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¤ ‘ -ÂrealŽ‘ ³/EllipseŽ‘Cœ «::‘Ïget‘‰ffŽ–®axis‘‰ffŽ“vŽ‘+ùž«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂifŽ‘´ú«(Ïis‘‰ffŽ‘®el‘‚Øliptic‘ÿ}'alŽ‘0ì–«(‘ª®))‘ÂreturnŽ‘(溫(2Ž‘8á·–8à«(Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH«(Ïnumb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜ointsŽ‘JÀ©±=«4Ž‘)“·“Ïget‘‰ffŽ‘®c‘ÿ}'enterŽ‘.v'«(–ª¨))±:ÏmagnitudeŽ‘.=r«(“));Ž¡‘ÂelseŽ‘+ØáreturnŽ‘O¿›ÝINVALID_REALŽ’Eß«;Ž¡‘ -·gŽŸÂ1156.‘ üNon-const‘ÕTv®9ersion.Ž¦·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘ ³/Ïget‘‰ffŽ–®axis‘‰ffŽ“vŽ‘K¬É«(‘ª®);ŽŸÂ1157.Ž¦·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘ ³/EllipseŽ‘Cœ «::‘Ïget‘‰ffŽ–®axis‘‰ffŽ“vŽ‘+ùž«(‘ª®)Ž¡‘ -·fŽ¡‘ÂifŽ‘´ú«(Ïis‘‰ffŽ‘®el‘‚Øliptic‘ÿ}'alŽ‘0ì–«(‘ª®))‘Ïaxis‘‰ffŽ‘®vŽ‘"Œö«=‘Ç((Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH«(Ïnumb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜ointsŽ‘JÀ©±=«4Ž‘)–8à·“Ïget‘‰ffŽ‘®c‘ÿ}'enterŽ‘.v'«(–ª¨))±:ÏmagnitudeŽ‘.=r«(“)–8à·“«2Ž‘8á);Ž¡‘ÂelseŽ‘+ØáÏaxis‘‰ffŽ‘®vŽ‘Ie׫=‘ÇÝINVALID_REALŽ‘BM\«;Ž¡‘ÂreturnŽ‘7æ¼Ïaxis‘‰ffŽ‘®vŽ‘R¬š«;Ž¡‘ -·gŽŸÂ1158.‘ üGet–ÕThorizon®9tal“axis.ŽŽŽŒ‹Fª Šn ý‘ì«326–ÂCONST‘ÕX­VERSION’ ol3DLDFPRÃŽG“·x«1159Ž €n ý•@PÂ1159.‘ üconst‘ÕTv®9ersion.Ž¤·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·Ž© ‘ -ÂrealŽ‘ ³/Ïget‘‰ffŽ–®axis‘‰ffŽ“hŽ‘Kàx«(‘ª®)‘UUÂconstŽ‘*¢«;ŽŸÂ1160.Ž¡·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¦‘ -ÂrealŽ‘ ³/EllipseŽ‘Cœ «::‘Ïget‘‰ffŽ–®axis‘‰ffŽ“hŽ‘,-M«(‘ª®)‘UUÂconstŽŽ¦‘ -·fŽ¦‘ÂifŽ‘´ú«(Ïis‘‰ffŽ‘®el‘‚Øliptic‘ÿ}'alŽ‘0ì–«(‘ª®))‘ÂreturnŽ‘(溫((Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH«(0Ž‘)–8à·“Ïget‘‰ffŽ‘®c‘ÿ}'enterŽ‘.v'«(–ª¨))±:ÏmagnitudeŽ‘.=r«(“)–8à·“«2Ž‘8á);Ž¦‘ÂelseŽ‘+ØáreturnŽ‘O¿›ÝINVALID_REALŽ’Eß«;Ž¦‘ -·gŽŸÂ1161.‘ üNon-const‘ÕTv®9ersion.Ž¡·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·Ž¦‘ -ÂrealŽ‘ ³/Ïget‘‰ffŽ–®axis‘‰ffŽ“hŽ‘Kàx«(‘ª®);ŽŸÂ1162.Ž¡·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¦‘ -ÂrealŽ‘ ³/EllipseŽ‘Cœ «::‘Ïget‘‰ffŽ–®axis‘‰ffŽ“hŽ‘,-M«(‘ª®)Ž¦‘ -·fŽ¦‘ÂifŽ‘´ú«(Ïis‘‰ffŽ‘®el‘‚Øliptic‘ÿ}'alŽ‘0ì–«(‘ª®))‘Ïaxis‘‰ffŽ‘®hŽ‘"À¥«=‘Ç(Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH«(0Ž‘)–8à·“Ïget‘‰ffŽ‘®c‘ÿ}'enterŽ‘.v'«(–ª¨))±:ÏmagnitudeŽ‘.=r«(“)–8à·“«2Ž‘8á;Ž¦‘ÂelseŽ‘+ØáÏaxis‘‰ffŽ‘®hŽ‘I™†«=‘ÇÝINVALID_REALŽ‘BM\«;Ž¦‘ÂreturnŽ‘7æ¼Ïaxis‘‰ffŽ‘®hŽ‘RàI«;Ž¦‘ -·gŽŸÂ1163.– üAngle‘èpQÇoin®9t.“Ïangle‘‰ffŽ‘®p‘ÿ}'ointŽ‘<Ù¹«(‘ª®)–ežreturns“a“pGoinš¸ãt“on“the“ellipse“giv˜en“an“angle.‘¢¡E ectiv˜ely‘ÿ*ª,‘i°Ïp‘ÿ}'ointŽ‘˜<«[0Ž‘]“isŽ¦rotated–† abGout“the“cenš¸ãter“in“the“plane“of“the“ellipse“and“the“in˜tersection“of“the“ra˜y“from“the“cen˜ter“throughŽ¦Ïp‘ÿ}'ointŽ‘.Œ«[0Ž‘]–UUand“the“ellipse“is“returned.Ž¦‘ -[¬LDF‘T2003.07.27.«]Ž‘Y;TO–UUDO:“T‘ÿ*ªry“to“get“the“rotation“to“alw•¸ãa“ys–UUgo“in“the“direction“I“wš¸ãould“lik˜e.ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¦‘ -«[¬LDF‘T2003.07.01.«]Ž‘YvBUG‘à FIX:–Ã)No¸ãw“returning“ÏbppŽ‘º±:Ï rstŽ‘µª±:ÏptŽ‘ §Æ«if“it's“not“equal“to“ÝINVALID_POINTŽ‘H‰j«.‘»COtherwise,Ž¦ÏbppŽ‘öé±:Ïse–ÿ}'c“ondŽ‘§Ç±:ÏptŽ‘ Òm«is–íÐreturned.›;9The“latter“ma¸ãy“bGe“a“v‘ÿqÇalid“ÂP•®9oin“tŽ‘ˆ«,‘ïor“ÝINVALID_POINTŽ‘H´«.˜Before,‘ïÝINVALID_POINTŽŽ¦«w¸ãas–M*returned“if“ÏbppŽ›D±:Ï rstŽ‘µª±:bŽ‘—Ô«and“ÏbppŽ˜±:Ïse–ÿ}'c“ondŽ‘§Ç±:bŽ‘—Ô«w¸ãere“ÏfalseŽ‘ün«,›NÌbut“this“is“the“case,˜if“the“inš¸ãtersection“pGoin˜ts“didn'tŽ¦lie–UUon“the“line“segmenš¸ãt“bGet˜w˜een“Ïc‘ÿ}'enterŽ‘"´5«and“Ïpt0Ž‘¾«.Ž¦‘ +¬[²LDF‘T2003.07.27.¬]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¡‘ +­realŽ‘ ³/±get‘‰ffŽ–®numeric›ÿ}'al‘‰ffŽ“e˜c˜c˜entricityŽ’‘¸¹¬(‘ª®)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹LýРŠn ý‘ì¬332›¯GET–ÕXNUMERICAL“ECCENTRICITY’ÄDI3DLDF-1.1.5.1˜°x¬1189Ž €n ý•@P­1189.Ž©°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¤ ‘ +­realŽ‘ ³/EllipseŽ‘Cœ ¬::‘±get‘‰ffŽ–®numeric›ÿ}'al‘‰ffŽ“e˜c˜c˜entricityŽ‘rŽ¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼±numeric–ÿ}'al‘‰ffŽ‘®e“c“c“entricityŽ’˜¸Š¬;Ž¡‘ +°gŽŸ­1190.‘ üGet‘ÕTaxes.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.07.20.¬]Ž‘Z©?Rewrote–öYthe“­constŽ‘$Áÿ¬v¸ãersions“of“the“functions“in“this“section,‘^™and“added“non-­constŽŽ¡¬vš¸ãersions.‘_All–Vof“them“no˜w“c˜hec˜k“whether“°Ž‘W±thisŽ‘&c¬is“still“elliptical“using“±is‘‰ffŽ‘®el‘‚ØlipseŽ‘*M$¬(‘ª®).‘_If“it“is,‘(‰the“v‘ÿqÇalue“±axis‘‰ffŽ‘®vŽ‘!Š¬orŽ¡±axis‘‰ffŽ‘®hŽ‘·¬should›½òha•¸ãv“e˜is˜recalculated,‘Øand˜this˜v‘ÿqÇalue˜is˜returned.‘«In˜the˜non-­constŽ‘“?¬v“ersions,‘رaxis‘‰ffŽ‘®vŽ‘"[é¬or˜±axis‘‰ffŽ‘®hŽŽ¡¬is–‰ºreset“to“the“new“v‘ÿqÇalue.‘õIf“°Ž‘‰»±thisŽ‘ÿ+¬is“no“longer“elliptical,›–Óthe“function“returns“´INVALID_REALŽ‘Cþ¬,˜and“±axis‘‰ffŽ‘®hŽ‘" ¬orŽ¡±axis‘‰ffŽ‘®vŽ‘3¬is–UUset“to“´INVALID_REALŽ‘F0î¬in“the“non-­constŽ‘*¢¬v¸ãersions.Ž¡‘ +[²LDF‘T2003.07.20.¬]Ž‘X¸±axis‘‰ffŽ‘®hŽ‘ul¬and‘_Ò±axis‘‰ffŽ‘®vŽ‘…‚¬are–_ÒupGdated“b¸ãy“the“transformation“functions,‘íand“these“are“presumablyŽ¡the–only“ones“that“could“cause“an“­EllipseŽ‘* +ý¬to“bGecome“non-elliptical.‘¤ýSo,‘@c•¸ãhec“king–and“recalculating“themŽ¡here–UUis“probably“redundan•¸ãt.‘qÇHo“w“ev“er,–UUthis“maš¸ãy“c˜hange,“so“it's“safer“to“do“this“here.Ž¡‘ +[²LDF‘T2003.07.25.¬]Ž‘XUþBUG‘¢ëFIX:‘£±axis‘‰ffŽ‘®hŽ‘ ?½¬and‘£±axis‘‰ffŽ‘®vŽ‘ ¬wš¸ãere–£toGo“small“b˜y“half.‘6^No˜w“m˜ultiplying“b˜y“2“in“all“v˜ersionsŽ¡of‘UU±get‘‰ffŽ–®axis‘‰ffŽ“hŽ‘.‚ž¬(›ª®)–UUand“±get‘‰ffŽ–®axis‘‰ffŽ“vŽ‘.Nï¬(˜).Ž¦ŸüÈ„`ÕÁGŽŽ¤­1191.‘ üGet–ÕTv®9ertical“axis.Ž¡1192.‘ üconst‘ÕTv®9ersion.Ž¦°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°ŽŸ ‘ +­realŽ‘ ³/±get‘‰ffŽ–®axis‘‰ffŽ“vŽ‘K¬É¬(‘ª®)‘UU­constŽ‘*¢¬;Ž¡­1193.Ž¦°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¤ ‘ +­realŽ‘ ³/EllipseŽ‘Cœ ¬::‘±get‘‰ffŽ–®axis‘‰ffŽ“vŽ‘+ùž¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­ifŽ‘´ú¬(±is‘‰ffŽ‘®el‘‚Øliptic‘ÿ}'alŽ‘0ì–¬(‘ª®))‘­returnŽ‘(溬(2Ž‘8á°–8à¬(±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(±numb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜ointsŽ‘JÀ©µ=¬4Ž‘)“°“±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘.v'¬(–ª¨))µ:±magnitudeŽ‘.=r¬(“));Ž¡‘­elseŽ‘+ØáreturnŽ‘O¿›´INVALID_REALŽ’E߬;Ž¡‘ +°gŽŸ­1194.‘ üNon-const‘ÕTv®9ersion.Ž¦°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¡‘ +­realŽ‘ ³/±get‘‰ffŽ–®axis‘‰ffŽ“vŽ‘K¬É¬(‘ª®);ŽŸ­1195.Ž¦°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¡‘ +­realŽ‘ ³/EllipseŽ‘Cœ ¬::‘±get‘‰ffŽ–®axis‘‰ffŽ“vŽ‘+ùž¬(‘ª®)Ž¡‘ +°fŽ¡‘­ifŽ‘´ú¬(±is‘‰ffŽ‘®el‘‚Øliptic‘ÿ}'alŽ‘0ì–¬(‘ª®))‘±axis‘‰ffŽ‘®vŽ‘"Œö¬=‘Ç((±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(±numb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜ointsŽ‘JÀ©µ=¬4Ž‘)–8à°“±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘.v'¬(–ª¨))µ:±magnitudeŽ‘.=r¬(“)–8à°“¬2Ž‘8á);Ž¡‘­elseŽ‘+Øá±axis‘‰ffŽ‘®vŽ‘Ie׬=‘Ç´INVALID_REALŽ‘BM\¬;Ž¡‘­returnŽ‘7æ¼±axis‘‰ffŽ‘®vŽ‘R¬š¬;Ž¡‘ +°gŽŸ­1196.‘ üGet–ÕThorizon®9tal“axis.ŽŽŽŒ‹MP Šn ý‘ì°x¬1197–¯3DLDF-1.1.5.1’ûÖ­CONST‘ÕX¯VERSION“¬333Ž €n ý•@P­1197.‘ üconst‘ÕTv®9ersion.Ž¤°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž© ‘ +­realŽ‘ ³/±get‘‰ffŽ–®axis‘‰ffŽ“hŽ‘Kàx¬(‘ª®)‘UU­constŽ‘*¢¬;ŽŸ­1198.Ž¡°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¦‘ +­realŽ‘ ³/EllipseŽ‘Cœ ¬::‘±get‘‰ffŽ–®axis‘‰ffŽ“hŽ‘,-M¬(‘ª®)‘UU­constŽŽ¦‘ +°fŽ¦‘­ifŽ‘´ú¬(±is‘‰ffŽ‘®el‘‚Øliptic‘ÿ}'alŽ‘0ì–¬(‘ª®))‘­returnŽ‘(溬((±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(0Ž‘)–8à°“±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘.v'¬(–ª¨))µ:±magnitudeŽ‘.=r¬(“)–8à°“¬2Ž‘8á);Ž¦‘­elseŽ‘+ØáreturnŽ‘O¿›´INVALID_REALŽ’E߬;Ž¦‘ +°gŽŸ­1199.‘ üNon-const‘ÕTv®9ersion.Ž¡°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¦‘ +­realŽ‘ ³/±get‘‰ffŽ–®axis‘‰ffŽ“hŽ‘Kàx¬(‘ª®);ŽŸ­1200.Ž¡°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¦‘ +­realŽ‘ ³/EllipseŽ‘Cœ ¬::‘±get‘‰ffŽ–®axis‘‰ffŽ“hŽ‘,-M¬(‘ª®)Ž¦‘ +°fŽ¦‘­ifŽ‘´ú¬(±is‘‰ffŽ‘®el‘‚Øliptic‘ÿ}'alŽ‘0ì–¬(‘ª®))‘±axis‘‰ffŽ‘®hŽ‘"À¥¬=‘Ç(±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(0Ž‘)–8à°“±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘.v'¬(–ª¨))µ:±magnitudeŽ‘.=r¬(“)–8à°“¬2Ž‘8á;Ž¦‘­elseŽ‘+Øá±axis‘‰ffŽ‘®hŽ‘I™†¬=‘Ç´INVALID_REALŽ‘BM\¬;Ž¦‘­returnŽ‘7æ¼±axis‘‰ffŽ‘®hŽ‘RàI¬;Ž¦‘ +°gŽŸ­1201.– üAngle‘èpQÇoin®9t.“±angle‘‰ffŽ‘®p‘ÿ}'ointŽ‘<Ù¹¬(‘ª®)–ežreturns“a“pGoinš¸ãt“on“the“ellipse“giv˜en“an“angle.‘¢¡E ectiv˜ely‘ÿ*ª,‘i°±p‘ÿ}'ointŽ‘˜<¬[0Ž‘]“isŽ¦rotated–† abGout“the“cenš¸ãter“in“the“plane“of“the“ellipse“and“the“in˜tersection“of“the“ra˜y“from“the“cen˜ter“throughŽ¦±p‘ÿ}'ointŽ‘.Œ¬[0Ž‘]–UUand“the“ellipse“is“returned.Ž¦‘ +[²LDF‘T2003.07.27.¬]Ž‘Y;TO–UUDO:“T‘ÿ*ªry“to“get“the“rotation“to“alw•¸ãa“ys–UUgo“in“the“direction“I“wš¸ãould“lik˜e.ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ +¬[²LDF‘T2003.07.01.¬]Ž‘YvBUG‘à FIX:–Ã)No¸ãw“returning“±bppŽ‘ºµ:± rstŽ‘µªµ:±ptŽ‘ §Æ¬if“it's“not“equal“to“´INVALID_POINTŽ‘H‰j¬.‘»COtherwise,Ž¦±bppŽ‘öéµ:±se–ÿ}'c“ondŽ‘§Çµ:±ptŽ‘ Òm¬is–íÐreturned.›;9The“latter“ma¸ãy“bGe“a“v‘ÿqÇalid“­P•®9oin“tŽ‘ˆ¬,‘ïor“´INVALID_POINTŽ‘H´¬.˜Before,‘ï´INVALID_POINTŽŽ¦¬w¸ãas–M*returned“if“±bppŽ›Dµ:± rstŽ‘µªµ:bŽ‘—Ô¬and“±bppŽ˜µ:±se–ÿ}'c“ondŽ‘§Çµ:bŽ‘—Ô¬w¸ãere“±falseŽ‘ün¬,›NÌbut“this“is“the“case,˜if“the“inš¸ãtersection“pGoin˜ts“didn'tŽ¦lie–UUon“the“line“segmenš¸ãt“bGet˜w˜een“±c‘ÿ}'enterŽ‘"´5¬and“±pt0Ž‘¾¬.Ž¦‘ BUG‘Œ‹FIX:–Œ™Noš¸ãw“c˜hec˜king“to“mak˜e“sure“that“the“in˜tersection“pGoin˜t“lies“in“the“propGer“direction.‘’No˜w“thatŽ¦the–UUinš¸ãtersection“pGoin˜t“doGesn't“ha˜v˜e“to“bGe“on“the“line“segmen˜t,“it's“necessary“to“c˜hec˜k“this.Ž¦‘ -[¬LDF‘T2003.07.20.«]Ž‘XŠ No¸ãw–×'using“Ïget‘‰ffŽ–®axis‘‰ffŽ“vŽ‘-ÐÁ«(›ª®)“and“Ïget‘‰ffŽ–®axis‘‰ffŽ“hŽ‘.p«(˜),‘ðcinstead“of“accessing“Ïaxis‘‰ffŽ‘®hŽ‘ §Û«and“Ïaxis‘‰ffŽ‘®vŽ‘ t,«directly‘ÿ*ª.Ž¦‘ -[¬LDF‘T2003.07.27.«]Ž‘Xé5Made‘6OÂconstŽ– œ«.›gpMade‘6OÏangleŽ‘,ñ«argumen¸ãt‘6OÂconstŽ“«.˜No¸ãw–6Ousing“Ïget‘‰ffŽ‘®c‘ÿ}'enterŽ‘/s–«(‘ª®)“instead“of“Ïc‘ÿ}'enterŽ‘?Ú«.Ž¡ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·Ž¦‘ -ÂP•®9oin“tŽ‘(ïžÏangle‘‰ffŽ‘®p‘ÿ}'ointŽ‘ZI[«(ÂconstŽ‘*¢realŽ‘4ÝÐÏangleŽ‘Lž#«)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹G-Z Šn ý‘ì·x«1164–­3DLDFPRÃŽG’ {ANGLE‘ÕXPOINT“«327Ž €n ý•@PÂ1164.Ž©·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¤ ‘ -ÂP•®9oin“tŽ‘(ïžEllipseŽ‘KØ{«::‘Ïangle‘‰ffŽ‘®p‘ÿ}'ointŽ‘2YÁ«(ÂconstŽ‘*¢realŽ‘4ÝÐÏangleŽ‘Lž#«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂP•®9oin“tŽ‘2ïŸÏCenterŽ‘TÑS«=‘ÇÏget‘‰ffŽ‘®c‘ÿ}'enterŽ‘/_«(‘ª¨);Ž¡‘ÂP•®9oin“tŽ‘2ïŸÏnormalŽ‘V o«=‘ÇÏget‘‰ffŽ‘®normalŽ‘3QŒ«(‘ª¨);Ž¦‘ÏnormalŽ‘4Vº±:ÏshiftŽ‘}«(ÏCenterŽ‘œ«);Ž¦‘ÂP•®9oin“tŽ‘2ïŸÏpt0Ž‘Eò«=‘ÇÏget‘‰ffŽ‘®p‘ÿ}'ointŽ‘*)`«(0Ž‘);Ž¦‘Ïpt0Ž‘&0U·«=ŽŽ‘8…©ÏCenterŽ‘W E«;Ž¡‘Ïpt0Ž‘#i=±:Ïunit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u«(ÏtrueŽ‘Ę«);Ž¡‘Ïpt0Ž‘&0U·«=ŽŽ‘5¾ŒÏmaxŽ‘Ic'«(Ïget‘‰ffŽ–®axis‘‰ffŽ“hŽ‘+-I«(–ª¨)±;“Ïget‘‰ffŽ–®axis‘‰ffŽ“vŽ‘,¤B«(“))±=«2Ž‘;Ž¡‘±=·‘ÿý«[¬LDF‘T2002.11.06.«]Ž‘T7Ïpt0Ž‘fÆÇ«will–UUeither“lie“on“the“pšGerimeter“of“the“ÂEllipseŽ‘(“ƒ«or“b˜ey¸ãond“it.‘o·±=Ž¡‘Ïpt0Ž‘#i=±:ÏshiftŽ‘}«(ÏCenterŽ‘œ«);Ž¡‘Ïpt0Ž‘#i=±:Ïr‘ÿ}'otateŽ‘o>«(ÏCenterŽ‘œ±;‘ª¨ÏnormalŽ‘"`±;‘ª¨ÏangleŽ‘jû«);Ž¦‘Âb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘edðÏbppŽ‘x"ñ«=‘ÇÏinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘TS÷«(ÏCenterŽ‘œ±;‘ª¨Ïpt0Ž‘ã«);Ž¡‘ÂP•®9oin“tŽ‘2ïŸÏdir–ÿ}'e“ction‘‰ffŽ‘®lineŽ‘mj«(Ïpt0Ž‘¢·‘8àÏCenterŽ‘!S|«);Ž¦‘Ïdir–ÿ}'e“ction‘‰ffŽ‘®lineŽ‘N{%±:Ïunit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u«(ÏtrueŽ‘Ę«);Ž¦‘ÂP•®9oin“tŽ‘2ïŸÏdir–ÿ}'e“ction‘‰ffŽ‘®ptŽ‘f4«;Ž¦‘ÂifŽ‘´ú«(ÏbppŽ‘öé±:Ï rstŽ‘µª±:ÏptŽ‘ «µ·6«=‘ÇÝINVALID_POINTŽ‘GY«)‘·fŽ¡‘Ïdir–ÿ}'e“ction‘‰ffŽ‘®ptŽ‘T «=‘ÇÏbppŽ‘¾±:Ï rstŽ‘µª±:ÏptŽ‘ ä«;Ž¡‘Ïdir–ÿ}'e“ction‘‰ffŽ‘®ptŽ‘T ·«=ŽŽ‘f`ÓÏCenterŽ’…{o«;Ž¡‘Ïdir–ÿ}'e“ction‘‰ffŽ‘®ptŽ‘QDg±:Ïunit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u«(ÏtrueŽ‘Ę«);Ž¡‘ÂifŽ‘)´û«(Ïdir–ÿ}'e“ction‘‰ffŽ‘®ptŽ‘6 |·‘ÇÏdir–ÿ}'e“ction‘‰ffŽ‘®lineŽ‘=B;«)‘ÂreturnŽ‘(æºÏbppŽ‘8Ý£±:Ï rstŽ‘µª±:ÏptŽ‘ ä«;Ž¡‘·gŽ¡‘ÂreturnŽ‘7æ¼ÏbppŽ‘GÝ¥±:Ïse–ÿ}'c“ondŽ‘§Ç±:ÏptŽ‘ ä«;Ž¡‘ -·gŽŸÂ1165.– üEqualitš®9y‘ÿ -«.“«TO‘¡ÞDO:–¢4I'll“need“to“de ne“ÂP˜athŽ‘3œ«::Ž‘$ÁÚÂopQÇeratorŽ‘PX·Ž‘X­«(‘ª¨)“in“order“to“bGe“able“to“de ne“thisŽ¡function.Ž¦·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·Ž¡«#ÂifŽ‘ ´ø«0ŽŽ¡‘ -ÂvirtualŽ‘/Ôb•QÇo“olŽ‘I/:opQÇeratorŽ‘tÅï·Ž‘| «(ÂconstŽ‘*¢EllipseŽ‘ChЫ&Ž‘K/î±eŽ‘O×ï«);Ž¡#ÂendifŽŽŽŽŒ‹H;– Šn ý‘ì«328–­EQUALITY’/ÃC3DLDFPRÃŽG“·x«1166Ž €n ý•@PÂ1166.Ž©·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¤ «#ÂifŽ‘ ´ø«0ŽŽ¡‘ -ÂvirtualŽ‘/Ôb•QÇo“olŽ‘I/:EllipseŽ‘l«::Ž‘r¦UÂopQÇeratorŽ’ž= -·Ž’¦(«(ÂconstŽ‘*¢EllipseŽ‘ChЫ&Ž‘K/î±eŽ‘O×ï«)Ž¡‘ -·f‘ª¨gŽ¡«#ÂendifŽŽŸ1167.‘ üLošQÇcation–ÕTof“a“p˜oin®9t.‘ ü«[¬LDF‘T2003.07.25.«]Ž‘Zˆ6This–UUfunction“o•¸ãv“erloadsŽ¡ÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘i÷œ«::‘Ïlo–ÿ}'c“ationŽ‘#Á«(‘ª®).‘=³It's–¹simpler,‘ØWbšGecause“it“do˜esn't“need“to“cop¸ãy“the“ÂEllipseŽ‘'[«and“transformŽ¡the–UUcopš¸ãy“in˜to“a“ma‘Ž8jor“plane.‘qÇNor“doGes“it“require“the“use“of“ÏsolveŽ‘ «(‘ª®).Ž¡‘ -[¬LDF‘T2003.07.25.«]Ž‘Y&ZIf–stthe“ÂP•®9oin“tŽ‘"0«argumen¸ãt“±P‘׫lies“in“the“same“plane“as“·Ž‘suÏthisŽ‘_+«,‘zûÏlo–ÿ}'c“ationŽ‘&.«.Ž¡-1Ž‘ UV±m–Ç>“d«.‘qDZP‘¸ä«lies–UUoutside“the“ÂEllipseŽ‘%>.«.Ž¡1Ž‘ UV±m–Ç<“d«.‘qDZP‘¸ä«lies–UUinside“the“pGerimeter“of“the“ÂEllipseŽ‘%>.«.Ž¡-2Ž‘ UV±P‘¸ä«is–UUnot“in“the“same“plane“as“the“ÂEllipseŽ‘%>.«.Ž¡-3Ž‘ UVThe‘UUÂEllipseŽ‘(“ƒ«is‘UUnon-elliptical.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ -«[¬LDF‘T2003.07.25.«]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/ÔsignedŽ‘RýÊshortŽ‘pÈmÏlo–ÿ}'c“ationŽ’“‰ê«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]±pŽ‘Ié]«)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹IEè Šn ý‘ì·x«1168›­3DLDFPRÃŽG’øãLOCA‘ÿJªTION–ÕXOF“A“POINT˜«329Ž €n ý•@PÂ1168.Ž©·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¤ ‘ -ÂsignedŽ‘-o÷shortŽ‘K:šEllipseŽ‘n#w«::‘Ïlo–ÿ}'c“ationŽ‘#Á«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]±pŽ‘Ié]«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·–ÿý«true“·±=Ž¡‘ÂrealŽ‘*³0Ïax‘‰ffŽ‘®hŽ‘AL«=‘ÇÏget‘‰ffŽ–®axis‘‰ffŽ“hŽ‘-ôa«(‘ª¨);Ž¡‘ÂrealŽ‘*³0Ïax‘‰ffŽ‘®vŽ‘AV«=‘ÇÏget‘‰ffŽ–®axis‘‰ffŽ“vŽ‘-À²«(‘ª¨);Ž¦‘ÂifŽ‘´ú«(Ïax‘‰ffŽ‘®hŽ‘˜Õ·‘ÇÝINVALID_REALŽ‘D†<·_‘8àÏax‘‰ffŽ‘®vŽ‘ž·‘ÇÝINVALID_REALŽ‘BM\«)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘8÷f·‘A½Ý"ERROR!È ÝInÈ ÝEllipse::Ž‘qAlocation():\n"Ž’É|·Ž¡‘2Ý"EllipseÈ ÝisÈ Ýnon-elliŽ’šÿÉptical.È ÝReturningÈ Ý-3Ž’ÿ.\n\n"Ž’&Ìû·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½·Ž‘I­Û«3Ž‘N­Ü;Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(·:±pŽ‘:Ïis‘‰ffŽ–®on‘‰ffŽ“planeŽ‘1‚Ú«(Ïget‘‰ffŽ‘®planeŽ‘(vè«(‘ª¨)))‘·fŽ¡‘Ïc‘ÿ}'errŽ‘8²z·‘üÑÝ"WARNING!È ÝInÈ ÝEllipseŽ‘pü•::location():\n"Ž’Íž·Ž¡‘2Ý"PointÈ Ýdoesn'tÈ ÝlieÈ ÝiŽ’šÿÉnÈ ÝplaneÈ ÝofÈ ÝEllipse.\Ž’ÿn"Ž’Í·‘ÇÝ"ReturningÈ Ý-2.\n\n"Ž‘iÔ_·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½·Ž‘I­Û«2Ž‘N­Ü;Ž¡‘·gŽ¦‘ÂrealŽ‘*³0Ïmax‘‰ffŽ‘®axŽ‘NŒó«=‘ÇÏmaxŽ‘k³«(Ïax‘‰ffŽ‘®hŽ‘ѽ±;‘ª¨Ïax‘‰ffŽ‘®vŽ‘H¶«);Ž¡‘ÂP•®9oin“tŽ‘2qŽ‘:‰a«=‘DZpŽ‘ -ø·‘8àÏget‘‰ffŽ‘®fo‘ÿ}'cusŽ‘)zq«(0Ž‘);Ž¡‘ÂrealŽ‘*³0ÏmagŽ‘@Ã&«=‘DZqŽ‘™Â:ÏmagnitudeŽ‘.=r«(‘ª¨);Ž¦‘±qŽ‘™Ä«=‘DZpŽ‘ -ø·‘8àÏget‘‰ffŽ‘®fo‘ÿ}'cusŽ‘)zq«(1Ž‘);Ž¡‘ÏmagŽ‘*ø«+=ŽŽ‘‘ÇÏmax‘‰ffŽ‘®axŽ‘#Ùë)‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"PointÈ ÝliesÈ ÝoutsideÈ Ž‘kÆÜÝofÈ ÝperimeterÈ ÝofÈ Ý|EllŽ’ÔÆ ipse|.\n"Ž’Œí«;Ž¡‘ÂreturnŽ‘Aæ½·Ž‘I­Û«1Ž‘N­Ü;Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"PointÈ ÝliesÈ ÝinsideÈ ÝoŽ‘kÆÜfÈ ÝperimeterÈ ÝofÈ Ý|ElliŽ’ÔÆ pse|.\n"Ž’ÿLð«;Ž¡‘ÂreturnŽ‘A潫1Ž‘Fæ¾;Ž¡‘·gŽ¡‘ -gŽ¤Â1169.‘ üIn•®9tersection‘ÕTpQÇoin“ts.Ž¡1170.‘ üP•®9oin“t‘ÕTargumen“ts.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ -«[¬LDF‘T2003.07.27.«]Ž‘Y;Made–UUthe“argumen¸ãts“ÂconstŽ‘!÷P•®9oin“tŽ‘@o”«&Ž‘H6².Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/Ôb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ’€òÂÏinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ’Ò¡«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]Ïp0Ž‘Pø±;‘ª¨ÂconstŽ‘ÕJP•®9oin“tŽ‘>Äç«&Ž‘FŒÏp1Ž‘R¢Å«)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹JN Šn ý‘ì«330›ÂPOINT‘ÕX­AR•ÃŽGUMENTS’üÛÍ3DLDFPR“G˜·x«1171Ž €n ý•@PÂ1171.Ž©·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¤ ‘ -Âb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘[dïEllipseŽ‘~MÌ«::‘Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]Ïpt0Ž‘TJ˜±;‘ª¨ÂconstŽ‘ÕJP•®9oin“tŽ‘>Äç«&Ž‘FŒÏpt1Ž‘Uõ@«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼Regu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ’¡ÞX«::‘Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã«(Ïc‘ÿ}'enterŽ‘ ‹±;‘ª¨Ïpt0Ž–ã±;‘ª¨Ïpt1Ž“«);Ž¡‘ -·gŽŸÂ1172.› üP•®9ath‘adargumen“t.˜«This–ð„function“just“c•¸ãhec“ks–ð„to“bGe“sure“that“ÂP®9athŽ‘rl±pŽ‘&jð«is“a“line,‘®extracts“the“ÂP•®9oin“tsŽ‘#«,Ž¡and–UUcalls“the“vš¸ãersion“with“ÂP•®9oin“tŽ‘"Dò«argumen˜ts,“returning“the“latter's“return“v‘ÿqÇalue.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.07.09.«]Ž‘Y;Made‘UUÂvirtualŽ‘%Ó«.Ž¡‘ -[¬LDF‘T2003.07.27.«]Ž‘Y;Made–UUargumen¸ãt“±pŽ‘ ²ª«a“ÂconstŽ‘!÷P®9athŽ‘=f°«&Ž‘E-Î.‘qÇChanged,“so“that“Ïis‘‰ffŽ‘®line‘ÿ}'arŽ‘(jÒ«(‘ª®)“is“used,“andŽ¡Ïget‘‰ffŽ–®last‘‰ffŽ“p‘ÿ}'ointŽ‘:$>«(‘ª®)–UUrather“than“Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘*·«(1Ž‘).Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/Ôb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ’€òÂÏinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ’Ò¡«(ÂconstŽ‘*¢P®9athŽ‘:[«&Ž‘AØy±pŽ‘Fày«)‘UUÂconstŽ‘*¢«;ŽŸÂ1173.Ž¦·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¡‘ -Âb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘[dïEllipseŽ‘~MÌ«::‘Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã«(ÂconstŽ‘*¢P®9athŽ‘:[«&Ž‘AØy±pŽ‘Fày«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂifŽ‘´ú«(·:±pŽ‘:Ïis‘‰ffŽ‘®line‘ÿ}'arŽ‘%}«(‘ª¨))‘·fŽ¡‘Ïc‘ÿ}'errŽ‘6D·‘K›Ý"ERROR!È ÝInÈ ÝEllipse::Ž‘nK_intersection_points(Ž’×K#constÈ ÝPath&):\n"Ž’1ö·Ž¡‘2Ý"PathÈ ÝargumentÈ ÝisÈ ÝnoŽ’šÿÉn-linear.\n"Ž’ÞÁ·‘´Ý"Haven'tÈ ÝprogrammedÈ Ž‘lxÝthisÈ ÝcaseÈ Ýyet.\n"Ž’ÉÅa·Ž¡‘2Ý"ReturningÈ ÝINVALID_BŽ’šÿÉOOL_POINT_PAIR."Ž’òM·‘ÇÏend‘‚ØlŽ–ò·‘ÇÏend‘‚ØlŽ“·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½ÝINVALID_BOOL_POINT_PAIRŽ’»,à«;Ž¡‘·gŽ¡‘ÂreturnŽ‘7æ¼Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ’‰s›«(±pŽ‘:Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH«(0Ž‘)±;‘ª¨pŽ‘²¨:Ïget‘‰ffŽ–®last‘‰ffŽ“p‘ÿ}'ointŽ‘:$>«(‘ª¨));Ž¡‘ -·gŽŸÂ1174.– üEllipse‘ÕTargumen®9t.“«TO–UUDO:“Read“through“and“explain.‘qÇ[¬LDF‘T2002.11.06.«]ŽŽ¡‘ -TO–UUDO:“[¬LDF‘T2003.07.20.«]Ž‘R]The“folloš¸ãwing“coGde“found“only“one“in˜tersection:Ž¦#ÂifŽ‘ ´ø«0ŽŽ¡‘ -ÂEllipseŽ‘/>/±tŽ‘2Ú¡«(ÏoriginŽ‘ö!±;‘ª¨«5Ž–ª©±;‘ª¨«4Ž“±;‘ª¨«90ŽŽ‘ ªª);Ž¡‘ -ÂCircleŽ‘+¸‚±cŽ‘0 ]«(ÏoriginŽ‘ö!±;‘ª¨«3Ž‘ª©±;‘ª¨«90ŽŽ‘ ªª);Ž¦‘ -±cŽ‘SÜ:ÏshiftŽ‘}«(3Ž‘);Ž¡‘ -±cŽ‘SÜ:Ïr‘ÿ}'otateŽ‘o>«(0Ž‘±;‘ª¨«0Ž‘ª©±;‘ª¨«30ŽŽ‘ ªª);Ž¦‘ -Âb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜quadrupleŽ‘yæ¬Ïbp‘ÿ}'qŽ’‹ßà«=‘DZtŽ‘cŠ:Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘QŒß«(±cŽ‘SÛ«);Ž¡#ÂendifŽŽŽŽŒ‹K[ - Šn ý‘ì·x«1175›­3DLDFPR•ÃŽG’÷âòÂELLIPSE‘ÕX­AR“GUMENT˜«331Ž €n ý•@PÂ1175.‘ ü«[¬LDF‘T2003.07.20.«]Ž‘ZWhen‘Õ7±cŽ‘ þI«wš¸ãas–Õ7rotated“b˜y“15Ÿü^ÿºŽ‘n«or“45Ÿü^ÿºŽ‘˜ä«,‘î×Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘T{¶«(‘ª®)“found“bGoth“in˜tersections.Ž¤ T‘ÿ*ªry–o}to“ nd“out“wh•¸ãy!‘À?I‘ovw“an“t–o}to“write“a“ÂCircleŽ‘%B&«vš¸ãersion“with“an“ÂEllipseŽ‘(ÇÓ«argumen˜t,‘vand“vice“v˜ersa.‘À?If“I‘ovdo,‘vIŽ¡maš¸ãy–UUnot“ha˜v˜e“to“w˜orry“abGout“this“problem.Ž¡‘ -If–y¼the“Ïverb‘ÿ}'oseŽ‘'„Õ«argumenš¸ãt“is“ÏtrueŽ‘>T«,‘‚Õinformation“abGout“the“in˜tersection“pGoin˜ts“is“prin˜ted“to“standard“output.Ž¡[¬LDF‘T2003.07.01.«]ŽŽ¡‘ -If–æthe“ÂEllipsesŽ‘.™á«are“coplanar,‘CŠthe“inš¸ãtersection“pGoin˜ts“of“the“pGerimeters“of“the“ÂEllipsesŽ‘.™á«are“returned.‘­{IfŽ¡the–A9planes“of“the“ÂEllipsesŽ‘,ô‡«are“p•Gerp“endicular–A9or“skš¸ãew,‘E>the“in˜tersection“line“of“the“planes“is“found.‘kThen,‘E>theŽ¡in•¸ãtersection›UUpGoin“ts˜of˜the˜this˜line˜with˜the˜ÂEllipsesŽ‘)Çj«,˜if˜they˜exist.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.04.12.«]Ž‘Xd´Actually‘ÿ*ª,‘Òƒit–±ÎloGoks“as“if“the“equations“Dr.“Sc•¸ãh“w“ardmann›±Îga“v“e˜me˜w“on't˜do˜the˜tric“k.‘;ETheyŽ¡assume–ŠºbšGoth“ellipses“are“cen¸ãtered“ab˜out“the“origin.‘÷When“I‘Š­tried“to“ha•¸ãv“e–ŠºMathematica“solv¸ãe“the“equationsŽ¡for‘•ƒ±xŸü^ÿ®2Ž›|s±=aŸü^ÿ®2Ž‘à«+–c©±y[ÙŸü^ÿ®2Ž‘ØL±=bŸü^ÿ®2Ž‘®‚«=‘2(±x“·“±m«)Ÿü^ÿ®2Ž˜±=cŸü^ÿ®2Ž‘à«+“(±y‘¿‚·“±n«)Ÿü^ÿ®2Ž˜±=dŸü^ÿ®2Ž˜«,‘¥Mathematica–•ƒprošGduced“solutions“that“to˜ok“up“o•¸ãv“er‘•ƒ35,000Ž¡lines–UUof“text!Ž¡‘ -[¬LDF‘T2002.04.12.«]Ž‘Y8±I'v¸ãe–…Ërewritten“the“other“cases“(parallel,›‘èp•Gerp“endicular,˜and–…Ësk¸ãew)“in“this“function“com-Ž¡pletely‘ÿ*ª,‘áŸand–ıit“seems“likš¸ãe“it“w˜asn't“really“w˜orth“the“e ort.‘A‘The“new“v˜ersion“doGes“ho˜w˜ev˜er“mak˜e“use“of“ÂPlanesŽŽ¡«and‘sÒÂLinesŽ‘U‘«,›{qwhic¸ãh–sÒis“not“a“bad“thing,˜and“it“c•¸ãhec“ks–sÒwhether“the“in¸ãtersection“ÂP•®9oin“tsŽ‘' («are“on“the“ÂEllipseŽ‘%\««,˜soŽ¡it–UUw¸ãasn't“a“total“loss.Ž¡‘ -[¬LDF‘T2002.04.12.«]Ž‘X¾}I'vš¸ãe– —written“to“Dr.“Sc˜h˜w˜ardmann“and“ask˜ed“him“abGout“this“problem.‘Y3It“ma˜y“just“bGe“m˜yŽ¡ignorance,‘?por–9÷pGerhaps“I'vš¸ãe“o˜v˜erloGok˜ed“something“simple.‘h¨I'm“not“tošGo“hop˜eful,›?pho•¸ãw“ev“er,˜so–9÷I'll“probably“ha•¸ãv“eŽ¡to–UUimplemenš¸ãt“the“n˜umerical“solution“I'd“started,“after“all.Ž¡‘ -[¬LDF‘T2002.04.12.«]Ž‘YZRemo•¸ãv“ed–§old“de nition.‘gDr.“Ulricš¸ãh“Sc˜h˜w˜ardmann“of“the“Gesellsc˜haft“fG‘ú¸âur“wissensc˜haft-Ž¡lic•¸ãhe›Ó¶Datenv“erarbGeitung,–óNG‘úÿÿottingen,“German•¸ãy˜sho“w“ed˜me˜ho“w˜to˜use˜Mathematica's˜\Solv“e"˜command˜toŽ¡solvš¸ãe–\gthe“systems“of“equations“that“describGe“the“in˜tersections“bGet˜w˜een“t˜w˜o“ellipses.‘†ýTherefore,‘^+I'v˜e“remo˜v˜edŽ¡the–UUold“de nition“of“this“function,“whicš¸ãh“w˜asn't“complete,“an˜yw˜a˜y‘ÿ*ª,“and“I'll“put“in“a“new“de nition“soGon.Ž¡‘ -[¬LDF‘T2002.04.14.«]Ž‘XÒAbGout–"to“start“wš¸ãork“on“implemen˜ting“the“coplanar“case“again.‘_¶The“equations“proGducedŽ¡bš¸ãy–ÆMathematica“will“w˜ork“for“the“case“that“the“ellipses“ha˜v˜e“the“same“cen˜ter.‘ZBI‘´will“catc˜h“the“case“that“theyŽ¡are–!¤congruenš¸ãt“and“ha˜v˜e“the“same“cen˜ter“and“the“case“that“they“are“non-congruen˜t“and“ha˜v˜e“the“same“cen˜terŽ¡bGefore–UUgoing“on“to“implemenš¸ãt“a“n˜umerical“solution“for“the“case“that“they“ha˜v˜e“di eren˜t“cen˜ters.Ž¡‘ -[¬LDF‘T2002.04.14.«]Ž‘YÑîChanged–argumenš¸ãt“from“ÂconstŽ‘#]EllipseŽ‘I>«&Ž‘Udto“ÂEllipseŽ‘&á«,‘Qusince“I‘Ôw˜as“ha˜ving“to“cop˜y“it,Ž¡an•¸ãyw“a“y‘ÿ*ª.Ž¡‘ -[¬LDF‘T2003.07.01.«]Ž‘Y;Added‘UUÏverb‘ÿ}'oseŽ‘'<«argumen¸ãt.Ž¡‘ -[¬LDF‘T2003.07.01.«]Ž‘Y&ÍChanged›sç\p•Gerp“endicular˜and˜sk¸ãew˜case".‘Í|Debugged˜coplanar˜case,‘{‹where˜the˜ÂEllipsesŽŽ¡«don't›UUha•¸ãv“e˜the˜same˜cen“ters˜and/or˜axis˜orien“tation.Ž¡‘ -[¬LDF‘T2003.07.06.«]Ž‘ZyüMade–Ça“minor“c¸ãhange“to“the“conditional“that“determines“whether“the“ÂEllipsesŽ‘0A«areŽ¡coplanar–UUor“not.Ž¡‘ -[¬LDF‘T2003.08.14.«]Ž‘Y;Setting‘UUÏverb‘ÿ}'oseŽ‘'<«to‘UUÏtrueŽ‘oB«if‘UUÝVERBOSE_GLOBALŽ–P°è«is‘UUÏtrueŽ‘í«.‘qÇAdded‘UUÝVERBOSE_GLOBALŽ“«toŽ¡Èpspglb.web‘UU«toGda¸ãy‘ÿ*ª.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·ŽŸ ‘ -ÂvirtualŽ‘/Ôb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜quadrupleŽ’ŸtÏinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ’ñ^«(ÂEllipseŽ‘%>.±eŽ‘)æ/;‘ª¨Âb•QÇo“olŽ‘LÏverb‘ÿ}'oseŽ‘>¤ƒ«=‘ÇÏfalseŽ‘v\«)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹Lgü Šn ý‘ì«332›ÂELLIPSE‘ÕX­AR•ÃŽGUMENT’÷âò3DLDFPR“G˜·x«1176Ž €n ý•@PÂ1176.Ž©·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¤ ‘ -Âb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜quadrupleŽ‘z²`EllipseŽ’›=«::‘Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã«(ÂEllipseŽ‘& â±eŽ‘*±ã;‘ª¨Âb•QÇo“olŽ‘ÂÏverb‘ÿ}'oseŽ‘<©«)‘! ÂconstŽ‘öV·f‘! 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-«[¬LDF‘T2003.07.20.«]Ž‘X/¾No¸ãw–|Øusing“Ïget‘‰ffŽ–®axis‘‰ffŽ“vŽ‘-vr«(›ª®)“and“Ïget‘‰ffŽ–®axis‘‰ffŽ“hŽ‘-ª!«(˜),‘¨%instead“of“accessing“Ïaxis‘‰ffŽ‘®hŽ‘ó=«and“Ïaxis‘‰ffŽ‘®vŽ‘¿Ž«directly‘ÿ*ª.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¡‘ -ÂifŽ‘´ù«(ÏfabsŽ–2Ò«(ÏfabsŽ“«(Ïthis‘‰ffŽ‘®planeŽ‘+‡ú±:Ïdistanc‘ÿ}'eŽ›$Eý«)–8à·“ÏfabsŽ‘k²«(Ïe‘‰ffŽ‘®planeŽ‘ ŠÖ±:Ïdistanc‘ÿ}'eŽ˜«))–DZ<“ÂP•®9oin“tŽ‘ad«::Ž‘%ï¢ÏepsilonŽ‘E^¦«(‘ª¨))‘UU·fŽ¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"EllipsesÈ ÝareÈ ÝcoplanŽ‘kÆÜar.\n"Ž’Ž”J·‘ÇÏ ushŽ‘€«;Ž¡‘ -·gŽ¦‘ -ÂrealŽ‘ ³/Ïax‘‰ffŽ‘®hŽ‘7L«=‘ÇÏget‘‰ffŽ–®axis‘‰ffŽ“hŽ‘-ôa«(‘ª¨);Ž¡‘ -ÂrealŽ‘ ³/Ïax‘‰ffŽ‘®vŽ‘7U«=‘ÇÏget‘‰ffŽ–®axis‘‰ffŽ“vŽ‘-À²«(‘ª¨);ŽŽŽŒ‹Mz: Šn ý‘ì·x«1178›­3DLDFPR•ÃŽG’÷âòÂELLIPSE‘ÕX­AR“GUMENT˜«333Ž €n ý•@PÂ1178.‘ ü«Congruenš¸ãt,‘1same–'ýloGcation“and“axis“orien˜tation.‘bª[¬LDF‘T2002.04.15.«]Ž‘S=ŒAdded“c˜hec˜k“for“the“axis“orien˜ta-Ž¤ tion.‘.ÎIf–”Wthe“axes“are“not“all“vš¸ãertical“or“horizon˜tal,‘¤then“this“fails“( oating“exception).‘.ÎThis“means“that“theŽ¡circular–¬ñcase“will“not“bšGe“caugh¸ãt“here,‘ÂØbut“I‘¬Úplan“to“program“a“sp˜ecialization“for“ÂCirclesŽ‘&™Y«,‘ÂØso“this“shouldn'tŽ¡cause–UUtoGo“m•¸ãuc“h–UUof“a“problem.Ž¡‘ -[¬LDF‘T2002.04.14.«]Ž‘Y;Added–UUthis“section.Ž¡‘ -This–´routine“only“wš¸ãorks“if“the“axis“orien˜tation“of“the“ÂEllipsesŽ‘-u}«is“the“same,‘ŒËor“rotated“90Ÿü^ÿºŽ›˜«or“180Ÿü^ÿºŽ˜«abGoutŽ¡an–øaxis“through“the“cen¸ãter“in“the“direction“of“the“normal“to“the“plane“of“the“ÂEllipseŽ‘%ÿÑ«,‘G`or“in“the“oppGositeŽ¡direction.‘MThe–žœaxis“orienš¸ãtation“is“tested“on“the“basis“of“the“v˜ector“from“the“cen˜ter“to“Ïp‘ÿ}'ointsŽ‘Ã1«[0Ž‘].‘MIf“the“axisŽ¡orien¸ãtation–òcis“the“same,‘¦or“rotated“180Ÿü^ÿºŽ‘‹G«abšGout“the“ab˜o•¸ãv“e-men“tioned–òcaxis,‘¦then“Ïaxis‘‰ffŽ‘®hŽ‘"ÞS«of“·Ž‘òdÏthisŽ‘Ð}«m¸ãust“equalŽ¡Ïaxis‘‰ffŽ‘®hŽ‘+¹«of‘2,±eŽ‘ Y«and‘2,Ïaxis‘‰ffŽ‘®vŽ›!*6«of‘2,·Ž‘2-ÏthisŽ‘P«m¸ãust–2,equal“Ïaxis‘‰ffŽ‘®vŽ˜«of“±eŽ‘Ú-«.‘fIf“the“axis“orien¸ãtation“is“rotated“at“an“angle“of“·«90Ÿü^ÿºŽ‘˜ä«,Ž¡then‘UUÏaxis‘‰ffŽ‘®hŽ‘!¤7«of‘UU·Ž‘UVÏthisŽ‘–a«m¸ãust–UUequal“Ïaxis‘‰ffŽ‘®vŽ›!pˆ«of“±eŽ‘ R««and“Ïaxis‘‰ffŽ‘®vŽ˜«of“·Ž‘UVÏthisŽ‘–a«m¸ãust“equal“Ïaxis‘‰ffŽ‘®hŽ‘!¤7«of“±eŽ‘ýV«.Ž¡‘ -The–M§ô±:ÏshowŽ‘Šÿ«(Ý"normal_point"Ž‘J>«);Ž¦‘ -ÂP•®9oin“tŽ‘(ïžÏe‘‰ffŽ–®axis‘‰ffŽ“orientation‘‰ffŽ“r–ÿ}'otate“dŽ’˜ø@«(Ïe‘‰ffŽ–®axis‘‰ffŽ“orientationŽ‘NPÉ«);ŽŽŽŒ‹N„š Šn ý‘ì«334›ÂELLIPSE‘ÕX­AR•ÃŽGUMENT’÷âò3DLDFPR“G˜·x«1179Ž €n ý•@PÂ1179.‘ ü«[¬LDF‘T2002.09.26.«]Ž‘Z)kST–ÿ*ªAR“T›örHERE.–öŠAdded“the“ÂifŽ‘L·«condition.‘R.I˜think“this“should“bGe“done,‘ but“I˜shouldŽ¤ c•¸ãhec“k–Pto“bGe“sure.‘pApparenš¸ãtly“I‘Oÿha˜v˜en't“programmed“the“case“that“the“cen˜ters“aren't“the“same,‘Qbut“it“w˜ouldŽ¡bGe–UUeasy“enough“to“do,“I“think.Ž©·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¡‘ -ÂifŽ‘pð«(Ïe‘‰ffŽ–®axis‘‰ffŽ“orientationŽ‘Qá·6«=‘ÇÏthis‘‰ffŽ–®axis‘‰ffŽ“orientationŽ‘\«)‘Ïe‘‰ffŽ–®axis‘‰ffŽ“orientation‘‰ffŽ“r–ÿ}'otate“dŽ‘u¢±:Ïr‘ÿ}'otateŽ‘o>«(ÏoriginŽ‘ö!±;‘ª¨Ïnormal‘‰ffŽ‘®p‘ÿ}'ointŽ‘;Rœ±;‘ª¨«90ŽŽ‘ ªª);Ž¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘Ïe‘‰ffŽ–®axis‘‰ffŽ“orientation‘‰ffŽ“r–ÿ}'otate“dŽ‘u¢±:ÏshowŽ‘Šÿ«(Ý"e_axis_orientation"Ž‘i†,«);Ž¡‘ -ÂifŽ‘3~«(ÏthisŽ‘붟±~ŽŽ‘ë·Ïc‘ÿ}'enterŽ‘47·‘™õ±eŽ‘Aö:Ïc‘ÿ}'enterŽ‘–÷^–8«((Ïthis‘‰ffŽ–®axis‘‰ffŽ“orientationŽ‘\çâ·‘™õÏe‘‰ffŽ–®axis‘‰ffŽ“orientationŽ‘Twö·_“Ïthis‘‰ffŽ–®axis‘‰ffŽ“orientationŽ‘_u·Ž¡‘(Ž‘/Ç"Ïe‘‰ffŽ–®axis‘‰ffŽ“orientationŽ‘~ë«)–°·_“«(Ïthis‘‰ffŽ–®axis‘‰ffŽ“orientationŽ‘\·‘ÇÏe‘‰ffŽ–®axis‘‰ffŽ“orientation‘‰ffŽ“r–ÿ}'otate“dŽ‘tîj·_“Ïthis‘‰ffŽ–®axis‘‰ffŽ“orientationŽ‘^3µ·Ž¡‘(Ž‘/Ç"Ïe‘‰ffŽ–®axis‘‰ffŽ“orientation‘‰ffŽ“r–ÿ}'otate“dŽ’ŸÏÄ«)))‘·fŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"CentersÈ ÝandÈ ÝaxisÈ ÝorŽ‘kÆÜientationÈ ÝareÈ ÝtheÈ ÝsaŽ’ÔÆ me.\n"Ž’÷”·‘ÇÏ ushŽ‘€«;Ž¡‘(±=·‘'«[¬LDF‘T2002.04.14.«]Ž‘T6‹Picš¸ãk–lthe“maxim˜um“of“Ïaxis‘‰ffŽ‘®hŽ‘!Ò‹«and“Ïaxis‘‰ffŽ‘®vŽ‘!žÜ«and“m˜ultiply“it“b˜y“1.5.‘·EW‘ÿ*ªe'll“use“aŽ¡‘2line–gBsegmenš¸ãt“of“this“length“to“ nd“in˜tersection“pGoin˜ts“with“the“t˜w˜o“ÂEllipsesŽ‘)ÙW«.‘§Using“this“lengthŽ¡‘2guaran•¸ãtees›UUw“e'll˜ nd˜them.‘qÇActually‘ÿ*ª,˜ÏmaxŽ‘ùð«(Ïaxis‘‰ffŽ‘®hŽ‘ù±;‘ª¨Ïaxis‘‰ffŽ‘®vŽ‘p†«)˜ough“t˜to˜do˜the˜tric“k.‘o·±=Ž¦‘ÂP•®9oin“tŽ‘2ïŸÏpt0Ž‘BXÚ«;Ž¦‘ÂifŽ‘´ú«(Ïax‘‰ffŽ‘®hŽ‘˜Õ·‘ÇÏax‘‰ffŽ‘®vŽ‘e&«)‘Ïpt0Ž‘0S«=‘ÇÏget‘‰ffŽ‘®p‘ÿ}'ointŽ‘*)`«(0Ž‘);Ž¡‘ÂelseŽ‘+ØáÏpt0Ž‘> 4«=‘ÇÏget‘‰ffŽ‘®p‘ÿ}'ointŽ‘*)`«(Ïnumb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜ointsŽ‘JÀ©±=«4Ž‘);Ž¡‘Ïpt0Ž‘&0U·«=ŽŽ‘8…©Ïc‘ÿ}'enterŽ‘T4«;Ž¡‘Ïpt0Ž‘&0U·«=ŽŽ‘5¾Œ1±:«5ŽŽ‘B…«;Ž¡‘Ïpt0Ž‘#i=±:ÏshiftŽ‘}«(Ïc‘ÿ}'enterŽ‘ ‹«);Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïthis‘‰ffŽ‘®planeŽ‘I‡ý±:ÏnormalŽ‘ V¸±:ÏshowŽ‘Šÿ«(Ý"normal"Ž‘*†P«);Ž¡‘Ïc‘ÿ}'enterŽ‘: Ž±:ÏshowŽ‘Šÿ«(Ý"center"Ž‘*†P«);Ž¡‘·g‘±=·‘ «[¬LDF‘T2002.04.14.«]Ž‘TeW‘ÿ*ªe'll–^lrotate“Ïpt0Ž‘&«around“the“normal“to“the“plane“of“the“ellipse“from“Ïc‘ÿ}'enterŽ‘g÷«,Ž¡‘2i.e.,–UUthe“line“segmen¸ãt“from“Ïc‘ÿ}'enterŽ‘"´5«to“Ïpt1Ž‘¾«.‘o·±=Ž¦‘ÂP•®9oin“tŽ‘2ïŸÏpt1Ž‘BXÚ«(Ïthis‘‰ffŽ‘®planeŽ‘+‡ú±:ÏnormalŽ‘ V¸«);Ž¦‘Ïpt1Ž‘#i=±:ÏshiftŽ‘}«(Ïc‘ÿ}'enterŽ‘ ‹«);Ž¡‘ÂifŽ‘Ð «(ÝDEBUGŽ–ÆY«)‘Ïpt1Ž‘i;±:ÏshowŽ‘Šÿ«(Ý"pt1"Ž“«);‘±=·‘«[¬LDF‘T2002.04.14.«]Ž‘T>[Ïpt2Ž‘gý«is–pgthe“in¸ãtersection“of“the“line“from“Ïc‘ÿ}'enterŽŽ¡‘2«to‘UUÏpt0Ž›å«with‘UU·Ž‘UVÏthisŽ‘A «,–UUand“Ïpt3Ž˜«is“the“in¸ãtersection“of“the“same“line“with“±eŽ‘ýV«.‘o·±=Ž¦‘ÂP•®9oin“tŽ‘2ïŸÏpt2Ž‘BXÚ«;Ž¡‘ÂP•®9oin“tŽ‘2ïŸÏpt3Ž‘BXÚ«;Ž¡‘Âb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘edðÏbpp‘‰ffŽ‘®thisŽ’ˆÑ0«;Ž¡‘Âb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘edðÏbpp‘‰ffŽ‘®eŽ‘}ÂF«;Ž¡‘Âb•QÇo“olŽ‘-ñmÏc‘ÿ}'ongruent‘‰ffŽ‘® agŽ‘pt¾«=‘LuÏtrueŽ‘ «;‘±=·‘P«[¬LDF‘T2002.04.14.«]Ž‘T¨AW‘ÿ*ªe'll–¥Z nd“inš¸ãtersection“pGoin˜ts“for“ v˜e“v‘ÿqÇaluesŽ¡‘(of‘›üÏpt0Ž‘7«.‘E»If–›üone“set“of“inš¸ãtersection“pGoin˜ts“are“not“the“same,‘­¥this“means“the“w˜e“ÂEllipsesŽ‘-ª «are“notŽ¡‘(congruenš¸ãt–UUand“in“the“same“loGcation,“so“w˜e“break“out“of“the“loGop.‘o·±=Ž¦‘ÂforŽ‘%舫(Âin®9tŽ‘¤÷±iŽ‘Þ«=‘Ç0Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«5Ž“;‘ÿý±iŽ‘ññŸÿ®+‘ÿ+ŽŽ‘¹«)‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"iÈ Ý==È Ý"Ž‘*Ôƒ·‘DZiŽ‘ $·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ÂifŽ‘)´û«(±iŽ‘9 ·6«=‘Ç0Ž‘Ç)‘Ïpt0Ž‘i;±:Ïr‘ÿ}'otateŽ‘o>«(Ïc‘ÿ}'enterŽ‘ ‹±;‘ª¨Ïpt1Ž‘ã±;‘ª¨«30ŽŽ‘ ªª);Ž¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïpt0Ž‘i;±:Ïdotlab‘ÿ}'elŽ‘!ÿó«(Ý"0"Ž‘F_«);Ž¡‘Ïbpp‘‰ffŽ‘®thisŽ‘D3[«=‘ÇÏinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘TS÷«(Ïc‘ÿ}'enterŽ‘ ‹±;‘ª¨Ïpt0Ž‘ã«);Ž¡‘Ïbpp‘‰ffŽ‘®eŽ‘9$q«=‘DZeŽ‘o:Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘QŒß«(Ïc‘ÿ}'enterŽ‘ ‹±;‘ª¨Ïpt0Ž‘ã«);Ž¡‘ÂifŽ‘)´û«(Ïbpp‘‰ffŽ‘®thisŽ‘#l@±:Ï rstŽ‘µª±:bŽ‘·‘ÇÏtrueŽ‘‹°«)‘·fŽ¡‘(ÂifŽ‘3´ü«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"firstÈ ÝisÈ ÝanÈ ÝinterseŽ‘kÆÜctionÈ ÝpointÈ Ý(this).\Ž’ÔÆ n"Ž’ßÍ«;Ž¡‘(Ïpt2Ž‘:0W«=‘ÇÏbpp‘‰ffŽ‘®thisŽ‘&3X±:Ï rstŽ‘µª±:ÏptŽ‘ ä«;Ž¡‘·gŽ¡‘ÂelseŽ‘4.7ifŽ‘?ã/«(Ïbpp‘‰ffŽ‘®thisŽ‘#l@±:Ïse–ÿ}'c“ondŽ‘§Ç±:bŽ‘·‘ÇÏtrueŽ‘‹°«)‘·fŽ¡‘(ÂifŽ‘3´ü«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"secondÈ ÝisÈ ÝanÈ ÝintersŽ‘kÆÜectionÈ ÝpointÈ Ý(this).Ž’ÔÆ \n"Ž’å ÿ«;Ž¡‘(Ïpt2Ž‘:0W«=‘ÇÏbpp‘‰ffŽ‘®thisŽ‘&3X±:Ïse–ÿ}'c“ondŽ‘§Ç±:ÏptŽ‘ ä«;Ž¡‘·gŽ¡‘ÂelseŽ‘5Øâ·fŽŽŽŒ‹O“$ Šn ý‘ì·x«1179›­3DLDFPR•ÃŽG’÷âòÂELLIPSE‘ÕX­AR“GUMENT˜«335Ž €n ý•@P‘(Ïc‘ÿ}'errŽ‘A:²·‘…Ý"InÈ ÝEllipse::interseŽ‘o„Ìction_points(EllipseŽ’Ø„).\n"Ž’ùÏñ·Ž¤ ‘<Ý"ThisÈ Ýcan'tÈ ÝhappenÈ Ý(Ž’¤ÿÊthis)!\n"Ž’×/·‘ÇÝ"WillÈ ÝtryÈ ÝtoÈ ÝcontinuŽ‘kÆÜe.\n\n"Ž’“ÔG·‘ÇÏ ushŽ‘€«;Ž¡‘(Ïpt2Ž‘:0W«=‘ÇÝINVALID_POINTŽ‘GY«;Ž¡‘·gŽ¡‘ÂifŽ‘)´û«(Ïbpp‘‰ffŽ‘®eŽ‘]V±:Ï rstŽ‘µª±:bŽ‘·‘ÇÏtrueŽ‘‹°«)‘·fŽ¡‘(ÂifŽ‘3´ü«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"firstÈ ÝisÈ ÝanÈ ÝinterseŽ‘kÆÜctionÈ ÝpointÈ Ý(e).\n"Ž’Ð «;Ž¡‘(Ïpt3Ž‘:0W«=‘ÇÏbpp‘‰ffŽ‘®eŽ‘$n±:Ï rstŽ‘µª±:ÏptŽ‘ ä«;Ž¡‘·gŽ¡‘ÂelseŽ‘4.7ifŽ‘?ã/«(Ïbpp‘‰ffŽ‘®eŽ‘]V±:Ïse–ÿ}'c“ondŽ‘§Ç±:bŽ‘·‘ÇÏtrueŽ‘‹°«)‘·fŽ¡‘(ÂifŽ‘3´ü«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"secondÈ ÝisÈ ÝanÈ ÝintersŽ‘kÆÜectionÈ ÝpointÈ Ý(e).\n"Ž’ÕM«;Ž¡‘(Ïpt3Ž‘:0W«=‘ÇÏbpp‘‰ffŽ‘®eŽ‘$n±:Ïse–ÿ}'c“ondŽ‘§Ç±:ÏptŽ‘ ä«;Ž¡‘·gŽ¡‘ÂelseŽ‘5Øâ·fŽ¡‘(Ïc‘ÿ}'errŽ‘A:²·‘…Ý"InÈ ÝEllipse::interseŽ‘o„Ìction_points(EllipseŽ’Ø„).\n"Ž’ùÏñ·Ž¡‘<Ý"ThisÈ Ýcan'tÈ ÝhappenÈ Ý(Ž’¤ÿÊe)!\nWillÈ ÝtryÈ ÝtoÈ ÝconŽ’ ÿŽtinue.\n\n"Ž’K í·‘ÇÏ ushŽ‘€«;Ž¡‘(Ïpt3Ž‘:0W«=‘ÇÝINVALID_POINTŽ‘GY«;Ž¡‘·gŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘(Ïpt2Ž‘7i?±:ÏshowŽ‘Šÿ«(Ý"2"Ž‘F_«);Ž¡‘(Ïpt2Ž‘7i?±:Ïdotlab‘ÿ}'elŽ‘!ÿó«(Ý"2"Ž‘F_«);Ž¡‘(Ïpt3Ž‘7i?±:ÏshowŽ‘Šÿ«(Ý"3"Ž‘F_«);Ž¡‘(Ïpt3Ž‘7i?±:Ïdotlab‘ÿ}'elŽ‘!ÿó«(Ý"3"Ž‘F_±;‘ª¨Ý"bot"Ž‘q«);Ž¡‘·gŽ¡‘ÂifŽ‘)´û«(Ïpt2Ž‘0S·‘ÇÝINVALID_POINTŽ–IÆ9·_‘8àÏpt3Ž›i3·‘ÇÝINVALID_POINTŽ“·_‘8àÏpt2Ž˜·6«=‘ÇÏpt3Ž‘0S«)‘·fŽ¡‘(ÂifŽ‘3´ü«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EllipsesÈ ÝareÈ ÝnotÈ ÝcoŽ‘kÆÜngruent.È ÝBreaking.\nŽ’ÔÆ "Ž’Ú«;Ž¡‘(Ïc‘ÿ}'ongruent‘‰ffŽ‘® agŽ‘iýø«=‘ÇÏfalseŽ‘v\«;Ž¡‘(ÂbreakŽ‘D¡h«;Ž¡‘·gŽ¡‘ÂelseŽ‘5Øâcon•®9tin“ueŽ‘`¿—«;Ž¡‘·g‘±=·‘ÿýÂforŽ‘“+·±=Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"congruent_flagÈ Ý==È Ý"Ž‘o\·‘ÇÏc‘ÿ}'ongruent‘‰ffŽ‘® agŽ‘DÅ ·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(Ïc‘ÿ}'ongruent‘‰ffŽ‘® agŽ‘Aýô·‘ÇÏtrueŽ‘‹°«)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘6F0·‘‡Ý"WARNING!È ÝInÈ ÝEllipseŽ‘nK::intersection_pointŽ’×s(Ellipse).\n"Ž’'&Ô·Ž¡‘2Ý"EllipsesÈ ÝareÈ ÝcongruŽ’šÿÉentÈ ÝandÈ ÝinÈ ÝtheÈ ÝsameÈ Ž’ÿÝlocation.\n"Ž’Iè@·Ž¡‘2Ý"ReturningÈ ÝINVALID_BŽ’šÿÉOOL_POINT_QUADRUPLE.Ž’ÿ\n\n"Ž’!Œþ·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½ÝINVALID_BOOL_POINT_QUADRUPLEŽ’ÕlÑ«;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"AllÈ ÝfiveÈ ÝpointsÈ ÝareŽ‘kÆÜÈ ÝnotÈ ÝonÈ ÝbothÈ ÝellipseŽ’ÔÆ s.\n"Ž’òT·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¡‘ -g‘±=·‘ÿý«End–UUof“test“of“congruency“and“same“loGcation.‘o·±=Ž¡‘=·‘ÿý«[¬LDF‘T2002.09.26.«]Ž‘T7ST–ÿ*ªAR“T–UUHERE.“Programm“this“case!!‘o·±=Ž¡‘ -ÂelseŽ‘ .5ifŽ‘+ã-«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘-'2·‘ÍùÝ"TheÈ ÝcentersÈ ÝareÈ ÝdifŽ‘nͽferent,È ÝorÈ ÝtheÈ ÝaxisŽ’×ÍÈ ÝorientationÈ Ý"Ž’'¡¸·Ž¡‘(Ý"isÈ Ýdifferent,È ÝorÈ ÝboŽ’ÿÈth.È Ý"Ž’®9·‘ÇÝ"Haven'tÈ ÝprogrammedÈ Ž‘kÆÜÝthisÈ ÝcaseÈ Ýyet.\n"Ž’Å«;Ž¡‘ -·gŽŸ‘ -ÂEllipseŽ‘/>/Ïc‘ÿ}'opyŽ‘CÎ'«(·Ž‘ÏthisŽ‘ë·«);Ž¡‘ -ÂP•®9oin“tŽ‘(ïžÏc–ÿ}'opy‘‰ffŽ‘®c“enterŽ‘[ÑÝ«(Ïc‘ÿ}'opyŽ‘ø±:Ïget‘‰ffŽ‘®c‘ÿ}'enterŽ‘,=G«(‘ª¨));Ž¡‘ -ÂT‘ÿ -«ransformŽ‘AÈÓ±tŽ‘EeE«;Ž¡‘ -ÂT‘ÿ -«ransformŽ‘AÈÓÏt‘‰ffŽ‘®inverseŽ‘h×è«;ŽŽŽŒ‹P©Û Šn ý‘ì«336›ÂELLIPSE‘ÕX­AR•ÃŽGUMENT’÷âò3DLDFPR“G˜·x«1180Ž €n ý•@PÂ1180.‘ ü«Shift–UUto“origin“(if“necessary).Ž©·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¤ ‘ -ÂifŽ‘´ù«(Ïc–ÿ}'opy‘‰ffŽ‘®c“enterŽ‘5©W·6«=‘ÇÏoriginŽ‘½9«)‘·fŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"ShiftingÈ ÝcopyÈ ÝtoÈ ÝorŽ‘kÆÜigin.\n"Ž’™D·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¡‘±tŽ‘œt:ÏshiftŽ‘}«(·Ž‘ÇÏc–ÿ}'opy‘‰ffŽ‘®c“enterŽ‘:©]±:Ïget‘‰ffŽ‘®xŽ‘Žg«(–ª¨)±;“·Ž‘ qÆÏc–ÿ}'opy‘‰ffŽ‘®c“enterŽ›»«;Ž¡‘Ïc–ÿ}'opy‘‰ffŽ‘®c“enterŽ‘I©Y·«=ŽŽ‘Y7±tŽ‘\Ô«;Ž¡‘±eŽ‘o·«=ŽŽ‘*ýR±tŽ‘.™Ä«;Ž¡‘ -·gŽ¡‘ -ÂelseŽ‘ .5ifŽ‘+ã-«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"copyÈ ÝisÈ ÝalreadyÈ ÝatÈ Ž‘kÆÜÝorigin.\n"Ž’£”>·‘ÇÏ ushŽ‘€«;Ž¡‘ -·gŽŸÂ1181.‘ ü«Get–UUcoGordinates“of“normal.Ž¦·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘ ³/Ïnormal‘‰ffŽ‘®xŽ‘LNZ«=‘ÇÏthis‘‰ffŽ‘®planeŽ‘.O±:ÏnormalŽ‘ V¸±:Ïget‘‰ffŽ‘®xŽ‘Žg«(‘ª¨);Ž¡‘ -ÂrealŽ‘ ³/Ïnormal‘‰ffŽ‘®yŽ‘L4 «=‘ÇÏthis‘‰ffŽ‘®planeŽ‘.O±:ÏnormalŽ‘ V¸±:Ïget‘‰ffŽ‘®yŽ‘t«(‘ª¨);Ž¡‘ -ÂrealŽ‘ ³/Ïnormal‘‰ffŽ‘®zŽ‘KÇô«=‘ÇÏthis‘‰ffŽ‘®planeŽ‘.O±:ÏnormalŽ‘ V¸±:Ïget‘‰ffŽ‘®zŽ‘«(‘ª¨);ŽŽŽŒ‹Q·ü Šn ý‘ì·x«1182›­3DLDFPR•ÃŽG’÷âòÂELLIPSE‘ÕX­AR“GUMENT˜«337Ž €n ý•@PÂ1182.‘ ü«Determine–- the“orien¸ãtation“of“the“ellipse“and“rotate,‘5if“it's“not“already“in“a“plane“parallel“to“a“ma‘Ž8jorŽ¤ plane.‘‘ÐRotating–`the“ÂEllipseŽ‘(¨ß«can“cause“inaccuracies“in“the“coGordinate“v‘ÿqÇalues,‘b®so“if“the“ellipse“is“already“in“aŽ¡ma›Ž8jor–UUplane,“(i.e.,“one“p•Gerp“endicular–UUto“a“ma˜jor“axis),“wš¸ãe“lea˜v˜e“it“where“it“is.ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.08.27.«]Ž‘YyCommenš¸ãted-out–`“the“declaration“of“ÝOTHERŽ‘&ì«,‘ccbGecause“it's“nev˜er“used.‘“I‘`ha˜v˜en't“deleted“it,Ž¡just–UUin“case.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¤ ‘ -ÂunsignedŽ‘:7shortŽ‘X²ÏorientationŽ’‰tñ«;Ž¡‘ -ÂconstŽ‘(*£unsignedŽ‘Xa±shortŽ‘v,TÝX_YŽ’‰9Ë«=‘Ç0Ž‘Ç;Ž¡‘ -ÂconstŽ‘(*£unsignedŽ‘Xa±shortŽ‘v,TÝX_ZŽ’‰9Ë«=‘Ç1Ž‘Ç;Ž¡‘ -ÂconstŽ‘(*£unsignedŽ‘Xa±shortŽ‘v,TÝZ_YŽ’‰9Ë«=‘Ç2Ž‘Ç;Ž¡#ÂifŽ‘ ´ø«0ŽŽ¡‘ -ÂconstŽ‘(*£unsignedŽ‘Xa±shortŽ‘v,TÝOTHERŽ’“¹Å«=‘Ç3Ž‘Ç;Ž¡#ÂendifŽŽ©‘ -ifŽ‘´ù«(Ïnormal‘‰ffŽ‘®xŽ‘+›+·‘Ç«0Ž– ÿù·^‘8àÏnormal‘‰ffŽ‘®yŽ‘-¹º·‘Ç«0Ž“·^‘8àÏnormal‘‰ffŽ‘®zŽ‘-M¥·‘Ç«0Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘+8¾·‘ƒÝ"ERROR!È ÝInÈ ÝEllipse::Ž‘m‚Úintersection_points(Ž’Ö‚ž):\n"Ž’õÌ ·‘ƒÝ"NormalÈ Ý==È Ý0.È Ý"Ž‘XLg·Ž¡‘(Ý"ReturningÈ ÝINVALID_BŽ’ÿÈOOL_POINT_QUADRUPLE\Ž’ùÿŒn\n"Ž’M·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘7æ¼ÝINVALID_BOOL_POINT_QUADRUPLEŽ’ËlЫ;Ž¡‘ -·gŽ¡‘ -ÂelseŽ‘ .5ifŽ‘+ã-«(Ïnormal‘‰ffŽ‘®xŽ‘+›+·‘Ç«0Ž‘ ÿù·^‘8àÏnormal‘‰ffŽ‘®yŽ‘-¹º·‘Ç«0Ž‘Ç)‘±=·‘ÿý«Ellipse–UUlies“in“a“plane“parallel“to“x-y“plane.‘o·±=Ž¡‘ -·fŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EllipseÈ ÝliesÈ ÝinÈ ÝaÈ ÝpŽ‘kÆÜlaneÈ ÝparallelÈ ÝtoÈ Ýx-yŽ’ÔÆ È Ýplane\n"Ž’T·‘ÇÏ ushŽ‘€«;Ž¡‘ÏorientationŽ‘H:Y«=‘ÇÝX_YŽ‘ w«;Ž¡‘ -·gŽ¡‘ -ÂelseŽ‘ .5ifŽ‘+ã-«(Ïnormal‘‰ffŽ‘®xŽ‘+›+·‘Ç«0Ž‘ ÿù·^‘8àÏnormal‘‰ffŽ‘®zŽ‘-M¥·‘Ç«0Ž‘Ç)‘±=·‘ÿý«Ellipse–UUlies“in“a“plane“parallel“to“x-z“plane.‘o·±=Ž¡‘ -·fŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EllipseÈ ÝliesÈ ÝinÈ ÝaÈ ÝpŽ‘kÆÜlaneÈ ÝparallelÈ ÝtoÈ Ýx-zŽ’ÔÆ È Ýplane\n"Ž’T·‘ÇÏ ushŽ‘€«;Ž¡‘ÏorientationŽ‘H:Y«=‘ÇÝX_ZŽ‘ w«;Ž¡‘ -·gŽ¡‘ -ÂelseŽ‘ .5ifŽ‘+ã-«(Ïnormal‘‰ffŽ‘®zŽ‘+Å·‘Ç«0Ž‘ ÿù·^‘8àÏnormal‘‰ffŽ‘®yŽ‘-¹º·‘Ç«0Ž‘Ç)‘±=·‘ÿý«Ellipse–UUlies“in“a“plane“parallel“to“z-y“plane.‘o·±=Ž¡‘ -·fŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EllipseÈ ÝliesÈ ÝinÈ ÝaÈ ÝpŽ‘kÆÜlaneÈ ÝparallelÈ ÝtoÈ Ýz-yŽ’ÔÆ È Ýplane\n"Ž’T·‘ÇÏ ushŽ‘€«;Ž¡‘ÏorientationŽ‘H:Y«=‘ÇÝZ_YŽ‘ w«;Ž¡‘ -·gŽ¡‘ -ÂelseŽ‘0Øá±=·‘ÿý«Ellipse–UUdoGesn't“lie“in“a“plane“parallel“to“a“ma‘Ž8jor“plane.‘o·±=Ž¡‘ -·fŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EllipseÈ Ýdoesn'tÈ ÝlieŽ‘kÆÜÈ ÝinÈ ÝaÈ ÝplaneÈ ÝparallelŽ’ÔÆ È ÝtoÈ ÝaÈ ÝmajorÈ Ýplane.\nŽ’=Æd"Ž’FSá·‘ÇÏ 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o¬=‘DZget‘‰ffŽ‘®normalŽ‘3QŒ¬(‘ª¨);Ž¦‘±normalŽ‘4Vºµ:±shiftŽ‘}¬(±CenterŽ‘œ¬);Ž¦‘­P•®9oin“tŽ‘2pt0Ž‘Eò¬=‘DZget‘‰ffŽ‘®p‘ÿ}'ointŽ‘*)`¬(0Ž‘);Ž¦‘±pt0Ž‘&0U°¬=ŽŽ‘8…©±CenterŽ‘W E¬;Ž¡‘±pt0Ž‘#i=µ:±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u¬(±trueŽ‘ʬ);Ž¡‘±pt0Ž‘&0U°¬=ŽŽ‘5¾Œ±maxŽ‘Ic'¬(±get‘‰ffŽ–®axis‘‰ffŽ“hŽ‘+-I¬(–ª¨)µ;“±get‘‰ffŽ–®axis‘‰ffŽ“vŽ‘,¤B¬(“))µ=¬2Ž‘;Ž¡‘µ=°‘ÿý¬[²LDF‘T2002.11.06.¬]Ž‘T7±pt0Ž‘fÆǬwill–UUeither“lie“on“the“pšGerimeter“of“the“­EllipseŽ‘(“ƒ¬or“b˜ey¸ãond“it.‘o°µ=Ž¡‘±pt0Ž‘#i=µ:±shiftŽ‘}¬(±CenterŽ‘œ¬);Ž¡‘±pt0Ž‘#i=µ:±r‘ÿ}'otateŽ‘o>¬(±CenterŽ‘œµ;‘ª¨±normalŽ‘"`µ;‘ª¨±angleŽ‘jû¬);Ž¦‘­b•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘edð±bppŽ‘x"ñ¬=‘DZinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘TS÷¬(±CenterŽ‘œµ;‘ª¨±pt0Ž‘ã¬);Ž¡‘­P•®9oin“tŽ‘2dir–ÿ}'e“ction‘‰ffŽ‘®lineŽ‘mj¬(±pt0Ž‘¢°‘8à±CenterŽ‘!S|¬);Ž¦‘±dir–ÿ}'e“ction‘‰ffŽ‘®lineŽ‘N{%µ:±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u¬(±trueŽ‘ʬ);Ž¦‘­P•®9oin“tŽ‘2dir–ÿ}'e“ction‘‰ffŽ‘®ptŽ‘f4¬;Ž¦‘­ifŽ‘´ú¬(±bppŽ‘öéµ:± rstŽ‘µªµ:±ptŽ‘ «µ°6¬=‘Ç´INVALID_POINTŽ‘GY¬)‘°fŽ¡‘±dir–ÿ}'e“ction‘‰ffŽ‘®ptŽ‘T ¬=‘DZbppŽ‘¾µ:± rstŽ‘µªµ:±ptŽ‘ ä¬;Ž¡‘±dir–ÿ}'e“ction‘‰ffŽ‘®ptŽ‘T °¬=ŽŽ‘f`Ó±CenterŽ’…{o¬;Ž¡‘±dir–ÿ}'e“ction‘‰ffŽ‘®ptŽ‘QDgµ:±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u¬(±trueŽ‘ʬ);Ž¡‘­ifŽ‘)´û¬(±dir–ÿ}'e“ction‘‰ffŽ‘®ptŽ‘6 |°‘DZdir–ÿ}'e“ction‘‰ffŽ‘®lineŽ‘=B;¬)‘­returnŽ‘(溱bppŽ‘8Ý£µ:± rstŽ‘µªµ:±ptŽ‘ ä¬;Ž¡‘°gŽ¡‘­returnŽ‘7æ¼±bppŽ‘GÝ¥µ:±se–ÿ}'c“ondŽ‘§Çµ:±ptŽ‘ ä¬;Ž¡‘ +°gŽŸ­1203.– üEqualitš®9y‘ÿ +«.“¬TO‘¡ÞDO:–¢4I'll“need“to“de ne“­P˜athŽ‘3œ¬::Ž‘$ÁÚ­opQÇeratorŽ‘PX°Ž‘X­¬(‘ª¨)“in“order“to“bGe“able“to“de ne“thisŽ¡function.Ž¦°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¡¬#­ifŽ‘ ´ø¬0ŽŽ¡‘ +­virtualŽ‘/Ôb•QÇo“olŽ‘I/:opQÇeratorŽ‘tÅï°Ž‘| ¬(­constŽ‘*¢EllipseŽ‘ChЬ&Ž‘K/îµeŽ‘O×ï¬);Ž¡#­endifŽŽŽŽŒ‹O#A Šn ý‘ì°x¬1204–¯3DLDF-1.1.5.1’'O­EQUALITY“¬335Ž €n ý•@P­1204.Ž©°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¤ ¬#­ifŽ‘ ´ø¬0ŽŽ¡‘ +­virtualŽ‘/Ôb•QÇo“olŽ‘I/:EllipseŽ‘l¬::Ž‘r¦U­opQÇeratorŽ’ž= +°Ž’¦(¬(­constŽ‘*¢EllipseŽ‘ChЬ&Ž‘K/îµeŽ‘O×ï¬)Ž¡‘ +°f‘ª¨gŽ¡¬#­endifŽŽŸ1205.‘ üLošQÇcation–ÕTof“a“p˜oin®9t.‘ ü¬[²LDF‘T2003.07.25.¬]Ž‘Zˆ6This–UUfunction“o•¸ãv“erloadsŽ¡­Regu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘i÷œ¬::‘±lo–ÿ}'c“ationŽ‘#Á¬(‘ª®).‘=³It's–¹simpler,‘ØWbšGecause“it“do˜esn't“need“to“cop¸ãy“the“­EllipseŽ‘'[¬and“transformŽ¡the–UUcopš¸ãy“in˜to“a“ma‘Ž8jor“plane.‘qÇNor“doGes“it“require“the“use“of“±solveŽ‘ ¬(‘ª®).Ž¡‘ +[²LDF‘T2003.07.25.¬]Ž‘Y&ZIf–stthe“­P•®9oin“tŽ‘"0¬argumen¸ãt“µP‘׬lies“in“the“same“plane“as“°Ž‘su±thisŽ‘_+¬,‘zû±lo–ÿ}'c“ationŽ‘&.¬.Ž¡-1Ž‘ UVµm–Ç>“d¬.‘qǵP‘¸ä¬lies–UUoutside“the“­EllipseŽ‘%>.¬.Ž¡1Ž‘ UVµm–Ç<“d¬.‘qǵP‘¸ä¬lies–UUinside“the“pGerimeter“of“the“­EllipseŽ‘%>.¬.Ž¡-2Ž‘ UVµP‘¸ä¬is–UUnot“in“the“same“plane“as“the“­EllipseŽ‘%>.¬.Ž¡-3Ž‘ UVThe‘UU­EllipseŽ‘(“ƒ¬is‘UUnon-elliptical.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ +¬[²LDF‘T2003.07.25.¬]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔsignedŽ‘RýÊshortŽ‘pÈm±lo–ÿ}'c“ationŽ’“‰ê¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié]¬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹P-• Šn ý‘ì¬336›¯LOCA‘ÿJªTION–ÕXOF“A“POINT’ðoy3DLDF-1.1.5.1˜°x¬1206Ž €n ý•@P­1206.Ž©°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¤ ‘ +­signedŽ‘-o÷shortŽ‘K:šEllipseŽ‘n#w¬::‘±lo–ÿ}'c“ationŽ‘#Á¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié]¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­b•QÇo“olŽ‘-¡h´DEBUGŽ‘K.Ù¬=‘DZfalseŽ‘v\¬;‘µ=°–ÿý¬true“°µ=Ž¡‘­realŽ‘*³0±ax‘‰ffŽ‘®hŽ‘AL¬=‘DZget‘‰ffŽ–®axis‘‰ffŽ“hŽ‘-ôa¬(‘ª¨);Ž¡‘­realŽ‘*³0±ax‘‰ffŽ‘®vŽ‘AV¬=‘DZget‘‰ffŽ–®axis‘‰ffŽ“vŽ‘-À²¬(‘ª¨);Ž¦‘­ifŽ‘´ú¬(±ax‘‰ffŽ‘®hŽ‘˜Õ°‘Ç´INVALID_REALŽ‘D†<°_‘8à±ax‘‰ffŽ‘®vŽ‘ž°‘Ç´INVALID_REALŽ‘BM\¬)‘°fŽ¡‘±c‘ÿ}'errŽ‘8÷f°‘A½´"ERROR!® ´In® ´Ellipse::Ž‘qAlocation():\n"Ž’É|°Ž¡‘2´"Ellipse® ´is® ´non-elliŽ’šÿÉptical.® ´Returning® ´-3Ž’ÿ.\n\n"Ž’&Ìû°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½°Ž‘I­Û¬3Ž‘N­Ü;Ž¡‘°gŽ¡‘­ifŽ‘´ú¬(°:µpŽ‘:±is‘‰ffŽ–®on‘‰ffŽ“planeŽ‘1‚Ú¬(±get‘‰ffŽ‘®planeŽ‘(vè¬(‘ª¨)))‘°fŽ¡‘±c‘ÿ}'errŽ‘8²z°‘üÑ´"WARNING!® ´In® ´EllipseŽ‘pü•::location():\n"Ž’Íž°Ž¡‘2´"Point® ´doesn't® ´lie® ´iŽ’šÿÉn® ´plane® ´of® ´Ellipse.\Ž’ÿn"Ž’Í°‘Ç´"Returning® ´-2.\n\n"Ž‘iÔ_°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½°Ž‘I­Û¬2Ž‘N­Ü;Ž¡‘°gŽ¦‘­realŽ‘*³0±max‘‰ffŽ‘®axŽ‘NŒó¬=‘DZmaxŽ‘k³¬(±ax‘‰ffŽ‘®hŽ‘ѽµ;‘ª¨±ax‘‰ffŽ‘®vŽ‘H¶¬);Ž¡‘­P•®9oin“tŽ‘2qŽ‘:‰a¬=‘ǵpŽ‘ +ø°‘8à±get‘‰ffŽ‘®fo‘ÿ}'cusŽ‘)zq¬(0Ž‘);Ž¡‘­realŽ‘*³0±magŽ‘@Ã&¬=‘ǵqŽ‘™Â:±magnitudeŽ‘.=r¬(‘ª¨);Ž¦‘µqŽ‘™Ä¬=‘ǵpŽ‘ +ø°‘8à±get‘‰ffŽ‘®fo‘ÿ}'cusŽ‘)zq¬(1Ž‘);Ž¡‘±magŽ‘*ø¬+=ŽŽ‘‘DZmax‘‰ffŽ‘®axŽ‘#Ùì)‘°fŽ¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Point® ´lies® ´outside® Ž‘kÆÜ´of® ´perimeter® ´of® ´|EllŽ’ÔÆ ipse|.\n"Ž’Œí¬;Ž¡‘­returnŽ‘Aæ½°Ž‘I­Û¬1Ž‘N­Ü;Ž¡‘°gŽ¡‘­elseŽ‘+Øá°fŽ¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Point® ´lies® ´inside® ´oŽ‘kÆÜf® ´perimeter® ´of® ´|ElliŽ’ÔÆ pse|.\n"Ž’ÿLð¬;Ž¡‘­returnŽ‘A潬1Ž‘Fæ¾;Ž¡‘°gŽ¡‘ +gŽ¤­1207.‘ üIn•®9tersection‘ÕTpQÇoin“ts.Ž¡1208.‘ üP•®9oin“t‘ÕTargumen“ts.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ +¬[²LDF‘T2003.07.27.¬]Ž‘Y;Made–UUthe“argumen¸ãts“­constŽ‘!÷P•®9oin“tŽ‘@o”¬&Ž‘H6².Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/Ôb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ’€ò±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ’Ò¡¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±p0Ž‘Pøµ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±p1Ž‘R¢Å¬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹Q60 Šn ý‘ì°x¬1209–¯3DLDF-1.1.5.1’ôh7­POINT‘ÕX¯ARÃŽGUMENTS“¬337Ž €n ý•@P­1209.Ž©°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¤ ‘ +­b•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘[dïEllipseŽ‘~M̬::‘±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±pt0Ž‘TJ˜µ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±pt1Ž‘Uõ@¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼Regu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ’¡ÞX¬::‘±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã¬(±c‘ÿ}'enterŽ‘ ‹µ;‘ª¨±pt0Ž–ãµ;‘ª¨±pt1Ž“¬);Ž¡‘ +°gŽŸ­1210.› üP•®9ath‘adargumen“t.˜¬This–ð„function“just“c•¸ãhec“ks–ð„to“bGe“sure“that“­P®9athŽ‘rlµpŽ‘&jð¬is“a“line,‘®extracts“the“­P•®9oin“tsŽ‘#¬,Ž¡and–UUcalls“the“vš¸ãersion“with“­P•®9oin“tŽ‘"Dò¬argumen˜ts,“returning“the“latter's“return“v‘ÿqÇalue.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.07.09.¬]Ž‘Y;Made‘UU­virtualŽ‘%Ó¬.Ž¡‘ +[²LDF‘T2003.07.27.¬]Ž‘Y;Made–UUargumen¸ãt“µpŽ‘ ²ª¬a“­constŽ‘!÷P®9athŽ‘=f°¬&Ž‘E-Î.‘qÇChanged,“so“that“±is‘‰ffŽ‘®line‘ÿ}'arŽ‘(jÒ¬(‘ª®)“is“used,“andŽ¡±get‘‰ffŽ–®last‘‰ffŽ“p‘ÿ}'ointŽ‘:$>¬(‘ª®)–UUrather“than“±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘*·¬(1Ž‘).Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/Ôb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ’€ò±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ’Ò¡¬(­constŽ‘*¢P®9athŽ‘:[¬&Ž‘AØyµpŽ‘Fày¬)‘UU­constŽ‘*¢¬;ŽŸ­1211.Ž¦°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¡‘ +­b•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘[dïEllipseŽ‘~M̬::‘±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã¬(­constŽ‘*¢P®9athŽ‘:[¬&Ž‘AØyµpŽ‘Fày¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­ifŽ‘´ú¬(°:µpŽ‘:±is‘‰ffŽ‘®line‘ÿ}'arŽ‘%}¬(‘ª¨))‘°fŽ¡‘±c‘ÿ}'errŽ‘6D°‘K›´"ERROR!® ´In® ´Ellipse::Ž‘nK_intersection_points(Ž’×K#const® ´Path&):\n"Ž’1ö°Ž¡‘2´"Path® ´argument® ´is® ´noŽ’šÿÉn-linear.\n"Ž’ÞÁ°‘´´"Haven't® ´programmed® Ž‘lx´this® ´case® ´yet.\n"Ž’ÉÅa°Ž¡‘2´"Returning® ´INVALID_BŽ’šÿÉOOL_POINT_PAIR."Ž’òM°‘DZend‘‚ØlŽ–ò°‘DZend‘‚ØlŽ“°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½´INVALID_BOOL_POINT_PAIRŽ’»,à¬;Ž¡‘°gŽ¡‘­returnŽ‘7æ¼±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ’‰s›¬(µpŽ‘:±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(0Ž‘)µ;‘ª¨pŽ‘²¨:±get‘‰ffŽ–®last‘‰ffŽ“p‘ÿ}'ointŽ‘:$>¬(‘ª¨));Ž¡‘ +°gŽŸ­1212.– üEllipse‘ÕTargumen®9t.“¬TO–UUDO:“Read“through“and“explain.‘qÇ[²LDF‘T2002.11.06.¬]ŽŽ¡‘ +The‘å™±stepŽ‘æ¬argumenš¸ãt–å™is“used“in“the“case“that“the“­EllipsesŽ‘.=G¬ha˜v˜e“di eren˜t“cen˜ters“and/or“axis“orien˜tation.Ž¡It–’is“the“n•¸ãum“bšGer–’of“degrees“of“rotation“p˜erformed“while“the“algorithm“is“searcš¸ãhing“for“an“in˜tersection.‘'ØTheŽ¡default–UUis“3,“whicš¸ãh“should“w˜ork“as“long“as“the“­EllipsesŽ‘-¿¬don't“di er“toGo“m˜uc˜h“in“size.‘qÇ[²LDF‘T2004.01.12.¬]ŽŽ¡‘ +If–y¼the“±verb‘ÿ}'oseŽ‘'„Õ¬argumenš¸ãt“is“±trueŽ‘>T¬,‘‚Õinformation“abGout“the“in˜tersection“pGoin˜ts“is“prin˜ted“to“standard“output.Ž¡[²LDF‘T2003.07.01.¬]ŽŽ¡‘ +If–æthe“­EllipsesŽ‘.™á¬are“coplanar,‘CŠthe“inš¸ãtersection“pGoin˜ts“of“the“pGerimeters“of“the“­EllipsesŽ‘.™á¬are“returned.‘­{IfŽ¡the–A9planes“of“the“­EllipsesŽ‘,ô‡¬are“p•Gerp“endicular–A9or“skš¸ãew,‘E>the“in˜tersection“line“of“the“planes“is“found.‘kThen,‘E>theŽ¡in•¸ãtersection›UUpGoin“ts˜of˜the˜this˜line˜with˜the˜­EllipsesŽ‘)Çj¬,˜if˜they˜exist.Ž¡‘ +TO–UUDO:“[²LDF‘T2003.07.20.¬]Ž‘R]The“folloš¸ãwing“coGde“found“only“one“in˜tersection:Ž¦#­ifŽ‘ ´ø¬0ŽŽ¡‘ +­EllipseŽ‘/>/µtŽ‘2Ú¡¬(±originŽ‘ö!µ;‘ª¨¬5Ž–ª©µ;‘ª¨¬4Ž“µ;‘ª¨¬90ŽŽ‘ ªª);Ž¡‘ +­CircleŽ‘+¸‚µcŽ‘0 ]¬(±originŽ‘ö!µ;‘ª¨¬3Ž‘ª©µ;‘ª¨¬90ŽŽ‘ ªª);Ž¦‘ +µcŽ‘SÜ:±shiftŽ‘}¬(3Ž‘);Ž¡‘ +µcŽ‘SÜ:±r‘ÿ}'otateŽ‘o>¬(0Ž‘µ;‘ª¨¬0Ž‘ª©µ;‘ª¨¬30ŽŽ‘ ªª);Ž¦‘ +­b•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜quadrupleŽ‘y欱bp‘ÿ}'qŽ’‹ßà¬=‘ǵtŽ‘cŠ:±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘QŒß¬(µcŽ‘SÛ¬);Ž¡#­endifŽŽŽŽŒ‹RB» Šn ý‘ì¬338–­ELLIPSE‘ÕX¯ARÃŽGUMENT’ïo\3DLDF-1.1.5.1“°x¬1213Ž €n ý•@P­1213.‘ ü¬When‘ƒRµcŽ‘ Z¬wš¸ãas–ƒRrotated“b˜y“15Ÿü^ÿ¶Ž‘6¬or“45Ÿü^ÿ¶Ž‘˜ä¬,‘ŽÒ±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘U±¬(‘ª®)“found“bGoth“in˜tersections.‘û¿T‘ÿ*ªry“to“ nd“outŽ¤ wh•¸ãy!‘d¼I‘.*w“an“t–.4to“write“a“­CircleŽ‘$¿”¬vš¸ãersion“with“an“­EllipseŽ‘(EA¬argumen˜t,‘6and“vice“v˜ersa.‘d¼If“I–.*do,‘6I“ma˜y–.4not“ha˜v˜e“toŽ¡w¸ãorry–UUabGout“this“problem.ŽŸ­1214.‘ ü¬[²LDF‘T2003.07.20.¬]ŽŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.04.12.¬]Ž‘Xd´Actually‘ÿ*ª,‘Òƒit–±ÎloGoks“as“if“the“equations“Dr.“Sc•¸ãh“w“ardmann›±Îga“v“e˜me˜w“on't˜do˜the˜tric“k.‘;ETheyŽ¡assume–ŠºbšGoth“ellipses“are“cen¸ãtered“ab˜out“the“origin.‘÷When“I‘Š­tried“to“ha•¸ãv“e–ŠºMathematica“solv¸ãe“the“equationsŽ¡for‘•ƒµxŸü^ÿ³2Ž›|sµ=aŸü^ÿ³2Ž‘à¬+–c©µy[ÙŸü^ÿ³2Ž‘ØLµ=bŸü^ÿ³2Ž‘®‚¬=‘2(µx“°“µm¬)Ÿü^ÿ³2Ž˜µ=cŸü^ÿ³2Ž‘à¬+“(µy‘¿‚°“µn¬)Ÿü^ÿ³2Ž˜µ=dŸü^ÿ³2Ž˜¬,‘¥Mathematica–•ƒprošGduced“solutions“that“to˜ok“up“o•¸ãv“er‘•ƒ35,000Ž¡lines–UUof“text!Ž¡‘ +[²LDF‘T2002.04.12.¬]Ž‘Y8±I'v¸ãe–…Ërewritten“the“other“cases“(parallel,›‘èp•Gerp“endicular,˜and–…Ësk¸ãew)“in“this“function“com-Ž¡pletely‘ÿ*ª,‘áŸand–ıit“seems“likš¸ãe“it“w˜asn't“really“w˜orth“the“e ort.‘A‘The“new“v˜ersion“doGes“ho˜w˜ev˜er“mak˜e“use“of“­PlanesŽŽ¡¬and‘sÒ­LinesŽ‘U‘¬,›{qwhic¸ãh–sÒis“not“a“bad“thing,˜and“it“c•¸ãhec“ks–sÒwhether“the“in¸ãtersection“­P•®9oin“tsŽ‘' (¬are“on“the“­EllipseŽ‘%\«¬,˜soŽ¡it–UUw¸ãasn't“a“total“loss.Ž¡‘ +[²LDF‘T2002.04.12.¬]Ž‘X¾}I'vš¸ãe– —written“to“Dr.“Sc˜h˜w˜ardmann“and“ask˜ed“him“abGout“this“problem.‘Y3It“ma˜y“just“bGe“m˜yŽ¡ignorance,‘?por–9÷pGerhaps“I'vš¸ãe“o˜v˜erloGok˜ed“something“simple.‘h¨I'm“not“tošGo“hop˜eful,›?pho•¸ãw“ev“er,˜so–9÷I'll“probably“ha•¸ãv“eŽ¡to–UUimplemenš¸ãt“the“n˜umerical“solution“I'd“started,“after“all.Ž¡‘ +[²LDF‘T2002.04.12.¬]Ž‘YZRemo•¸ãv“ed–§old“de nition.‘gDr.“Ulricš¸ãh“Sc˜h˜w˜ardmann“of“the“Gesellsc˜haft“fG‘ú¸âur“wissensc˜haft-Ž¡lic•¸ãhe›Ó¶Datenv“erarbGeitung,–óNG‘úÿÿottingen,“German•¸ãy˜sho“w“ed˜me˜ho“w˜to˜use˜Mathematica's˜\Solv“e"˜command˜toŽ¡solvš¸ãe–\gthe“systems“of“equations“that“describGe“the“in˜tersections“bGet˜w˜een“t˜w˜o“ellipses.‘†ýTherefore,‘^+I'v˜e“remo˜v˜edŽ¡the–UUold“de nition“of“this“function,“whicš¸ãh“w˜asn't“complete,“an˜yw˜a˜y‘ÿ*ª,“and“I'll“put“in“a“new“de nition“soGon.Ž¡‘ +[²LDF‘T2002.04.14.¬]Ž‘XÒAbGout–"to“start“wš¸ãork“on“implemen˜ting“the“coplanar“case“again.‘_¶The“equations“proGducedŽ¡bš¸ãy–ÆMathematica“will“w˜ork“for“the“case“that“the“ellipses“ha˜v˜e“the“same“cen˜ter.‘ZBI‘´will“catc˜h“the“case“that“theyŽ¡are–!¤congruenš¸ãt“and“ha˜v˜e“the“same“cen˜ter“and“the“case“that“they“are“non-congruen˜t“and“ha˜v˜e“the“same“cen˜terŽ¡bGefore–UUgoing“on“to“implemenš¸ãt“a“n˜umerical“solution“for“the“case“that“they“ha˜v˜e“di eren˜t“cen˜ters.Ž¡‘ +[²LDF‘T2002.04.14.¬]Ž‘YÑîChanged–argumenš¸ãt“from“­constŽ‘#]EllipseŽ‘I>¬&Ž‘Udto“­EllipseŽ‘&á¬,‘Qusince“I‘Ôw˜as“ha˜ving“to“cop˜y“it,Ž¡an•¸ãyw“a“y‘ÿ*ª.Ž¡‘ +[²LDF‘T2003.07.01.¬]Ž‘Y;Added‘UU±verb‘ÿ}'oseŽ‘'<¬argumen¸ãt.Ž¡‘ +[²LDF‘T2003.07.01.¬]Ž‘Y&ÍChanged›sç\p•Gerp“endicular˜and˜sk¸ãew˜case".‘Í|Debugged˜coplanar˜case,‘{‹where˜the˜­EllipsesŽŽ¡¬don't›UUha•¸ãv“e˜the˜same˜cen“ters˜and/or˜axis˜orien“tation.Ž¡‘ +[²LDF‘T2003.07.06.¬]Ž‘ZyüMade–Ça“minor“c¸ãhange“to“the“conditional“that“determines“whether“the“­EllipsesŽ‘0A¬areŽ¡coplanar–UUor“not.Ž¡‘ +[²LDF‘T2003.08.14.¬]Ž‘Y;Setting‘UU±verb‘ÿ}'oseŽ‘'<¬to‘UU±trueŽ‘oB¬if‘UU´VERBOSE_GLOBALŽ–P°è¬is‘UU±trueŽ‘í¬.‘qÇAdded‘UU´VERBOSE_GLOBALŽ“¬toŽ¡®pspglb.web‘UU¬toGda¸ãy‘ÿ*ª.Ž¡‘ +[²LDF‘T2004.01.12.¬]Ž‘Y;Added‘UU­realŽ‘ƒ±stepŽ‘/¡Œ¬argumen¸ãt,–UUwith“3“as“its“default“v‘ÿqÇalue.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¤ ‘ +­virtualŽ‘0wDb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜quadrupleŽ’¡G_±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ’òÔ>¬(­EllipseŽ‘&'žµeŽ‘*ÏŸ;‘ª¨­constŽ‘ ¾ºrealŽ‘8[X±stepŽ‘Në3¬=‘L'3Ž‘ L(µ;‘ª¨­b•QÇo“olŽŽ¡‘±verb‘ÿ}'oseŽ‘AXx¬=‘DZfalseŽ‘v\¬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹SSn Šn ý‘ì°x¬1215–¯3DLDF-1.1.5.1’ïo\­ELLIPSE‘ÕX¯ARÃŽGUMENT“¬339Ž €n ý•@P­1215.Ž©°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¤ ‘ +­b•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜quadrupleŽ‘yíEllipseŽ’œÖm¬::‘±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã¬(­EllipseŽ‘%EµeŽ‘)í;‘ª¨­constŽ‘Ü.realŽ‘6–@±stepŽ‘HÙôµ;‘ª¨­b•QÇo“olŽ‘Rò±verb‘ÿ}'oseŽ‘;äO¬)‘\9­constŽ‘1†°fŽ¡‘2­b•QÇo“olŽ‘K¡k´DEBUGŽ‘i.ܬ=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¦‘­ifŽ‘)´û¬(´VERBOSE_GLOBALŽ‘J>¬)‘±verb‘ÿ}'oseŽ‘(Xu¬=‘DZtrueŽ‘‹°¬;Ž¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÿ9°_‘8à±verb‘ÿ}'oseŽ‘"Ê=¬)Ž¡‘(±c‘ÿ}'outŽ‘>|°‘#T´"Entering® ´Ellipse::iŽ‘l#ntersection_points(EŽ’Õ"Üllipse® ´e,® ´const® ´boolŽ’>" ® ´verbose)"Ž’vL>°Ž¡‘<±end‘‚ØlŽ‘OñȬ;Ž¦‘­b•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜quadrupleŽ’æ®±bp‘ÿ}'qŽ’Ÿßâ¬=‘Ç´INVALID_BOOL_POINT_QUADRUPLEŽ’–M,¬;Ž¡‘­PlaneŽ‘>6»±this‘‰ffŽ‘®planeŽ‘l…ͬ=‘DZthisŽ‘²ÎŸµ~ŽŽ‘²Ï±get‘‰ffŽ‘®planeŽ‘@)·¬(‘ª¨);Ž¡‘­PlaneŽ‘>6»±e‘‰ffŽ‘®planeŽ‘aˆ©¬=‘ǵeŽ‘o:±get‘‰ffŽ‘®planeŽ‘(vè¬(‘ª¨);Ž¦‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘(±this‘‰ffŽ‘®planeŽ‘S‡þµ:±showŽ‘Šÿ¬(´"this_plane:"Ž‘DÆA¬);Ž¡‘(±e‘‰ffŽ‘®planeŽ‘HŠÚµ:±showŽ‘Šÿ¬(´"e_plane:"Ž‘5J¬);Ž¡‘°gŽ¡‘­ifŽ‘)´û¬(±this‘‰ffŽ‘®planeŽ‘+‡úµ:±normalŽ–#а‘DZe‘‰ffŽ‘®planeŽ‘#Qîµ:±normalŽ‘"˜°_‘8à±this‘‰ffŽ‘®planeŽ‘-ÀÚµ:±normalŽ“°‘ÇŽ‘ +Ž6±e‘‰ffŽ‘®planeŽ‘+ µ:±normalŽ‘ V¸¬)‘UU°fŽŸ­1216.‘ ü¬Coplanar‘UUcase.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.07.20.¬]Ž‘X/¾No¸ãw–|Øusing“±get‘‰ffŽ–®axis‘‰ffŽ“vŽ‘-vr¬(›ª®)“and“±get‘‰ffŽ–®axis‘‰ffŽ“hŽ‘-ª!¬(˜),‘¨%instead“of“accessing“±axis‘‰ffŽ‘®hŽ‘ó=¬and“±axis‘‰ffŽ‘®vŽ‘¿Ž¬directly‘ÿ*ª.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¡‘ +­ifŽ‘´ù¬(±fabsŽ–2Ò¬(±fabsŽ“¬(±this‘‰ffŽ‘®planeŽ‘+‡úµ:±distanc‘ÿ}'eŽ›$Eý¬)–8à°“±fabsŽ‘k²¬(±e‘‰ffŽ‘®planeŽ‘ ŠÖµ:±distanc‘ÿ}'eŽ˜¬))–ǵ<“­P•®9oin“tŽ‘ad¬::Ž‘%epsilonŽ‘E^¦¬(‘ª¨))‘UU°fŽ¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"Ellipses® ´are® ´coplanŽ‘kÆÜar.\n"Ž’Ž”J°‘DZ ushŽ‘€¬;Ž¡‘ +°gŽ¦‘ +­realŽ‘ ³/±ax‘‰ffŽ‘®hŽ‘7L¬=‘DZget‘‰ffŽ–®axis‘‰ffŽ“hŽ‘-ôa¬(‘ª¨);Ž¡‘ +­realŽ‘ ³/±ax‘‰ffŽ‘®vŽ‘7U¬=‘DZget‘‰ffŽ–®axis‘‰ffŽ“vŽ‘-À²¬(‘ª¨);ŽŽŽŒ‹Td@ Šn ý‘ì¬340–­ELLIPSE‘ÕX¯ARÃŽGUMENT’ïo\3DLDF-1.1.5.1“°x¬1217Ž €n ý•@P­1217.‘ ü¬Congruenš¸ãt,‘1same–'ýloGcation“and“axis“orien˜tation.‘bª[²LDF‘T2002.04.15.¬]Ž‘S=ŒAdded“c˜hec˜k“for“the“axis“orien˜ta-Ž¤ tion.‘.ÎIf–”Wthe“axes“are“not“all“vš¸ãertical“or“horizon˜tal,‘¤then“this“fails“( oating“exception).‘.ÎThis“means“that“theŽ¡circular–¬ñcase“will“not“bšGe“caugh¸ãt“here,‘ÂØbut“I‘¬Úplan“to“program“a“sp˜ecialization“for“­CirclesŽ‘&™Y¬,‘ÂØso“this“shouldn'tŽ¡cause–UUtoGo“m•¸ãuc“h–UUof“a“problem.Ž¡‘ +[²LDF‘T2002.04.14.¬]Ž‘Y;Added–UUthis“section.Ž¡‘ +This–´routine“only“wš¸ãorks“if“the“axis“orien˜tation“of“the“­EllipsesŽ‘-u}¬is“the“same,‘ŒËor“rotated“90Ÿü^ÿ¶Ž›˜¬or“180Ÿü^ÿ¶Ž˜¬abGoutŽ¡an–øaxis“through“the“cen¸ãter“in“the“direction“of“the“normal“to“the“plane“of“the“­EllipseŽ‘%ÿѬ,‘G`or“in“the“oppGositeŽ¡direction.‘MThe–žœaxis“orienš¸ãtation“is“tested“on“the“basis“of“the“v˜ector“from“the“cen˜ter“to“±p‘ÿ}'ointsŽ‘Ã1¬[0Ž‘].‘MIf“the“axisŽ¡orien¸ãtation–òcis“the“same,‘¦or“rotated“180Ÿü^ÿ¶Ž‘‹G¬abšGout“the“ab˜o•¸ãv“e-men“tioned–òcaxis,‘¦then“±axis‘‰ffŽ‘®hŽ‘"ÞS¬of“°Ž‘òd±thisŽ‘Ð}¬m¸ãust“equalŽ¡±axis‘‰ffŽ‘®hŽ‘+¹¬of‘2,µeŽ‘ Y¬and‘2,±axis‘‰ffŽ‘®vŽ›!*6¬of‘2,°Ž‘2-±thisŽ‘P¬m¸ãust–2,equal“±axis‘‰ffŽ‘®vŽ˜¬of“µeŽ‘Ú-¬.‘fIf“the“axis“orien¸ãtation“is“rotated“at“an“angle“of“°¬90Ÿü^ÿ¶Ž‘˜ä¬,Ž¡then‘UU±axis‘‰ffŽ‘®hŽ‘!¤7¬of‘UU°Ž‘UV±thisŽ‘–a¬m¸ãust–UUequal“±axis‘‰ffŽ‘®vŽ›!pˆ¬of“µeŽ‘ R«¬and“±axis‘‰ffŽ‘®vŽ˜¬of“°Ž‘UV±thisŽ‘–a¬m¸ãust“equal“±axis‘‰ffŽ‘®hŽ‘!¤7¬of“µeŽ‘ýV¬.Ž¡‘ +The–M§ôµ:±showŽ‘Šÿ¬(´"normal_point"Ž‘J>¬);Ž¦‘ +­P•®9oin“tŽ‘(ïž±e‘‰ffŽ–®axis‘‰ffŽ“orientation‘‰ffŽ“r–ÿ}'otate“dŽ’˜ø@¬(±e‘‰ffŽ–®axis‘‰ffŽ“orientationŽ‘NPɬ);ŽŽŽŒ‹UnÌ Šn ý‘ì°x¬1218–¯3DLDF-1.1.5.1’ïo\­ELLIPSE‘ÕX¯ARÃŽGUMENT“¬341Ž €n ý•@P­1218.‘ ü¬[²LDF‘T2002.09.26.¬]Ž‘Z)kST–ÿ*ªAR“T›örHERE.–öŠAdded“the“­ifŽ‘L·¬condition.‘R.I˜think“this“should“bGe“done,‘ but“I˜shouldŽ¤ c•¸ãhec“k–Pto“bGe“sure.‘pApparenš¸ãtly“I‘Oÿha˜v˜en't“programmed“the“case“that“the“cen˜ters“aren't“the“same,‘Qbut“it“w˜ouldŽ¡bGe–UUeasy“enough“to“do,“I“think.Ž©°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¡‘ +­ifŽ‘pð¬(±e‘‰ffŽ–®axis‘‰ffŽ“orientationŽ‘Qá°6¬=‘DZthis‘‰ffŽ–®axis‘‰ffŽ“orientationŽ‘\¬)‘±e‘‰ffŽ–®axis‘‰ffŽ“orientation‘‰ffŽ“r–ÿ}'otate“dŽ‘u¢µ:±r‘ÿ}'otateŽ‘o>¬(±originŽ‘ö!µ;‘ª¨±normal‘‰ffŽ‘®p‘ÿ}'ointŽ‘;Rœµ;‘ª¨¬90ŽŽ‘ ªª);Ž¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±e‘‰ffŽ–®axis‘‰ffŽ“orientation‘‰ffŽ“r–ÿ}'otate“dŽ‘u¢µ:±showŽ‘Šÿ¬(´"e_axis_orientation"Ž‘i†,¬);Ž¡‘ +­ifŽ‘3~¬(±thisŽ‘붟µ~ŽŽ‘ë·±c‘ÿ}'enterŽ‘47°‘™õµeŽ‘Aö:±c‘ÿ}'enterŽ‘–ð^–8¬((±this‘‰ffŽ–®axis‘‰ffŽ“orientationŽ‘\çâ°‘™õ±e‘‰ffŽ–®axis‘‰ffŽ“orientationŽ‘Twö°_“±this‘‰ffŽ–®axis‘‰ffŽ“orientationŽ‘_u°Ž¡‘(Ž‘/Ç"±e‘‰ffŽ–®axis‘‰ffŽ“orientationŽ‘~ë¬)–°°_“¬(±this‘‰ffŽ–®axis‘‰ffŽ“orientationŽ‘\°‘DZe‘‰ffŽ–®axis‘‰ffŽ“orientation‘‰ffŽ“r–ÿ}'otate“dŽ‘tîj°_“±this‘‰ffŽ–®axis‘‰ffŽ“orientationŽ‘^3µ°Ž¡‘(Ž‘/Ç"±e‘‰ffŽ–®axis‘‰ffŽ“orientation‘‰ffŽ“r–ÿ}'otate“dŽ’ŸÏĬ)))‘°fŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Centers® ´and® ´axis® ´orŽ‘kÆÜientation® ´are® ´the® ´saŽ’ÔÆ me.\n"Ž’÷”°‘DZ ushŽ‘€¬;Ž¡‘(µ=°‘'¬[²LDF‘T2002.04.14.¬]Ž‘T6‹Picš¸ãk–lthe“maxim˜um“of“±axis‘‰ffŽ‘®hŽ‘!Ò‹¬and“±axis‘‰ffŽ‘®vŽ‘!žÜ¬and“m˜ultiply“it“b˜y“1.5.‘·EW‘ÿ*ªe'll“use“aŽ¡‘2line–gBsegmenš¸ãt“of“this“length“to“ nd“in˜tersection“pGoin˜ts“with“the“t˜w˜o“­EllipsesŽ‘)ÙW¬.‘§Using“this“lengthŽ¡‘2guaran•¸ãtees›UUw“e'll˜ nd˜them.‘qÇActually‘ÿ*ª,˜±maxŽ‘ùð¬(±axis‘‰ffŽ‘®hŽ‘ùµ;‘ª¨±axis‘‰ffŽ‘®vŽ‘p†¬)˜ough“t˜to˜do˜the˜tric“k.‘o°µ=Ž¦‘­P•®9oin“tŽ‘2pt0Ž‘BXÚ¬;Ž¦‘­ifŽ‘´ú¬(±ax‘‰ffŽ‘®hŽ‘˜Õ°‘DZax‘‰ffŽ‘®vŽ‘e&¬)‘±pt0Ž‘0S¬=‘DZget‘‰ffŽ‘®p‘ÿ}'ointŽ‘*)`¬(0Ž‘);Ž¡‘­elseŽ‘+Øá±pt0Ž‘> 4¬=‘DZget‘‰ffŽ‘®p‘ÿ}'ointŽ‘*)`¬(±numb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜ointsŽ‘JÀ©µ=¬4Ž‘);Ž¡‘±pt0Ž‘&0U°¬=ŽŽ‘8…©±c‘ÿ}'enterŽ‘T4¬;Ž¡‘±pt0Ž‘&0U°¬=ŽŽ‘5¾Œ1µ:¬5ŽŽ‘B…«;Ž¡‘±pt0Ž‘#i=µ:±shiftŽ‘}¬(±c‘ÿ}'enterŽ‘ ‹¬);Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±this‘‰ffŽ‘®planeŽ‘I‡ýµ:±normalŽ‘ V¸µ:±showŽ‘Šÿ¬(´"normal"Ž‘*†P¬);Ž¡‘±c‘ÿ}'enterŽ‘: Žµ:±showŽ‘Šÿ¬(´"center"Ž‘*†P¬);Ž¡‘°g‘µ=°‘ ¬[²LDF‘T2002.04.14.¬]Ž‘TeW‘ÿ*ªe'll–^lrotate“±pt0Ž‘&¬around“the“normal“to“the“plane“of“the“ellipse“from“±c‘ÿ}'enterŽ‘g÷¬,Ž¡‘2i.e.,–UUthe“line“segmen¸ãt“from“±c‘ÿ}'enterŽ‘"´5¬to“±pt1Ž‘¾¬.‘o°µ=Ž¦‘­P•®9oin“tŽ‘2pt1Ž‘BXÚ¬(±this‘‰ffŽ‘®planeŽ‘+‡úµ:±normalŽ‘ V¸¬);Ž¦‘±pt1Ž‘#i=µ:±shiftŽ‘}¬(±c‘ÿ}'enterŽ‘ ‹¬);Ž¡‘­ifŽ‘Ð ¬(´DEBUGŽ–ÆY¬)‘±pt1Ž‘i;µ:±showŽ‘Šÿ¬(´"pt1"Ž“¬);‘µ=°‘¬[²LDF‘T2002.04.14.¬]Ž‘T>[±pt2Ž‘gý¬is–pgthe“in¸ãtersection“of“the“line“from“±c‘ÿ}'enterŽŽ¡‘2¬to‘UU±pt0Ž›å¬with‘UU°Ž‘UV±thisŽ‘A ¬,–UUand“±pt3Ž˜¬is“the“in¸ãtersection“of“the“same“line“with“µeŽ‘ýV¬.‘o°µ=Ž¦‘­P•®9oin“tŽ‘2pt2Ž‘BXÚ¬;Ž¡‘­P•®9oin“tŽ‘2pt3Ž‘BXÚ¬;Ž¡‘­b•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘edð±bpp‘‰ffŽ‘®thisŽ’ˆÑ0¬;Ž¡‘­b•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘edð±bpp‘‰ffŽ‘®eŽ‘}ÂF¬;Ž¡‘­b•QÇo“olŽ‘-ñm±c‘ÿ}'ongruent‘‰ffŽ‘® agŽ‘pt¾¬=‘Lu±trueŽ‘ ¬;‘µ=°‘P¬[²LDF‘T2002.04.14.¬]Ž‘T¨AW‘ÿ*ªe'll–¥Z nd“inš¸ãtersection“pGoin˜ts“for“ v˜e“v‘ÿqÇaluesŽ¡‘(of‘›ü±pt0Ž‘7¬.‘E»If–›üone“set“of“inš¸ãtersection“pGoin˜ts“are“not“the“same,‘­¥this“means“the“w˜e“­EllipsesŽ‘-ª ¬are“notŽ¡‘(congruenš¸ãt–UUand“in“the“same“loGcation,“so“w˜e“break“out“of“the“loGop.‘o°µ=Ž¦‘­forŽ‘%般(­in®9tŽ‘¤÷µiŽ‘Þ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ5Ž“;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)‘°fŽ¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"i® ´==® ´"Ž‘*Ôƒ°‘ǵiŽ‘ $°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘­ifŽ‘)´û¬(µiŽ‘9 °6¬=‘Ç0Ž‘Ç)‘±pt0Ž‘i;µ:±r‘ÿ}'otateŽ‘o>¬(±c‘ÿ}'enterŽ‘ ‹µ;‘ª¨±pt1Ž‘ãµ;‘ª¨¬30ŽŽ‘ ªª);Ž¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±pt0Ž‘i;µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(´"0"Ž‘F_¬);Ž¡‘±bpp‘‰ffŽ‘®thisŽ‘D3[¬=‘DZinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘TS÷¬(±c‘ÿ}'enterŽ‘ ‹µ;‘ª¨±pt0Ž‘ã¬);Ž¡‘±bpp‘‰ffŽ‘®eŽ‘9$q¬=‘ǵeŽ‘o:±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘QŒß¬(±c‘ÿ}'enterŽ‘ ‹µ;‘ª¨±pt0Ž‘ã¬);Ž¡‘­ifŽ‘)´û¬(±bpp‘‰ffŽ‘®thisŽ‘#l@µ:± rstŽ‘µªµ:bŽ‘°‘DZtrueŽ‘‹°¬)‘°fŽ¡‘(­ifŽ‘3´ü¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"first® ´is® ´an® ´interseŽ‘kÆÜction® ´point® ´(this).\Ž’ÔÆ n"Ž’ßͬ;Ž¡‘(±pt2Ž‘:0W¬=‘DZbpp‘‰ffŽ‘®thisŽ‘&3Xµ:± rstŽ‘µªµ:±ptŽ‘ ä¬;Ž¡‘°gŽ¡‘­elseŽ‘4.7ifŽ‘?ã/¬(±bpp‘‰ffŽ‘®thisŽ‘#l@µ:±se–ÿ}'c“ondŽ‘§Çµ:bŽ‘°‘DZtrueŽ‘‹°¬)‘°fŽ¡‘(­ifŽ‘3´ü¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"second® ´is® ´an® ´intersŽ‘kÆÜection® ´point® ´(this).Ž’ÔÆ \n"Ž’å ÿ¬;Ž¡‘(±pt2Ž‘:0W¬=‘DZbpp‘‰ffŽ‘®thisŽ‘&3Xµ:±se–ÿ}'c“ondŽ‘§Çµ:±ptŽ‘ ä¬;Ž¡‘°gŽ¡‘­elseŽ‘5Øâ°fŽŽŽŒ‹V}Y Šn ý‘ì¬342–­ELLIPSE‘ÕX¯ARÃŽGUMENT’ïo\3DLDF-1.1.5.1“°x¬1218Ž €n ý•@P‘(±c‘ÿ}'errŽ‘A:²°‘…´"In® ´Ellipse::interseŽ‘o„Ìction_points(EllipseŽ’Ø„).\n"Ž’ùÏñ°Ž¤ ‘<´"This® ´can't® ´happen® ´(Ž’¤ÿÊthis)!\n"Ž’×/°‘Ç´"Will® ´try® ´to® ´continuŽ‘kÆÜe.\n\n"Ž’“ÔG°‘DZ ushŽ‘€¬;Ž¡‘(±pt2Ž‘:0W¬=‘Ç´INVALID_POINTŽ‘GY¬;Ž¡‘°gŽ¡‘­ifŽ‘)´û¬(±bpp‘‰ffŽ‘®eŽ‘]Vµ:± rstŽ‘µªµ:bŽ‘°‘DZtrueŽ‘‹°¬)‘°fŽ¡‘(­ifŽ‘3´ü¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"first® ´is® ´an® ´interseŽ‘kÆÜction® ´point® ´(e).\n"Ž’Ð ¬;Ž¡‘(±pt3Ž‘:0W¬=‘DZbpp‘‰ffŽ‘®eŽ‘$nµ:± rstŽ‘µªµ:±ptŽ‘ ä¬;Ž¡‘°gŽ¡‘­elseŽ‘4.7ifŽ‘?ã/¬(±bpp‘‰ffŽ‘®eŽ‘]Vµ:±se–ÿ}'c“ondŽ‘§Çµ:bŽ‘°‘DZtrueŽ‘‹°¬)‘°fŽ¡‘(­ifŽ‘3´ü¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"second® ´is® ´an® ´intersŽ‘kÆÜection® ´point® ´(e).\n"Ž’ÕM¬;Ž¡‘(±pt3Ž‘:0W¬=‘DZbpp‘‰ffŽ‘®eŽ‘$nµ:±se–ÿ}'c“ondŽ‘§Çµ:±ptŽ‘ ä¬;Ž¡‘°gŽ¡‘­elseŽ‘5Øâ°fŽ¡‘(±c‘ÿ}'errŽ‘A:²°‘…´"In® ´Ellipse::interseŽ‘o„Ìction_points(EllipseŽ’Ø„).\n"Ž’ùÏñ°Ž¡‘<´"This® ´can't® ´happen® ´(Ž’¤ÿÊe)!\nWill® ´try® ´to® ´conŽ’ ÿŽtinue.\n\n"Ž’K í°‘Ç± ushŽ‘€¬;Ž¡‘(±pt3Ž‘:0W¬=‘Ç´INVALID_POINTŽ‘GY¬;Ž¡‘°gŽ¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘(±pt2Ž‘7i?µ:±showŽ‘Šÿ¬(´"2"Ž‘F_¬);Ž¡‘(±pt2Ž‘7i?µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(´"2"Ž‘F_¬);Ž¡‘(±pt3Ž‘7i?µ:±showŽ‘Šÿ¬(´"3"Ž‘F_¬);Ž¡‘(±pt3Ž‘7i?µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(´"3"Ž‘F_µ;‘ª¨´"bot"Ž‘q¬);Ž¡‘°gŽ¡‘­ifŽ‘)´û¬(±pt2Ž‘0S°‘Ç´INVALID_POINTŽ–IÆ9°_‘8à±pt3Ž›i3°‘Ç´INVALID_POINTŽ“°_‘8à±pt2Ž˜°6¬=‘DZpt3Ž‘0S¬)‘°fŽ¡‘(­ifŽ‘3´ü¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Ellipses® ´are® ´not® ´coŽ‘kÆÜngruent.® ´Breaking.\nŽ’ÔÆ "Ž’Ú¬;Ž¡‘(±c‘ÿ}'ongruent‘‰ffŽ‘® agŽ‘iýø¬=‘DZfalseŽ‘v\¬;Ž¡‘(­breakŽ‘D¡h¬;Ž¡‘°gŽ¡‘­elseŽ‘5Øâcon•®9tin“ueŽ‘`¿—¬;Ž¡‘°g‘µ=°‘ÿý­forŽ‘“+°µ=Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"congruent_flag® ´==® ´"Ž‘o\°‘DZc‘ÿ}'ongruent‘‰ffŽ‘® agŽ‘DÅ °‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘°gŽ¡‘­ifŽ‘´ú¬(±c‘ÿ}'ongruent‘‰ffŽ‘® agŽ‘Aýô°‘DZtrueŽ‘‹°¬)‘°fŽ¡‘±c‘ÿ}'errŽ‘6F0°‘‡´"WARNING!® ´In® ´EllipseŽ‘nK::intersection_pointŽ’×s(Ellipse).\n"Ž’'&Ô°Ž¡‘2´"Ellipses® ´are® ´congruŽ’šÿÉent® ´and® ´in® ´the® ´same® Ž’ÿ´location.\n"Ž’Iè@°Ž¡‘2´"Returning® ´INVALID_BŽ’šÿÉOOL_POINT_QUADRUPLE.Ž’ÿ\n\n"Ž’!Œþ°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½´INVALID_BOOL_POINT_QUADRUPLEŽ’ÕlѬ;Ž¡‘°gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"All® ´five® ´points® ´areŽ‘kÆÜ® ´not® ´on® ´both® ´ellipseŽ’ÔÆ s.\n"Ž’òT°‘DZ ushŽ‘€¬;Ž¡‘°gŽ¡‘ +g‘µ=°‘ÿý¬End–UUof“test“of“congruency“and“same“loGcation.‘o°µ=Ž¡‘=°‘ÿý¬[²LDF‘T2002.09.26.¬]Ž‘T7ST–ÿ*ªAR“T–UUHERE.“Programm“this“case!!‘o°µ=Ž¡‘ +­elseŽ‘ .5ifŽ‘+ã-¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘-'2°‘Íù´"The® ´centers® ´are® ´difŽ‘nͽferent,® ´or® ´the® ´axisŽ’×Í® ´orientation® ´"Ž’'¡¸°Ž¡‘(´"is® ´different,® ´or® ´boŽ’ÿÈth.® ´"Ž’®9°‘Ç´"Haven't® ´programmed® Ž‘kÆÜ´this® ´case® ´yet.\n"Ž’Ŭ;Ž¡‘ +°gŽŸ‘ +­EllipseŽ‘/>/±c‘ÿ}'opyŽ‘CÎ'¬(°Ž‘±thisŽ‘ë·¬);Ž¡‘ +­P•®9oin“tŽ‘(ïž±c–ÿ}'opy‘‰ffŽ‘®c“enterŽ‘[Ñݬ(±c‘ÿ}'opyŽ‘øµ:±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘,=G¬(‘ª¨));Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓµtŽ‘EeE¬;Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓ±t‘‰ffŽ‘®inverseŽ‘h×è¬;ŽŽŽŒ‹W” Šn ý‘ì°x¬1219–¯3DLDF-1.1.5.1’ïo\­ELLIPSE‘ÕX¯ARÃŽGUMENT“¬343Ž €n ý•@P­1219.‘ ü¬Shift–UUto“origin“(if“necessary).Ž©°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¤ ‘ +­ifŽ‘´ù¬(±c–ÿ}'opy‘‰ffŽ‘®c“enterŽ‘5©W°6¬=‘DZoriginŽ‘½9¬)‘°fŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"Shifting® ´copy® ´to® ´orŽ‘kÆÜigin.\n"Ž’™D°‘DZ ushŽ‘€¬;Ž¡‘°gŽ¡‘µtŽ‘œt:±shiftŽ‘}¬(°Ž‘DZc–ÿ}'opy‘‰ffŽ‘®c“enterŽ‘:©]µ:±get‘‰ffŽ‘®xŽ‘Žg¬(–ª¨)µ;“°Ž‘ qƱc–ÿ}'opy‘‰ffŽ‘®c“enterŽ›»¬;Ž¡‘±c–ÿ}'opy‘‰ffŽ‘®c“enterŽ‘I©Y°¬=ŽŽ‘Y7µtŽ‘\Ô¬;Ž¡‘µeŽ‘o°¬=ŽŽ‘*ýRµtŽ‘.™Ä¬;Ž¡‘ +°gŽ¡‘ +­elseŽ‘ .5ifŽ‘+ã-¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"copy® ´is® ´already® ´at® Ž‘kÆÜ´origin.\n"Ž’£”>°‘DZ ushŽ‘€¬;Ž¡‘ +°gŽŸ­1220.‘ ü¬Get–UUcoGordinates“of“normal.Ž¦°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¡‘ +­realŽ‘ ³/±normal‘‰ffŽ‘®xŽ‘LNZ¬=‘DZthis‘‰ffŽ‘®planeŽ‘.Oµ:±normalŽ‘ V¸µ:±get‘‰ffŽ‘®xŽ‘Žg¬(‘ª¨);Ž¡‘ +­realŽ‘ ³/±normal‘‰ffŽ‘®yŽ‘L4 ¬=‘DZthis‘‰ffŽ‘®planeŽ‘.Oµ:±normalŽ‘ V¸µ:±get‘‰ffŽ‘®yŽ‘t¬(‘ª¨);Ž¡‘ +­realŽ‘ ³/±normal‘‰ffŽ‘®zŽ‘KÇô¬=‘DZthis‘‰ffŽ‘®planeŽ‘.Oµ:±normalŽ‘ V¸µ:±get‘‰ffŽ‘®zŽ‘¬(‘ª¨);ŽŽŽŒ‹X¢9 Šn ý‘ì¬344–­ELLIPSE‘ÕX¯ARÃŽGUMENT’ïo\3DLDF-1.1.5.1“°x¬1221Ž €n ý•@P­1221.‘ ü¬Determine–- the“orien¸ãtation“of“the“ellipse“and“rotate,‘5if“it's“not“already“in“a“plane“parallel“to“a“ma‘Ž8jorŽ¤ plane.‘‘ÐRotating–`the“­EllipseŽ‘(¨ß¬can“cause“inaccuracies“in“the“coGordinate“v‘ÿqÇalues,‘b®so“if“the“ellipse“is“already“in“aŽ¡ma›Ž8jor–UUplane,“(i.e.,“one“p•Gerp“endicular–UUto“a“ma˜jor“axis),“wš¸ãe“lea˜v˜e“it“where“it“is.ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.08.27.¬]Ž‘YyCommenš¸ãted-out–`“the“declaration“of“´OTHERŽ‘&ì¬,‘ccbGecause“it's“nev˜er“used.‘“I‘`ha˜v˜en't“deleted“it,Ž¡just–UUin“case.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¤ ‘ +­unsignedŽ‘:7shortŽ‘X²±orientationŽ’‰tñ¬;Ž¡‘ +­constŽ‘(*£unsignedŽ‘Xa±shortŽ‘v,T´X_YŽ’‰9ˬ=‘Ç0Ž‘Ç;Ž¡‘ +­constŽ‘(*£unsignedŽ‘Xa±shortŽ‘v,T´X_ZŽ’‰9ˬ=‘Ç1Ž‘Ç;Ž¡‘ +­constŽ‘(*£unsignedŽ‘Xa±shortŽ‘v,T´Z_YŽ’‰9ˬ=‘Ç2Ž‘Ç;Ž¡#­ifŽ‘ ´ø¬0ŽŽ¡‘ +­constŽ‘(*£unsignedŽ‘Xa±shortŽ‘v,T´OTHERŽ’“¹Å¬=‘Ç3Ž‘Ç;Ž¡#­endifŽŽ©‘ +ifŽ‘´ù¬(±normal‘‰ffŽ‘®xŽ‘+›+°‘Ǭ0Ž– ÿù°^‘8à±normal‘‰ffŽ‘®yŽ‘-¹º°‘Ǭ0Ž“°^‘8à±normal‘‰ffŽ‘®zŽ‘-M¥°‘Ǭ0Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘+8¾°‘ƒ´"ERROR!® ´In® ´Ellipse::Ž‘m‚Úintersection_points(Ž’Ö‚ž):\n"Ž’õÌ °‘ƒ´"Normal® ´==® ´0.® ´"Ž‘XLg°Ž¡‘(´"Returning® ´INVALID_BŽ’ÿÈOOL_POINT_QUADRUPLE\Ž’ùÿŒn\n"Ž’M°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘7æ¼´INVALID_BOOL_POINT_QUADRUPLEŽ’ËlЬ;Ž¡‘ +°gŽ¡‘ +­elseŽ‘ .5ifŽ‘+ã-¬(±normal‘‰ffŽ‘®xŽ‘+›+°‘Ǭ0Ž‘ ÿù°^‘8à±normal‘‰ffŽ‘®yŽ‘-¹º°‘Ǭ0Ž‘Ç)‘µ=°‘ÿý¬Ellipse–UUlies“in“a“plane“parallel“to“x-y“plane.‘o°µ=Ž¡‘ +°fŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Ellipse® ´lies® ´in® ´a® ´pŽ‘kÆÜlane® ´parallel® ´to® ´x-yŽ’ÔÆ ® ´plane\n"Ž’T°‘DZ ushŽ‘€¬;Ž¡‘±orientationŽ‘H:Y¬=‘Ç´X_YŽ‘ w¬;Ž¡‘ +°gŽ¡‘ +­elseŽ‘ .5ifŽ‘+ã-¬(±normal‘‰ffŽ‘®xŽ‘+›+°‘Ǭ0Ž‘ ÿù°^‘8à±normal‘‰ffŽ‘®zŽ‘-M¥°‘Ǭ0Ž‘Ç)‘µ=°‘ÿý¬Ellipse–UUlies“in“a“plane“parallel“to“x-z“plane.‘o°µ=Ž¡‘ +°fŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Ellipse® ´lies® ´in® ´a® ´pŽ‘kÆÜlane® ´parallel® ´to® ´x-zŽ’ÔÆ ® ´plane\n"Ž’T°‘DZ ushŽ‘€¬;Ž¡‘±orientationŽ‘H:Y¬=‘Ç´X_ZŽ‘ w¬;Ž¡‘ +°gŽ¡‘ +­elseŽ‘ .5ifŽ‘+ã-¬(±normal‘‰ffŽ‘®zŽ‘+Å°‘Ǭ0Ž‘ ÿù°^‘8à±normal‘‰ffŽ‘®yŽ‘-¹º°‘Ǭ0Ž‘Ç)‘µ=°‘ÿý¬Ellipse–UUlies“in“a“plane“parallel“to“z-y“plane.‘o°µ=Ž¡‘ +°fŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Ellipse® ´lies® ´in® ´a® ´pŽ‘kÆÜlane® ´parallel® ´to® ´z-yŽ’ÔÆ ® ´plane\n"Ž’T°‘DZ ushŽ‘€¬;Ž¡‘±orientationŽ‘H:Y¬=‘Ç´Z_YŽ‘ w¬;Ž¡‘ +°gŽ¡‘ +­elseŽ‘0Øáµ=°‘ÿý¬Ellipse–UUdoGesn't“lie“in“a“plane“parallel“to“a“ma‘Ž8jor“plane.‘o°µ=Ž¡‘ +°fŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Ellipse® ´doesn't® ´lieŽ‘kÆÜ® ´in® ´a® ´plane® ´parallelŽ’ÔÆ ® ´to® ´a® ´major® ´plane.\nŽ’=Æd"Ž’FSᰑDZ ushŽ‘€¬;Ž¡‘-µ=°‘ÿý¬Put–UUit“in“x-z“plane.‘o°µ=Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c–ÿ}'opy‘‰ffŽ‘®c“enterŽ‘PâBµ:±dotlab‘ÿ}'elŽ‘!ÿó¬(´"c"Ž‘F_¬);Ž¡‘°gŽ¦‘­P•®9oin“tŽ‘2el‘‚Ølipse‘‰ffŽ‘®pt0Ž‘c们=‘DZc‘ÿ}'opyŽ‘Wµ:±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(0Ž‘);Ž¡‘­T‘ÿ +«ransformŽ‘KÈÔ±t0Ž‘VŸ¬;Ž¦‘±t0Ž‘L͵:±align‘‰ffŽ–®with‘‰ffŽ“axisŽ‘@²x¬(±c–ÿ}'opy‘‰ffŽ‘®c“enterŽ‘2â?µ;‘ª¨±el‘‚Ølipse‘‰ffŽ‘®pt0Ž‘/جµ;‘ª¨´'x'Ž‘ñ¬);Ž¡‘±c‘ÿ}'opyŽ‘+W°¬=ŽŽ‘:åI±t0Ž‘E2¬;Ž¡‘±c–ÿ}'opy‘‰ffŽ‘®c“enterŽ‘I©Y°¬=ŽŽ‘Y7±t0Ž‘c„[¬;Ž¡‘±el‘‚Ølipse‘‰ffŽ‘®pt0Ž‘Dõ°¬=ŽŽ‘TƒU±t0Ž‘^Ð ¬;Ž¡‘µeŽ‘o°¬=ŽŽ‘*ýR±t0Ž‘5J¬;Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘°fŽŽŽŒ‹Y¨  Šn ý‘ì°x¬1221–¯3DLDF-1.1.5.1’ïo\­ELLIPSE‘ÕX¯ARÃŽGUMENT“¬345Ž €n ý•@P‘±el‘‚Ølipse‘‰ffŽ‘®pt0Ž‘L.µ:±showŽ‘Šÿ¬(´"ellipse_pt0"Ž‘DÆA¬);Ž¤ ‘±el‘‚Ølipse‘‰ffŽ‘®pt0Ž‘L.µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(´"0"Ž‘F_¬);Ž¡‘°gŽ¤‘­P•®9oin“tŽ‘2el‘‚Ølipse‘‰ffŽ‘®pt4Ž‘c们=‘DZc‘ÿ}'opyŽ‘Wµ:±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(±numb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜ointsŽ‘JÀ©µ=¬4Ž‘);Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±el‘‚Ølipse‘‰ffŽ‘®pt4Ž‘3.µ:±showŽ‘Šÿ¬(´"ellipse_pt4"Ž‘DÆA¬);Ž¡‘­T‘ÿ +«ransformŽ‘KÈÔ±t1Ž‘VŸ¬;Ž¡‘±t1Ž‘L͵:±align‘‰ffŽ–®with‘‰ffŽ“axisŽ‘@²x¬(±c–ÿ}'opy‘‰ffŽ‘®c“enterŽ‘2â?µ;‘ª¨±el‘‚Ølipse‘‰ffŽ‘®pt4Ž‘/جµ;‘ª¨´'z'Ž‘ñ¬);Ž¤ ‘±c‘ÿ}'opyŽ‘+W°¬=ŽŽ‘:åI±t1Ž‘E2¬;Ž¡‘±c–ÿ}'opy‘‰ffŽ‘®c“enterŽ‘I©Y°¬=ŽŽ‘Y7±t1Ž‘c„[¬;Ž¡‘µeŽ‘o°¬=ŽŽ‘*ýR±t1Ž‘5J¬;Ž¡‘±el‘‚Ølipse‘‰ffŽ‘®pt4Ž‘Dõ°¬=ŽŽ‘TƒU±t1Ž‘^Ð ¬;Ž¡‘µtŽ‘cŒ°¬=ŽŽ‘)ññt0Ž‘4>Ž¬;Ž¡‘µtŽ‘cŒ°¬=ŽŽ‘)ññt1Ž‘4>Ž¬;Ž¡‘±orientationŽ‘H:Y¬=‘Ç´X_ZŽ‘ w¬;Ž¡‘ +°gŽ¡‘ +±t‘‰ffŽ‘®inverseŽ‘3Ö.¬=‘ǵtŽ‘cŠ:±inverseŽ‘ ‡¬(‘ª¨);Ž¤‘ +­P•®9oin“tŽ‘(ïž±e‘‰ffŽ‘®c‘ÿ}'enterŽ‘Pë¬=‘ǵeŽ‘o:±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘,=G¬(‘ª¨);Ž¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽ¤ ‘±c–ÿ}'opy‘‰ffŽ‘®c“enterŽ‘FâAµ:±showŽ‘Šÿ¬(´"copy_center"Ž‘DÆA¬);Ž¡‘±e‘‰ffŽ‘®c‘ÿ}'enterŽ‘8Q7µ:±showŽ‘Šÿ¬(´"e_center"Ž‘5J¬);Ž¡‘ +°gŽŽŽŒ‹Z¸A Šn ý‘ì¬346–­ELLIPSE‘ÕX¯ARÃŽGUMENT’ïo\3DLDF-1.1.5.1“°x¬1222Ž €n ý•@P­1222.‘ ü¬Ellipses›Eha•¸ãv“e˜the˜same˜cen“ter˜and˜orien“tation.‘XIf˜they˜do,‘®then˜there˜is˜an˜algebraic˜solution˜w“e˜canŽ¤ apply–UUto“ nd“the“inš¸ãtersection“pGoin˜ts.Ž©°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¡‘ +­P•®9oin“tŽ‘(ïž±c‘ÿ}'opy‘‰ffŽ–®axis‘‰ffŽ“orientationŽ’…Ñq¬(±c‘ÿ}'opyŽ‘øµ:±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(0Ž‘));Ž¦‘ +±c‘ÿ}'opy‘‰ffŽ–®axis‘‰ffŽ“orientationŽ‘i¨ì°¬=ŽŽ‘{þ@±c–ÿ}'opy‘‰ffŽ‘®c“enterŽ’®à¬;Ž¡‘ +±c‘ÿ}'opy‘‰ffŽ–®axis‘‰ffŽ“orientationŽ‘fáÔµ:±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u¬(±trueŽ‘ʬ);Ž¡‘ +±e‘‰ffŽ–®axis‘‰ffŽ“orientationŽ‘[â¬=‘ǵeŽ‘o:±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(0Ž‘);Ž¡‘ +±e‘‰ffŽ–®axis‘‰ffŽ“orientationŽ‘[â°¬=ŽŽ‘mm6±e‘‰ffŽ‘®c‘ÿ}'enterŽ’‘¾k¬;Ž¡‘ +±e‘‰ffŽ–®axis‘‰ffŽ“orientationŽ‘XPʵ:±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u¬(±trueŽ‘ʬ);‘7íifŽ‘Ï)¬((±e‘‰ffŽ‘®c‘ÿ}'enterŽ‘*L̬;Ž¦‘ +­P•®9oin“tŽ‘(ïž±pt20Ž‘=uI¬;Ž¡‘ +­P•®9oin“tŽ‘(ïž±pt21Ž‘=uI¬;Ž¡‘ +­P•®9oin“tŽ‘(ïž±pt22Ž‘=uI¬;Ž¡‘ +­P•®9oin“tŽ‘(ïž±pt23Ž‘=uI¬;Ž¡‘ +­realŽ‘ ³/µxŽ‘&jK¬;Ž¡‘ +­realŽ‘ ³/µyŽ‘%ö'¬;Ž¡‘ +­realŽ‘ ³/µaŽ‘(Ãw¬=‘DZax‘‰ffŽ‘®hŽ‘˜Õµ=¬2µ:¬0ŽŽ‘ Ç;Ž¡‘ +­realŽ‘ ³/µbŽ‘'Äñ¬=‘DZax‘‰ffŽ‘®vŽ‘e&µ=¬2µ:¬0ŽŽ‘ Ç;Ž¡‘ +­realŽ‘ ³/µcŽ‘'Î"¬=‘ǵeŽ‘o:±get‘‰ffŽ–®axis‘‰ffŽ“hŽ‘+-I¬(‘ª¨)µ=¬2µ:¬0ŽŽ‘ Ç;Ž¡‘ +­realŽ‘ ³/µdŽ‘(®¹¬=‘ǵeŽ‘o:±get‘‰ffŽ–®axis‘‰ffŽ“vŽ‘*ùš¬(‘ª¨)µ=¬2µ:¬0ŽŽ‘ Ç;Ž¦‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"a® ´==® ´"Ž‘*Ôƒ°‘ǵaŽ‘ +×`°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"b® ´==® ´"Ž‘*Ôƒ°‘ǵbŽ‘ ØÚ°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"c® ´==® ´"Ž‘*Ôƒ°‘ǵcŽ‘ â °‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"d® ´==® ´"Ž‘*Ôƒ°‘ǵdŽ‘ +¢°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘ +°gŽ¦‘ +­realŽ‘ ³/±aaŽ‘.úd¬=‘Ç(µaŽ–‚°‘8àµaŽ“¬);Ž¡‘ +­realŽ‘ ³/±bbŽ‘-Ñç¬=‘Ç(µbŽ–ƒŠ°‘8àµbŽ“¬);Ž¡‘ +­realŽ‘ ³/±c‘ÿ}'cŽ‘->,¬=‘Ç(µcŽ–Œ»°‘8àµcŽ“¬);Ž¡‘ +­realŽ‘ ³/±ddŽ‘/>Š¬=‘Ç(µdŽ–mR°‘8àµdŽ“¬);Ž¦‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"aa® ´==® ´"Ž‘0€°‘DZaaŽ‘M°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"bb® ´==® ´"Ž‘0€°‘DZbbŽ‘åа‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"cc® ´==® ´"Ž‘0€°‘DZc‘ÿ}'cŽ‘R°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"dd® ´==® ´"Ž‘0€°‘DZddŽ‘Rs°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘ +°gŽ¦‘ +­realŽ‘ ³/±denominatorŽ‘Y[ý¬;Ž¡‘ +­realŽ‘ ³/±numer‘ÿ}'atorŽ‘O…=¬;Ž¦‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"x® ´coordinate.\n"Ž‘\M¬;Ž¡‘ +±denominatorŽ‘Eoç¬=‘Ç(±aaŽ‘ ¸ý°–8à¬((±bbŽ‘ €°“±c‘ÿ}'cŽ‘ üŬ)µ=±ddŽ‘ ÄC¬))“°“±ddŽ‘ ý#¬;Ž¡‘ +±numer‘ÿ}'atorŽ‘;™'¬=‘DZbbŽ‘W˜°–8à¬(±aaŽ‘ ¸ý°“±c‘ÿ}'cŽ‘ üŬ);Ž¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"numerator® ´==® ´"Ž‘TÔk°‘DZnumer‘ÿ}'atorŽ‘4`>°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"denominator® ´==® ´"Ž‘_Te°‘DZdenominatorŽ‘>6þ°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(±denominatorŽ‘;o民Ǭ0Ž‘Ç)‘°fŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"x® ´==® ´INVALID_REAL.\Ž‘kÆÜn"Ž‘vÍ>¬;ŽŽŽŒ‹[¾“ Šn ý‘ì°x¬1222–¯3DLDF-1.1.5.1’ïo\­ELLIPSE‘ÕX¯ARÃŽGUMENT“¬347Ž €n ý•@P‘µxŽ‘~6¬=‘Ç´INVALID_REALŽ‘BM\¬;Ž¤ ‘ +°gŽ¡‘ +­elseŽ‘!Øà°fŽ¡‘­tryŽ‘)3°fŽ¡‘µxŽ‘&~7¬=‘Ç°Ž‘ +Ž6¬(µcŽ‘Œ»°‘8à±sqrtŽ‘èÙ¬(1Ž‘8á°‘8à¬(±numer‘ÿ}'atorŽ‘.Òµ=±denominatorŽ‘8¨Î¬)));Ž¡‘°gŽ©‘­catc®9hŽ‘.í׬(–ª¨µ:“:“:Ž‘ÿ÷¬)Ž¡‘°fŽ¡‘µxŽ‘&~7¬=‘Ç´INVALID_REALŽ‘BM\¬;Ž¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"x® ´==® ´INVALID_REAL\nŽ‘kÆÜ"Ž‘qA¬;Ž¡‘°gŽ¡‘ gŽ¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"xÈ Ý==È Ý"Ž‘*Ôƒ·‘DZxŽ‘ EL·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"yÈ Ýcoordinate:\n"Ž‘\M«;Ž¡‘ -·gŽ¡‘ -Ïnumer‘ÿ}'atorŽ‘;™'«=‘DZbŽ‘ J¢·‘8àÏsqrtŽ‘èÙ«(ÏfabsŽ‘2Ò«(ÏaaŽ‘ ¸ý·‘8àÏc‘ÿ}'cŽ‘ üÅ«));Ž¡‘ -ÏdenominatorŽ‘Eoç«=‘ÇÏsqrtŽ‘w«(ÏfabsŽ‘2Ò«(ÏaaŽ‘ ¸ý·–8à«((ÏbbŽ‘ €·“Ïc‘ÿ}'cŽ‘ üÅ«)±=ÏddŽ‘ ÄC«)));Ž¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"numeratorÈ Ý==È Ý"Ž‘TÔk·‘ÇÏnumer‘ÿ}'atorŽ‘4`>·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"denominatorÈ Ý==È Ý"Ž‘_Te·‘ÇÏdenominatorŽ‘>6þ·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ -·gŽ¡‘ -ÂifŽ‘´ù«(ÏdenominatorŽ‘;oæ·‘Ç«0Ž‘Ç)‘·fŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"yÈ Ý==È ÝINVALID_REAL.\Ž‘kÆÜn"Ž‘vÍ>«;Ž¡‘±yŽ‘ -«=‘ÇÝINVALID_REALŽ‘BM\«;Ž¡‘ -·gŽ¡‘ -ÂelseŽ‘!Øà·fŽ¡‘ÂtryŽ‘)3·fŽ¡‘±yŽ‘& -«=‘Ç·Ž‘ -Ž6«(Ïnumer‘ÿ}'atorŽ‘.Ò±=ÏdenominatorŽ‘8¨Î«);Ž¡‘·gŽ¦‘Âcatc®9hŽ‘.í׫(–ª¨±:“:“:Ž‘ÿ÷«)Ž¡‘·fŽ¡‘±yŽ‘& -«=‘ÇÝINVALID_REALŽ‘BM\«;Ž¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"yÈ Ý==È ÝINVALID_REAL\nŽ‘kÆÜ"Ž‘qA«;Ž¡‘·gŽ¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"x® ´==® ´"Ž‘*Ôƒ°‘ǵxŽ‘ EL°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"y® ´coordinate:\n"Ž‘\M¬;Ž¡‘ +°gŽ¡‘ 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qƱyŽ‘´¾;‘ª¨«0Ž‘ª©);Ž¡‘ÂifŽ‘´ú«(±yŽ‘ -·6«=‘Ç0Ž‘ ÿù·^‘8à±xŽ‘ -··6«=‘Ç0Ž‘Ç)‘·fŽ¡‘Ïpt22Ž‘2…®±:ÏsetŽ‘ x„«(±xŽ‘·;‘ª¨·Ž‘ qƱyŽ‘´¾;‘ª¨«0Ž‘ª©);Ž¡‘Ïpt23Ž‘2…®±:ÏsetŽ‘ x„«(·Ž‘DZxŽ‘ ~:;‘ª¨yŽ‘í ;‘ª¨«0Ž‘ª©);Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘Ïpt22Ž‘5LÆ«=‘ÇÝINVALID_POINTŽ‘GY«;Ž¡‘Ïpt23Ž‘5LÆ«=‘ÇÝINVALID_POINTŽ‘GY«;Ž¡‘·gŽ¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"y® ´==® ´"Ž‘*Ôƒ°‘ǵyŽ‘ +Ñ(°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘ +°gŽŽŽŒ‹\РŠn ý‘ì¬348–­ELLIPSE‘ÕX¯ARÃŽGUMENT’ïo\3DLDF-1.1.5.1“°x¬1223Ž €n ý•@P­1223.‘ ü¬The–UUellipses“can“inš¸ãtersect“at“no“pGoin˜ts,“t˜w˜o“pGoin˜ts,“or“four“pGoin˜ts.Ž¤ °Ž‘ +¬If–UUthey“do“not“inš¸ãtersect,“then“one“of“the“ellipses“m˜ust“bGe“inside“the“other.Ž¡°Ž‘ +¬If–UUthey“inš¸ãtersect“at“t˜w˜o“pGoin˜ts,“then“either“µx–Ǭ=“0–UUor“µy‘"ñ¬=‘Ç0“(but“not“bGoth).Ž¡°Ž‘ +¬Otherwise,–UUthey“inš¸ãtersect“at“four“pGoin˜ts.ŽŸ°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¡‘ +­ifŽ‘´ù¬(µxŽ‘~4°‘Ç´INVALID_REALŽ‘D†<°_‘8àµyŽ‘ +Bð°‘Ç´INVALID_REALŽ‘BM\¬)‘°fŽ¡‘±c‘ÿ}'errŽ‘,‡Ó°‘Ò+´"WARNING!® ´In® 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qƱyŽ‘´¾;‘ª¨xŽ‘aÄ«);Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘Ïpt22Ž‘5LÆ«=‘ÇÝINVALID_POINTŽ‘GY«;Ž¡‘Ïpt23Ž‘5LÆ«=‘ÇÝINVALID_POINTŽ‘GY«;Ž¡‘·gŽ¡‘ +­elseŽ‘ .5ifŽ‘+ã-¬(±orientationŽ‘4:W°‘Ç´Z_YŽ‘ w¬)‘°fŽ¡‘±pt20Ž‘(…­µ:±setŽ‘ x„¬(0Ž‘µ;‘ª¨yŽ‘í ;‘ª¨xŽ‘aĬ);Ž¡‘±pt21Ž‘(…­µ:±setŽ‘ x„¬(0Ž‘µ;‘ª¨°Ž‘ qƵyŽ‘´¾;‘ª¨°Ž‘ qƵxŽ‘(â¬);Ž¡‘­ifŽ‘´ú¬(µxŽ‘~4°6¬=‘Ç0Ž‘ ÿù°^‘8àµyŽ‘ +Bð°6¬=‘Ç0Ž‘Ç)‘°fŽ¡‘±pt22Ž‘2…®µ:±setŽ‘ x„¬(0Ž‘µ;‘ª¨yŽ‘í ;‘ª¨°Ž‘ qƵxŽ‘(â¬);Ž¡‘±pt23Ž‘2…®µ:±setŽ‘ x„¬(0Ž‘µ;‘ª¨°Ž‘ qƵyŽ‘´¾;‘ª¨xŽ‘aĬ);Ž¡‘°gŽ¡‘­elseŽ‘+Øá°fŽ¡‘±pt22Ž‘5LƬ=‘Ç´INVALID_POINTŽ‘GY¬;Ž¡‘±pt23Ž‘5LƬ=‘Ç´INVALID_POINTŽ‘GY¬;Ž¡‘°gŽ¡‘ gŽ¡‘ -ÂelseŽ‘!Øà·fŽ¡‘Ïc‘ÿ}'errŽ‘,Ì¿·‘Ý"ERROR!È ÝInÈ ÝEllipse::Ž‘oÛintersection_points(Ž’ØŸEllipse).\n"Ž’³ú·Ž¡‘(Ý"ThisÈ Ýcan'tÈ Ýhappen!È Ž’ÿÈÝorientationÈ ÝhasÈ ÝinvaŽ’ùÿŒlidÈ Ývalue:È Ý"Ž’>O×·‘ÊÏorientationŽ‘;M·Ž¡‘(Ïend‘‚ØlŽ‘>¸Þ·‘ÇÝ"WillÈ ÝtoÈ ÝtryÈ ÝtoÈ ÝcontŽ‘kÆÜinue.\n\n"Ž’£”>·‘ÇÏ ushŽ‘€«;Ž¡‘ -·gŽ¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘·fŽŽŽŒ‹VíÞ Šn ý‘ì«342›ÂELLIPSE‘ÕX­AR•ÃŽGUMENT’÷âò3DLDFPR“G˜·x«1184Ž €n ý•@P‘Ïpt20Ž‘(…­±:ÏshowŽ‘Šÿ«(Ý"pt20"Ž‘ 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ÿù·^‘8àÏss‘‰ffŽ‘®eŽ‘¸W·‘Ç«0Ž‘Ç)‘·fŽ¡‘Ïpt20Ž‘+LÅ·«=ŽŽ‘:ÚüÏt‘‰ffŽ‘®inverseŽ‘aê«;Ž¡‘Ïpt21Ž‘+LÅ·«=ŽŽ‘:ÚüÏt‘‰ffŽ‘®inverseŽ‘aê«;Ž¡‘Ïbp‘ÿ}'qŽ‘#2±:Ï rstŽ‘µª±:bŽ‘«=‘ÇÏtrueŽ‘‹°«;Ž¡‘Ïbp‘ÿ}'qŽ‘#2±:Ï rstŽ‘µª±:ÏptŽ‘ «µ«=‘ÇÏpt20Ž‘Lë;Ž¡‘Ïbp‘ÿ}'qŽ‘#2±:Ïse–ÿ}'c“ondŽ‘§Ç±:bŽ‘«=‘ÇÏtrueŽ‘‹°«;Ž¡‘Ïbp‘ÿ}'qŽ‘#2±:Ïse–ÿ}'c“ondŽ‘§Ç±:ÏptŽ‘ «µ«=‘ÇÏpt21Ž‘Lë;Ž¡‘ÂifŽ‘´ú«(Ïpt22Ž‘L÷6«=‘ÇÝINVALID_POINTŽ‘GY«)‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EllipsesÈ ÝintersectÈ Ž‘kÆÜÝatÈ ÝfourÈ Ýpoints.\n"Ž’ÊÍ«;Ž¡‘Ïpt22Ž‘5LÆ·«=ŽŽ‘DÚýÏt‘‰ffŽ‘®inverseŽ‘kê«;Ž¡‘Ïbp‘ÿ}'qŽ‘-2±:Ïthir‘ÿ}'dŽ‘Üj±:bŽ‘«=‘ÇÏtrueŽ‘‹°«;Ž¡‘Ïbp‘ÿ}'qŽ‘-2±:Ïthir‘ÿ}'dŽ‘Üj±:ÏptŽ‘ «µ«=‘ÇÏpt22Ž‘Lë;Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EllipsesÈ ÝintersectÈ Ž‘kÆÜÝatÈ ÝtwoÈ Ýpoints.\n"Ž’Å«;Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(Ïpt23Ž‘L÷6«=‘ÇÝINVALID_POINTŽ‘GY«)‘·fŽ¡‘Ïpt23Ž‘5LÆ·«=ŽŽ‘DÚýÏt‘‰ffŽ‘®inverseŽ‘kê«;Ž¡‘Ïbp‘ÿ}'qŽ‘-2±:ÏfourthŽ‘xù±:bŽ‘«=‘ÇÏtrueŽ‘‹°«;Ž¡‘Ïbp‘ÿ}'qŽ‘-2±:ÏfourthŽ‘xù±:ÏptŽ‘ «µ«=‘ÇÏpt23Ž‘Lë;Ž¡‘·gŽ¡‘ÂreturnŽ‘7æ¼Ïbp‘ÿ}'qŽ‘GØ«;Ž¡‘ -·g‘±=·‘ÿýÂifŽ‘_·±=Ž¡‘ -ÂelseŽ‘!Øà·fŽ¡‘Ïc‘ÿ}'errŽ‘)|À·‘ÇÝ"WARNING!È ÝInÈ ÝEllipseŽ‘kÆÜ::intersection_pointŽ’ÔÆ s(Ellipse).\n"Ž’ÌÞ«;Ž¡‘Ïss‘‰ffŽ‘®eŽ‘(y«=‘DZeŽ‘o:Ïlo–ÿ}'c“ationŽ‘"Á}«(Ïc‘ÿ}'opyŽ‘ø±:Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH«(0Ž‘));Ž¡‘ÂifŽ‘´ú«(Ïss‘‰ffŽ‘®eŽ‘w·‘Ç«1Ž‘Ç)‘Ïc‘ÿ}'errŽ‘|¾·‘ÇÝ"*thisÈ ÝisÈ ÝinsideÈ ÝofÈ Ž‘kÆÜÝe.\n"Ž’†5«;Ž¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(Ïss‘‰ffŽ‘®eŽ‘w·‘ÇŽ‘ -Ž6«1Ž‘Ž7)‘Ïc‘ÿ}'errŽ‘|¾·‘ÇÝ"eÈ ÝisÈ ÝinsideÈ ÝofÈ Ý*thiŽ‘kÆÜs.\n"Ž’†5«;Ž¡‘ÂelseŽ‘+Øá·fŽ¡‘Ïc‘ÿ}'errŽ‘3|Á·‘ÇÝ"ThisÈ Ýcan'tÈ Ýhappen!È Ž‘kÆÜÝInvalidÈ ÝvalueÈ ÝforÈ ÝssŽ’ÔÆ _e:È Ý"Ž’òT·‘ÇÏss‘‰ffŽ‘®eŽ‘F·‘ÇÏend‘‚ØlŽ‘¸Ú«;Ž¡‘·gŽ¡‘Ïc‘ÿ}'errŽ‘)|À·‘ÇÝ"NoÈ Ýintersection.\n"Ž‘o\·‘ÇÝ"ReturningÈ ÝINVALID_BŽ‘kÆÜOOL_POINT_QUADRUPLE.Ž’ÔÆ \n\n"Ž’ïŒù«;Ž¡‘ÂreturnŽ‘7æ¼ÝINVALID_BOOL_POINT_QUADRUPLEŽ’ËlЫ;Ž¡‘ -·gŽ¡‘ -g‘±=·‘ÿý«End–UUof“\Ellipses“ha•¸ãv“e–UUthe“same“cenš¸ãter“and“axis“orien˜tation".‘o·±=ŽŽŽŒ‹Wú) Šn ý‘ì·x«1185›­3DLDFPR•ÃŽG’÷âòÂELLIPSE‘ÕX­AR“GUMENT˜«343Ž €n ý•@PÂ1185.‘ ü«Ellipses›ýóha•¸ãv“e˜di 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ÝEllipŽ’ÿÈseÈ Ýintersections.È Ý"Ž’ø ·‘ÇÝ"ThisÈ ÝcanÈ ÝtakeÈ ÝsomeÈ Ž‘kÆÜÝtime...\n\n"Ž’®8·‘ÇÏ ushŽ‘€«;Ž¡‘ÂforŽ‘%舫(ÂrealŽ‘³.±iŽ‘ì:«=‘Ç0Ž‘Ç;‘ÿý±iŽ– 9 <‘Ç«360ŽŽ‘Ç;‘ÿý±iŽ“«+=ŽŽ‘Ž]±:«5ŽŽ‘%U{)‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"iÈ Ý==È Ý"Ž‘*Ôƒ·‘DZiŽ‘ $·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘Ïcurr‘‰ffŽ‘®p‘ÿ}'ointŽ‘N -«=‘ÇÏc‘ÿ}'opyŽ‘W±:Ïangle‘‰ffŽ‘®p‘ÿ}'ointŽ‘1Y½«(±iŽ‘qô«);Ž¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïcurr‘‰ffŽ‘®p‘ÿ}'ointŽ‘2Bü±:ÏshowŽ‘Šÿ«(Ý"curr_point"Ž‘?†D«);Ž¡‘Ïcurr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘Y«=‘DZeŽ‘o:Ïlo–ÿ}'c“ationŽ‘"Á}«(Ïcurr‘‰ffŽ‘®p‘ÿ}'ointŽ‘-Bü«);Ž¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"curr_locationÈ Ý==È Ý"Ž‘iÔ_·‘ÇÏcurr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘>d·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ÂifŽ‘)´û«(Ïcurr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘;·‘Ç«0Ž‘Ç)‘·fŽ¡‘(ÂifŽ‘3´ü«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘2Ïc‘ÿ}'outŽ‘H T·‘ÇÝ"FoundÈ ÝanÈ ÝintersectiŽ‘kÆÜonÈ Ýpoint!\n"Ž’«M «;Ž¡‘2Ïcurr‘‰ffŽ‘®p‘ÿ}'ointŽ‘_C±:ÏshowŽ‘Šÿ«(Ý"curr_point:"Ž‘DÆA«);Ž¡‘(·gŽ¡‘(h‘ª¨«Handle–UUinš¸ãtersection“pGoin˜t‘@­1186‘ª¨·iŽ¡‘(±iŽ‘.9«+=ŽŽ‘@Žd±:«5ŽŽ‘HU‚;Ž¡‘(Ïsave‘‰ffŽ‘®angleŽ‘X›à«=‘DZiŽ‘9 «;Ž¡‘(Ïcurr‘‰ffŽ‘®p‘ÿ}'ointŽ‘X -«=‘ÇÏc‘ÿ}'opyŽ‘W±:Ïangle‘‰ffŽ‘®p‘ÿ}'ointŽ‘1Y½«(±iŽ‘qô«);Ž¡‘(Ïlo–ÿ}'c“ation‘‰ffŽ‘®switchŽ‘l ö«=‘DZeŽ‘o:Ïlo–ÿ}'c“ationŽ‘"Á}«(Ïcurr‘‰ffŽ‘®p‘ÿ}'ointŽ‘-Bü«);Ž¡‘(Âcon•®9tin“ueŽ‘R湫;Ž¡‘·g‘±=·‘ÿýÂifŽ‘ _ «.‘qÇEnd–UUof“\F‘ÿ*ªound“an“inš¸ãtersection“pGoin˜t".‘o·±=Ž¡‘ÂelseŽ‘4.7ifŽ‘?ã/«(±iŽ‘9 ·‘Ç«0Ž‘Ç)‘·fŽ¡‘(Ïlo–ÿ}'c“ation‘‰ffŽ‘®switchŽ‘l ö«=‘ÇÏcurr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘;«;Ž¡‘(Ïsave‘‰ffŽ‘®angleŽ‘X›à«=‘Ç0Ž‘Ç;Ž¡‘(Âcon•®9tin“ueŽ‘R湫;Ž¡‘·gŽ¡‘ÂelseŽ‘4.7ifŽ‘?ã/«(Ïcurr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘;·‘Ç«1Ž‘Ç)‘·fŽ¡‘(ÂifŽ‘3´ü«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"PointÈ ÝisÈ ÝinsideÈ Ýe.\Ž‘kÆÜn"Ž‘vÍ>«;Ž¡‘·gŽ¡‘ÂelseŽ‘4.7ifŽ‘?ã/«(Ïcurr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘;·‘ÇŽ‘ -Ž6«1Ž‘Ž7)‘·fŽ¡‘(ÂifŽ‘3´ü«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"PointÈ ÝisÈ ÝoutsideÈ Ýe.Ž‘kÆÜ\n"Ž‘| ;«;Ž¡‘·gŽ¡‘ÂelseŽ‘5Øâ·fŽŽŽŒ‹X· Šn ý‘ì«344›ÂELLIPSE‘ÕX­AR•ÃŽGUMENT’÷âò3DLDFPR“G˜·x«1185Ž €n ý•@P‘(Ïc‘ÿ}'errŽ‘A:²·‘…Ý"ERROR!È ÝInÈ ÝEllipse::Ž‘o„Ìintersection_points(Ž’Ø„):\n"Ž’ùÏñ·Ž¤ ‘<Ý"ThisÈ Ýcan'tÈ Ýhappen!È Ž’¤ÿÊÝcurr_locationÈ ÝhasÈ ÝbaŽ’ ÿŽdÈ Ývalue:È Ý"Ž’Ga ·‘[1Ïcurr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘AŒO·Ž¡‘<Ý"È Ý"Ž‘O }·‘ÇÝ"ReturningÈ ÝINVALID_BŽ‘kÆÜOOL_POINT_QUADRUPLE\Ž’ÔÆ n\n"Ž’í·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾ÝINVALID_BOOL_POINT_QUADRUPLEŽ’ßlÒ«;Ž¡‘·gŽ¡‘ÂifŽ‘)´û«(Ïcurr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘;·6«=‘ÇÏlo–ÿ}'c“ation‘‰ffŽ‘®switchŽ‘D ò«)‘·fŽ¡‘(ÂifŽ‘3´ü«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘2Ïc‘ÿ}'outŽ‘H T·‘ÇÝ"FoundÈ ÝaÈ Ýtransition!Ž‘kÆÜ\n"Ž‘| ;«;Ž¡‘2Ïc‘ÿ}'outŽ‘H T·‘ÇÝ"iÈ Ý==È Ý"Ž‘*Ôƒ·‘DZiŽ‘ $·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘2Ïc‘ÿ}'outŽ‘H T·‘ÇÝ"save_angleÈ Ý==È Ý"Ž‘Zh·‘ÇÏsave‘‰ffŽ‘®angleŽ‘3bô·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘2Ïc‘ÿ}'outŽ‘H T·‘ÇÝ"curr_locationÈ Ý==È Ý"Ž‘iÔ_·‘ÇÏcurr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘>d·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘2Ïc‘ÿ}'outŽ‘H T·‘ÇÝ"location_switchÈ Ý==È Ž‘kÆÜÝ"Ž‘tTY·‘ÇÏlo–ÿ}'c“ation‘‰ffŽ‘®switchŽ‘FÓ -·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘(·gŽ¡‘(ÂifŽ‘3´ü«(Ïlo–ÿ}'c“ation‘‰ffŽ‘®switchŽ‘D ò·‘Ç«1Ž‘Ç)‘·fŽ¡‘2Ïin‘‰ffŽ‘®angleŽ‘XåÛ«=‘ÇÏsave‘‰ffŽ‘®angleŽ‘0›Ü«;Ž¡‘2Ïout‘‰ffŽ‘®angleŽ‘^J«=‘DZiŽ‘9 «;Ž¡‘(·gŽ¡‘(ÂelseŽ‘?Øã·fŽ¡‘2Ïin‘‰ffŽ‘®angleŽ‘XåÛ«=‘DZiŽ‘9 «;Ž¡‘2Ïout‘‰ffŽ‘®angleŽ‘^J«=‘ÇÏsave‘‰ffŽ‘®angleŽ‘0›Ü«;Ž¡‘(·gŽ¡‘(ÂwhileŽ‘FC0«(ÏtrueŽ‘Ę«)‘·fŽ¡‘2Ïtest‘‰ffŽ‘®angleŽ‘_ŠÐ«=‘Ç(Ïin‘‰ffŽ‘®angleŽ‘&Wž«+‘8àÏout‘‰ffŽ‘®angleŽ‘+t «)±=«2Ž‘;Ž¡‘2Ïcurr‘‰ffŽ‘®p‘ÿ}'ointŽ‘b -«=‘ÇÏc‘ÿ}'opyŽ‘W±:Ïangle‘‰ffŽ‘®p‘ÿ}'ointŽ‘1Y½«(Ïtest‘‰ffŽ‘®angleŽ‘*ó«);Ž¡‘2Ïcurr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘m -«=‘DZeŽ‘o:Ïlo–ÿ}'c“ationŽ‘"Á}«(Ïcurr‘‰ffŽ‘®p‘ÿ}'ointŽ‘-Bü«);Ž¡‘2ÂifŽ‘=´ý«(Ïcurr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘;·‘Ç«0Ž‘Ç)‘·fŽ¡‘<ÂifŽ‘G´þ«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘FÏc‘ÿ}'outŽ‘\ V·‘ÇÝ"FoundÈ ÝanÈ ÝintersectiŽ‘kÆÜonÈ Ýpoint!\n"Ž’«M «;Ž¡‘FÏcurr‘‰ffŽ‘®p‘ÿ}'ointŽ‘sC±:ÏshowŽ‘Šÿ«(Ý"curr_point:"Ž‘DÆA«);Ž¡‘<·gŽ¡‘<h‘ª¨«Handle–UUinš¸ãtersection“pGoin˜t‘@­1186‘ª¨·iŽ¡‘<±iŽ‘B9«=‘ÇÏ o‘ÿ}'orŽ‘+®«(Ïtest‘‰ffŽ‘®angleŽ‘*ó«);Ž¡‘<±iŽ‘B9«+=ŽŽ‘TŽf±:«5ŽŽ‘\U„;Ž¡‘<ÂifŽ‘G´þ«(±iŽ‘9 <‘ÇÏtest‘‰ffŽ‘®angleŽ‘-ŠË«)‘±iŽ‘ 9 «+=ŽŽ‘Ž`±:«5ŽŽ‘%U~;Ž¡‘<Ïsave‘‰ffŽ‘®angleŽ‘l›â«=‘DZiŽ‘9 «;Ž¡‘<Ïcurr‘‰ffŽ‘®p‘ÿ}'ointŽ‘l -«=‘ÇÏc‘ÿ}'opyŽ‘W±:Ïangle‘‰ffŽ‘®p‘ÿ}'ointŽ‘1Y½«(±iŽ‘qô«);Ž¡‘<Ïlo–ÿ}'c“ation‘‰ffŽ‘®switchŽ’€ ø«=‘DZeŽ‘o:Ïlo–ÿ}'c“ationŽ‘"Á}«(Ïcurr‘‰ffŽ‘®p‘ÿ}'ointŽ‘-Bü«);Ž¡‘<ÂbreakŽ‘X¡j«;Ž¡‘2·gŽ¡‘2ÂelseŽ‘H.9ifŽ‘Sã1«(Ïcurr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘;·‘Ç«1Ž‘Ç)‘·fŽ¡‘<Ïin‘‰ffŽ‘®angleŽ‘båÜ«=‘ÇÏtest‘‰ffŽ‘®angleŽ‘-ŠË«;Ž¡‘<Âcon•®9tin“ueŽ‘f滫;Ž¡‘2·gŽ¡‘2ÂelseŽ‘H.9ifŽ‘Sã1«(Ïcurr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘;·‘ÇŽ‘ -Ž6«1Ž‘Ž7)‘·fŽ¡‘<Ïout‘‰ffŽ‘®angleŽ‘hK«=‘ÇÏtest‘‰ffŽ‘®angleŽ‘-ŠË«;Ž¡‘<Âcon•®9tin“ueŽ‘f滫;Ž¡‘2·gŽ¡‘2ÂelseŽ‘IØä·fŽ¡‘<Ïc‘ÿ}'errŽ‘SÆ4·‘ˆÝ"ERROR!È ÝInÈ ÝEllipse::Ž‘nLintersection_points(Ž’×Ellipse).\n"Ž’¦Ü·Ž¡‘PÝ"ThisÈ Ýcan'tÈ Ýhappen!È Ž’¸ÿÌÝInvalidÈ ÝvalueÈ ÝforÈ ÝcuŽ’!ÿrr_location:È Ý"Ž’oSà·‘NÏcurr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘?r·Ž¡‘PÝ"\nReturningÈ ÝINVALIDŽ’¸ÿÌ_BOOL_POINT_QUADRUPLŽ’!ÿE.\n\n"Ž’J û·‘ÇÏ ushŽ‘€«;Ž¡‘<ÂreturnŽ‘_æÀÝINVALID_BOOL_POINT_QUADRUPLEŽ’ólÔ«;ŽŽŽŒ‹Y¸ Šn ý‘ì·x«1185›­3DLDFPR•ÃŽG’÷âòÂELLIPSE‘ÕX­AR“GUMENT˜«345Ž €n ý•@P‘2·gŽ¤ ‘(g‘±=·‘ÿýÂwhileŽ‘$íÑ·±=Ž¡‘·g‘±=·‘ÿýÂifŽ‘_·±=Ž¡‘·g‘±=·‘ÿýÂforŽ‘“+·±=Ž¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"FinishedÈ ÝsearchingÈ Ž‘kÆÜÝforÈ ÝEllipseÈ ÝintersecŽ’ÔÆ tions."Ž’üÔ ·‘ÇÏend‘‚ØlŽ–ò·‘ÇÏend‘‚ØlŽ“·‘ÇÏ ushŽ‘€«;Ž¡‘ -·g‘±=·‘ÿý«End–UUof“\Ellipses“ha•¸ãv“e›UUdi eren“t˜cen“ters˜and/or˜axis˜orien“tation".‘o·±=Ž¡‘ -·g‘±=·‘ÿý«End–UUof“coplanar“case.‘o·±=ŽŸÂ1186.‘ ü«Handle–UUinš¸ãtersection“pGoin˜t.ŽŸ·h‘ª¨«Handle–UUinš¸ãtersection“pGoin˜t‘@­1186‘ª¨·i‘ÇŽ¡‘ -fŽ¡‘€Ÿÿ®+‘ÿ+ŽŽ‘ G"Ïinterse‘ÿ}'ction‘‰ffŽ‘®ctrŽ‘diZ«;Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"intersection_ctrÈ Ý==Ž‘kÆÜÈ Ý"Ž‘y”V·‘ÇÏinterse‘ÿ}'ction‘‰ffŽ‘®ctrŽ‘I°h·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(Ïinterse‘ÿ}'ction‘‰ffŽ‘®ctrŽ‘FéP·‘Ç«1Ž‘Ç)‘·fŽ¡‘Ïbp‘ÿ}'qŽ‘-2±:Ï rstŽ‘µª±:bŽ‘«=‘ÇÏtrueŽ‘‹°«;Ž¡‘Ïbp‘ÿ}'qŽ‘-2±:Ï rstŽ‘µª±:ÏptŽ‘ «µ«=‘ÇÏcurr‘‰ffŽ‘®p‘ÿ}'ointŽ‘0 -«;Ž¡‘Ïbp‘ÿ}'qŽ‘-2±:Ï rstŽ‘µª±:ÏptŽ‘ «µ·«=ŽŽ‘9ìÏt‘‰ffŽ‘®inverseŽ‘CI«;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(Ïinterse‘ÿ}'ction‘‰ffŽ‘®ctrŽ‘FéP·‘Ç«2Ž‘Ç)‘·fŽ¡‘Ïbp‘ÿ}'qŽ‘-2±:Ïse–ÿ}'c“ondŽ‘§Ç±:bŽ‘«=‘ÇÏtrueŽ‘‹°«;Ž¡‘Ïbp‘ÿ}'qŽ‘-2±:Ïse–ÿ}'c“ondŽ‘§Ç±:ÏptŽ‘ «µ«=‘ÇÏcurr‘‰ffŽ‘®p‘ÿ}'ointŽ‘0 -«;Ž¡‘Ïbp‘ÿ}'qŽ‘-2±:Ïse–ÿ}'c“ondŽ‘§Ç±:ÏptŽ‘ «µ·«=ŽŽ‘9ìÏt‘‰ffŽ‘®inverseŽ‘CI«;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(Ïinterse‘ÿ}'ction‘‰ffŽ‘®ctrŽ‘FéP·‘Ç«3Ž‘Ç)‘·fŽ¡‘Ïbp‘ÿ}'qŽ‘-2±:Ïthir‘ÿ}'dŽ‘Üj±:bŽ‘«=‘ÇÏtrueŽ‘‹°«;Ž¡‘Ïbp‘ÿ}'qŽ‘-2±:Ïthir‘ÿ}'dŽ‘Üj±:ÏptŽ‘ «µ«=‘ÇÏcurr‘‰ffŽ‘®p‘ÿ}'ointŽ‘0 -«;Ž¡‘Ïbp‘ÿ}'qŽ‘-2±:Ïthir‘ÿ}'dŽ‘Üj±:ÏptŽ‘ «µ·«=ŽŽ‘9ìÏt‘‰ffŽ‘®inverseŽ‘CI«;Ž¡‘·gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(Ïinterse‘ÿ}'ction‘‰ffŽ‘®ctrŽ‘FéP·‘Ç«4Ž‘Ç)‘·fŽ¡‘Ïbp‘ÿ}'qŽ‘-2±:ÏfourthŽ‘xù±:bŽ‘«=‘ÇÏtrueŽ‘‹°«;Ž¡‘Ïbp‘ÿ}'qŽ‘-2±:ÏfourthŽ‘xù±:ÏptŽ‘ «µ«=‘ÇÏcurr‘‰ffŽ‘®p‘ÿ}'ointŽ‘0 -«;Ž¡‘Ïbp‘ÿ}'qŽ‘-2±:ÏfourthŽ‘xù±:ÏptŽ‘ «µ·«=ŽŽ‘9ìÏt‘‰ffŽ‘®inverseŽ‘CI«;Ž¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÿ9·_‘8àÏverb‘ÿ}'oseŽ‘"Ê=«)‘·fŽ¡‘(Ïc‘ÿ}'outŽ‘?KR·‘òÝ"InÈ ÝEllipse::interseŽ‘lñÛction_points(EllipseŽ’ÕñŸÈ Ýe,È ÝconstÈ ÝboolÈ ÝverboŽ’>ñcse)"Ž’XiÖ·Ž¡‘<Ý"FoundÈ ÝfourthÈ ÝintersŽ’¤ÿÊectionÈ Ýpoint.\n"Ž’üM·‘ÇÝ"ReturningÈ Ýbpq.\n\n"Ž‘lMD«;Ž¡‘·gŽ¡‘ÂreturnŽ‘Aæ½Ïbp‘ÿ}'qŽ‘QÙ«;Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘Ïc‘ÿ}'errŽ‘6‹·‘ÕsÝ"ERROR!È ÝInÈ ÝEllipse::Ž‘nÕ7intersection_points(Ž’×ÔûEllipse).\n"Ž’0²·Ž¡‘2Ý"ThisÈ Ýcan'tÈ Ýhappen!È Ž’šÿÉ ÝInvalidÈ ÝvalueÈ ÝforÈ Ý"Ž’ ;η‘µÙÝ"intersection_ctr:È Ý"Ž‘rñÞ·Ž¡‘2Ïinterse‘ÿ}'ction‘‰ffŽ‘®ctrŽ‘xéU·‘ÇÝ".\nReturningÈ ÝINVALIŽ‘kÆÜD_BOOL_POINT_QUADRUPŽ’ÔÆ LE.\n\n"Ž’ÿLð«;Ž¡‘ÂreturnŽ‘Aæ½ÝINVALID_BOOL_POINT_QUADRUPLEŽ’ÕlÑ«;Ž¡‘·gŽ¡‘ -gŽŸ ­This–ÕXco.±eŽ‘)æ/;‘ª¨ÂconstŽ‘ÕJb•QÇo“olŽ‘9v°Ïverb‘ÿ}'oseŽ‘Z «).‘qÇ[¬LDF‘T2003.07.01.«]ŽŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.07.01.«]Ž‘Y;Added–UUthis“section.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h‘ª¨«Chec•¸ãk›UUin“tersection˜pGoin“t˜loGcations‘@­1189‘ª¨·i‘ÇŽ¤ ‘ -ÂifŽ‘´ù«(Ïtemp‘‰ffŽ‘®b–ÿ}'o“olŽ‘*Êu«)‘·fŽ¡‘ÂifŽ‘´ú«(Ïverb‘ÿ}'oseŽ‘ ‘]«)‘·fŽ¡‘ÂifŽ‘)´û«(Ïs‘‰ffŽ‘®tŽ‘T·‘Ç«0Ž‘ ÿù·^‘8àÏs‘‰ffŽ‘®eŽ‘¡—·‘Ç«0Ž‘Ç)Ž¡‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÏtemp‘‰ffŽ‘®stringŽ‘8Â;·‘ÇÝ"È ÝpointÈ ÝliesÈ ÝonÈ ÝtheÈ Ž‘kÆÜÝperimeterÈ ÝofÈ ÝbothÈ ÝelŽ’ÔÆ lipses.\n"Ž’ Ìê«;Ž¡‘ÂelseŽ‘4.7ifŽ‘?ã/«(Ïs‘‰ffŽ‘®tŽ‘T·‘Ç«0Ž‘Ç)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÏtemp‘‰ffŽ‘®stringŽ‘8Â;·‘ÇÝ"È ÝpointÈ ÝliesÈ ÝonÈ ÝtheÈ Ž‘kÆÜÝperimeterÈ ÝofÈ Ý*this.\Ž’ÔÆ n"Ž’ßÍ«;Ž¡‘ÂelseŽ‘4.7ifŽ‘?ã/«(Ïs‘‰ffŽ‘®tŽ‘T·‘ÇŽ‘ -Ž6«1Ž‘Ž7)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÏtemp‘‰ffŽ‘®stringŽ‘8Â;·‘ÇÝ"È ÝpointÈ ÝliesÈ ÝoutsideŽ‘kÆÜÈ Ý*this.\n"Ž’ Í&«;Ž¡‘ÂelseŽ‘4.7ifŽ‘?ã/«(Ïs‘‰ffŽ‘®tŽ‘T·‘Ç«1Ž‘Ç)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÏtemp‘‰ffŽ‘®stringŽ‘8Â;·‘ÇÝ"È ÝpointÈ ÝliesÈ ÝinsideÈ Ž‘kÆÜÝ*this.\n"Ž’›)«;Ž¡‘ÂelseŽ‘4.7ifŽ‘?ã/«(Ïs‘‰ffŽ‘®tŽ‘T·‘ÇŽ‘ -Ž6«2Ž‘Ž7)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÏtemp‘‰ffŽ‘®stringŽ‘8Â;·‘ÇÝ"È ÝpointÈ Ýdoesn'tÈ ÝlieÈ Ž‘kÆÜÝinÈ ÝtheÈ ÝplaneÈ ÝofÈ Ý*thiŽ’ÔÆ s.\n"Ž’ïŒù«;Ž¡‘ÂifŽ‘)´û«(Ïs‘‰ffŽ‘®eŽ‘h··‘Ç«0Ž‘ ÿù·^‘8àÏs‘‰ffŽ‘®tŽ‘Œø·6«=‘Ç0Ž‘Ç)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÏtemp‘‰ffŽ‘®stringŽ‘8Â;·‘ÇÝ"È ÝpointÈ ÝliesÈ ÝonÈ ÝtheÈ Ž‘kÆÜÝperimeterÈ ÝofÈ Ýe.\n"Ž’ÊÍ«;Ž¡‘ÂifŽ‘)´û«(Ïs‘‰ffŽ‘®eŽ‘h··‘ÇŽ‘ -Ž6«1Ž‘Ž7)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÏtemp‘‰ffŽ‘®stringŽ‘8Â;·‘ÇÝ"È ÝpointÈ ÝliesÈ ÝoutsideŽ‘kÆÜÈ Ýe.\n"Ž’‹Í2«;Ž¡‘ÂelseŽ‘4.7ifŽ‘?ã/«(Ïs‘‰ffŽ‘®eŽ‘h··‘Ç«1Ž‘Ç)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÏtemp‘‰ffŽ‘®stringŽ‘8Â;·‘ÇÝ"È ÝpointÈ ÝliesÈ ÝinsideÈ Ž‘kÆÜÝe.\n"Ž’†5«;Ž¡‘ÂelseŽ‘4.7ifŽ‘?ã/«(Ïs‘‰ffŽ‘®eŽ‘h··‘ÇŽ‘ -Ž6«2Ž‘Ž7)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÏtemp‘‰ffŽ‘®stringŽ‘8Â;·‘ÇÝ"È ÝpointÈ Ýdoesn'tÈ ÝlieÈ Ž‘kÆÜÝinÈ ÝtheÈ ÝplaneÈ ÝofÈ Ýe.\nŽ’ÔÆ "Ž’Ú«;Ž¡‘·gŽ¡‘ -gŽŸ ­This–ÕXcoO×°‘ʱorientationŽ‘;M°Ž¡‘(±end‘‚ØlŽ‘>¸Þ°‘Ç´"Will® ´to® ´try® ´to® ´contŽ‘kÆÜinue.\n\n"Ž’£”>°‘DZ ushŽ‘€¬;Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽŽŽŒ‹]Ø0 Šn ý‘ì°x¬1223–¯3DLDF-1.1.5.1’ïo\­ELLIPSE‘ÕX¯ARÃŽGUMENT“¬349Ž €n ý•@P‘±pt20Ž‘(…­µ:±showŽ‘Šÿ¬(´"pt20"Ž‘ V¬);Ž¤ ‘±pt20Ž‘(…­µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(´"20"Ž‘†\¬);Ž¡‘±pt21Ž‘(…­µ:±showŽ‘Šÿ¬(´"pt21"Ž‘ V¬);Ž¡‘±pt21Ž‘(…­µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(´"21"Ž‘†\¬);Ž¡‘±pt22Ž‘(…­µ:±showŽ‘Šÿ¬(´"pt22"Ž‘ V¬);Ž¡‘±pt22Ž‘(…­µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(´"22"Ž‘†\¬);Ž¡‘±pt23Ž‘(…­µ:±showŽ‘Šÿ¬(´"pt23"Ž‘ V¬);Ž¡‘±pt23Ž‘(…­µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(´"23"Ž‘†\¬);Ž¡‘ +°gŽ©Ø‘ +­signedŽ‘-o÷shortŽ‘K:š±ss‘‰ffŽ‘®c‘ÿ}'opyŽ‘k¦%¬;Ž¡‘ +­signedŽ‘-o÷shortŽ‘K:š±ss‘‰ffŽ‘®eŽ‘\òù¬;Ž¦‘ +­ifŽ‘´ù¬(±pt20Ž‘Lð6¬=‘Ç´INVALID_POINTŽ‘GY¬)‘°fŽ¡‘±ss‘‰ffŽ‘®c‘ÿ}'opyŽ‘72¥¬=‘DZc‘ÿ}'opyŽ‘Wµ:±lo–ÿ}'c“ationŽ‘"Á}¬(±pt20Ž‘…«¬);Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"ss_copy® ´==® ´"Ž‘JTq°‘DZss‘‰ffŽ‘®c‘ÿ}'opyŽ‘%ù»°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘±ss‘‰ffŽ‘®eŽ‘(y¬=‘ǵeŽ‘o:±lo–ÿ}'c“ationŽ‘"Á}¬(±pt20Ž‘…«¬);Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"ss_e® ´==® ´"Ž‘:”z°‘DZss‘‰ffŽ‘®eŽ‘F°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(±ss‘‰ffŽ‘®c‘ÿ}'opyŽ‘#2£°‘Ǭ0Ž‘ ÿù°^‘8à±ss‘‰ffŽ‘®eŽ‘¸W°‘Ǭ0Ž‘Ç)‘°fŽ¡‘±pt20Ž‘+LÅ°¬=ŽŽ‘:Úü±t‘‰ffŽ‘®inverseŽ‘aê¬;Ž¡‘±pt21Ž‘+LÅ°¬=ŽŽ‘:Úü±t‘‰ffŽ‘®inverseŽ‘aê¬;Ž¡‘±bp‘ÿ}'qŽ‘#2µ:± rstŽ‘µªµ:bŽ‘¬=‘DZtrueŽ‘‹°¬;Ž¡‘±bp‘ÿ}'qŽ‘#2µ:± rstŽ‘µªµ:±ptŽ‘ «µ¬=‘DZpt20Ž‘Lì;Ž¡‘±bp‘ÿ}'qŽ‘#2µ:±se–ÿ}'c“ondŽ‘§Çµ:bŽ‘¬=‘DZtrueŽ‘‹°¬;Ž¡‘±bp‘ÿ}'qŽ‘#2µ:±se–ÿ}'c“ondŽ‘§Çµ:±ptŽ‘ «µ¬=‘DZpt21Ž‘Lì;Ž¡‘­ifŽ‘´ú¬(±pt22Ž‘Lð6¬=‘Ç´INVALID_POINTŽ‘GY¬)‘°fŽ¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Ellipses® ´intersect® Ž‘kÆÜ´at® ´four® ´points.\n"Ž’Êͬ;Ž¡‘±pt22Ž‘5LÆ°¬=ŽŽ‘DÚý±t‘‰ffŽ‘®inverseŽ‘kê¬;Ž¡‘±bp‘ÿ}'qŽ‘-2µ:±thir‘ÿ}'dŽ‘Üjµ:bŽ‘¬=‘DZtrueŽ‘‹°¬;Ž¡‘±bp‘ÿ}'qŽ‘-2µ:±thir‘ÿ}'dŽ‘Üjµ:±ptŽ‘ «µ¬=‘DZpt22Ž‘Lì;Ž¡‘°gŽ¡‘­elseŽ‘+Øá°fŽ¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Ellipses® ´intersect® Ž‘kÆÜ´at® ´two® ´points.\n"Ž’Ŭ;Ž¡‘°gŽ¡‘­ifŽ‘´ú¬(±pt23Ž‘Lð6¬=‘Ç´INVALID_POINTŽ‘GY¬)‘°fŽ¡‘±pt23Ž‘5LÆ°¬=ŽŽ‘DÚý±t‘‰ffŽ‘®inverseŽ‘kê¬;Ž¡‘±bp‘ÿ}'qŽ‘-2µ:±fourthŽ‘xùµ:bŽ‘¬=‘DZtrueŽ‘‹°¬;Ž¡‘±bp‘ÿ}'qŽ‘-2µ:±fourthŽ‘xùµ:±ptŽ‘ «µ¬=‘DZpt23Ž‘Lì;Ž¡‘°gŽ¡‘­returnŽ‘7æ¼±bp‘ÿ}'qŽ‘Gج;Ž¡‘ +°g‘µ=°‘ÿý­ifŽ‘_°µ=Ž¡‘ +­elseŽ‘!Øà°fŽ¡‘±c‘ÿ}'errŽ‘)|À°‘Ç´"WARNING!® ´In® ´EllipseŽ‘kÆÜ::intersection_pointŽ’ÔÆ s(Ellipse).\n"Ž’ÌÞ¬;Ž¡‘±ss‘‰ffŽ‘®eŽ‘(y¬=‘ǵeŽ‘o:±lo–ÿ}'c“ationŽ‘"Á}¬(±c‘ÿ}'opyŽ‘øµ:±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(0Ž‘));Ž¡‘­ifŽ‘´ú¬(±ss‘‰ffŽ‘®eŽ‘w°‘Ǭ1Ž‘Ç)‘±c‘ÿ}'errŽ‘|¾°‘Ç´"*this® ´is® ´inside® ´of® Ž‘kÆÜ´e.\n"Ž’†5¬;Ž¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±ss‘‰ffŽ‘®eŽ‘w°‘ÇŽ‘ +Ž6¬1Ž‘Ž7)‘±c‘ÿ}'errŽ‘|¾°‘Ç´"e® ´is® ´inside® ´of® ´*thiŽ‘kÆÜs.\n"Ž’†5¬;Ž¡‘­elseŽ‘+Øá°fŽ¡‘±c‘ÿ}'errŽ‘3|Á°‘Ç´"This® ´can't® ´happen!® Ž‘kÆÜ´Invalid® ´value® ´for® ´ssŽ’ÔÆ _e:® ´"Ž’òT°‘DZss‘‰ffŽ‘®eŽ‘F°‘DZend‘‚ØlŽ‘¸Ú¬;Ž¡‘°gŽ¡‘±c‘ÿ}'errŽ‘)|À°‘Ç´"No® ´intersection.\n"Ž‘o\°‘Ç´"Returning® ´INVALID_BŽ‘kÆÜOOL_POINT_QUADRUPLE.Ž’ÔÆ \n\n"Ž’ïŒù¬;Ž¡‘­returnŽ‘7æ¼´INVALID_BOOL_POINT_QUADRUPLEŽ’ËlЬ;Ž¡‘ +°gŽ¡‘ +g‘µ=°‘ÿý¬End–UUof“\Ellipses“ha•¸ãv“e–UUthe“same“cenš¸ãter“and“axis“orien˜tation".‘o°µ=ŽŽŽŒ‹^ä~ Šn ý‘ì¬350–­ELLIPSE‘ÕX¯ARÃŽGUMENT’ïo\3DLDF-1.1.5.1“°x¬1224Ž €n ý•@P­1224.‘ üEllipsesŽ‘5ê¬ha•¸ãv“e›÷ÿdi eren“t˜cen“ters˜and/or˜axis˜orien“tation.‘YÅThere˜is˜no˜simple˜algebraic˜solution˜forŽ¤ this–UUcase,“so“I“ha•¸ãv“e–UUto“implemenš¸ãt“a“n˜umerical“one“here.Ž©°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¡‘ +­elseŽ‘!Øà°fŽ¡‘­ifŽ‘ Ìh¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ò°‘˜Î´"The® ´two® ´ellipses® ´doŽ‘m˜’n't® ´have® ´the® ´same® ´ceŽ’Ö˜Vnter® ´and/or® ´"Ž’÷e°Ž¡‘2´"the® ´axis® ´orientatioŽ’šÿÉn® ´is® ´different.\n"Ž’úû¬;Ž¦‘­P•®9oin“tŽ‘2curr‘‰ffŽ‘®p‘ÿ}'ointŽ‘`2›¬;Ž¡‘­signedŽ‘7oøshortŽ‘U:›±curr‘‰ffŽ‘®lo–ÿ}'c“ationŽ’Žˆ¬;Ž¡‘­signedŽ‘7oøshortŽ‘U:›±lo–ÿ}'c“ation‘‰ffŽ‘®switchŽ’–u¬;Ž¡‘­unsignedŽ‘D7shortŽ‘b³±interse‘ÿ}'ction‘‰ffŽ‘®ctrŽ’¨ë¬=‘Ç0Ž‘Ç;Ž¡‘­realŽ‘*³0±save‘‰ffŽ‘®angleŽ‘X‡ô¬;Ž¡‘­realŽ‘*³0±in‘‰ffŽ‘®angleŽ‘NÑî¬;Ž¡‘­realŽ‘*³0±out‘‰ffŽ‘®angleŽ‘Sî]¬;Ž¡‘­realŽ‘*³0±test‘‰ffŽ‘®angleŽ‘Uvã¬;Ž¦‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘µeŽ‘"¨:±showŽ‘Šÿ¬(´"e:"Ž‘†\¬);Ž¡‘±c‘ÿ}'opyŽ‘2ûµ:±showŽ‘Šÿ¬(´"copy:"Ž‘%FS¬);Ž¡‘°gŽ¡‘±c‘ÿ}'outŽ‘/N°‘õW´"In® ´Ellipse::interseŽ‘põction_points():\n"Ž’×𤰎¡‘(´"Searching® ´for® ´EllipŽ’ÿÈse® ´intersections.® ´"Ž’ø °‘Ç´"This® ´can® ´take® ´some® Ž‘kÆÜ´time...\n\n"Ž’®8°‘DZ ushŽ‘€¬;Ž¡‘­forŽ‘%般(­realŽ‘³.µiŽ‘ì:¬=‘Ç0Ž‘Ç;‘ÿýµiŽ– 9 <‘Ǭ360ŽŽ‘Ç;‘ÿýµiŽ“¬+=ŽŽ‘Ž]±stepŽ‘/Ò¬)‘°fŽ¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"i® ´==® ´"Ž‘*Ôƒ°‘ǵiŽ‘ $°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘±curr‘‰ffŽ‘®p‘ÿ}'ointŽ‘N +¬=‘DZc‘ÿ}'opyŽ‘Wµ:±angle‘‰ffŽ‘®p‘ÿ}'ointŽ‘1Y½¬(µiŽ‘qô¬);Ž¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±curr‘‰ffŽ‘®p‘ÿ}'ointŽ‘2Büµ:±showŽ‘Šÿ¬(´"curr_point"Ž‘?†D¬);Ž¡‘±curr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘Y¬=‘ǵeŽ‘o:±lo–ÿ}'c“ationŽ‘"Á}¬(±curr‘‰ffŽ‘®p‘ÿ}'ointŽ‘-Bü¬);Ž¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"curr_location® ´==® ´"Ž‘iÔ_°‘DZcurr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘>d°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘­ifŽ‘)´û¬(±curr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘;°‘Ǭ0Ž‘Ç)‘°fŽ¡‘(­ifŽ‘3´ü¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘2±c‘ÿ}'outŽ‘H T°‘Ç´"Found® ´an® ´intersectiŽ‘kÆÜon® ´point!\n"Ž’«M ¬;Ž¡‘2±curr‘‰ffŽ‘®p‘ÿ}'ointŽ‘_Cµ:±showŽ‘Šÿ¬(´"curr_point:"Ž‘DÆA¬);Ž¡‘(°gŽ¡‘(h‘ª¨¬Handle–UUinš¸ãtersection“pGoin˜t‘@¯1225‘ª¨°iŽ¡‘(µiŽ‘.9¬+=ŽŽ‘@Ždµ:¬5ŽŽ‘HU‚;Ž¡‘(±save‘‰ffŽ‘®angleŽ‘X›à¬=‘ǵiŽ‘9 ¬;Ž¡‘(±curr‘‰ffŽ‘®p‘ÿ}'ointŽ‘X +¬=‘DZc‘ÿ}'opyŽ‘Wµ:±angle‘‰ffŽ‘®p‘ÿ}'ointŽ‘1Y½¬(µiŽ‘qô¬);Ž¡‘(±lo–ÿ}'c“ation‘‰ffŽ‘®switchŽ‘l ö¬=‘ǵeŽ‘o:±lo–ÿ}'c“ationŽ‘"Á}¬(±curr‘‰ffŽ‘®p‘ÿ}'ointŽ‘-Bü¬);Ž¡‘(­con•®9tin“ueŽ‘R湬;Ž¡‘°g‘µ=°‘ÿý­ifŽ‘ _ ¬.‘qÇEnd–UUof“\F‘ÿ*ªound“an“inš¸ãtersection“pGoin˜t".‘o°µ=Ž¡‘­elseŽ‘4.7ifŽ‘?ã/¬(µiŽ‘9 °‘Ǭ0Ž‘Ç)‘°fŽ¡‘(±lo–ÿ}'c“ation‘‰ffŽ‘®switchŽ‘l ö¬=‘DZcurr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘;¬;Ž¡‘(±save‘‰ffŽ‘®angleŽ‘X›à¬=‘Ç0Ž‘Ç;Ž¡‘(­con•®9tin“ueŽ‘R湬;Ž¡‘°gŽ¡‘­elseŽ‘4.7ifŽ‘?ã/¬(±curr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘;°‘Ǭ1Ž‘Ç)‘°fŽ¡‘(­ifŽ‘3´ü¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Point® ´is® ´inside® ´e.\Ž‘kÆÜn"Ž‘vÍ>¬;Ž¡‘°gŽ¡‘­elseŽ‘4.7ifŽ‘?ã/¬(±curr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘;°‘ÇŽ‘ +Ž6¬1Ž‘Ž7)‘°fŽ¡‘(­ifŽ‘3´ü¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Point® ´is® ´outside® ´e.Ž‘kÆÜ\n"Ž‘| ;¬;Ž¡‘°gŽ¡‘­elseŽ‘5Øâ°fŽŽŽŒ‹_ó Šn ý‘ì°x¬1224–¯3DLDF-1.1.5.1’ïo\­ELLIPSE‘ÕX¯ARÃŽGUMENT“¬351Ž €n ý•@P‘(±c‘ÿ}'errŽ‘A:²°‘…´"ERROR!® ´In® ´Ellipse::Ž‘o„Ìintersection_points(Ž’Ø„):\n"Ž’ùÏñ°Ž¤ ‘<´"This® ´can't® ´happen!® Ž’¤ÿÊ´curr_location® ´has® ´baŽ’ ÿŽd® ´value:® ´"Ž’Ga °‘[1±curr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘AŒO°Ž¡‘<´"® ´"Ž‘O }°‘Ç´"Returning® ´INVALID_BŽ‘kÆÜOOL_POINT_QUADRUPLE\Ž’ÔÆ n\n"Ž’í°‘Ç± ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾´INVALID_BOOL_POINT_QUADRUPLEŽ’ßlÒ¬;Ž¡‘°gŽ¡‘­ifŽ‘)´û¬(±curr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘;°6¬=‘DZlo–ÿ}'c“ation‘‰ffŽ‘®switchŽ‘D ò¬)‘°fŽ¡‘(­ifŽ‘3´ü¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘2±c‘ÿ}'outŽ‘H T°‘Ç´"Found® ´a® ´transition!Ž‘kÆÜ\n"Ž‘| ;¬;Ž¡‘2±c‘ÿ}'outŽ‘H T°‘Ç´"i® ´==® ´"Ž‘*Ôƒ°‘ǵiŽ‘ $°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘2±c‘ÿ}'outŽ‘H T°‘Ç´"save_angle® ´==® ´"Ž‘Zh°‘DZsave‘‰ffŽ‘®angleŽ‘3bô°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘2±c‘ÿ}'outŽ‘H T°‘Ç´"curr_location® ´==® ´"Ž‘iÔ_°‘DZcurr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘>d°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘2±c‘ÿ}'outŽ‘H T°‘Ç´"location_switch® ´==® Ž‘kÆÜ´"Ž‘tTY°‘DZlo–ÿ}'c“ation‘‰ffŽ‘®switchŽ‘FÓ +°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘(°gŽ¡‘(­ifŽ‘3´ü¬(±lo–ÿ}'c“ation‘‰ffŽ‘®switchŽ‘D ò°‘Ǭ1Ž‘Ç)‘°fŽ¡‘2±in‘‰ffŽ‘®angleŽ‘XåÛ¬=‘DZsave‘‰ffŽ‘®angleŽ‘0›Ü¬;Ž¡‘2±out‘‰ffŽ‘®angleŽ‘^J¬=‘ǵiŽ‘9 ¬;Ž¡‘(°gŽ¡‘(­elseŽ‘?Øã°fŽ¡‘2±in‘‰ffŽ‘®angleŽ‘XåÛ¬=‘ǵiŽ‘9 ¬;Ž¡‘2±out‘‰ffŽ‘®angleŽ‘^J¬=‘DZsave‘‰ffŽ‘®angleŽ‘0›Ü¬;Ž¡‘(°gŽ¡‘(­whileŽ‘FC0¬(±trueŽ‘ʬ)‘°fŽ¡‘2±test‘‰ffŽ‘®angleŽ‘_ŠÐ¬=‘Ç(±in‘‰ffŽ‘®angleŽ‘&Wž¬+‘8à±out‘‰ffŽ‘®angleŽ‘+t ¬)µ=¬2Ž‘;Ž¡‘2±curr‘‰ffŽ‘®p‘ÿ}'ointŽ‘b +¬=‘DZc‘ÿ}'opyŽ‘Wµ:±angle‘‰ffŽ‘®p‘ÿ}'ointŽ‘1Y½¬(±test‘‰ffŽ‘®angleŽ‘*ó¬);Ž¡‘2±curr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘m +¬=‘ǵeŽ‘o:±lo–ÿ}'c“ationŽ‘"Á}¬(±curr‘‰ffŽ‘®p‘ÿ}'ointŽ‘-Bü¬);Ž¡‘2­ifŽ‘=´ý¬(±curr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘;°‘Ǭ0Ž‘Ç)‘°fŽ¡‘<­ifŽ‘G´þ¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘F±c‘ÿ}'outŽ‘\ V°‘Ç´"Found® ´an® ´intersectiŽ‘kÆÜon® ´point!\n"Ž’«M ¬;Ž¡‘F±curr‘‰ffŽ‘®p‘ÿ}'ointŽ‘sCµ:±showŽ‘Šÿ¬(´"curr_point:"Ž‘DÆA¬);Ž¡‘<°gŽ¡‘<h‘ª¨¬Handle–UUinš¸ãtersection“pGoin˜t‘@¯1225‘ª¨°iŽ¡‘<µiŽ‘B9¬=‘DZ o‘ÿ}'orŽ‘+®¬(±test‘‰ffŽ‘®angleŽ‘*ó¬);Ž¡‘<µiŽ‘B9¬+=ŽŽ‘TŽfµ:¬5ŽŽ‘\U„;Ž¡‘<­ifŽ‘G´þ¬(µiŽ‘9 <‘DZtest‘‰ffŽ‘®angleŽ‘-ŠË¬)‘µiŽ‘ 9 ¬+=ŽŽ‘Ž`µ:¬5ŽŽ‘%U~;Ž¡‘<±save‘‰ffŽ‘®angleŽ‘l›â¬=‘ǵiŽ‘9 ¬;Ž¡‘<±curr‘‰ffŽ‘®p‘ÿ}'ointŽ‘l +¬=‘DZc‘ÿ}'opyŽ‘Wµ:±angle‘‰ffŽ‘®p‘ÿ}'ointŽ‘1Y½¬(µiŽ‘qô¬);Ž¡‘<±lo–ÿ}'c“ation‘‰ffŽ‘®switchŽ’€ ø¬=‘ǵeŽ‘o:±lo–ÿ}'c“ationŽ‘"Á}¬(±curr‘‰ffŽ‘®p‘ÿ}'ointŽ‘-Bü¬);Ž¡‘<­breakŽ‘X¡j¬;Ž¡‘2°gŽ¡‘2­elseŽ‘H.9ifŽ‘Sã1¬(±curr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘;°‘Ǭ1Ž‘Ç)‘°fŽ¡‘<±in‘‰ffŽ‘®angleŽ‘båܬ=‘DZtest‘‰ffŽ‘®angleŽ‘-ŠË¬;Ž¡‘<­con•®9tin“ueŽ‘f滬;Ž¡‘2°gŽ¡‘2­elseŽ‘H.9ifŽ‘Sã1¬(±curr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘;°‘ÇŽ‘ +Ž6¬1Ž‘Ž7)‘°fŽ¡‘<±out‘‰ffŽ‘®angleŽ‘hK¬=‘DZtest‘‰ffŽ‘®angleŽ‘-ŠË¬;Ž¡‘<­con•®9tin“ueŽ‘f滬;Ž¡‘2°gŽ¡‘2­elseŽ‘IØä°fŽ¡‘<±c‘ÿ}'errŽ‘SÆ4°‘ˆ´"ERROR!® ´In® ´Ellipse::Ž‘nLintersection_points(Ž’×Ellipse).\n"Ž’¦Ü°Ž¡‘P´"This® ´can't® ´happen!® Ž’¸ÿÌ´Invalid® ´value® ´for® ´cuŽ’!ÿrr_location:® ´"Ž’oSà°‘N±curr‘‰ffŽ‘®lo–ÿ}'c“ationŽ‘?r°Ž¡‘P´"\nReturning® ´INVALIDŽ’¸ÿÌ_BOOL_POINT_QUADRUPLŽ’!ÿE.\n\n"Ž’J û°‘DZ ushŽ‘€¬;Ž¡‘<­returnŽ‘_æÀ´INVALID_BOOL_POINT_QUADRUPLEŽ’ólÔ¬;ŽŽŽŒ‹` Šn ý‘ì¬352–­ELLIPSE‘ÕX¯ARÃŽGUMENT’ïo\3DLDF-1.1.5.1“°x¬1224Ž €n ý•@P‘2°gŽ¤ ‘(g‘µ=°‘ÿý­whileŽ‘$íÑ°µ=Ž¡‘°g‘µ=°‘ÿý­ifŽ‘_°µ=Ž¡‘°g‘µ=°‘ÿý­forŽ‘“+°µ=Ž¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"Finished® ´searching® Ž‘kÆÜ´for® ´Ellipse® ´intersecŽ’ÔÆ tions."Ž’üÔ °‘DZend‘‚ØlŽ–ò°‘DZend‘‚ØlŽ“°‘DZ ushŽ‘€¬;Ž¡‘ +°g‘µ=°‘ÿý¬End–UUof“\Ellipses“ha•¸ãv“e›UUdi eren“t˜cen“ters˜and/or˜axis˜orien“tation".‘o°µ=Ž¡‘ +°g‘µ=°‘ÿý¬End–UUof“coplanar“case.‘o°µ=ŽŸ­1225.‘ ü¬Handle–UUinš¸ãtersection“pGoin˜t.ŽŸ°h‘ª¨¬Handle–UUinš¸ãtersection“pGoin˜t‘@¯1225‘ª¨°i‘ÇŽ¡‘ +fŽ¡‘€Ÿÿ³+‘ÿ+ŽŽ‘ G"±interse‘ÿ}'ction‘‰ffŽ‘®ctrŽ‘diZ¬;Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"intersection_ctr® ´==Ž‘kÆÜ® ´"Ž‘y”V°‘DZinterse‘ÿ}'ction‘‰ffŽ‘®ctrŽ‘I°h°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘°gŽ¡‘­ifŽ‘´ú¬(±interse‘ÿ}'ction‘‰ffŽ‘®ctrŽ‘FéP°‘Ǭ1Ž‘Ç)‘°fŽ¡‘±bp‘ÿ}'qŽ‘-2µ:± rstŽ‘µªµ:bŽ‘¬=‘DZtrueŽ‘‹°¬;Ž¡‘±bp‘ÿ}'qŽ‘-2µ:± rstŽ‘µªµ:±ptŽ‘ «µ¬=‘DZcurr‘‰ffŽ‘®p‘ÿ}'ointŽ‘0 +¬;Ž¡‘±bp‘ÿ}'qŽ‘-2µ:± rstŽ‘µªµ:±ptŽ‘ «µ°¬=ŽŽ‘9ì±t‘‰ffŽ‘®inverseŽ‘CI¬;Ž¡‘°gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±interse‘ÿ}'ction‘‰ffŽ‘®ctrŽ‘FéP°‘Ǭ2Ž‘Ç)‘°fŽ¡‘±bp‘ÿ}'qŽ‘-2µ:±se–ÿ}'c“ondŽ‘§Çµ:bŽ‘¬=‘DZtrueŽ‘‹°¬;Ž¡‘±bp‘ÿ}'qŽ‘-2µ:±se–ÿ}'c“ondŽ‘§Çµ:±ptŽ‘ «µ¬=‘DZcurr‘‰ffŽ‘®p‘ÿ}'ointŽ‘0 +¬;Ž¡‘±bp‘ÿ}'qŽ‘-2µ:±se–ÿ}'c“ondŽ‘§Çµ:±ptŽ‘ «µ°¬=ŽŽ‘9ì±t‘‰ffŽ‘®inverseŽ‘CI¬;Ž¡‘°gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±interse‘ÿ}'ction‘‰ffŽ‘®ctrŽ‘FéP°‘Ǭ3Ž‘Ç)‘°fŽ¡‘±bp‘ÿ}'qŽ‘-2µ:±thir‘ÿ}'dŽ‘Üjµ:bŽ‘¬=‘DZtrueŽ‘‹°¬;Ž¡‘±bp‘ÿ}'qŽ‘-2µ:±thir‘ÿ}'dŽ‘Üjµ:±ptŽ‘ «µ¬=‘DZcurr‘‰ffŽ‘®p‘ÿ}'ointŽ‘0 +¬;Ž¡‘±bp‘ÿ}'qŽ‘-2µ:±thir‘ÿ}'dŽ‘Üjµ:±ptŽ‘ «µ°¬=ŽŽ‘9ì±t‘‰ffŽ‘®inverseŽ‘CI¬;Ž¡‘°gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±interse‘ÿ}'ction‘‰ffŽ‘®ctrŽ‘FéP°‘Ǭ4Ž‘Ç)‘°fŽ¡‘±bp‘ÿ}'qŽ‘-2µ:±fourthŽ‘xùµ:bŽ‘¬=‘DZtrueŽ‘‹°¬;Ž¡‘±bp‘ÿ}'qŽ‘-2µ:±fourthŽ‘xùµ:±ptŽ‘ «µ¬=‘DZcurr‘‰ffŽ‘®p‘ÿ}'ointŽ‘0 +¬;Ž¡‘±bp‘ÿ}'qŽ‘-2µ:±fourthŽ‘xùµ:±ptŽ‘ «µ°¬=ŽŽ‘9ì±t‘‰ffŽ‘®inverseŽ‘CI¬;Ž¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÿ9°_‘8à±verb‘ÿ}'oseŽ‘"Ê=¬)‘°fŽ¡‘(±c‘ÿ}'outŽ‘?KR°‘ò´"In® ´Ellipse::interseŽ‘lñÛction_points(EllipseŽ’ÕñŸ® ´e,® ´const® ´bool® ´verboŽ’>ñcse)"Ž’XiÖ°Ž¡‘<´"Found® ´fourth® ´intersŽ’¤ÿÊection® ´point.\n"Ž’üM°‘Ç´"Returning® ´bpq.\n\n"Ž‘lMD¬;Ž¡‘°gŽ¡‘­returnŽ‘Aæ½±bp‘ÿ}'qŽ‘QÙ¬;Ž¡‘°gŽ¡‘­elseŽ‘+Øá°fŽ¡‘±c‘ÿ}'errŽ‘6‹°‘Õs´"ERROR!® ´In® ´Ellipse::Ž‘nÕ7intersection_points(Ž’×ÔûEllipse).\n"Ž’0²°Ž¡‘2´"This® ´can't® ´happen!® Ž’šÿÉ ´Invalid® ´value® ´for® ´"Ž’ ;ΰ‘µÙ´"intersection_ctr:® ´"Ž‘rñÞ°Ž¡‘2±interse‘ÿ}'ction‘‰ffŽ‘®ctrŽ‘xéU°‘Ç´".\nReturning® ´INVALIŽ‘kÆÜD_BOOL_POINT_QUADRUPŽ’ÔÆ LE.\n\n"Ž’ÿLð¬;Ž¡‘­returnŽ‘Aæ½´INVALID_BOOL_POINT_QUADRUPLEŽ’ÕlѬ;Ž¡‘°gŽ¡‘ +gŽŸ ¯This–ÕXco.µeŽ‘)æ/;‘ª¨­constŽ‘ÕJb•QÇo“olŽ‘9v°±verb‘ÿ}'oseŽ‘Z ¬).‘qÇ[²LDF‘T2003.07.01.¬]ŽŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.07.01.¬]Ž‘Y;Added–UUthis“section.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h‘ª¨¬Chec•¸ãk›UUin“tersection˜pGoin“t˜loGcations‘@¯1228‘ª¨°i‘ÇŽ¤ ‘ +­ifŽ‘´ù¬(±temp‘‰ffŽ‘®b–ÿ}'o“olŽ‘*Êu¬)‘°fŽ¡‘­ifŽ‘´ú¬(±verb‘ÿ}'oseŽ‘ ‘]¬)‘°fŽ¡‘­ifŽ‘)´û¬(±s‘‰ffŽ‘®tŽ‘T°‘Ǭ0Ž‘ ÿù°^‘8à±s‘‰ffŽ‘®eŽ‘¡—°‘Ǭ0Ž‘Ç)Ž¡‘(±c‘ÿ}'outŽ‘> S°‘DZtemp‘‰ffŽ‘®stringŽ‘8Â;°‘Ç´"® ´point® ´lies® ´on® ´the® Ž‘kÆÜ´perimeter® ´of® ´both® ´elŽ’ÔÆ lipses.\n"Ž’ Ìê¬;Ž¡‘­elseŽ‘4.7ifŽ‘?ã/¬(±s‘‰ffŽ‘®tŽ‘T°‘Ǭ0Ž‘Ç)‘±c‘ÿ}'outŽ‘ O°‘DZtemp‘‰ffŽ‘®stringŽ‘8Â;°‘Ç´"® ´point® ´lies® ´on® ´the® Ž‘kÆÜ´perimeter® ´of® ´*this.\Ž’ÔÆ n"Ž’ßͬ;Ž¡‘­elseŽ‘4.7ifŽ‘?ã/¬(±s‘‰ffŽ‘®tŽ‘T°‘ÇŽ‘ +Ž6¬1Ž‘Ž7)‘±c‘ÿ}'outŽ‘ O°‘DZtemp‘‰ffŽ‘®stringŽ‘8Â;°‘Ç´"® ´point® ´lies® ´outsideŽ‘kÆÜ® ´*this.\n"Ž’ Í&¬;Ž¡‘­elseŽ‘4.7ifŽ‘?ã/¬(±s‘‰ffŽ‘®tŽ‘T°‘Ǭ1Ž‘Ç)‘±c‘ÿ}'outŽ‘ O°‘DZtemp‘‰ffŽ‘®stringŽ‘8Â;°‘Ç´"® ´point® ´lies® ´inside® Ž‘kÆÜ´*this.\n"Ž’›)¬;Ž¡‘­elseŽ‘4.7ifŽ‘?ã/¬(±s‘‰ffŽ‘®tŽ‘T°‘ÇŽ‘ +Ž6¬2Ž‘Ž7)‘±c‘ÿ}'outŽ‘ O°‘DZtemp‘‰ffŽ‘®stringŽ‘8Â;°‘Ç´"® ´point® ´doesn't® ´lie® Ž‘kÆÜ´in® ´the® ´plane® ´of® ´*thiŽ’ÔÆ s.\n"Ž’ïŒù¬;Ž¡‘­ifŽ‘)´û¬(±s‘‰ffŽ‘®eŽ‘h·°‘Ǭ0Ž‘ ÿù°^‘8à±s‘‰ffŽ‘®tŽ‘Œø°6¬=‘Ç0Ž‘Ç)‘±c‘ÿ}'outŽ‘ O°‘DZtemp‘‰ffŽ‘®stringŽ‘8Â;°‘Ç´"® ´point® ´lies® ´on® ´the® Ž‘kÆÜ´perimeter® ´of® ´e.\n"Ž’Êͬ;Ž¡‘­ifŽ‘)´û¬(±s‘‰ffŽ‘®eŽ‘h·°‘ÇŽ‘ +Ž6¬1Ž‘Ž7)‘±c‘ÿ}'outŽ‘ O°‘DZtemp‘‰ffŽ‘®stringŽ‘8Â;°‘Ç´"® ´point® ´lies® ´outsideŽ‘kÆÜ® ´e.\n"Ž’‹Í2¬;Ž¡‘­elseŽ‘4.7ifŽ‘?ã/¬(±s‘‰ffŽ‘®eŽ‘h·°‘Ǭ1Ž‘Ç)‘±c‘ÿ}'outŽ‘ O°‘DZtemp‘‰ffŽ‘®stringŽ‘8Â;°‘Ç´"® ´point® ´lies® ´inside® Ž‘kÆÜ´e.\n"Ž’†5¬;Ž¡‘­elseŽ‘4.7ifŽ‘?ã/¬(±s‘‰ffŽ‘®eŽ‘h·°‘ÇŽ‘ +Ž6¬2Ž‘Ž7)‘±c‘ÿ}'outŽ‘ O°‘DZtemp‘‰ffŽ‘®stringŽ‘8Â;°‘Ç´"® ´point® ´doesn't® ´lie® Ž‘kÆÜ´in® ´the® ´plane® ´of® ´e.\nŽ’ÔÆ "Ž’Ú¬;Ž¡‘°gŽ¡‘ +gŽŸ ¯This–ÕXco³2Ïaxis‘‰ffŽ–®h‘‰ffŽ“halfŽ‘qTC«=‘ÇÏaxis‘‰ffŽ‘®hŽ‘À¥±=«2Ž‘;Ž¡‘(ÂrealŽ‘>³2Ïaxis‘‰ffŽ–®v‘‰ffŽ“halfŽ‘pÑj«=‘ÇÏaxis‘‰ffŽ‘®vŽ‘Œö±=«2Ž‘;Ž¦‘(ÂifŽ‘3j§«(ÏfabsŽ‘2Ò«(Ïaxis‘‰ffŽ‘®hŽ‘Ä·‘¤7Ïold‘‰ffŽ–®axis‘‰ffŽ“hŽ‘-ï«)–DZ>“ÂP•®9oin“tŽ‘ad«::Ž‘%ï¢ÏepsilonŽ›E^¦«(‘ª¨)–¤7·_“ÏfabsŽ‘× «(Ïaxis‘‰ffŽ‘®vŽ‘j·“Ïold‘‰ffŽ–®axis‘‰ffŽ“vŽ‘,ß@«)–DZ>“ÂP•®9oin“tŽ‘ad«::Ž‘%ï¢ÏepsilonŽ˜«(‘ª¨))‘·fŽ¡‘2ÂifŽ‘?ß«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘O·‘õâÝ"RecalculatingÈ ÝlineaŽ‘nõ¦r_eccentricity,È Ý"Ž’α½·Ž¡‘PÝ"numerical_eccentricŽ’¸ÿÌityÈ ÝandÈ Ýfoci.\n"Ž’M·‘ÇÏ ushŽ‘€«;Ž¡‘2ÂifŽ‘=´ý«(Ïaxis‘‰ffŽ‘®hŽ‘À¥·‘ÇÏaxis‘‰ffŽ‘®vŽ‘Œö«)‘·fŽ¡‘<Ïline–ÿ}'ar‘‰ffŽ‘®e“c“c“entricityŽ’sù«=‘ÇÏsqrtŽ‘w«((Ïaxis‘‰ffŽ–®h‘‰ffŽ“halfŽ–2Ù·‘8àÏaxis‘‰ffŽ–®h‘‰ffŽ“halfŽ“«)–8à·“«(Ïaxis‘‰ffŽ–®v‘‰ffŽ“halfŽ›1·“Ïaxis‘‰ffŽ–®v‘‰ffŽ“halfŽ˜«));Ž¡‘<Ïnumeric–ÿ}'al‘‰ffŽ‘®e“c“c“entricityŽ’Ÿ˜ì«=‘ÇÏline–ÿ}'ar‘‰ffŽ‘®e“c“c“entricityŽ‘Qsó±=Ïaxis‘‰ffŽ–®h‘‰ffŽ“halfŽ‘/Ùù«;Ž¡‘<Ïfo‘ÿ}'cus1Ž‘[zH«=‘ÇÏfo‘ÿ}'cus0Ž‘"AZ«=‘Ç(Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH«(0Ž‘)–8à·“Ïget‘‰ffŽ‘®c‘ÿ}'enterŽ‘.v'«(‘ª¨));Ž¡‘2·gŽ¡‘2ÂelseŽ‘IØä·fŽ¡‘<Ïline–ÿ}'ar‘‰ffŽ‘®e“c“c“entricityŽ’sù«=‘ÇÏsqrtŽ‘w«((Ïaxis‘‰ffŽ–®v‘‰ffŽ“halfŽ–1·‘8àÏaxis‘‰ffŽ–®v‘‰ffŽ“halfŽ“«)–8à·“«(Ïaxis‘‰ffŽ–®h‘‰ffŽ“halfŽ›2Ù·“Ïaxis‘‰ffŽ–®h‘‰ffŽ“halfŽ˜«));Ž¡‘<Ïnumeric–ÿ}'al‘‰ffŽ‘®e“c“c“entricityŽ’Ÿ˜ì«=‘ÇÏline–ÿ}'ar‘‰ffŽ‘®e“c“c“entricityŽ‘Qsó±=Ïaxis‘‰ffŽ–®v‘‰ffŽ“halfŽ‘/W «;Ž¡‘<Ïfo‘ÿ}'cus1Ž‘[zH«=‘ÇÏfo‘ÿ}'cus0Ž‘"AZ«=‘Ç(Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH«(Ïnumb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜ointsŽ‘JÀ©±=«4Ž‘)–8à·“Ïget‘‰ffŽ‘®c‘ÿ}'enterŽ‘.v'«(‘ª¨));Ž¡‘2·gŽ¡‘2Ïfo‘ÿ}'cus0Ž‘N³/±:Ïunit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u«(ÏtrueŽ‘Ę«);Ž¡‘2Ïfo‘ÿ}'cus1Ž‘N³/±:Ïunit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u«(ÏtrueŽ‘Ę«);Ž¡‘2Ïfo‘ÿ}'cus0Ž‘QzG·«=ŽŽ‘a~·Ž‘hÏœÏline–ÿ}'ar‘‰ffŽ‘®e“c“c“entricityŽ’·|w«;Ž¡‘2Ïfo‘ÿ}'cus1Ž‘QzG·«=ŽŽ‘a~Ïline–ÿ}'ar‘‰ffŽ‘®e“c“c“entricityŽ’¯µY«;Ž¡‘2Ïfo‘ÿ}'cus1Ž‘QzG·«=ŽŽ‘a~Ïfo‘ÿ}'cus0Ž‘}»¨±:ÏshiftŽ‘}«(Ïget‘‰ffŽ‘®c‘ÿ}'enterŽ‘,=G«(‘ª¨));Ž¡‘(·gŽ¡‘(ÂelseŽ‘>.8ifŽ‘Iã0«(ÝDEBUGŽ‘ÆY«)Ž¡‘2Ïc‘ÿ}'outŽ‘H T·‘ÇÝ"axis_hÈ ÝandÈ Ýaxis_vÈ ÝaŽ‘kÆÜreÈ Ýunchanged.\n"Ž’Ã,·‘ÇÝ"NotÈ ÝrecalculatingÈ ÝfŽ‘kÆÜoci.\n"Ž’“ÔG·‘ÇÏ ushŽ‘€«;Ž¡‘·g‘±=·‘ÿýÂifŽ‘´õ«(Ïis‘‰ffŽ‘®el‘‚Øliptic‘ÿ}'alŽ‘0ì–«(‘ª®))‘ÿý·±=Ž¡‘ÂelseŽ‘5Øâ·fŽ¡‘(Ïc‘ÿ}'errŽ‘?¿¢·‘ øÝ"WARNING!È ÝInÈ ÝEllipseŽ‘n ¼::do_transform(constŽ’× €È ÝTransform&):\n"Ž’0™°·Ž¡‘<Ý"ThisÈ ÝtransformationŽ’¤ÿÊÈ ÝhasÈ ÝmadeÈ Ý*thisÈ Ýnon-Ž’ ÿŽelliptical!"Ž’PLê·‘ÇÏend‘‚ØlŽ–ò·‘ÇÏend‘‚ØlŽ“·‘ÇÏ ushŽ‘€«;Ž¡‘(Ïaxis‘‰ffŽ‘®hŽ‘EÀ©«=‘ÇÏaxis‘‰ffŽ‘®vŽ‘ T«=‘ÇÏline–ÿ}'ar‘‰ffŽ‘®e“c“c“entricityŽ‘T; «=‘ÇÝINVALID_REALŽ‘BM\«;Ž¡‘(Ïnumeric–ÿ}'al‘‰ffŽ‘®e“c“c“entricityŽ’‹˜ê«=‘ÇÝINVALID_REALŽ‘BM\«;Ž¡‘·gŽ¡‘gŽ¡‘ÂreturnŽ‘7æ¼±tŽ‘;ƒ.«;Ž¡‘ -·gŽŽŽŒ‹_dV Šn ý‘ì·x«1194–­3DLDFPRÃŽG’,­5OPERA‘ÿJªTOR“«351Ž €n ý•@PÂ1194.‘ üOpQÇerator.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ -«[¬LDF‘T2002.04.12.«]Ž‘Y;Added–UUthis“section.Ž¡‘ -[¬LDF‘T2003.07.20.«]Ž‘YÅâChanged,›Beso–üthat“it“calls“Ïdo‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘=­0«(‘ª®)“with“Ïche‘ÿ}'ckŽ‘ ¬‚·‘,ÏtrueŽ‘ÇÄ«,˜so“that“Ïis‘‰ffŽ‘®el‘‚Øliptic‘ÿ}'alŽ‘4ÿ’«(‘ª®)“isŽ¡called.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·Ž© ‘ -ÂvirtualŽ‘/ÔT‘ÿ -«ransformŽ‘gV¦opQÇeratorŽ’’í[·«=ŽŽŽ’Ÿ´z(ÂconstŽ‘*¢T‘ÿ -«ransformŽ‘Uót«&Ž‘]º’±tŽ‘aW«);ŽŸÂ1195.Ž¡·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¦‘ -ÂT‘ÿ -«ransformŽ‘AÈÓEllipseŽ‘d±°«::Ž‘k?îÂopQÇeratorŽ’–Ö£·«=ŽŽŽ’£Â(ÂconstŽ‘*¢T‘ÿ -«ransformŽ‘Uót«&Ž‘]º’±tŽ‘aW«)Ž¦‘ -·fŽ¦‘ÂreturnŽ‘7æ¼Ïdo‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘q€ð«(±tŽ‘œr;‘ª¨ÏtrueŽ‘o@«);Ž¦‘ -·gŽŸÂ1196.‘ üRotation–ÕTaround“the“main“axes.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ -«[¬LDF‘T2003.07.25.«]Ž‘YäChanged,‘hso–1that“Ïdo‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘=ËQ«(‘ª®)“is“called“with“Ïche‘ÿ}'ckŽ‘ üÛ·‘5dÏfalseŽ‘䨫.‘Rotation“can“neitherŽ¦cš¸ãhange–/æthe“lengths“of“Ïaxis‘‰ffŽ‘®hŽ‘!YY«or“Ïaxis‘‰ffŽ‘®vŽ‘õÄ«,‘7cnor“mak˜e“an“ÂEllipseŽ‘(H¥«non-elliptical,‘7cso“there's“no“need“to“c˜hec˜k“·Ž‘/çÏthisŽŽ¦«after‘UUrotation.Ž¡ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·Ž¦‘ -ÂvirtualŽ‘/ÔT‘ÿ -«ransformŽ‘gV¦Ïr‘ÿ}'otateŽ’Åä«(ÂconstŽ‘*¢realŽ‘4ÝбxŽ‘:”ì;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±yŽ‘>’ˆ«=‘Ç0Ž–DZ;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±zŽ‘>f®«=‘Ç0Ž“);ŽŸÂ1197.Ž¡·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¦‘ -ÂT‘ÿ -«ransformŽ‘AÈÓEllipseŽ‘d±°«::‘Ïr‘ÿ}'otateŽ‘oB«(ÂconstŽ‘*¢realŽ‘4ÝбxŽ‘:”ì;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±yŽ‘;Ëp;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆx±zŽ‘;Ÿ–«)Ž¦‘ -·fŽ¦‘ÂT‘ÿ -«ransformŽ‘KÈÔ±tŽ‘OeF«;Ž¡‘±tŽ‘œt:Ïr‘ÿ}'otateŽ‘o>«(±xŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁÆ«);Ž¦‘ÂreturnŽ‘7æ¼Ïdo‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘q€ð«(±tŽ‘œr;‘ª¨ÏfalseŽ‘Yì«);Ž¦‘ -·gŽŸÂ1198.‘ üScale.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ -«[¬LDF‘T2003.07.20.«]Ž‘Y;Added›UUc•¸ãhec“k˜for˜whether˜·Ž‘UVÏthisŽ‘–a«is˜still˜elliptical˜after˜the˜scaling˜opGeration.Ž¡ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·Ž¦‘ -ÂvirtualŽ‘/ÔT‘ÿ -«ransformŽ‘gV¦Ïsc‘ÿ}'aleŽ‘} ˜«(ÂrealŽ‘³.±xŽ‘jJ;‘ª¨ÂrealŽ‘]Ö±yŽ‘ gæ«=‘Ç1Ž–DZ;‘ª¨ÂrealŽ‘]Ö±zŽ‘ < «=‘Ç1Ž“);ŽŽŽŒ‹`wΠŠn ý‘ì«352–­SCALE’ArC3DLDFPRÃŽG“·x«1199Ž €n ý•@PÂ1199.Ž©·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¤ ‘ -ÂT‘ÿ -«ransformŽ‘AÈÓEllipseŽ‘d±°«::‘Ïsc‘ÿ}'aleŽ‘´ö«(ÂrealŽ‘³.±xŽ‘jJ;‘ª¨ÂrealŽ‘]Ö±yŽ‘ Î;‘ª¨ÂrealŽ‘]Ö±zŽ‘tô«)Ž¡‘ -·fŽ¡‘ÂT‘ÿ -«ransformŽ‘KÈÔ±tŽ‘OeF«;Ž¦‘±tŽ‘œt:Ïsc‘ÿ}'aleŽ‘´ò«(±xŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁÆ«);Ž¡‘ÂreturnŽ‘7漫(·Ž‘ÏthisŽ‘²Ï·«=ŽŽ‘(A±tŽ‘+Ýx«);Ž¡‘ -·gŽŸÂ1200.‘ üShear.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.07.20.«]Ž‘Y;Added›UUc•¸ãhec“k˜for˜whether˜·Ž‘UVÏthisŽ‘–a«is˜still˜elliptical˜after˜the˜shearing˜opGeration.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/ÔT‘ÿ -«ransformŽ‘gV¦Ïshe‘ÿ}'arŽ‘Šà«(ÂrealŽ‘³.ÏxyŽ‘!—±;‘ª¨ÂrealŽ‘]ÖÏxzŽ‘%œÀ«=‘Ç0Ž–DZ;‘ª¨ÂrealŽ‘]ÖÏyxŽ‘&Zœ«=‘Ç0Ž“±;‘ª¨ÂrealŽ‘]ÖÏyzŽ‘%Ô6«=‘Ç0Ž“±;‘ª¨ÂrealŽ‘]ÖÏzxŽ‘%–Y«=‘Ç0Ž“±;‘ª¨ÂrealŽ‘]ÖÏzyŽ‘%|«=‘Ç0Ž“);ŽŸÂ1201.Ž¦·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ -«ransformŽ‘AÈÓEllipseŽ‘d±°«::‘Ïshe‘ÿ}'arŽ‘4>«(ÂrealŽ‘³.ÏxyŽ‘!—±;‘ª¨ÂrealŽ‘]ÖÏxzŽ‘"Õ¨±;‘ª¨ÂrealŽ‘]ÖÏyxŽ‘#“„±;‘ª¨ÂrealŽ‘]ÖÏyzŽ‘# ±;‘ª¨ÂrealŽ‘]ÖÏzxŽ‘"ÏA±;‘ª¨ÂrealŽ‘]ÖÏzyŽ‘"´ð«)Ž¡‘ -·fŽ¡‘ÂT‘ÿ -«ransformŽ‘KÈÔ±tŽ‘OeF«;Ž¦‘±tŽ‘œt:Ïshe‘ÿ}'arŽ‘4:«(ÏxyŽ‘ -ãç±;‘ª¨ÏxzŽ‘ "z±;‘ª¨ÏyxŽ‘ àV±;‘ª¨ÏyzŽ‘ Yð±;‘ª¨ÏzxŽ‘ ±;‘ª¨ÏzyŽ‘ «);Ž¡‘ÂreturnŽ‘7漫(·Ž‘ÏthisŽ‘²Ï·«=ŽŽ‘(A±tŽ‘+Ýx«);Ž¡‘ -·gŽ¤Â1202.‘ üShift.Ž¡1203.‘ üreal‘ÕTargumen®9ts.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ -«[¬LDF‘T2003.07.25.«]Ž‘Z&zChanged,‘»$so–s”that“Ïdo‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘> È«(‘ª®)“is“called“with“Ïche‘ÿ}'ckŽ‘!®·‘¤*ÏfalseŽ‘Sn«.‘Ì„Shifting“can“neitherŽ¡cš¸ãhange–/æthe“lengths“of“Ïaxis‘‰ffŽ‘®hŽ‘!YY«or“Ïaxis‘‰ffŽ‘®vŽ‘õÄ«,‘7cnor“mak˜e“an“ÂEllipseŽ‘(H¥«non-elliptical,‘7cso“there's“no“need“to“c˜hec˜k“·Ž‘/çÏthisŽŽ¡«after‘UUshifting.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/ÔT‘ÿ -«ransformŽ‘gV¦ÏshiftŽ‘{t#«(ÂrealŽ‘³.ÏxxŽ‘!±f±;‘ª¨ÂrealŽ‘]ÖÏyyŽ‘&@K«=‘Ç0Ž–DZ;‘ª¨ÂrealŽ‘]ÖÏzzŽ‘%ó«=‘Ç0Ž“);ŽŸÂ1204.Ž¦·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ -«ransformŽ‘AÈÓEllipseŽ‘d±°«::‘ÏshiftŽ‘«(ÂrealŽ‘³.ÏxxŽ‘!±f±;‘ª¨ÂrealŽ‘]ÖÏyyŽ‘#y3±;‘ª¨ÂrealŽ‘]ÖÏzzŽ‘"HÛ«)Ž¡‘ -·fŽ¡‘ÂT‘ÿ -«ransformŽ‘KÈÔ±tŽ‘OeF«;Ž¦‘±tŽ‘œt:ÏshiftŽ‘}«(ÏxxŽ‘ -þ8±;‘ª¨ÏyyŽ‘ Ʊ;‘ª¨ÏzzŽ‘ •­«);Ž¡‘ÂreturnŽ‘7æ¼Ïdo‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘q€ð«(±tŽ‘œr;‘ª¨ÏfalseŽ‘Yì«);Ž¡‘ -·gŽŸÂ1205.‘ üP•®9oin“t‘ÕTargumen“t.Ž¦·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/ÔT‘ÿ -«ransformŽ‘gV¦ÏshiftŽ‘{t#«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]±pŽ‘Ié]«);ŽŽŽŒ‹a‚R Šn ý‘ì·x«1206›­3DLDFPR•ÃŽG’”µÂPOINT‘ÕX­AR“GUMENT˜«353Ž €n ý•@PÂ1206.Ž©·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¤ ‘ -ÂT‘ÿ -«ransformŽ‘AÈÓEllipseŽ‘d±°«::‘ÏshiftŽ‘«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]±pŽ‘Ié]«)Ž¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼ÏshiftŽ‘L9«(±pŽ‘:Ïget‘‰ffŽ‘®xŽ‘Žg«(–ª¨)±;“pŽ›²¨:Ïget‘‰ffŽ‘®yŽ‘t«(“)±;“pŽ˜:Ïget‘‰ffŽ‘®zŽ‘«(“));Ž¡‘ -·gŽ¤Â1207.‘ üShift‘ÕTtimes.Ž¡1208.‘ üreal‘ÕTargumen®9ts.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ -«[¬LDF‘T2003.07.25.«]Ž‘Y;No¸ãw–UUpšGerforming“Ïshift‘‰ffŽ‘®timesŽ‘2A«(‘ª®)“on“Ïfo‘ÿ}'cus0Ž‘#]Ô«and“Ïfo‘ÿ}'cus1Ž‘ «,“to˜o.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/Ôv®9oidŽ‘H‹¬Ïshift‘‰ffŽ‘®timesŽ‘wwç«(ÂrealŽ‘³.±xŽ‘jJ;‘ª¨ÂrealŽ‘]Ö±yŽ‘ gæ«=‘Ç1Ž–DZ;‘ª¨ÂrealŽ‘]Ö±zŽ‘ < «=‘Ç1Ž“);ŽŸÂ1209.Ž¦·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙEllipseŽ‘E涫::‘Ïshift‘‰ffŽ‘®timesŽ‘/ì?«(ÂrealŽ‘³.±xŽ‘jJ;‘ª¨ÂrealŽ‘]Ö±yŽ‘ Î;‘ª¨ÂrealŽ‘]Ö±zŽ‘tô«)Ž¡‘ -·fŽ¡‘ÂP®9athŽ‘-‘j«::Ž‘4¨Ïshift‘‰ffŽ‘®timesŽ‘c ã«(±xŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁÆ«);Ž¡‘Ïfo‘ÿ}'cus1Ž‘0³,±:Ïshift‘‰ffŽ‘®timesŽ‘.ì;«(±xŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁÆ«);Ž¡‘Ïfo‘ÿ}'cus0Ž‘0³,±:Ïshift‘‰ffŽ‘®timesŽ‘.ì;«(±xŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁÆ«);Ž¡‘Ïc‘ÿ}'enterŽ‘0 ±:Ïshift‘‰ffŽ‘®timesŽ‘.ì;«(±xŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁÆ«);Ž¡‘ÂreturnŽ‘4‘g«;Ž¡‘ -·gŽŸÂ1210.‘ üP•®9oin“t‘ÕTargumen“t.Ž¦·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/Ôv®9oidŽ‘H‹¬Ïshift‘‰ffŽ‘®timesŽ‘wwç«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]±pŽ‘Ié]«);ŽŸÂ1211.Ž¦·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙEllipseŽ‘E涫::‘Ïshift‘‰ffŽ‘®timesŽ‘/ì?«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]±pŽ‘Ié]«)Ž¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼Ïshift‘‰ffŽ‘®timesŽ‘fÒ÷«(±pŽ‘:Ïget‘‰ffŽ‘®xŽ‘Žg«(–ª¨)±;“pŽ›²¨:Ïget‘‰ffŽ‘®yŽ‘t«(“)±;“pŽ˜:Ïget‘‰ffŽ‘®zŽ‘«(“));Ž¡‘ -·gŽŸÂ1212.‘ üRotatation–ÕTaround“an“arbitrary“axis.ŽŽŽŒ‹bô Šn ý‘ì«354›ÂPOINT‘ÕX­AR•ÃŽGUMENTS’üÛÍ3DLDFPR“G˜·x«1213Ž €n ý•@PÂ1213.‘ üP•®9oin“t‘ÕTargumen“ts.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ -«[¬LDF‘T2003.05.02.«]Ž‘YËSChanged–mname“of“this“function“from“Ïr–ÿ}'otate‘‰ffŽ‘®ar“oundŽ‘@„ü«(›ª®)“to“Ïr‘ÿ}'otateŽ‘‡««(˜).‘»This“function“no¸ãwŽ¡o•¸ãv“erloads‘UUÏr‘ÿ}'otateŽ‘Ä“«(‘ª®)–UUwith“three“ÂrealŽ‘ƒ«argumen¸ãts.Ž¡‘ -[¬LDF‘T2003.07.25.«]Ž‘YäChanged,‘hso–1that“Ïdo‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘=ËQ«(‘ª®)“is“called“with“Ïche‘ÿ}'ckŽ‘ üÛ·‘5dÏfalseŽ‘䨫.‘Rotation“can“neitherŽ¡cš¸ãhange–/æthe“lengths“of“Ïaxis‘‰ffŽ‘®hŽ‘!YY«or“Ïaxis‘‰ffŽ‘®vŽ‘õÄ«,‘7cnor“mak˜e“an“ÂEllipseŽ‘(H¥«non-elliptical,‘7cso“there's“no“need“to“c˜hec˜k“·Ž‘/çÏthisŽŽ¡«after‘UUrotation.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂEllipseŽ‘(“ƒ«functions‘@­1106“·i‘Ç«+·Ž© ‘ -ÂvirtualŽ‘/ÔT‘ÿ -«ransformŽ‘gV¦Ïr‘ÿ}'otateŽ’Åä«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]Ïp0Ž‘Pø±;‘ª¨ÂconstŽ‘ÕJP•®9oin“tŽ‘>Äç«&Ž‘FŒÏp1Ž‘R¢Å±;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆxÏangleŽ‘Qã«=‘Ç180ŽŽ‘Ç);ŽŸÂ1214.Ž¡·h–ª¨«De ne‘UUÂEllipseŽ‘(“ƒ«functions‘@­1107“·i‘Ç«+·Ž¦‘ -ÂT‘ÿ 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-·fŽ¡‘ÂRectangleŽ‘I”ìÏr0Ž‘WÉ«=‘ÇÏout‘‰ffŽ‘®r–ÿ}'e“ctangleŽ‘;¹±«(‘ª¨);Ž¡‘Âb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘edðÏbpp0Ž‘}øÏ«=‘ÇÏinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘TS÷«(Ïr0Ž‘ 1ű:Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ–'bH«(0Ž›)±;‘ª¨Ïr0Ž‘ Üm±:Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ“«(2Ž˜));Ž¡‘Âb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘edðÏbpp1Ž‘}øÏ«=‘ÇÏinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘TS÷«(Ïr0Ž‘ 1ű:Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ–'bH«(1Ž›)±;‘ª¨Ïr0Ž‘ Üm±:Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ“«(3Ž˜));Ž¦‘ÂifŽ‘ „n«(Ïbpp0Ž‘ÌDZ:Ï rstŽ‘µª±:ÏptŽ–t·‘ ×ÝINVALID_POINTŽ›KªE·_‘Ã-Ïbpp0Ž‘ô±:Ïse–ÿ}'c“ondŽ‘§Ç±:ÏptŽ“·‘ ×ÝINVALID_POINTŽ˜·_‘Ã-Ïbpp1Ž‘ô±:Ï rstŽ‘µª±:ÏptŽ“·Ž¡‘2ÝINVALID_POINTŽ‘xÿ&·_‘8àÏbpp1Ž‘§±:Ïse–ÿ}'c“ondŽ‘§Ç±:ÏptŽ‘ «µ·‘ÇÝINVALID_POINTŽ‘GY«)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘3|Á·‘ÇÝ"IntersectionÈ Ýdidn'tŽ‘kÆÜÈ Ýwork.\n"Ž’žTA·‘ÇÝ"ReturningÈ ÝemptyÈ ÝrecŽ‘kÆÜtangle.\n\n"Ž’®8·‘ÇÏ ushŽ‘€«;Ž¦‘ÂRectangleŽ‘S”íÏr2Ž‘^Ʋ«;Ž¦‘ÂreturnŽ‘Aæ½Ïr2Ž‘M‚«;Ž¡‘·gŽ¦‘ÂRectangleŽ‘I”ìÏr1Ž‘TƱ«(Ïbpp0Ž‘ÌDZ:Ïse–ÿ}'c“ondŽ‘§Ç±:ÏptŽ– ä±;‘ª¨Ïbpp1Ž›wo±:Ï rstŽ‘µª±:ÏptŽ“±;‘ª¨Ïbpp0Ž˜±:Ï 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nition.Ž¡The–UUDEC“compiler“complained,“but“GCC“didn't.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂCircleŽ‘% Ö«functions‘@­1239“·i‘Ç«+·Ž¡‘ -ÂstaticŽ‘)HÚCircleŽ‘K[·Ž‘P\Ïcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“cir‘ÿ}'cleŽ’š ª«(ÂconstŽ‘*¢CircleŽ‘?ã#·Ž‘Dã$±pŽ‘L²<«=‘Ç0Ž‘Ç);ŽŽŽŒ‹mûO Šn ý‘ì·x«1248‘­3DLDFPRšÃŽG’Î^ýOPTIONAL–ÕXPOINTER“AR˜GUMENT‘«365Ž €n ý•@PÂ1248.Ž©·h–ª¨«De ne‘UUÂCircleŽ‘% Ö«functions‘@­1240“·i‘Ç«+·Ž¤ ‘ -ÂCircleŽ‘+¸‚·Ž‘0¸ƒÂCircleŽ‘P³«::‘Ïcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“cir‘ÿ}'cleŽ‘K R«(ÂconstŽ‘*¢CircleŽ‘?ã#·Ž‘Dã$±pŽ‘Ië$«)Ž¡‘ -·fŽ¡‘ÂCircleŽ‘5¸ƒ·Ž‘:¸„±cŽ‘AÓw«=‘ÇÂnewŽ‘Ïœ«(ÂCircleŽ‘c,«);Ž¦‘ÂifŽ‘´ú«(±pŽ‘Ï·6«=‘Ç0Ž–Ç)‘·Ž‘ -±cŽ‘ô«=‘Ç·Ž“±pŽ‘ Ï«;Ž¡‘±cŽ‘SÝŸ~ŽŽ‘SÞÏon‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘V¿è«=‘ÇÏtrueŽ‘‹°«;Ž¡‘±cŽ‘SÝŸ~ŽŽ‘SÞÏcycle‘‰ffŽ‘®switchŽ‘T«=‘ÇÏtrueŽ‘‹°«;Ž¡‘±cŽ‘SÝŸ~ŽŽ‘SÞÏline‘‰ffŽ‘®switchŽ‘N½·«=‘ÇÏfalseŽ‘v\«;Ž¡‘ÂreturnŽ‘7æ¼±cŽ‘<:—«;Ž¡‘ -·gŽŸÂ1249.‘ üRequired–ÕTCircle“argumen®9t.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.07.27.«]Ž‘Y;Made‘UUnon-inline.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂCircleŽ‘% 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üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.11.10.«]Ž‘Y;Changed–UUand“simpli ed“this“function.‘qÇIt“no¸ãw“uses“ÂEllipseŽ‘&>2«::Ž‘,ÌpÂopQÇeratorŽ‘Xc%«=Ž‘`*C(‘ª¨).Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂCircleŽ‘% Ö«functions‘@­1239“·i‘Ç«+·ŽŸ ‘ -ÂCircleŽ‘+¸‚«&Ž‘3 ÂopQÇeratorŽ‘_U«=Ž‘fÝs(ÂconstŽ‘*¢CircleŽ‘?ã#«&Ž‘GªA±cŽ‘Kþ«);ŽŽŽŒ‹n~ Šn ý‘ì«366›ÂCIR®9CLE‘ÕX­AR•ÃŽGUMENT’û±)3DLDFPR“G˜·x«1254Ž €n ý•@PÂ1254.Ž©·h–ª¨«De ne‘UUÂCircleŽ‘% Ö«functions‘@­1240“·i‘Ç«+·Ž¤ ‘ -ÂCircleŽ‘+¸‚«&Ž‘3 ÂCircleŽ‘RâЫ::Ž‘YqÂopQÇeratorŽ’…ë=Ž’ŒÎá(ÂconstŽ‘*¢CircleŽ‘?ã#«&Ž‘GªA±cŽ‘Kþ«)Ž¡‘ -·fŽ¡‘Ïr‘ÿ}'adiusŽ‘2=«=‘DZcŽ‘ó:Ïr‘ÿ}'adiusŽ‘È#«;Ž¡‘ÂEllipseŽ‘6èß«::Ž‘=wÂopQÇeratorŽ‘i Ò«=Ž‘pÔð(±cŽ‘SÛ«);Ž¡‘ÂreturnŽ‘7æ¼·Ž‘<æ½ÏthisŽ‘MÒs«;Ž¡‘ -·gŽŸÂ1255.– üEllipse‘8‚argumen®9t.“«This–Š/function“returns“a“reference“to“·Ž‘ Š0ÏthisŽ‘uæ«,‘×ewhic¸ãh“can“bGe“used“for“furtherŽ¡assignmen¸ãt.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.11.10.«]Ž‘Y;Changed–UUand“simpli ed“this“function.‘qÇIt“no¸ãw“uses“ÂEllipseŽ‘&>2«::Ž‘,ÌpÂopQÇeratorŽ‘Xc%«=Ž‘`*C(‘ª¨).Ž¡‘ -[¬LDF‘T2003.08.14.«]Ž‘YTAdded–¡coGde“for“handling“the“case“that“±eŽ›I:Ïaxis‘‰ffŽ‘®vŽ‘fù«and“±eŽ˜:Ïaxis‘‰ffŽ‘®hŽ‘š¨«di er“bš¸ãy“a“small“amoun˜t,Ž¡pšGossible–UUdue“to“imprecision“(see“b˜elo¸ãw).Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂCircleŽ‘% Ö«functions‘@­1239“·i‘Ç«+·Ž¡‘ -ÂCircleŽ‘+¸‚«&Ž‘3 ÂopQÇeratorŽ‘_U«=Ž‘fÝs(ÂconstŽ‘*¢EllipseŽ‘ChЫ&Ž‘K/î±eŽ‘O×ï«);ŽŽŽŒ‹oØ Šn ý‘ì·x«1256›­3DLDFPR•ÃŽG’÷âòÂELLIPSE‘ÕX­AR“GUMENT˜«367Ž €n ý•@PÂ1256.‘ ü«If‘sù±eŽ‘ú:Ïaxis‘‰ffŽ‘®vŽ‘Œö·6«=‘DZeŽ‘o:Ïaxis‘‰ffŽ‘®hŽ‘ù«,›¡ it's–sùquite“pGossible“that“the“di erence“is“negligible,˜and“the“result“of“imprecisionŽ¤ resulting–…nfrom“the“represenš¸ãtation“of“ oating“pGoin˜t“n˜um˜bšGers,‘‘tor“calculations“p˜erformed“on“them.‘Therefore,Ž¡wš¸ãe–qcompare“the“absolute“v‘ÿqÇalue“of“their“di erence“with“ÂP•®9oin“tŽ‘›½«::‘ÏepsilonŽ‘ o«(‘ª®)“instead“of“c˜hec˜king“whether“they'reŽ¡equal.‘qÇ[¬LDF‘T2003.08.14.«]ŽŽ¡‘ -It's–1also“pšGossible“that“one“of“them“has“an“in¸ãteger“v‘ÿqÇalue,–Ÿi.e.,“it–1has“only“zero˜es“follo¸ãwing“the“decimal“p˜oin¸ãt,Ž¡and–)the“other“deviates“bš¸ãy“a“small“amoun˜t.‘c In“this“case,‘1òw˜e“w˜an˜t“to“set“Ïr‘ÿ}'adiusŽ‘"U«to“half“of“the“former,‘1òbGecauseŽ¡it's–úðprobably“the“correct“v‘ÿqÇalue.‘b˜So,›$Vif“Ïe‘‰ffŽ–®axis‘‰ffŽ“vŽ‘*ã‘·‘ÛÏ o‘ÿ}'orŽ‘?¯«(Ïe‘‰ffŽ–®axis‘‰ffŽ“vŽ‘# ˆ«),˜w¸ãe“set“Ïr‘ÿ}'adiusŽ‘#¾«to“Ïe‘‰ffŽ–®axis‘‰ffŽ“vŽ‘'x±=«2Ž‘.‘b˜Otherwise,Ž¡wš¸ãe–Tset“Ïr‘ÿ}'adiusŽ‘$pS«to“Ïe‘‰ffŽ–®axis‘‰ffŽ“hŽ‘+ég«without“further“ado.‘nIf“Ïe‘‰ffŽ–®axis‘‰ffŽ“hŽ‘,ÿ·‘o°Ï o‘ÿ}'orŽ‘ÔF«(Ïe‘‰ffŽ–®axis‘‰ffŽ“hŽ‘#A7«),‘“Èso“m˜uc˜h“the“bGetter,‘“Èand“ifŽ¡it–Úisn't,›/|neither“it“nor“Ïe‘‰ffŽ–®axis‘‰ffŽ“vŽ‘+<«has“an“in¸ãteger“v‘ÿqÇalue,˜so“it“doGesn't“matter“whicš¸ãh“one“w˜e“use“to“set“Ïr‘ÿ}'adiusŽ‘Ëý«.Ž¡[¬LDF‘T2003.08.14.«]ŽŽ©·h–ª¨«De ne‘UUÂCircleŽ‘% Ö«functions‘@­1240“·i‘Ç«+·Ž¡‘ -ÂCircleŽ‘+¸‚«&Ž‘3 ÂCircleŽ‘RâЫ::Ž‘YqÂopQÇeratorŽ’…ë=Ž’ŒÎá(ÂconstŽ‘*¢EllipseŽ‘ChЫ&Ž‘K/î±eŽ‘O×ï«)Ž¡‘ -·fŽ¡‘ÂrealŽ‘*³0Ïe‘‰ffŽ–®axis‘‰ffŽ“vŽ‘P‡Ð«=‘DZeŽ‘o:Ïget‘‰ffŽ–®axis‘‰ffŽ“vŽ‘*ùš«(‘ª¨);Ž¡‘ÂrealŽ‘*³0Ïe‘‰ffŽ–®axis‘‰ffŽ“hŽ‘P»«=‘DZeŽ‘o:Ïget‘‰ffŽ–®axis‘‰ffŽ“hŽ‘+-I«(‘ª¨);Ž¦‘ÂifŽ‘´ú«(Ïe‘‰ffŽ–®axis‘‰ffŽ“vŽ‘%Ô ·6«=‘ÇÏe‘‰ffŽ–®axis‘‰ffŽ“hŽ‘&O«)‘·fŽ¡‘ÂifŽ‘)´û«(ÏfabsŽ‘2Ò«(Ïe‘‰ffŽ–®axis‘‰ffŽ“vŽ‘%Fh·‘8àÏe‘‰ffŽ–®axis‘‰ffŽ“hŽ‘%z«)–DZ>“ÂP•®9oin“tŽ‘ad«::Ž‘%ï¢ÏepsilonŽ‘E^¦«(‘ª¨))‘·fŽ¡‘(Ïc‘ÿ}'errŽ‘=”Ü·‘ß2Ý"ERROR!È ÝInÈ ÝCircle::oŽ‘kÞöperator=(Ellipse).\nŽ’ÔÞº"Ž’Ý„Q·‘ß2Ý"EllipseÈ ÝhasÈ ÝunequalŽ‘kÞöÈ Ýaxes.È Ý"Ž’™Dx·Ž¡‘<Ý"Can'tÈ ÝperformÈ ÝassigŽ’¤ÿÊnment.È ÝReturning.\n\Ž’ ÿŽn"Ž’ð«;Ž¡‘(ÂreturnŽ‘Kæ¾·Ž‘Pæ¿ÏthisŽ‘aÒu«;Ž¡‘·gŽ¡‘ÂelseŽ‘4.7ifŽ‘?ã/«(Ïe‘‰ffŽ–®axis‘‰ffŽ“vŽ–%Ô ·‘ÇÏ o‘ÿ}'orŽ‘+®«(Ïe‘‰ffŽ–®axis‘‰ffŽ“vŽ‘# ˆ«))‘Ïr‘ÿ}'adiusŽ‘#;«=‘ÇÏe‘‰ffŽ–®axis‘‰ffŽ“vŽ“±=«2±:«0ŽŽ‘ Ç;Ž¡‘ÂelseŽ‘5ØâÏr‘ÿ}'adiusŽ‘Th«=‘ÇÏe‘‰ffŽ–®axis‘‰ffŽ“hŽ‘&O±=«2±:«0ŽŽ‘ Ç;Ž¡‘·gŽ¡‘ÂelseŽ‘+ØáÏr‘ÿ}'adiusŽ‘Jh«=‘DZeŽ‘o:Ïget‘‰ffŽ–®axis‘‰ffŽ“vŽ‘*ùš«(‘ª¨)±=«2±:«0ŽŽ‘ Ç;Ž¡‘ÂEllipseŽ‘6èß«::Ž‘=wÂopQÇeratorŽ‘i Ò«=Ž‘pÔð(±eŽ‘¨«);Ž¡‘ÂreturnŽ‘7æ¼·Ž‘<æ½ÏthisŽ‘MÒs«;Ž¡‘ -·gŽ¤Â1257.‘ üReturning–ÕTelemen®9ts“and“information.Ž¡1258.– üIs‘pcircular.“«T‘ÿ*ªests–Ûçwhether“·Ž‘ÛèÏthisŽ‘£…«is“circular.‘|OpGerations“suc¸ãh“as“Ïsc‘ÿ}'aleŽ‘Ù«(›ª®)“and“Ïshe‘ÿ}'arŽ‘!«(˜)“can“causeŽ¤ ÂCirclesŽ‘&A½«to–UUbGecome“non-circular.‘qÇ[¬LDF‘T2003.07.25.«]ŽŽ¡‘ -Ïis‘‰ffŽ‘®cir‘ÿ}'cularŽ‘7¥«(›ª®)–„ rst“tests“whether“·Ž‘…ÏthisŽ‘¿«is“planar“using“Ïis‘‰ffŽ‘®planarŽ‘+@«(˜).›]×If“it's“not,‘%{ÏfalseŽ‘îC«is“returned.˜Otherwise,Ž¡the‘ÂP•®9oin“tŽ‘#šl±pŽ‘,¢~«is–set“to“·Ž‘ «(Ïp‘ÿ}'ointsŽ‘$•«[0Ž‘]),‘*Áand“ÂP•®9oin“tŽ‘#šl±cŽ‘+îY«=“Ïget‘‰ffŽ‘®c‘ÿ}'enterŽ‘0=Y«(‘ª®)“is“is“subtracted“from“±pŽ‘ «.‘qþ±pŽ‘ yþ:ÏmagnitudeŽ‘.=r«(‘ª¨)“isŽ¡then–UUstored“in“ÂrealŽ‘ƒÏmag0Ž‘2æZ«.‘qÇ[¬LDF‘T2003.07.25.«]ŽŽ¡‘ -Then,‘ÂıpŽ‘ -hã«is–žset“to“eac¸ãh“of“the“other“ÂP•®9oin“tsŽ‘%_«on“the“ÂCircleŽ‘#Ÿj«in“turn,‘ÂıcŽ‘ ´¾«is“subtracted“from“±pŽ›¦«,‘ÂÄand“±pŽ˜:ÏmagnitudeŽ‘.=r«(‘ª¨)Ž¡is–-:stored“in“ÂrealŽ‘¸MÏmagŽ‘-+«.‘diIf“the“absolute“v‘ÿqÇalue“of“the“di erence“ÏmagŽ‘^÷‘è«Ïmag0Ž‘ó¼«is“greater“than“ÂP•®9oin“tŽ‘dž«::‘ÏepsilonŽ‘ o«(‘ª®),Ž¡Ïis‘‰ffŽ‘®cir‘ÿ}'cularŽ‘-¥«(‘ª®)–Àimmediated“returns“ÏfalseŽ‘/«.‘ñIf“ÏfabsŽ‘²’«(ÏmagŽ‘H¯·‘ÿÑÏmag0Ž‘ݨ«)–¸r·“ÂP•®9oin“tŽ‘!R¾«::Ž‘'àüÏepsilonŽ‘GP«(‘ª¨)–Àfor“all“of“the“ÂP•®9oin“tsŽŽ¡·Ž‘«(Ïp‘ÿ}'ointsŽ‘$•«[±nŽ‘š«])–UUfor“±n–Ç>“«0,‘UUÏis‘‰ffŽ‘®cir‘ÿ}'cularŽ‘0úr«(‘ª®)–UUreturns“ÏtrueŽ‘í«.‘qÇ[¬LDF‘T2003.07.25.«]ŽŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.07.25.«]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂCircleŽ‘% Ö«functions‘@­1239“·i‘Ç«+·Ž¡‘ -Âb•QÇo“olŽ‘#¡gÏis‘‰ffŽ‘®cir‘ÿ}'cularŽ‘QF„«(Âv®9oidŽ‘¨ƒ«)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹pè Šn ý‘ì«368›­IS‘ÕXCIR•ÃŽCULAR’%~õ3DLDFPR“G˜·x«1259Ž €n ý•@PÂ1259.Ž©·h–ª¨«De ne‘UUÂCircleŽ‘% Ö«functions‘@­1240“·i‘Ç«+·Ž¤ ‘ -Âb•QÇo“olŽ‘#¡gCircleŽ‘C—«::‘Ïis‘‰ffŽ‘®cir‘ÿ}'cularŽ‘.¥!«(Âv®9oidŽ‘¨ƒ«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏtrueŽ‘‹°«;‘±=·–ÿý«false“·±=Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EnteringÈ ÝCircle::isŽ‘kÆÜ_circular().\n"Ž’» «;Ž¡‘ÂifŽ‘´ú«(·:Ïis‘‰ffŽ‘®planarŽ‘(&«(‘ª¨))‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)Ž¡‘(Ïc‘ÿ}'errŽ‘=Ök·‘ ÁÝ"InÈ ÝCircle::is_circuŽ‘l …lar():È Ý"Ž’™Ç–·‘ ÁÝ"*thisÈ ÝisÈ Ýnon-planarŽ‘l ….È ÝReturningÈ Ýfalse."Ž’Ó‡u·Ž¡‘<Ïend‘‚ØlŽ‘R¸à·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½ÏfalseŽ‘V–«;Ž¡‘·gŽ¦‘ÂP•®9oin“tŽ‘2pŽ‘7÷Ÿ«;Ž¡‘ÂP•®9oin“tŽ‘2cŽ‘: -’«=‘ÇÏget‘‰ffŽ‘®c‘ÿ}'enterŽ‘/_«(‘ª¨);Ž¡‘ÂrealŽ‘*³0Ïmag0Ž‘C‘«;Ž¡‘ÂrealŽ‘*³0ÏmagŽ‘=ü«;Ž¦‘Âv®9ectorŽ‘3ªJ·hÂP•®9oin“tŽ‘ï·Ž‘#ïži‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W«=‘ÇÏp‘ÿ}'ointsŽ‘ë­±:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¡‘±pŽ‘Ï«=‘Ç·Ž‘ÇŽ‘ ÇÏiterŽ‘Ÿÿ®+‘ÿ+ŽŽ‘,·‘8à±cŽ‘Œ»«;Ž¡‘Ïmag0Ž‘/¤ñ«=‘DZpŽ‘Ï:ÏmagnitudeŽ‘.=r«(‘ª¨);Ž¡‘ÂforŽ‘%舫(Âin®9tŽ‘¤÷±iŽ‘Þ«=‘Ç1Ž‘Ç;‘ÿýÏiterŽ‘’·6«=‘ÇÏp‘ÿ}'ointsŽ‘ë­±:ÏendŽ‘ಫ(‘ª¨);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘±pŽ‘%Ï«=‘Ç·Ž‘ÇŽ‘ ÇÏiterŽ‘Êø·‘8à±cŽ‘Œ»«;Ž¡‘ÏmagŽ‘4ù«=‘DZpŽ‘Ï:ÏmagnitudeŽ‘.=r«(‘ª¨);Ž¡‘ÂifŽ‘)´û«(ÏfabsŽ‘2Ò«(ÏmagŽ‘¾·‘8àÏmag0Ž‘·«)–DZ>“ÂP•®9oin“tŽ‘ad«::Ž‘%ï¢ÏepsilonŽ‘E^¦«(‘ª¨))‘·fŽ¡‘(ÂifŽ‘5?æ«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'errŽ‘ì·‘YFÝ"PointÈ Ý"Ž‘58Ü·‘YF±iŽ‘$€·‘YFÝ"È Ýdoesn'tÈ ÝlieÈ ÝonÈ ÝCirŽ‘nY -cle.\n"Ž’˜ø£·Ž¡‘FÝ"ExitingÈ ÝCircle::is_Ž’®ÿËcircular().\n"Ž’ûÍ!·‘ÇÝ"ReturningÈ Ýfalse.\n\Ž‘kÆÜn"Ž‘y”V·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾ÏfalseŽ‘`–«;Ž¡‘·gŽ¡‘€Ÿÿ®+‘ÿ+ŽŽ‘*G#±iŽ‘-¹«;Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ExitingÈ ÝCircle::is_Ž‘kÆÜcircular().È ÝReturninŽ’ÔÆ gÈ Ýtrue.\n"Ž’ ”·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘7æ¼ÏtrueŽ‘J«T«;Ž¡‘ -·gŽŸÂ1260.‘ üGet‘ÕTradius.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.05.10.«]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂCircleŽ‘% Ö«functions‘@­1239“·i‘Ç«+·Ž¡‘ -ÂinlineŽ‘)ŠIrealŽ‘@=wÏget‘‰ffŽ‘®r‘ÿ}'adiusŽ‘l9V«(‘ª®)Ž¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼Ïr‘ÿ}'adiusŽ‘S®ß«;Ž¡‘ -·gŽŸÂ1261.– üGet‘ÕTdiameter.“«[¬LDF‘T2002.05.10.«]Ž‘Zˆ6Added–UUthis“function.Ž¦·h–ª¨«Declare‘UUÂCircleŽ‘% Ö«functions‘@­1239“·i‘Ç«+·Ž¡‘ -ÂinlineŽ‘)ŠIrealŽ‘@=wÏget‘‰ffŽ‘®diameterŽ‘x<(«(‘ª®)Ž¡‘ -·fŽ¡‘ÂreturnŽ‘7漫(2Ž‘8á·‘8àÏr‘ÿ}'adiusŽ‘«);Ž¡‘ -·gŽŽŽŒ‹q)g Šn ý‘ì·x«1262–­3DLDFPRÃŽG’žçINTERSECTIONS“«369Ž €n ý•@PÂ1262.– üIn®9tersections.“«Neither–|¡GCC›|—nor“the“DEC˜compiler“could“resolv¸ãe“a“call“to“Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘U €«(‘ª®)Ž¤ with‘¥;ÂP•®9oin“tŽ‘ 侫argumenš¸ãts–¥;to“ÂEllipseŽ‘%Ž«::‘Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã«(‘ª®),‘Èsafter“a“ÂCircleŽ‘#­¢«v˜ersion“with“a“ÂCircleŽ‘#­¢«argumen˜t“hadŽ¡bGeen–¤declared.‘^TO›¤DO:“I˜didn't“think“this“w¸ãould“happGen,‘·Åso“I˜should“probably“review“the“rules“go•¸ãv“erningŽ¡resolution–UUof“calls“to“functions“on“ob‘Ž8jects“of“deriv¸ãed“classes.‘qÇ[¬LDF‘T2003.07.09.«]ŽŽ¡‘ -Therefore,‘/ÔI'vš¸ãe–&tadded“ÂCircleŽ‘$°«v˜ersions“of“this“function,‘/Ôwith“ÂP•®9oin“tŽ‘!ç0«and“ÂP®9athŽ‘ÞL«argumen˜ts,‘/Ôthat“simply“callŽ¡the‘UUÂEllipseŽ‘(“ƒ«vš¸ãersions,–UUand“return“their“return“v‘ÿqÇalues.‘qÇThis“solv˜es“the“problem.‘qÇ[¬LDF‘T2003.07.09.«]ŽŽ¡‘ -The–Ï¡program“executed“correctly“under“Linš¸ãux,‘î4after“I‘Ï‚recompiled“with“GCC.“Ho˜w˜ev˜er,›î4under“T‘ÿ*ªru65,˜theŽ¡program–ÑNcaused“a“\Memory“fault"“error.‘å³After“I‘Ñ/remo•¸ãv“ed–ÑNthe“ob‘Ž8ject“ les,‘ðMand“recompiled“(with“the“DECŽ¡compiler),–UUthe“problem“disappGeared.‘qÇ[¬LDF‘T2003.07.09.«]ŽŽ¡‘ -[¬LDF‘T2003.07.18.«]Ž‘Y;TO–UUDO:“Add“ÂCircleŽ‘"¸…«::‘Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã«(ÂconstŽ‘*¢EllipseŽ‘ChЫ&Ž‘K/î)“andŽ¡ÂEllipseŽ‘"èÝ«::‘Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã«(ÂconstŽ‘*¢CircleŽ‘?ã#«&Ž‘GªA).Ž©Â1263.‘ üP•®9oin“t‘ÕTargumen“t.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.07.09.«]Ž‘Y;Added–UUthis“function.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂCircleŽ‘% Ö«functions‘@­1239“·i‘Ç«+·ŽŸ ‘ -ÂvirtualŽ‘/Ôb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ’€òÂÏinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ’Ò¡«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]Ïpt0Ž‘TJ˜±;‘ª¨ÂconstŽ‘ÕJP•®9oin“tŽ‘>Äç«&Ž‘FŒÏpt1Ž‘Uõ@«)‘UUÂconstŽ‘*¢«;Ž¦Â1264.Ž¡·h–ª¨«De ne‘UUÂCircleŽ‘% Ö«functions‘@­1240“·i‘Ç«+·Ž¤ ‘ -Âb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘[dïCircleŽ‘zÈ«::‘Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]Ïpt0Ž‘TJ˜±;‘ª¨ÂconstŽ‘ÕJP•®9oin“tŽ‘>Äç«&Ž‘FŒÏpt1Ž‘Uõ@«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼EllipseŽ‘ZÏ™«::‘Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã«(Ïpt0Ž‘i;±;‘ª¨Ïpt1Ž‘ã«);Ž¡‘ -·gŽ¦Â1265.‘ üP•®9ath‘ÕTargumen“t.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.07.09.«]Ž‘Y;Added–UUthis“function.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂCircleŽ‘% Ö«functions‘@­1239“·i‘Ç«+·ŽŸ ‘ -ÂvirtualŽ‘/Ôb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ’€òÂÏinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ’Ò¡«(ÂconstŽ‘*¢P®9athŽ‘:[«&Ž‘AØy±pŽ‘Fày«)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹r4Ù Šn ý‘ì«370›ÂP–ÿ -«A“TH‘ÕX­AR•ÃŽGUMENT’Í–3DLDFPR“G˜·x«1266Ž €n ý•@PÂ1266.Ž©·h–ª¨«De ne‘UUÂCircleŽ‘% Ö«functions‘@­1240“·i‘Ç«+·Ž¤ ‘ -Âb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘[dïCircleŽ‘zÈ«::‘Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã«(ÂconstŽ‘*¢P®9athŽ‘:[«&Ž‘AØy±pŽ‘Fày«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼EllipseŽ‘ZÏ™«::‘Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã«(±pŽ‘«);Ž¡‘ -·gŽŸÂ1267.‘ üCircle‘ÕTargumen®9t.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.07.20.«]Ž‘Yê5W›ÿ*ªrote–7Othe“de nition“of“this“function.‘´T˜ested“all“cases.‘´It“should“probably“bGe“testedŽ¡more‘UUthoroughly‘ÿ*ª.Ž¡‘ -[¬LDF‘T2003.08.14.«]Ž‘X´!Made‘;Ïverb‘ÿ}'oseŽ›&“Ó«argumen¸ãt–;non-ÂconstŽ‘ÕM«.‘U¿Setting“Ïverb‘ÿ}'oseŽ˜«to“ÏtrueŽ‘Ç«if“ÝVERBOSE_GLOBALŽ‘P´«is“ÏtrueŽ‘ÅÓ«.Ž¡Added‘UUÝVERBOSE_GLOBALŽ‘P°è«to–UUÈpspglb.web“«toGda¸ãy‘ÿ*ª.Ž¡‘ -[¬LDF‘T2003.08.27.«]Ž‘Y;Remo•¸ãv“ed–UUthe“declaration“ÂrealŽ‘ƒÏc‘‰ffŽ‘®r‘ÿ}'adiusŽ‘Am¥«=“±cŽ‘©0:Ïr‘ÿ}'adiusŽ‘È#«,“since“Ïc‘‰ffŽ‘®r‘ÿ}'adiusŽ‘*ºw«wš¸ãas“nev˜er“used.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂCircleŽ‘% Ö«functions‘@­1239“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/Ôb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜quadrupleŽ’ŸtÏinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ’ñ^«(ÂconstŽ‘*¢CircleŽ‘?ã#«&Ž‘GªA±cŽ‘Kþ;‘ª¨Âb•QÇo“olŽ‘LÏverb‘ÿ}'oseŽ‘>¤ƒ«=‘ÇÏfalseŽ‘v\«)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹s@j Šn ý‘ì·x«1268›­3DLDFPR•ÃŽG’û±)ÂCIR®9CLE‘ÕX­AR“GUMENT˜«371Ž €n ý•@PÂ1268.Ž©·h–ª¨«De ne‘UUÂCircleŽ‘% Ö«functions‘@­1240“·i‘Ç«+·Ž¤ ‘ -Âb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜quadrupleŽ‘yæ¬CircleŽ’™IÜ«::‘Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã«(ÂconstŽ‘*¢CircleŽ‘?ã#«&Ž‘GªA±cŽ‘Kþ;‘ª¨Âb•QÇo“olŽ‘LÏverb‘ÿ}'oseŽ‘;Ýk«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂifŽ‘´ú«(ÝVERBOSE_GLOBALŽ‘J>«)‘Ïverb‘ÿ}'oseŽ‘(Xu«=‘ÇÏtrueŽ‘‹°«;Ž¡‘ÂifŽ‘";¼«(ÝDEBUGŽ‘®c·_‘è -Ïverb‘ÿ}'oseŽ‘$yg«)‘Ïc‘ÿ}'outŽ‘V7·‘ýÝ"*******************Ž‘oüÄ***\n"Ž’—·Ž¡‘2Ý"\nEnteringÈ ÝCircle::Ž’šÿÉintersection_points(Ž’ÿconstÈ ÝCircle&)\n\n"Ž’hE¼«;Ž¦‘Âb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜quadrupleŽ’ƒæ­Ïbp‘ÿ}'qŽ’•ßá«=‘ÇÝINVALID_BOOL_POINT_QUADRUPLEŽ’–M,«;Ž¡‘ÂPlaneŽ‘46ºÏthis‘‰ffŽ‘®planeŽ‘b…Ì«=‘ÇÏget‘‰ffŽ‘®planeŽ‘+>«(‘ª¨);Ž¡‘ÂPlaneŽ‘46ºÏc‘‰ffŽ‘®planeŽ‘Wˆ¨«=‘DZcŽ‘ó:Ïget‘‰ffŽ‘®planeŽ‘(vè«(‘ª¨);Ž¦‘ÂifŽ‘´ú«(·:«(Ïthis‘‰ffŽ‘®planeŽ‘+‡ú±:ÏnormalŽ–#з‘ÇÏc‘‰ffŽ‘®planeŽ‘#Qî±:ÏnormalŽ‘"˜·_‘8àÏthis‘‰ffŽ‘®planeŽ‘-ÀÚ±:ÏnormalŽ“·‘ÇŽ‘ -Ž6Ïc‘‰ffŽ‘®planeŽ‘+ ±:ÏnormalŽ‘ V¸«))‘·fŽ¡‘ÂifŽ‘+íÌ«(Ïverb‘ÿ}'oseŽ‘$Eq·_‘´ÝDEBUGŽ‘zm«)‘Ïc‘ÿ}'outŽ‘ÔR·‘{Ý"CirclesÈ ÝareÈ Ýnon-copŽ‘ozßlanar.È Ý"Ž’ |J·Ž¡‘<Ý"CallingÈ ÝEllipse::inŽ’¤ÿÊtersection_points()\Ž’ ÿŽn\n"Ž’&M·‘ÇÏ ushŽ‘€«;Ž¡‘Ïbp‘ÿ}'qŽ‘/ù7«=‘ÇÂEllipseŽ‘%¯õ«::Ž‘,>3Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘}Ë«(±cŽ‘SÛ;‘ª¨Ïverb‘ÿ}'oseŽ‘"<«);Ž¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)Ž¡‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÝ"ExitingÈ ÝCircle::intŽ‘kÆÜersection_points(conŽ’ÔÆ stÈ ÝCircle&)"Ž’ü·‘ÇÏend‘‚ØlŽ–ò·‘ÇÏend‘‚ØlŽ“·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½Ïbp‘ÿ}'qŽ‘QÙ«;Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘ÂifŽ‘)´û«(Ïverb‘ÿ}'oseŽ‘"Ê=·_‘8àÝDEBUGŽ‘ÿ9«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"CirclesÈ ÝareÈ ÝcoplanaŽ‘kÆÜr.\n"Ž’†5«;Ž¦‘ÂrealŽ‘4³1ÏdistŽ‘H†¶«=‘Ç(±cŽ‘SÛ:Ïc‘ÿ}'enterŽ–Bk·‘8àÏc‘ÿ}'enterŽ“«)±:ÏmagnitudeŽ‘.=r«(‘ª¨);Ž¦‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"distÈ Ý==È Ý"Ž‘:”z·‘ÇÏdistŽ‘š·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ÂifŽ‘)´û«(ÏdistŽ‘Ó…·‘Ç«0Ž‘Ç)‘·fŽ¡‘(ÂifŽ‘3´ü«(Ïverb‘ÿ}'oseŽ‘"Ê=·_‘8àÝDEBUGŽ‘ÿ9«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"CirclesÈ ÝhaveÈ ÝsameÈ ÝcŽ‘kÆÜenter.\n"Ž’›)«;Ž¡‘(ÂifŽ‘3´ü«(Ïr‘ÿ}'adiusŽ‘;·‘DZcŽ‘ó:Ïr‘ÿ}'adiusŽ‘È#«)‘·fŽ¡‘2ÂifŽ‘=´ý«(Ïverb‘ÿ}'oseŽ‘"Ê=·_‘8àÝDEBUGŽ‘ÿ9«)‘·fŽ¡‘<Ïc‘ÿ}'outŽ‘Rnâ·‘¥Ý"CirclesÈ ÝareÈ ÝcongrueŽ‘lint.È Ý"Ž’‰ñg·‘¥Ý"ReturningÈ ÝINVALID_BŽ‘liOOL_POINT_QUADRUPLE.Ž’Õ-\ŽŽ¡‘P\n\n"Ž‘my·‘ÇÏ ushŽ‘€«;Ž¡‘2·gŽ¡‘2ÂifŽ‘>/T«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ì5·‘’þÝ"\nExitingÈ ÝCircle::iŽ‘l’Ântersection_points(cŽ’Õ’†onstÈ ÝCircle&)."Ž’(k¿·Ž¡‘PÏend‘‚ØlŽ‘f¸â·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘2ÂreturnŽ‘Uæ¿ÝINVALID_BOOL_POINT_QUADRUPLEŽ’élÓ«;Ž¡‘(·gŽ¡‘(ÂelseŽ‘>.8ifŽ‘Iã0«(Ïr‘ÿ}'adiusŽ‘;±>‘ÇcŽ‘ó:Ïr‘ÿ}'adiusŽ‘È#«)‘·fŽ¡‘2ÂifŽ‘=´ý«(Ïverb‘ÿ}'oseŽ‘"Ê=·_‘8àÝDEBUGŽ‘ÿ9«)‘·fŽ¡‘<Ïc‘ÿ}'outŽ‘R¦ä·‘M§Ý"*thisÈ ÝandÈ ÝcÈ ÝlieÈ ÝoutŽ‘lMksideÈ ÝofÈ ÝeachÈ Ýother.È Ž’ÕM/ÝNoÈ Ýintersections."Ž’7¡·‘M§Ïend‘‚ØlŽ‘·Ž¡‘PÝ"ReturningÈ ÝINVALID_BŽ’¸ÿÌOOL_POINT_QUADRUPLE.Ž’!ÿ\n\n"Ž’?·‘ÇÏ ushŽ‘€«;Ž¡‘2·gŽ¡‘2ÂifŽ‘>/T«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ì5·‘’þÝ"\nExitingÈ ÝCircle::iŽ‘l’Ântersection_points(cŽ’Õ’†onstÈ ÝCircle&)."Ž’(k¿·Ž¡‘PÏend‘‚ØlŽ‘f¸â·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘2ÂreturnŽ‘Uæ¿ÝINVALID_BOOL_POINT_QUADRUPLEŽ’élÓ«;Ž¡‘(·gŽ¡‘(ÂelseŽ‘>.8ifŽ‘Iã0«(Ïr‘ÿ}'adiusŽ‘;±<‘ÇcŽ‘ó:Ïr‘ÿ}'adiusŽ‘È#«)‘·fŽ¡‘2ÂifŽ‘=´ý«(Ïverb‘ÿ}'oseŽ‘"Ê=·_‘8àÝDEBUGŽ‘ÿ9«)‘·fŽ¡‘<Ïc‘ÿ}'outŽ‘Tôì·‘›¯Ý"*thisÈ ÝliesÈ ÝinsideÈ ÝcŽ‘n›s.È ÝNoÈ Ýintersections."Ž’ݽN·‘›¯Ïend‘‚ØlŽ‘) ·Ž¡‘PÝ"ReturningÈ ÝINVALID_BŽ’¸ÿÌOOL_POINT_QUADRUPLE.Ž’!ÿ\n\n"Ž’?·‘ÇÏ ushŽ‘€«;Ž¡‘2·gŽ¡‘2ÂifŽ‘>/T«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ì5·‘’þÝ"\nExitingÈ ÝCircle::iŽ‘l’Ântersection_points(cŽ’Õ’†onstÈ ÝCircle&)."Ž’(k¿·Ž¡‘PÏend‘‚ØlŽ‘f¸â·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘2ÂreturnŽ‘Uæ¿ÝINVALID_BOOL_POINT_QUADRUPLEŽ’élÓ«;ŽŽŽŒ‹tF‡ Šn ý‘ì«372›ÂCIR®9CLE‘ÕX­AR•ÃŽGUMENT’û±)3DLDFPR“G˜·x«1268Ž €n ý•@P‘(·gŽ¤ ‘(ÂelseŽ‘?Øã·fŽ¡‘2Ïc‘ÿ}'errŽ‘GÜ«·‘'Ý"ERROR!È ÝInÈ Ý"Ž‘EÔD·‘'Ý"|Circle::intersectiŽ‘l&Äon_points(constÈ ÝCircŽ’Õ&ˆle&)|"Ž’øSÞ·‘'Ïend‘‚ØlŽ‘?·Ž¡‘FÝ"ThisÈ Ýcan'tÈ Ýhappen!"Ž’²Ç‹·‘AXÝ"radiusÈ Ýand/orÈ Ýc.radŽ‘lAiusÈ ÝhaveÈ ÝinvalidÈ ÝvalŽ’Õ@àues:\n"Ž’ýÈ‹·Ž¡‘FÝ"radiusÈ Ý=È Ý"Ž’„¾ì·‘xžÏr‘ÿ}'adiusŽ‘$¹_·‘xžÏend‘‚ØlŽ–âþ·‘xžÝ"c.radiusÈ Ý=È Ý"Ž‘M·}·‘xž±cŽ‘Ìy:Ïr‘ÿ}'adiusŽ‘ @Á·‘xžÏend‘‚ØlŽ“·Ž¡‘FÝ"ReturningÈ ÝINVALID_BŽ’®ÿËOOL_POINT_QUADRUPLE.Ž’ÿ\n\n"Ž’5·‘ÇÏ ushŽ‘€«;Ž¡‘2ÂifŽ‘>/T«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ì5·‘’þÝ"\nExitingÈ ÝCircle::iŽ‘l’Ântersection_points(cŽ’Õ’†onstÈ ÝCircle&)."Ž’(k¿·Ž¡‘PÏend‘‚ØlŽ‘f¸â·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘2ÂreturnŽ‘Uæ¿ÝINVALID_BOOL_POINT_QUADRUPLEŽ’élÓ«;Ž¡‘(·gŽ¡‘g‘±=·‘ÿýÂifŽ‘´õ«(ÏdistŽ‘Ó…·‘Ç«0Ž‘Ç)‘ÿý·±=Ž¡‘ÂelseŽ‘4.7ifŽ‘?ã/«(ÏdistŽ‘Ó…±>‘Ç«(Ïr‘ÿ}'adiusŽ‘«+‘8à±cŽ‘Œ»:Ïr‘ÿ}'adiusŽ‘È#«))‘·fŽ¡‘(ÂifŽ‘3´ü«(Ïverb‘ÿ}'oseŽ‘"Ê=·_‘8àÝDEBUGŽ‘ÿ9«)Ž¡‘2Ïc‘ÿ}'outŽ‘HÛu·‘‚9Ý"*thisÈ ÝandÈ ÝcÈ ÝlieÈ ÝoutŽ‘lýsideÈ ÝofÈ ÝeachÈ Ýother.È Ž’ÕÁÝ"Ž’ÞÊ_·‘‚9Ý"NoÈ Ýintersections.\nŽ‘lý"Ž‘uÊ›·Ž¡‘FÝ"ReturningÈ ÝINVALID_BŽ’®ÿËOOL_POINT_QUADRUPLE.Ž’ÿ\n\n"Ž’5·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂifŽ‘3ËK«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘E|·‘ìEÝ"\nExitingÈ ÝCircle::iŽ‘kì ntersection_points(cŽ’ÔëÍonstÈ ÝCircle&)."Ž’'M·‘ìEÏend‘‚ØlŽ‘ÊL·Ž¡‘FÏend‘‚ØlŽ‘\¸á·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾ÝINVALID_BOOL_POINT_QUADRUPLEŽ’ßlÒ«;Ž¡‘·gŽ¡‘ÂelseŽ‘4.7ifŽ‘?ã/«(ÏdistŽ‘Ó…·‘Ç«(Ïr‘ÿ}'adiusŽ‘«+‘8à±cŽ‘Œ»:Ïr‘ÿ}'adiusŽ‘È#«))‘·fŽ¡‘(ÂifŽ‘4œa«(Ïverb‘ÿ}'oseŽ‘#d€·_‘Ó#ÝDEBUGŽ‘™|«)‘Ïc‘ÿ}'outŽ‘¡ö·‘H¿Ý"thisÈ ÝandÈ ÝcÈ ÝhaveÈ ÝaÈ ÝtŽ‘mHƒangentÈ ÝonÈ ÝtheÈ ÝoutsidŽ’ÖHGeÈ Ý"Ž’ê×e·Ž¡‘FÝ"(oneÈ ÝintersectionÈ ÝpŽ’®ÿËoint).\n"Ž’ÞÆ«;Ž¡‘(Ïbp‘ÿ}'qŽ‘72 ±:Ï rstŽ‘µª±:ÏptŽ‘ ä±:ÏsetŽ‘ x„«(±cŽ‘SÛ:Ïc‘ÿ}'enterŽ–Bk·‘8àÏc‘ÿ}'enterŽ“«);Ž¡‘(Ïbp‘ÿ}'qŽ‘72 ±:Ï rstŽ‘µª±:ÏptŽ‘ ä±:Ïunit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u«(ÏtrueŽ‘Ę«);Ž¡‘(Ïbp‘ÿ}'qŽ‘72 ±:Ï rstŽ‘µª±:ÏptŽ‘ «µ·«=ŽŽ‘9ìÏr‘ÿ}'adiusŽ‘8«;Ž¡‘(Ïbp‘ÿ}'qŽ‘72 ±:Ï rstŽ‘µª±:ÏptŽ‘ ä±:ÏshiftŽ‘}«(Ïc‘ÿ}'enterŽ‘ ‹«);Ž¡‘(Ïbp‘ÿ}'qŽ‘72 ±:Ï rstŽ‘µª±:bŽ‘«=‘ÇÏtrueŽ‘‹°«;Ž¡‘(ÂifŽ‘3ËK«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘E|·‘ìEÝ"\nExitingÈ ÝCircle::iŽ‘kì ntersection_points(cŽ’ÔëÍonstÈ ÝCircle&)."Ž’'M·‘ìEÏend‘‚ØlŽ‘ÊL·Ž¡‘FÏend‘‚ØlŽ‘\¸á·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾Ïbp‘ÿ}'qŽ‘[Ú«;Ž¡‘·gŽ¡‘ÂelseŽ‘4.7ifŽ‘?ã/«(ÏdistŽ‘Ó…·‘ÇÏmaxŽ‘k³«(Ïr‘ÿ}'adiusŽ–È#±;‘ª¨cŽ›þƒ:Ïr‘ÿ}'adiusŽ“«)–8à·“ÏminŽ‘]õ«(Ïr‘ÿ}'adiusŽ–È#±;‘ª¨cŽ˜:Ïr‘ÿ}'adiusŽ“«))‘·fŽ¡‘(ÂifŽ‘4œa«(Ïverb‘ÿ}'oseŽ‘#d€·_‘Ó#ÝDEBUGŽ‘™|«)‘Ïc‘ÿ}'outŽ‘¡ö·‘H¿Ý"*thisÈ ÝandÈ ÝcÈ ÝhaveÈ ÝaÈ Ž‘mHƒÝtangentÈ ÝonÈ ÝtheÈ ÝinsidŽ’ÖHGeÈ Ý"Ž’ê×e·Ž¡‘FÝ"(oneÈ ÝintersectionÈ ÝpŽ’®ÿËoint).\n"Ž’ÞÆ«;Ž¡‘(ÂifŽ‘3´ü«(Ïr‘ÿ}'adiusŽ‘;±>‘ÇcŽ‘ó:Ïr‘ÿ}'adiusŽ‘È#«)‘·fŽ¡‘2ÂifŽ‘=´ý«(Ïverb‘ÿ}'oseŽ‘"Ê=·_‘8àÝDEBUGŽ‘ÿ9«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"cÈ ÝliesÈ ÝwithinÈ Ý*thisŽ‘kÆÜ.\n"Ž’M8«;Ž¡‘2Ïbp‘ÿ}'qŽ‘A2!±:Ï rstŽ‘µª±:ÏptŽ‘ ä±:ÏsetŽ‘ x„«(±cŽ‘SÛ:Ïc‘ÿ}'enterŽ–Bk·‘8àÏc‘ÿ}'enterŽ“«);Ž¡‘(·gŽ¡‘(ÂelseŽ‘?Øã·fŽ¡‘2ÂifŽ‘=´ý«(Ïverb‘ÿ}'oseŽ‘"Ê=·_‘8àÝDEBUGŽ‘ÿ9«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"*thisÈ ÝliesÈ ÝwithinÈ ÝcŽ‘kÆÜ.\n"Ž’M8«;Ž¡‘2Ïbp‘ÿ}'qŽ‘A2!±:Ï rstŽ‘µª±:ÏptŽ‘ ä±:ÏsetŽ‘ x„«(Ïc‘ÿ}'enterŽ‘Bk·‘8à±cŽ‘Œ»:Ïc‘ÿ}'enterŽ‘ ‹«);Ž¡‘(·gŽ¡‘(Ïbp‘ÿ}'qŽ‘72 ±:Ï rstŽ‘µª±:ÏptŽ‘ ä±:Ïunit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u«(ÏtrueŽ‘Ę«);Ž¡‘(Ïbp‘ÿ}'qŽ‘72 ±:Ï rstŽ‘µª±:ÏptŽ‘ «µ·«=ŽŽ‘9ìÏr‘ÿ}'adiusŽ‘8«;Ž¡‘(Ïbp‘ÿ}'qŽ‘72 ±:Ï rstŽ‘µª±:ÏptŽ‘ ä±:ÏshiftŽ‘}«(Ïc‘ÿ}'enterŽ‘ ‹«);Ž¡‘(Ïbp‘ÿ}'qŽ‘72 ±:Ï rstŽ‘µª±:bŽ‘«=‘ÇÏtrueŽ‘‹°«;Ž¡‘(ÂifŽ‘3ËK«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘E|·‘ìEÝ"\nExitingÈ ÝCircle::iŽ‘kì ntersection_points(cŽ’ÔëÍonstÈ ÝCircle&)."Ž’'M·‘ìEÏend‘‚ØlŽ‘ÊL·Ž¡‘FÏend‘‚ØlŽ‘\¸á·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾Ïbp‘ÿ}'qŽ‘[Ú«;Ž¡‘·gŽ¡‘ÂelseŽ‘4.7ifŽ‘?ã/«(ÏdistŽ‘Ó…±<‘Ç«(Ïr‘ÿ}'adiusŽ‘«+‘8à±cŽ‘Œ»:Ïr‘ÿ}'adiusŽ‘È#«))‘·fŽ¡‘(ÂifŽ‘3´ü«(ÏdistŽ‘Ó…±>‘ÇÏmaxŽ‘k³«(Ïr‘ÿ}'adiusŽ–È#±;‘ª¨cŽ›þƒ:Ïr‘ÿ}'adiusŽ“«)–8à·“ÏminŽ‘]õ«(Ïr‘ÿ}'adiusŽ–È#±;‘ª¨cŽ˜:Ïr‘ÿ}'adiusŽ“«))‘·fŽŽŽŒ‹uWÿ Šn ý‘ì·x«1268›­3DLDFPR•ÃŽG’û±)ÂCIR®9CLE‘ÕX­AR“GUMENT˜«373Ž €n ý•@P‘2ÂifŽ‘=´ý«(Ïverb‘ÿ}'oseŽ‘"Ê=·_‘8àÝDEBUGŽ‘ÿ9«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"tÈ ÝandÈ ÝcÈ ÝhaveÈ Ý2È ÝinteŽ‘kÆÜrsections.\n"Ž’°«;Ž©‘2ÂrealŽ‘H³3±aŽ‘PÃ{«=‘ÇÏr‘ÿ}'adiusŽ‘;«;Ž¤ ‘2ÂrealŽ‘H³3ÏbbŽ‘UÑë«=‘DZcŽ‘ó:Ïr‘ÿ}'adiusŽ‘·‘8à±cŽ‘Œ»:Ïr‘ÿ}'adiusŽ‘È#«;Ž¡‘2ÂrealŽ‘H³3Ïb‘ÿ}'etaŽ‘]àÈ«=‘Ç2Ž‘ ÿù·‘8àÏatanŽ‘ªÀ«(ÏsqrtŽ‘¯ù«((ÏbbŽ‘ €·–8à«((ÏdistŽ›EM·“±aŽ‘‚«)“·“«(ÏdistŽ˜·“±aŽ‘‚«)))±=«(((ÏdistŽ˜«+“±aŽ‘‚«)“·“«(ÏdistŽ˜«+“±aŽ‘‚«))“·“ÏbbŽ‘ €«)));Ž¦‘2Ïb‘ÿ}'etaŽ‘G-š·«=ŽŽ‘V»Ñ180ŽŽ‘e»Ô±=ÝPIŽ‘ b«;Ž¡‘2ÂifŽ‘=´ý«(Ïverb‘ÿ}'oseŽ‘"Ê=·_‘8àÝDEBUGŽ‘ÿ9«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"betaÈ Ý==È Ý"Ž‘:”z·‘ÇÏb‘ÿ}'etaŽ‘ô­·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¦‘2ÂP•®9oin“tŽ‘PPŽ‘X¾¿«(±cŽ‘SÛ:Ïc‘ÿ}'enterŽ–Bk·‘8àÏc‘ÿ}'enterŽ“«);Ž¦‘2±PŽ‘9Ï":Ïunit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u«(ÏtrueŽ‘Ę«);Ž¡‘2±PŽ‘<–:·«=ŽŽ‘L$qÏr‘ÿ}'adiusŽ‘g씫;Ž¡‘2±PŽ‘9Ï":ÏshiftŽ‘}«(Ïc‘ÿ}'enterŽ‘ ‹«);Ž¦‘2ÂP•®9oin“tŽ‘Pï¢ÏnormalŽ‘t r«=‘ÇÏget‘‰ffŽ‘®normalŽ‘3QŒ«(‘ª¨);Ž¦‘2ÏnormalŽ‘RV½±:ÏshiftŽ‘}«(Ïc‘ÿ}'enterŽ‘ ‹«);Ž¡‘2ÂifŽ‘=´ý«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘<±PŽ‘CÏ#:Ïdotlab‘ÿ}'elŽ‘!ÿó«(Ý"P"Ž‘F_«);Ž¡‘<±PŽ‘CÏ#:ÏshowŽ‘Šÿ«(Ý"P"Ž‘F_«);Ž¡‘<ÏnormalŽ‘\V¾±:ÏshowŽ‘Šÿ«(Ý"normal"Ž‘*†P«);Ž¡‘2·gŽ¡‘2Ïbp‘ÿ}'qŽ‘A2!±:Ï rstŽ‘µª±:bŽ‘«=‘ÇÏtrueŽ‘‹°«;Ž¡‘2Ïbp‘ÿ}'qŽ‘A2!±:Ï rstŽ‘µª±:ÏptŽ‘ «µ«=‘DZPŽ‘ -–5«;Ž¡‘2Ïbp‘ÿ}'qŽ‘A2!±:Ï rstŽ‘µª±:ÏptŽ‘ ä±:Ïr‘ÿ}'otateŽ‘o>«(Ïc‘ÿ}'enterŽ‘ ‹±;‘ª¨ÏnormalŽ‘"`±;‘ª¨Ïb‘ÿ}'etaŽ‘%«);Ž¡‘2ÂifŽ‘=´ý«(ÝDEBUGŽ‘ÆY«)‘Ïbp‘ÿ}'qŽ‘2±:Ï rstŽ‘µª±:ÏptŽ‘ ä±:ÏshowŽ‘Šÿ«(Ý"bpq.first.pt"Ž‘J>«);Ž¡‘2Ïbp‘ÿ}'qŽ‘A2!±:Ïse–ÿ}'c“ondŽ‘§Ç±:bŽ‘«=‘ÇÏtrueŽ‘‹°«;Ž¡‘2Ïbp‘ÿ}'qŽ‘A2!±:Ïse–ÿ}'c“ondŽ‘§Ç±:ÏptŽ‘ «µ«=‘DZPŽ‘ -–5«;Ž¡‘2Ïbp‘ÿ}'qŽ‘A2!±:Ïse–ÿ}'c“ondŽ‘§Ç±:ÏptŽ‘ ä±:Ïr‘ÿ}'otateŽ‘o>«(Ïc‘ÿ}'enterŽ‘ ‹±;‘ª¨ÏnormalŽ‘"`±;‘ª¨·Ž‘ qÆÏb‘ÿ}'etaŽ‘ØC«);Ž¡‘2ÂifŽ‘=´ý«(ÝDEBUGŽ‘ÆY«)‘Ïbp‘ÿ}'qŽ‘2±:Ïse–ÿ}'c“ondŽ‘§Ç±:ÏptŽ‘ ä±:ÏshowŽ‘Šÿ«(Ý"bpq.second.pt"Ž‘OF;«);Ž¡‘2ÂifŽ‘>/T«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ì5·‘’þÝ"\nExitingÈ ÝCircle::iŽ‘l’Ântersection_points(cŽ’Õ’†onstÈ ÝCircle&)."Ž’(k¿·Ž¡‘PÏend‘‚ØlŽ‘f¸â·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘2ÂreturnŽ‘Uæ¿Ïbp‘ÿ}'qŽ‘eÛ«;Ž¡‘(·gŽ¡‘(ÂelseŽ‘>.8ifŽ‘Iã0«(Ïr‘ÿ}'adiusŽ‘;±>‘ÇcŽ‘ó:Ïr‘ÿ}'adiusŽ‘È#«)‘·fŽ¡‘2ÂifŽ‘=´ý«(Ïverb‘ÿ}'oseŽ‘"Ê=·_‘8àÝDEBUGŽ‘ÿ9«)Ž¡‘<Ïc‘ÿ}'outŽ‘R[w·‘:Ý"cÈ ÝliesÈ ÝwithinÈ Ý*thisŽ‘lþ,È ÝdifferentÈ ÝcentersÈ Ž’ÕÂÝ"Ž’ÝÊa·‘:Ý"(noÈ Ýintersections).Ž‘lþ\n"Ž‘J—·Ž¡‘PÝ"ReturningÈ ÝINVALID_BŽ’¸ÿÌOOL_POINT_QUADRUPLE.Ž’!ÿ\n"Ž’2Eï«;Ž¡‘2ÂifŽ‘>/T«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ì5·‘’þÝ"\nExitingÈ ÝCircle::iŽ‘l’Ântersection_points(cŽ’Õ’†onstÈ ÝCircle&)."Ž’(k¿·Ž¡‘PÏend‘‚ØlŽ‘f¸â·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘2ÂreturnŽ‘Uæ¿ÝINVALID_BOOL_POINT_QUADRUPLEŽ’élÓ«;Ž¡‘(·gŽ¡‘(ÂelseŽ‘?Øã·fŽ¡‘2ÂifŽ‘=´ý«(Ïverb‘ÿ}'oseŽ‘"Ê=·_‘8àÝDEBUGŽ‘ÿ9«)Ž¡‘<Ïc‘ÿ}'outŽ‘R[w·‘:Ý"*thisÈ ÝliesÈ ÝwithinÈ ÝcŽ‘lþ,È ÝdifferentÈ ÝcentersÈ Ž’ÕÂÝ"Ž’ÝÊa·‘:Ý"(noÈ Ýintersections).Ž‘lþ\n"Ž‘J—·Ž¡‘PÝ"ReturningÈ ÝINVALID_BŽ’¸ÿÌOOL_POINT_QUADRUPLE.Ž’!ÿ\n"Ž’2Eï«;Ž¡‘2ÂifŽ‘>/T«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ì5·‘’þÝ"\nExitingÈ ÝCircle::iŽ‘l’Ântersection_points(cŽ’Õ’†onstÈ ÝCircle&)."Ž’(k¿·Ž¡‘PÏend‘‚ØlŽ‘f¸â·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘2ÂreturnŽ‘Uæ¿ÝINVALID_BOOL_POINT_QUADRUPLEŽ’élÓ«;Ž¡‘(·gŽ¡‘g‘±=·‘ÿýÂelseŽ‘.1ifŽ‘&ã)«(ÏdistŽ‘Ó…±<‘Ç«(Ïr‘ÿ}'adiusŽ‘«+‘8à±cŽ‘Œ»:Ïr‘ÿ}'adiusŽ‘È#«))‘ÿý·±=Ž¡‘ÂelseŽ‘5Øâ·fŽ¡‘(Ïc‘ÿ}'errŽ‘?â·‘,mÝ"ERROR!È ÝInÈ ÝCircle::iŽ‘n,1ntersection_points(cŽ’×+õonstÈ ÝCircle&):"Ž’+ž·Ž¡‘<Ý"ThisÈ Ýcan'tÈ Ýhappen!\Ž’¤ÿÊnThisÈ ÝcaseÈ Ýisn'tÈ ÝaccŽ’ ÿŽountedÈ Ýfor.\n"Ž’]Úe·Ž¡‘<Ý"ReturningÈ ÝINVALID_BŽ’¤ÿÊOOL_POINT_QUADRUPLE.Ž’ ÿŽ"Ž’ ·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;ŽŽŽŒ‹viŸ Šn ý‘ì«374›ÂCIR®9CLE‘ÕX­AR•ÃŽGUMENT’û±)3DLDFPR“G˜·x«1268Ž €n ý•@P‘(ÂifŽ‘3ËK«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘E|·‘ìEÝ"\nExitingÈ ÝCircle::iŽ‘kì ntersection_points(cŽ’ÔëÍonstÈ ÝCircle&)."Ž’'M·‘ìEÏend‘‚ØlŽ‘ÊL·Ž¤ ‘FÏend‘‚ØlŽ‘\¸á·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾ÝINVALID_BOOL_POINT_QUADRUPLEŽ’ßlÒ«;Ž¡‘·gŽ¡‘g‘±=·‘ÿýÂelseŽ‘.1«(Coplanar‘UUcase).‘o·±=Ž¡‘ -·gŽ©Â1269.– üReg‘°¡‰ffs4Ž‘#ÕP®9olygon‘Áfunctions.“«[¬LDF‘T2003.06.13.«]Ž‘ZÀÔ«(ÂconstŽ‘¡ColorŽ‘=­“«&Ž‘Et±Ïddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘y}Z±;‘ª¨ÂconstŽ‘ÄIstringŽ‘@Ø•Ïddashe‘ÿ}'dŽ‘d¦±;‘ª¨ÂconstŽ‘ÄIstringŽŽ¡‘2Ïpp‘ÿ}'enŽ‘G6(±;‘ª¨ÂPictureŽ‘*œ -«&Ž‘2c(Ïpictur‘ÿ}'eŽ‘Qkþ«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂCircleŽ‘5¸ƒ±cŽ‘<Óv«=‘ÇÏin‘‰ffŽ‘®cir‘ÿ}'cleŽ‘'‰a«(‘ª¨);Ž¦‘±cŽ‘SÝ:Ïdr‘ÿ}'awŽ‘(Û«(Ïddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘4©±;‘ª¨Ïddashe‘ÿ}'dŽ‘$ñ¹±;‘ª¨Ïpp‘ÿ}'enŽ‘à˱;‘ª¨Ïpictur‘ÿ}'eŽ‘ ³~«);Ž¡‘ÂreturnŽ‘7æ¼±cŽ‘<:—«;Ž¡‘ -·gŽŸÂ1273.‘ üPicture–ÕTargumen®9t“ rst.Ž¦·h–ª¨«De ne‘UUÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘H)^«functions‘@­1027“·i‘Ç«+·Ž¡‘ -ÂCircleŽ‘+þÃRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘n}{«::‘Ïdr›ÿ}'aw‘‰ffŽ–®in‘‰ffŽ“cir˜cleŽ‘>Ô«(ÂPictureŽ‘)7£«&Ž‘0þÁÏpictur‘ÿ}'eŽ‘P—±;‘ª¨ÂconstŽ‘ ‹ColorŽ‘@¿«&Ž‘GÍÝÏddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘{Ö†±;‘ª¨ÂconstŽ‘ ‹stringŽŽ¡‘2Ïddashe‘ÿ}'dŽ‘UG±;‘ª¨ÂconstŽ‘ÕJstringŽ‘@ú—Ïpp‘ÿ}'enŽ‘V0º«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼Ïdr›ÿ}'aw‘‰ffŽ–®in‘‰ffŽ“cir˜cleŽ‘t錫(Ïddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘4©±;‘ª¨Ïddashe‘ÿ}'dŽ‘$ñ¹±;‘ª¨Ïpp‘ÿ}'enŽ‘à˱;‘ª¨Ïpictur‘ÿ}'eŽ‘ ³~«);Ž¡‘ -·gŽŸÂ1274.‘ üSurrounding‘ÕTcircle.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.06.13.«]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«De ne‘UUÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘H)^«functions‘@­1027“·i‘Ç«+·Ž¡‘ -ÂCircleŽ‘+¸‚Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘n7:«::‘Ïout‘‰ffŽ‘®cir‘ÿ}'cleŽ‘*Þ¼«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂCircleŽ‘5¸ƒ±cŽ‘: ^«;Ž¦‘ÂifŽ‘´ú«(·:Ïis‘‰ffŽ‘®planarŽ‘(&«(‘ª¨))‘·fŽ¡‘Ïc‘ÿ}'errŽ‘3²ƒ·‘üÚÝ"ERROR!È ÝInÈ ÝReg_PolygŽ‘küžon::out_circle():\n"Ž’ؤ·‘üÚÝ"Reg_PolygonÈ ÝisÈ Ýnon-Ž‘küžplanar.\n"Ž’£ÿ·Ž¡‘2Ý"ReturningÈ ÝemptyÈ ÝCirŽ’šÿÉcle.\n\n"Ž’Í.·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½±cŽ‘F:˜«;Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(Ïp‘ÿ}'ointsŽ‘$•±:ÏsizeŽ‘\«(‘ª¨)–DZ<“«3Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'errŽ‘8(¢·‘rùÝ"ERROR!È ÝInÈ ÝReg_PolygŽ‘pr½on::out_circle():\n"Ž’ákâ·Ž¡‘2Ý"Reg_PolygonÈ ÝhasÈ ÝlesŽ’šÿÉsÈ ÝthanÈ Ý3È ÝPoints.\n"Ž’ ·‘ÇÝ"ReturningÈ ÝemptyÈ ÝCirŽ‘kÆÜcle.\n\n"Ž’žTA·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½±cŽ‘F:˜«;Ž¡‘·gŽ¦‘ÂP•®9oin“tŽ‘2ïŸÏnormalŽ‘V o«=‘ÇÏget‘‰ffŽ‘®normalŽ‘3QŒ«(‘ª¨);Ž¦‘ÏnormalŽ‘4Vº±:ÏshiftŽ‘}«(Ïc‘ÿ}'enterŽ‘ ‹«);Ž¡‘±cŽ‘SÝ:ÏsetŽ‘ x„«(ÏoriginŽ‘ö!±;‘ª¨«2Ž‘㉷‘8àÏr‘ÿ}'adiusŽ‘«);Ž¦‘ÂT‘ÿ -«ransformŽ‘KÈÔ±tŽ‘OeF«;Ž¦‘±tŽ‘œt:Ïalign‘‰ffŽ–®with‘‰ffŽ“axisŽ‘@²x«(Ïc‘ÿ}'enterŽ‘ ‹±;‘ª¨ÏnormalŽ‘"`±;‘ª¨Ý'y'Ž‘ñ«);Ž¡‘±cŽ‘õ·«=ŽŽ‘*©,±tŽ‘.Ež:ÏinverseŽ‘ ‡«(‘ª¨);Ž¡‘ÂreturnŽ‘7æ¼±cŽ‘<:—«;Ž¡‘ -·gŽŸÂ1275.‘ üDra®9w–ÕTsurrounding“circle.ŽŽŽŒ‹x… Šn ý‘ì«376–­NORMAL‘ÕXVERSION’ 33DLDFPRÃŽG“·x«1276Ž €n ý•@PÂ1276.‘ üNormal‘ÕTv®9ersion.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ© ‘ -«[¬LDF‘T2003.06.13.«]Ž‘Y;Added–UUthis“function.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«De ne‘UUÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘H)^«functions‘@­1027“·i‘Ç«+·Ž¦‘ -ÂCircleŽ‘,"ÿRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘n¡·«::‘Ïdr›ÿ}'aw‘‰ffŽ–®out‘‰ffŽ“cir˜cleŽ‘CC«(ÂconstŽ‘•ColorŽ‘>¤«&Ž‘Fk­Ïddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘ztV±;‘ª¨ÂconstŽ‘ ?ÇstringŽ‘AÏ‘Ïddashe‘ÿ}'dŽ‘e¢±;‘ª¨ÂconstŽŽ¦‘2stringŽ‘S%RÏpp‘ÿ}'enŽ‘h[u±;‘ª¨ÂPictureŽ‘*œ -«&Ž‘2c(Ïpictur‘ÿ}'eŽ‘Qkþ«)‘UUÂconstŽŽ¦‘ -·fŽ¦‘ÂCircleŽ‘5¸ƒ±cŽ‘<Óv«=‘ÇÏout‘‰ffŽ‘®cir‘ÿ}'cleŽ‘,¥Ð«(‘ª¨);Ž¡‘±cŽ‘SÝ:Ïdr‘ÿ}'awŽ‘(Û«(Ïddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘4©±;‘ª¨Ïddashe‘ÿ}'dŽ‘$ñ¹±;‘ª¨Ïpp‘ÿ}'enŽ‘à˱;‘ª¨Ïpictur‘ÿ}'eŽ‘ ³~«);Ž¦‘ÂreturnŽ‘7æ¼±cŽ‘<:—«;Ž¦‘ -·gŽŸÂ1277.‘ üPicture–ÕTargumen®9t“ rst.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ -«[¬LDF‘T2003.06.13.«]Ž‘Y;Added–UUthis“function.Ž¡ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«De ne‘UUÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘H)^«functions‘@­1027“·i‘Ç«+·Ž¦‘ -ÂCircleŽ‘+ê¢Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘niZ«::‘Ïdr›ÿ}'aw‘‰ffŽ–®out‘‰ffŽ“cir˜cleŽ‘CC«(ÂPictureŽ‘)#‚«&Ž‘0ê Ïpictur‘ÿ}'eŽ‘Oóv±;‘ª¨ÂconstŽ‘ jColorŽ‘?Þ}«&Ž‘G¥›Ïddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘{®D±;‘ª¨ÂconstŽ‘ jstringŽŽ¦‘2Ïddashe‘ÿ}'dŽ‘UG±;‘ª¨ÂconstŽ‘ÕJstringŽ‘@ú—Ïpp‘ÿ}'enŽ‘V0º«)‘UUÂconstŽŽ¦‘ -·fŽ¦‘ÂreturnŽ‘7æ¼Ïdr›ÿ}'aw‘‰ffŽ–®out‘‰ffŽ“cir˜cleŽ‘zû«(Ïddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘4©±;‘ª¨Ïddashe‘ÿ}'dŽ‘$ñ¹±;‘ª¨Ïpp‘ÿ}'enŽ‘à˱;‘ª¨Ïpictur‘ÿ}'eŽ‘ ³~«);Ž¦‘ -·gŽŸÂ1278.› üPutting–ÕTCircle“together.˜«This–UUis“what's“compiled.Ž¡‘ -·h–ª¨«Include‘UU les‘@­11“·iŽ¦‘ -h‘ª¨«V‘ÿ*ªersion–UUconš¸ãtrol“iden˜ti er‘@­10‘ª¨·iŽ¦‘ -h–ª¨«De ne‘UUÂclassŽ‘5¦CircleŽ‘@ØÖ­1237“·iŽ¦‘ -h–ª¨«De ne‘UUÂCircleŽ‘% Ö«functions‘@­1240“·iŽ¦‘ -h–ª¨«De ne‘UUÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘H)^«functions‘@­1027“·iŽŽŽŒ‹y‘ Šn ý‘ì·x«1279›­3DLDFPRÃŽG’ÒWPUTTING–ÕXÂCIR®9CLE“­TOGETHER˜«377Ž €n ý•@PÂ1279.‘ ü«This–UUis“what's“written“to“Ècircles.h«.Ž©·h‘ª¨Ýcircles.hŽ‘:ðö­1279‘ª¨·i‘ÇŽ¤ ‘ -h–ª¨«De ne‘UUÂclassŽ‘5¦CircleŽ‘@ØÖ­1237“·iŽŸÂ1280.– üP®9atterns“(Èpatterns.webÂ).‘#f«[¬LDF‘T2002.09.21.«]Ž‘r  NOTE:–UUWhen“y¸ãou“add“a“new“È.web“« le“andŽ¡mo•¸ãv“e–‡coGde“to“it“bš¸ãy“cop˜ying“it“from“another“È.web“« le,‘Šremem˜bGer“to“c˜hange“the“name“of“the“header“ le“thatŽ¡it–UUwrites.‘qÇOtherwise,“this“can“cause“problems“and“it's“not“ob¸ãvious“what's“caused“them.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.09.21.«]Ž‘X"Started–ousing“this“ le“again.›% Mo•¸ãv“ed‘oÏhex‘‰ffŽ–®p‘ÿ}'attern‘‰ffŽ“1Ž‘=êu«(‘ª®)–ohere.˜Made“the“appropriate“c¸ãhangesŽ¡to–UUÈcmplprsp.web“«and“Èmain.web«.Ž¡‘ -[¬LDF‘T2003.11.12.«]Ž‘ZCáRemo•¸ãv“ed–ûthe“vš¸ãersion“con˜trol“iden˜ti ers“from“the“CWEB‘© les“for“the“distribution“ofŽ¡3DLDF–UU1.1.‘qÇThey're“still“used“in“mš¸ãy“dev˜elopmen˜t“v˜ersions.Ž¡‘ -[¬LDF‘T2003.12.10.«]Ž‘YQ‘Put–ž«the“vš¸ãersion“con˜trol“iden˜ti ers“bac˜k“in˜to“m˜y“release“v˜ersions“for“3DLDF‘ž™1.1.4.‘MÊI'v˜eŽ¡already–"¯put“some“of“them“bacš¸ãk“in,‘,Ñno˜w“I'm“doing“the“rest“of“them.‘`åHo˜w˜ev˜er,‘,Ñthe“release“v˜ersions“are“no˜w“inŽ¡their–UUoš¸ãwn“R˜CS“repGository‘ÿ*ª.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h‘ª¨«V‘ÿ*ªersion–UUconš¸ãtrol“iden˜ti er‘@­10‘ª¨·i‘Ç«+·Ž¡‘ -ÂstaticŽ‘)HÚstringŽ‘Jn'Ïr‘ÿ}'cs‘‰ffŽ‘®idŽ‘g(«=‘ÇÝ"$Id:È Ýpatterns.web,vŽ‘kÆÜÈ Ý1.2È Ý2003/12/10È Ý16:1Ž’ÔÆ 2:59È Ýlfinsto1È ÝExpÈ Ý$"Ž’>LÌ«;ŽŸÂ1281.‘ üInclude‘ÕT les.Ž¦·h–ª¨«Include‘UU les‘@­11“·i‘Ç«+·Ž¡«#ÂincludeŽ‘'Ø~Ý"loader.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"pspglb.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"io.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"colors.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"transfor.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"shapes.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"pictures.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"points.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"lines.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"planes.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"paths.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"curves.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"polygons.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"rectangs.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"ellipses.h"ŽŽ¡«#ÂincludeŽ‘'Ø~Ý"circles.h"ŽŽ¤Â1282.‘ üPlane‘ÕTtesselations.Ž¡1283.‘ üHexagonal–ÕTtesselation“1.Ž¤ ‘ -«[¬LDF‘T2003.08.10.«]Ž‘Y;TO–UUDO:“Change,“so“that“it's“pGossible“to“put“the“pattern“in¸ãto“a“rectangular“area.ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.09.22.«]Ž‘X£×Added–ðñargumenš¸ãts.‘PQÏhex‘‰ffŽ–®p‘ÿ}'attern‘‰ffŽ“1Ž‘?ˬ«(‘ª®)“can“no˜w“bGe“used“to“mak˜e“a“pattern“with“up“to“threeŽ¡nested–(ühexagons“whicš¸ãh“can“bGe“dra˜wn“and“ lled.‘bÿEac˜h“hexagon“has“its“o˜wn“argumen˜t“for“the“dra˜w“color,‘1ÛtheŽ¡ ll–ëÔcolor“and“the“pšGen“to“b˜e“used.‘NœÏhex‘‰ffŽ–®p‘ÿ}'attern‘‰ffŽ“1Ž‘?É÷«(‘ª®)“do˜es“not“ha•¸ãv“e›ëÔargumen“ts˜for˜dash˜patterns,‘îbut˜they˜couldŽ¡bGe–zýadded,›„gif“necessary‘ÿ*ª.‘âÀIf“the“argumen¸ãt“for“the“diameter“of“the“middle“or“the“inner“hexagon“is“0,˜then“thatŽ¡hexagon–‰(is“not“draš¸ãwn“or“ lled.‘ @In“this“case,‘–the“argumen˜ts“for“the“dra˜w“and“ ll“colors“are“ignored“for“thatŽ¡hexagon.‘PqThe–ñQdefault“pšGen“for“the“outer“hexagon“is“thic•¸ãk“er–ñQthan“the“p˜ens“for“the“other“t•¸ãw“o–ñQ(.5mm“and“.3mm,Ž¡respGectiv¸ãely).ŽŽŽŒ‹zš& Šn ý‘ì«378‘­HEXAšÃŽGONAL–ÕXTESSELA‘ÿJªTION“1’ß—;3DLDFPR˜G‘·x«1283Ž €n ý•@P‘ -[¬LDF‘T2002.09.20.«]Ž‘Y3NRewrote–€hthis“function.‘òÿIt“noš¸ãw“w˜orks“with“the“new“Ïpr–ÿ}'oje“ctŽ‘!÷v«(›ª®)“function.‘òÿÏhex‘‰ffŽ–®p‘ÿ}'attern‘‰ffŽ“1Ž‘@nZ«(˜)Ž¤ makš¸ães–í¯a“\honeycom˜b"“pattern“on“the“x-z“plane“using“a“single“hexagon“(i.e.,‘Æthere“aren't“nested“hexagonsŽ¡yš¸ãet,‘•äas–ˆûin“the“old“v˜ersion).‘ ¹In“the“next“v˜ersion,‘•äI‘ˆîplan“to“add“argumen˜ts“for“optionally“putting“t˜w˜o“smallerŽ¡hexagons–UUinside“the“large“one,“and“for“ lling“and“un lling.Ž¡‘ -This–5Övš¸ãersion“con˜tains“argumen˜ts“for“the“dra˜wing“command,‘­öincluding“a“ÂPictureŽ‘0¹«argumen˜t,‘­öso“thatŽ¡Ïhex‘‰ffŽ–®p‘ÿ}'attern‘‰ffŽ“1Ž‘;{[«(‘ª®)–UUneed“not“bGe“put“on¸ãto“Ïcurr–ÿ}'ent‘‰ffŽ‘®pictur“eŽ‘E{«.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h›ª¨«Declare–UUP¸ãattern“functions‘@­1283˜·i‘ÇŽ¤ ‘ -ÂunsignedŽ‘;_‚in®9tŽ‘N,ìÏhex‘‰ffŽ–®p‘ÿ}'attern‘‰ffŽ“1Ž’‰¨G«(ÂrealŽ‘Û¡Ïdiameter‘‰ffŽ‘®outerŽ‘^§§«=‘µ+5Ž– µ,±;‘ª¨ÂrealŽ‘†IÏdiameter‘‰ffŽ‘®midd‘‚ØleŽ‘fƒa«=‘µ+0Ž“±;‘ª¨ÂrealŽŽ¡‘Ïdiameter‘‰ffŽ‘®innerŽ‘c”ñ«=‘û:0Ž–û;±;‘ª¨ÂunsignedŽ‘2þshortŽ‘OêéÏ rst‘‰ffŽ‘®r‘ÿ}'owŽ‘xà™«=‘û:5Ž“±;‘ª¨ÂunsignedŽ‘2þshortŽ‘OêéÏdouble‘‰ffŽ‘®r‘ÿ}'owsŽ’†Î«=‘û:10ŽŽ‘ û<±;‘ª¨ÂunsignedŽŽ¡‘shortŽ‘;ʦÏr‘ÿ}'ow‘‰ffŽ‘®shiftŽ‘eÓR«=‘Ç2Ž‘DZ;Ž¡‘ª°=·‘ÿý«Argumenš¸ãts–UUfor“the“dra˜wing“and“ lling“commands.‘o·±=Ž¡‘ -ÂColorŽ‘)¤ôÏdr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜outerŽ‘u¤+«=‘Ç·Ž‘ÇÂColorsŽ‘)Ÿ÷«::Ž‘0.5Ïdefault‘‰ffŽ‘®c‘ÿ}'olorŽ‘gª±;‘ª©=·–ÿý«Outer“·±=Ž¡‘ -ÂColorŽ‘)`ZÏ l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“outerŽ‘l ­«=‘Ç·Ž‘ÇÂColorsŽ‘)Ÿ÷«::Ž‘0.5Ïb–ÿ}'ackgr“ound‘‰ffŽ‘®c“olorŽ‘zr±;‘ª¨ÂColorŽ‘! Ïdr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜midd‘‚ØleŽ‘s;J«=‘Ç·Ž‘ÇÂColorsŽ‘)Ÿ÷«::Ž‘0.5Ïdefault‘‰ffŽ‘®c‘ÿ}'olorŽ‘gª±;Ž¡‘=·–ÿý«Middle“·±=Ž¡‘ -ÂColorŽ‘)TuÏ l›‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“midd˜leŽ‘r0Ú«=‘Ç·Ž‘ÇÂColorsŽ‘)Ÿ÷«::Ž‘0.5Ïb–ÿ}'ackgr“ound‘‰ffŽ‘®c“olorŽ‘zr±;‘ª¨ÂColorŽ‘ ÿÏdr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜innerŽ‘m,«=‘Ç·Ž‘ÇÂColorsŽ‘)Ÿ÷«::Ž‘0.5Ïdefault‘‰ffŽ‘®c‘ÿ}'olorŽ‘gª±;Ž¡‘=·–ÿý«Inner“·±=Ž¡‘ -ÂColorŽ‘)¤ôÏ l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“innerŽ‘lÓ «=‘Ç·Ž‘ÇÂColorsŽ‘)Ÿ÷«::Ž‘0.5Ïb–ÿ}'ackgr“ound‘‰ffŽ‘®c“olorŽ‘zr±;‘ª¨ÂstringŽ‘"ÏõÏp‘ÿ}'en‘‰ffŽ‘®outerŽ‘PKЫ=‘ÇÝ"pencircleÈ ÝscaledÈ Ý.5Ž‘kÆÜmm"Ž‘| ;±;Ž¡‘ÂstringŽ‘?%PÏp‘ÿ}'en‘‰ffŽ‘®midd‘‚ØleŽ‘rÒ=«=‘ÇÝ"pencircleÈ ÝscaledÈ Ý.3Ž‘kÆÜmm"Ž–| ;±;‘ª¨ÂstringŽ‘"ÏõÏp‘ÿ}'en‘‰ffŽ‘®innerŽ‘PΩ«=‘ÇÝ"pencircleÈ ÝscaledÈ Ý.3Ž‘kÆÜmm"Ž“±;Ž¡‘ÂPictureŽ‘Fñe«&Ž‘N¸ƒÏpictur‘ÿ}'eŽ‘pˆq«=‘ÇÏcurr–ÿ}'ent‘‰ffŽ‘®pictur“eŽ‘Dìß±;‘ª¨ÂunsignedŽ‘1á¶in®9tŽ‘C†­Ïmax‘‰ffŽ‘®hexagonsŽ’„ c«=‘Ç1000ŽŽ‘Ç);Ž¤ ­See–ÕXalso“sections“1286“and“1289.Ž¡This–ÕXco‘8­«25ŽŽ‘ 8¯)‘±=·‘D$«[¬LDF‘T2002.09.22.«]Ž‘T…This–™|can't“bšGe“ÂelseŽ‘ ×ifŽ‘&ö«b˜ecause“the“preceding“conditionŽ¡‘(migh•¸ãt›UUha“v“e˜proGduced˜a˜v‘ÿqÇalue˜±>‘Ç«25.‘o·±=Ž¡‘·fŽ¡‘Ïc‘ÿ}'errŽ‘3Šš·‘ÔñÝ"ERROR!È ÝInÈ Ýhex_patteŽ‘kÔµrn_1():\n"Ž’£¯ð·‘ÔñÝ"first_rowÈ ÝhasÈ ÝinvalŽ‘kÔµidÈ Ývalue:È Ý"Ž’¨ïí·‘ÔñÏ rst‘‰ffŽ‘®r‘ÿ}'owŽ‘+¤X·Ž¡‘2Ý"ItÈ ÝcanÈ ÝbeÈ ÝatÈ ÝmostÈ Ý2Ž’šÿÉ5.\n"Ž’¸:·‘ÇÝ"SettingÈ Ýfirst_rowÈ ÝtŽ‘kÆÜoÈ Ý25.\n"Ž’™D·‘ÇÏ ushŽ‘€«;Ž¡‘Ï rst‘‰ffŽ‘®r‘ÿ}'owŽ‘FÁ‘«=‘Ç25ŽŽ‘ Ç;Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(Ï l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“outerŽ‘B«S·‘ÇŽ‘ÇÂColorsŽ‘)Ÿ÷«::Ž‘0.5Ïdefault‘‰ffŽ‘®c‘ÿ}'olorŽ‘gª«)Ž¡‘(±=·‘Ý_«LDF‘2®2002.09.24.›f=Changed–2·this,‘9£bGecause“I'm“no¸ãw“using“ÂclassŽ‘ðjColorŽ‘=r¿«instead“of“ÂstringsŽ‘%c«.˜No¸ãw“itŽ¡‘2loGoks–]blikš¸ãe“I'm“going“to“ha˜v˜e“to“use“\·Ž‘ÂColorsŽ‘&Øß«::Ž‘-gÏb–ÿ}'ackgr“ound‘‰ffŽ‘®c“olorŽ‘w«u«"“as“a“placeholder.‘‰îI'm“going“toŽ¡‘2ha•¸ãv“e–{€to“c•¸ãhec“k–{€to“see“what“the“consequences“of“this“c¸ãhange“are“here.–äG!!“[¬LDF‘T2002.09.22.«]Ž‘T¬ThisŽ¡‘2is–)necessary‘ÿ*ª,‘ŒbGecause“ÂP®9athŽ‘‘«::‘Ï l‘‚ØlŽ‘ É÷«(›ª®)“in¸ãterprets“\Ý""Ž‘ 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Ý==È Ý"Ž’‰TM·‘ÇÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh±:ÏsizeŽ‘\«(‘ª¨)–Ç·“Ïend‘‚ØlŽ‘ò·“Ï ushŽ‘€«;Ž¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"rectangles.size()È Ý=Ž‘kÆÜ=È Ý"Ž‘~ÔS·‘ÇÏr–ÿ}'e“ctanglesŽ‘.g]±:ÏsizeŽ‘\«(‘ª¨)–Ç·“Ïend‘‚ØlŽ‘ò·“Ï ushŽ‘€«;Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ExitingÈ ÝSolid::operŽ‘kÆÜator=().\n"Ž’¦ #«;Ž¡‘ÂreturnŽ‘7æ¼·Ž‘<æ½ÏthisŽ‘MÒs«;Ž¡‘ -·gŽŸÂ1309.‘ üCop®9ying.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.05.06.«]Ž‘X—¶BUG›ä³FIX:–äÐChanged“±sŽ‘ -y «from“ÂShapQÇeŽ‘$µ­·Ž‘,š~«to“ÂSolidŽ‘Gw·Ž‘$Gx«.‘LFI˜noticed“this“bug“when“I˜tried“to“cop¸ãyŽ¡a‘UUÂPictureŽ‘,F·«conš¸ãtaining–UUa“ÂCubQÇoidŽ‘(¤ï«,“and“the“cop˜y“con˜tained“a“single“empt˜y“ÂShapQÇeŽ‘%–··Ž‘-ì «on“Ïshap‘ÿ}'esŽ‘ CÞ«.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·ŽŸ ‘ -ÂvirtualŽ‘/ÔShapQÇeŽ‘QÏ6·Ž‘VÏ7Ïget‘‰ffŽ‘®c‘ÿ}'opyŽ‘{’ë«(‘ª®)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹Š’¦ Šn ý‘ì«394–­COPYING’4Å3DLDFPRÃŽG“·x«1310Ž €n ý•@PÂ1310.Ž©·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¤ ‘ -ÂShapQÇeŽ‘,Ac·Ž‘1AdÂSolidŽ‘K¿?«::‘Ïget‘‰ffŽ‘®c‘ÿ}'opyŽ‘%ø«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂSolidŽ‘0Ó.·Ž‘5Ó/±sŽ‘=JG«=‘ÇÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“solidŽ‘IèÓ«(‘ª¨);Ž¦‘·Ž‘±sŽ‘ w«=‘Ç·Ž‘ÇÏthisŽ‘²Ï«;Ž¡‘ÂreturnŽ‘7æ¼dynamicu½‰™šs4Ž‘ÔwcastŽ‘{W·hÂShapQÇeŽ‘"Ab·Ž‘'Aci«(±sŽ‘°«);Ž¡‘ -·gŽŸÂ1311.‘ üSet–ÕTon“free“store.Ž¦·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·Ž¡‘ -ÂinlineŽ‘)ŠIvirtualŽ‘Ob•QÇo“olŽ‘h¹‚Ïset‘‰ffŽ–®on‘‰ffŽ“fr–ÿ}'e“e‘‰ffŽ‘®stor“eŽ’°Y«(Âb•QÇo“olŽ‘¡f±bŽ‘ ³(«=‘ÇÏtrueŽ‘‹°«)Ž¡‘ -·fŽ¡‘Ïon‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘Nl «=‘DZbŽ‘«;Ž¡‘ÂreturnŽ‘7æ¼±bŽ‘<1f«;Ž¡‘ -·gŽŸÂ1312.› üReturning–ÕTelemen®9ts“and“information.˜«[¬LDF‘T2003.04.11.«]Ž‘Zˆ6The–UUfunctions“Ïget‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ‘<ö¹«(‘ª®),Ž¡Ïget‘‰ffŽ–®cir‘ÿ}'cle‘‰ffŽ“ptrŽ‘9??«(–ª®),‘§ZÏget‘‰ffŽ–®el‘‚Ølipse‘‰ffŽ“ptrŽ‘Aܦ«(“),‘§ZÏget‘‰ffŽ–®p‘ÿ}'ath‘‰ffŽ“ptrŽ‘8êâ«(“),‘§ZÏget‘‰ffŽ›®r–ÿ}'e“ctangle‘‰ffŽ˜ptrŽ‘Lúz«(“),‘§Zand‘cÀÏget‘‰ffŽ›®r–ÿ}'e“g‘‰ffŽ˜p“olygon‘‰ffŽ˜ptrŽ‘W ë«(“)–cÀall“returnŽ¡ÂconstŽ‘¤ð«pGoinš¸ãters–Ï£to“ÂShapQÇeŽ‘"»°«,‘î6ÂCircleŽ‘"Qb«,‘î6ÂEllipseŽ‘%׫,–î6etc.‘à±Therefore,“they–Ï£m˜ust“bGe“in˜v˜ok˜ed“in“suc˜h“a“w˜a˜y‘ÿ*ª,‘î6that“theŽ¡ÂconstŽ‘뜫quali er–Ois“not“discarded.‘\ÅF‘ÿ*ªor“example,›"êfollo¸ãwing“ÂDoQÇdecahedronŽ‘Nì,±dŽ‘T ž«(ÏoriginŽ‘ö!±;‘ª¨«5Ž‘ª©);,˜t•¸ãw“o›Ow“a“ys˜of˜in“v“okingŽ¡Ïget‘‰ffŽ›®r–ÿ}'e“g‘‰ffŽ˜p“olygon‘‰ffŽ˜ptrŽ–R¦+«(‘ª®)›UUare:‘qÇÂconstŽ‘"œiRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘gpr·Ž‘lpsÏptrŽ‘}tR«=‘DZdŽ‘ûŠ:Ïget‘‰ffŽ›®r–ÿ}'e“g‘‰ffŽ˜p“olygon‘‰ffŽ˜ptrŽ“«(5Ž‘);˜andŽ¡ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘DÔ ±AŽ‘O"«=‘Ç·Ž‘DZdŽ‘ û‹:Ïget‘‰ffŽ›®r–ÿ}'e“g‘‰ffŽ˜p“olygon‘‰ffŽ˜ptrŽ‘R¦+«(5Ž‘);.ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.05.09.«]Ž‘Y;Changed–UUthe“names“of“Ïget‘‰ffŽ‘®shap‘ÿ}'eŽ‘,O«(›ª®),“Ïget‘‰ffŽ‘®cir‘ÿ}'cleŽ‘+ìï«(˜),“Ïget‘‰ffŽ‘®el‘‚ØlipseŽ‘/âü«(˜),“Ïget‘‰ffŽ‘®p‘ÿ}'athŽ‘&õ@«(˜),Ž¡Ïget‘‰ffŽ‘®r–ÿ}'e“ctangleŽ‘7«{«(›ª®),–UUand“Ïget‘‰ffŽ›®r–ÿ}'e“g‘‰ffŽ˜p“olygonŽ‘EWã«(˜)“to“Ïget‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ‘<ö¹«(˜),“Ïget‘‰ffŽ–®cir‘ÿ}'cle‘‰ffŽ“ptrŽ‘<””«(˜),“Ïget‘‰ffŽ–®el‘‚Ølipse‘‰ffŽ“ptrŽ‘@Š¡«(˜),“Ïget‘‰ffŽ–®p‘ÿ}'ath‘‰ffŽ“ptrŽ‘7˜Ý«(˜),Ž¡Ïget‘‰ffŽ›®r–ÿ}'e“ctangle‘‰ffŽ˜ptrŽ‘HS «(–ª®),›Fand‘¶Ïget‘‰ffŽ›®r–ÿ}'e“g‘‰ffŽ˜p“olygon‘‰ffŽ˜ptrŽ‘W\A«(“).‘” The–¶names“without“\‘‰ffŽ‘®ÏptrŽ‘êÚ«"“w¸ãere“confusing,˜bGecause“theyŽ¡didn't–UUmakš¸ãe“clear“that“the“functions“returned“pGoin˜ters.Ž¦ŸüÈ„`ÕÁGŽŽŸÂ1313.‘ üGet‘ÕTcen®9ter.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.05.06.«]Ž‘Y;Added–UUthis“function.Ž¡‘ -[¬LDF‘T2003.08.10.«]Ž‘Y;Made–UUthis“function“ÂconstŽ‘*¢«.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/ÔconstŽ‘M¸vP•®9oin“tŽ‘l¨«&Ž‘to1Ïget‘‰ffŽ‘®c‘ÿ}'enterŽ’ ¬x«(‘ª®)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹‹ Šn ý‘ì·x«1314–­3DLDFPRÃŽG’#â'GET‘ÕXCENTER“«395Ž €n ý•@PÂ1314.Ž©·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¤ ‘ -ÂconstŽ‘(*£P•®9oin“tŽ‘G@«&Ž‘Ná^ÂSolidŽ‘i_9«::‘Ïget‘‰ffŽ‘®c‘ÿ}'enterŽ‘-=K«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼Ïc‘ÿ}'enterŽ‘SðG«;Ž¡‘ -·gŽŸÂ1315.‘ üGetting‘ÕTShapQÇes.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.04.30.«]Ž‘Y;Changed–UUthe“functions“Ïget‘‰ffŽ–®cir‘ÿ}'cle‘‰ffŽ“ptrŽ‘<””«(›ª®),“Ïget‘‰ffŽ–®el‘‚Ølipse‘‰ffŽ“ptrŽ‘@Š¡«(˜),“Ïget‘‰ffŽ–®p‘ÿ}'ath‘‰ffŽ“ptrŽ‘7˜Ý«(˜),Ž¡Ïget‘‰ffŽ›®r–ÿ}'e“ctangle‘‰ffŽ˜ptrŽ‘HS «(–ª®),‘T`and‘T"Ïget‘‰ffŽ›®r–ÿ}'e“g‘‰ffŽ˜p“olygon‘‰ffŽ˜ptrŽ‘UúM«(“).›qaThey–T"no“longer“use“Ïget‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ‘<õ†«(‘ª®).˜There's“no“go•Go“d‘T"reasonŽ¡for–UUcasting“pGoinš¸ãters“from“one“t˜ypGe“to“another.‘qÇI“rather“doubt“that“Ïget‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ‘<ö¹«(‘ª®)“is“needed,“an˜yw˜a˜y‘ÿ*ª.Ž¦ŸüÈ„`ÕÁGŽŽŸÂ1316.‘ üGet–%ShapšQÇe“p˜oin®9ter.‘ ü«[¬LDF‘T2003.05.30.«]Ž‘[¬)This–yHfunction“copies“one“of“the“ob‘Ž8jects“on“one“of“theŽ¡v¸ãectors–íSof“ÂShapQÇeŽ‘(Ƴ·Ž‘2´«bšGelonging“to“the“ÂSolidŽ‘k*«,‘SRand“returns“a“p˜oin¸ãter“to“ÂShapQÇeŽ‘(Ƴ«that“p˜oinš¸ãts“to“the“cop˜y‘ÿ*ª.Ž¡Curren•¸ãtly‘ÿ*ª,›Ina‘FtÂSolidŽ‘ -¿«con“tains–Ftthe“v¸ãectors“Ïcir‘ÿ}'clesŽ‘ÒØ«,˜Ïel‘‚ØlipsesŽ‘#Ëß«,˜Ïp‘ÿ}'athsŽ‘Ú«,˜Ïr–ÿ}'e“ctanglesŽ‘.鳫,˜and“Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘99Ä«.‘lÑThe“argumen¸ãtŽ¡Ïshap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘1öØ«indicates–"whicš¸ãh“v˜ector“should“bšGe“accessed.‘Ø -Normally‘ÿ*ª,‘UFthe“corresp˜onding“ÂpublicŽ‘'‚staticŽ‘G—›constŽŽ¡«data–mmem¸ãbšGers“ÝCIRCLEŽ‘$só«,‘³¯ÝELLIPSEŽ‘)ú«,‘³¯ÝPATHŽ‘: «,‘³¯ÝRECTANGLEŽ‘4yü«,‘³¯or“ÝREG_POLYGONŽ‘C!«should“b˜e“passed“as“the“Ïshap–ÿ}'e‘‰ffŽ‘®typ“eŽŽ¡«argumen¸ãt,–UUe.g.,“ÂCircleŽ‘% Ö·Ž‘* ×Ïc‘‰ffŽ‘®ptrŽ‘Cç«=“Âstaticu½‰™šs4Ž‘ÔwcastŽ‘7Ò÷·hÂCircleŽ‘!¸·Ž‘&¸‚i«(Ïget‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ‘9¡d«(ÂSolidŽ‘}Û«::Ž‘! ÝCIRCLEŽ‘Ao±;‘ª¨«3Ž‘ª©)).Ž¡‘ -[¬LDF‘T2003.04.30.«]Ž‘Y;This–UUfunction“wš¸ãas“mainly“in˜tended“for“use“in“the“functions“Ïget‘‰ffŽ–®cir‘ÿ}'cle‘‰ffŽ“ptrŽ‘<””«(‘ª®),Ž¡Ïget‘‰ffŽ–®el‘‚Ølipse‘‰ffŽ“ptrŽ‘=5L«(‘ª®),–Ãetc.,“and–ž†wš¸ãas“not“in˜tended“for“use“in“user“coGde.‘4ØI‘žWno˜w“doubt“whether“this“function“is“neededŽ¡at–UUall,“espšGecially“since“it“is“no“longer“used“in“the“functions“men¸ãtioned“ab˜o•¸ãv“e.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.04.11.«]Ž‘Y;Added–UUthis“function.Ž¡‘ -[¬LDF‘T2003.04.30.«]Ž‘XM5Noš¸ãw–šOusing“Ïget‘‰ffŽ‘®c‘ÿ}'opyŽ‘'^«(‘ª®)“instead“of“Âstaticu½‰™šs4Ž‘ÔwcastŽ‘7ñ·hÂconstŽ‘oœShapQÇeŽ‘>õø·Ž‘Cõùi«(‘ª¨).‘3pThe“w˜a˜y“it“w˜as“causedŽ¡compilation–UUerrors“under“T‘ÿ*ªru64“(DEC“ALPHA).Ž¡‘ -[¬LDF‘T2003.05.30.«]Ž‘XïChanged–<return“v‘ÿqÇalue“to“ÂShapQÇeŽ‘%dG·Ž‘- e«from“ÂconstŽ‘!M‡ShapQÇeŽ‘Cu±·Ž‘Hu²«.‘i_The“w•¸ãa“y–<it“w¸ãas“bGefore“causedŽ¡\Memory–UUfault"“errors“at“run-time.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/ÔShapQÇeŽ‘QÏ6·Ž‘VÏ7Ïget‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ’p›«(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SÏshap–ÿ}'e‘‰ffŽ‘®typ“eŽ’š±;‘ª¨ÂconstŽ‘ÕJunsignedŽ‘P XshortŽ‘mÖû±sŽ‘r†û«)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹Œ¬< Šn ý‘ì«396›­GET–ÕXSHAPE“POINTER’ã3DLDFPRÃŽG˜·x«1317Ž €n ý•@PÂ1317.Ž©·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¤ ‘ -ÂShapQÇeŽ‘,Ac·Ž‘1AdÂSolidŽ‘K¿?«::‘Ïget‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ‘:¡h«(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SÏshap–ÿ}'e‘‰ffŽ‘®typ“eŽ’š±;‘ª¨ÂconstŽ‘ÕJunsignedŽ‘P XshortŽ‘mÖû±sŽ‘r†û«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"EnteringÈ ÝSolid::getŽ‘kÆÜ_shape_ptr().\n"Ž’Ã,·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(Ïshap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘0›Ú·‘ÇÝCIRCLEŽ‘"Ín«)‘·fŽ¡‘ÂifŽ‘)´û«(±sŽ‘w<‘ÇÏcir‘ÿ}'clesŽ‘S|±:ÏsizeŽ‘\«(‘ª¨))‘·fŽ¡‘(ÂreturnŽ‘Kæ¾Ïcir‘ÿ}'clesŽ‘hs"«[±sŽ‘°«]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®c‘ÿ}'opyŽ‘(õ«(‘ª¨);Ž¡‘·gŽ¡‘ÂelseŽ‘5Øâ·fŽ¡‘(Ïc‘ÿ}'errŽ‘=|·‘ÇÝ"ERROR!È ÝInÈ ÝSolid::geŽ‘kÆÜt_shape_ptr():\n"Ž’ÈT)·‘ÇÝ"sÈ Ý("Ž‘ T‰·‘DZsŽ‘ ->0·‘ÇÝ")È Ý>È Ýcircles.size()È Ž‘kÆÜÝ("Ž‘y”V·Ž¡‘<Ïcir‘ÿ}'clesŽ‘XŒj±:ÏsizeŽ‘\«(‘ª¨)–Ç·“Ý")\nReturningÈ ÝaÈ ÝnullŽ‘kÆÜÈ ÝpointerÈ Ý(0).\n\n"Ž’Í”&·“Ï ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾staticu½‰™šs4Ž‘ÔwcastŽ’€d`·hÂShapQÇeŽ‘"Ab·Ž‘'Aci«(0Ž‘);Ž¡‘·gŽ¡‘gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(Ïshap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘0›Ú·‘ÇÝELLIPSEŽ‘( k«)‘·fŽ¡‘ÂifŽ‘)´û«(±sŽ‘w<‘ÇÏel‘‚ØlipsesŽ‘#I‰±:ÏsizeŽ‘\«(‘ª¨))‘·fŽ¡‘(ÂreturnŽ‘Kæ¾Ïel‘‚ØlipsesŽ‘li/«[±sŽ‘°«]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®c‘ÿ}'opyŽ‘(õ«(‘ª¨);Ž¡‘·gŽ¡‘ÂelseŽ‘5Øâ·fŽ¡‘(Ïc‘ÿ}'errŽ‘A è·‘T>Ý"ERROR!È ÝInÈ ÝSolid::geŽ‘oTt_shape_ptr():\n"Ž’Ïnu·‘T>Ý"sÈ Ý("Ž‘'nÕ·Ž¡‘<±sŽ‘GÎì·‘æÝ")È Ý>È Ýellipses.size()Ž‘pªÈ Ý("Ž’‡ƒï·‘æÏel‘‚ØlipsesŽ‘'¡W±:ÏsizeŽ‘\«(‘ª¨)‘æ·Ž¡‘<Ý")\nReturningÈ ÝaÈ ÝnullŽ’¤ÿÊÈ ÝpointerÈ Ý(0).\n\n"Ž’Í·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾staticu½‰™šs4Ž‘ÔwcastŽ’€d`·hÂShapQÇeŽ‘"Ab·Ž‘'Aci«(0Ž‘);Ž¡‘·gŽ¡‘gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(Ïshap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘0›Ú·‘ÇÝPATHŽ‘Mt«)‘·fŽ¡‘ÂifŽ‘)´û«(±sŽ‘w<‘ÇÏp‘ÿ}'athsŽ‘Wű:ÏsizeŽ‘\«(‘ª¨))‘·fŽ¡‘(ÂreturnŽ‘Kæ¾Ïp‘ÿ}'athsŽ‘cwk«[±sŽ‘°«]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®c‘ÿ}'opyŽ‘(õ«(‘ª¨);Ž¡‘·gŽ¡‘ÂelseŽ‘5Øâ·fŽ¡‘(Ïc‘ÿ}'errŽ‘=•$·‘ßzÝ"ERROR!È ÝInÈ ÝSolid::geŽ‘kß>t_shape_ptr():\n"Ž’È„í·‘ßzÝ"sÈ Ý("Ž‘ …M·‘ßz±sŽ‘ -nô·‘ßzÝ")È Ý>È Ýpaths.size()È Ý("Ž‘oE ·Ž¡‘<Ïp‘ÿ}'athsŽ‘S³±:ÏsizeŽ‘\«(‘ª¨)–Ç·“Ý")\nReturningÈ ÝaÈ ÝnullŽ‘kÆÜÈ ÝpointerÈ Ý(0).\n\n"Ž’Í”&·“Ï ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾staticu½‰™šs4Ž‘ÔwcastŽ’€d`·hÂShapQÇeŽ‘"Ab·Ž‘'Aci«(0Ž‘);Ž¡‘·gŽ¡‘gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(Ïshap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘0›Ú·‘ÇÝRECTANGLEŽ‘2e«)‘·fŽ¡‘ÂifŽ‘)´û«(±sŽ‘w<‘ÇÏr–ÿ}'e“ctanglesŽ‘.g]±:ÏsizeŽ‘\«(‘ª¨))‘·fŽ¡‘(ÂreturnŽ‘Kæ¾Ïr–ÿ}'e“ctanglesŽ‘w‡«[±sŽ‘°«]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®c‘ÿ}'opyŽ‘(õ«(‘ª¨);Ž¡‘·gŽ¡‘ÂelseŽ‘5Øâ·fŽ¡‘(Ïc‘ÿ}'errŽ‘A è·‘T>Ý"ERROR!È ÝInÈ ÝSolid::geŽ‘oTt_shape_ptr():\n"Ž’Ïnu·‘T>Ý"sÈ Ý("Ž‘'nÕ·Ž¡‘<±sŽ‘GGô·‘—îÝ")È Ý>È Ýrectangles.sizeŽ‘o—²()È Ý("Ž’õù·‘—îÏr–ÿ}'e“ctanglesŽ‘283±:ÏsizeŽ‘\«(‘ª¨)‘—î·Ž¡‘<Ý")\nReturningÈ ÝaÈ ÝnullŽ’¤ÿÊÈ ÝpointerÈ Ý(0).\n\n"Ž’Í·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾staticu½‰™šs4Ž‘ÔwcastŽ’€d`·hÂShapQÇeŽ‘"Ab·Ž‘'Aci«(0Ž‘);Ž¡‘·gŽ¡‘gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(Ïshap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘0›Ú·‘ÇÝREG_POLYGONŽ‘= _«)‘·fŽ¡‘ÂifŽ‘)´û«(±sŽ‘w<‘ÇÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh±:ÏsizeŽ‘\«(‘ª¨))‘·fŽŽŽŒ‹º± Šn ý‘ì·x«1317›­3DLDFPRÃŽG’ãGET–ÕXSHAPE“POINTER˜«397Ž €n ý•@P‘(ÂreturnŽ‘Kæ¾Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ’Ú«[±sŽ‘°«]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®c‘ÿ}'opyŽ‘(õ«(‘ª¨);Ž¤ ‘·gŽ¡‘ÂelseŽ‘5Øâ·fŽ¡‘(Ïc‘ÿ}'errŽ‘A è·‘T>Ý"ERROR!È ÝInÈ ÝSolid::geŽ‘oTt_shape_ptr():\n"Ž’Ïnu·‘T>Ý"sÈ Ý("Ž‘'nÕ·Ž¡‘<±sŽ‘FÅî·‘èÝ")È Ý>È Ýreg_polygons.siŽ‘o¬ze()È Ý("Ž’šqç·‘èÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘< 8±:ÏsizeŽ‘\«(‘ª¨)‘è·Ž¡‘<Ý")\nReturningÈ ÝaÈ ÝnullŽ’¤ÿÊÈ ÝpointerÈ Ý(0).\n\n"Ž’Í·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾staticu½‰™šs4Ž‘ÔwcastŽ’€d`·hÂShapQÇeŽ‘"Ab·Ž‘'Aci«(0Ž‘);Ž¡‘·gŽ¡‘gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘Ïc‘ÿ}'errŽ‘3ÓK·‘¢Ý"ERROR!È ÝInÈ ÝSolid::geŽ‘lft_shape_ptr():\n"Ž’É=·‘¢Ý"InvalidÈ ÝvalueÈ ÝforÈ ÝsŽ‘lfhape_type:È Ý"Ž’®ÁL·Ž¡‘2Ïshap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘b›ß·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÝ"ReturningÈ ÝaÈ ÝnullÈ ÝpoŽ‘kÆÜinterÈ Ý(0).\n\n"Ž’½Ô/·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½staticu½‰™šs4Ž‘ÔwcastŽ‘vd_·hÂShapQÇeŽ‘"Ab·Ž‘'Aci«(0Ž‘);Ž¡‘·gŽ¡‘ -gŽ©Â1318.‘ üGet–ÕTCircle“pQÇoin®9ter.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.04.11.«]Ž‘Y;Added–UUthis“function.Ž¡‘ -[¬LDF‘T2003.04.30.«]Ž‘Y;Changed–UUthis“function,“so“that“it“no“longer“uses“Ïget‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ‘<ö¹«(‘ª®).Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·ŽŸ ‘ -ÂvirtualŽ‘/ÔconstŽ‘M¸vCircleŽ‘op÷·Ž‘tpøÏget‘‰ffŽ–®cir‘ÿ}'cle‘‰ffŽ“ptrŽ’­°7«(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±sŽ‘pÜS«)‘UUÂconstŽ‘*¢«;Ž¦Â1319.Ž¡·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¤ ‘ -ÂconstŽ‘(*£CircleŽ‘Iã$·Ž‘Nã%ÂSolidŽ‘ia«::‘Ïget‘‰ffŽ–®cir‘ÿ}'cle‘‰ffŽ“ptrŽ‘:?C«(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±sŽ‘pÜS«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂifŽ‘´ú«(Ïcir‘ÿ}'clesŽ‘Œd±:ÏsizeŽ‘\«(‘ª¨)–DZ>“sŽ‘w«)‘·fŽ¡‘ÂreturnŽ‘Aæ½Ïcir‘ÿ}'clesŽ‘^s!«[±sŽ‘°«];Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘ÂreturnŽ‘Aæ½staticu½‰™šs4Ž‘ÔwcastŽ‘vd_·hÂconstŽ‘*¢CircleŽ‘?ã#·Ž‘Dã$i«(0Ž‘);Ž¡‘·gŽ¡‘ -gŽ¦Â1320.‘ üGet–ÕTEllipse“pQÇoin®9ter.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.04.11.«]Ž‘Y;Added–UUthis“function.Ž¡‘ -[¬LDF‘T2003.04.30.«]Ž‘Y;Changed–UUthis“function,“so“that“it“no“longer“uses“Ïget‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ‘<ö¹«(‘ª®).Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·ŽŸ ‘ -ÂvirtualŽ‘/ÔconstŽ‘M¸vEllipseŽ‘rö¤·Ž‘wö¥Ïget‘‰ffŽ–®el‘‚Ølipse‘‰ffŽ“ptrŽ’µ+ñ«(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±sŽ‘pÜS«)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹ŽÉl Šn ý‘ì«398›­GET–ÕXÂELLIPSE“­POINTER’íö3DLDFPRÃŽG˜·x«1321Ž €n ý•@PÂ1321.Ž©·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¤ ‘ -ÂconstŽ‘(*£EllipseŽ‘MhÑ·Ž‘RhÒÂSolidŽ‘læ­«::‘Ïget‘‰ffŽ–®el‘‚Ølipse‘‰ffŽ“ptrŽ‘>5P«(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±sŽ‘pÜS«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂifŽ‘´ú«(Ïel‘‚ØlipsesŽ‘ ‚q±:ÏsizeŽ‘\«(‘ª¨)–DZ>“sŽ‘w«)‘·fŽ¡‘ÂreturnŽ‘Aæ½Ïel‘‚ØlipsesŽ‘bi.«[±sŽ‘°«];Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘ÂreturnŽ‘Aæ½staticu½‰™šs4Ž‘ÔwcastŽ‘vd_·hÂconstŽ‘*¢EllipseŽ‘ChзŽ‘HhÑi«(0Ž‘);Ž¡‘·gŽ¡‘ -gŽŸÂ1322.‘ üGet–ÕTPš®9ath“pQÇoin˜ter.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.04.11.«]Ž‘Y;Added–UUthis“function.Ž¡‘ -[¬LDF‘T2003.04.30.«]Ž‘Y;Changed–UUthis“function,“so“that“it“no“longer“uses“Ïget‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ‘<ö¹«(‘ª®).Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/ÔconstŽ‘M¸vP®9athŽ‘iŸ/·Ž‘nŸ0Ïget‘‰ffŽ–®p‘ÿ}'ath‘‰ffŽ“ptrŽ’¢â¸«(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±sŽ‘pÜS«)‘UUÂconstŽ‘*¢«;ŽŸÂ1323.Ž¦·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¡‘ -ÂconstŽ‘(*£P®9athŽ‘D\·Ž‘I]ÂSolidŽ‘c8«::‘Ïget‘‰ffŽ–®p‘ÿ}'ath‘‰ffŽ“ptrŽ‘5CŒ«(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±sŽ‘pÜS«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂifŽ‘´ú«(Ïp‘ÿ}'athsŽ‘­±:ÏsizeŽ‘\«(‘ª¨)–DZ>“sŽ‘w«)‘·fŽ¡‘ÂreturnŽ‘Aæ½Ïp‘ÿ}'athsŽ‘Ywj«[±sŽ‘°«];Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘ÂreturnŽ‘Aæ½staticu½‰™šs4Ž‘ÔwcastŽ‘vd_·hÂconstŽ‘*¢P®9athŽ‘:[·Ž‘?\i«(0Ž‘);Ž¡‘·gŽ¡‘ -gŽŸÂ1324.‘ üGet–ÕTRectangle“pQÇoin®9ter.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.04.11.«]Ž‘Y;Added–UUthis“function.Ž¡‘ -[¬LDF‘T2003.04.30.«]Ž‘Y;Changed–UUthis“function,“so“that“it“no“longer“uses“Ïget‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ‘<ö¹«(‘ª®).Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/ÔconstŽ‘M¸vRectangleŽ’ƒM`·Ž’ˆMaÏget‘‰ffŽ›®r–ÿ}'e“ctangle‘‰ffŽ˜ptrŽ’Р«(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±sŽ‘pÜS«)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹Ô† Šn ý‘ì·x«1325›­3DLDFPRÃŽG’ÔÇìGET–ÕXÂRECT‘ÿ -«ANGLE“­POINTER˜«399Ž €n ý•@PÂ1325.Ž©·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¤ ‘ -ÂconstŽ‘(*£RectangleŽ‘]¿·Ž‘b¿ŽÂSolidŽ‘}=i«::‘Ïget‘‰ffŽ›®r–ÿ}'e“ctangle‘‰ffŽ˜ptrŽ‘IS$«(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±sŽ‘pÜS«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂifŽ‘´ú«(Ïr–ÿ}'e“ctanglesŽ‘+ E±:ÏsizeŽ‘\«(‘ª¨)–DZ>“sŽ‘w«)‘·fŽ¡‘ÂreturnŽ‘Aæ½Ïr–ÿ}'e“ctanglesŽ‘m‡«[±sŽ‘°«];Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘ÂreturnŽ‘Aæ½staticu½‰™šs4Ž‘ÔwcastŽ‘vd_·hÂconstŽ‘*¢RectangleŽ‘S¿Œ·Ž‘X¿i«(0Ž‘);Ž¡‘·gŽ¡‘ -gŽŸÂ1326.‘ üGet–ÕTReg‘°¡‰ffs4Ž‘#ÕPš®9olygon“pQÇoin˜ter.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.04.11.«]Ž‘Y;Added–UUthis“function.Ž¡‘ -[¬LDF‘T2003.04.30.«]Ž‘Y;Changed–UUthis“function,“so“that“it“no“longer“uses“Ïget‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ‘<ö¹«(‘ª®).Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/ÔconstŽ‘M¸vRegu½‰™šs4Ž‘ÔwP®9olygonŽ’’Œ·Ž’—Œ€Ïget‘‰ffŽ›®r–ÿ}'e“g‘‰ffŽ˜p“olygon‘‰ffŽ˜ptrŽ’ê2««(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±sŽ‘pÜS«)‘UUÂconstŽ‘*¢«;ŽŸÂ1327.Ž¦·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¡‘ -ÂconstŽ‘(*£Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘lþ¬·Ž‘qþ­ÂSolidŽ’Œ|ˆ«::‘Ïget‘‰ffŽ›®r–ÿ}'e“g‘‰ffŽ˜p“olygon‘‰ffŽ˜ptrŽ‘S¦/«(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±sŽ‘pÜS«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂifŽ‘´ú«(Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP±:ÏsizeŽ‘\«(‘ª¨)–DZ>“sŽ‘w«)‘·fŽ¡‘ÂreturnŽ‘Aæ½Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘wÚ «[±sŽ‘°«];Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘ÂreturnŽ‘Aæ½staticu½‰™šs4Ž‘ÔwcastŽ‘vd_·hÂconstŽ‘*¢Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘bþ«·Ž‘gþ¬i«(0Ž‘);Ž¡‘·gŽ¡‘ -gŽŸÂ1328.› üGetting– ÍShapQÇe“cen®9ters.˜«[¬LDF‘T2003.04.30.«]Ž‘[—TO–cèDO:›d.I“think˜it˜migh¸ãt˜b•Ge˜p“ossible˜to˜co“de˜theŽ¡functions–UUin“this“section“more“succinctly‘ÿ*ª.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.04.11.«]Ž‘Y;Added–UUthis“section.Ž¦ŸüÈ„`ÕÁGŽŽŽŽŒ‹Ý® Šn ý‘ì«400›­GET–ÕXSHAPE“CENTER’o3DLDFPRÃŽG˜·x«1329Ž €n ý•@PÂ1329.› üGet–7•ShapQÇe“cen®9ter.˜«This–‰afunction“returns“the“cen¸ãter“of“the“ÂCircleŽ‘"ì«,‘ÖdÂEllipseŽ‘&¿=«,‘ÖdÂRectangleŽ‘7ù«,‘ÖdorŽ¤ ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘E¼ž«n•¸ãum“bšGer‘=ê±sŽ‘ +Ô«in‘=êÏcir‘ÿ}'clesŽ‘ ÊN«,‘xÏel‘‚ØlipsesŽ‘$ú«,‘xÏr–ÿ}'e“ctanglesŽ‘0S«,–xor‘=êÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:1:«,“resp˜ectiv¸ãely‘ÿ*ª.‘+…If‘=ê±sŽ‘ +Ô«is–=êlarger“thanŽ¡·hÏve‘ÿ}'ctor‘·i±:‘UUÏsizeŽ‘p±«(‘ª®),–UUan“error“message“is“issued“and“ÝINVALID_POINTŽ‘Kpë«is“returned.Ž¡‘ -One–q)of“the“folloš¸ãwing“ÂpublicŽ‘& 'staticŽ‘E„ÔconstŽ‘cËJ«data“mem˜bšGers“of“ÂSolidŽ‘ `)«can“(and“probably“should)“b˜e“used“asŽ¡the‘UUÏshap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘4l«argumen¸ãt:‘qÇÝCIRCLEŽ‘$x«,‘UUÝELLIPSEŽ‘(›¨«,‘UUÝRECTANGLEŽ‘3¢«,–UUand“ÝREG_POLYGONŽ‘=›œ«.Ž¡‘ -!!‘ZNote–¢Æthat“this“function“will“ha•¸ãv“e–¢Æto“bGe“cš¸ãhanged,‘¶"if“new“v˜ectors“of“ÂShapQÇeŽ‘&1™«pGoin˜ters“are“added“to“ÂclassŽŽ¡SolidŽ‘}׫!ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.10.16.«]Ž‘Y;Added–UUthis“function.Ž¡‘ -[¬LDF‘T2003.04.09.«]Ž‘Y;Mo•¸ãv“ed–UUthis“function“from“ÂP®9olyhedronŽ‘@¸w«to“ÂSolidŽ‘Ó,«.Ž¡‘ -[¬LDF‘T2003.04.11.«]Ž‘X-ŸChanged–z¹this“function“from“Ïget‘‰ffŽ–®p›ÿ}'olygon‘‰ffŽ“c˜enterŽ‘RÚ¤«(›ª®)“to“Ïget‘‰ffŽ–®shap›ÿ}'e‘‰ffŽ“c˜enterŽ‘Ièá«(˜).‘(éAdded“the“Âc®9harŽŽ¡«argumenš¸ãt‘Á„Ïshap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘5WÊ«to–Á„indicate“whether“it“should“return“the“cen˜ter“of“a“ÂCircleŽ‘"$°«,‘ÜÂEllipseŽ‘%Åi«,‘ÜÂRectangleŽ‘6%«,‘ÜorŽ¡ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘A~´«.Ž¡‘ -[¬LDF‘T2003.04.11.«]Ž‘Y;Changed–UUthe“Ïshap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘4l«argumen¸ãt“from“Âc®9harŽ‘¿ž«to“ÂconstŽ‘!÷unsignedŽ‘Q·shortŽ‘l,S«.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·Ž¤ ‘ -ÂvirtualŽ‘/˜;constŽ‘MÍDP•®9oin“tŽ‘lÇH«&Ž‘tŽfÏget‘‰ffŽ–®shap›ÿ}'e‘‰ffŽ“c˜enterŽ’»üŽ«(ÂconstŽ‘5 unsignedŽ‘Nv~shortŽ‘lKˆÏshap–ÿ}'e‘‰ffŽ‘®typ“eŽ’š J±;‘ª¨ÂconstŽ‘ß±unsignedŽ‘P!&shortŽ‘mö0±sŽ‘r¦0«)Ž¡‘ÂconstŽ‘8ÕP«;ŽŽŽŒ‹‘æ° Šn ý‘ì·x«1330›­3DLDFPRÃŽG’oGET–ÕXSHAPE“CENTER˜«401Ž €n ý•@PÂ1330.ŽŸ·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¤ ‘ -ÂconstŽ‘(F(P•®9oin“tŽ‘GQJ«&Ž‘OhÂSolidŽ‘i–C«::‘Ïget‘‰ffŽ–®shap›ÿ}'e‘‰ffŽ“c˜enterŽ‘Hn,«(ÂconstŽ‘F'unsignedŽ‘N˜ºshortŽ‘l~âÏshap–ÿ}'e‘‰ffŽ‘®typ“eŽ’šS¤±;‘ª¨ÂconstŽ‘ðÏunsignedŽ‘PCbshortŽ‘n)Š±sŽ‘rÙŠ«)Ž¡‘2ÂconstŽŽ¡‘ -·fŽ¡‘ÂifŽ‘´ú«(Ïshap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘0›Ú·‘ÇÝCIRCLEŽ‘"Ín«)‘·fŽ¡‘ÂifŽ‘)´û«(±sŽ‘w<‘ÇÏcir‘ÿ}'clesŽ‘S|±:ÏsizeŽ‘\«(–ª¨))‘ÂreturnŽ‘(æºÏcir‘ÿ}'clesŽ‘Es«[±sŽ‘°«]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®c‘ÿ}'enterŽ‘0=H«(“);Ž¡‘ÂelseŽ‘5Øâ·fŽ¡‘(Ïc‘ÿ}'errŽ‘@ W·‘S­Ý"ERROR!È ÝInÈ ÝSolid::geŽ‘nSqt_shape_center():\n"Ž’Ý-J·‘S­Ý"sÈ Ý("Ž‘%m³·‘S­±sŽ‘WZ·Ž¡‘<Ý")È Ý>È Ýcircles.size()È Ž’¤ÿÊÝ("Ž’³>Ù·‘8­Ïcir‘ÿ}'clesŽ‘ű:ÏsizeŽ‘\«(‘ª¨)–8­·“Ý")\nReturningÈ ÝINVALIŽ‘l8qD_POINT.\n\n"Ž’´7_·Ž¡‘<Ï ushŽ‘Q¹«;Ž¡‘(ÂreturnŽ‘Kæ¾ÝINVALID_POINTŽ’¬ÿ«;Ž¡‘·gŽ¡‘gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(Ïshap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘0›Ú·‘ÇÝELLIPSEŽ‘( k«)‘·fŽ¡‘ÂifŽ‘)´û«(±sŽ‘w<‘ÇÏel‘‚ØlipsesŽ‘#I‰±:ÏsizeŽ‘\«(–ª¨))‘ÂreturnŽ‘(æºÏel‘‚ØlipsesŽ‘Ii+«[±sŽ‘°«]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®c‘ÿ}'enterŽ‘0=H«(“);Ž¡‘ÂelseŽ‘5Øâ·fŽ¡‘(Ïc‘ÿ}'errŽ‘@ W·‘S­Ý"ERROR!È ÝInÈ ÝSolid::geŽ‘nSqt_shape_center():\n"Ž’Ý-J·‘S­Ý"sÈ Ý("Ž‘%m³·‘S­±sŽ‘WZ·Ž¡‘<Ý")È Ý>È Ýellipses.size()Ž’¤ÿÊÈ Ý("Ž’¸ES·‘ÿ*Ïel‘‚ØlipsesŽ‘#›±:ÏsizeŽ‘\«(‘ª¨)–ÿ*·“Ý")\nReturningÈ ÝINVALIŽ‘kþîD_POINT.\n\n"Ž’³ÄY·Ž¡‘<Ï ushŽ‘Q¹«;Ž¡‘(ÂreturnŽ‘Kæ¾ÝINVALID_POINTŽ’¬ÿ«;Ž¡‘·gŽ¡‘gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(Ïshap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘0›Ú·‘ÇÝRECTANGLEŽ‘2e«)‘·fŽ¡‘ÂifŽ‘)´û«(±sŽ‘w<‘ÇÏr–ÿ}'e“ctanglesŽ‘.g]±:ÏsizeŽ‘\«(–ª¨))‘ÂreturnŽ‘(æºÏr–ÿ}'e“ctanglesŽ‘T†ÿ«[±sŽ‘°«]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®c‘ÿ}'enterŽ‘0=H«(“);Ž¡‘ÂelseŽ‘5Øâ·fŽ¡‘(Ïc‘ÿ}'errŽ‘@§‘·‘ñçÝ"ERROR!È ÝInÈ ÝSolid::geŽ‘nñ«t_shape_center():\n"Ž’Þi¾·‘ñçÝ"sÈ Ý("Ž‘&ª'·Ž¡‘<±sŽ‘GGô·‘—îÝ")È Ý>È Ýrectangles.sizeŽ‘o—²()È Ý("Ž’õù·‘—îÏr–ÿ}'e“ctanglesŽ‘283±:ÏsizeŽ‘\«(‘ª¨)‘—î·Ž¡‘<Ý")\nReturningÈ ÝINVALIŽ’¤ÿÊD_POINT.\n\n"Ž’ì#·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾ÝINVALID_POINTŽ’¬ÿ«;Ž¡‘·gŽ¡‘gŽ¡‘ÂelseŽ‘*.6ifŽ‘5ã.«(Ïshap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘0›Ú·‘ÇÝREG_POLYGONŽ‘= _«)‘·fŽ¡‘ÂifŽ‘)´û«(±sŽ‘w<‘ÇÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh±:ÏsizeŽ‘\«(–ª¨))‘ÂreturnŽ‘(æºÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘^Ú -«[±sŽ‘°«]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®c‘ÿ}'enterŽ‘0=H«(“);Ž¡‘ÂelseŽ‘5Øâ·fŽ¡‘(Ïc‘ÿ}'errŽ‘@§‘·‘ñçÝ"ERROR!È ÝInÈ ÝSolid::geŽ‘nñ«t_shape_center():\n"Ž’Þi¾·‘ñçÝ"sÈ Ý("Ž‘&ª'·Ž¡‘<±sŽ‘FÅî·‘èÝ")È Ý>È Ýreg_polygons.siŽ‘o¬ze()È Ý("Ž’šqç·‘èÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘< 8±:ÏsizeŽ‘\«(‘ª¨)‘è·Ž¡‘<Ý")\nReturningÈ ÝINVALIŽ’¤ÿÊD_POINT.\n\n"Ž’ì#·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾ÝINVALID_POINTŽ’¬ÿ«;Ž¡‘·gŽ¡‘gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘Ïc‘ÿ}'errŽ‘8(¢·‘rùÝ"ERROR!È ÝInÈ ÝSolid::geŽ‘pr½t_shape_center():\n"Ž’ákâ·Ž¡‘2Ý"InvalidÈ ÝargumentÈ ÝfoŽ’šÿÉrÈ Ýshape_type:È Ý"Ž’𯷑ثÏshap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘9†·‘Ø«Ïend‘‚ØlŽ‘£·Ž¡‘2Ý"ReturningÈ ÝINVALID_PŽ’šÿÉOINT.\n\n"Ž’ÒÍ+·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘Aæ½ÝINVALID_POINTŽ’†¬þ«;Ž¡‘·gŽ¡‘ -gŽŽŽŒ‹’ﯠŠn ý‘ì«402‘­GET–ÕXCIRšÃŽCLE“CENTER’šé3DLDFPR˜G‘·x«1331Ž €n ý•@PÂ1331.‘ üGet–ÕTCircle“cen®9ter.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ© ‘ -«[¬LDF‘T2003.04.11.«]Ž‘Y;Added–UUthis“function.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·Ž¦‘ -ÂvirtualŽ‘/ÔconstŽ‘M¸vP•®9oin“tŽ‘l¨«&Ž‘to1Ïget‘‰ffŽ–®cir›ÿ}'cle‘‰ffŽ“c˜enterŽ’»{4«(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±sŽ‘pÜS«)‘UUÂconstŽ‘*¢«;ŽŸÂ1332.Ž¡·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¦‘ -ÂconstŽ‘(*£P•®9oin“tŽ‘G@«&Ž‘Ná^ÂSolidŽ‘i_9«::‘Ïget‘‰ffŽ–®cir›ÿ}'cle‘‰ffŽ“c˜enterŽ‘H «(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±sŽ‘pÜS«)‘UUÂconstŽŽ¦‘ -·fŽ¦‘ÂreturnŽ‘7æ¼Ïget‘‰ffŽ–®shap›ÿ}'e‘‰ffŽ“c˜enterŽ‘Tä«(ÝCIRCLEŽ‘ V±;‘ª¨sŽ‘Z¨«);Ž¦‘ -·gŽŸÂ1333.‘ üGet–ÕTEllipse“cen®9ter.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ -«[¬LDF‘T2003.04.11.«]Ž‘Y;Added–UUthis“function.Ž¡ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·Ž¦‘ -ÂvirtualŽ‘/ÔconstŽ‘M¸vP•®9oin“tŽ‘l¨«&Ž‘to1Ïget‘‰ffŽ–®el‘‚Ølipse‘‰ffŽ“c‘ÿ}'enterŽ’¿qA«(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±sŽ‘pÜS«)‘UUÂconstŽ‘*¢«;ŽŸÂ1334.Ž¡·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¦‘ -ÂconstŽ‘(*£P•®9oin“tŽ‘G@«&Ž‘Ná^ÂSolidŽ‘i_9«::‘Ïget‘‰ffŽ–®el‘‚Ølipse‘‰ffŽ“c‘ÿ}'enterŽ‘L«(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±sŽ‘pÜS«)‘UUÂconstŽŽ¦‘ -·fŽ¦‘ÂreturnŽ‘7æ¼Ïget‘‰ffŽ–®shap›ÿ}'e‘‰ffŽ“c˜enterŽ‘Tä«(ÝELLIPSEŽ‘%FS±;‘ª¨sŽ‘Z¨«);Ž¦‘ -·gŽŸÂ1335.‘ üGet–ÕTRectangle“cen®9ter.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ -«[¬LDF‘T2003.04.11.«]Ž‘Y;Added–UUthis“function.Ž¡ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·Ž¦‘ -ÂvirtualŽ‘/ÔconstŽ‘M¸vP•®9oin“tŽ‘l¨«&Ž‘to1Ïget‘‰ffŽ›®r–ÿ}'e“ctangle‘‰ffŽ˜c“enterŽ’Ê«(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±sŽ‘pÜS«)‘UUÂconstŽ‘*¢«;ŽŸÂ1336.Ž¡·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¦‘ -ÂconstŽ‘(*£P•®9oin“tŽ‘G@«&Ž‘Ná^ÂSolidŽ‘i_9«::‘Ïget‘‰ffŽ›®r–ÿ}'e“ctangle‘‰ffŽ˜c“enterŽ‘Wè«(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±sŽ‘pÜS«)‘UUÂconstŽŽ¦‘ -·fŽ¦‘ÂreturnŽ‘7æ¼Ïget‘‰ffŽ–®shap›ÿ}'e‘‰ffŽ“c˜enterŽ‘Tä«(ÝRECTANGLEŽ‘/ÆM±;‘ª¨sŽ‘Z¨«);Ž¦‘ -·gŽŽŽŒ‹“ýŒ Šn ý‘ì·x«1337›­3DLDFPRÃŽG’ÉÚàGET–ÕXÂREG‘°¡‰ffs4Ž‘#ÕPOL‘ÿ -«YGON“­CENTER˜«403Ž €n ý•@PÂ1337.‘ üGet–ÕTReg‘°¡‰ffs4Ž‘#ÕPš®9olygon“cen˜ter.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ© ‘ -«[¬LDF‘T2003.04.11.«]Ž‘Y;Added–UUthis“function.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·Ž¦‘ -ÂvirtualŽ‘/ÔconstŽ‘M¸vP•®9oin“tŽ‘l¨«&Ž‘to1Ïget‘‰ffŽ›®r–ÿ}'e“g‘‰ffŽ˜p“olygon‘‰ffŽ˜c“enterŽ’Ôâ «(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±sŽ‘pÜS«)‘UUÂconstŽ‘*¢«;ŽŸÂ1338.Ž¡·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¦‘ -ÂconstŽ‘(*£P•®9oin“tŽ‘G@«&Ž‘Ná^ÂSolidŽ‘i_9«::‘Ïget‘‰ffŽ›®r–ÿ}'e“g‘‰ffŽ˜p“olygon‘‰ffŽ˜c“enterŽ‘aró«(ÂconstŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±sŽ‘pÜS«)‘UUÂconstŽŽ¦‘ -·fŽ¦‘ÂreturnŽ‘7æ¼Ïget‘‰ffŽ–®shap›ÿ}'e‘‰ffŽ“c˜enterŽ‘Tä«(ÝREG_POLYGONŽ‘:FG±;‘ª¨sŽ‘Z¨«);Ž¦‘ -·gŽŸÂ1339.‘ üIs–ÕTon“free“store.Ž¡·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·Ž¦‘ -ÂvirtualŽ‘/Ôb•QÇo“olŽ‘I/:Ïis‘‰ffŽ–®on‘‰ffŽ“fr–ÿ}'e“e‘‰ffŽ‘®stor“eŽ’‹ª«(‘ª®)‘UUÂconstŽ‘*¢«;ŽŸÂ1340.Ž¡·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¦‘ -Âb•QÇo“olŽ‘#¡gSolidŽ‘>B«::‘Ïis‘‰ffŽ–®on‘‰ffŽ“fr–ÿ}'e“e‘‰ffŽ‘®stor“eŽ‘CzÙ«(‘ª®)‘UUÂconstŽŽ¦‘ -·fŽ¦‘Âb•QÇo“olŽ‘-¡h±bŽ‘4³*«=‘ÇÏtrueŽ‘‹°«;Ž¡‘ÂreturnŽ‘7æ¼±bŽ‘<1f«;Ž¦‘ -·gŽŸÂ1341.‘ üSho®9w.Ž¡·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·Ž¦‘ -ÂvirtualŽ‘/Õ[v®9oidŽ‘IºÏshowŽ‘_¥¹«(ÂstringŽ‘!lÔÏtextŽ‘6î«=‘>NÝ""Ž‘D°±;‘ª¨Âc®9harŽ‘\xÏc–ÿ}'o“or“dsŽ‘:¤R«=‘>NÝ'w'Ž‘„­±;‘ª¨ÂconstŽ‘ Ñb•QÇo“olŽ‘:¾Ïdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘bíD«=‘>NÏtrueŽ‘æ±;‘ª¨ÂconstŽ‘ Ñb•QÇo“olŽŽ¦‘Ïdo‘‰ffŽ‘®applyŽ‘Gd«=‘ŒÏtrueŽ‘Ó$±;‘ª¨ÂF‘ÿ -«oQÇcusŽ‘" )·Ž‘' *±fŽ‘0'œ«=‘Œ0Ž‘±;‘ª¨ÂconstŽ‘ *unsignedŽ‘PbshortŽ‘nW›Ïpr‘ÿ}'ojŽ’„Yê«=‘ŒÂPro‘£ŽjectionsŽ‘=Úð«::Ž‘Di.ÝPERSPŽ‘_/‡±;‘ª¨ÂconstŽ‘ *realŽŽ¦‘ÏfactorŽ‘;Êù«=‘Ç1Ž‘Ç)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹”– Šn ý‘ì«404›­SHO•ÃŽW’C’E3DLDFPR“G˜·x«1342Ž €n ý•@PÂ1342.Ž©·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¤ ‘ -Âv®9oidŽ‘#ŒhSolidŽ‘> -C«::‘ÏshowŽ‘‹«(ÂstringŽ‘!³ÜÏtextŽ‘3 ¨±;‘ª¨Âc®9harŽ‘£€Ïc–ÿ}'o“or“dsŽ‘7­ ±;‘ª¨ÂconstŽ‘ cÙb•QÇo“olŽ‘:“ÎÏdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘`=±;‘ª¨ÂconstŽ‘ cÙb•QÇo“olŽ‘:“ÎÏdo‘‰ffŽ‘®applyŽ‘`ž£±;‘ª¨ÂF‘ÿ -«oQÇcusŽŽ¡‘2·Ž‘7±fŽ‘<øì;‘ª¨ÂconstŽ‘ÕJunsignedŽ‘P XshortŽ‘mÖûÏpr‘ÿ}'ojŽ’€Ê¾±;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆxÏfactorŽ‘QŒV«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂifŽ‘´ú«(ÏtextŽ‘ä·‘ÇÝ""Ž‘ Íz«)‘ÏtextŽ‘ä«=‘ÇÝ"Solid:"Ž‘-Mh«;Ž¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÏtextŽ‘åü·‘ÇÏend‘‚ØlŽ‘¸Ú«;Ž¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"on_free_storeÈ Ý==È Ý"Ž‘iÔ_·‘ÇÏon‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘=3"·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¦‘ÂstringstreamŽ‘W,¹±gŽ‘\Mœ«;Ž¡‘Âin®9tŽ‘%¤ù±iŽ‘)í«;Ž¦‘ÂifŽ‘´ú«(Ïp‘ÿ}'athsŽ‘­±:ÏsizeŽ‘\«(‘ª¨)–DZ>“«0Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"ShowingÈ Ýpaths.\n"Ž‘aÍJ«;Ž¡‘±iŽ‘$9«=‘Ç0Ž‘Ç;Ž¡‘ÂforŽ‘/艫(Âv®9ectorŽ‘ªH·hÂP®9athŽ‘æ¹·Ž‘ æºi‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W«=‘ÇÏp‘ÿ}'athsŽ–Wű:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏp‘ÿ}'athsŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘(±gŽ‘/çÿ·‘ÇÝ"PathÈ Ý"Ž‘*Ôƒ·‘DZiŽ‘¹ Ÿÿ®+‘ÿ+ŽŽ‘GD·‘ÇÝ":"Ž‘ w«;Ž¡‘((·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:ÏshowŽ‘Šÿ«(±gŽ‘ ã:ÏstrŽ‘ 7«(–ª¨)±;“Ïc–ÿ}'o“or“dsŽ‘´4±;“Ïdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘'Sà±;“Ïdo‘‰ffŽ‘®applyŽ‘'µ}±;“fŽ‘£Ž;“Ïpr‘ÿ}'ojŽ‘žk±;“ÏfactorŽ‘®†«);Ž¡‘(±gŽ‘- ç:ÏstrŽ‘ 7«(Ý""Ž‘ b«);Ž¡‘·gŽ¡‘gŽ¡‘ÂelseŽ‘+ØáÏc‘ÿ}'outŽ‘Aù0·‘ÇÝ"pathsÈ ÝisÈ Ýempty.\n"Ž‘g G«;Ž¡‘ÂifŽ‘´ú«(Ïcir‘ÿ}'clesŽ‘Œd±:ÏsizeŽ‘\«(‘ª¨)–DZ>“«0Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"ShowingÈ Ýcircles.\n"Ž‘lMD«;Ž¡‘±iŽ‘$9«=‘Ç0Ž‘Ç;Ž¡‘ÂforŽ‘/艫(Âv®9ectorŽ‘ªH·hÂCircleŽ‘!¸·Ž‘&¸‚i‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W«=‘ÇÏcir‘ÿ}'clesŽ–S|±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏcir‘ÿ}'clesŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘(±gŽ‘/çÿ·‘ÇÝ"CircleÈ Ý"Ž‘5T}·‘DZiŽ‘¹ Ÿÿ®+‘ÿ+ŽŽ‘GD·‘ÇÝ":"Ž‘ w«;Ž¡‘((·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:ÏshowŽ‘Šÿ«(±gŽ‘ ã:ÏstrŽ‘ 7«(–ª¨)±;“Ïc–ÿ}'o“or“dsŽ‘´4±;“Ïdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘'Sà±;“Ïdo‘‰ffŽ‘®applyŽ‘'µ}±;“fŽ‘£Ž;“Ïpr‘ÿ}'ojŽ‘žk±;“ÏfactorŽ‘®†«);Ž¡‘(±gŽ‘- ç:ÏstrŽ‘ 7«(Ý""Ž‘ b«);Ž¡‘·gŽ¡‘gŽ¡‘ÂelseŽ‘+ØáÏc‘ÿ}'outŽ‘Aù0·‘ÇÝ"circlesÈ ÝisÈ Ýempty.\nŽ‘kÆÜ"Ž‘qA«;Ž¡‘ÂifŽ‘´ú«(Ïel‘‚ØlipsesŽ‘ ‚q±:ÏsizeŽ‘\«(‘ª¨)–DZ>“«0Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"ShowingÈ Ýellipses.\nŽ‘kÆÜ"Ž‘qA«;Ž¡‘±iŽ‘$9«=‘Ç0Ž‘Ç;Ž¡‘ÂforŽ‘/艫(Âv®9ectorŽ‘ªH·hÂEllipseŽ‘%>.·Ž‘*>/i‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W«=‘ÇÏel‘‚ØlipsesŽ–#I‰±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏel‘‚ØlipsesŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘(±gŽ‘/çÿ·‘ÇÝ"EllipseÈ Ý"Ž‘:”z·‘DZiŽ‘¹ Ÿÿ®+‘ÿ+ŽŽ‘GD·‘ÇÝ":"Ž‘ w«;Ž¡‘((·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:ÏshowŽ‘Šÿ«(±gŽ‘ ã:ÏstrŽ‘ 7«(–ª¨)±;“Ïc–ÿ}'o“or“dsŽ‘´4±;“Ïdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘'Sà±;“Ïdo‘‰ffŽ‘®applyŽ‘'µ}±;“fŽ‘£Ž;“Ïpr‘ÿ}'ojŽ‘žk±;“ÏfactorŽ‘®†«);Ž¡‘(±gŽ‘- ç:ÏstrŽ‘ 7«(Ý""Ž‘ b«);Ž¡‘·gŽ¡‘gŽ¡‘ÂelseŽ‘+ØáÏc‘ÿ}'outŽ‘Aù0·‘ÇÝ"ellipsesÈ ÝisÈ Ýempty.\Ž‘kÆÜn"Ž‘vÍ>«;Ž¡‘ÂifŽ‘´ú«(Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP±:ÏsizeŽ‘\«(‘ª¨)–DZ>“«0Ž‘Ç)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"ShowingÈ Ýreg_polygonŽ‘kÆÜs.\n"Ž’†5«;Ž¡‘±iŽ‘$9«=‘Ç0Ž‘Ç;Ž¡‘ÂforŽ‘/M«(Âv®9ectorŽ‘ªH·hÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘D8ÿ·Ž‘I9i‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W«=‘ÇÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ–8ºh±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘dóÏiterŽ‘÷ ·6«=‘ÇÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ“±:ÏendŽ‘ಫ(˜);Ž¡‘<€Ÿÿ®+‘ÿ+ŽŽ‘HG&ÏiterŽ‘Y$«)‘·fŽ¡‘(±gŽ‘/çÿ·‘ÇÝ"PolygonÈ Ý"Ž‘:”z·‘DZiŽ‘¹ Ÿÿ®+‘ÿ+ŽŽ‘GD·‘ÇÝ":"Ž‘ w«;Ž¡‘((·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:ÏshowŽ‘Šÿ«(±gŽ‘ ã:ÏstrŽ‘ 7«(–ª¨)±;“Ïc–ÿ}'o“or“dsŽ‘´4±;“Ïdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘'Sà±;“Ïdo‘‰ffŽ‘®applyŽ‘'µ}±;“fŽ‘£Ž;“Ïpr‘ÿ}'ojŽ‘žk±;“ÏfactorŽ‘®†«);Ž¡‘(±gŽ‘- ç:ÏstrŽ‘ 7«(Ý""Ž‘ b«);Ž¡‘·gŽ¡‘gŽ¡‘ÂelseŽ‘+ØáÏc‘ÿ}'outŽ‘Aù0·‘ÇÝ"reg_polygonsÈ ÝisÈ 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nition“with“a“real“one.‘ONo˜w,‘±ƒÏcle‘ÿ}'arŽ‘Ú\«(‘ª®)“is“called“forŽ¡all–UUof“the“ob‘Ž8jects“in“the“ÂSolidŽ‘Ó,«.ŽŸ·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/Ôv®9oidŽ‘H‹¬Ïcle‘ÿ}'arŽ‘^´…«(‘ª®);Ž¦Â1344.Ž©·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙSolidŽ‘={´«::‘Ïcle‘ÿ}'arŽ‘(Ý«(‘ª®)Ž¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EnteringÈ ÝSolid::cleŽ‘kÆÜar().\n"Ž’™D·‘ÇÏ ushŽ‘€«;Ž¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂP®9athŽ‘æ¹·Ž‘ æºi‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘ÇÏp‘ÿ}'athsŽ–Wű:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏp‘ÿ}'athsŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïcle‘ÿ}'arŽ‘(Ù«(˜);Ž¡‘Ïp‘ÿ}'athsŽ‘+¯±:Ïcle‘ÿ}'arŽ‘(Ù«(‘ª¨);Ž¡‘ÂforŽ‘%åì«(Âv®9ectorŽ‘ªH·hÂCircleŽ‘!µå·Ž‘&µæi‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘ÇÏcir‘ÿ}'clesŽ–S|±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ýaÏiterŽ‘w·6«=‘ÇÏcir‘ÿ}'clesŽ“±:ÏendŽ‘ಫ(˜);‘}aŸÿ®+‘ÿ+ŽŽ‘DÏiterŽ‘"«)‘(·Ž‘Ž‘ 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-ÏiterŽ‘Ë«)±:Ïcle‘ÿ}'arŽ‘(Ù«(‘ª¨);Ž¡‘Ïr–ÿ}'e“ctanglesŽ‘? G±:Ïcle‘ÿ}'arŽ‘(Ù«(‘ª¨);Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ExitingÈ ÝSolid::cleaŽ‘kÆÜr().\n"Ž’“ÔG·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘4‘g«;Ž¡‘ -·gŽ¤Â1345.‘ üT‘ÿ -«ransformations.Ž¡1346.‘ üMultiplying–ÕTb®9y“a“T‘ÿ -«ransform.Ž¦·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·ŽŸ ‘ -ÂvirtualŽ‘/ÔT‘ÿ -«ransformŽ‘gV¦opQÇeratorŽ’’í[·«=ŽŽŽ’Ÿ´z(ÂconstŽ‘*¢T‘ÿ -«ransformŽ‘Uót«&Ž‘]º’±tŽ‘aW«);ŽŽŽŒ‹–"c Šn ý‘ì«406›­MUL–ÿJªTIPL“YING–ÕXBY“A“ÂTRANSF®9ORM’¹é÷­3DLDFPRÃŽG˜·x«1347Ž €n ý•@PÂ1347.Ž©·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¤ ‘ -ÂT‘ÿ -«ransformŽ‘AÈÓSolidŽ‘\F®«::Ž‘bÔìÂopQÇeratorŽ’Žk¡·«=ŽŽŽ’›2À(ÂconstŽ‘*¢T‘ÿ -«ransformŽ‘Uót«&Ž‘]º’±tŽ‘aW«)Ž¡‘ -·fŽ¡‘Ïc‘ÿ}'enterŽ‘2Ð¥·«=ŽŽ‘B^ܱtŽ‘EûN«;Ž¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂP®9athŽ‘æ¹·Ž‘ æºi‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘ÇÏp‘ÿ}'athsŽ–Wű:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏp‘ÿ}'athsŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·Ž‘ -Ž‘ÏiterŽ‘"’·«=ŽŽ‘2 O±tŽ‘5¼Á«;Ž¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂEllipseŽ‘%>.·Ž‘*>/i‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘ÇÏel‘‚ØlipsesŽ–#I‰±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏel‘‚ØlipsesŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·Ž‘ -Ž‘ÏiterŽ‘"’·«=ŽŽ‘2 O±tŽ‘5¼Á«;Ž¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂCircleŽ‘!¸·Ž‘&¸‚i‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘ÇÏcir‘ÿ}'clesŽ–S|±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏcir‘ÿ}'clesŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·Ž‘ -Ž‘ÏiterŽ‘"’·«=ŽŽ‘2 O±tŽ‘5¼Á«;Ž¡‘ÂforŽ‘&QË«(Âv®9ectorŽ‘ªH·hÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘E=L·Ž‘J=Mi‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=Ú¼«=‘v‡Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ–9i×±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘i@ÏiterŽ‘ªÅ·6«=‘v‡Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ“±:ÏendŽ‘ಫ(˜);Ž¡‘2€Ÿÿ®+‘ÿ+ŽŽ‘>G%ÏiterŽ‘O#«)‘·Ž‘ -Ž‘ÏiterŽ‘"’·«=ŽŽ‘2 O±tŽ‘5¼Á«;Ž¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂRectangleŽ‘5”ê·Ž‘:”ëi‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘ÇÏr–ÿ}'e“ctanglesŽ–.g]±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏr–ÿ}'e“ctanglesŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)Ž¡‘·Ž‘#Ž‘(ÏiterŽ‘;’·«=ŽŽ‘K R±tŽ‘N¼Ä«;Ž¡‘ÂreturnŽ‘7æ¼±tŽ‘;ƒ.«;Ž¡‘ -·gŽŸÂ1348.‘ üApplying–ÕTa“transformation.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.01.05.«]Ž‘Z‡{Added–Ô•this“function.‘ï†It's“noš¸ãw“needed“bGecause“I'v˜e“made“Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Jôt«(‘ª®)“a“pureŽ¡ÂvirtualŽ‘$Þ2«function–¥´in“ÂclassŽ‘ÖdShapQÇeŽ‘;Âq«.‘7.·Ž‘*>/i‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘ÇÏel‘‚ØlipsesŽ–#I‰±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏel‘‚ØlipsesŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨);Ž¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂCircleŽ‘!¸·Ž‘&¸‚i‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘ÇÏcir‘ÿ}'clesŽ–S|±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏcir‘ÿ}'clesŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)Ž¡‘(·Ž‘Ž‘ 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-«ransformŽ‘AÈÓSolidŽ‘\F®«::‘Ïsc‘ÿ}'aleŽ‘´ö«(ÂrealŽ‘³.ÏxxŽ‘!±f±;‘ª¨ÂrealŽ‘]ÖÏyyŽ‘#y3±;‘ª¨ÂrealŽ‘]ÖÏzzŽ‘"HÛ«)Ž¡‘ -·fŽ¡‘ÂT‘ÿ -«ransformŽ‘KÈÔ±tŽ‘OeF«;Ž¦‘±tŽ‘œt:Ïsc‘ÿ}'aleŽ‘´ò«(ÏxxŽ‘ -þ8±;‘ª¨ÏyyŽ‘ Ʊ;‘ª¨ÏzzŽ‘ •­«);Ž¡‘·Ž‘ÏthisŽ‘,²Ñ·«=ŽŽ‘«(ÂrealŽ‘³.ÏxyŽ‘!—±;‘ª¨ÂrealŽ‘]ÖÏxzŽ‘"Õ¨±;‘ª¨ÂrealŽ‘]ÖÏyxŽ‘#“„±;‘ª¨ÂrealŽ‘]ÖÏyzŽ‘# ±;‘ª¨ÂrealŽ‘]ÖÏzxŽ‘"ÏA±;‘ª¨ÂrealŽ‘]ÖÏzyŽ‘"´ð«)Ž¡‘ -·fŽ¡‘ÂT‘ÿ -«ransformŽ‘KÈÔ±tŽ‘OeF«;Ž¦‘±tŽ‘œt:Ïshe‘ÿ}'arŽ‘4:«(ÏxyŽ‘ -ãç±;‘ª¨ÏxzŽ‘ "z±;‘ª¨ÏyxŽ‘ àV±;‘ª¨ÏyzŽ‘ Yð±;‘ª¨ÏzxŽ‘ ±;‘ª¨ÏzyŽ‘ «);Ž¡‘·Ž‘ÏthisŽ‘,²Ñ·«=ŽŽ‘«(ÏxxŽ‘ -þ8±;‘ª¨ÏyyŽ‘ Ʊ;‘ª¨ÏzzŽ‘ •­«);Ž¡‘·Ž‘ÏthisŽ‘,²Ñ·«=ŽŽ‘Äç«&Ž‘FŒÏp1Ž‘R¢Å±;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆxÏangleŽ‘Qã«=‘Ç180ŽŽ‘Ç);ŽŸÂ1362.Ž¦·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¡‘ -ÂT‘ÿ -«ransformŽ‘AÈÓSolidŽ‘\F®«::‘Ïr‘ÿ}'otateŽ‘oB«(ÂconstŽ‘*¢P•®9oin“tŽ‘=?«&Ž‘Dá]Ïp0Ž‘Pø±;‘ª¨ÂconstŽ‘ÕJP•®9oin“tŽ‘>Äç«&Ž‘FŒÏp1Ž‘R¢Å±;‘ª¨ÂconstŽ‘ÕJrealŽ‘6ˆxÏangleŽ‘NHË«)Ž¡‘ -·fŽ¡‘ÂT‘ÿ -«ransformŽ‘KÈÔ±tŽ‘OeF«;Ž¦‘±tŽ‘œt:Ïr‘ÿ}'otateŽ‘o>«(Ïp0Ž‘ À±;‘ª¨Ïp1Ž‘ Áh±;‘ª¨ÏangleŽ‘jû«);Ž¡‘·Ž‘ÏthisŽ‘,²Ñ·«=ŽŽ‘uC«&Ž‘FuC«&Ž‘F›·‘ånÝ"WARNING!È ÝInÈ ÝSolid::Ž‘lå2extract():\n"Ž’µá·‘ånÝ"PathÈ ÝcannotÈ ÝbeÈ ÝprojŽ‘lå2ected.È Ý"Ž’›Pð·Ž¡‘<Ý"ReturningÈ ÝemptyÈ ÝvecŽ’¤ÿÊtorÈ Ý.\n"Ž’üM·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾±vŽ‘Q{«;Ž¡‘(ÂbreakŽ‘D¡h«;Ž¡‘·gŽ¡‘gŽ¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂEllipseŽ‘%>.·Ž‘*>/i‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘ÇÏel‘‚ØlipsesŽ–#I‰±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏel‘‚ØlipsesŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘«(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨);Ž¡‘ÂifŽ‘)´û«(·:«(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïpr–ÿ}'oje“ctŽ‘w«(±fŽ‘øæ;‘ª¨Ïpr‘ÿ}'ojŽ‘žk±;‘ª¨ÏfactorŽ‘®†«))‘·fŽ¡‘(Ïc‘ÿ}'errŽ‘>8Á·‘ƒÝ"WARNING!È ÝInÈ ÝSolid::Ž‘l‚Ûextract():\n"Ž’´Ì3·‘ƒÝ"EllipseÈ ÝcannotÈ ÝbeÈ ÝpŽ‘l‚Ûrojected.È Ý"Ž’ªL9·Ž¡‘<Ý"ReturningÈ ÝemptyÈ ÝvecŽ’¤ÿÊtorÈ Ý.\n"Ž’üM·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾±vŽ‘Q{«;Ž¡‘(ÂbreakŽ‘D¡h«;Ž¡‘·gŽ¡‘gŽ¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂCircleŽ‘!¸·Ž‘&¸‚i‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘ÇÏcir‘ÿ}'clesŽ–S|±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏcir‘ÿ}'clesŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘«(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨);Ž¡‘ÂifŽ‘)´û«(·:«(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïpr–ÿ}'oje“ctŽ‘w«(±fŽ‘øæ;‘ª¨Ïpr‘ÿ}'ojŽ‘žk±;‘ª¨ÏfactorŽ‘®†«))‘·fŽ¡‘(Ïc‘ÿ}'errŽ‘>Y‰·‘£ßÝ"WARNING!È ÝInÈ ÝSolid::Ž‘l££extract():\n"Ž’µ ÷‘£ßÝ"CircleÈ ÝcannotÈ ÝbeÈ ÝprŽ‘l££ojected.È Ý"Ž’¥MÌ·Ž¡‘<Ý"ReturningÈ ÝemptyÈ ÝvecŽ’¤ÿÊtorÈ Ý.\n"Ž’üM·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾±vŽ‘Q{«;Ž¡‘(ÂbreakŽ‘D¡h«;Ž¡‘·gŽ¡‘gŽ¡‘ÂforŽ‘&QË«(Âv®9ectorŽ‘ªH·hÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘E=L·Ž‘J=Mi‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=Ú¼«=‘v‡Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ–9i×±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘i@ÏiterŽ‘ªÅ·6«=‘v‡Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ“±:ÏendŽ‘ಫ(˜);Ž¡‘2€Ÿÿ®+‘ÿ+ŽŽ‘>G%ÏiterŽ‘O#«)‘·fŽ¡‘«(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨);Ž¡‘ÂifŽ‘)´û«(·:«(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïpr–ÿ}'oje“ctŽ‘w«(±fŽ‘øæ;‘ª¨Ïpr‘ÿ}'ojŽ‘žk±;‘ª¨ÏfactorŽ‘®†«))‘·fŽ¡‘(Ïc‘ÿ}'errŽ‘>8Á·‘ƒÝ"WARNING!È ÝInÈ ÝSolid::Ž‘l‚Ûextract():\n"Ž’´Ì3·‘ƒÝ"PolygonÈ ÝcannotÈ ÝbeÈ ÝpŽ‘l‚Ûrojected.È Ý"Ž’ªL9·Ž¡‘<Ý"ReturningÈ ÝemptyÈ ÝvecŽ’¤ÿÊtorÈ Ý.\n"Ž’üM·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾±vŽ‘Q{«;Ž¡‘(ÂbreakŽ‘D¡h«;Ž¡‘·gŽ¡‘gŽ¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂRectangleŽ‘5”ê·Ž‘:”ëi‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘ÇÏr–ÿ}'e“ctanglesŽ–.g]±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏr–ÿ}'e“ctanglesŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘«(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«(‘ª¨);Ž¡‘ÂifŽ‘)´û«(·:«(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïpr–ÿ}'oje“ctŽ‘w«(±fŽ‘øæ;‘ª¨Ïpr‘ÿ}'ojŽ‘žk±;‘ª¨ÏfactorŽ‘®†«))‘·fŽ¡‘(Ïc‘ÿ}'errŽ‘=÷2·‘AˆÝ"WARNING!È ÝInÈ ÝSolid::Ž‘lALextract():\n"Ž—´I·‘AˆÝ"RectangleÈ ÝcannotÈ ÝbeŽ‘lALÈ Ýprojected.È Ý"Ž“·Ž¡‘<Ý"ReturningÈ ÝemptyÈ ÝvecŽ’¤ÿÊtorÈ Ý.\n"Ž’üM·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾±vŽ‘Q{«;Ž¡‘(ÂbreakŽ‘D¡h«;Ž¡‘·gŽ¡‘gŽ¡‘±vŽ‘4¿:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÏthisŽ‘붫);ŽŽŽŒ‹šYÕ Šn ý‘ì«410›­EXTRA•ÃŽCT’2ÐÉ3DLDFPR“G˜·x«1365Ž €n ý•@P‘ÂreturnŽ‘7æ¼±vŽ‘=y«;Ž¤ ‘ -·gŽŸÂ1366.‘ üSet‘ÕTextremes.ŽŸ·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/Ôb•QÇo“olŽ‘I/:Ïset‘‰ffŽ‘®extr‘ÿ}'emesŽ‘ðë(‘ª®);ŽŽŽŒ‹›k. Šn ý‘ì·x«1367–­3DLDFPRÃŽG’®SET‘ÕXEXTREMES“«411Ž €n ý•@PÂ1367.Ž©·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¤ ‘ -Âb•QÇo“olŽ‘#¡gSolidŽ‘>B«::‘Ïset‘‰ffŽ‘®extr‘ÿ}'emesŽ‘7Á«(‘ª®)Ž¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EnteringÈ ÝSolid::setŽ‘kÆÜ_extremes()"Ž’®8·‘ÇÝ"\n"Ž‘Œ·‘ÇÏ ushŽ‘€«;Ž¦‘Âv‘ÿ\ralarra®9yŽ‘=ZC·hÂrealŽ‘]Ù·i‘UU±vŽ‘Š«;Ž¦‘±vŽ‘4¿:Ïr‘ÿ}'esizeŽ‘i«(6Ž‘±;‘ª¨«0Ž‘ª©);‘±=·‘Ó«LDF›X*2002.12.13.–zHAdded.“Needed–X+for“compiling“under“GNU/Lin¸ãux“using“GCC˜onŽ¡‘(the–UUIn¸ãtel“i686“computer“gwdu101.gwdg.de.‘o·±=Ž¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂP®9athŽ‘æ¹·Ž‘ æºi‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘ÇÏp‘ÿ}'athsŽ–Wű:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏp‘ÿ}'athsŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘ÂifŽ‘)´û«(·:«(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ‘®extr‘ÿ}'emesŽ‘6Á‰«(‘ª¨))‘·fŽ¡‘(Ïc‘ÿ}'errŽ‘Bp×·‘»-Ý"ERROR!È ÝInÈ ÝSolid::seŽ‘pºñt_extremes():\n"Ž’ÌüV·Ž¡‘<Ý"Path::set_extremes(Ž’¤ÿÊ)È ÝreturnedÈ Ýfalse.È Ý"Ž’ ·‘ÇÝ"ReturningÈ Ýfalse.\n\Ž‘kÆÜn"Ž‘y”V·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾ÏfalseŽ‘`–«;Ž¡‘·gŽ¡‘±vŽ‘%ûØ«=‘Ç(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïget‘‰ffŽ‘®extr‘ÿ}'emesŽ‘7D`«(‘ª¨);Ž¡‘ÂforŽ‘/艫(Âin®9tŽ‘¤÷±iŽ‘Þ«=‘Ç0Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«3Ž“;‘ýŸÿ®+‘ÿ+ŽŽ‘G±iŽ‘¹«)‘±=·‘ÿý«Minima.‘o·±=Ž¡‘·fŽ¡‘(Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘|U«[±iŽ›qô«]–Ç=“ÏminŽ‘ì-«(Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ«[±iŽ˜«]±;‘ª¨vŽ‘ße«[±iŽ˜«]);Ž¡‘·gŽ¡‘ÂforŽ‘/艫(Âin®9tŽ‘¤÷±iŽ‘Þ«=‘Ç3Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«6Ž“;‘ýŸÿ®+‘ÿ+ŽŽ‘G±iŽ‘¹«)‘±=·‘ÿý«Maxima.‘o·±=Ž¡‘·fŽ¡‘(Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘|U«[±iŽ›qô«]–Ç=“ÏmaxŽ‘k³«(Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ«[±iŽ˜«]±;‘ª¨vŽ‘ße«[±iŽ˜«]);Ž¡‘·gŽ¡‘gŽ¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂEllipseŽ‘%>.·Ž‘*>/i‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘ÇÏel‘‚ØlipsesŽ–#I‰±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏel‘‚ØlipsesŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘ÂifŽ‘)´û«(·:«(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ‘®extr‘ÿ}'emesŽ‘6Á‰«(‘ª¨))‘·fŽ¡‘(Ïc‘ÿ}'errŽ‘Bp×·‘»-Ý"ERROR!È ÝInÈ ÝSolid::seŽ‘pºñt_extremes():\n"Ž’ÌüV·Ž¡‘<Ý"Path::set_extremes(Ž’¤ÿÊ)È ÝreturnedÈ Ýfalse.È Ý"Ž’ ·‘ÇÝ"ReturningÈ Ýfalse.\n\Ž‘kÆÜn"Ž‘y”V·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾ÏfalseŽ‘`–«;Ž¡‘·gŽ¡‘±vŽ‘%ûØ«=‘Ç(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïget‘‰ffŽ‘®extr‘ÿ}'emesŽ‘7D`«(‘ª¨);Ž¡‘ÂforŽ‘/艫(Âin®9tŽ‘¤÷±iŽ‘Þ«=‘Ç0Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«3Ž“;‘ýŸÿ®+‘ÿ+ŽŽ‘G±iŽ‘¹«)‘±=·‘ÿý«Minima.‘o·±=Ž¡‘·fŽ¡‘(Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘|U«[±iŽ›qô«]–Ç=“ÏminŽ‘ì-«(Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ«[±iŽ˜«]±;‘ª¨vŽ‘ße«[±iŽ˜«]);Ž¡‘·gŽ¡‘ÂforŽ‘/艫(Âin®9tŽ‘¤÷±iŽ‘Þ«=‘Ç3Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«6Ž“;‘ýŸÿ®+‘ÿ+ŽŽ‘G±iŽ‘¹«)‘±=·‘ÿý«Maxima.‘o·±=Ž¡‘·fŽ¡‘(Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘|U«[±iŽ›qô«]–Ç=“ÏmaxŽ‘k³«(Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ«[±iŽ˜«]±;‘ª¨vŽ‘ße«[±iŽ˜«]);Ž¡‘·gŽ¡‘gŽ¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂCircleŽ‘!¸·Ž‘&¸‚i‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘ÇÏcir‘ÿ}'clesŽ–S|±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏcir‘ÿ}'clesŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘ÂifŽ‘)´û«(·:«(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ‘®extr‘ÿ}'emesŽ‘6Á‰«(‘ª¨))‘·fŽ¡‘(Ïc‘ÿ}'errŽ‘Bp×·‘»-Ý"ERROR!È ÝInÈ ÝSolid::seŽ‘pºñt_extremes():\n"Ž’ÌüV·Ž¡‘<Ý"Path::set_extremes(Ž’¤ÿÊ)È ÝreturnedÈ Ýfalse.È Ý"Ž’ ·‘ÇÝ"ReturningÈ Ýfalse.\n\Ž‘kÆÜn"Ž‘y”V·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾ÏfalseŽ‘`–«;Ž¡‘·gŽ¡‘±vŽ‘%ûØ«=‘Ç(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïget‘‰ffŽ‘®extr‘ÿ}'emesŽ‘7D`«(‘ª¨);Ž¡‘ÂforŽ‘/艫(Âin®9tŽ‘¤÷±iŽ‘Þ«=‘Ç0Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«3Ž“;‘ýŸÿ®+‘ÿ+ŽŽ‘G±iŽ‘¹«)‘±=·‘ÿý«Minima.‘o·±=Ž¡‘·fŽ¡‘(Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘|U«[±iŽ›qô«]–Ç=“ÏminŽ‘ì-«(Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ«[±iŽ˜«]±;‘ª¨vŽ‘ße«[±iŽ˜«]);ŽŽŽŒ‹œl~ Šn ý‘ì«412–­SET‘ÕXEXTREMES’®3DLDFPRÃŽG“·x«1367Ž €n ý•@P‘·gŽ¤ ‘ÂforŽ‘/艫(Âin®9tŽ‘¤÷±iŽ‘Þ«=‘Ç3Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«6Ž“;‘ýŸÿ®+‘ÿ+ŽŽ‘G±iŽ‘¹«)‘±=·‘ÿý«Maxima.‘o·±=Ž¡‘·fŽ¡‘(Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘|U«[±iŽ›qô«]–Ç=“ÏmaxŽ‘k³«(Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ«[±iŽ˜«]±;‘ª¨vŽ‘ße«[±iŽ˜«]);Ž¡‘·gŽ¡‘gŽ¡‘ÂforŽ‘&QË«(Âv®9ectorŽ‘ªH·hÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘E=L·Ž‘J=Mi‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=Ú¼«=‘v‡Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ–9i×±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘i@ÏiterŽ‘ªÅ·6«=‘v‡Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ“±:ÏendŽ‘ಫ(˜);Ž¡‘2€Ÿÿ®+‘ÿ+ŽŽ‘>G%ÏiterŽ‘O#«)‘·fŽ¡‘ÂifŽ‘)´û«(·:«(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ‘®extr‘ÿ}'emesŽ‘6Á‰«(‘ª¨))‘·fŽ¡‘(Ïc‘ÿ}'errŽ‘Bp×·‘»-Ý"ERROR!È ÝInÈ ÝSolid::seŽ‘pºñt_extremes():\n"Ž’ÌüV·Ž¡‘<Ý"Path::set_extremes(Ž’¤ÿÊ)È ÝreturnedÈ Ýfalse.È Ý"Ž’ ·‘ÇÝ"ReturningÈ Ýfalse.\n\Ž‘kÆÜn"Ž‘y”V·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾ÏfalseŽ‘`–«;Ž¡‘·gŽ¡‘±vŽ‘%ûØ«=‘Ç(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïget‘‰ffŽ‘®extr‘ÿ}'emesŽ‘7D`«(‘ª¨);Ž¡‘ÂforŽ‘/艫(Âin®9tŽ‘¤÷±iŽ‘Þ«=‘Ç0Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«3Ž“;‘ýŸÿ®+‘ÿ+ŽŽ‘G±iŽ‘¹«)‘±=·‘ÿý«Minima.‘o·±=Ž¡‘·fŽ¡‘(Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘|U«[±iŽ›qô«]–Ç=“ÏminŽ‘ì-«(Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ«[±iŽ˜«]±;‘ª¨vŽ‘ße«[±iŽ˜«]);Ž¡‘·gŽ¡‘ÂforŽ‘/艫(Âin®9tŽ‘¤÷±iŽ‘Þ«=‘Ç3Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«6Ž“;‘ýŸÿ®+‘ÿ+ŽŽ‘G±iŽ‘¹«)‘±=·‘ÿý«Maxima.‘o·±=Ž¡‘·fŽ¡‘(Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘|U«[±iŽ›qô«]–Ç=“ÏmaxŽ‘k³«(Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ«[±iŽ˜«]±;‘ª¨vŽ‘ße«[±iŽ˜«]);Ž¡‘·gŽ¡‘gŽ¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂRectangleŽ‘5”ê·Ž‘:”ëi‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘ÇÏr–ÿ}'e“ctanglesŽ–.g]±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏr–ÿ}'e“ctanglesŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘ÂifŽ‘)´û«(·:«(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ‘®extr‘ÿ}'emesŽ‘6Á‰«(‘ª¨))‘·fŽ¡‘(Ïc‘ÿ}'errŽ‘Bp×·‘»-Ý"ERROR!È ÝInÈ ÝSolid::seŽ‘pºñt_extremes():\n"Ž’ÌüV·Ž¡‘<Ý"Path::set_extremes(Ž’¤ÿÊ)È ÝreturnedÈ Ýfalse.È Ý"Ž’ ·‘ÇÝ"ReturningÈ Ýfalse.\n\Ž‘kÆÜn"Ž‘y”V·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂreturnŽ‘Kæ¾ÏfalseŽ‘`–«;Ž¡‘·gŽ¡‘±vŽ‘%ûØ«=‘Ç(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïget‘‰ffŽ‘®extr‘ÿ}'emesŽ‘7D`«(‘ª¨);Ž¡‘ÂforŽ‘/艫(Âin®9tŽ‘¤÷±iŽ‘Þ«=‘Ç0Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«3Ž“;‘ýŸÿ®+‘ÿ+ŽŽ‘G±iŽ‘¹«)‘±=·‘ÿý«Minima.‘o·±=Ž¡‘·fŽ¡‘(Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘|U«[±iŽ›qô«]–Ç=“ÏminŽ‘ì-«(Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ«[±iŽ˜«]±;‘ª¨vŽ‘ße«[±iŽ˜«]);Ž¡‘·gŽ¡‘ÂforŽ‘/艫(Âin®9tŽ‘¤÷±iŽ‘Þ«=‘Ç3Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«6Ž“;‘ýŸÿ®+‘ÿ+ŽŽ‘G±iŽ‘¹«)‘±=·‘ÿý«Maxima.‘o·±=Ž¡‘·fŽ¡‘(Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘|U«[±iŽ›qô«]–Ç=“ÏmaxŽ‘k³«(Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ«[±iŽ˜«]±;‘ª¨vŽ‘ße«[±iŽ˜«]);Ž¡‘·gŽ¡‘gŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ExitingÈ ÝSolid::set_Ž‘kÆÜextremes()"Ž’¨Ô;·‘ÇÝ"\n"Ž‘Œ·‘ÇÏ ushŽ‘€«;Ž¡‘ÂreturnŽ‘7æ¼ÏtrueŽ‘J«T«;Ž¡‘ -·gŽ©Â1368.‘ üGet‘ÕTextremes.ŽŸ·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·Ž¡‘ -ÂinlineŽ‘)ŠIvirtualŽ‘OconstŽ‘mB¾v‘ÿ\ralarra®9yŽ’–œÿ·hÂrealŽ‘]Ù·i‘UUÏget‘‰ffŽ‘®extr‘ÿ}'emesŽ‘:™µ«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7æ¼Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ’‹ë «;Ž¡‘ -·gŽ¦Â1369.‘ üGet–ÕTminim®9um“z.ŽŸ·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·ŽŽŽŒ‹~R Šn ý‘ì·x«1369›­3DLDFPRÃŽG’³GET–ÕXMINIMUM“Z˜«413Ž €n ý•@P‘ -ÂvirtualŽ‘/ÔrealŽ‘FAÏget‘‰ffŽ–®minimum‘‰ffŽ“zŽ’‰žÚ«(‘ª®)‘UUÂconstŽ‘*¢«;ŽŸÂ1370.Ž©·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¤ ‘ -ÂrealŽ‘ ³/SolidŽ‘;1 -«::‘Ïget‘‰ffŽ–®minimum‘‰ffŽ“zŽ‘D]Ü«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"EnteringÈ ÝSolid::getŽ‘kÆÜ_minimum_z()"Ž’³T5·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"projective_extremesŽ‘kÆÜ[4]È Ý==È Ý"Ž’™D·‘ÇÏpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘VËi«[4Ž‘]–Ç·“Ïend‘‚ØlŽ‘ò·“Ï ushŽ‘€«;Ž¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"ExitingÈ ÝSolid::get_Ž‘kÆÜminimum_z()"Ž’®8·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¡‘ÂreturnŽ‘7æ¼Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ’‹ë «[4Ž‘];Ž¡‘ -·gŽŸÂ1371.‘ üGet–ÕTmaxim®9um“z.Ž¦·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/ÔrealŽ‘FAÏget‘‰ffŽ–®maximum‘‰ffŽ“zŽ’Š®«(‘ª®)‘UUÂconstŽ‘*¢«;ŽŸÂ1372.Ž¦·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘ ³/SolidŽ‘;1 -«::‘Ïget‘‰ffŽ–®maximum‘‰ffŽ“zŽ‘Em«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"EnteringÈ ÝSolid::getŽ‘kÆÜ_maximum_z()"Ž’³T5·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"projective_extremesŽ‘kÆÜ[5]È Ý==È Ý"Ž’™D·‘ÇÏpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘VËi«[5Ž‘]–Ç·“Ïend‘‚ØlŽ‘ò·“Ï ushŽ‘€«;Ž¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"ExitingÈ ÝSolid::get_Ž‘kÆÜmaximum_z()"Ž’®8·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¡‘ÂreturnŽ‘7æ¼Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ’‹ë «[5Ž‘];Ž¡‘ -·gŽŸÂ1373.› üGet–ÕTmean“z.˜«[¬LDF‘T2003.05.16.«]Ž‘Zˆ6Added–UUthis“function.Ž¦·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/ÔrealŽ‘FAÏget‘‰ffŽ–®me‘ÿ}'an‘‰ffŽ“zŽ‘v÷ «(‘ª®)‘UUÂconstŽ‘*¢«;ŽŸÂ1374.Ž¦·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘ ³/SolidŽ‘;1 -«::‘Ïget‘‰ffŽ–®me‘ÿ}'an‘‰ffŽ“zŽ‘1¶«(‘ª®)‘UUÂconstŽŽ¡‘ -·fŽ¡‘ÂreturnŽ‘7漫((Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ«[4Ž›]–8à+“Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘V=1«[5Ž˜])±=«2Ž˜);Ž¡‘ -·gŽŸÂ1375.‘ üSuppress‘ÕToutput.Ž¦·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/Ôv®9oidŽ‘H‹¬Ïsuppr‘ÿ}'ess‘‰ffŽ‘®outputŽ’r.«(‘ª®);ŽŽŽŒ‹ž Šn ý‘ì«414–­SUPPRESS‘ÕXOUTPUT’ e÷3DLDFPRÃŽG“·x«1376Ž €n ý•@PÂ1376.Ž©·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¤ ‘ -Âv®9oidŽ‘"ýÙSolidŽ‘={´«::‘Ïsuppr‘ÿ}'ess‘‰ffŽ‘®outputŽ‘E憫(‘ª®)Ž¡‘ -·fŽ¡‘Ïdo‘‰ffŽ‘®outputŽ‘A½M«=‘ÇÏfalseŽ‘v\«;Ž¡‘ÂreturnŽ‘4‘g«;Ž¡‘ -·gŽŸÂ1377.‘ üUnsuppress‘ÕToutput.Ž¦·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/Ôv®9oidŽ‘H‹¬Ïunsuppr‘ÿ}'ess‘‰ffŽ‘®outputŽ’˜oR«(‘ª®);ŽŸÂ1378.Ž¦·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¡‘ -Âv®9oidŽ‘"ýÙSolidŽ‘={´«::‘Ïunsuppr‘ÿ}'ess‘‰ffŽ‘®outputŽ‘P㪫(‘ª®)Ž¡‘ -·fŽ¡‘Ïdo‘‰ffŽ‘®outputŽ‘A½M«=‘ÇÏtrueŽ‘‹°«;Ž¡‘ÂreturnŽ‘4‘g«;Ž¡‘ -·gŽŸÂ1379.– üOutput.“«[¬LDF‘T2002.10.02.«]Ž‘Zˆ6In‘UUÂPictureŽ‘)ñf«::‘ÏoutputŽ‘D«(‘ª®),‘UUÏshap‘ÿ}'esŽ‘#™3«is–UUsorted“according“to“the“v‘ÿqÇalues“inŽ¡Ïpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘W¸á«for–´eacš¸ãh“ÂShapQÇeŽ‘" «.‘wHo˜w˜ev˜er,‘Ì^it's“pGossible“(and“ev˜en“lik˜ely)“that“the“individual“ÂP®9athsŽ‘$ƒÀ«inŽ¡a‘Ü -ÂSolidŽ‘!5ë«are–Ü -not“ordered“in“sucš¸ãh“a“w˜a˜y“that“they“will“bGe“output“in“the“correct“order.‘åTherefore,‘ý·I‘ÛçdeclareŽ¡a‘™Âv®9ectorŽ‘#ºá·hÂShapQÇeŽ‘"ü¦·Ž‘'ü§i‘™±sŽ‘ Ñ2«and–™put“the“ÂP®9athsŽ‘%;Ò«from“Ïp‘ÿ}'athsŽ‘¡F«,‘?jÏcir‘ÿ}'clesŽ‘ ËΫ,‘?jÏel‘‚ØlipsesŽ‘$ÁÛ«,‘?jÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:2º«,‘?jand“Ïr–ÿ}'e“ctanglesŽ‘3Áw«on¸ãtoŽ¡it.›FôThen–ñ¹I‘ñ‘sort“±sŽ‘ “r«and“call“ÏoutputŽ‘!ù«(‘ª®)“for“eac¸ãh“ÂShapQÇeŽ‘"ÝÆ«.˜Currenš¸ãtly‘ÿ*ª,‘ÒÏoutputŽ‘!(«(‘ª®)“will“resolv˜e“to“ÂP®9athŽ‘ƒ!«::‘ÏoutputŽ‘D«(‘ª®),Ž¡bšGecause‘zÏoutputŽ‘ º«(‘ª®)–zhasn't“b˜een“o•¸ãv“erloaded–zfor“ÂCircleŽ‘!d¦«,‘?ÂEllipseŽ‘$û«,‘?ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘Dó«,‘?or“ÂRectangleŽ‘8B‰«(and“probablyŽ¡w¸ãon't‘UUbGe).Ž¡‘ -The›Àin•¸ãv“oGcation˜of˜Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘.j«(‘ª®)˜in˜eac“h˜of˜the˜four˜lo•Gops˜dep“ends˜on˜the˜fact˜that˜ÂP®9athŽ‘£(«::‘Ïextr‘ÿ}'actŽ‘Âs«(‘ª®)˜returnsŽ¡a‘{:Âv®9ectorŽ‘( ¼«conš¸ãtaining–{:only“one“elemen˜t.‘ãuThat's“wh˜y“I‘zîuse“Ïfr‘ÿ}'ontŽ‘ÄË«(‘ª®).‘ãuThere“is“no“opGerator“or“function“forŽ¡concatenating‘UUÂv®9ectorsŽ‘'ˆÙ«,–UUat“least“I“couldn't“ nd“one“in“Stroustrup.‘qÇTO“DO:“Get“reference!Ž¦·h–ª¨«Declare‘UUÂSolidŽ‘ («functions‘@­1299“·i‘Ç«+·Ž¡‘ -ÂvirtualŽ‘/Ôv®9oidŽ‘H‹¬ÏoutputŽ‘ešì«(‘ª®);ŽŽŽŒ‹Ÿ˜ß Šn ý‘ì·x«1380–­3DLDFPRÃŽG’8\/OUTPUT“«415Ž €n ý•@PÂ1380.Ž©·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¤ ‘ -Âv®9oidŽ‘"ýÙSolidŽ‘={´«::‘ÏoutputŽ‘D«(‘ª®)Ž¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EnteringÈ ÝSolid::outŽ‘kÆÜput().\n"Ž’›)«;Ž¦‘Âv®9ectorŽ‘3ªJ·hÂShapQÇeŽ‘"Ab·Ž‘'Aci‘UU±sŽ‘U«;Ž¦‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂP®9athŽ‘æ¹·Ž‘ æºi‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘ÇÏp‘ÿ}'athsŽ–Wű:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏp‘ÿ}'athsŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)Ž¡‘±sŽ‘"°:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«((·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïget‘‰ffŽ‘®c‘ÿ}'opyŽ‘$ô«(‘ª¨));Ž¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂCircleŽ‘!¸·Ž‘&¸‚i‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘ÇÏcir‘ÿ}'clesŽ–S|±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏcir‘ÿ}'clesŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)Ž¡‘±sŽ‘"°:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«((·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïget‘‰ffŽ‘®c‘ÿ}'opyŽ‘$ô«(‘ª¨));Ž¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂEllipseŽ‘%>.·Ž‘*>/i‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘ÇÏel‘‚ØlipsesŽ–#I‰±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏel‘‚ØlipsesŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)Ž¡‘±sŽ‘"°:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«((·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïget‘‰ffŽ‘®c‘ÿ}'opyŽ‘$ô«(‘ª¨));Ž¡‘ÂforŽ‘&QË«(Âv®9ectorŽ‘ªH·hÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘E=L·Ž‘J=Mi‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=Ú¼«=‘v‡Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ–9i×±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘i@ÏiterŽ‘ªÅ·6«=‘v‡Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ“±:ÏendŽ‘ಫ(˜);Ž¡‘2€Ÿÿ®+‘ÿ+ŽŽ‘>G%ÏiterŽ‘O#«)‘±sŽ‘ °:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«((·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïget‘‰ffŽ‘®c‘ÿ}'opyŽ‘$ô«(‘ª¨));Ž¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂRectangleŽ‘5”ê·Ž‘:”ëi‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘ÇÏr–ÿ}'e“ctanglesŽ–.g]±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏr–ÿ}'e“ctanglesŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)Ž¡‘±sŽ‘"°:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«((·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïget‘‰ffŽ‘®c‘ÿ}'opyŽ‘$ô«(‘ª¨));Ž¡‘ÏsortŽ‘&2Ô«(±sŽ‘°:Ïb–ÿ}'e“ginŽ‘¾¨«(–ª¨)±;“sŽ‘Z¨:ÏendŽ‘ಫ(“)±;“ÂCompareu½‰™šs4Ž–Ôwmaxim®9umu½‰™šs4Ž“zŽ‘pOŠ«(“));Ž¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂShapQÇeŽ‘"Ab·Ž‘'Aci‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘DZsŽ–w:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘DZsŽ“:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘«(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:ÏoutputŽ‘@«(‘ª¨);Ž¡‘ÂdeleteŽ‘?ƽ«(·Ž‘ÏiterŽ‘Êÿ«);Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ExitingÈ ÝSolid::outpŽ‘kÆÜut().\n"Ž’–M,«;Ž¡‘ -·gŽŸÂ1381.‘ üDra®9wing–ÕTand“ lling.ŽŽŽŒ‹ ¢â Šn ý‘ì«416›­DRA‘ÿ8WING–ÕXAND“FILLING’ö‘E3DLDFPRÃŽG˜·x«1382Ž €n ý•@PÂ1382.‘ ü«ProGcess–èËvš¸ãectors“for“Ïdr‘ÿ}'aw‘«().‘M™[¬LDF‘T2002.10.09.«]Ž‘RéIAdded“this“section.‘M™The“same“things“are“done“to“eac˜hŽ¤ of– ¦the“ÂShapQÇeŽ‘'-Y·Ž‘0N«v¸ãectors“Ïp‘ÿ}'athsŽ‘±S«,‘SzÏel‘‚ØlipsesŽ‘$Õë«,‘SzÏcir‘ÿ}'clesŽ‘ ßÞ«,‘SzÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:FÊ«,›Szand“Ïr–ÿ}'e“ctanglesŽ‘/Àë«,˜so“I'v¸ãe“put“the“coGde“in“thisŽ¡named–UUsection.‘qÇEacš¸ãh“time“it“it's“used,“ÏiterŽ‘u¨«is“an“iterator“for“a“di eren˜t“v˜ector.Ž©·h›ª¨«ProGcess–UUv¸ãectors“for“Ïdr‘ÿ}'awŽ‘~0«(‘ª®)‘@­1382˜·i‘ÇŽ¡‘ -fŽ¡‘ÂifŽ‘´ú«(Ïc‘‰ffŽ‘®iterŽ‘ÙÀ·6«=‘DZvŽ‘ûÕ:ÏendŽ‘ಫ(‘ª¨))‘·fŽ¡‘Ïc‘ÿ}'olor‘‰ffŽ‘®ptrŽ‘GÇ@«=‘Ç·Ž‘ÇÏc‘‰ffŽ‘®iterŽ‘!YÁŸÿ®+‘ÿ+ŽŽ‘- á«;Ž¡‘·gŽ¡‘«(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ–® l‘‚Øl‘‰ffŽ“dr‘ÿ}'aw‘‰ffŽ“valueŽ‘N\ö«(ÝDRAWŽ‘†\«);‘±=·‘ÿý«LDF–UU2002.10.09.‘qÇAdded“coGde“for“handling“Ïdr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘2AŽ«.‘o·±=Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"color_ptr->get_use_Ž‘kÆÜname()È Ý==È Ý"Ž’¨Ô;·‘ÇÏc‘ÿ}'olor‘‰ffŽ‘®ptrŽ‘'Ç=Ÿ±~ŽŽ‘-Ç>Ïget‘‰ffŽ–®use‘‰ffŽ“nameŽ‘h}D«(‘ª¨)–Ç·“Ïend‘‚ØlŽ‘ò·“Ï ushŽ‘€«;Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(Ïc‘ÿ}'olor‘‰ffŽ‘®ptrŽ‘%%Ÿ±~ŽŽ‘+&Ïget‘‰ffŽ–®use‘‰ffŽ“nameŽ‘e¶,«(‘ª¨)–Ç·“ÏfalseŽ‘v\«)‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"AllocatingÈ ÝmemoryÈ ÝfŽ‘kÆÜorÈ ÝColor.\n"Ž’®8·‘ÇÏ ushŽ‘€«;Ž¦‘ÂColorŽ‘=¤ö·Ž‘B¤÷±cŽ‘I¿ê«=‘ÇÂColorŽ‘ º«::Ž‘&¤øÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“c‘ÿ}'olorŽ‘nø«(‘ª¨);Ž¦‘·Ž‘#±cŽ‘*÷«=‘Ç·Ž‘ÇÏc‘ÿ}'olor‘‰ffŽ‘®ptrŽ‘.Ç>«;Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ–®dr›ÿ}'aw‘‰ffŽ“c˜olorŽ‘>«(±cŽ‘SÛ«);Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"color_ptr->get_nameŽ‘kÆÜ()È Ý==È Ý"Ž’“ÔG·‘ÇÏc‘ÿ}'olor‘‰ffŽ‘®ptrŽ‘'Ç=Ÿ±~ŽŽ‘-Ç>Ïget‘‰ffŽ‘®nameŽ‘VÀþ«(‘ª¨)–Ç·“Ïend‘‚ØlŽ‘ò·“Ï ushŽ‘€«;Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ–®dr›ÿ}'aw‘‰ffŽ“c˜olorŽ‘>«(Ïc‘ÿ}'olor‘‰ffŽ‘®ptrŽ‘'%«);Ž¡‘·gŽ¡‘«(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ–® l‘‚Øl‘‰ffŽ“c‘ÿ}'olorŽ‘5I:«(Âstaticu½‰™šs4Ž‘ÔwcastŽ‘4}¢·hÂColorŽ‘¤ó·Ž‘$¤ôi«(0Ž‘));Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ–®dash‘‰ffŽ“p‘ÿ}'atternŽ‘FÝ–«(Ïddashe‘ÿ}'dŽ‘#G«);Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ‘®p‘ÿ}'enŽ‘ʘ«(Ïpp‘ÿ}'enŽ‘6#«);Ž¡‘ -·gŽŸ ­This–ÕXco(i·hÂconstŽ‘~!ColorŽ‘>v“·Ž‘Cv”i‘¨Ô±vŽ‘ /Ñ«=‘R@ÂColorsŽ‘%+«::Ž‘+¹\Ïdefault‘‰ffŽ–®c›ÿ}'olor‘‰ffŽ“ve˜ctorŽ’€Ó–±;‘ª¨ÂconstŽ‘ (ÉstringŽŽ¡‘Ïddashe‘ÿ}'dŽ‘D,«=‘ÇÝ""Ž– Íz±;‘ª¨ÂconstŽ‘ÕJstringŽ‘@ú—Ïpp‘ÿ}'enŽ‘X÷Ò«=‘ÇÝ""Ž“±;‘ª¨ÂPictureŽ‘*œ -«&Ž‘2c(Ïpictur‘ÿ}'eŽ‘T3«=‘ÇÏcurr–ÿ}'ent‘‰ffŽ‘®pictur“eŽ‘Dìß«)‘UUÂconstŽ‘*¢«;ŽŽŽŒ‹¡¯ Šn ý‘ì·x«1384–­3DLDFPRÃŽG’BßDRA‘ÿ8W“«417Ž €n ý•@PÂ1384.Ž©·h–ª¨«De ne‘UUÂSolidŽ‘ («functions‘@­1300“·i‘Ç«+·Ž¤ ‘ -Âv®9oidŽ‘"Î:SolidŽ‘=L«::‘Ïdr‘ÿ}'awŽ‘(ß«(ÂconstŽ‘ûv®9ectorŽ‘=¥K·hÂconstŽ‘ûColorŽ‘=pW·Ž‘BpXi‘%¶±vŽ‘Zs;‘ª¨ÂconstŽ‘¥«stringŽ‘@›YÏddashe‘ÿ}'dŽ‘câj±;‘ª¨ÂconstŽ‘¥«stringŽ‘@›YÏpp‘ÿ}'enŽ‘UÑ|±;‘ª¨ÂPictureŽŽ¡‘2«&Ž‘9Ç#Ïpictur‘ÿ}'eŽ‘XÏù«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EnteringÈ ÝSolid::draŽ‘kÆÜw():"Ž’‰TM·‘ÇÝ"\n"Ž‘Œ·‘ÇÏ ushŽ‘€«;Ž¦‘ÂSolidŽ‘0Ó.·Ž‘5Ó/±sŽ‘=JG«=‘ÇÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“solidŽ‘IèÓ«(‘ª¨);Ž¦‘·Ž‘±sŽ‘ w«=‘Ç·Ž‘ÇÏthisŽ‘²Ï«;Ž¦‘ÂconstŽ‘2*¤ColorŽ‘QÏ—·Ž‘VϘÏc‘ÿ}'olor‘‰ffŽ‘®ptrŽ’€–Õ«=‘ÇÂColorsŽ‘$Ÿö«::Ž‘+.4Ïdefault‘‰ffŽ‘®c‘ÿ}'olorŽ‘bª«;Ž¦‘Âv®9ectorŽ‘3ªJ·hÂconstŽ‘*¢ColorŽ‘=Ï•·Ž‘BÏ–i‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûc‘‰ffŽ‘®iterŽ‘_\»«=‘DZvŽ‘ûÕ:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂP®9athŽ‘æ¹·Ž‘ æºi‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W«=‘DZsŽ‘wŸ~ŽŽ‘ wÏp‘ÿ}'athsŽ–#Ʊ:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘DZsŽ‘wŸ~ŽŽ‘ wÏp‘ÿ}'athsŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘h›ª¨«ProGcess–UUv¸ãectors“for“Ïdr‘ÿ}'awŽ‘~0«(‘ª®)‘@­1382˜·iŽ¡‘gŽ¡‘Ïc‘‰ffŽ‘®iterŽ‘/Ù«=‘DZvŽ‘ûÕ:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂCircleŽ‘!¸·Ž‘&¸‚i‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W«=‘DZsŽ‘wŸ~ŽŽ‘ wÏcir‘ÿ}'clesŽ–(}±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘DZsŽ‘wŸ~ŽŽ‘ wÏcir‘ÿ}'clesŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘h›ª¨«ProGcess–UUv¸ãectors“for“Ïdr‘ÿ}'awŽ‘~0«(‘ª®)‘@­1382˜·iŽ¡‘gŽ¡‘Ïc‘‰ffŽ‘®iterŽ‘/Ù«=‘DZvŽ‘ûÕ:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂEllipseŽ‘%>.·Ž‘*>/i‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W«=‘DZsŽ‘wŸ~ŽŽ‘ wÏel‘‚ØlipsesŽ–+ùŠ±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘DZsŽ‘wŸ~ŽŽ‘ wÏel‘‚ØlipsesŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘h›ª¨«ProGcess–UUv¸ãectors“for“Ïdr‘ÿ}'awŽ‘~0«(‘ª®)‘@­1382˜·iŽ¡‘g‘±=·‘ÿýÂforŽ‘“+·±=Ž¡‘Ïc‘‰ffŽ‘®iterŽ‘/Ù«=‘DZvŽ‘ûÕ:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¡‘ÂforŽ‘'«$«(Âv®9ectorŽ‘ªH·hÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘F–¥·Ž‘K–¦i‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘Z«=‘¶±sŽ‘fŸ~ŽŽ‘fÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘DYi±:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¡‘2ÏiterŽ‘E’·6«=‘DZsŽ‘wŸ~ŽŽ‘ wÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘Aji±:ÏendŽ‘ಫ(‘ª¨);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘h›ª¨«ProGcess–UUv¸ãectors“for“Ïdr‘ÿ}'awŽ‘~0«(‘ª®)‘@­1382˜·iŽ¡‘gŽ¡‘ÂforŽ‘&6¡«(Âv®9ectorŽ‘ªH·hÂRectangleŽ‘5ã·Ž‘:ãi‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W—:«=‘IA±sŽ‘ùAŸ~ŽŽ‘ ùBÏr–ÿ}'e“ctanglesŽ–7™‡±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘NÏiterŽ‘bU·6«=‘IA±sŽ‘ùAŸ~ŽŽ‘ ùBÏr–ÿ}'e“ctanglesŽ“±:ÏendŽ‘ಫ(˜);Ž¡‘2€Ÿÿ®+‘ÿ+ŽŽ‘>G%ÏiterŽ‘O#«)‘·fŽ¡‘h›ª¨«ProGcess–UUv¸ãectors“for“Ïdr‘ÿ}'awŽ‘~0«(‘ª®)‘@­1382˜·iŽ¡‘gŽ¡‘Ïpictur‘ÿ}'eŽ‘5Ïð«+=ŽŽ‘H%DÂdynamicu½‰™šs4Ž‘ÔwcastŽ’‹–·hÂShapQÇeŽ‘"Ab·Ž‘'Aci«(±sŽ‘°«);Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"ExitingÈ ÝSolid::drawŽ‘kÆÜ():"Ž’„P·‘ÇÝ"\n"Ž‘Œ·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¡‘ -gŽŽŽŒ‹¢¼€ Šn ý‘ì«418–­DRA‘ÿ8W’Bß3DLDFPRÃŽG“·x«1385Ž €n ý•@PÂ1385.‘ ü«ProGcess–Ž:vš¸ãectors“for“Ï l‘‚Øl‘‰«().‘v[¬LDF‘T2002.10.09.«]Ž‘T]•Added“this“section.‘vThe“same“things“are“done“to“eac˜hŽ¤ of– ¦the“ÂShapQÇeŽ‘'-Y·Ž‘0N«v¸ãectors“Ïp‘ÿ}'athsŽ‘±S«,‘SzÏel‘‚ØlipsesŽ‘$Õë«,‘SzÏcir‘ÿ}'clesŽ‘ ßÞ«,‘SzÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:FÊ«,›Szand“Ïr–ÿ}'e“ctanglesŽ‘/Àë«,˜so“I'v¸ãe“put“the“coGde“in“thisŽ¡named–UUsection.‘qÇEacš¸ãh“time“it“it's“used,“ÏiterŽ‘u¨«is“an“iterator“for“a“di eren˜t“v˜ector.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.08.10.«]Ž‘Y;No¸ãw–UUsetting“pšGen“to“Ý""Ž‘[·«,“b˜ecause“I'vš¸ãe“remo˜v˜ed“the“pGen“argumen˜t“from“Ï l‘‚ØlŽ‘H«(‘ª®).Ž¤ŸüÈ„`ÕÁGŽŽ¡·h›ª¨«ProGcess–UUv¸ãectors“for“Ï l‘‚ØlŽ‘H«(‘ª®)‘@­1385˜·i‘ÇŽ¤ ‘ -fŽ¡‘ÂifŽ‘´ú«(Ïc‘‰ffŽ‘®iterŽ‘ÙÀ·6«=‘DZvŽ‘ûÕ:ÏendŽ‘ಫ(‘ª¨))‘·fŽ¡‘Ïc‘ÿ}'olor‘‰ffŽ‘®ptrŽ‘GÇ@«=‘Ç·Ž‘ÇÏc‘‰ffŽ‘®iterŽ‘!YÁŸÿ®+‘ÿ+ŽŽ‘- á«;Ž¡‘·gŽ¡‘«(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ–® l‘‚Øl‘‰ffŽ“dr‘ÿ}'aw‘‰ffŽ“valueŽ‘N\ö«(ÝFILLŽ‘†\«);Ž¡‘±=·‘ÿý«LDF–UU2002.10.09.‘qÇAdded“coGde“for“handling“Ïdr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘5–ã«and“Ï l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘(íª«.‘o·±=Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"color_ptr->get_use_Ž‘kÆÜname()È Ý==È Ý"Ž’¨Ô;·‘ÇÏc‘ÿ}'olor‘‰ffŽ‘®ptrŽ‘'Ç=Ÿ±~ŽŽ‘-Ç>Ïget‘‰ffŽ–®use‘‰ffŽ“nameŽ‘h}D«(‘ª¨)–Ç·“Ïend‘‚ØlŽ‘ò·“Ï ushŽ‘€«;Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(Ïc‘ÿ}'olor‘‰ffŽ‘®ptrŽ‘%%Ÿ±~ŽŽ‘+&Ïget‘‰ffŽ–®use‘‰ffŽ“nameŽ‘e¶,«(‘ª¨)–Ç·“ÏfalseŽ‘v\«)‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"AllocatingÈ ÝmemoryÈ ÝfŽ‘kÆÜorÈ ÝColor.\n"Ž’®8·‘ÇÏ ushŽ‘€«;Ž¤‘ÂColorŽ‘=¤ö·Ž‘B¤÷±cŽ‘I¿ê«=‘ÇÂColorŽ‘ º«::Ž‘&¤øÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“c‘ÿ}'olorŽ‘nø«(‘ª¨);Ž¡‘·Ž‘#±cŽ‘*÷«=‘Ç·Ž‘ÇÏc‘ÿ}'olor‘‰ffŽ‘®ptrŽ‘.Ç>«;Ž¤ ‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ–® l‘‚Øl‘‰ffŽ“c‘ÿ}'olorŽ‘5I:«(±cŽ‘SÛ«);Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"color_ptr->get_nameŽ‘kÆÜ()È Ý==È Ý"Ž’“ÔG·‘ÇÏc‘ÿ}'olor‘‰ffŽ‘®ptrŽ‘'Ç=Ÿ±~ŽŽ‘-Ç>Ïget‘‰ffŽ‘®nameŽ‘VÀþ«(‘ª¨)–Ç·“Ïend‘‚ØlŽ‘ò·“Ï ushŽ‘€«;Ž¡‘(·Ž‘Ž‘ 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l‘‚ØlŽ‘H«(‘ª®)‘@­1385˜·iŽ¡‘gŽ¡‘Ïc‘‰ffŽ‘®iterŽ‘/Ù«=‘DZvŽ‘ûÕ:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂEllipseŽ‘%>.·Ž‘*>/i‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W«=‘DZsŽ‘wŸ~ŽŽ‘ wÏel‘‚ØlipsesŽ–+ùŠ±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘DZsŽ‘wŸ~ŽŽ‘ wÏel‘‚ØlipsesŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘h›ª¨«ProGcess–UUv¸ãectors“for“Ï l‘‚ØlŽ‘H«(‘ª®)‘@­1385˜·iŽ¡‘gŽ¡‘Ïc‘‰ffŽ‘®iterŽ‘/Ù«=‘DZvŽ‘ûÕ:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¡‘ÂforŽ‘'«$«(Âv®9ectorŽ‘ªH·hÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘F–¥·Ž‘K–¦i‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘Z«=‘¶±sŽ‘fŸ~ŽŽ‘fÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘DYi±:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¡‘2ÏiterŽ‘E’·6«=‘DZsŽ‘wŸ~ŽŽ‘ wÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘Aji±:ÏendŽ‘ಫ(‘ª¨);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘h›ª¨«ProGcess–UUv¸ãectors“for“Ï l‘‚ØlŽ‘H«(‘ª®)‘@­1385˜·iŽ¡‘gŽ¡‘Ïc‘‰ffŽ‘®iterŽ‘/Ù«=‘DZvŽ‘ûÕ:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¡‘ÂforŽ‘&6¡«(Âv®9ectorŽ‘ªH·hÂRectangleŽ‘5ã·Ž‘:ãi‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W—:«=‘IA±sŽ‘ùAŸ~ŽŽ‘ ùBÏr–ÿ}'e“ctanglesŽ–7™‡±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘NÏiterŽ‘bU·6«=‘IA±sŽ‘ùAŸ~ŽŽ‘ ùBÏr–ÿ}'e“ctanglesŽ“±:ÏendŽ‘ಫ(˜);Ž¡‘2€Ÿÿ®+‘ÿ+ŽŽ‘>G%ÏiterŽ‘O#«)‘·fŽ¡‘h›ª¨«ProGcess–UUv¸ãectors“for“Ï l‘‚ØlŽ‘H«(‘ª®)‘@­1385˜·iŽ¡‘gŽ¡‘Ïpictur‘ÿ}'eŽ‘5Ïð«+=ŽŽ‘H%DÂdynamicu½‰™šs4Ž‘ÔwcastŽ’‹–·hÂShapQÇeŽ‘"Ab·Ž‘'Aci«(±sŽ‘°«);Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"ExitingÈ ÝSolid::fillŽ‘kÆÜ():"Ž’„P·‘ÇÝ"\n"Ž‘Œ·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¡‘ -gŽŽŽŒ‹¤Ú Šn ý‘ì«420–­FILL’JŠy3DLDFPRÃŽG“·x«1388Ž €n ý•@PÂ1388.‘ ü«ProGcess–­õv¸ãectors“for“Ï l‘‚Øldr‘ÿ}'aw‘«().‘{¨[¬LDF‘T2002.10.09.«]Ž‘TÜ‚Added“this“section.‘{¨The“same“things“are“done“toŽ¤ eacš¸ãh–ö‘of“the“ÂShapQÇeŽ‘&Ù/·Ž‘/ÏÁ«v˜ectors“Ïp‘ÿ}'athsŽ‘‡>«,‘ßÏel‘‚ØlipsesŽ‘$¡P«,‘ßÏcir‘ÿ}'clesŽ‘ «C«,‘ßÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:/«,›ßand“Ïr–ÿ}'e“ctanglesŽ‘/–Ö«,˜so“I'v¸ãe“put“the“coGde“inŽ¡this–UUnamed“section.‘qÇEacš¸ãh“time“it“it's“used,“ÏiterŽ‘u¨«is“an“iterator“for“a“di eren˜t“v˜ector.Ž©›b·h›ª¨«ProGcess–UUv¸ãectors“for“Ï l‘‚Øldr‘ÿ}'awŽ‘$¼À«(‘ª®)‘@­1388˜·i‘ÇŽ¡‘ -fŽ¡‘ÂifŽ‘´ú«(Ïdr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜iterŽ‘D•û·6«=‘ÇÏdr–ÿ}'aw‘‰ffŽ‘®c“olorsŽ‘5ˆ¥±:ÏendŽ‘ಫ(‘ª¨))‘·fŽ¡‘Ïdr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜ptrŽ‘`Ç«=‘Ç·Ž‘ÇÏdr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜iterŽ‘JüŸÿ®+‘ÿ+ŽŽ‘UÝ«;Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(Ï l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“iterŽ‘;B·6«=‘ÇÏ l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorsŽ‘,4Á±:ÏendŽ‘ಫ(‘ª¨))‘·fŽ¡‘Ï l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“ptrŽ‘V³ã«=‘Ç·Ž‘ÇÏ l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“iterŽ‘@Ÿÿ®+‘ÿ+ŽŽ‘L‰8«;Ž¡‘·gŽ¡‘«(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ–® l‘‚Øl‘‰ffŽ“dr‘ÿ}'aw‘‰ffŽ“valueŽ‘N\ö«(ÝFILLDRAWŽ‘*†P«);Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4€·‘&ÝÝ"draw_color_ptr->getŽ‘l&¡_use_name()È Ý==È Ý"Ž’ÃÓ¶·‘&ÝÏdr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜ptrŽ‘@g‰Ÿ±~ŽŽ‘FgŠÏget‘‰ffŽ–®use‘‰ffŽ“nameŽ’«(‘ª¨)–&Ý·“Ïend‘‚ØlŽ‘?|·Ž¡‘2Ï ushŽ‘G¹«;Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(Ïdr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜ptrŽ‘=@¬Ÿ±~ŽŽ‘C@­Ïget‘‰ffŽ–®use‘‰ffŽ“nameŽ‘}ö³«(‘ª¨)–Ç·“ÏfalseŽ‘v\«)‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"AllocatingÈ ÝmemoryÈ ÝfŽ‘kÆÜorÈ ÝColor.\n"Ž’®8·‘ÇÏ ushŽ‘€«;Ž¦‘ÂColorŽ‘=¤ö·Ž‘B¤÷±cŽ‘I¿ê«=‘ÇÂColorŽ‘ º«::Ž‘&¤øÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“c‘ÿ}'olorŽ‘nø«(‘ª¨);Ž¦‘·Ž‘#±cŽ‘*÷«=‘Ç·Ž‘ÇÏdr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜ptrŽ‘GÅ«;Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ–®dr›ÿ}'aw‘‰ffŽ“c˜olorŽ‘>«(±cŽ‘SÛ«);Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)Ž¡‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÝ"draw_color_ptr->getŽ‘kÆÜ_name()È Ý==È Ý"Ž’®8·‘ÇÏdr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜ptrŽ‘@ÄŸ±~ŽŽ‘FÅÏget‘‰ffŽ‘®nameŽ‘o…«(‘ª¨)–Ç·“Ïend‘‚ØlŽ‘ò·“Ï ushŽ‘€«;Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ–®dr›ÿ}'aw‘‰ffŽ“c˜olorŽ‘>«(Ïdr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜ptrŽ‘?@¬«);Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"fill_color_ptr->getŽ‘kÆÜ_use_name()È Ý==È Ý"Ž’Ã,·‘ÇÏ l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“ptrŽ‘6³àŸ±~ŽŽ‘<³áÏget‘‰ffŽ–®use‘‰ffŽ“nameŽ‘wiç«(‘ª¨)–Ç·“Ïend‘‚ØlŽ‘ò·“Ï ushŽ‘€«;Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(Ï l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“ptrŽ‘3ìÈŸ±~ŽŽ‘9ìÉÏget‘‰ffŽ–®use‘‰ffŽ“nameŽ‘t¢Ï«(‘ª¨)–Ç·“ÏfalseŽ‘v\«)‘·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"AllocatingÈ ÝmemoryÈ ÝfŽ‘kÆÜorÈ ÝColor.\n"Ž’®8·‘ÇÏ ushŽ‘€«;Ž¦‘ÂColorŽ‘=¤ö·Ž‘B¤÷±cŽ‘I¿ê«=‘ÇÂColorŽ‘ º«::Ž‘&¤øÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“c‘ÿ}'olorŽ‘nø«(‘ª¨);Ž¦‘·Ž‘#±cŽ‘*÷«=‘Ç·Ž‘ÇÏ l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“ptrŽ‘=³á«;Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ–® l‘‚Øl‘‰ffŽ“c‘ÿ}'olorŽ‘5I:«(±cŽ‘SÛ«);Ž¡‘·gŽ¡‘ÂelseŽ‘+Øá·fŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)Ž¡‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÝ"fill_color_ptr->getŽ‘kÆÜ_name()È Ý==È Ý"Ž’®8·‘ÇÏ l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“ptrŽ‘6³àŸ±~ŽŽ‘<³áÏget‘‰ffŽ‘®nameŽ‘e­¡«(‘ª¨)–Ç·“Ïend‘‚ØlŽ‘ò·“Ï ushŽ‘€«;Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ–® l‘‚Øl‘‰ffŽ“c‘ÿ}'olorŽ‘5I:«(Ï l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“ptrŽ‘5ìÈ«);Ž¡‘·gŽ¡‘«(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ‘®p‘ÿ}'enŽ‘ʘ«(Ïpp‘ÿ}'enŽ‘6#«);Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ–®dash‘‰ffŽ“p‘ÿ}'atternŽ‘FÝ–«(Ïddashe‘ÿ}'dŽ‘#G«);Ž¡‘ -·gŽŸ ›b­This–ÕXcoQU·hÂconstŽ‘§ ColorŽ‘>Èk·Ž–CÈli‘ÑÀÏdr–ÿ}'aw‘‰ffŽ‘®c“olorsŽ‘6“M±;‘ª¨ÂconstŽ‘ Qµv®9ectorŽ‘?ûý·hÂconstŽ‘§ ColorŽ‘>Èk·Ž“iŽ¡‘2Ï l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorsŽ‘[m®±;‘ª¨ÂconstŽ‘ÕJstringŽ‘@ú—Ïddashe‘ÿ}'dŽ‘dA¨±;‘ª¨ÂconstŽ‘ÕJstringŽ‘@ú—Ïpp‘ÿ}'enŽ‘V0º±;‘ª¨ÂPictureŽ‘*œ -«&Ž‘2c(Ïpictur‘ÿ}'eŽ‘Qkþ«)‘UUÂconstŽŽ¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EnteringÈ ÝSolid::filŽ‘kÆÜldraw():"Ž’žTA·‘ÇÝ"\n"Ž‘Œ·‘ÇÏ ushŽ‘€«;Ž¦‘ÂSolidŽ‘0Ó.·Ž‘5Ó/±sŽ‘=JG«=‘ÇÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“solidŽ‘IèÓ«(‘ª¨);Ž¦‘·Ž‘±sŽ‘ w«=‘Ç·Ž‘ÇÏthisŽ‘²Ï«;Ž¦‘ÂconstŽ‘2*¤ColorŽ‘QÏ—·Ž‘VϘÏdr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜ptrŽ’–D«;Ž¡‘ÂconstŽ‘2*¤ColorŽ‘QÏ—·Ž‘VÏ˜Ï l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“ptrŽ’Œ¼`«;Ž¦‘Âv®9ectorŽ‘3ªJ·hÂconstŽ‘*¢ColorŽ‘=Ï•·Ž‘BÏ–i‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûdr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜iterŽ’ˆö«=‘ÇÏdr–ÿ}'aw‘‰ffŽ‘®c“olorsŽ‘5ˆ¥±:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¡‘Âv®9ectorŽ‘3ªJ·hÂconstŽ‘*¢ColorŽ‘=Ï•·Ž‘BÏ–i‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚û l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“iterŽ‘~Å«=‘ÇÏ l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorsŽ‘,4Á±:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂP®9athŽ‘æ¹·Ž‘ æºi‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W«=‘DZsŽ‘wŸ~ŽŽ‘ wÏp‘ÿ}'athsŽ–#Ʊ:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘DZsŽ‘wŸ~ŽŽ‘ wÏp‘ÿ}'athsŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘h›ª¨«ProGcess–UUv¸ãectors“for“Ï l‘‚Øldr‘ÿ}'awŽ‘$¼À«(‘ª®)‘@­1388˜·iŽ¡‘gŽ¡‘Ïdr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜iterŽ‘X•ý«=‘ÇÏdr–ÿ}'aw‘‰ffŽ‘®c“olorsŽ‘5ˆ¥±:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¡‘Ï l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“iterŽ‘OB«=‘ÇÏ l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorsŽ‘,4Á±:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂCircleŽ‘!¸·Ž‘&¸‚i‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W«=‘DZsŽ‘wŸ~ŽŽ‘ wÏcir‘ÿ}'clesŽ–(}±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘DZsŽ‘wŸ~ŽŽ‘ wÏcir‘ÿ}'clesŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘h›ª¨«ProGcess–UUv¸ãectors“for“Ï l‘‚Øldr‘ÿ}'awŽ‘$¼À«(‘ª®)‘@­1388˜·iŽ¡‘gŽ¡‘Ïdr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜iterŽ‘X•ý«=‘ÇÏdr–ÿ}'aw‘‰ffŽ‘®c“olorsŽ‘5ˆ¥±:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¡‘Ï l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“iterŽ‘OB«=‘ÇÏ l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorsŽ‘,4Á±:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂEllipseŽ‘%>.·Ž‘*>/i‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W«=‘DZsŽ‘wŸ~ŽŽ‘ wÏel‘‚ØlipsesŽ–+ùŠ±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘DZsŽ‘wŸ~ŽŽ‘ wÏel‘‚ØlipsesŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘h›ª¨«ProGcess–UUv¸ãectors“for“Ï l‘‚Øldr‘ÿ}'awŽ‘$¼À«(‘ª®)‘@­1388˜·iŽ¡‘gŽ¡‘Ïdr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜iterŽ‘X•ý«=‘ÇÏdr–ÿ}'aw‘‰ffŽ‘®c“olorsŽ‘5ˆ¥±:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¡‘Ï l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“iterŽ‘OB«=‘ÇÏ l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorsŽ‘,4Á±:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¡‘ÂforŽ‘'«$«(Âv®9ectorŽ‘ªH·hÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘F–¥·Ž‘K–¦i‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘Z«=‘¶±sŽ‘fŸ~ŽŽ‘fÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘DYi±:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¡‘2ÏiterŽ‘E’·6«=‘DZsŽ‘wŸ~ŽŽ‘ wÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘Aji±:ÏendŽ‘ಫ(‘ª¨);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘h›ª¨«ProGcess–UUv¸ãectors“for“Ï l‘‚Øldr‘ÿ}'awŽ‘$¼À«(‘ª®)‘@­1388˜·iŽ¡‘gŽ¡‘ÂforŽ‘&6¡«(Âv®9ectorŽ‘ªH·hÂRectangleŽ‘5ã·Ž‘:ãi‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W—:«=‘IA±sŽ‘ùAŸ~ŽŽ‘ ùBÏr–ÿ}'e“ctanglesŽ–7™‡±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘NÏiterŽ‘bU·6«=‘IA±sŽ‘ùAŸ~ŽŽ‘ ùBÏr–ÿ}'e“ctanglesŽ“±:ÏendŽ‘ಫ(˜);Ž¡‘2€Ÿÿ®+‘ÿ+ŽŽ‘>G%ÏiterŽ‘O#«)‘·fŽ¡‘h›ª¨«ProGcess–UUv¸ãectors“for“Ï l‘‚Øldr‘ÿ}'awŽ‘$¼À«(‘ª®)‘@­1388˜·iŽ¡‘gŽ¡‘Ïpictur‘ÿ}'eŽ‘5Ïð«+=ŽŽ‘H%DÂdynamicu½‰™šs4Ž‘ÔwcastŽ’‹–·hÂShapQÇeŽ‘"Ab·Ž‘'Aci«(±sŽ‘°«);Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"ExitingÈ ÝSolid::fillŽ‘kÆÜdraw():"Ž’™D·‘ÇÝ"\n"Ž‘Œ·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¡‘ -gŽŽŽŒ‹¦ýû Šn ý‘ì«422–­FILLDRA‘ÿ8W’/¦3DLDFPRÃŽG“·x«1391Ž €n ý•@PÂ1391.‘ ü«ProGcess–±Îv¸ãectors“for“Ïundr‘ÿ}'aw‘«().‘‡3[¬LDF‘T2002.10.09.«]Ž‘TëæAdded“this“section.‘‡3The“same“things“are“done“toŽ¤ eacš¸ãh–ö‘of“the“ÂShapQÇeŽ‘&Ù/·Ž‘/ÏÁ«v˜ectors“Ïp‘ÿ}'athsŽ‘‡>«,‘ßÏel‘‚ØlipsesŽ‘$¡P«,‘ßÏcir‘ÿ}'clesŽ‘ «C«,‘ßÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:/«,›ßand“Ïr–ÿ}'e“ctanglesŽ‘/–Ö«,˜so“I'v¸ãe“put“the“coGde“inŽ¡this–UUnamed“section.‘qÇEacš¸ãh“time“it“it's“used,“ÏiterŽ‘u¨«is“an“iterator“for“a“di eren˜t“v˜ector.Ž©·h›ª¨«ProGcess–UUv¸ãectors“for“Ïundr‘ÿ}'awŽ‘${T«(‘ª®)‘@­1391˜·i‘ÇŽ¡‘ -fŽ¡‘«(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ–® l‘‚Øl‘‰ffŽ“dr‘ÿ}'aw‘‰ffŽ“valueŽ‘N\ö«(ÝUNDRAWŽ‘ V«);Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ–®dr›ÿ}'aw‘‰ffŽ“c˜olorŽ‘>«(Âstaticu½‰™šs4Ž‘ÔwcastŽ‘4}¢·hÂColorŽ‘¤ó·Ž‘$¤ôi«(0Ž‘));Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ–® l‘‚Øl‘‰ffŽ“c‘ÿ}'olorŽ‘5I:«(Âstaticu½‰™šs4Ž‘ÔwcastŽ‘4}¢·hÂColorŽ‘¤ó·Ž‘$¤ôi«(0Ž‘));Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ–®dash‘‰ffŽ“p‘ÿ}'atternŽ‘FÝ–«(Ïddashe‘ÿ}'dŽ‘#G«);Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ‘®p‘ÿ}'enŽ‘ʘ«(Ïpp‘ÿ}'enŽ‘6#«);Ž¡‘ -·gŽŸ ­This–ÕXco.·Ž‘*>/i‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W«=‘DZsŽ‘wŸ~ŽŽ‘ wÏel‘‚ØlipsesŽ–+ùŠ±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘DZsŽ‘wŸ~ŽŽ‘ wÏel‘‚ØlipsesŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘h›ª¨«ProGcess–UUv¸ãectors“for“Ïundr‘ÿ}'awŽ‘${T«(‘ª®)‘@­1391˜·iŽ¡‘gŽ¡‘ÂforŽ‘'«$«(Âv®9ectorŽ‘ªH·hÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘F–¥·Ž‘K–¦i‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘Z«=‘¶±sŽ‘fŸ~ŽŽ‘fÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘DYi±:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¡‘2ÏiterŽ‘E’·6«=‘DZsŽ‘wŸ~ŽŽ‘ wÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘Aji±:ÏendŽ‘ಫ(‘ª¨);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘h›ª¨«ProGcess–UUv¸ãectors“for“Ïundr‘ÿ}'awŽ‘${T«(‘ª®)‘@­1391˜·iŽ¡‘gŽ¡‘ÂforŽ‘&6¡«(Âv®9ectorŽ‘ªH·hÂRectangleŽ‘5ã·Ž‘:ãi‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W—:«=‘IA±sŽ‘ùAŸ~ŽŽ‘ ùBÏr–ÿ}'e“ctanglesŽ–7™‡±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘NÏiterŽ‘bU·6«=‘IA±sŽ‘ùAŸ~ŽŽ‘ ùBÏr–ÿ}'e“ctanglesŽ“±:ÏendŽ‘ಫ(˜);Ž¡‘2€Ÿÿ®+‘ÿ+ŽŽ‘>G%ÏiterŽ‘O#«)‘·fŽ¡‘h›ª¨«ProGcess–UUv¸ãectors“for“Ïundr‘ÿ}'awŽ‘${T«(‘ª®)‘@­1391˜·iŽ¡‘gŽ¡‘Ïpictur‘ÿ}'eŽ‘5Ïð«+=ŽŽ‘H%DÂdynamicu½‰™šs4Ž‘ÔwcastŽ’‹–·hÂShapQÇeŽ‘"Ab·Ž‘'Aci«(±sŽ‘°«);Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"ExitingÈ ÝSolid::undrŽ‘kÆÜaw():"Ž’Ž”J·‘ÇÝ"\n"Ž‘Œ·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¡‘ -gŽŽŽŒ‹§r Šn ý‘ì·x«1394–­3DLDFPRÃŽG’6#IUNDRA‘ÿ8W“«423Ž €n ý•@PÂ1394.‘ ü«ProGcess–UUv¸ãectors“for“Ïun l‘‚Øl‘‰«().ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ -«[¬LDF‘T2002.10.09.«]Ž‘Y‡Added–Ü¡this“section.‘ªThe“same“things“are“done“to“eacš¸ãh“of“the“ÂShapQÇeŽ‘&¥O·Ž‘/ñ«v˜ectors“Ïp‘ÿ}'athsŽ‘mN«,Ž¡Ïel‘‚ØlipsesŽ‘ ‚q«,‘­Ïcir‘ÿ}'clesŽ‘ 9l«,‘­Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘9 X«,–­and‘›~Ïr–ÿ}'e“ctanglesŽ‘/;ë,“so–›~I'vš¸ãe“put“the“coGde“in“this“named“section.‘DAEac˜h“time“it“it'sŽ¡used,‘UUÏiterŽ‘u¨«is–UUan“iterator“for“a“di erenš¸ãt“v˜ector.Ž¡‘ -[¬LDF‘T2003.08.10.«]Ž‘Y;Noš¸ãw–UUsetting“pGen“to“Ý""Ž‘[·«,“since“I'v˜e“remo˜v˜ed“the“pGen“argumen˜t“to“Ïun l‘‚ØlŽ‘l«(‘ª®).Ž¤ŸüÈ„`ÕÁGŽŽ¡·h›ª¨«ProGcess–UUv¸ãectors“for“Ïun l‘‚ØlŽ‘l«(‘ª®)‘@­1394˜·i‘ÇŽ¤ ‘ -fŽ¡‘«(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ–® l‘‚Øl‘‰ffŽ“dr‘ÿ}'aw‘‰ffŽ“valueŽ‘N\ö«(ÝUNFILLŽ‘ V«);Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ–®dr›ÿ}'aw‘‰ffŽ“c˜olorŽ‘>«(Âstaticu½‰™šs4Ž‘ÔwcastŽ‘4}¢·hÂColorŽ‘¤ó·Ž‘$¤ôi«(0Ž‘));Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ–® l‘‚Øl‘‰ffŽ“c‘ÿ}'olorŽ‘5I:«(Âstaticu½‰™šs4Ž‘ÔwcastŽ‘4}¢·hÂColorŽ‘¤ó·Ž‘$¤ôi«(0Ž‘));Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ–®dash‘‰ffŽ“p‘ÿ}'atternŽ‘FÝ–«(Ý""Ž‘ b«);Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ‘®p‘ÿ}'enŽ‘ʘ«(Ý""Ž‘ b«);Ž¡‘ -·gŽŸ ­This–ÕXco.·Ž‘*>/i‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W«=‘DZsŽ‘wŸ~ŽŽ‘ wÏel‘‚ØlipsesŽ–+ùŠ±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘DZsŽ‘wŸ~ŽŽ‘ wÏel‘‚ØlipsesŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘h›ª¨«ProGcess–UUv¸ãectors“for“Ïun l‘‚ØlŽ‘l«(‘ª®)‘@­1394˜·iŽ¡‘gŽ¡‘ÂforŽ‘'«$«(Âv®9ectorŽ‘ªH·hÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘F–¥·Ž‘K–¦i‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘Z«=‘¶±sŽ‘fŸ~ŽŽ‘fÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘DYi±:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¡‘2ÏiterŽ‘E’·6«=‘DZsŽ‘wŸ~ŽŽ‘ wÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘Aji±:ÏendŽ‘ಫ(‘ª¨);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘h›ª¨«ProGcess–UUv¸ãectors“for“Ïun l‘‚ØlŽ‘l«(‘ª®)‘@­1394˜·iŽ¡‘gŽ¡‘ÂforŽ‘&6¡«(Âv®9ectorŽ‘ªH·hÂRectangleŽ‘5ã·Ž‘:ãi‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W—:«=‘IA±sŽ‘ùAŸ~ŽŽ‘ ùBÏr–ÿ}'e“ctanglesŽ–7™‡±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘NÏiterŽ‘bU·6«=‘IA±sŽ‘ùAŸ~ŽŽ‘ ùBÏr–ÿ}'e“ctanglesŽ“±:ÏendŽ‘ಫ(˜);Ž¡‘2€Ÿÿ®+‘ÿ+ŽŽ‘>G%ÏiterŽ‘O#«)‘·fŽ¡‘h›ª¨«ProGcess–UUv¸ãectors“for“Ïun l‘‚ØlŽ‘l«(‘ª®)‘@­1394˜·iŽ¡‘gŽ¡‘Ïpictur‘ÿ}'eŽ‘5Ïð«+=ŽŽ‘H%DÂdynamicu½‰™šs4Ž‘ÔwcastŽ’‹–·hÂShapQÇeŽ‘"Ab·Ž‘'Aci«(±sŽ‘°«);Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"ExitingÈ ÝSolid::unfiŽ‘kÆÜll():"Ž’Ž”J·‘ÇÝ"\n"Ž‘Œ·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¡‘ -gŽŽŽŒ‹©,™ Šn ý‘ì·x«1397–­3DLDFPRÃŽG’=αUNFILL“«425Ž €n ý•@PÂ1397.‘ ü«ProGcess–Ç;v¸ãectors“for“Ïun l‘‚Øldr‘ÿ}'aw‘«().‘Çz[¬LDF‘T2002.10.09.«]Ž‘UAšAdded“this“section.‘ÇzThe“same“things“are“doneŽ¤ to–J^eacš¸ãh“of“the“ÂShapQÇeŽ‘%€É·Ž‘-Ë(«v˜ectors“Ïp‘ÿ}'athsŽ‘Û «,‘LÏel‘‚ØlipsesŽ‘#Ï«,‘LÏcir‘ÿ}'clesŽ‘Øô«,‘LÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘9?à«,›Land“Ïr–ÿ}'e“ctanglesŽ‘.꣫,˜so“I'v¸ãe“put“the“coGde“inŽ¡this–UUnamed“section.‘qÇEacš¸ãh“time“it“it's“used,“ÏiterŽ‘u¨«is“an“iterator“for“a“di eren˜t“v˜ector.Ž©·h›ª¨«ProGcess–UUv¸ãectors“for“Ïun l‘‚Øldr‘ÿ}'awŽ‘/¹ä«(‘ª®)‘@­1397˜·i‘ÇŽ¡‘ -fŽ¡‘«(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ–® l‘‚Øl‘‰ffŽ“dr‘ÿ}'aw‘‰ffŽ“valueŽ‘N\ö«(ÝUNFILLDRAWŽ‘5J«);Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ–®dr›ÿ}'aw‘‰ffŽ“c˜olorŽ‘>«(Âstaticu½‰™šs4Ž‘ÔwcastŽ‘4}¢·hÂColorŽ‘¤ó·Ž‘$¤ôi«(0Ž‘));Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ–® l‘‚Øl‘‰ffŽ“c‘ÿ}'olorŽ‘5I:«(Âstaticu½‰™šs4Ž‘ÔwcastŽ‘4}¢·hÂColorŽ‘¤ó·Ž‘$¤ôi«(0Ž‘));Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ–®dash‘‰ffŽ“p‘ÿ}'atternŽ‘FÝ–«(Ïddashe‘ÿ}'dŽ‘#G«);Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïset‘‰ffŽ‘®p‘ÿ}'enŽ‘ʘ«(Ïpp‘ÿ}'enŽ‘6#«);Ž¡‘ -·gŽŸ ­This–ÕXco.·Ž‘*>/i‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W«=‘DZsŽ‘wŸ~ŽŽ‘ wÏel‘‚ØlipsesŽ–+ùŠ±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘DZsŽ‘wŸ~ŽŽ‘ wÏel‘‚ØlipsesŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘h›ª¨«ProGcess–UUv¸ãectors“for“Ïun l‘‚Øldr‘ÿ}'awŽ‘/¹ä«(‘ª®)‘@­1397˜·iŽ¡‘gŽ¡‘ÂforŽ‘'«$«(Âv®9ectorŽ‘ªH·hÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘F–¥·Ž‘K–¦i‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘Z«=‘¶±sŽ‘fŸ~ŽŽ‘fÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘DYi±:Ïb–ÿ}'e“ginŽ‘¾¨«(‘ª¨);Ž¡‘2ÏiterŽ‘E’·6«=‘DZsŽ‘wŸ~ŽŽ‘ wÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘Aji±:ÏendŽ‘ಫ(‘ª¨);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘h›ª¨«ProGcess–UUv¸ãectors“for“Ïun l‘‚Øldr‘ÿ}'awŽ‘/¹ä«(‘ª®)‘@­1397˜·iŽ¡‘gŽ¡‘ÂforŽ‘&6¡«(Âv®9ectorŽ‘ªH·hÂRectangleŽ‘5ã·Ž‘:ãi‘«::Ž‘ŽBÏc–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W—:«=‘IA±sŽ‘ùAŸ~ŽŽ‘ ùBÏr–ÿ}'e“ctanglesŽ–7™‡±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘NÏiterŽ‘bU·6«=‘IA±sŽ‘ùAŸ~ŽŽ‘ 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ushŽ‘€«;Ž¡‘(ÂforŽ‘9芫(Âv®9ectorŽ‘ªH·hÂP•®9oin“tŽ‘šH·i‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7pt‘‰ffŽ‘®iterŽ‘IHK«=‘DZvŽ–ûÕ:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏpt‘‰ffŽ‘®iterŽ‘$¯·6«=‘DZvŽ“:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏpt‘‰ffŽ‘®iterŽ‘./«)Ž¡‘2±wŽ‘9m§:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(·Ž‘Ïpt‘‰ffŽ‘®iterŽ‘!çý«);Ž¡‘·gŽ¡‘gŽ¡‘ÂreturnŽ‘7æ¼±wŽ‘?T^«;Ž¡‘ -·gŽ¡«#ÂendifŽŽŸ ­This–ÕXco³2±axis‘‰ffŽ–®h‘‰ffŽ“halfŽ‘qTC¬=‘DZaxis‘‰ffŽ‘®hŽ‘À¥µ=¬2Ž‘;Ž¡‘(­realŽ‘>³2±axis‘‰ffŽ–®v‘‰ffŽ“halfŽ‘pÑj¬=‘DZaxis‘‰ffŽ‘®vŽ‘Œöµ=¬2Ž‘;Ž¦‘(­ifŽ‘3j§¬(±fabsŽ‘2Ò¬(±axis‘‰ffŽ‘®hŽ‘Ä°‘¤7±old‘‰ffŽ–®axis‘‰ffŽ“hŽ‘-ï¬)–ǵ>“­P•®9oin“tŽ‘ad¬::Ž‘%epsilonŽ›E^¦¬(‘ª¨)–¤7°_“±fabsŽ‘× ¬(±axis‘‰ffŽ‘®vŽ‘j°“±old‘‰ffŽ–®axis‘‰ffŽ“vŽ‘,ß@¬)–ǵ>“­P•®9oin“tŽ‘ad¬::Ž‘%epsilonŽ˜¬(‘ª¨))‘°fŽ¡‘2­ifŽ‘?߬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘O°‘õâ´"Recalculating® ´lineaŽ‘nõ¦r_eccentricity,® ´"Ž’α½°Ž¡‘P´"numerical_eccentricŽ’¸ÿÌity® ´and® ´foci.\n"Ž’M°‘DZ ushŽ‘€¬;Ž¡‘2­ifŽ‘=´ý¬(±axis‘‰ffŽ‘®hŽ‘À¥°‘DZaxis‘‰ffŽ‘®vŽ‘Œö¬)‘°fŽ¡‘<±line–ÿ}'ar‘‰ffŽ‘®e“c“c“entricityŽ’sù¬=‘DZsqrtŽ‘w¬((±axis‘‰ffŽ–®h‘‰ffŽ“halfŽ–2Ù°‘8à±axis‘‰ffŽ–®h‘‰ffŽ“halfŽ“¬)–8à°“¬(±axis‘‰ffŽ–®v‘‰ffŽ“halfŽ›1°“±axis‘‰ffŽ–®v‘‰ffŽ“halfŽ˜¬));Ž¡‘<±numeric–ÿ}'al‘‰ffŽ‘®e“c“c“entricityŽ’Ÿ˜ì¬=‘DZline–ÿ}'ar‘‰ffŽ‘®e“c“c“entricityŽ‘Qsóµ=±axis‘‰ffŽ–®h‘‰ffŽ“halfŽ‘/Ùù¬;Ž¡‘<±fo‘ÿ}'cus1Ž‘[zH¬=‘DZfo‘ÿ}'cus0Ž‘"AZ¬=‘Ç(±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(0Ž‘)–8à°“±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘.v'¬(‘ª¨));Ž¡‘2°gŽ¡‘2­elseŽ‘IØä°fŽ¡‘<±line–ÿ}'ar‘‰ffŽ‘®e“c“c“entricityŽ’sù¬=‘DZsqrtŽ‘w¬((±axis‘‰ffŽ–®v‘‰ffŽ“halfŽ–1°‘8à±axis‘‰ffŽ–®v‘‰ffŽ“halfŽ“¬)–8à°“¬(±axis‘‰ffŽ–®h‘‰ffŽ“halfŽ›2Ù°“±axis‘‰ffŽ–®h‘‰ffŽ“halfŽ˜¬));Ž¡‘<±numeric–ÿ}'al‘‰ffŽ‘®e“c“c“entricityŽ’Ÿ˜ì¬=‘DZline–ÿ}'ar‘‰ffŽ‘®e“c“c“entricityŽ‘Qsóµ=±axis‘‰ffŽ–®v‘‰ffŽ“halfŽ‘/W ¬;Ž¡‘<±fo‘ÿ}'cus1Ž‘[zH¬=‘DZfo‘ÿ}'cus0Ž‘"AZ¬=‘Ç(±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(±numb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜ointsŽ‘JÀ©µ=¬4Ž‘)–8à°“±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘.v'¬(‘ª¨));Ž¡‘2°gŽ¡‘2±fo‘ÿ}'cus0Ž‘N³/µ:±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u¬(±trueŽ‘ʬ);Ž¡‘2±fo‘ÿ}'cus1Ž‘N³/µ:±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u¬(±trueŽ‘ʬ);Ž¡‘2±fo‘ÿ}'cus0Ž‘QzG°¬=ŽŽ‘a~°Ž‘hÏœ±line–ÿ}'ar‘‰ffŽ‘®e“c“c“entricityŽ’·|w¬;Ž¡‘2±fo‘ÿ}'cus1Ž‘QzG°¬=ŽŽ‘a~±line–ÿ}'ar‘‰ffŽ‘®e“c“c“entricityŽ’¯µY¬;Ž¡‘2±fo‘ÿ}'cus1Ž‘QzG°¬=ŽŽ‘a~±fo‘ÿ}'cus0Ž‘}»¨µ:±shiftŽ‘}¬(±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘,=G¬(‘ª¨));Ž¡‘(°gŽ¡‘(­elseŽ‘>.8ifŽ‘Iã0¬(´DEBUGŽ‘ÆY¬)Ž¡‘2±c‘ÿ}'outŽ‘H T°‘Ç´"axis_h® ´and® ´axis_v® ´aŽ‘kÆÜre® ´unchanged.\n"Ž’Ã,°‘Ç´"Not® ´recalculating® ´fŽ‘kÆÜoci.\n"Ž’“ÔG°‘DZ ushŽ‘€¬;Ž¡‘°g‘µ=°‘ÿý­ifŽ‘´õ¬(±is‘‰ffŽ‘®el‘‚Øliptic‘ÿ}'alŽ‘0ì–¬(‘ª®))‘ÿý°µ=Ž¡‘­elseŽ‘5Øâ°fŽ¡‘(±c‘ÿ}'errŽ‘?¿¢°‘ ø´"WARNING!® ´In® ´EllipseŽ‘n ¼::do_transform(constŽ’× €® ´Transform&):\n"Ž’0™°°Ž¡‘<´"This® ´transformationŽ’¤ÿÊ® ´has® ´made® ´*this® ´non-Ž’ ÿŽelliptical!"Ž’PL갑DZend‘‚ØlŽ–ò°‘DZend‘‚ØlŽ“°‘DZ ushŽ‘€¬;Ž¡‘(±axis‘‰ffŽ‘®hŽ‘EÀ©¬=‘DZaxis‘‰ffŽ‘®vŽ‘ T¬=‘DZline–ÿ}'ar‘‰ffŽ‘®e“c“c“entricityŽ‘T; ¬=‘Ç´INVALID_REALŽ‘BM\¬;Ž¡‘(±numeric–ÿ}'al‘‰ffŽ‘®e“c“c“entricityŽ’‹˜ê¬=‘Ç´INVALID_REALŽ‘BM\¬;Ž¡‘°gŽ¡‘gŽ¡‘­returnŽ‘7æ¼µtŽ‘;ƒ.¬;Ž¡‘ +°gŽŽŽŒ‹fNÑ Šn ý‘ì¬358–¯OPERA‘ÿJªTOR’$9Ÿ3DLDF-1.1.5.1“°x¬1233Ž €n ý•@P­1233.‘ üOpQÇerator.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ +¬[²LDF‘T2002.04.12.¬]Ž‘Y;Added–UUthis“section.Ž¡‘ +[²LDF‘T2003.07.20.¬]Ž‘YÅâChanged,›Beso–üthat“it“calls“±do‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘=­0¬(‘ª®)“with“±che‘ÿ}'ckŽ‘ ¬‚°‘,±trueŽ‘ÇĬ,˜so“that“±is‘‰ffŽ‘®el‘‚Øliptic‘ÿ}'alŽ‘4ÿ’¬(‘ª®)“isŽ¡called.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž© ‘ +­virtualŽ‘/ÔT‘ÿ +«ransformŽ‘gV¦opQÇeratorŽ’’í[°¬=ŽŽŽ’Ÿ´z(­constŽ‘*¢T‘ÿ +«ransformŽ‘Uót¬&Ž‘]º’µtŽ‘aW¬);ŽŸ­1234.Ž¡°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¦‘ +­T‘ÿ +«ransformŽ‘AÈÓEllipseŽ‘d±°¬::Ž‘k?î­opQÇeratorŽ’–Ö£°¬=ŽŽŽ’£Â(­constŽ‘*¢T‘ÿ +«ransformŽ‘Uót¬&Ž‘]º’µtŽ‘aW¬)Ž¦‘ +°fŽ¦‘­returnŽ‘7æ¼±do‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘q€ð¬(µtŽ‘œr;‘ª¨±trueŽ‘o@¬);Ž¦‘ +°gŽŸ­1235.‘ üRotation–ÕTaround“the“main“axes.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ +¬[²LDF‘T2003.07.25.¬]Ž‘YäChanged,‘hso–1that“±do‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘=ËQ¬(‘ª®)“is“called“with“±che‘ÿ}'ckŽ‘ üÛ°‘5d±falseŽ‘䨬.‘Rotation“can“neitherŽ¦cš¸ãhange–/æthe“lengths“of“±axis‘‰ffŽ‘®hŽ‘!YY¬or“±axis‘‰ffŽ‘®vŽ‘õĬ,‘7cnor“mak˜e“an“­EllipseŽ‘(H¥¬non-elliptical,‘7cso“there's“no“need“to“c˜hec˜k“°Ž‘/ç±thisŽŽ¦¬after‘UUrotation.Ž¡ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¦‘ +­virtualŽ‘/ÔT‘ÿ +«ransformŽ‘gV¦±r‘ÿ}'otateŽ’Åä¬(­constŽ‘*¢realŽ‘4ÝеxŽ‘:”ì;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµyŽ‘>’ˆ¬=‘Ç0Ž–ǵ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµzŽ‘>f®¬=‘Ç0Ž“);ŽŸ­1236.Ž¡°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¦‘ +­T‘ÿ +«ransformŽ‘AÈÓEllipseŽ‘d±°¬::‘±r‘ÿ}'otateŽ‘oB¬(­constŽ‘*¢realŽ‘4ÝеxŽ‘:”ì;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµyŽ‘;Ëp;‘ª¨­constŽ‘ÕJrealŽ‘6ˆxµzŽ‘;Ÿ–¬)Ž¦‘ +°fŽ¦‘­T‘ÿ +«ransformŽ‘KÈÔµtŽ‘OeF¬;Ž¡‘µtŽ‘œt:±r‘ÿ}'otateŽ‘o>¬(µxŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁƬ);Ž¦‘­returnŽ‘7æ¼±do‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘q€ð¬(µtŽ‘œr;‘ª¨±falseŽ‘Yì¬);Ž¦‘ +°gŽŸ­1237.‘ üScale.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ +¬[²LDF‘T2003.07.20.¬]Ž‘Y;Added›UUc•¸ãhec“k˜for˜whether˜°Ž‘UV±thisŽ‘–a¬is˜still˜elliptical˜after˜the˜scaling˜opGeration.Ž¡ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¦‘ +­virtualŽ‘/ÔT‘ÿ +«ransformŽ‘gV¦±sc‘ÿ}'aleŽ‘} ˜¬(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ gæ¬=‘Ç1Ž–ǵ;‘ª¨­realŽ‘]ÖµzŽ‘ < ¬=‘Ç1Ž“);ŽŽŽŒ‹gbM Šn ý‘ì°x¬1238–¯3DLDF-1.1.5.1’8þ­SCALE“¬359Ž €n ý•@P­1238.Ž©°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¤ ‘ +­T‘ÿ +«ransformŽ‘AÈÓEllipseŽ‘d±°¬::‘±sc‘ÿ}'aleŽ‘´ö¬(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ Î;‘ª¨­realŽ‘]ÖµzŽ‘tô¬)Ž¡‘ +°fŽ¡‘­T‘ÿ +«ransformŽ‘KÈÔµtŽ‘OeF¬;Ž¦‘µtŽ‘œt:±sc‘ÿ}'aleŽ‘´ò¬(µxŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁƬ);Ž¡‘­returnŽ‘7漬(°Ž‘±thisŽ‘²Ï°¬=ŽŽ‘(AµtŽ‘+Ýx¬);Ž¡‘ +°gŽŸ­1239.‘ üShear.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.07.20.¬]Ž‘Y;Added›UUc•¸ãhec“k˜for˜whether˜°Ž‘UV±thisŽ‘–a¬is˜still˜elliptical˜after˜the˜shearing˜opGeration.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔT‘ÿ +«ransformŽ‘gV¦±she‘ÿ}'arŽ‘Šà¬(­realŽ‘³.±xyŽ‘!—µ;‘ª¨­realŽ‘]Ö±xzŽ‘%œÀ¬=‘Ç0Ž–ǵ;‘ª¨­realŽ‘]Ö±yxŽ‘&Zœ¬=‘Ç0Ž“µ;‘ª¨­realŽ‘]Ö±yzŽ‘%Ô6¬=‘Ç0Ž“µ;‘ª¨­realŽ‘]Ö±zxŽ‘%–Y¬=‘Ç0Ž“µ;‘ª¨­realŽ‘]Ö±zyŽ‘%|¬=‘Ç0Ž“);ŽŸ­1240.Ž¦°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓEllipseŽ‘d±°¬::‘±she‘ÿ}'arŽ‘4>¬(­realŽ‘³.±xyŽ‘!—µ;‘ª¨­realŽ‘]Ö±xzŽ‘"Õ¨µ;‘ª¨­realŽ‘]Ö±yxŽ‘#“„µ;‘ª¨­realŽ‘]Ö±yzŽ‘# µ;‘ª¨­realŽ‘]Ö±zxŽ‘"ÏAµ;‘ª¨­realŽ‘]Ö±zyŽ‘"´ð¬)Ž¡‘ +°fŽ¡‘­T‘ÿ +«ransformŽ‘KÈÔµtŽ‘OeF¬;Ž¦‘µtŽ‘œt:±she‘ÿ}'arŽ‘4:¬(±xyŽ‘ +ãçµ;‘ª¨±xzŽ‘ "zµ;‘ª¨±yxŽ‘ àVµ;‘ª¨±yzŽ‘ Yðµ;‘ª¨±zxŽ‘ µ;‘ª¨±zyŽ‘ ¬);Ž¡‘­returnŽ‘7漬(°Ž‘±thisŽ‘²Ï°¬=ŽŽ‘(AµtŽ‘+Ýx¬);Ž¡‘ +°gŽ¤­1241.‘ üShift.Ž¡1242.‘ üreal‘ÕTargumen®9ts.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ +¬[²LDF‘T2003.07.25.¬]Ž‘Z&zChanged,‘»$so–s”that“±do‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘> Ȭ(‘ª®)“is“called“with“±che‘ÿ}'ckŽ‘!®°‘¤*±falseŽ‘Sn¬.‘Ì„Shifting“can“neitherŽ¡cš¸ãhange–/æthe“lengths“of“±axis‘‰ffŽ‘®hŽ‘!YY¬or“±axis‘‰ffŽ‘®vŽ‘õĬ,‘7cnor“mak˜e“an“­EllipseŽ‘(H¥¬non-elliptical,‘7cso“there's“no“need“to“c˜hec˜k“°Ž‘/ç±thisŽŽ¡¬after‘UUshifting.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔT‘ÿ +«ransformŽ‘gV¦±shiftŽ‘{t#¬(­realŽ‘³.±xxŽ‘!±fµ;‘ª¨­realŽ‘]Ö±yyŽ‘&@K¬=‘Ç0Ž–ǵ;‘ª¨­realŽ‘]Ö±zzŽ‘%ó¬=‘Ç0Ž“);ŽŸ­1243.Ž¦°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓEllipseŽ‘d±°¬::‘±shiftŽ‘¬(­realŽ‘³.±xxŽ‘!±fµ;‘ª¨­realŽ‘]Ö±yyŽ‘#y3µ;‘ª¨­realŽ‘]Ö±zzŽ‘"HÛ¬)Ž¡‘ +°fŽ¡‘­T‘ÿ +«ransformŽ‘KÈÔµtŽ‘OeF¬;Ž¦‘µtŽ‘œt:±shiftŽ‘}¬(±xxŽ‘ +þ8µ;‘ª¨±yyŽ‘ Ƶ;‘ª¨±zzŽ‘ •­¬);Ž¡‘­returnŽ‘7æ¼±do‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘q€ð¬(µtŽ‘œr;‘ª¨±falseŽ‘Yì¬);Ž¡‘ +°gŽŸ­1244.‘ üP•®9oin“t‘ÕTargumen“t.Ž¦°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔT‘ÿ +«ransformŽ‘gV¦±shiftŽ‘{t#¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié]¬);ŽŽŽŒ‹hlÓ Šn ý‘ì¬360–­POINT‘ÕX¯ARÃŽGUMENT’ù!3DLDF-1.1.5.1“°x¬1245Ž €n ý•@P­1245.Ž©°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¤ ‘ +­T‘ÿ +«ransformŽ‘AÈÓEllipseŽ‘d±°¬::‘±shiftŽ‘¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié]¬)Ž¡‘ +°fŽ¡‘­returnŽ‘7æ¼±shiftŽ‘L9¬(µpŽ‘:±get‘‰ffŽ‘®xŽ‘Žg¬(–ª¨)µ;“pŽ›²¨:±get‘‰ffŽ‘®yŽ‘t¬(“)µ;“pŽ˜:±get‘‰ffŽ‘®zŽ‘¬(“));Ž¡‘ +°gŽ¤­1246.‘ üShift‘ÕTtimes.Ž¡1247.‘ üreal‘ÕTargumen®9ts.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ +¬[²LDF‘T2003.07.25.¬]Ž‘Y;No¸ãw–UUpšGerforming“±shift‘‰ffŽ‘®timesŽ‘2A¬(‘ª®)“on“±fo‘ÿ}'cus0Ž‘#]Ô¬and“±fo‘ÿ}'cus1Ž‘ ¬,“to˜o.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/Ôv®9oidŽ‘H‹¬±shift‘‰ffŽ‘®timesŽ‘wwç¬(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ gæ¬=‘Ç1Ž–ǵ;‘ª¨­realŽ‘]ÖµzŽ‘ < ¬=‘Ç1Ž“);ŽŸ­1248.Ž¦°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙEllipseŽ‘E涬::‘±shift‘‰ffŽ‘®timesŽ‘/ì?¬(­realŽ‘³.µxŽ‘jJ;‘ª¨­realŽ‘]ÖµyŽ‘ Î;‘ª¨­realŽ‘]ÖµzŽ‘tô¬)Ž¡‘ +°fŽ¡‘­P®9athŽ‘-‘j¬::Ž‘4¨±shift‘‰ffŽ‘®timesŽ‘c ã¬(µxŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁƬ);Ž¡‘±fo‘ÿ}'cus1Ž‘0³,µ:±shift‘‰ffŽ‘®timesŽ‘.ì;¬(µxŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁƬ);Ž¡‘±fo‘ÿ}'cus0Ž‘0³,µ:±shift‘‰ffŽ‘®timesŽ‘.ì;¬(µxŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁƬ);Ž¡‘±c‘ÿ}'enterŽ‘0 µ:±shift‘‰ffŽ‘®timesŽ‘.ì;¬(µxŽ‘·;‘ª¨yŽ‘í ;‘ª¨zŽ‘ÁƬ);Ž¡‘­returnŽ‘4‘g¬;Ž¡‘ +°gŽŸ­1249.‘ üP•®9oin“t‘ÕTargumen“t.Ž¦°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/Ôv®9oidŽ‘H‹¬±shift‘‰ffŽ‘®timesŽ‘wwç¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié]¬);ŽŸ­1250.Ž¦°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙEllipseŽ‘E涬::‘±shift‘‰ffŽ‘®timesŽ‘/ì?¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]µpŽ‘Ié]¬)Ž¡‘ +°fŽ¡‘­returnŽ‘7æ¼±shift‘‰ffŽ‘®timesŽ‘fÒ÷¬(µpŽ‘:±get‘‰ffŽ‘®xŽ‘Žg¬(–ª¨)µ;“pŽ›²¨:±get‘‰ffŽ‘®yŽ‘t¬(“)µ;“pŽ˜:±get‘‰ffŽ‘®zŽ‘¬(“));Ž¡‘ +°gŽŸ­1251.‘ üRotatation–ÕTaround“an“arbitrary“axis.ŽŽŽŒ‹ixw Šn ý‘ì°x¬1252–¯3DLDF-1.1.5.1’ôh7­POINT‘ÕX¯ARÃŽGUMENTS“¬361Ž €n ý•@P­1252.‘ üP•®9oin“t‘ÕTargumen“ts.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ +¬[²LDF‘T2003.05.02.¬]Ž‘YËSChanged–mname“of“this“function“from“±r–ÿ}'otate‘‰ffŽ‘®ar“oundŽ‘@„ü¬(›ª®)“to“±r‘ÿ}'otateŽ‘‡«¬(˜).‘»This“function“no¸ãwŽ¡o•¸ãv“erloads‘UU±r‘ÿ}'otateŽ‘Ä“¬(‘ª®)–UUwith“three“­realŽ‘ƒ¬argumen¸ãts.Ž¡‘ +[²LDF‘T2003.07.25.¬]Ž‘YäChanged,‘hso–1that“±do‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘=ËQ¬(‘ª®)“is“called“with“±che‘ÿ}'ckŽ‘ üÛ°‘5d±falseŽ‘䨬.‘Rotation“can“neitherŽ¡cš¸ãhange–/æthe“lengths“of“±axis‘‰ffŽ‘®hŽ‘!YY¬or“±axis‘‰ffŽ‘®vŽ‘õĬ,‘7cnor“mak˜e“an“­EllipseŽ‘(H¥¬non-elliptical,‘7cso“there's“no“need“to“c˜hec˜k“°Ž‘/ç±thisŽŽ¡¬after‘UUrotation.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž© ‘ +­virtualŽ‘/ÔT‘ÿ +«ransformŽ‘gV¦±r‘ÿ}'otateŽ’Åä¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±p0Ž‘Pøµ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±p1Ž‘R¢Åµ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±angleŽ‘Qã¬=‘Ç180ŽŽ‘Ç);ŽŸ­1253.Ž¡°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¦‘ +­T‘ÿ +«ransformŽ‘AÈÓEllipseŽ‘d±°¬::‘±r‘ÿ}'otateŽ‘oB¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±p0Ž‘Pøµ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±p1Ž‘R¢Åµ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±angleŽ‘NHˬ)Ž¦‘ +°fŽ¦‘­T‘ÿ +«ransformŽ‘KÈÔµtŽ‘OeF¬;Ž¡‘µtŽ‘œt:±r‘ÿ}'otateŽ‘o>¬(±p0Ž‘ Àµ;‘ª¨±p1Ž‘ Áhµ;‘ª¨±angleŽ‘jû¬);Ž¦‘­returnŽ‘7æ¼±do‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘q€ð¬(µtŽ‘œr;‘ª¨±falseŽ‘Yì¬);Ž¦‘ +°gŽŸ­1254.‘ üP•®9ath‘ÕTargumen“ts.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ +¬[²LDF‘T2003.05.02.¬]Ž‘YËSChanged–mname“of“this“function“from“±r–ÿ}'otate‘‰ffŽ‘®ar“oundŽ‘@„ü¬(›ª®)“to“±r‘ÿ}'otateŽ‘‡«¬(˜).‘»This“function“no¸ãwŽ¦o•¸ãv“erloads‘UU±r‘ÿ}'otateŽ‘Ä“¬(‘ª®)–UUwith“three“­realŽ‘ƒ¬argumen¸ãts.Ž¡ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¦‘ +­virtualŽ‘/ÔT‘ÿ +«ransformŽ‘gV¦±r‘ÿ}'otateŽ’Åä¬(­constŽ‘*¢P®9athŽ‘:[¬&Ž‘AØyµpŽ‘Fày;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±angleŽ‘Qã¬=‘Ç180ŽŽ‘Ç);ŽŽŽŒ‹j¹ Šn ý‘ì¬362›­P–ÿ +«A“TH‘ÕX¯ARÃŽGUMENTS’ú¡3DLDF-1.1.5.1˜°x¬1255Ž €n ý•@P­1255.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ© ‘ +¬[²LDF‘T2003.04.27.¬]Ž‘Y;Changed‘UU±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘*·¬(1Ž‘)–UUto“±get‘‰ffŽ–®last‘‰ffŽ“p‘ÿ}'ointŽ‘=y“¬(‘ª®).Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¦‘ +­T‘ÿ +«ransformŽ‘AÈÓEllipseŽ‘d±°¬::‘±r‘ÿ}'otateŽ‘oB¬(­constŽ‘*¢P®9athŽ‘:[¬&Ž‘AØyµpŽ‘Fày;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±angleŽ‘NHˬ)Ž¦‘ +°fŽ¦‘­ifŽ‘´ú¬(°:µpŽ‘:±is‘‰ffŽ‘®line‘ÿ}'arŽ‘%}¬(‘ª¨))‘°fŽ¦‘±c‘ÿ}'errŽ‘7ã·°‘.´"ERROR!® ´In® ´Ellipse::Ž‘p-Òrotate(Path,® ´real).\Ž’Ù-–n"Ž’ëb°Ž¦‘2´"Path® ´is® ´not® ´a® ´line.Ž’šÿÉ® ´Returning® ´INVALID_Ž’ÿTRANSFORM.\n\n"Ž’SEȬ;Ž¦‘­returnŽ‘Aæ½´INVALID_TRANSFORMŽ’›¬ò¬;Ž¦‘°gŽ¦‘­returnŽ‘7æ¼±r‘ÿ}'otateŽ‘RUú¬(µpŽ‘:±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(0Ž‘)µ;‘ª¨pŽ‘²¨:±get‘‰ffŽ–®last‘‰ffŽ“p‘ÿ}'ointŽ‘:$>¬(–ª¨)µ;“±angleŽ‘jû¬);Ž¦‘ +°gŽ¤­1256.‘ üRectangles.Ž¡1257.‘ üSurrounding‘ÕTrectangle.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ +¬[²LDF‘T2003.07.18.¬]Ž‘Y;Made‘UU­constŽ‘*¢¬.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¦‘ +­RectangleŽ‘?”ë±out‘‰ffŽ‘®r–ÿ}'e“ctangleŽ‘x‡„¬(‘ª®)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹kŠœ Šn ý‘ì°x¬1258–¯3DLDF-1.1.5.1’Û£SURRÃŽOUNDING‘ÕXRECT‘ÿJªANGLE“¬363Ž €n ý•@P­1258.Ž©°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¤ ‘ +­RectangleŽ‘?”ëEllipseŽ‘b}Ȭ::‘±out‘‰ffŽ‘®r–ÿ}'e“ctangleŽ‘9ò¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­P•®9oin“tŽ‘2CŽ‘:Ìk¬(±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘,=G¬(‘ª®));Ž¡‘­P•®9oin“tŽ‘2pt0Ž‘BXÚ¬(±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(0Ž‘));Ž¡‘­P•®9oin“tŽ‘2pt1Ž‘BXÚ¬(±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(±numb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜ointsŽ‘JÀ©µ=¬2Ž‘));Ž¡‘­P®9athŽ‘/æ»±p‘ÿ}'a0Ž‘@—¬(±pt0Ž‘i;µ;‘ª¨±pt1Ž‘ã¬);Ž¡‘­P•®9oin“tŽ‘2pt2Ž‘BXÚ¬(±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(±numb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜ointsŽ‘JÀ©µ=¬4Ž‘));Ž¡‘­P•®9oin“tŽ‘2pt3Ž‘BXÚ¬(±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(3Ž‘8á°‘8à±numb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜ointsŽ‘Lù‰µ=¬4Ž‘));Ž¡‘­P•®9oin“tŽ‘2pt4Ž‘BXÚ¬(±pt1Ž‘i;¬);Ž¦‘±pt4Ž‘&0U°¬=ŽŽ‘8…©µCŽ‘@bu¬;Ž¦‘­P•®9oin“tŽ‘2pt5Ž‘BXÚ¬(±pt2Ž‘i;¬);Ž¦‘±pt5Ž‘#i=µ:±shiftŽ‘}¬(±pt4Ž‘i;¬);Ž¦‘­P•®9oin“tŽ‘2pt6Ž‘BXÚ¬(±pt3Ž‘i;¬);Ž¦‘±pt6Ž‘#i=µ:±shiftŽ‘}¬(±pt4Ž‘i;¬);Ž¦‘­P•®9oin“tŽ‘2pt7Ž‘BXÚ¬(±pt0Ž‘i;¬);Ž¦‘±pt7Ž‘&0U°¬=ŽŽ‘8…©µCŽ‘@bu¬;Ž¦‘­P•®9oin“tŽ‘2pt8Ž‘BXÚ¬(±pt2Ž‘i;¬);Ž¦‘±pt8Ž‘#i=µ:±shiftŽ‘}¬(±pt7Ž‘i;¬);Ž¦‘­P•®9oin“tŽ‘2pt9Ž‘BXÚ¬(±pt3Ž‘i;¬);Ž¦‘±pt9Ž‘#i=µ:±shiftŽ‘}¬(±pt7Ž‘i;¬);Ž¡#­ifŽ‘ ´ø¬0ŽŽ¡‘±pt0Ž‘#i=µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(´"0"Ž‘F_¬);Ž¡‘±pt1Ž‘#i=µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(´"1"Ž‘F_¬);Ž¡‘±pt2Ž‘#i=µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(´"2"Ž‘F_¬);Ž¡‘±pt3Ž‘#i=µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(´"3"Ž‘F_¬);Ž¡‘±pt5Ž‘#i=µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(´"5"Ž‘F_¬);Ž¡‘±pt6Ž‘#i=µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(´"6"Ž‘F_¬);Ž¡‘±pt8Ž‘#i=µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(´"8"Ž‘F_¬);Ž¡‘±pt9Ž‘#i=µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(´"9"Ž‘F_¬);Ž¡#­endifŽŽ¦‘RectangleŽ‘I”ìµrŽ‘N_¬(±pt6Ž‘i;µ;‘ª¨±pt9Ž–ãµ;‘ª¨±pt8Ž“µ;‘ª¨±pt5Ž“¬);Ž¦‘­returnŽ‘7æ¼µrŽ‘<°Ð¬;Ž¡‘ +°gŽŸ­1259.‘ üInscribQÇed‘ÕTrectangle.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.07.18.¬]Ž‘Y;Made‘UU­constŽ‘*¢¬.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¡‘ +­RectangleŽ‘?”ë±in‘‰ffŽ‘®r–ÿ}'e“ctangleŽ‘sk¬(‘ª®)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹lr Šn ý‘ì¬364–¯INSCRIBED‘ÕXRECT‘ÿJªANGLE’ì~¿3DLDF-1.1.5.1“°x¬1260Ž €n ý•@P­1260.Ž©°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¤ ‘ +­RectangleŽ‘?”ëEllipseŽ‘b}Ȭ::‘±in‘‰ffŽ‘®r–ÿ}'e“ctangleŽ‘4Ö.¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­RectangleŽ‘I”ì±r0Ž‘Wɬ=‘DZout‘‰ffŽ‘®r–ÿ}'e“ctangleŽ‘;¹±¬(‘ª¨);Ž¡‘­b•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘edð±bpp0Ž‘}øϬ=‘DZinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘TS÷¬(±r0Ž‘ 1ŵ:±get‘‰ffŽ‘®p‘ÿ}'ointŽ–'bH¬(0Ž›)µ;‘ª¨±r0Ž‘ Ümµ:±get‘‰ffŽ‘®p‘ÿ}'ointŽ“¬(2Ž˜));Ž¡‘­b•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘edð±bpp1Ž‘}øϬ=‘DZinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘TS÷¬(±r0Ž‘ 1ŵ:±get‘‰ffŽ‘®p‘ÿ}'ointŽ–'bH¬(1Ž›)µ;‘ª¨±r0Ž‘ Ümµ:±get‘‰ffŽ‘®p‘ÿ}'ointŽ“¬(3Ž˜));Ž¦‘­ifŽ‘ „n¬(±bpp0Ž‘Ìǵ:± rstŽ‘µªµ:±ptŽ–t°‘ ×´INVALID_POINTŽ›KªE°_‘Ã-±bpp0Ž‘ôµ:±se–ÿ}'c“ondŽ‘§Çµ:±ptŽ“°‘ ×´INVALID_POINTŽ˜°_‘Ã-±bpp1Ž‘ôµ:± rstŽ‘µªµ:±ptŽ“°Ž¡‘2´INVALID_POINTŽ‘xÿ&°_‘8à±bpp1Ž‘§µ:±se–ÿ}'c“ondŽ‘§Çµ:±ptŽ‘ «µ°‘Ç´INVALID_POINTŽ‘GY¬)‘°fŽ¡‘±c‘ÿ}'errŽ‘3|Á°‘Ç´"Intersection® ´didn'tŽ‘kÆÜ® ´work.\n"Ž’žTA°‘Ç´"Returning® ´empty® ´recŽ‘kÆÜtangle.\n\n"Ž’®8°‘DZ ushŽ‘€¬;Ž¦‘­RectangleŽ‘S”í±r2Ž‘^Ʋ¬;Ž¦‘­returnŽ‘Aæ½±r2Ž‘M‚¬;Ž¡‘°gŽ¦‘­RectangleŽ‘I”ì±r1Ž‘TƱ¬(±bpp0Ž‘Ìǵ:±se–ÿ}'c“ondŽ‘§Çµ:±ptŽ– äµ;‘ª¨±bpp1Ž›woµ:± rstŽ‘µªµ:±ptŽ“µ;‘ª¨±bpp0Ž˜µ:± rstŽ‘µªµ:±ptŽ“µ;‘ª¨±bpp1Ž˜µ:±se–ÿ}'c“ondŽ‘§Çµ:±ptŽ“¬);Ž¦‘­returnŽ‘7æ¼±r1Ž‘C¬;Ž¡‘ +°gŽŸ­1261.‘ üDra®9w–ÕTsurrounding“rectangle.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.07.01.¬]Ž‘YFChanged–j`the“return“v‘ÿqÇalue“from“­v®9oidŽ‘}C¬to“­RectangleŽ‘5©õ¬.‘°çNo¸ãw“the“surrounding“­RectangleŽŽ¡¬is‘UUreturned.Ž¡‘ +[²LDF‘T2003.07.18.¬]Ž‘Y;Made‘UU­constŽ‘*¢¬.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¡‘ +­RectangleŽ‘@Y¯±dr›ÿ}'aw‘‰ffŽ–®out‘‰ffŽ“r˜e˜ctangleŽ’‘ŒÏ¬(­constŽ‘ïfColorŽ‘?Y¬&Ž‘G ;±ddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘7í¬=‘ °Ž‘  +­ColorsŽ‘*çè¬::Ž‘1v&±default‘‰ffŽ‘®c‘ÿ}'olorŽ‘hòµ;‘ª¨­stringŽŽ¡‘±ddashe‘ÿ}'dŽ‘D,¬=‘Ç´""Ž– Ízµ;‘ª¨­stringŽ‘"Ïõ±pp‘ÿ}'enŽ‘:Í0¬=‘Ç´""Ž“µ;‘ª¨­PictureŽ‘*œ +¬&Ž‘2c(±pictur‘ÿ}'eŽ‘T3¬=‘DZcurr–ÿ}'ent‘‰ffŽ‘®pictur“eŽ‘Dì߬)‘UU­constŽ‘*¢¬;ŽŸ­1262.Ž¦°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¡‘ +­RectangleŽ‘@`hEllipseŽ‘cIE¬::‘±dr›ÿ}'aw‘‰ffŽ–®out‘‰ffŽ“r˜e˜ctangleŽ‘R3$¬(­constŽ‘öColorŽ‘?f¬&Ž‘G-­±ddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘{6Vµ;‘ª¨­stringŽ‘#›r±ddashe‘ÿ}'dŽ‘F⃵;‘ª¨­stringŽŽ¡‘2±pp‘ÿ}'enŽ‘G6(µ;‘ª¨­PictureŽ‘*œ +¬&Ž‘2c(±pictur‘ÿ}'eŽ‘Qkþ¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­RectangleŽ‘I”ìµrŽ‘Q&¬=‘DZout‘‰ffŽ‘®r–ÿ}'e“ctangleŽ‘;¹±¬(‘ª¨);Ž¦‘µrŽ‘Ê:±dr‘ÿ}'awŽ‘(Û¬(±ddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘4©µ;‘ª¨±ddashe‘ÿ}'dŽ‘$ñ¹µ;‘ª¨±pp‘ÿ}'enŽ‘à˵;‘ª¨±pictur‘ÿ}'eŽ‘ ³~¬);Ž¡‘­returnŽ‘7æ¼µrŽ‘<°Ð¬;Ž¡‘ +°gŽŸ­1263.‘ üDra®9w–ÕTinscribQÇed“rectangle.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.07.01.¬]Ž‘YO‹Changed–œ¥the“return“v‘ÿqÇalue“from“­v®9oidŽ‘áͬto“­RectangleŽ‘5Ü:¬.‘G¸No¸ãw“the“inscribGed“­RectangleŽ‘9x߬isŽ¡returned.Ž¡‘ +[²LDF‘T2003.07.18.¬]Ž‘Y;Made‘UU­constŽ‘*¢¬.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1146“°i‘Ǭ+°Ž¡‘ +­RectangleŽ‘@mi±dr›ÿ}'aw‘‰ffŽ–®in‘‰ffŽ“r˜e˜ctangleŽ’Œ„¬(­constŽ‘ ColorŽ‘?€‘¬&Ž‘GG¯±ddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘€@¬=‘/è°Ž‘ /é­ColorsŽ‘+Ǭ::Ž‘1—±default‘‰ffŽ‘®c‘ÿ}'olorŽ‘iàµ;‘ª¨­stringŽŽ¡‘±ddashe‘ÿ}'dŽ‘D,¬=‘Ç´""Ž– Ízµ;‘ª¨­stringŽ‘"Ïõ±pp‘ÿ}'enŽ‘:Í0¬=‘Ç´""Ž“µ;‘ª¨­PictureŽ‘*œ +¬&Ž‘2c(±pictur‘ÿ}'eŽ‘T3¬=‘DZcurr–ÿ}'ent‘‰ffŽ‘®pictur“eŽ‘Dì߬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹mš Šn ý‘ì°x¬1264›¯3DLDF-1.1.5.1’ÎÅ DRA‘ÿ8W–ÕXINSCRIBED“RECT‘ÿJªANGLE˜¬365Ž €n ý•@P­1264.Ž©°h–ª¨¬De ne‘UU­EllipseŽ‘(“ƒ¬functions‘@¯1147“°i‘Ǭ+°Ž¤ ‘ +­RectangleŽ‘@tÚEllipseŽ‘c]·¬::‘±dr›ÿ}'aw‘‰ffŽ–®in‘‰ffŽ“r˜e˜ctangleŽ‘Mµ¬(­constŽ‘ +‘ColorŽ‘?s¬&Ž‘GV‘±ddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘{_:µ;‘ª¨­stringŽ‘#¯ä±ddashe‘ÿ}'dŽ‘Föõµ;‘ª¨­stringŽŽ¡‘2±pp‘ÿ}'enŽ‘G6(µ;‘ª¨­PictureŽ‘*œ +¬&Ž‘2c(±pictur‘ÿ}'eŽ‘Qkþ¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­RectangleŽ‘I”ìµrŽ‘Q&¬=‘DZin‘‰ffŽ‘®r–ÿ}'e“ctangleŽ‘6B¬(‘ª¨);Ž¦‘µrŽ‘Ê:±dr‘ÿ}'awŽ‘(Û¬(±ddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘4©µ;‘ª¨±ddashe‘ÿ}'dŽ‘$ñ¹µ;‘ª¨±pp‘ÿ}'enŽ‘à˵;‘ª¨±pictur‘ÿ}'eŽ‘ ³~¬);Ž¡‘­returnŽ‘7æ¼µrŽ‘<°Ð¬;Ž¡‘ +°gŽŸ­1265.– üRectangle‘Ëfunctions.“¬[²LDF‘T2003.07.18.¬]Ž‘Y °TO‘m”DO:–mÏAdd“±undr‘ÿ}'aw‘‰ffŽ–®in‘‰ffŽ“el‘‚ØlipseŽ‘NcЬ(–ª®),‘œ± 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o¬=‘DZget‘‰ffŽ‘®normalŽ‘3QŒ¬(‘ª¨);Ž¡‘±normalŽ‘4Vºµ:±shiftŽ‘}¬(µCŽ‘Ü̬);Ž¡‘­realŽ‘*³0±out‘‰ffŽ‘®distanc‘ÿ}'eŽ‘c;¬=‘Ç(±p0Ž‘O °‘8àµCŽ‘ +¬¬)µ:±magnitudeŽ‘.=r¬(‘ª¨);Ž¦‘­T‘ÿ +«ransformŽ‘KÈÔµtŽ‘OeF¬;Ž¦‘­realŽ‘*³0±h‘‰ffŽ‘®lengthŽ‘Q[¡¬=‘Ç(±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(1Ž‘)–8à°“±p0Ž‘O ¬)µ:±magnitudeŽ‘.=r¬(‘ª¨);Ž¦‘­realŽ‘*³0±v‘‰ffŽ‘®lengthŽ‘PØȬ=‘Ç(±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘'bH¬(3Ž‘)–8à°“±p0Ž‘O ¬)µ:±magnitudeŽ‘.=r¬(‘ª¨);Ž¡‘±p0Ž‘"ÝÚ°¬=ŽŽ‘2lµMŽ‘?ýÓ°¬=ŽŽ‘OŒ +µCŽ‘Z/î°¬=ŽŽ‘i¾%µtŽ‘mZ—:±align‘‰ffŽ–®with‘‰ffŽ“axisŽ‘@²x¬(µCŽ‘ÜÌ;‘ª¨±normalŽ‘"`µ;‘ª¨´'y'Ž‘ñ¬);Ž¡‘­P•®9oin“tŽ‘2x‘‰ffŽ–®axis‘‰ffŽ“ptŽ‘Y»¼¬(1Ž‘);Ž¦‘­realŽ‘*³0±angleŽ‘E:›¬=‘ǵMŽ‘ ‘Â:±angleŽ‘ÀS¬(±x‘‰ffŽ–®axis‘‰ffŽ“ptŽ‘&̬);Ž¡‘±p0Ž‘"ÝÚ°¬=ŽŽ‘2lµMŽ‘?ýÓ°¬=ŽŽ‘OŒ +µtŽ‘S(|:±r‘ÿ}'otateŽ‘o>¬(0Ž‘µ;‘ª¨±angleŽ‘jû¬);Ž¦‘­ifŽ‘´ú¬(µMŽ‘ +ʪ:±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u¬(‘ª¨)–Ç°6¬=“±x‘‰ffŽ–®axis‘‰ffŽ“ptŽ‘)“5¬)‘°fŽ¦‘±c‘ÿ}'errŽ‘3|Á°‘Ç´"WARNING!® ´In® ´|RectanŽ‘kÆÜgle::in_ellipse()|:\Ž’ÔÆ n"Ž’â”°‘Ç´"M® ´is® ´not® ´(1,® ´0,® ´0)!Ž‘kÆÜ\n"Ž‘| ;¬;Ž¦‘µMŽ‘(Ê­:±showŽ‘Šÿ¬(´"M:"Ž‘†\¬);Ž¦‘(µ=°‘ÿý¬I'd–UUrather“output“this“to“±stderrŽ‘yè¬,“but“I“don't“ha•¸ãv“e–UUa“w•¸ãa“y–UUto“do“this“y¸ãet.‘qÇ[²LDF‘T2003.07.18.¬]Ž‘U$©°µ=Ž¦‘±c‘ÿ}'outŽ‘4 R°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¦‘°gŽ¡‘­EllipseŽ‘9>0µeŽ‘=æ1¬(±originŽ‘ö!µ;‘ª¨±h‘‰ffŽ‘®lengthŽ‘%Œµ;‘ª¨±v‘‰ffŽ‘®lengthŽ‘% (¬);Ž¦‘­b•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘edð±bppŽ‘x"ñ¬=‘ǵeŽ‘o:±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘QŒß¬(±originŽ‘ö!µ;‘ª¨±p0Ž‘ Áh¬);Ž¦‘­realŽ‘*³0±in‘‰ffŽ‘®distanc‘ÿ}'eŽ‘[W˜¬;Ž¡‘­ifŽ‘´ú¬(±bppŽ‘öéµ:± rstŽ‘µªµ:bŽ‘Jª¬)‘°fŽ¦‘±in‘‰ffŽ‘®distanc‘ÿ}'eŽ‘Qkƒ¬=‘DZbppŽ‘¾µ:± rstŽ‘µªµ:±ptŽ‘ äµ:±magnitudeŽ‘.=r¬(‘ª¨);Ž¦‘°gŽ¦‘­elseŽ‘*.6ifŽ‘5ã.¬(±bppŽ‘öéµ:±se–ÿ}'c“ondŽ‘§Çµ:bŽ‘Jª¬)‘°fŽ¦‘±in‘‰ffŽ‘®distanc‘ÿ}'eŽ‘Qkƒ¬=‘DZbppŽ‘¾µ:±se–ÿ}'c“ondŽ‘§Çµ:±ptŽ‘ äµ:±magnitudeŽ‘.=r¬(‘ª¨);Ž¦‘°gŽ¦‘­elseŽ‘+Øá°fŽ¦‘±c‘ÿ}'errŽ‘8-°‘P„´"ERROR!® ´In® ´|RectanglŽ‘pPHe::out_ellipse()|:\nŽ’ÙP "Ž’æfõ°Ž¦‘2´"Couldn't® ´find® ´interŽ’šÿÉsection® ´point.\n"Ž’÷°‘Ç´"Returning® ´empty® ´EllŽ‘kÆÜipse.\n\n"Ž’£”>°‘DZ 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+­v®9oidŽ‘"¹4±setŽ‘01¸¬(­constŽ‘åýP•®9oin“tŽ‘<õ¬&Ž‘DX±c–ÿ}'c“enterŽ‘dx\µ;‘ª¨­constŽ‘¥realŽ‘5ÿ.±ddiameterŽ‘b擵;‘ª¨­constŽ‘¥realŽ‘5ÿ.±angle‘‰ffŽ‘®xŽ‘YL"¬=‘Ç0Ž–ǵ;‘ª¨­constŽ‘¥realŽ‘5ÿ.±angle‘‰ffŽ‘®yŽ‘Y1Ѭ=‘Ç0Ž“µ;Ž¡‘­constŽ‘;ôŠrealŽ‘Rq±angle‘‰ffŽ‘®zŽ‘u8+¬=‘Ç0Ž‘ǵ;‘ª¨­constŽ‘Ÿ/unsignedŽ‘O "shortŽ‘m4ª±nnumb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜ointsŽ’À[³¬=‘Ç´DEFAULT_NUMBER_OF_POINTSŽ’M8¬);ŽŽŽŒ‹tæ  Šn ý‘ì¬372–¯SETTING‘ÕXFUNCTION’ý§3DLDF-1.1.5.1“°x¬1284Ž €n ý•@P­1284.Ž©uO°h–ª¨¬De ne‘UU­CircleŽ‘% Ö¬functions‘@¯1279“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘#wîCircleŽ‘BÛ¬::‘±setŽ‘xˆ¬(­constŽ‘¤·P•®9oin“tŽ‘>i¬&Ž‘EÕ‡±c–ÿ}'c“enterŽ‘eõе;‘ª¨­constŽ‘ O_realŽ‘7|¢±ddiameterŽ‘ddµ;‘ª¨­constŽ‘ O_realŽ‘7|¢±angle‘‰ffŽ‘®xŽ‘X~µ;‘ª¨­constŽ‘ O_realŽŽ¡‘2±angle‘‰ffŽ‘®yŽ‘Rkµ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±angle‘‰ffŽ‘®zŽ‘V‡îµ;‘ª¨­constŽ‘ÕJunsignedŽ‘P XshortŽ‘mÖû±nnumb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜ointsŽ’¾6ì¬)Ž¡‘ +°fŽ¡‘­CircleŽ‘5¸ƒµcŽ‘: ^¬(±c–ÿ}'c“enterŽ‘ Iµ;‘ª¨±ddiameterŽ‘.’ µ;‘ª¨±angle‘‰ffŽ‘®xŽ‘"0„µ;‘ª¨±angle‘‰ffŽ‘®yŽ‘"3µ;‘ª¨±angle‘‰ffŽ‘®zŽ‘!ªµ;‘ª¨±nnumb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜ointsŽ‘R +™¬);Ž¦‘°Ž‘±thisŽ‘,²Ñ¬=‘ǵcŽ‘ó¬;Ž¡‘­returnŽ‘4‘g¬;Ž¡‘ +°gŽ¤­1285.‘ üPseudo-constructor–ÕTfor“dynamic“alloQÇcation.Ž¡1286.‘ üP•®9oin“ter‘ÕTargumen“t.ŽŸªŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ +¬[²LDF‘T2003.07.27.¬]Ž‘Y;Made–UUnon-inline.‘qÇMade“argumen¸ãt“µpŽ‘ ²ª­constŽ‘)ÝLCircleŽ‘K•Í°Ž‘P•Î¬.Ž¡‘ +[²LDF‘T2003.08.10.¬]Ž‘XĤRemo•¸ãv“ed–¾rede nition“of“the“default“argumen¸ãt“­constŽ‘ øÉCircleŽ‘Bm³°Ž‘Gm´µpŽ‘O‡r¬=“0Ž‘ #}from“the“de nition.Ž¡The–UUDEC“compiler“complained,“but“GCC“didn't.Ž¡‘ +[²LDF‘T2003.12.30.¬]Ž‘WëÉReplaced‘8ã­CircleŽ‘!œ¬::‘±cr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“cir‘ÿ}'cleŽ‘K R¬(‘ª®)–8ãwith“a“spGecialization“of“­templateŽ‘/ +A°h­classŽ‘ÃßµCŽ‘! «°i“µCŽ‘ +¯°Ž‘°±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘>¥t¬(‘ª¨)Ÿ€„ +Ž¡for‘UU­CircleŽ‘!¸¬.Ž¡‘ +[²LDF‘T2003.12.30.¬]Ž‘Y;Changed–UUthe“argumenš¸ãt.‘qÇIt's“no˜w“a“­constŽ‘!÷CircleŽ‘C8x°Ž‘H8y¬.Ž¡‘ +[²LDF‘T2003.12.30.¬]Ž‘YÂÿRemo•¸ãv“ed–default“argumen¸ãt“\0",‘>ÊbGecause“this“caused“a“compiler“error“when“using“theŽ¡DEC–UU²C‘€Ÿÿ³+‘ÿ+ŽŽ‘œu¬compiler.‘qÇApparenš¸ãtly‘ÿ*ª,“it“suces“to“declare“a“default“argumen˜t“in“the“template“declaration.ŽŸŸüÈ„`ÕÁGŽŽ¦°h›ª¨¬Declare–UUnon-mem¸ãbGer“template“functions“for“­CircleŽ‘%ø…¯1286˜°i‘ÇŽ¡‘ +­CircleŽ‘+¸‚°Ž‘0¸ƒ±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘`HG¬(­constŽ‘*¢CircleŽ‘?ã#°Ž‘Dã$µcŽ‘I6ÿ¬);Ž¤ uO¯See–ÕXalso“section“1287.Ž¡This–ÕXco¥t¬(‘ª¨)Ÿ€„ +Ž¡for‘UU­CircleŽ‘!¸¬.Ž¡‘ +[²LDF‘T2003.12.30.¬]Ž‘Y;Changed–UUargumen¸ãt“from“­CircleŽ‘% Ö¬to“­constŽ‘!÷CircleŽ‘C8x¬&Ž‘Jÿ–.ŽŸŸüÈ„`ÕÁGŽŽ¦°h›ª¨¬Declare–UUnon-mem¸ãbGer“template“functions“for“­CircleŽ‘%ø…¯1286˜°i‘Ǭ+°Ž¡‘ +­CircleŽ‘+¸‚°Ž‘0¸ƒ±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘`HG¬(­constŽ‘*¢CircleŽ‘?ã#¬&Ž‘GªAµcŽ‘Kþ¬);Ž©­1288.– üDestructor.“¬[²LDF‘T2002.10.09.¬]Ž‘Zˆ6Remo•¸ãv“ed–UUthe“destructor.‘qÇ­P®9athŽ‘/¬::Ž‘$‘m°Ž‘,X‹­P®9athŽ‘Déï¬(‘ª¨)“or“­P®9athŽ‘潬::‘±cle‘ÿ}'arŽ‘(ݬ(‘ª®)Ž¡should– bšGe“used“instead,‘Kunless“I‘õadd“dynamically“allo˜cated“data“mem¸ãb˜ers“to“­CircleŽ‘$u<¬(rather“than“­EllipseŽ‘'úé¬orŽ¡­P®9athŽ‘‘d¬).Ž¦­1289.‘ üAssignmen®9t.Ž¦1290.– üCircle‘…äargumen®9t.“¬This–Íyfunction“returns“a“reference“to“°Ž‘ Íz±thisŽ‘¹0¬,‘+‚whic¸ãh“can“bGe“used“for“furtherŽ¡assignmen¸ãt.ŽŸªŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.11.10.¬]Ž‘Y;Changed–UUand“simpli ed“this“function.‘qÇIt“no¸ãw“uses“­EllipseŽ‘&>2¬::Ž‘,Ìp­opQÇeratorŽ‘Xc%¬=Ž‘`*C(‘ª¨).ŽŸŸüÈ„`ÕÁGŽŽŽŽŒ‹uê• Šn ý‘ì°x¬1290–¯3DLDF-1.1.5.1’ó=“­CIR®9CLE‘ÕX¯ARÃŽGUMENT“¬373Ž €n ý•@P°h–ª¨¬Declare‘UU­CircleŽ‘% Ö¬functions‘@¯1278“°i‘Ǭ+°Ž¤ ‘ +­CircleŽ‘+¸‚¬&Ž‘3 ­opQÇeratorŽ‘_U¬=Ž‘fÝs(­constŽ‘*¢CircleŽ‘?ã#¬&Ž‘GªAµcŽ‘Kþ¬);Ž©­1291.ŽŸ°h–ª¨¬De ne‘UU­CircleŽ‘% Ö¬functions‘@¯1279“°i‘Ǭ+°Ž¡‘ +­CircleŽ‘+¸‚¬&Ž‘3 ­CircleŽ‘RâЬ::Ž‘Yq­opQÇeratorŽ’…ì=Ž’ŒÎá(­constŽ‘*¢CircleŽ‘?ã#¬&Ž‘GªAµcŽ‘Kþ¬)Ž¡‘ +°fŽ¡‘±r‘ÿ}'adiusŽ‘2=¬=‘ǵcŽ‘ó:±r‘ÿ}'adiusŽ‘È#¬;Ž¡‘­EllipseŽ‘6è߬::Ž‘=w­opQÇeratorŽ‘i Ò¬=Ž‘pÔð(µcŽ‘SÛ¬);Ž¡‘­returnŽ‘7æ¼°Ž‘<æ½±thisŽ‘MÒs¬;Ž¡‘ +°gŽ¦­1292.– üEllipse‘8‚argumen®9t.“¬This–Š/function“returns“a“reference“to“°Ž‘ Š0±thisŽ‘uæ¬,‘×ewhic¸ãh“can“bGe“used“for“furtherŽ¡assignmen¸ãt.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.11.10.¬]Ž‘Y;Changed–UUand“simpli ed“this“function.‘qÇIt“no¸ãw“uses“­EllipseŽ‘&>2¬::Ž‘,Ìp­opQÇeratorŽ‘Xc%¬=Ž‘`*C(‘ª¨).Ž¡‘ +[²LDF‘T2003.08.14.¬]Ž‘YTAdded–¡coGde“for“handling“the“case“that“µeŽ›I:±axis‘‰ffŽ‘®vŽ‘fù¬and“µeŽ˜:±axis‘‰ffŽ‘®hŽ‘š¨¬di er“bš¸ãy“a“small“amoun˜t,Ž¡pšGossible–UUdue“to“imprecision“(see“b˜elo¸ãw).Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­CircleŽ‘% Ö¬functions‘@¯1278“°i‘Ǭ+°ŽŸ ‘ +­CircleŽ‘+¸‚¬&Ž‘3 ­opQÇeratorŽ‘_U¬=Ž‘fÝs(­constŽ‘*¢EllipseŽ‘ChЬ&Ž‘K/îµeŽ‘O×ï¬);ŽŽŽŒ‹vúJ Šn ý‘ì¬374–­ELLIPSE‘ÕX¯ARÃŽGUMENT’ïo\3DLDF-1.1.5.1“°x¬1293Ž €n ý•@P­1293.‘ ü¬If‘sùµeŽ‘ú:±axis‘‰ffŽ‘®vŽ‘Œö°6¬=‘ǵeŽ‘o:±axis‘‰ffŽ‘®hŽ‘ù¬,›¡ it's–sùquite“pGossible“that“the“di erence“is“negligible,˜and“the“result“of“imprecisionŽ¤ resulting–…nfrom“the“represenš¸ãtation“of“ oating“pGoin˜t“n˜um˜bšGers,‘‘tor“calculations“p˜erformed“on“them.‘Therefore,Ž¡wš¸ãe–qcompare“the“absolute“v‘ÿqÇalue“of“their“di erence“with“­P•®9oin“tŽ‘›½¬::‘±epsilonŽ‘ o¬(‘ª®)“instead“of“c˜hec˜king“whether“they'reŽ¡equal.‘qÇ[²LDF‘T2003.08.14.¬]ŽŽ¡‘ +It's–1also“pšGossible“that“one“of“them“has“an“in¸ãteger“v‘ÿqÇalue,–Ÿi.e.,“it–1has“only“zero˜es“follo¸ãwing“the“decimal“p˜oin¸ãt,Ž¡and–)the“other“deviates“bš¸ãy“a“small“amoun˜t.‘c In“this“case,‘1òw˜e“w˜an˜t“to“set“±r‘ÿ}'adiusŽ‘"U¬to“half“of“the“former,‘1òbGecauseŽ¡it's–úðprobably“the“correct“v‘ÿqÇalue.‘b˜So,›$Vif“±e‘‰ffŽ–®axis‘‰ffŽ“vŽ‘*ã‘°‘Û± o‘ÿ}'orŽ‘?¯¬(±e‘‰ffŽ–®axis‘‰ffŽ“vŽ‘# ˆ¬),˜w¸ãe“set“±r‘ÿ}'adiusŽ‘#¾¬to“±e‘‰ffŽ–®axis‘‰ffŽ“vŽ‘'xµ=¬2Ž‘.‘b˜Otherwise,Ž¡wš¸ãe–Tset“±r‘ÿ}'adiusŽ‘$pS¬to“±e‘‰ffŽ–®axis‘‰ffŽ“hŽ‘+ég¬without“further“ado.‘nIf“±e‘‰ffŽ–®axis‘‰ffŽ“hŽ‘,ÿ°‘o°± o‘ÿ}'orŽ‘ÔF¬(±e‘‰ffŽ–®axis‘‰ffŽ“hŽ‘#A7¬),‘“Èso“m˜uc˜h“the“bGetter,‘“Èand“ifŽ¡it–Úisn't,›/|neither“it“nor“±e‘‰ffŽ–®axis‘‰ffŽ“vŽ‘+<¬has“an“in¸ãteger“v‘ÿqÇalue,˜so“it“doGesn't“matter“whicš¸ãh“one“w˜e“use“to“set“±r‘ÿ}'adiusŽ‘Ëý¬.Ž¡[²LDF‘T2003.08.14.¬]ŽŽ©°h–ª¨¬De ne‘UU­CircleŽ‘% Ö¬functions‘@¯1279“°i‘Ǭ+°Ž¡‘ +­CircleŽ‘+¸‚¬&Ž‘3 ­CircleŽ‘RâЬ::Ž‘Yq­opQÇeratorŽ’…ì=Ž’ŒÎá(­constŽ‘*¢EllipseŽ‘ChЬ&Ž‘K/îµeŽ‘O×ï¬)Ž¡‘ +°fŽ¡‘­realŽ‘*³0±e‘‰ffŽ–®axis‘‰ffŽ“vŽ‘P‡Ð¬=‘ǵeŽ‘o:±get‘‰ffŽ–®axis‘‰ffŽ“vŽ‘*ùš¬(‘ª¨);Ž¡‘­realŽ‘*³0±e‘‰ffŽ–®axis‘‰ffŽ“hŽ‘P»¬=‘ǵeŽ‘o:±get‘‰ffŽ–®axis‘‰ffŽ“hŽ‘+-I¬(‘ª¨);Ž¦‘­ifŽ‘´ú¬(±e‘‰ffŽ–®axis‘‰ffŽ“vŽ‘%Ô °6¬=‘DZe‘‰ffŽ–®axis‘‰ffŽ“hŽ‘&O¬)‘°fŽ¡‘­ifŽ‘)´û¬(±fabsŽ‘2Ò¬(±e‘‰ffŽ–®axis‘‰ffŽ“vŽ‘%Fh°‘8à±e‘‰ffŽ–®axis‘‰ffŽ“hŽ‘%z¬)–ǵ>“­P•®9oin“tŽ‘ad¬::Ž‘%epsilonŽ‘E^¦¬(‘ª¨))‘°fŽ¡‘(±c‘ÿ}'errŽ‘=”Ü°‘ß2´"ERROR!® ´In® ´Circle::oŽ‘kÞöperator=(Ellipse).\nŽ’ÔÞº"Ž’Ý„Q°‘ß2´"Ellipse® ´has® ´unequalŽ‘kÞö® ´axes.® ´"Ž’™Dx°Ž¡‘<´"Can't® ´perform® ´assigŽ’¤ÿÊnment.® ´Returning.\n\Ž’ ÿŽn"Ž’ð¬;Ž¡‘(­returnŽ‘Kæ¾°Ž‘P濱thisŽ‘aÒu¬;Ž¡‘°gŽ¡‘­elseŽ‘4.7ifŽ‘?ã/¬(±e‘‰ffŽ–®axis‘‰ffŽ“vŽ–%Ô °‘DZ o‘ÿ}'orŽ‘+®¬(±e‘‰ffŽ–®axis‘‰ffŽ“vŽ‘# ˆ¬))‘±r‘ÿ}'adiusŽ‘#;¬=‘DZe‘‰ffŽ–®axis‘‰ffŽ“vŽ“µ=¬2µ:¬0ŽŽ‘ Ç;Ž¡‘­elseŽ‘5Øâ±r‘ÿ}'adiusŽ‘Th¬=‘DZe‘‰ffŽ–®axis‘‰ffŽ“hŽ‘&Oµ=¬2µ:¬0ŽŽ‘ Ç;Ž¡‘°gŽ¡‘­elseŽ‘+Øá±r‘ÿ}'adiusŽ‘Jh¬=‘ǵeŽ‘o:±get‘‰ffŽ–®axis‘‰ffŽ“vŽ‘*ùš¬(‘ª¨)µ=¬2µ:¬0ŽŽ‘ Ç;Ž¡‘­EllipseŽ‘6è߬::Ž‘=w­opQÇeratorŽ‘i Ò¬=Ž‘pÔð(µeŽ‘¨¬);Ž¡‘­returnŽ‘7æ¼°Ž‘<æ½±thisŽ‘MÒs¬;Ž¡‘ +°gŽ¤­1294.‘ üReturning–ÕTelemen®9ts“and“information.Ž¡1295.– üIs‘pcircular.“¬T‘ÿ*ªests–Ûçwhether“°Ž‘Ûè±thisŽ‘£…¬is“circular.‘|OpGerations“suc¸ãh“as“±sc‘ÿ}'aleŽ‘Ù¬(›ª®)“and“±she‘ÿ}'arŽ‘!¬(˜)“can“causeŽ¤ ­CirclesŽ‘&A½¬to–UUbGecome“non-circular.‘qÇ[²LDF‘T2003.07.25.¬]ŽŽ¡‘ +±is‘‰ffŽ‘®cir‘ÿ}'cularŽ‘7¥¬(›ª®)–„ rst“tests“whether“°Ž‘…±thisŽ‘¿¬is“planar“using“±is‘‰ffŽ‘®planarŽ‘+@¬(˜).›]×If“it's“not,‘%{±falseŽ‘îC¬is“returned.˜Otherwise,Ž¡the‘­P•®9oin“tŽ‘#šlµpŽ‘,¢~¬is–set“to“°Ž‘ ¬(±p‘ÿ}'ointsŽ‘$•¬[0Ž‘]),‘*Áand“­P•®9oin“tŽ‘#šlµcŽ‘+îY¬=“±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘0=Y¬(‘ª®)“is“is“subtracted“from“µpŽ‘ ¬.‘qþµpŽ‘ yþ:±magnitudeŽ‘.=r¬(‘ª¨)“isŽ¡then–UUstored“in“­realŽ‘ƒ±mag0Ž‘2æZ¬.‘qÇ[²LDF‘T2003.07.25.¬]ŽŽ¡‘ +Then,‘ÂĵpŽ‘ +hã¬is–žset“to“eac¸ãh“of“the“other“­P•®9oin“tsŽ‘%_¬on“the“­CircleŽ‘#Ÿj¬in“turn,‘ÂĵcŽ‘ ´¾¬is“subtracted“from“µpŽ›¦¬,‘ÂÄand“µpŽ˜:±magnitudeŽ‘.=r¬(‘ª¨)Ž¡is–-:stored“in“­realŽ‘¸M±magŽ‘-+¬.‘diIf“the“absolute“v‘ÿqÇalue“of“the“di erence“±magŽ‘^ð‘諱mag0Ž‘ó¼¬is“greater“than“­P•®9oin“tŽ‘dž¬::‘±epsilonŽ‘ o¬(‘ª®),Ž¡±is‘‰ffŽ‘®cir‘ÿ}'cularŽ‘-¥¬(‘ª®)–Àimmediated“returns“±falseŽ‘/¬.‘ñIf“±fabsŽ‘²’¬(±magŽ‘H¯°‘ÿѱmag0Ž‘ݨ¬)–¸r°“­P•®9oin“tŽ‘!R¾¬::Ž‘'àü±epsilonŽ‘GP¬(‘ª¨)–Àfor“all“of“the“­P•®9oin“tsŽŽ¡°Ž‘¬(±p‘ÿ}'ointsŽ‘$•¬[µnŽ‘š¬])–UUfor“µn–Ç>“¬0,‘UU±is‘‰ffŽ‘®cir‘ÿ}'cularŽ‘0úr¬(‘ª®)–UUreturns“±trueŽ‘í¬.‘qÇ[²LDF‘T2003.07.25.¬]ŽŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.07.25.¬]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­CircleŽ‘% Ö¬functions‘@¯1278“°i‘Ǭ+°Ž¡‘ +­b•QÇo“olŽ‘#¡g±is‘‰ffŽ‘®cir‘ÿ}'cularŽ‘QF„¬(­v®9oidŽ‘¨ƒ¬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹w Šn ý‘ì°x¬1296–¯3DLDF-1.1.5.1’ _IS‘ÕXCIRÃŽCULAR“¬375Ž €n ý•@P­1296.Ž©°h–ª¨¬De ne‘UU­CircleŽ‘% Ö¬functions‘@¯1279“°i‘Ǭ+°Ž¤ ‘ +­b•QÇo“olŽ‘#¡gCircleŽ‘C—¬::‘±is‘‰ffŽ‘®cir‘ÿ}'cularŽ‘.¥!¬(­v®9oidŽ‘¨ƒ¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­b•QÇo“olŽ‘-¡h´DEBUGŽ‘K.Ù¬=‘DZtrueŽ‘‹°¬;‘µ=°–ÿý¬false“°µ=Ž¦‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Entering® ´Circle::isŽ‘kÆÜ_circular().\n"Ž’» ¬;Ž¡‘­ifŽ‘´ú¬(°:±is‘‰ffŽ‘®planarŽ‘(&¬(‘ª¨))‘°fŽ¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)Ž¡‘(±c‘ÿ}'errŽ‘=Ök°‘ Á´"In® ´Circle::is_circuŽ‘l …lar():® ´"Ž’™Ç–°‘ Á´"*this® ´is® ´non-planarŽ‘l ….® ´Returning® ´false."Ž’Ó‡u°Ž¡‘<±end‘‚ØlŽ‘R¸à°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½±falseŽ‘V–¬;Ž¡‘°gŽ¦‘­P•®9oin“tŽ‘2pŽ‘7÷Ÿ¬;Ž¡‘­P•®9oin“tŽ‘2cŽ‘: +’¬=‘DZget‘‰ffŽ‘®c‘ÿ}'enterŽ‘/_¬(‘ª¨);Ž¡‘­realŽ‘*³0±mag0Ž‘C‘¬;Ž¡‘­realŽ‘*³0±magŽ‘=ü¬;Ž¦‘­v®9ectorŽ‘3ªJ°h­P•®9oin“tŽ‘ï°Ž‘#ïži‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘DZp‘ÿ}'ointsŽ‘ë­µ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¡‘µpŽ‘Ϭ=‘Ç°Ž‘ÇŽ‘ DZiterŽ‘Ÿÿ³+‘ÿ+ŽŽ‘,°‘8àµcŽ‘Œ»¬;Ž¡‘±mag0Ž‘/¤ñ¬=‘ǵpŽ‘Ï:±magnitudeŽ‘.=r¬(‘ª¨);Ž¡‘­forŽ‘%般(­in®9tŽ‘¤÷µiŽ‘Þ¬=‘Ç1Ž‘Ç;‘ÿý±iterŽ‘’°6¬=‘DZp‘ÿ}'ointsŽ‘ë­µ:±endŽ‘ಬ(‘ª¨);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘µpŽ‘%Ϭ=‘Ç°Ž‘ÇŽ‘ DZiterŽ‘Êø°‘8àµcŽ‘Œ»¬;Ž¡‘±magŽ‘4ù¬=‘ǵpŽ‘Ï:±magnitudeŽ‘.=r¬(‘ª¨);Ž¡‘­ifŽ‘)´û¬(±fabsŽ‘2Ò¬(±magŽ‘¾°‘8à±mag0Ž‘·¬)–ǵ>“­P•®9oin“tŽ‘ad¬::Ž‘%epsilonŽ‘E^¦¬(‘ª¨))‘°fŽ¡‘(­ifŽ‘5?æ¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'errŽ‘ì°‘YF´"Point® ´"Ž‘58Ü°‘YFµiŽ‘$€°‘YF´"® ´doesn't® ´lie® ´on® ´CirŽ‘nY +cle.\n"Ž’˜ø£°Ž¡‘F´"Exiting® ´Circle::is_Ž’®ÿËcircular().\n"Ž’ûÍ!°‘Ç´"Returning® ´false.\n\Ž‘kÆÜn"Ž‘y”V°‘DZ ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾±falseŽ‘`–¬;Ž¡‘°gŽ¡‘€Ÿÿ³+‘ÿ+ŽŽ‘*G#µiŽ‘-¹¬;Ž¡‘°gŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Exiting® ´Circle::is_Ž‘kÆÜcircular().® ´ReturninŽ’ÔÆ g® ´true.\n"Ž’ ”°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘7æ¼±trueŽ‘J«T¬;Ž¡‘ +°gŽŸ­1297.‘ üGet‘ÕTradius.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.05.10.¬]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­CircleŽ‘% Ö¬functions‘@¯1278“°i‘Ǭ+°Ž¡‘ +­inlineŽ‘)ŠIrealŽ‘@=w±get‘‰ffŽ‘®r‘ÿ}'adiusŽ‘l9V¬(‘ª®)Ž¡‘ +°fŽ¡‘­returnŽ‘7æ¼±r‘ÿ}'adiusŽ‘S®ß¬;Ž¡‘ +°gŽŸ­1298.– üGet‘ÕTdiameter.“¬[²LDF‘T2002.05.10.¬]Ž‘Zˆ6Added–UUthis“function.Ž¦°h–ª¨¬Declare‘UU­CircleŽ‘% Ö¬functions‘@¯1278“°i‘Ǭ+°Ž¡‘ +­inlineŽ‘)ŠIrealŽ‘@=w±get‘‰ffŽ‘®diameterŽ‘x<(¬(‘ª®)Ž¡‘ +°fŽ¡‘­returnŽ‘7漬(2Ž‘8á°‘8à±r‘ÿ}'adiusŽ‘¬);Ž¡‘ +°gŽŽŽŒ‹x‰ Šn ý‘ì¬376–¯INTERSECTIONS’+Q3DLDF-1.1.5.1“°x¬1299Ž €n ý•@P­1299.– üIn®9tersections.“¬Neither–|¡GCC›|—nor“the“DEC˜compiler“could“resolv¸ãe“a“call“to“±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘U €¬(‘ª®)Ž¤ with‘¥;­P•®9oin“tŽ‘ 侬argumenš¸ãts–¥;to“­EllipseŽ‘%Ž¬::‘±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã¬(‘ª®),‘Èsafter“a“­CircleŽ‘#­¢¬v˜ersion“with“a“­CircleŽ‘#­¢¬argumen˜t“hadŽ¡bGeen–¤declared.‘^TO›¤DO:“I˜didn't“think“this“w¸ãould“happGen,‘·Åso“I˜should“probably“review“the“rules“go•¸ãv“erningŽ¡resolution–UUof“calls“to“functions“on“ob‘Ž8jects“of“deriv¸ãed“classes.‘qÇ[²LDF‘T2003.07.09.¬]ŽŽ¡‘ +Therefore,‘/ÔI'vš¸ãe–&tadded“­CircleŽ‘$°¬v˜ersions“of“this“function,‘/Ôwith“­P•®9oin“tŽ‘!ç0¬and“­P®9athŽ‘ÞL¬argumen˜ts,‘/Ôthat“simply“callŽ¡the‘UU­EllipseŽ‘(“ƒ¬vš¸ãersions,–UUand“return“their“return“v‘ÿqÇalues.‘qÇThis“solv˜es“the“problem.‘qÇ[²LDF‘T2003.07.09.¬]ŽŽ¡‘ +The–Ï¡program“executed“correctly“under“Linš¸ãux,‘î4after“I‘Ï‚recompiled“with“GCC.“Ho˜w˜ev˜er,›î4under“T‘ÿ*ªru65,˜theŽ¡program–ÑNcaused“a“\Memory“fault"“error.‘å³After“I‘Ñ/remo•¸ãv“ed–ÑNthe“ob‘Ž8ject“ les,‘ðMand“recompiled“(with“the“DECŽ¡compiler),–UUthe“problem“disappGeared.‘qÇ[²LDF‘T2003.07.09.¬]ŽŽ¡‘ +[²LDF‘T2003.07.18.¬]Ž‘Y;TO–UUDO:“Add“­CircleŽ‘"¸…¬::‘±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã¬(­constŽ‘*¢EllipseŽ‘ChЬ&Ž‘K/î)“andŽ¡­EllipseŽ‘"èݬ::‘±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã¬(­constŽ‘*¢CircleŽ‘?ã#¬&Ž‘GªA).Ž©­1300.‘ üP•®9oin“t‘ÕTargumen“t.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.07.09.¬]Ž‘Y;Added–UUthis“function.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­CircleŽ‘% Ö¬functions‘@¯1278“°i‘Ǭ+°ŽŸ ‘ +­virtualŽ‘/Ôb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ’€ò±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ’Ò¡¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±pt0Ž‘TJ˜µ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±pt1Ž‘Uõ@¬)‘UU­constŽ‘*¢¬;Ž¦­1301.Ž¡°h–ª¨¬De ne‘UU­CircleŽ‘% Ö¬functions‘@¯1279“°i‘Ǭ+°Ž¤ ‘ +­b•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘[dïCircleŽ‘zȬ::‘±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±pt0Ž‘TJ˜µ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±pt1Ž‘Uõ@¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼EllipseŽ‘ZÏ™¬::‘±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã¬(±pt0Ž‘i;µ;‘ª¨±pt1Ž‘ã¬);Ž¡‘ +°gŽ¦­1302.‘ üP•®9ath‘ÕTargumen“t.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.07.09.¬]Ž‘Y;Added–UUthis“function.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­CircleŽ‘% Ö¬functions‘@¯1278“°i‘Ǭ+°ŽŸ ‘ +­virtualŽ‘/Ôb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ’€ò±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ’Ò¡¬(­constŽ‘*¢P®9athŽ‘:[¬&Ž‘AØyµpŽ‘Fày¬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹yÿ Šn ý‘ì°x¬1303›¯3DLDF-1.1.5.1’ÿZ­P–ÿ +«A“TH‘ÕX¯ARÃŽGUMENT˜¬377Ž €n ý•@P­1303.Ž©°h–ª¨¬De ne‘UU­CircleŽ‘% Ö¬functions‘@¯1279“°i‘Ǭ+°Ž¤ ‘ +­b•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜pairŽ‘[dïCircleŽ‘zȬ::‘±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã¬(­constŽ‘*¢P®9athŽ‘:[¬&Ž‘AØyµpŽ‘Fày¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼EllipseŽ‘ZÏ™¬::‘±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã¬(µpŽ‘¬);Ž¡‘ +°gŽŸ­1304.‘ üCircle‘ÕTargumen®9t.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.07.20.¬]Ž‘Yê5W›ÿ*ªrote–7Othe“de nition“of“this“function.‘´T˜ested“all“cases.‘´It“should“probably“bGe“testedŽ¡more‘UUthoroughly‘ÿ*ª.Ž¡‘ +[²LDF‘T2003.08.14.¬]Ž‘X´!Made‘;±verb‘ÿ}'oseŽ›&“Ó¬argumen¸ãt–;non-­constŽ‘ÕM¬.‘U¿Setting“±verb‘ÿ}'oseŽ˜¬to“±trueŽ‘Ǭif“´VERBOSE_GLOBALŽ‘P´¬is“±trueŽ‘ÅÓ¬.Ž¡Added‘UU´VERBOSE_GLOBALŽ‘P°è¬to–UU®pspglb.web“¬toGda¸ãy‘ÿ*ª.Ž¡‘ +[²LDF‘T2003.08.27.¬]Ž‘Y;Remo•¸ãv“ed–UUthe“declaration“­realŽ‘ƒ±c‘‰ffŽ‘®r‘ÿ}'adiusŽ‘Am¥¬=“µcŽ‘©0:±r‘ÿ}'adiusŽ‘È#¬,“since“±c‘‰ffŽ‘®r‘ÿ}'adiusŽ‘*ºw¬wš¸ãas“nev˜er“used.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­CircleŽ‘% Ö¬functions‘@¯1278“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/Ôb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜quadrupleŽ’Ÿt±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ’ñ^¬(­constŽ‘*¢CircleŽ‘?ã#¬&Ž‘GªAµcŽ‘Kþ;‘ª¨­b•QÇo“olŽ‘L±verb‘ÿ}'oseŽ‘>¤ƒ¬=‘DZfalseŽ‘v\¬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹z+’ Šn ý‘ì¬378–­CIR®9CLE‘ÕX¯ARÃŽGUMENT’ó=“3DLDF-1.1.5.1“°x¬1305Ž €n ý•@P­1305.Ž©°h–ª¨¬De ne‘UU­CircleŽ‘% Ö¬functions‘@¯1279“°i‘Ǭ+°Ž¤ ‘ +­b•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜quadrupleŽ‘yæ¬CircleŽ’™Iܬ::‘±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘RŒã¬(­constŽ‘*¢CircleŽ‘?ã#¬&Ž‘GªAµcŽ‘Kþ;‘ª¨­b•QÇo“olŽ‘L±verb‘ÿ}'oseŽ‘;Ýk¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­b•QÇo“olŽ‘-¡h´DEBUGŽ‘K.Ù¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¦‘­ifŽ‘´ú¬(´VERBOSE_GLOBALŽ‘J>¬)‘±verb‘ÿ}'oseŽ‘(Xu¬=‘DZtrueŽ‘‹°¬;Ž¡‘­ifŽ‘";¼¬(´DEBUGŽ‘®c°_‘è +±verb‘ÿ}'oseŽ‘$yg¬)‘±c‘ÿ}'outŽ‘V7°‘ý´"*******************Ž‘oüÄ***\n"Ž’—°Ž¡‘2´"\nEntering® ´Circle::Ž’šÿÉintersection_points(Ž’ÿconst® ´Circle&)\n\n"Ž’hE¼¬;Ž¦‘­b•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜quadrupleŽ’ƒæ­±bp‘ÿ}'qŽ’•ßá¬=‘Ç´INVALID_BOOL_POINT_QUADRUPLEŽ’–M,¬;Ž¡‘­PlaneŽ‘46º±this‘‰ffŽ‘®planeŽ‘b…̬=‘DZget‘‰ffŽ‘®planeŽ‘+>¬(‘ª¨);Ž¡‘­PlaneŽ‘46º±c‘‰ffŽ‘®planeŽ‘Wˆ¨¬=‘ǵcŽ‘ó:±get‘‰ffŽ‘®planeŽ‘(vè¬(‘ª¨);Ž¦‘­ifŽ‘´ú¬(°:¬(±this‘‰ffŽ‘®planeŽ‘+‡úµ:±normalŽ–#а‘DZc‘‰ffŽ‘®planeŽ‘#Qîµ:±normalŽ‘"˜°_‘8à±this‘‰ffŽ‘®planeŽ‘-ÀÚµ:±normalŽ“°‘ÇŽ‘ +Ž6±c‘‰ffŽ‘®planeŽ‘+ µ:±normalŽ‘ V¸¬))‘°fŽ¡‘­ifŽ‘+í̬(±verb‘ÿ}'oseŽ‘$Eq°_‘´´DEBUGŽ‘zm¬)‘±c‘ÿ}'outŽ‘ÔR°‘{´"Circles® ´are® ´non-copŽ‘ozßlanar.® ´"Ž’ |J°Ž¡‘<´"Calling® ´Ellipse::inŽ’¤ÿÊtersection_points()\Ž’ ÿŽn\n"Ž’&M°‘DZ ushŽ‘€¬;Ž¡‘±bp‘ÿ}'qŽ‘/ù7¬=‘Ç­EllipseŽ‘%¯õ¬::Ž‘,>3±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘}ˬ(µcŽ‘SÛ;‘ª¨±verb‘ÿ}'oseŽ‘"<¬);Ž¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)Ž¡‘(±c‘ÿ}'outŽ‘> S°‘Ç´"Exiting® ´Circle::intŽ‘kÆÜersection_points(conŽ’ÔÆ st® ´Circle&)"Ž’ü°‘DZend‘‚ØlŽ–ò°‘DZend‘‚ØlŽ“°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½±bp‘ÿ}'qŽ‘QÙ¬;Ž¡‘°gŽ¡‘­elseŽ‘+Øá°fŽ¡‘­ifŽ‘)´û¬(±verb‘ÿ}'oseŽ‘"Ê=°_‘8à´DEBUGŽ‘ÿ9¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Circles® ´are® ´coplanaŽ‘kÆÜr.\n"Ž’†5¬;Ž¦‘­realŽ‘4³1±distŽ‘H†¶¬=‘Ç(µcŽ‘SÛ:±c‘ÿ}'enterŽ–Bk°‘8à±c‘ÿ}'enterŽ“¬)µ:±magnitudeŽ‘.=r¬(‘ª¨);Ž¦‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"dist® ´==® ´"Ž‘:”z°‘DZdistŽ‘š°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘­ifŽ‘)´û¬(±distŽ‘Ó…°‘Ǭ0Ž‘Ç)‘°fŽ¡‘(­ifŽ‘3´ü¬(±verb‘ÿ}'oseŽ‘"Ê=°_‘8à´DEBUGŽ‘ÿ9¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Circles® ´have® ´same® ´cŽ‘kÆÜenter.\n"Ž’›)¬;Ž¡‘(­ifŽ‘3´ü¬(±r‘ÿ}'adiusŽ‘;°‘ǵcŽ‘ó:±r‘ÿ}'adiusŽ‘È#¬)‘°fŽ¡‘2­ifŽ‘=´ý¬(±verb‘ÿ}'oseŽ‘"Ê=°_‘8à´DEBUGŽ‘ÿ9¬)‘°fŽ¡‘<±c‘ÿ}'outŽ‘Rnâ°‘¥´"Circles® ´are® ´congrueŽ‘lint.® ´"Ž’‰ñg°‘¥´"Returning® ´INVALID_BŽ‘liOOL_POINT_QUADRUPLE.Ž’Õ-\ŽŽ¡‘P\n\n"Ž‘my°‘DZ ushŽ‘€¬;Ž¡‘2°gŽ¡‘2­ifŽ‘>/T¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ì5°‘’þ´"\nExiting® ´Circle::iŽ‘l’Ântersection_points(cŽ’Õ’†onst® ´Circle&)."Ž’(k¿°Ž¡‘P±end‘‚ØlŽ‘f¸â°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘2­returnŽ‘Uæ¿´INVALID_BOOL_POINT_QUADRUPLEŽ’élÓ¬;Ž¡‘(°gŽ¡‘(­elseŽ‘>.8ifŽ‘Iã0¬(±r‘ÿ}'adiusŽ‘;µ>‘ÇcŽ‘ó:±r‘ÿ}'adiusŽ‘È#¬)‘°fŽ¡‘2­ifŽ‘=´ý¬(±verb‘ÿ}'oseŽ‘"Ê=°_‘8à´DEBUGŽ‘ÿ9¬)‘°fŽ¡‘<±c‘ÿ}'outŽ‘R¦ä°‘M§´"*this® ´and® ´c® ´lie® ´outŽ‘lMkside® ´of® ´each® ´other.® Ž’ÕM/´No® ´intersections."Ž’7¡°‘M§±end‘‚ØlŽ‘°Ž¡‘P´"Returning® ´INVALID_BŽ’¸ÿÌOOL_POINT_QUADRUPLE.Ž’!ÿ\n\n"Ž’?°‘DZ ushŽ‘€¬;Ž¡‘2°gŽ¡‘2­ifŽ‘>/T¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ì5°‘’þ´"\nExiting® ´Circle::iŽ‘l’Ântersection_points(cŽ’Õ’†onst® ´Circle&)."Ž’(k¿°Ž¡‘P±end‘‚ØlŽ‘f¸â°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘2­returnŽ‘Uæ¿´INVALID_BOOL_POINT_QUADRUPLEŽ’élÓ¬;Ž¡‘(°gŽ¡‘(­elseŽ‘>.8ifŽ‘Iã0¬(±r‘ÿ}'adiusŽ‘;µ<‘ÇcŽ‘ó:±r‘ÿ}'adiusŽ‘È#¬)‘°fŽ¡‘2­ifŽ‘=´ý¬(±verb‘ÿ}'oseŽ‘"Ê=°_‘8à´DEBUGŽ‘ÿ9¬)‘°fŽ¡‘<±c‘ÿ}'outŽ‘Tôì°‘›¯´"*this® ´lies® ´inside® ´cŽ‘n›s.® ´No® ´intersections."Ž’ݽN°‘›¯±end‘‚ØlŽ‘) °Ž¡‘P´"Returning® ´INVALID_BŽ’¸ÿÌOOL_POINT_QUADRUPLE.Ž’!ÿ\n\n"Ž’?°‘DZ ushŽ‘€¬;Ž¡‘2°gŽ¡‘2­ifŽ‘>/T¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ì5°‘’þ´"\nExiting® ´Circle::iŽ‘l’Ântersection_points(cŽ’Õ’†onst® ´Circle&)."Ž’(k¿°Ž¡‘P±end‘‚ØlŽ‘f¸â°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘2­returnŽ‘Uæ¿´INVALID_BOOL_POINT_QUADRUPLEŽ’élÓ¬;ŽŽŽŒ‹{1´ Šn ý‘ì°x¬1305–¯3DLDF-1.1.5.1’ó=“­CIR®9CLE‘ÕX¯ARÃŽGUMENT“¬379Ž €n ý•@P‘(°gŽ¤ ‘(­elseŽ‘?Øã°fŽ¡‘2±c‘ÿ}'errŽ‘GÜ«°‘'´"ERROR!® ´In® ´"Ž‘EÔD°‘'´"|Circle::intersectiŽ‘l&Äon_points(const® ´CircŽ’Õ&ˆle&)|"Ž’øSÞ°‘'±end‘‚ØlŽ‘?°Ž¡‘F´"This® ´can't® ´happen!"Ž’²Ç‹°‘AX´"radius® ´and/or® ´c.radŽ‘lAius® ´have® ´invalid® ´valŽ’Õ@àues:\n"Ž’ýÈ‹°Ž¡‘F´"radius® ´=® ´"Ž’„¾ì°‘xž±r‘ÿ}'adiusŽ‘$¹_°‘xž±end‘‚ØlŽ–âþ°‘xž´"c.radius® ´=® ´"Ž‘M·}°‘xžµcŽ‘Ìy:±r‘ÿ}'adiusŽ‘ @Á°‘xž±end‘‚ØlŽ“°Ž¡‘F´"Returning® ´INVALID_BŽ’®ÿËOOL_POINT_QUADRUPLE.Ž’ÿ\n\n"Ž’5°‘DZ ushŽ‘€¬;Ž¡‘2­ifŽ‘>/T¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ì5°‘’þ´"\nExiting® ´Circle::iŽ‘l’Ântersection_points(cŽ’Õ’†onst® ´Circle&)."Ž’(k¿°Ž¡‘P±end‘‚ØlŽ‘f¸â°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘2­returnŽ‘Uæ¿´INVALID_BOOL_POINT_QUADRUPLEŽ’élÓ¬;Ž¡‘(°gŽ¡‘g‘µ=°‘ÿý­ifŽ‘´õ¬(±distŽ‘Ó…°‘Ǭ0Ž‘Ç)‘ÿý°µ=Ž¡‘­elseŽ‘4.7ifŽ‘?ã/¬(±distŽ‘Ó…µ>‘Ǭ(±r‘ÿ}'adiusŽ‘¬+‘8àµcŽ‘Œ»:±r‘ÿ}'adiusŽ‘È#¬))‘°fŽ¡‘(­ifŽ‘3´ü¬(±verb‘ÿ}'oseŽ‘"Ê=°_‘8à´DEBUGŽ‘ÿ9¬)Ž¡‘2±c‘ÿ}'outŽ‘HÛu°‘‚9´"*this® ´and® ´c® ´lie® ´outŽ‘lýside® ´of® ´each® ´other.® Ž’ÕÁ´"Ž’ÞÊ_°‘‚9´"No® ´intersections.\nŽ‘lý"Ž‘uÊ›°Ž¡‘F´"Returning® ´INVALID_BŽ’®ÿËOOL_POINT_QUADRUPLE.Ž’ÿ\n\n"Ž’5°‘DZ ushŽ‘€¬;Ž¡‘(­ifŽ‘3ËK¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘E|°‘ìE´"\nExiting® ´Circle::iŽ‘kì ntersection_points(cŽ’ÔëÍonst® ´Circle&)."Ž’'M°‘ìE±end‘‚ØlŽ‘ÊL°Ž¡‘F±end‘‚ØlŽ‘\¸á°‘DZ ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾´INVALID_BOOL_POINT_QUADRUPLEŽ’ßlÒ¬;Ž¡‘°gŽ¡‘­elseŽ‘4.7ifŽ‘?ã/¬(±distŽ‘Ó…°‘Ǭ(±r‘ÿ}'adiusŽ‘¬+‘8àµcŽ‘Œ»:±r‘ÿ}'adiusŽ‘È#¬))‘°fŽ¡‘(­ifŽ‘4œa¬(±verb‘ÿ}'oseŽ‘#d€°_‘Ó#´DEBUGŽ‘™|¬)‘±c‘ÿ}'outŽ‘¡ö°‘H¿´"this® ´and® ´c® ´have® ´a® ´tŽ‘mHƒangent® ´on® ´the® ´outsidŽ’ÖHGe® ´"Ž’ê×e°Ž¡‘F´"(one® ´intersection® ´pŽ’®ÿËoint).\n"Ž’ÞƬ;Ž¡‘(±bp‘ÿ}'qŽ‘72 µ:± rstŽ‘µªµ:±ptŽ‘ äµ:±setŽ‘ x„¬(µcŽ‘SÛ:±c‘ÿ}'enterŽ–Bk°‘8à±c‘ÿ}'enterŽ“¬);Ž¡‘(±bp‘ÿ}'qŽ‘72 µ:± rstŽ‘µªµ:±ptŽ‘ äµ:±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u¬(±trueŽ‘ʬ);Ž¡‘(±bp‘ÿ}'qŽ‘72 µ:± rstŽ‘µªµ:±ptŽ‘ «µ°¬=ŽŽ‘9ì±r‘ÿ}'adiusŽ‘8¬;Ž¡‘(±bp‘ÿ}'qŽ‘72 µ:± rstŽ‘µªµ:±ptŽ‘ äµ:±shiftŽ‘}¬(±c‘ÿ}'enterŽ‘ ‹¬);Ž¡‘(±bp‘ÿ}'qŽ‘72 µ:± rstŽ‘µªµ:bŽ‘¬=‘DZtrueŽ‘‹°¬;Ž¡‘(­ifŽ‘3ËK¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘E|°‘ìE´"\nExiting® ´Circle::iŽ‘kì ntersection_points(cŽ’ÔëÍonst® ´Circle&)."Ž’'M°‘ìE±end‘‚ØlŽ‘ÊL°Ž¡‘F±end‘‚ØlŽ‘\¸á°‘DZ ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾±bp‘ÿ}'qŽ‘[Ú¬;Ž¡‘°gŽ¡‘­elseŽ‘4.7ifŽ‘?ã/¬(±distŽ‘Ó…°‘DZmaxŽ‘k³¬(±r‘ÿ}'adiusŽ–È#µ;‘ª¨cŽ›þƒ:±r‘ÿ}'adiusŽ“¬)–8à°“±minŽ‘]õ¬(±r‘ÿ}'adiusŽ–È#µ;‘ª¨cŽ˜:±r‘ÿ}'adiusŽ“¬))‘°fŽ¡‘(­ifŽ‘4œa¬(±verb‘ÿ}'oseŽ‘#d€°_‘Ó#´DEBUGŽ‘™|¬)‘±c‘ÿ}'outŽ‘¡ö°‘H¿´"*this® ´and® ´c® ´have® ´a® Ž‘mHƒ´tangent® ´on® ´the® ´insidŽ’ÖHGe® ´"Ž’ê×e°Ž¡‘F´"(one® ´intersection® ´pŽ’®ÿËoint).\n"Ž’ÞƬ;Ž¡‘(­ifŽ‘3´ü¬(±r‘ÿ}'adiusŽ‘;µ>‘ÇcŽ‘ó:±r‘ÿ}'adiusŽ‘È#¬)‘°fŽ¡‘2­ifŽ‘=´ý¬(±verb‘ÿ}'oseŽ‘"Ê=°_‘8à´DEBUGŽ‘ÿ9¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"c® ´lies® ´within® ´*thisŽ‘kÆÜ.\n"Ž’M8¬;Ž¡‘2±bp‘ÿ}'qŽ‘A2!µ:± rstŽ‘µªµ:±ptŽ‘ äµ:±setŽ‘ x„¬(µcŽ‘SÛ:±c‘ÿ}'enterŽ–Bk°‘8à±c‘ÿ}'enterŽ“¬);Ž¡‘(°gŽ¡‘(­elseŽ‘?Øã°fŽ¡‘2­ifŽ‘=´ý¬(±verb‘ÿ}'oseŽ‘"Ê=°_‘8à´DEBUGŽ‘ÿ9¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"*this® ´lies® ´within® ´cŽ‘kÆÜ.\n"Ž’M8¬;Ž¡‘2±bp‘ÿ}'qŽ‘A2!µ:± rstŽ‘µªµ:±ptŽ‘ äµ:±setŽ‘ x„¬(±c‘ÿ}'enterŽ‘Bk°‘8àµcŽ‘Œ»:±c‘ÿ}'enterŽ‘ ‹¬);Ž¡‘(°gŽ¡‘(±bp‘ÿ}'qŽ‘72 µ:± rstŽ‘µªµ:±ptŽ‘ äµ:±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u¬(±trueŽ‘ʬ);Ž¡‘(±bp‘ÿ}'qŽ‘72 µ:± rstŽ‘µªµ:±ptŽ‘ «µ°¬=ŽŽ‘9ì±r‘ÿ}'adiusŽ‘8¬;Ž¡‘(±bp‘ÿ}'qŽ‘72 µ:± rstŽ‘µªµ:±ptŽ‘ äµ:±shiftŽ‘}¬(±c‘ÿ}'enterŽ‘ ‹¬);Ž¡‘(±bp‘ÿ}'qŽ‘72 µ:± rstŽ‘µªµ:bŽ‘¬=‘DZtrueŽ‘‹°¬;Ž¡‘(­ifŽ‘3ËK¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘E|°‘ìE´"\nExiting® ´Circle::iŽ‘kì ntersection_points(cŽ’ÔëÍonst® ´Circle&)."Ž’'M°‘ìE±end‘‚ØlŽ‘ÊL°Ž¡‘F±end‘‚ØlŽ‘\¸á°‘DZ ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾±bp‘ÿ}'qŽ‘[Ú¬;Ž¡‘°gŽ¡‘­elseŽ‘4.7ifŽ‘?ã/¬(±distŽ‘Ó…µ<‘Ǭ(±r‘ÿ}'adiusŽ‘¬+‘8àµcŽ‘Œ»:±r‘ÿ}'adiusŽ‘È#¬))‘°fŽ¡‘(­ifŽ‘3´ü¬(±distŽ‘Ó…µ>‘DZmaxŽ‘k³¬(±r‘ÿ}'adiusŽ–È#µ;‘ª¨cŽ›þƒ:±r‘ÿ}'adiusŽ“¬)–8à°“±minŽ‘]õ¬(±r‘ÿ}'adiusŽ–È#µ;‘ª¨cŽ˜:±r‘ÿ}'adiusŽ“¬))‘°fŽŽŽŒ‹|C/ Šn ý‘ì¬380–­CIR®9CLE‘ÕX¯ARÃŽGUMENT’ó=“3DLDF-1.1.5.1“°x¬1305Ž €n ý•@P‘2­ifŽ‘=´ý¬(±verb‘ÿ}'oseŽ‘"Ê=°_‘8à´DEBUGŽ‘ÿ9¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"t® ´and® ´c® ´have® ´2® ´inteŽ‘kÆÜrsections.\n"Ž’°¬;Ž©‘2­realŽ‘H³3µaŽ‘PÃ{¬=‘DZr‘ÿ}'adiusŽ‘;¬;Ž¤ ‘2­realŽ‘H³3±bbŽ‘UÑë¬=‘ǵcŽ‘ó:±r‘ÿ}'adiusŽ‘°‘8àµcŽ‘Œ»:±r‘ÿ}'adiusŽ‘È#¬;Ž¡‘2­realŽ‘H³3±b‘ÿ}'etaŽ‘]àȬ=‘Ç2Ž‘ ÿù°‘8à±atanŽ‘ªÀ¬(±sqrtŽ‘¯ù¬((±bbŽ‘ €°–8à¬((±distŽ›EM°“µaŽ‘‚¬)“°“¬(±distŽ˜°“µaŽ‘‚¬)))µ=¬(((±distŽ˜¬+“µaŽ‘‚¬)“°“¬(±distŽ˜¬+“µaŽ‘‚¬))“°“±bbŽ‘ €¬)));Ž¦‘2±b‘ÿ}'etaŽ‘G-š°¬=ŽŽ‘V»Ñ180ŽŽ‘e»Ôµ=´PIŽ‘ b¬;Ž¡‘2­ifŽ‘=´ý¬(±verb‘ÿ}'oseŽ‘"Ê=°_‘8à´DEBUGŽ‘ÿ9¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"beta® ´==® ´"Ž‘:”z°‘DZb‘ÿ}'etaŽ‘ô­°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¦‘2­P•®9oin“tŽ‘PPŽ‘X¾¿¬(µcŽ‘SÛ:±c‘ÿ}'enterŽ–Bk°‘8à±c‘ÿ}'enterŽ“¬);Ž¦‘2µPŽ‘9Ï":±unit‘‰ffŽ‘®ve‘ÿ}'ctorŽ‘0•u¬(±trueŽ‘ʬ);Ž¡‘2µPŽ‘<–:°¬=ŽŽ‘L$q±r‘ÿ}'adiusŽ‘g씬;Ž¡‘2µPŽ‘9Ï":±shiftŽ‘}¬(±c‘ÿ}'enterŽ‘ ‹¬);Ž¦‘2­P•®9oin“tŽ‘PnormalŽ‘t r¬=‘DZget‘‰ffŽ‘®normalŽ‘3QŒ¬(‘ª¨);Ž¦‘2±normalŽ‘RV½µ:±shiftŽ‘}¬(±c‘ÿ}'enterŽ‘ ‹¬);Ž¡‘2­ifŽ‘=´ý¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘<µPŽ‘CÏ#:±dotlab‘ÿ}'elŽ‘!ÿó¬(´"P"Ž‘F_¬);Ž¡‘<µPŽ‘CÏ#:±showŽ‘Šÿ¬(´"P"Ž‘F_¬);Ž¡‘<±normalŽ‘\V¾µ:±showŽ‘Šÿ¬(´"normal"Ž‘*†P¬);Ž¡‘2°gŽ¡‘2±bp‘ÿ}'qŽ‘A2!µ:± rstŽ‘µªµ:bŽ‘¬=‘DZtrueŽ‘‹°¬;Ž¡‘2±bp‘ÿ}'qŽ‘A2!µ:± rstŽ‘µªµ:±ptŽ‘ «µ¬=‘ǵPŽ‘ +–5¬;Ž¡‘2±bp‘ÿ}'qŽ‘A2!µ:± rstŽ‘µªµ:±ptŽ‘ äµ:±r‘ÿ}'otateŽ‘o>¬(±c‘ÿ}'enterŽ‘ ‹µ;‘ª¨±normalŽ‘"`µ;‘ª¨±b‘ÿ}'etaŽ‘%¬);Ž¡‘2­ifŽ‘=´ý¬(´DEBUGŽ‘ÆY¬)‘±bp‘ÿ}'qŽ‘2µ:± rstŽ‘µªµ:±ptŽ‘ äµ:±showŽ‘Šÿ¬(´"bpq.first.pt"Ž‘J>¬);Ž¡‘2±bp‘ÿ}'qŽ‘A2!µ:±se–ÿ}'c“ondŽ‘§Çµ:bŽ‘¬=‘DZtrueŽ‘‹°¬;Ž¡‘2±bp‘ÿ}'qŽ‘A2!µ:±se–ÿ}'c“ondŽ‘§Çµ:±ptŽ‘ «µ¬=‘ǵPŽ‘ +–5¬;Ž¡‘2±bp‘ÿ}'qŽ‘A2!µ:±se–ÿ}'c“ondŽ‘§Çµ:±ptŽ‘ äµ:±r‘ÿ}'otateŽ‘o>¬(±c‘ÿ}'enterŽ‘ ‹µ;‘ª¨±normalŽ‘"`µ;‘ª¨°Ž‘ qƱb‘ÿ}'etaŽ‘ØC¬);Ž¡‘2­ifŽ‘=´ý¬(´DEBUGŽ‘ÆY¬)‘±bp‘ÿ}'qŽ‘2µ:±se–ÿ}'c“ondŽ‘§Çµ:±ptŽ‘ äµ:±showŽ‘Šÿ¬(´"bpq.second.pt"Ž‘OF;¬);Ž¡‘2­ifŽ‘>/T¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ì5°‘’þ´"\nExiting® ´Circle::iŽ‘l’Ântersection_points(cŽ’Õ’†onst® ´Circle&)."Ž’(k¿°Ž¡‘P±end‘‚ØlŽ‘f¸â°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘2­returnŽ‘U濱bp‘ÿ}'qŽ‘eÛ¬;Ž¡‘(°gŽ¡‘(­elseŽ‘>.8ifŽ‘Iã0¬(±r‘ÿ}'adiusŽ‘;µ>‘ÇcŽ‘ó:±r‘ÿ}'adiusŽ‘È#¬)‘°fŽ¡‘2­ifŽ‘=´ý¬(±verb‘ÿ}'oseŽ‘"Ê=°_‘8à´DEBUGŽ‘ÿ9¬)Ž¡‘<±c‘ÿ}'outŽ‘R[w°‘:´"c® ´lies® ´within® ´*thisŽ‘lþ,® ´different® ´centers® Ž’Õ´"Ž’ÝÊa°‘:´"(no® ´intersections).Ž‘lþ\n"Ž‘J—°Ž¡‘P´"Returning® ´INVALID_BŽ’¸ÿÌOOL_POINT_QUADRUPLE.Ž’!ÿ\n"Ž’2Eï¬;Ž¡‘2­ifŽ‘>/T¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ì5°‘’þ´"\nExiting® ´Circle::iŽ‘l’Ântersection_points(cŽ’Õ’†onst® ´Circle&)."Ž’(k¿°Ž¡‘P±end‘‚ØlŽ‘f¸â°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘2­returnŽ‘Uæ¿´INVALID_BOOL_POINT_QUADRUPLEŽ’élÓ¬;Ž¡‘(°gŽ¡‘(­elseŽ‘?Øã°fŽ¡‘2­ifŽ‘=´ý¬(±verb‘ÿ}'oseŽ‘"Ê=°_‘8à´DEBUGŽ‘ÿ9¬)Ž¡‘<±c‘ÿ}'outŽ‘R[w°‘:´"*this® ´lies® ´within® ´cŽ‘lþ,® ´different® ´centers® Ž’Õ´"Ž’ÝÊa°‘:´"(no® ´intersections).Ž‘lþ\n"Ž‘J—°Ž¡‘P´"Returning® ´INVALID_BŽ’¸ÿÌOOL_POINT_QUADRUPLE.Ž’!ÿ\n"Ž’2Eï¬;Ž¡‘2­ifŽ‘>/T¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ì5°‘’þ´"\nExiting® ´Circle::iŽ‘l’Ântersection_points(cŽ’Õ’†onst® ´Circle&)."Ž’(k¿°Ž¡‘P±end‘‚ØlŽ‘f¸â°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘2­returnŽ‘Uæ¿´INVALID_BOOL_POINT_QUADRUPLEŽ’élÓ¬;Ž¡‘(°gŽ¡‘g‘µ=°‘ÿý­elseŽ‘.1ifŽ‘&ã)¬(±distŽ‘Ó…µ<‘Ǭ(±r‘ÿ}'adiusŽ‘¬+‘8àµcŽ‘Œ»:±r‘ÿ}'adiusŽ‘È#¬))‘ÿý°µ=Ž¡‘­elseŽ‘5Øâ°fŽ¡‘(±c‘ÿ}'errŽ‘?â°‘,m´"ERROR!® ´In® ´Circle::iŽ‘n,1ntersection_points(cŽ’×+õonst® ´Circle&):"Ž’+ž°Ž¡‘<´"This® ´can't® ´happen!\Ž’¤ÿÊnThis® ´case® ´isn't® ´accŽ’ ÿŽounted® ´for.\n"Ž’]Úe°Ž¡‘<´"Returning® ´INVALID_BŽ’¤ÿÊOOL_POINT_QUADRUPLE.Ž’ ÿŽ"Ž’ °‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;ŽŽŽŒ‹}TÔ Šn ý‘ì°x¬1305–¯3DLDF-1.1.5.1’ó=“­CIR®9CLE‘ÕX¯ARÃŽGUMENT“¬381Ž €n ý•@P‘(­ifŽ‘3ËK¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘E|°‘ìE´"\nExiting® ´Circle::iŽ‘kì ntersection_points(cŽ’ÔëÍonst® ´Circle&)."Ž’'M°‘ìE±end‘‚ØlŽ‘ÊL°Ž¤ ‘F±end‘‚ØlŽ‘\¸á°‘DZ ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾´INVALID_BOOL_POINT_QUADRUPLEŽ’ßlÒ¬;Ž¡‘°gŽ¡‘g‘µ=°‘ÿý­elseŽ‘.1¬(Coplanar‘UUcase).‘o°µ=Ž¡‘ +°gŽ©­1306.– üReg‘°¡‰ffs4Ž‘#ÕP®9olygon‘Áfunctions.“¬[²LDF‘T2003.06.13.¬]Ž‘ZÀÔ¬(­constŽ‘¡ColorŽ‘=­“¬&Ž‘Et±±ddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘y}Zµ;‘ª¨­constŽ‘ÄIstringŽ‘@Ø•±ddashe‘ÿ}'dŽ‘d¦µ;‘ª¨­constŽ‘ÄIstringŽŽ¡‘2±pp‘ÿ}'enŽ‘G6(µ;‘ª¨­PictureŽ‘*œ +¬&Ž‘2c(±pictur‘ÿ}'eŽ‘Qkþ¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­CircleŽ‘5¸ƒµcŽ‘<Óv¬=‘DZin‘‰ffŽ‘®cir‘ÿ}'cleŽ‘'‰a¬(‘ª¨);Ž¦‘µcŽ‘SÝ:±dr‘ÿ}'awŽ‘(Û¬(±ddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘4©µ;‘ª¨±ddashe‘ÿ}'dŽ‘$ñ¹µ;‘ª¨±pp‘ÿ}'enŽ‘à˵;‘ª¨±pictur‘ÿ}'eŽ‘ ³~¬);Ž¡‘­returnŽ‘7æ¼µcŽ‘<:—¬;Ž¡‘ +°gŽŸ­1310.‘ üPicture–ÕTargumen®9t“ rst.Ž¦°h–ª¨¬De ne‘UU­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘H)^¬functions‘@¯1071“°i‘Ǭ+°Ž¡‘ +­CircleŽ‘+þÃRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘n}{¬::‘±dr›ÿ}'aw‘‰ffŽ–®in‘‰ffŽ“cir˜cleŽ‘>Ô¬(­PictureŽ‘)7£¬&Ž‘0þÁ±pictur‘ÿ}'eŽ‘P—µ;‘ª¨­constŽ‘ ‹ColorŽ‘@¿¬&Ž‘GÍݱddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘{Ö†µ;‘ª¨­constŽ‘ ‹stringŽŽ¡‘2±ddashe‘ÿ}'dŽ‘UGµ;‘ª¨­constŽ‘ÕJstringŽ‘@ú—±pp‘ÿ}'enŽ‘V0º¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼±dr›ÿ}'aw‘‰ffŽ–®in‘‰ffŽ“cir˜cleŽ‘t錬(±ddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘4©µ;‘ª¨±ddashe‘ÿ}'dŽ‘$ñ¹µ;‘ª¨±pp‘ÿ}'enŽ‘à˵;‘ª¨±pictur‘ÿ}'eŽ‘ ³~¬);Ž¡‘ +°gŽŸ­1311.‘ üSurrounding‘ÕTcircle.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.06.13.¬]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬De ne‘UU­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘H)^¬functions‘@¯1071“°i‘Ǭ+°Ž¡‘ +­CircleŽ‘+¸‚Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘n7:¬::‘±out‘‰ffŽ‘®cir‘ÿ}'cleŽ‘*Þ¼¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­CircleŽ‘5¸ƒµcŽ‘: ^¬;Ž¦‘­ifŽ‘´ú¬(°:±is‘‰ffŽ‘®planarŽ‘(&¬(‘ª¨))‘°fŽ¡‘±c‘ÿ}'errŽ‘3²ƒ°‘üÚ´"ERROR!® ´In® ´Reg_PolygŽ‘küžon::out_circle():\n"Ž’ؤ°‘üÚ´"Reg_Polygon® ´is® ´non-Ž‘küžplanar.\n"Ž’£ÿ°Ž¡‘2´"Returning® ´empty® ´CirŽ’šÿÉcle.\n\n"Ž’Í.°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½µcŽ‘F:˜¬;Ž¡‘°gŽ¡‘­ifŽ‘´ú¬(±p‘ÿ}'ointsŽ‘$•µ:±sizeŽ‘\¬(‘ª¨)–ǵ<“¬3Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'errŽ‘8(¢°‘rù´"ERROR!® ´In® ´Reg_PolygŽ‘pr½on::out_circle():\n"Ž’ákâ°Ž¡‘2´"Reg_Polygon® ´has® ´lesŽ’šÿÉs® ´than® ´3® ´Points.\n"Ž’ °‘Ç´"Returning® ´empty® ´CirŽ‘kÆÜcle.\n\n"Ž’žTA°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½µcŽ‘F:˜¬;Ž¡‘°gŽ¦‘­P•®9oin“tŽ‘2normalŽ‘V o¬=‘DZget‘‰ffŽ‘®normalŽ‘3QŒ¬(‘ª¨);Ž¦‘±normalŽ‘4Vºµ:±shiftŽ‘}¬(±c‘ÿ}'enterŽ‘ ‹¬);Ž¡‘µcŽ‘SÝ:±setŽ‘ x„¬(±originŽ‘ö!µ;‘ª¨¬2Ž‘㉰‘8à±r‘ÿ}'adiusŽ‘¬);Ž¦‘­T‘ÿ +«ransformŽ‘KÈÔµtŽ‘OeF¬;Ž¦‘µtŽ‘œt:±align‘‰ffŽ–®with‘‰ffŽ“axisŽ‘@²x¬(±c‘ÿ}'enterŽ‘ ‹µ;‘ª¨±normalŽ‘"`µ;‘ª¨´'y'Ž‘ñ¬);Ž¡‘µcŽ‘õ°¬=ŽŽ‘*©,µtŽ‘.Ež:±inverseŽ‘ ‡¬(‘ª¨);Ž¡‘­returnŽ‘7æ¼µcŽ‘<:—¬;Ž¡‘ +°gŽŸ­1312.‘ üDra®9w–ÕTsurrounding“circle.ŽŽŽŒ‹pW Šn ý‘ì°x¬1313–¯3DLDF-1.1.5.1’ NORMAL‘ÕXVERSION“¬383Ž €n ý•@P­1313.‘ üNormal‘ÕTv®9ersion.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ© ‘ +¬[²LDF‘T2003.06.13.¬]Ž‘Y;Added–UUthis“function.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬De ne‘UU­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘H)^¬functions‘@¯1071“°i‘Ǭ+°Ž¦‘ +­CircleŽ‘,"ÿRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘n¡·¬::‘±dr›ÿ}'aw‘‰ffŽ–®out‘‰ffŽ“cir˜cleŽ‘CC¬(­constŽ‘•ColorŽ‘>¤¬&Ž‘Fk­±ddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘ztVµ;‘ª¨­constŽ‘ ?ÇstringŽ‘AÏ‘±ddashe‘ÿ}'dŽ‘e¢µ;‘ª¨­constŽŽ¦‘2stringŽ‘S%R±pp‘ÿ}'enŽ‘h[uµ;‘ª¨­PictureŽ‘*œ +¬&Ž‘2c(±pictur‘ÿ}'eŽ‘Qkþ¬)‘UU­constŽŽ¦‘ +°fŽ¦‘­CircleŽ‘5¸ƒµcŽ‘<Óv¬=‘DZout‘‰ffŽ‘®cir‘ÿ}'cleŽ‘,¥Ð¬(‘ª¨);Ž¡‘µcŽ‘SÝ:±dr‘ÿ}'awŽ‘(Û¬(±ddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘4©µ;‘ª¨±ddashe‘ÿ}'dŽ‘$ñ¹µ;‘ª¨±pp‘ÿ}'enŽ‘à˵;‘ª¨±pictur‘ÿ}'eŽ‘ ³~¬);Ž¦‘­returnŽ‘7æ¼µcŽ‘<:—¬;Ž¦‘ +°gŽŸ­1314.‘ üPicture–ÕTargumen®9t“ rst.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ +¬[²LDF‘T2003.06.13.¬]Ž‘Y;Added–UUthis“function.Ž¡ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬De ne‘UU­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘H)^¬functions‘@¯1071“°i‘Ǭ+°Ž¦‘ +­CircleŽ‘+ê¢Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘niZ¬::‘±dr›ÿ}'aw‘‰ffŽ–®out‘‰ffŽ“cir˜cleŽ‘CC¬(­PictureŽ‘)#‚¬&Ž‘0ê ±pictur‘ÿ}'eŽ‘Oóvµ;‘ª¨­constŽ‘ jColorŽ‘?Þ}¬&Ž‘G¥›±ddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘{®Dµ;‘ª¨­constŽ‘ jstringŽŽ¦‘2±ddashe‘ÿ}'dŽ‘UGµ;‘ª¨­constŽ‘ÕJstringŽ‘@ú—±pp‘ÿ}'enŽ‘V0º¬)‘UU­constŽŽ¦‘ +°fŽ¦‘­returnŽ‘7æ¼±dr›ÿ}'aw‘‰ffŽ–®out‘‰ffŽ“cir˜cleŽ‘zû¬(±ddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘4©µ;‘ª¨±ddashe‘ÿ}'dŽ‘$ñ¹µ;‘ª¨±pp‘ÿ}'enŽ‘à˵;‘ª¨±pictur‘ÿ}'eŽ‘ ³~¬);Ž¦‘ +°gŽŸ­1315.› üPutting–ÕTCircle“together.˜¬This–UUis“what's“compiled.Ž¡‘ +°h–ª¨¬Include‘UU les‘@¯6“°iŽ¦‘ +h‘ª¨¬V‘ÿ*ªersion–UUconš¸ãtrol“iden˜ti er‘@¯5‘ª¨°iŽ¦‘ +h–ª¨¬De ne‘UU­classŽ‘5¦CircleŽ‘@ØÖ¯1276“°iŽ¦‘ +h–ª¨¬De ne‘UU­CircleŽ‘% Ö¬functions‘@¯1279“°iŽ¦‘ +h–ª¨¬De ne‘UU­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘H)^¬functions‘@¯1071“°iŽ¦‘ +h›ª¨¬Declare–UUnon-mem¸ãbGer“template“functions“for“­CircleŽ‘%ø…¯1286˜°iŽŽŽŒ‹€|Ì Šn ý‘ì¬384›¯PUTTING–ÕX­CIR®9CLE“¯TOGETHER’É¢Á3DLDF-1.1.5.1˜°x¬1316Ž €n ý•@P­1316.‘ ü¬This–UUis“what's“written“to“®circles.h¬.Ž©°h‘ª¨´circles.hŽ‘:ðö¯1316‘ª¨°i‘ÇŽ¤ ‘ +h–ª¨¬De ne‘UU­classŽ‘5¦CircleŽ‘@ØÖ¯1276“°iŽ¡‘ +h›ª¨¬Declare–UUnon-mem¸ãbGer“template“functions“for“­CircleŽ‘%ø…¯1286˜°iŽŸ­1317.– üP®9atterns“(®patterns.web­).‘#f¬[²LDF‘T2002.09.21.¬]Ž‘r  NOTE:–UUWhen“y¸ãou“add“a“new“®.web“¬ le“andŽ¡mo•¸ãv“e–‡coGde“to“it“bš¸ãy“cop˜ying“it“from“another“®.web“¬ le,‘Šremem˜bGer“to“c˜hange“the“name“of“the“header“ le“thatŽ¡it–UUwrites.‘qÇOtherwise,“this“can“cause“problems“and“it's“not“ob¸ãvious“what's“caused“them.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.09.21.¬]Ž‘X"Started–ousing“this“ le“again.›% Mo•¸ãv“ed‘o±hex‘‰ffŽ–®p‘ÿ}'attern‘‰ffŽ“1Ž‘=êu¬(‘ª®)–ohere.˜Made“the“appropriate“c¸ãhangesŽ¡to–UU®cmplprsp.web“¬and“®main.web¬.Ž¡‘ +[²LDF‘T2003.11.12.¬]Ž‘ZCáRemo•¸ãv“ed–ûthe“vš¸ãersion“con˜trol“iden˜ti ers“from“the“CWEB‘© les“for“the“distribution“ofŽ¡3DLDF–UU1.1.‘qÇThey're“still“used“in“mš¸ãy“dev˜elopmen˜t“v˜ersions.Ž¡‘ +[²LDF‘T2003.12.10.¬]Ž‘YQ‘Put–ž«the“vš¸ãersion“con˜trol“iden˜ti ers“bac˜k“in˜to“m˜y“release“v˜ersions“for“3DLDF‘ž™1.1.4.‘MÊI'v˜eŽ¡already–"¯put“some“of“them“bacš¸ãk“in,‘,Ñno˜w“I'm“doing“the“rest“of“them.‘`åHo˜w˜ev˜er,‘,Ñthe“release“v˜ersions“are“no˜w“inŽ¡their–UUoš¸ãwn“R˜CS“repGository‘ÿ*ª.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h‘ª¨¬V‘ÿ*ªersion–UUconš¸ãtrol“iden˜ti er‘@¯5‘ª¨°i‘Ǭ+°Ž¡‘ +­staticŽ‘)HÚstringŽ‘Jn'±r‘ÿ}'cs‘‰ffŽ‘®idŽ‘g(¬=‘Ç´"$Id:® ´patterns.web,vŽ‘kÆÜ® ´1.4® ´2004/01/12® ´21:3Ž’ÔÆ 1:19® ´lfinsto1® ´Exp® ´$"Ž’>L̬;ŽŸ­1318.‘ üInclude‘ÕT les.Ž¦°h–ª¨¬Include‘UU les‘@¯6“°i‘Ǭ+°Ž¡¬#­includeŽ‘'Ø~´"loader.h"ŽŽ¡¬#­includeŽ‘'Ø~´"pspglb.h"ŽŽ¡¬#­includeŽ‘'Ø~´"io.h"ŽŽ¡¬#­includeŽ‘'Ø~´"colors.h"ŽŽ¡¬#­includeŽ‘'Ø~´"transfor.h"ŽŽ¡¬#­includeŽ‘'Ø~´"shapes.h"ŽŽ¡¬#­includeŽ‘'Ø~´"pictures.h"ŽŽ¡¬#­includeŽ‘'Ø~´"points.h"ŽŽ¡¬#­includeŽ‘'Ø~´"lines.h"ŽŽ¡¬#­includeŽ‘'Ø~´"planes.h"ŽŽ¡¬#­includeŽ‘'Ø~´"paths.h"ŽŽ¡¬#­includeŽ‘'Ø~´"curves.h"ŽŽ¡¬#­includeŽ‘'Ø~´"polygons.h"ŽŽ¡¬#­includeŽ‘'Ø~´"rectangs.h"ŽŽ¡¬#­includeŽ‘'Ø~´"ellipses.h"ŽŽ¡¬#­includeŽ‘'Ø~´"circles.h"ŽŽ¤­1319.‘ üPlane‘ÕTtesselations.Ž¡1320.‘ üHexagonal–ÕTtesselation“1.Ž¤ ‘ +¬[²LDF‘T2003.08.10.¬]Ž‘Y;TO–UUDO:“Change,“so“that“it's“pGossible“to“put“the“pattern“in¸ãto“a“rectangular“area.ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.09.22.¬]Ž‘X£×Added–ðñargumenš¸ãts.‘PQ±hex‘‰ffŽ–®p‘ÿ}'attern‘‰ffŽ“1Ž‘?ˬ¬(‘ª®)“can“no˜w“bGe“used“to“mak˜e“a“pattern“with“up“to“threeŽ¡nested–(ühexagons“whicš¸ãh“can“bGe“dra˜wn“and“ lled.‘bÿEac˜h“hexagon“has“its“o˜wn“argumen˜t“for“the“dra˜w“color,‘1ÛtheŽ¡ ll–ëÔcolor“and“the“pšGen“to“b˜e“used.‘Nœ±hex‘‰ffŽ–®p‘ÿ}'attern‘‰ffŽ“1Ž‘?É÷¬(‘ª®)“do˜es“not“ha•¸ãv“e›ëÔargumen“ts˜for˜dash˜patterns,‘îbut˜they˜couldŽ¡bGe–zýadded,›„gif“necessary‘ÿ*ª.‘âÀIf“the“argumen¸ãt“for“the“diameter“of“the“middle“or“the“inner“hexagon“is“0,˜then“thatŽ¡hexagon–‰(is“not“draš¸ãwn“or“ lled.‘ @In“this“case,‘–the“argumen˜ts“for“the“dra˜w“and“ ll“colors“are“ignored“for“thatŽŽŽŒ‹…º Šn ý‘ì°x¬1320›¯3DLDF-1.1.5.1’×#¥HEXAÃŽGONAL–ÕXTESSELA‘ÿJªTION“1˜¬385Ž €n ý•@Phexagon.‘PqThe–ñQdefault“pšGen“for“the“outer“hexagon“is“thic•¸ãk“er–ñQthan“the“p˜ens“for“the“other“t•¸ãw“o–ñQ(.5mm“and“.3mm,Ž¤ respGectiv¸ãely).Ž¡‘ +[²LDF‘T2002.09.20.¬]Ž‘Y3NRewrote–€hthis“function.‘òÿIt“noš¸ãw“w˜orks“with“the“new“±pr–ÿ}'oje“ctŽ‘!÷v¬(›ª®)“function.‘òÿ±hex‘‰ffŽ–®p‘ÿ}'attern‘‰ffŽ“1Ž‘@nZ¬(˜)Ž¡makš¸ães–í¯a“\honeycom˜b"“pattern“on“the“x-z“plane“using“a“single“hexagon“(i.e.,‘Æthere“aren't“nested“hexagonsŽ¡yš¸ãet,‘•äas–ˆûin“the“old“v˜ersion).‘ ¹In“the“next“v˜ersion,‘•äI‘ˆîplan“to“add“argumen˜ts“for“optionally“putting“t˜w˜o“smallerŽ¡hexagons–UUinside“the“large“one,“and“for“ lling“and“un lling.Ž¡‘ +This–5Övš¸ãersion“con˜tains“argumen˜ts“for“the“dra˜wing“command,‘­öincluding“a“­PictureŽ‘0¹¬argumen˜t,‘­öso“thatŽ¡±hex‘‰ffŽ–®p‘ÿ}'attern‘‰ffŽ“1Ž‘;{[¬(‘ª®)–UUneed“not“bGe“put“on¸ãto“±curr–ÿ}'ent‘‰ffŽ‘®pictur“eŽ‘E{¬.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h›ª¨¬Declare–UUP¸ãattern“functions‘@¯1320˜°i‘ÇŽ¤ ‘ +­unsignedŽ‘;_‚in®9tŽ‘N,ì±hex‘‰ffŽ–®p‘ÿ}'attern‘‰ffŽ“1Ž’‰¨G¬(­realŽ‘Û¡±diameter‘‰ffŽ‘®outerŽ‘^§§¬=‘µ+5Ž– µ,µ;‘ª¨­realŽ‘†I±diameter‘‰ffŽ‘®midd‘‚ØleŽ‘fƒa¬=‘µ+0Ž“µ;‘ª¨­realŽŽ¡‘±diameter‘‰ffŽ‘®innerŽ‘c”ñ¬=‘û:0Ž–û;µ;‘ª¨­unsignedŽ‘2þshortŽ‘Oêé± rst‘‰ffŽ‘®r‘ÿ}'owŽ‘xà™¬=‘û:5Ž“µ;‘ª¨­unsignedŽ‘2þshortŽ‘Oêé±double‘‰ffŽ‘®r‘ÿ}'owsŽ’†Î¬=‘û:10ŽŽ‘ û<µ;‘ª¨­unsignedŽŽ¡‘shortŽ‘;ʦ±r‘ÿ}'ow‘‰ffŽ‘®shiftŽ‘eÓR¬=‘Ç2Ž‘ǵ;Ž¡‘ª°=°‘ÿý¬Argumenš¸ãts–UUfor“the“dra˜wing“and“ lling“commands.‘o°µ=Ž¡‘ +­ColorŽ‘)¤ô±dr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜outerŽ‘u¤+¬=‘Ç°Ž‘Ç­ColorsŽ‘)Ÿ÷¬::Ž‘0.5±default‘‰ffŽ‘®c‘ÿ}'olorŽ‘gªµ;‘ª©=°–ÿý¬Outer“°µ=Ž¡‘ +­ColorŽ‘)`Z± l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“outerŽ‘l ­¬=‘Ç°Ž‘Ç­ColorsŽ‘)Ÿ÷¬::Ž‘0.5±b–ÿ}'ackgr“ound‘‰ffŽ‘®c“olorŽ‘zrµ;‘ª¨­ColorŽ‘! ±dr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜midd‘‚ØleŽ‘s;J¬=‘Ç°Ž‘Ç­ColorsŽ‘)Ÿ÷¬::Ž‘0.5±default‘‰ffŽ‘®c‘ÿ}'olorŽ‘gªµ;Ž¡‘=°–ÿý¬Middle“°µ=Ž¡‘ +­ColorŽ‘)Tu± l›‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“midd˜leŽ‘r0Ú¬=‘Ç°Ž‘Ç­ColorsŽ‘)Ÿ÷¬::Ž‘0.5±b–ÿ}'ackgr“ound‘‰ffŽ‘®c“olorŽ‘zrµ;‘ª¨­ColorŽ‘ ÿ±dr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜innerŽ‘m,¬=‘Ç°Ž‘Ç­ColorsŽ‘)Ÿ÷¬::Ž‘0.5±default‘‰ffŽ‘®c‘ÿ}'olorŽ‘gªµ;Ž¡‘=°–ÿý¬Inner“°µ=Ž¡‘ +­ColorŽ‘)¤ô± l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“innerŽ‘lÓ ¬=‘Ç°Ž‘Ç­ColorsŽ‘)Ÿ÷¬::Ž‘0.5±b–ÿ}'ackgr“ound‘‰ffŽ‘®c“olorŽ‘zrµ;‘ª¨­stringŽ‘"Ïõ±p‘ÿ}'en‘‰ffŽ‘®outerŽ‘PKЬ=‘Ç´"pencircle® ´scaled® ´.5Ž‘kÆÜmm"Ž‘| ;µ;Ž¡‘­stringŽ‘?%P±p‘ÿ}'en‘‰ffŽ‘®midd‘‚ØleŽ‘rÒ=¬=‘Ç´"pencircle® ´scaled® ´.3Ž‘kÆÜmm"Ž–| ;µ;‘ª¨­stringŽ‘"Ïõ±p‘ÿ}'en‘‰ffŽ‘®innerŽ‘PΩ¬=‘Ç´"pencircle® ´scaled® ´.3Ž‘kÆÜmm"Ž“µ;Ž¡‘­PictureŽ‘Fñe¬&Ž‘N¸ƒ±pictur‘ÿ}'eŽ‘pˆq¬=‘DZcurr–ÿ}'ent‘‰ffŽ‘®pictur“eŽ‘Dìßµ;‘ª¨­unsignedŽ‘1á¶in®9tŽ‘C†­±max‘‰ffŽ‘®hexagonsŽ’„ c¬=‘Ç1000ŽŽ‘Ç);Ž¤ ¯See–ÕXalso“sections“1323“and“1326.Ž¡This–ÕXco‘8­¬25ŽŽ‘ 8¯)‘µ=°‘D$¬[²LDF‘T2002.09.22.¬]Ž‘T…This–™|can't“bšGe“­elseŽ‘ ×ifŽ‘&ö¬b˜ecause“the“preceding“conditionŽ¡‘(migh•¸ãt›UUha“v“e˜proGduced˜a˜v‘ÿqÇalue˜µ>‘Ǭ25.‘o°µ=Ž¡‘°fŽ¡‘±c‘ÿ}'errŽ‘3Šš°‘Ôñ´"ERROR!® ´In® ´hex_patteŽ‘kÔµrn_1():\n"Ž’£¯ð°‘Ôñ´"first_row® ´has® ´invalŽ‘kÔµid® ´value:® ´"Ž’¨ïí°‘Ôñ± rst‘‰ffŽ‘®r‘ÿ}'owŽ‘+¤X°Ž¡‘2´"It® ´can® ´be® ´at® ´most® ´2Ž’šÿÉ5.\n"Ž’¸:°‘Ç´"Setting® ´first_row® ´tŽ‘kÆÜo® ´25.\n"Ž’™D°‘DZ ushŽ‘€¬;Ž¡‘± rst‘‰ffŽ‘®r‘ÿ}'owŽ‘FÁ‘¬=‘Ç25ŽŽ‘ Ç;Ž¡‘°gŽ¡‘­ifŽ‘´ú¬(± l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“outerŽ‘B«S°‘ÇŽ‘Ç­ColorsŽ‘)Ÿ÷¬::Ž‘0.5±default‘‰ffŽ‘®c‘ÿ}'olorŽ‘gª¬)Ž¡‘(µ=°‘Ý_¬LDF‘2®2002.09.24.›f=Changed–2·this,‘9£bGecause“I'm“no¸ãw“using“­classŽ‘ðjColorŽ‘=r¿¬instead“of“­stringsŽ‘%c¬.˜No¸ãw“itŽ¡‘2loGoks–]blikš¸ãe“I'm“going“to“ha˜v˜e“to“use“\°Ž‘­ColorsŽ‘&Ø߬::Ž‘-g±b–ÿ}'ackgr“ound‘‰ffŽ‘®c“olorŽ‘w«u¬"“as“a“placeholder.‘‰îI'm“going“toŽ¡‘2ha•¸ãv“e–{€to“c•¸ãhec“k–{€to“see“what“the“consequences“of“this“c¸ãhange“are“here.–äG!!“[²LDF‘T2002.09.22.¬]Ž‘T¬ThisŽ¡‘2is–)necessary‘ÿ*ª,‘ŒbGecause“­P®9athŽ‘‘¬::‘± l‘‚ØlŽ‘ É÷¬(›ª®)“in¸ãterprets“\´""Ž‘ b¬"“as“´"black"Ž‘(Ç|¬.‘õDIn“±hex‘‰ffŽ–®p‘ÿ}'attern‘‰ffŽ“1Ž‘>ü„¬(˜),‘Œit“ma¸ãy“bGeŽ¡‘2necessary–to“ha•¸ãv“e–a“placeholder“for“a“± l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘)]¬,‘‰tand“it's“bšGetter“to“b˜e“able“to“use“\´""Ž‘ b¬"“than“toŽ¡‘2ha•¸ãv“e–UUto“t¸ãypGe“\±b–ÿ}'ackgr“oundŽ‘1uö¬".‘o°µ=Ž¡‘± l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“outerŽ‘`«V¬=‘Ç°Ž‘Ç­ColorsŽ‘)Ÿ÷¬::Ž‘0.5±b–ÿ}'ackgr“ound‘‰ffŽ‘®c“olorŽ‘zr¬;Ž¡‘­ifŽ‘´ú¬(± l›‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“midd˜leŽ‘HÜe°‘ÇŽ‘Ç­ColorsŽ‘)Ÿ÷¬::Ž‘0.5±default‘‰ffŽ‘®c‘ÿ}'olorŽ‘gª¬)‘± l›‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“midd˜leŽ‘MÜe¬=‘Ç°Ž‘Ç­ColorsŽ‘)Ÿ÷¬::Ž‘0.5±b–ÿ}'ackgr“ound‘‰ffŽ‘®c“olorŽ‘zr¬;Ž¡‘­ifŽ‘´ú¬(± l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“innerŽ‘C.,°‘ÇŽ‘Ç­ColorsŽ‘)Ÿ÷¬::Ž‘0.5±default‘‰ffŽ‘®c‘ÿ}'olorŽ‘gª¬)‘± l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“innerŽ‘H.,¬=‘Ç°Ž‘Ç­ColorsŽ‘)Ÿ÷¬::Ž‘0.5±b–ÿ}'ackgr“ound‘‰ffŽ‘®c“olorŽ‘zr¬;Ž¦‘­b•QÇo“olŽ‘-¨C±do‘‰ffŽ‘®midd‘‚ØleŽ‘Yô‚¬;‘µ=°‘ج[²LDF‘T2002.09.22.¬]Ž‘TíHaš¸ãving‘\0±do‘‰ffŽ‘®midd‘‚ØleŽ‘3Ÿ¬and‘\0±do‘‰ffŽ‘®innerŽ‘-Vf¬is–\0a“con˜v˜enience,‘]çso“I‘\.don'tŽ¡‘(ha•¸ãv“e–f-to“c•¸ãhec“k–f-whether“±diameter‘‰ffŽ‘®midd‘‚ØleŽ‘OG¬and“±diameter‘‰ffŽ‘®innerŽ‘If¬are“°‘ã*¬0“bGelo•¸ãw,‘jbwhic“h›f-w“ouldn't˜bGe˜asŽ¡‘(clearly‘UUunderstandable.‘o°µ=Ž¡‘­b•QÇo“olŽ‘-¡h±do‘‰ffŽ‘®innerŽ‘T?n¬;Ž¦‘±do‘‰ffŽ‘®midd‘‚ØleŽ‘CY¬=–Ç(±diameter‘‰ffŽ‘®midd‘‚ØleŽ‘K°“¬0Ž‘Ç)“?“±falseŽ‘=t¬:“±trueŽ‘‹°¬;Ž¡‘±do‘‰ffŽ‘®innerŽ‘=e ¬=–Ç(±diameter‘‰ffŽ‘®innerŽ‘E`Ì°“¬0Ž‘Ç)“?“±falseŽ‘=t¬:“±trueŽ‘‹°¬;Ž¦‘­P•®9oin“tŽ‘2pt0Ž‘BXÚ¬;‘µ=°‘ÿý¬origin.‘o°µ=Ž¡‘­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘XÔ ±p‘‰ffŽ‘®outerŽ‘yÒȬ(±pt0Ž‘i;µ;‘ª¨¬6Ž‘ª©µ;‘ª¨±diameter‘‰ffŽ‘®outerŽ‘CÁƒ¬);Ž¡‘­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘XÔ ±p‘‰ffŽ‘®midd‘‚ØleŽ’€Ú¬;Ž¡‘­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘Y ¹±p‘‰ffŽ‘®innerŽ‘z‹O¬;‘µ=°‘5«¬[²LDF‘T2002.09.22.¬]Ž‘Ts“The–‹middle“and“inner“hexagons“are“only“set“(andŽ¡‘(used)–UUif“±do‘‰ffŽ‘®midd‘‚ØleŽ‘2öé¬and/or“±do‘‰ffŽ‘®innerŽ‘-H°¬are“true.‘o°µ=Ž¦‘­ifŽ‘´ú¬(±do‘‰ffŽ‘®midd‘‚ØleŽ‘,L?¬)‘±p‘‰ffŽ‘®midd‘‚ØleŽ‘,/ϵ:±setŽ‘ x„¬(±pt0Ž‘i;µ;‘ª¨¬6Ž‘ª©µ;‘ª¨±diameter‘‰ffŽ‘®midd‘‚ØleŽ‘Iò•¬);Ž¡‘­ifŽ‘´ú¬(±do‘‰ffŽ‘®innerŽ‘&ž¬)‘±p‘‰ffŽ‘®innerŽ‘&–µ:±setŽ‘ x„¬(±pt0Ž‘i;µ;‘ª¨¬6Ž‘ª©µ;‘ª¨±diameter‘‰ffŽ‘®innerŽ‘DD\¬);Ž¦‘­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘XÔ ±p‘‰ffŽ–®outer‘‰ffŽ“c‘ÿ}'opyŽ’zl¬;‘µ=°‘ÿý¬These‘UU­Regu½‰™šs4Ž‘ÔwP®9olygonsŽ‘L²š¬are–UUused“for“cop¸ãying.‘o°µ=ŽŽŽŒ‹ƒ Z Šn ý‘ì°x¬1321›¯3DLDF-1.1.5.1’×#¥HEXAÃŽGONAL–ÕXTESSELA‘ÿJªTION“1˜¬387Ž €n ý•@P‘­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘XÔ 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l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“outerŽ‘B«S°‘ÇŽ‘Ç­ColorsŽ‘)Ÿ÷¬::Ž‘0.5±b–ÿ}'ackgr“ound‘‰ffŽ‘®c“olorŽ‘zr¬)Ž¡‘<±p‘‰ffŽ–®outer‘‰ffŽ“c‘ÿ}'opyŽ‘s¦gµ:±dr‘ÿ}'awŽ‘(Û¬(±dr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜outerŽ‘I8µ;‘ª¨´""Ž‘ ± +µ;‘ª¨±p‘ÿ}'en‘‰ffŽ‘®outerŽ‘,_kµ;‘ª¨±pictur‘ÿ}'eŽ‘ ³~¬);Ž¡‘2­elseŽ‘H.9ifŽ‘Sã1¬(±dr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜outerŽ‘Kÿ7°‘DZ l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“outerŽ‘B«S¬)‘±p‘‰ffŽ–®outer‘‰ffŽ“c‘ÿ}'opyŽ‘<¦aµ:± l‘‚ØlŽ‘ Éó¬(± l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“outerŽ‘?ä;µ;‘ª¨±pictur‘ÿ}'eŽ‘ ³~¬);Ž¡‘2­elseŽ‘IØä±p‘‰ffŽ–®outer‘‰ffŽ“c‘ÿ}'opyŽ’Eµ:± l‘‚Øldr‘ÿ}'awŽ‘!gk¬(±dr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜outerŽ‘I8µ;‘ª¨± l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“outerŽ‘AŽãµ;‘ª¨´""Ž‘ ± +µ;‘ª¨±p‘ÿ}'en‘‰ffŽ‘®outerŽ‘,_kµ;‘ª¨±pictur‘ÿ}'eŽ‘ ³~¬);Ž¡‘2­ifŽ‘=´ý¬(±do‘‰ffŽ‘®midd‘‚ØleŽ‘,L?¬)‘°fŽ¡‘<­ifŽ‘G´þ¬(± l›‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“midd˜leŽ‘HÜe°‘DZ l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“outerŽ‘B«S¬)Ž¡‘F±p‘‰ffŽ–®midd‘‚Øle‘‰ffŽ“c‘ÿ}'opyŽ’„*¬µ:±dr‘ÿ}'awŽ‘(Û¬(±dr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜midd‘‚ØleŽ‘Oi1µ;‘ª¨´""Ž‘ ± 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ushŽ‘€¬;Ž¡‘<­returnŽ‘_æÀ±hexagon‘‰ffŽ‘®ctrŽ’”¬;Ž¡‘2°gŽ¡‘2µtŽ‘8c¬=‘DZp‘‰ffŽ–®outer‘‰ffŽ“c‘ÿ}'opyŽ‘:myµ:±shiftŽ‘}¬(±right‘‰ffŽ‘®shiftŽ‘,—¬);Ž¡‘2­ifŽ‘=´ý¬(±do‘‰ffŽ‘®midd‘‚ØleŽ‘,L?¬)‘±p‘‰ffŽ–®midd‘‚Øle‘‰ffŽ“c‘ÿ}'opyŽ‘Eñ½°¬=ŽŽ‘UôµtŽ‘Yf¬;Ž¡‘2­ifŽ‘=´ý¬(±do‘‰ffŽ‘®innerŽ‘&ž¬)‘±p‘‰ffŽ–®inner‘‰ffŽ“c‘ÿ}'opyŽ‘?ðR°¬=ŽŽ‘O~‰µtŽ‘Sû¬;Ž¡‘(°gŽ¡‘gŽ¡‘±p‘‰ffŽ‘®outerŽ‘AÅØ°¬=ŽŽ‘QT±move‘‰ffŽ‘®b‘ÿ}'ackŽ‘|¬;Ž¡‘­ifŽ‘)´û¬(±do‘‰ffŽ‘®midd‘‚ØleŽ‘,L?¬)‘±p‘‰ffŽ‘®midd‘‚ØleŽ‘.öç°¬=ŽŽ‘>…±move‘‰ffŽ‘®b‘ÿ}'ackŽ‘l­¬;Ž¡‘­ifŽ‘)´û¬(±do‘‰ffŽ‘®innerŽ‘&ž¬)‘±p‘‰ffŽ‘®innerŽ‘)H®°¬=ŽŽ‘8Öå±move‘‰ffŽ‘®b‘ÿ}'ackŽ‘fþÙ¬;Ž¡‘€Ÿÿ³+‘ÿ+ŽŽ‘*G#±i‘‰ffŽ‘®minŽ‘C+[¬;Ž¡‘°gŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Exiting® ´hex_patternŽ‘kÆÜ_1().\n"Ž’™D°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘7æ¼±hexagon‘‰ffŽ‘®ctrŽ‘l¬;Ž¡‘ +°gŽ¤ ¯See–ÕXalso“sections“1324“and“1327.Ž¡This–ÕXcoµ;‘ª¨­realŽ‘Ö#±stepŽ‘+×µ;‘ª¨­unsignedŽ‘2Zin®9tŽ‘DwG±o setsŽ‘a$cµ;‘ª¨­v®9ectorŽ‘!Tð°h­constŽ‘¢ïColorŽ‘>À/°Ž‘CÀ0i‘Í¢±c‘ÿ}'olorsŽ‘N¨µ;‘ª¨­in®9tŽŽ¡‘2±ar‘ÿ}'c‘‰ffŽ‘®divisionsŽ‘j@%¬)Ž¡‘ 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+¬;Ž¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘(±outer‘‰ffŽ‘®cir‘ÿ}'cleŽ‘Z¯Èµ:±dr‘ÿ}'awŽ‘(Û¬(±blackŽ‘ Ôµ;‘ª¨´"evenly"Ž‘,0ø¬);Ž¡‘(±p0Ž‘4ĵ:±dotlab‘ÿ}'elŽ‘!ÿó¬(´"p0"Ž‘†\¬);Ž¡‘°gŽ¡‘±spir‘ÿ}'alŽ‘9ö¬+=ŽŽ‘LKV±p0Ž‘Xb¬;Ž¡‘€Ÿÿ³+‘ÿ+ŽŽ‘*G#±spir–ÿ}'al‘‰ffŽ‘®c“ounterŽ‘g‚ú¬;Ž¡‘°gŽ¡‘­returnŽ‘7æ¼±spir–ÿ}'al‘‰ffŽ‘®c“ounterŽ‘u"“¬;Ž¡‘ +°gŽ¤­1328.‘ üPutting–ÕTpatterns“together.Ž¡1329.‘ ü¬This–UUis“what's“compiled.ŽŸ‘ +°h–ª¨¬Include‘UU les‘@¯6“°iŽ¤ ‘ +h‘ª¨¬V‘ÿ*ªersion–UUconš¸ãtrol“iden˜ti er‘@¯5‘ª¨°iŽ¡‘ +h›ª¨¬Declare–UUP¸ãattern“functions‘@¯1320˜°iŽ¡‘ +h›ª¨¬De ne–UUP¸ãattern“functions‘@¯1321˜°iŽŽŽŒ‹Š*Ë Šn ý‘ì¬394‘¯PUTTING›ÕXP–ÿJªA“TTERNS˜TOGETHER’ÇA3DLDF-1.1.5.1‘°x¬1330Ž €n ý•@P­1330.‘ ü¬This–UUis“what's“written“to“®patterns.h¬.Ž©°h‘ª¨´patterns.hŽ‘@0ó¯1330‘ª¨°i‘ÇŽ¤ ‘ +h›ª¨¬Declare–UUP¸ãattern“functions‘@¯1320˜°iŽŸ­1331.– üSolid“(®solids.web­).‘Õó¬[²LDF‘T2002.11.12.¬]Ž‘mÞ-TO–UUDO:“Add“±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘/’œ¬(‘ª®).‘qÇMust“set“±c‘ÿ}'enterŽ‘"´5¬in“theŽ¡­P®9olyhedraŽ‘6Ö±¬bGefore–UUthis“is“useful.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.09.29.¬]Ž‘Y;Created–UUthis“ le.Ž¡‘ +[²LDF‘T2003.11.12.¬]Ž‘ZCáRemo•¸ãv“ed–ûthe“vš¸ãersion“con˜trol“iden˜ti ers“from“the“CWEB‘© les“for“the“distribution“ofŽ¡3DLDF–UU1.1.‘qÇThey're“still“used“in“mš¸ãy“dev˜elopmen˜t“v˜ersions.Ž¡‘ +[²LDF‘T2003.12.10.¬]Ž‘YQ‘Put–ž«the“vš¸ãersion“con˜trol“iden˜ti ers“bac˜k“in˜to“m˜y“release“v˜ersions“for“3DLDF‘ž™1.1.4.‘MÊI'v˜eŽ¡already–"¯put“some“of“them“bacš¸ãk“in,‘,Ñno˜w“I'm“doing“the“rest“of“them.‘`åHo˜w˜ev˜er,‘,Ñthe“release“v˜ersions“are“no˜w“inŽ¡their–UUoš¸ãwn“R˜CS“repGository‘ÿ*ª.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h‘ª¨¬V‘ÿ*ªersion–UUconš¸ãtrol“iden˜ti er‘@¯5‘ª¨°i‘Ǭ+°Ž¡‘ +­staticŽ‘)HÚstringŽ‘Jn'±r‘ÿ}'cs‘‰ffŽ‘®idŽ‘g(¬=‘Ç´"$Id:® ´solids.web,v® ´1Ž‘kÆÜ.5® ´2004/01/12® ´21:33:Ž’ÔÆ 23® ´lfinsto1® ´Exp® ´$"Ž’3ÌÒ¬;ŽŸ­1332.‘ üInclude‘ÕT les.Ž¦°h–ª¨¬Include‘UU les‘@¯6“°i‘Ǭ+°Ž¡¬#­includeŽ‘'Ø~´"loader.h"ŽŽ¡¬#­includeŽ‘'Ø~´"pspglb.h"ŽŽ¡¬#­includeŽ‘'Ø~´"creatnew.h"ŽŽ¡¬#­includeŽ‘'Ø~´"io.h"ŽŽ¡¬#­includeŽ‘'Ø~´"colors.h"ŽŽ¡¬#­includeŽ‘'Ø~´"transfor.h"ŽŽ¡¬#­includeŽ‘'Ø~´"shapes.h"ŽŽ¡¬#­includeŽ‘'Ø~´"pictures.h"ŽŽ¡¬#­includeŽ‘'Ø~´"points.h"ŽŽ¡¬#­includeŽ‘'Ø~´"lines.h"ŽŽ¡¬#­includeŽ‘'Ø~´"planes.h"ŽŽ¡¬#­includeŽ‘'Ø~´"paths.h"ŽŽ¡¬#­includeŽ‘'Ø~´"curves.h"ŽŽ¡¬#­includeŽ‘'Ø~´"polygons.h"ŽŽ¡¬#­includeŽ‘'Ø~´"rectangs.h"ŽŽ¡¬#­includeŽ‘'Ø~´"ellipses.h"ŽŽ¡¬#­includeŽ‘'Ø~´"circles.h"ŽŽŸ­1333.‘ üSolid–ÕTclass“de nition.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.09.30.¬]Ž‘Y2~Added–˜the“data“mem¸ãbGers“±cir‘ÿ}'clesŽ‘ ü¬,‘Š)±el‘‚ØlipsesŽ‘$ š¬,‘Š)±p‘ÿ}'olygonsŽ‘)ju¬,›Š)and“±p‘ÿ}'athsŽ‘E¬.‘ð‘On“the“one“hand,˜thisŽ¡is–s_wš¸ãasteful,‘ºâsince“most“if“not“all“­SolidsŽ‘&íѬwill“con˜tain“only“one“kind“of“­P®9athŽ‘ì;‘eon“the“other“hand,‘ºâit's“anŽ¡adv‘ÿqÇanš¸ãtage–~lto“bGe“able“to“ha˜v˜e“the“dra˜wing“and“ lling“functions“bGe“mem˜bGers“of“­SolidŽ‘üC¬,‘ˆ²since“they“don't“ha˜v˜eŽ¡to–ìÁkno¸ãw“what“kind“of“a“­P®9athŽ› jæ¬a“­P®9athŽ˜¬is,‘œin“order“to“draš¸ãw“or“ ll“it.‘8 This“w˜a˜y‘ÿ*ª,‘œI‘ìšdon't“ha˜v˜e“to“de ne“theŽ¡dra¸ãwing–UUand“ lling“functions“for“±Spher‘ÿ}'eŽ‘!X|¬,“±El‘‚ØlipsoidŽ‘*Ö¶¬,“­P®9olyhedronŽ‘=c"¬,“etc.Ž¡‘ +[²LDF‘T2002.10.01.¬]Ž‘Y;Added–UUthe“data“mem¸ãbGer“±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘WY¦¬.Ž¡‘ +[²LDF‘T2003.04.11.¬]Ž‘ZPAdded–*the“­staticŽ‘%-ØconstŽ‘D O¬data“mem¸ãbGers“´PATHŽ‘#†¬,‘ï´CIRCLEŽ‘$õu¬,‘ï´ELLIPSEŽ‘*5r¬,‘ï´REG_POLYGONŽ‘?5f¬,‘ïandŽ¡´RECTANGLEŽ‘/ÆM¬.‘qÇCurrenš¸ãtly‘ÿ*ª,–UUtheir“only“use“is“as“argumen˜ts“to“±get‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ‘<ö¹¬(›ª®)“and“±get‘‰ffŽ–®shap›ÿ}'e‘‰ffŽ“c˜enterŽ‘JÃ}¬(˜).Ž¡‘ +[²LDF‘T2003.04.11.¬]Ž‘Y(Renamed‘cB±p‘ÿ}'olygonsŽ‘,¦Ð¬to‘cB±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘9V’¬.‘›This–cBis“in“case“I‘c?decide“to“makš¸ãe“it“pGossible“to“ha˜v˜eŽ¡irregular–UUpGolygons.‘qÇIn“this“case,“I“maš¸ãy“de ne“a“­classŽ‘5¦P®9olygonŽ‘Jé¬and“deriv˜ed“­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘H)^¬from“it.Ž¦ŸüÈ„`ÕÁGŽŽŽŽŒ‹‹/È Šn ý‘ì°x¬1333›¯3DLDF-1.1.5.1’ÜÇ­SOLID–ÕX¯CLASS“DEFINITION˜¬395Ž €n ý•@P°h–ª¨¬De ne‘UU­classŽ‘5¦SolidŽ‘;ó¯1333“°i‘ÇŽ¤ ‘ +­classŽ‘$àRSolidŽ‘A³~¬:‘qÇ­publicŽ‘'ñShapQÇeŽ‘IFS°fŽ¡‘ +­protectedŽ‘:o™¬:‘­b•QÇo“olŽ‘¡f±on‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘VFX¬;Ž¡‘­P•®9oin“tŽ‘2c‘ÿ}'enterŽ‘Nù*¬;Ž¡‘­b•QÇo“olŽ‘-¡h±do‘‰ffŽ‘®outputŽ‘X—›¬;‘µ=°‘ÿý¬LDF‘UU2002.10.01.‘qÇAdded.‘o°µ=Ž¡‘­v®9ectorŽ‘3ªJ°h­CircleŽ‘!¸°Ž‘&¸‚i‘UU±cir‘ÿ}'clesŽ‘Ṭ;Ž¡‘­v®9ectorŽ‘3ªJ°h­EllipseŽ‘%>.°Ž‘*>/i‘UU±el‘‚ØlipsesŽ‘#×Ƭ;Ž¡‘­v®9ectorŽ‘3ªJ°h­P®9athŽ‘æ¹°Ž‘ æºi‘UU±p‘ÿ}'athsŽ‘æ¬;Ž¡‘­v®9ectorŽ‘3ªJ°h­RectangleŽ‘5”ê°Ž‘:”ëi‘UU±r–ÿ}'e“ctanglesŽ‘.õš¬;Ž¡‘­v®9ectorŽ‘3ªJ°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘DÔ °Ž‘IÔ +i‘UU±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘9H¥¬;Ž¡‘­v‘ÿ\ralarra®9yŽ‘=ZC°h­realŽ‘]Ù°i‘UU±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘WY¦¬;Ž¡‘ +­publicŽ‘)=Ö¬:‘­staticŽ‘$HÙconstŽ‘Bs{unsignedŽ‘rª‰shortŽ’u,´CIRCLEŽ’°{‚¬;Ž¡‘­staticŽ‘3HÛconstŽ‘Qs}unsignedŽ’ª‹shortŽ’Ÿu.´ELLIPSEŽ’Ä»¬;Ž¡‘­staticŽ‘3HÛconstŽ‘Qs}unsignedŽ’ª‹shortŽ’Ÿu.´PATHŽ’´ûŠ¬;Ž¡‘­staticŽ‘3HÛconstŽ‘Qs}unsignedŽ’ª‹shortŽ’Ÿu.´RECTANGLEŽ’Ï;{¬;Ž¡‘­staticŽ‘3HÛconstŽ‘Qs}unsignedŽ’ª‹shortŽ’Ÿu.´REG_POLYGONŽ’Ù»u¬;Ž©‘°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°iŽ¡‘ +g¬;ŽŸ ¯This–ÕXco c¬=‘Ç4Ž‘Ç;ŽŸ ¯This–ÕXcoV¬.‘gÁHo•¸ãw“ev“er,‘=G±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6Nµ<‘7C­SolidŽ‘ì]µ>Ž¡¬(‘ª®)–³Eis“used“in“the“draš¸ãwing“and“ lling“functions,‘ÊÀin“order“to“put“­SolidsŽ‘%m¬on˜to“­PicturesŽ‘-ØŽ¬.‘‹–If“w˜e“didn't“ha˜v˜e“aŽ¡constructor,‘þm±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘Yëq¬wš¸ãouldn't–è³initially“ha˜v˜e“the“righ˜t“size“and“±on‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘=vX¬and“±do‘‰ffŽ‘®outputŽ‘0Ç™¬w˜ouldŽ¡b•Goth›Áb“e˜±falseŽ‘1L¬(assuming˜the˜compiler˜set˜s˜the˜initial˜v‘ÿqÇalues˜of˜uninitialized˜­b•QÇo“olsŽ‘"WU¬to˜±falseŽ‘pH¬).‘´ÕNone˜of˜thisŽ¡wš¸ãould–ureally“matter,‘;bGecause“presumably“an“assignmen˜t“w˜ould“follo˜w“immediately‘ÿ*ª,‘;whic˜h“w˜ould“tak˜e“care“ofŽ¡ev¸ãerything,–UUbut“there's“no“harm“in“making“sure.Ž¦°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘ÇŽ¡‘ +­SolidŽ‘#}ج(‘ª®);Ž© ¯See–î'also“sections“1338,–ôZ1343,“1345,“1348,“1350,“1353,“1356,“1358,“1360,“1362,“1364,“1366,“1369,“1371,“1373,“1375,“1377,“1379,Ž¤ +‘1381,–òÕ1383,“1386,“1388,“1390,“1392,“1395,“1397,“1399,“1401,“1404,“1406,“1408,“1409,“1411,“1413,“1415,“1417,“1419,“1423,Ž¡‘1426,–ÕX1429,“1432,“1435,“and“1438.Ž¦This–ÕXcoO Šn ý‘ì¬396›¯DEF‘ÿ8A•ÃŽUL‘ÿJªT‘ÕXCONSTR“UCTOR’æÞ_3DLDF-1.1.5.1˜°x¬1337Ž €n ý•@P­1337.ŽŸ°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘ÇŽ¤ ‘ +­SolidŽ‘$}ܬ::‘­SolidŽ‘}Û¬(‘ª®)Ž¡‘ +°fŽ¡‘±on‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘Nl ¬=‘DZfalseŽ‘v\¬;Ž¡‘±do‘‰ffŽ‘®outputŽ‘A½M¬=‘DZtrueŽ‘‹°¬;Ž¡‘±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘hSµ:±r‘ÿ}'esizeŽ‘i¬(6Ž‘µ;‘ª¨¬0Ž‘ª©);Ž¡‘ +°gŽ© ¯See–î'also“sections“1339,–ôZ1344,“1346,“1347,“1349,“1351,“1354,“1357,“1359,“1361,“1363,“1365,“1367,“1370,“1372,“1374,“1376,“1378,Ž¤ +‘1380,–òÕ1382,“1384,“1387,“1389,“1391,“1393,“1396,“1398,“1400,“1402,“1405,“1407,“1410,“1412,“1414,“1416,“1418,“1420,“1424,Ž¡‘1427,–ÕX1430,“1433,“1436,“and“1439.Ž¦This–ÕXco‘Ǭ(0Ž‘)“)“;Ž¡‘°Ž‘#¬(±p‘ÿ}'athsŽ‘­µ:±b‘ÿ}'ackŽ‘üì(›ª¨))–Îb=“°Ž‘ÎcŽ‘ Îd±iterŽ‘™b¬;–óO°g“­forŽ‘yϬ(­v®9ectorŽ‘ªH°h­CircleŽ‘"V{°Ž‘'V|i‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘X[¬=‘ÎbµsŽ‘~b:±cir‘ÿ}'clesŽ‘Œdµ:±b–ÿ}'e“ginŽ‘¾¨¬(˜);Ž¡‘2±iterŽ‘E’°6¬=‘ǵsŽ‘w:±cir‘ÿ}'clesŽ‘Œdµ:±endŽ‘ಬ(‘ª¨);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)–UU°f“±cir‘ÿ}'clesŽ‘á¹µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(“±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<“­CircleŽ‘$™µ>‘Ǭ(0Ž‘)“)“;Ž¡‘°Ž‘#¬(±cir‘ÿ}'clesŽ‘Œdµ:±b‘ÿ}'ackŽ‘üì(›ª¨))–ƒ=“°Ž‘ƒŽ‘ ƒ±iterŽ‘N¬;–Æ%°g“­forŽ‘{¬(­v®9ectorŽ‘ªH°h­EllipseŽ‘%®þ°Ž‘*®ÿi‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘WѬ=‘ƒµsŽ‘3:±el‘‚ØlipsesŽ‘ ‚qµ:±b–ÿ}'e“ginŽ‘¾¨¬(˜);Ž¡‘2±iterŽ‘E’°6¬=‘ǵsŽ‘w:±el‘‚ØlipsesŽ‘ ‚qµ:±endŽ‘ಬ(‘ª¨);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)–UU°f“±el‘‚ØlipsesŽ‘#×Ƶ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(“±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<“­EllipseŽ‘(Fµ>‘Ǭ(0Ž‘)“)“;Ž¡‘°Ž‘#¬(±el‘‚ØlipsesŽ‘ ‚qµ:±b‘ÿ}'ackŽ‘üì(‘ª¨))–kÿ=“°Ž‘ lŽ‘l±iterŽ‘"6ÿ¬;–°°g“­forŽ‘Б¬(­v®9ectorŽ‘ªH°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽŽ¡‘2°Ž‘7i‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘Y&˜¬=‘ØŸµsŽ– ˆŸ:±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ›5óPµ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);‘=¶±iterŽ‘áS°6¬=‘ØŸµsŽ“:±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ˜µ:±endŽ‘ಬ(‘ª¨);Ž¡‘2€Ÿÿ³+‘ÿ+ŽŽ‘>G%±iterŽ‘O#¬)–UU°f“±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘9H¥µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(“±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<“­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘G›!µ>‘Ǭ(0Ž‘)“)“;Ž¡‘°Ž‘#¬(±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óPµ:±b‘ÿ}'ackŽ‘üì(‘ª¨))–D'=“°Ž‘ D(Ž‘D)±iterŽ‘"'¬;–È°g“­forŽ‘ Á¬(­v®9ectorŽ‘ªH°h­RectangleŽŽ¡‘2°Ž‘7i‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘X„Œ¬=‘6“µsŽ–æ“:±r–ÿ}'e“ctanglesŽ›+ Eµ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);‘Ü{±iterŽ‘Þ °6¬=‘6“µsŽ“:±r–ÿ}'e“ctanglesŽ˜µ:±endŽ‘ಬ(‘ª¨);‘\{Ÿÿ³+‘ÿ+ŽŽ‘#›±iterŽ‘")‘1Ó°fŽ¡‘2±r–ÿ}'e“ctanglesŽ‘] Jµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­RectangleŽ‘8\µ>‘Ǭ(0Ž‘)–UU)“;Ž¡‘°Ž‘#¬(±r–ÿ}'e“ctanglesŽ‘+ Eµ:±b‘ÿ}'ackŽ‘üì(‘ª¨))–Ç=“°Ž‘ÇŽ‘ DZiterŽ‘’¬;–UU°g“gŽ¤­1340.‘ üPseudo-constructor–ÕTfor“dynamic“alloQÇcation.Ž¡1341.‘ üP•®9oin“ter‘ÕTargumen“t.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ +¬[²LDF‘T2003.12.30.¬]Ž‘WëÉReplaced‘8ã­SolidŽ‘¶¾¬::‘±cr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“solidŽ‘H!¿¬(‘ª®)–8ãwith“a“spGecialization“of“­templateŽ‘/ +A°h­classŽ‘ÃßµCŽ‘! «°i“µCŽ‘ +¯°Ž‘°±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘>¥t¬(‘ª¨)Ÿ€„ +Ž¡for‘UU­SolidŽ‘Ó,¬.‘qÇThe–UUargumenš¸ãt“is“no˜w“­constŽ‘*¢¬.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h›ª¨¬Declare–UUnon-mem¸ãbGer“template“functions“for“­SolidŽ‘!0¯1341˜°i‘ÇŽ¡‘ +­SolidŽ‘&Ó-°Ž‘+Ó.±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘[bò¬(­constŽ‘*¢SolidŽ‘:ýΰŽ‘?ýϵcŽ‘DQª¬);Ž¤ ¯See–ÕXalso“section“1342.Ž¡This–ÕXco6¬)‘µ=°‘ÿý¬Makš¸ãe–UUsure“it's“not“self-assignmen˜t.‘o°µ=Ž¡‘(­returnŽ‘Kæ¾°Ž‘P濱thisŽ‘aÒu¬;Ž¡‘±c‘ÿ}'enterŽ‘=F¤¬=‘=µsŽ‘í:±c‘ÿ}'enterŽ‘ ‹¬;‘µ=°‘FɬLDF‘œ2002.10.06.‘F*Added–œ!this“line,‘­ÔbGecause“±c‘ÿ}'enterŽ‘#Aͬis“noš¸ãw“a“mem˜bGer“ofŽ¡‘2­SolidŽ‘K}ܬ.‘¼â°µ=‘=°‘5y¬[²LDF‘T2002.10.02.¬]Ž‘Ts/First,‘˜0call–ŠÑthe“destructor“on“all“of“the“elemen¸ãts“of“±p‘ÿ}'athsŽ‘~¬,Ž¡‘2±cir‘ÿ}'clesŽ‘NŒi¬,‘7–±el‘‚ØlipsesŽ‘#º¬,‘7–±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘9*æ¬,–7–and‘0&±r–ÿ}'e“ctanglesŽ‘.Ðk¬,“bšGecause–0&they'v¸ãe“b˜een“allo˜cated“dynamically‘ÿ*ª.‘ebThenŽ¡‘2clear–UUout“the“v¸ãectors.‘o°µ=Ž¡‘­ifŽ‘)´û¬(±p‘ÿ}'athsŽ‘­µ:±sizeŽ‘\¬(‘ª¨)–ǵ>“¬0Ž‘Ç)‘°fŽ¡‘(­forŽ‘9’ò¬(­v®9ectorŽ‘ªH°h­P®9athŽ‘‘!°Ž‘ ‘"i‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZp‘ÿ}'athsŽ–Wŵ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ªe±iterŽ‘<{°6¬=‘DZp‘ÿ}'athsŽ“µ:±endŽ‘ಬ(˜);‘*eŸÿ³+‘ÿ+ŽŽ‘ñ…±iterŽ‘!¼ƒ¬)‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±cle‘ÿ}'arŽ‘(Ù¬(˜);Ž¡‘(±p‘ÿ}'athsŽ‘?±µ:±cle‘ÿ}'arŽ‘(Ù¬(‘ª¨);Ž¡‘°gŽ¡‘­ifŽ‘)´û¬(±cir‘ÿ}'clesŽ‘Œdµ:±sizeŽ‘\¬(‘ª¨)–ǵ>“¬0Ž‘Ç)‘°fŽ¡‘(­forŽ‘9芬(­v®9ectorŽ‘ªH°h­CircleŽ‘!¸°Ž‘&¸‚i‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZcir‘ÿ}'clesŽ–S|µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZcir‘ÿ}'clesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)Ž¡‘2(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±cle‘ÿ}'arŽ‘(Ù¬(‘ª¨);Ž¡‘(±cir‘ÿ}'clesŽ‘DŒhµ:±cle‘ÿ}'arŽ‘(Ù¬(‘ª¨);Ž¡‘°gŽ¡‘­ifŽ‘)´û¬(±el‘‚ØlipsesŽ‘ ‚qµ:±sizeŽ‘\¬(‘ª¨)–ǵ>“¬0Ž‘Ç)‘°fŽ¡‘(­forŽ‘9芬(­v®9ectorŽ‘ªH°h­EllipseŽ‘%>.°Ž‘*>/i‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZel‘‚ØlipsesŽ–#I‰µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZel‘‚ØlipsesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)Ž¡‘2(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±cle‘ÿ}'arŽ‘(Ù¬(‘ª¨);Ž¡‘(±el‘‚ØlipsesŽ‘H‚uµ:±cle‘ÿ}'arŽ‘(Ù¬(‘ª¨);Ž¡‘°gŽ¡‘­ifŽ‘)´û¬(±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óPµ:±sizeŽ‘\¬(‘ª¨)–ǵ>“¬0Ž‘Ç)‘°fŽ¡‘(­forŽ‘:O¬(­v®9ectorŽ‘ªH°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘DóΰŽ‘IóÏi‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=`@¬=‘ü ±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ–8ï[µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘±iterŽ‘æË°6¬=‘ü ±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ“µ:±endŽ‘ಬ(˜);Ž¡‘F€Ÿÿ³+‘ÿ+ŽŽ‘RG'±iterŽ‘c%¬)‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±cle‘ÿ}'arŽ‘(Ù¬(‘ª¨);Ž¡‘(±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘]óTµ:±cle‘ÿ}'arŽ‘(Ù¬(‘ª¨);Ž¡‘°gŽ¡‘­ifŽ‘)´û¬(±r–ÿ}'e“ctanglesŽ‘+ Eµ:±sizeŽ‘\¬(‘ª¨)–ǵ>“¬0Ž‘Ç)‘°fŽ¡‘(­forŽ‘9芬(­v®9ectorŽ‘ªH°h­RectangleŽ‘5”ê°Ž‘:”ëi‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZr–ÿ}'e“ctanglesŽ–.g]µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZr–ÿ}'e“ctanglesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)Ž¡‘2(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±cle‘ÿ}'arŽ‘(Ù¬(‘ª¨);Ž¡‘(±r–ÿ}'e“ctanglesŽ‘S Iµ:±cle‘ÿ}'arŽ‘(Ù¬(‘ª¨);Ž¡‘°gŽŽŽŒ‹e­ Šn ý‘ì°x¬1347–¯3DLDF-1.1.5.1’U­ASSIGNMENT“¬399Ž €n ý•@P­1347.‘ ü¬No¸ãw,›zcreate–oƒnew“­P®9athŽ‘ç¬,˜­CircleŽ‘!¦¬,˜­EllipseŽ‘$†S¬,˜­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘D.¬,˜and“­RectangleŽ‘7›¬p•Goin¸ãters,˜allo“cate‘oƒmemoryŽ¤ for–øÙthem,›!ºassign“v‘ÿqÇalues“to“the“ob‘Ž8jects“they“pGoin¸ãt“to“from“µsŽ‘¨Ù¬,˜and“push“them“onš¸ãto“the“appropriate“v˜ectors.Ž¡[²LDF‘T2002.10.02.¬]ŽŽ©°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¡‘ +­P®9athŽ‘& \°Ž‘+ ]µpŽ‘0]¬;‘z÷­forŽ‘‰¬(­v®9ectorŽ‘ªH°h­P®9athŽ‘ [°Ž‘! \i‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘WSʬ=‘ѵsŽ–µÑ:±p‘ÿ}'athsŽ›­µ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);‘%Ÿ±iterŽ‘ön°6¬=‘ѵsŽ“:±p‘ÿ}'athsŽ˜µ:±endŽ‘ಬ(‘ª¨);‘¥ŸŸÿ³+‘ÿ+ŽŽ‘l¿±iterŽ‘"7½¬)‘z÷°fŽ¡‘µpŽ‘%Ϭ=‘DZcr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘5¬1µ<‘UU­P®9athŽ‘­Ñµ>‘Ǭ(0Ž‘);Ž¦‘ +±p‘ÿ}'athsŽ‘!®µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(µpŽ‘¬);Ž¡‘ +°Ž‘¬(±p‘ÿ}'athsŽ‘­µ:±b‘ÿ}'ackŽ‘üì(›ª¨))–G"=“°Ž‘ G#Ž‘G$±iterŽ‘"¬;–;ðg“­forŽ‘ +·¬(­v®9ectorŽ‘ªH°h­CircleŽ‘"žï°Ž‘'žði‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘X•¬=‘G"µsŽ‘÷":±cir‘ÿ}'clesŽ‘Œdµ:±b–ÿ}'e“ginŽ‘¾¨¬(˜);Ž¡‘±iterŽ‘1’°6¬=‘ǵsŽ‘w:±cir‘ÿ}'clesŽ‘Œdµ:±endŽ‘ಬ(‘ª¨);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)–UU°f“±cir‘ÿ}'clesŽ‘á¹µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(“±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<“­CircleŽ‘$™µ>‘Ǭ(0Ž‘)“)“;Ž¡‘ +°Ž‘¬(±cir‘ÿ}'clesŽ‘Œdµ:±b‘ÿ}'ackŽ‘üì(›ª¨))–ûÞ=“°Ž‘ûߎ‘ ûà±iterŽ‘ÆÞ¬;–™°g“­forŽ‘°c¬(­v®9ectorŽ‘ªH°h­EllipseŽ‘%÷r°Ž‘*÷si‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘XI׬=‘ûÞµsŽ‘«Þ:±el‘‚ØlipsesŽ‘ ‚qµ:±b–ÿ}'e“ginŽ‘¾¨¬(˜);Ž¡‘±iterŽ‘1’°6¬=‘ǵsŽ‘w:±el‘‚ØlipsesŽ‘ ‚qµ:±endŽ‘ಬ(‘ª¨);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)–UU°f“±el‘‚ØlipsesŽ‘#×Ƶ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(“±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<“­EllipseŽ‘(Fµ>‘Ǭ(0Ž‘)“)“;Ž¡‘ +°Ž‘¬(±el‘‚ØlipsesŽ‘ ‚qµ:±b‘ÿ}'ackŽ‘üì(›ª¨))–Ç=“°Ž‘ÇŽ‘ DZiterŽ‘’¬;–â6°g“­forŽ‘W¬(­v®9ectorŽ‘ªH°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘D`ê°Ž‘I`ëi‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘ǵsŽ‘w:±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óPµ:±b–ÿ}'e“ginŽ‘¾¨¬(˜);Ž¡‘±iterŽ‘1 e°6¬=‘ÕdµsŽ‘…d:±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óPµ:±endŽ‘ಬ(‘ª¨);‘ˆ‘Ÿÿ³+‘ÿ+ŽŽ‘O±±iterŽ‘"¯¬)–]é°f“±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘9Q9µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.¶;¬(“±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6K–µ<“­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘G²µ>‘Õd¬(0Ž‘)Ž¡‘)‘UU;Ž¡‘ +°Ž‘¬(±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óPµ:±b‘ÿ}'ackŽ‘üì(›ª¨))–Ç=“°Ž‘ÇŽ‘ DZiterŽ‘’¬;–3‹°g“­forŽ‘úG¬(­v®9ectorŽ‘ªH°h­RectangleŽ‘5s 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ushŽ‘€¬;Ž¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"rectangles.size()® ´=Ž‘kÆÜ=® ´"Ž‘~ÔS°‘DZr–ÿ}'e“ctanglesŽ‘.g]µ:±sizeŽ‘\¬(‘ª¨)–Ç°“±end‘‚ØlŽ‘ò°“± ushŽ‘€¬;Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Exiting® ´Solid::operŽ‘kÆÜator=().\n"Ž’¦ #¬;Ž¡‘ +­returnŽ‘-æ»°Ž‘2æ¼±thisŽ‘CÒr¬;‘UU°gŽŸ­1348.‘ üCop®9ying.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.05.06.¬]Ž‘X—¶BUG›ä³FIX:–äÐChanged“µsŽ‘ +y ¬from“­ShapQÇeŽ‘$µ­°Ž‘,š~¬to“­SolidŽ‘Gw°Ž‘$Gx¬.‘LFI˜noticed“this“bug“when“I˜tried“to“cop¸ãyŽ¡a‘UU­PictureŽ‘,F·¬conš¸ãtaining–UUa“­CubQÇoidŽ‘(¤ï¬,“and“the“cop˜y“con˜tained“a“single“empt˜y“­ShapQÇeŽ‘%–·°Ž‘-ì ¬on“±shap‘ÿ}'esŽ‘ CÞ¬.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔShapQÇeŽ‘QÏ6°Ž‘VÏ7±get‘‰ffŽ‘®c‘ÿ}'opyŽ‘{’ë¬(‘ª®)‘UU­constŽ‘*¢¬;ŽŸ­1349.Ž¦°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¡‘ +­ShapQÇeŽ‘,Ac°Ž‘1Ad­SolidŽ‘K¿?¬::‘±get‘‰ffŽ‘®c‘ÿ}'opyŽ‘%ø¬(‘ª®)‘UU­constŽ‘*¢°f‘UU­SolidŽ‘ (°Ž‘%(‚µsŽ‘--׬=‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­SolidŽ‘šDµ>‘Ǭ(0Ž‘);Ž¦‘°Ž‘#µsŽ‘*w¬=‘Ç°Ž‘DZthisŽ‘²Ï¬;Ž¡‘­returnŽ‘Aæ½dynamicu½‰™šs4Ž‘ÔwcastŽ’…WŽ°h­ShapQÇeŽ‘"Ab°Ž‘'Aci¬(µsŽ‘°¬);‘UU°gŽŸ­1350.‘ üSet–ÕTon“free“store.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2004.01.06.¬]Ž‘Y;Made‘UUnon-inline.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/Ôb•QÇo“olŽ‘I/:±set‘‰ffŽ–®on‘‰ffŽ“fr–ÿ}'e“e‘‰ffŽ‘®stor“eŽ’…¬(­b•QÇo“olŽ‘¡fµbŽ‘ ³(¬=‘DZtrueŽ‘‹°¬);ŽŽŽŒ‹u Šn ý‘ì¬400›¯SET–ÕXON“FREE“STORE’úSÇ3DLDF-1.1.5.1˜°x¬1351Ž €n ý•@P­1351.Ž©°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¤ ‘ +­b•QÇo“olŽ‘#¡gSolidŽ‘>B¬::‘±set‘‰ffŽ–®on‘‰ffŽ“fr–ÿ}'e“e‘‰ffŽ‘®stor“eŽ‘HUÛ¬(­b•QÇo“olŽ‘¡fµbŽ‘ì¬)Ž¡‘ +°fŽ¡‘±on‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘Nl ¬=‘ǵbŽ‘¬;Ž¡‘­returnŽ‘7æ¼µbŽ‘<1f¬;Ž¡‘ +°gŽŸ­1352.› üReturning–ÕTelemen®9ts“and“information.˜¬[²LDF‘T2003.04.11.¬]Ž‘Zˆ6The–UUfunctions“±get‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ‘<ö¹¬(‘ª®),Ž¡±get‘‰ffŽ–®cir‘ÿ}'cle‘‰ffŽ“ptrŽ‘9??¬(–ª®),‘§Z±get‘‰ffŽ–®el‘‚Ølipse‘‰ffŽ“ptrŽ‘Aܦ¬(“),‘§Z±get‘‰ffŽ–®p‘ÿ}'ath‘‰ffŽ“ptrŽ‘8êâ¬(“),‘§Z±get‘‰ffŽ›®r–ÿ}'e“ctangle‘‰ffŽ˜ptrŽ‘Lúz¬(“),‘§Zand‘cÀ±get‘‰ffŽ›®r–ÿ}'e“g‘‰ffŽ˜p“olygon‘‰ffŽ˜ptrŽ‘W ë¬(“)–cÀall“returnŽ¡­constŽ‘¤ð¬pGoinš¸ãters–Ï£to“­ShapQÇeŽ‘"»°¬,‘î6­CircleŽ‘"Qb¬,‘î6­EllipseŽ‘%׬,–î6etc.‘à±Therefore,“they–Ï£m˜ust“bGe“in˜v˜ok˜ed“in“suc˜h“a“w˜a˜y‘ÿ*ª,‘î6that“theŽ¡­constŽ‘뜬quali er–Ois“not“discarded.‘\ÅF‘ÿ*ªor“example,›"êfollo¸ãwing“­DoQÇdecahedronŽ‘Nì,µdŽ‘T ž¬(±originŽ‘ö!µ;‘ª¨¬5Ž‘ª©);,˜t•¸ãw“o›Ow“a“ys˜of˜in“v“okingŽ¡±get‘‰ffŽ›®r–ÿ}'e“g‘‰ffŽ˜p“olygon‘‰ffŽ˜ptrŽ–R¦+¬(‘ª®)›UUare:‘qÇ­constŽ‘"œiRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘gpr°Ž‘lps±ptrŽ‘}tR¬=‘ǵdŽ‘ûŠ:±get‘‰ffŽ›®r–ÿ}'e“g‘‰ffŽ˜p“olygon‘‰ffŽ˜ptrŽ“¬(5Ž‘);˜andŽ¡­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘DÔ µAŽ‘O"¬=‘Ç°Ž‘ǵdŽ‘ û‹:±get‘‰ffŽ›®r–ÿ}'e“g‘‰ffŽ˜p“olygon‘‰ffŽ˜ptrŽ‘R¦+¬(5Ž‘);.ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.05.09.¬]Ž‘Y;Changed–UUthe“names“of“±get‘‰ffŽ‘®shap‘ÿ}'eŽ‘,O¬(›ª®),“±get‘‰ffŽ‘®cir‘ÿ}'cleŽ‘+ìï¬(˜),“±get‘‰ffŽ‘®el‘‚ØlipseŽ‘/âü¬(˜),“±get‘‰ffŽ‘®p‘ÿ}'athŽ‘&õ@¬(˜),Ž¡±get‘‰ffŽ‘®r–ÿ}'e“ctangleŽ‘7«{¬(›ª®),–UUand“±get‘‰ffŽ›®r–ÿ}'e“g‘‰ffŽ˜p“olygonŽ‘EWã¬(˜)“to“±get‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ‘<ö¹¬(˜),“±get‘‰ffŽ–®cir‘ÿ}'cle‘‰ffŽ“ptrŽ‘<””¬(˜),“±get‘‰ffŽ–®el‘‚Ølipse‘‰ffŽ“ptrŽ‘@Š¡¬(˜),“±get‘‰ffŽ–®p‘ÿ}'ath‘‰ffŽ“ptrŽ‘7˜Ý¬(˜),Ž¡±get‘‰ffŽ›®r–ÿ}'e“ctangle‘‰ffŽ˜ptrŽ‘HS ¬(–ª®),›Fand‘¶±get‘‰ffŽ›®r–ÿ}'e“g‘‰ffŽ˜p“olygon‘‰ffŽ˜ptrŽ‘W\A¬(“).‘” The–¶names“without“\‘‰ffŽ‘®±ptrŽ‘êÚ¬"“w¸ãere“confusing,˜bGecause“theyŽ¡didn't–UUmakš¸ãe“clear“that“the“functions“returned“pGoin˜ters.Ž¦ŸüÈ„`ÕÁGŽŽŸ­1353.‘ üGet‘ÕTcen®9ter.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.05.06.¬]Ž‘Y;Added–UUthis“function.Ž¡‘ +[²LDF‘T2003.08.10.¬]Ž‘Y;Made–UUthis“function“­constŽ‘*¢¬.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔconstŽ‘M¸vP•®9oin“tŽ‘l¨¬&Ž‘to1±get‘‰ffŽ‘®c‘ÿ}'enterŽ’ ¬x¬(‘ª®)‘UU­constŽ‘*¢¬;ŽŸ­1354.Ž¦°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¡‘ +­constŽ‘(*£P•®9oin“tŽ‘G@¬&Ž‘Ná^­SolidŽ‘i_9¬::‘±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘-=K¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼±c‘ÿ}'enterŽ‘SðG¬;Ž¡‘ +°gŽŸ­1355.‘ üGetting‘ÕTShapQÇes.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.04.30.¬]Ž‘Y;Changed–UUthe“functions“±get‘‰ffŽ–®cir‘ÿ}'cle‘‰ffŽ“ptrŽ‘<””¬(›ª®),“±get‘‰ffŽ–®el‘‚Ølipse‘‰ffŽ“ptrŽ‘@Š¡¬(˜),“±get‘‰ffŽ–®p‘ÿ}'ath‘‰ffŽ“ptrŽ‘7˜Ý¬(˜),Ž¡±get‘‰ffŽ›®r–ÿ}'e“ctangle‘‰ffŽ˜ptrŽ‘HS ¬(–ª®),‘T`and‘T"±get‘‰ffŽ›®r–ÿ}'e“g‘‰ffŽ˜p“olygon‘‰ffŽ˜ptrŽ‘UúM¬(“).›qaThey–T"no“longer“use“±get‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ‘<õ†¬(‘ª®).˜There's“no“go•Go“d‘T"reasonŽ¡for–UUcasting“pGoinš¸ãters“from“one“t˜ypGe“to“another.‘qÇI“rather“doubt“that“±get‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ‘<ö¹¬(‘ª®)“is“needed,“an˜yw˜a˜y‘ÿ*ª.Ž¦ŸüÈ„`ÕÁGŽŽŽŽŒ‹‘Œk Šn ý‘ì°x¬1356›¯3DLDF-1.1.5.1’ø MGET–ÕXSHAPE“POINTER˜¬401Ž €n ý•@P­1356.‘ üGet–%ShapšQÇe“p˜oin®9ter.‘ ü¬[²LDF‘T2003.05.30.¬]Ž‘[¬)This–yHfunction“copies“one“of“the“ob‘Ž8jects“on“one“of“theŽ¤ v¸ãectors–íSof“­ShapQÇeŽ‘(Ƴ°Ž‘2´¬bšGelonging“to“the“­SolidŽ‘k*¬,‘SRand“returns“a“p˜oin¸ãter“to“­ShapQÇeŽ‘(Ƴ¬that“p˜oinš¸ãts“to“the“cop˜y‘ÿ*ª.Ž¡Curren•¸ãtly‘ÿ*ª,›Ina‘Ft­SolidŽ‘ +¿¬con“tains–Ftthe“v¸ãectors“±cir‘ÿ}'clesŽ‘Òج,˜±el‘‚ØlipsesŽ‘#Ë߬,˜±p‘ÿ}'athsŽ‘Ú¬,˜±r–ÿ}'e“ctanglesŽ‘.鳬,˜and“±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘99Ĭ.‘lÑThe“argumen¸ãtŽ¡±shap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘1öجindicates–"whicš¸ãh“v˜ector“should“bšGe“accessed.‘Ø +Normally‘ÿ*ª,‘UFthe“corresp˜onding“­publicŽ‘'‚staticŽ‘G—›constŽŽ¡¬data–mmem¸ãbšGers“´CIRCLEŽ‘$só¬,‘³¯´ELLIPSEŽ‘)ú¬,‘³¯´PATHŽ‘: ¬,‘³¯´RECTANGLEŽ‘4yü¬,‘³¯or“´REG_POLYGONŽ‘C!¬should“b˜e“passed“as“the“±shap–ÿ}'e‘‰ffŽ‘®typ“eŽŽ¡¬argumen¸ãt,–UUe.g.,“­CircleŽ‘% Ö°Ž‘* ×±c‘‰ffŽ‘®ptrŽ‘Cç¬=“­staticu½‰™šs4Ž‘ÔwcastŽ‘7Ò÷°h­CircleŽ‘!¸°Ž‘&¸‚i¬(±get‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ‘9¡d¬(­SolidŽ‘}Û¬::Ž‘! ´CIRCLEŽ‘Aoµ;‘ª¨¬3Ž‘ª©)).Ž¡‘ +[²LDF‘T2003.04.30.¬]Ž‘Y;This–UUfunction“wš¸ãas“mainly“in˜tended“for“use“in“the“functions“±get‘‰ffŽ–®cir‘ÿ}'cle‘‰ffŽ“ptrŽ‘<””¬(‘ª®),Ž¡±get‘‰ffŽ–®el‘‚Ølipse‘‰ffŽ“ptrŽ‘=5L¬(‘ª®),–Ãetc.,“and–ž†wš¸ãas“not“in˜tended“for“use“in“user“coGde.‘4ØI‘žWno˜w“doubt“whether“this“function“is“neededŽ¡at–UUall,“espšGecially“since“it“is“no“longer“used“in“the“functions“men¸ãtioned“ab˜o•¸ãv“e.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.04.11.¬]Ž‘Y;Added–UUthis“function.Ž¡‘ +[²LDF‘T2003.04.30.¬]Ž‘XM5Noš¸ãw–šOusing“±get‘‰ffŽ‘®c‘ÿ}'opyŽ‘'^¬(‘ª®)“instead“of“­staticu½‰™šs4Ž‘ÔwcastŽ‘7ñ°h­constŽ‘oœShapQÇeŽ‘>õø°Ž‘Cõùi¬(‘ª¨).‘3pThe“w˜a˜y“it“w˜as“causedŽ¡compilation–UUerrors“under“T‘ÿ*ªru64“(DEC“ALPHA).Ž¡‘ +[²LDF‘T2003.05.30.¬]Ž‘XïChanged–<return“v‘ÿqÇalue“to“­ShapQÇeŽ‘%dG°Ž‘- e¬from“­constŽ‘!M‡ShapQÇeŽ‘Cu±°Ž‘Hu²¬.‘i_The“w•¸ãa“y–<it“w¸ãas“bGefore“causedŽ¡\Memory–UUfault"“errors“at“run-time.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°ŽŸ ‘ +­virtualŽ‘/ÔShapQÇeŽ‘QÏ6°Ž‘VÏ7±get‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ’p›¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±shap–ÿ}'e‘‰ffŽ‘®typ“eŽ’šµ;‘ª¨­constŽ‘ÕJunsignedŽ‘P XshortŽ‘mÖûµsŽ‘r†û¬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹’e Šn ý‘ì¬402›¯GET–ÕXSHAPE“POINTER’ø M3DLDF-1.1.5.1˜°x¬1357Ž €n ý•@P­1357.Ž©°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¤ ‘ +­ShapQÇeŽ‘,Ac°Ž‘1Ad­SolidŽ‘K¿?¬::‘±get‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ‘:¡h¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,S±shap–ÿ}'e‘‰ffŽ‘®typ“eŽ’šµ;‘ª¨­constŽ‘ÕJunsignedŽ‘P XshortŽ‘mÖûµsŽ‘r†û¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­b•QÇo“olŽ‘-¡h´DEBUGŽ‘K.Ù¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¦‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"Entering® ´Solid::getŽ‘kÆÜ_shape_ptr().\n"Ž’Ã,°‘DZ ushŽ‘€¬;Ž¡‘°gŽ¡‘­ifŽ‘´ú¬(±shap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘0›Ú°‘Ç´CIRCLEŽ‘"Ín¬)‘°fŽ¡‘­ifŽ‘)´û¬(µsŽ‘w<‘DZcir‘ÿ}'clesŽ‘S|µ:±sizeŽ‘\¬(‘ª¨))‘°fŽ¡‘(­returnŽ‘Kæ¾±cir‘ÿ}'clesŽ‘hs"¬[µsŽ‘°¬]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®c‘ÿ}'opyŽ‘(õ¬(‘ª¨);Ž¡‘°gŽ¡‘­elseŽ‘5Øâ°fŽ¡‘(±c‘ÿ}'errŽ‘=|°‘Ç´"ERROR!® ´In® ´Solid::geŽ‘kÆÜt_shape_ptr():\n"Ž’ÈT)°‘Ç´"s® ´("Ž‘ T‰°‘ǵsŽ‘ +>0°‘Ç´")® ´>® ´circles.size()® Ž‘kÆÜ´("Ž‘y”V°Ž¡‘<±cir‘ÿ}'clesŽ‘XŒjµ:±sizeŽ‘\¬(‘ª¨)–Ç°“´")\nReturning® ´a® ´nullŽ‘kÆÜ® ´pointer® ´(0).\n\n"Ž’Í”&°“± ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾staticu½‰™šs4Ž‘ÔwcastŽ’€d`°h­ShapQÇeŽ‘"Ab°Ž‘'Aci¬(0Ž‘);Ž¡‘°gŽ¡‘gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±shap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘0›Ú°‘Ç´ELLIPSEŽ‘( k¬)‘°fŽ¡‘­ifŽ‘)´û¬(µsŽ‘w<‘DZel‘‚ØlipsesŽ‘#I‰µ:±sizeŽ‘\¬(‘ª¨))‘°fŽ¡‘(­returnŽ‘Kæ¾±el‘‚ØlipsesŽ‘li/¬[µsŽ‘°¬]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®c‘ÿ}'opyŽ‘(õ¬(‘ª¨);Ž¡‘°gŽ¡‘­elseŽ‘5Øâ°fŽ¡‘(±c‘ÿ}'errŽ‘A è°‘T>´"ERROR!® ´In® ´Solid::geŽ‘oTt_shape_ptr():\n"Ž’Ïnu°‘T>´"s® ´("Ž‘'nÕ°Ž¡‘<µsŽ‘GÎì°‘æ´")® ´>® ´ellipses.size()Ž‘pª® ´("Ž’‡ƒï°‘æ±el‘‚ØlipsesŽ‘'¡Wµ:±sizeŽ‘\¬(‘ª¨)‘æ°Ž¡‘<´")\nReturning® ´a® ´nullŽ’¤ÿÊ® ´pointer® ´(0).\n\n"Ž’Í°‘DZ ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾staticu½‰™šs4Ž‘ÔwcastŽ’€d`°h­ShapQÇeŽ‘"Ab°Ž‘'Aci¬(0Ž‘);Ž¡‘°gŽ¡‘gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±shap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘0›Ú°‘Ç´PATHŽ‘Mt¬)‘°fŽ¡‘­ifŽ‘)´û¬(µsŽ‘w<‘DZp‘ÿ}'athsŽ‘Wŵ:±sizeŽ‘\¬(‘ª¨))‘°fŽ¡‘(­returnŽ‘Kæ¾±p‘ÿ}'athsŽ‘cwk¬[µsŽ‘°¬]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®c‘ÿ}'opyŽ‘(õ¬(‘ª¨);Ž¡‘°gŽ¡‘­elseŽ‘5Øâ°fŽ¡‘(±c‘ÿ}'errŽ‘=•$°‘ßz´"ERROR!® ´In® ´Solid::geŽ‘kß>t_shape_ptr():\n"Ž’È„í°‘ßz´"s® ´("Ž‘ …M°‘ßzµsŽ‘ +nô°‘ßz´")® ´>® ´paths.size()® ´("Ž‘oE °Ž¡‘<±p‘ÿ}'athsŽ‘S³µ:±sizeŽ‘\¬(‘ª¨)–Ç°“´")\nReturning® ´a® ´nullŽ‘kÆÜ® ´pointer® ´(0).\n\n"Ž’Í”&°“± ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾staticu½‰™šs4Ž‘ÔwcastŽ’€d`°h­ShapQÇeŽ‘"Ab°Ž‘'Aci¬(0Ž‘);Ž¡‘°gŽ¡‘gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±shap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘0›Ú°‘Ç´RECTANGLEŽ‘2e¬)‘°fŽ¡‘­ifŽ‘)´û¬(µsŽ‘w<‘DZr–ÿ}'e“ctanglesŽ‘.g]µ:±sizeŽ‘\¬(‘ª¨))‘°fŽ¡‘(­returnŽ‘Kæ¾±r–ÿ}'e“ctanglesŽ‘w‡¬[µsŽ‘°¬]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®c‘ÿ}'opyŽ‘(õ¬(‘ª¨);Ž¡‘°gŽ¡‘­elseŽ‘5Øâ°fŽ¡‘(±c‘ÿ}'errŽ‘A è°‘T>´"ERROR!® ´In® ´Solid::geŽ‘oTt_shape_ptr():\n"Ž’Ïnu°‘T>´"s® ´("Ž‘'nÕ°Ž¡‘<µsŽ‘GGô°‘—î´")® ´>® ´rectangles.sizeŽ‘o—²()® ´("Ž’õù°‘—î±r–ÿ}'e“ctanglesŽ‘283µ:±sizeŽ‘\¬(‘ª¨)‘—î°Ž¡‘<´")\nReturning® ´a® ´nullŽ’¤ÿÊ® ´pointer® ´(0).\n\n"Ž’Í°‘DZ ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾staticu½‰™šs4Ž‘ÔwcastŽ’€d`°h­ShapQÇeŽ‘"Ab°Ž‘'Aci¬(0Ž‘);Ž¡‘°gŽ¡‘gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±shap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘0›Ú°‘Ç´REG_POLYGONŽ‘= _¬)‘°fŽ¡‘­ifŽ‘)´û¬(µsŽ‘w<‘DZr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºhµ:±sizeŽ‘\¬(‘ª¨))‘°fŽŽŽŒ‹“§± Šn ý‘ì°x¬1357›¯3DLDF-1.1.5.1’ø MGET–ÕXSHAPE“POINTER˜¬403Ž €n ý•@P‘(­returnŽ‘Kæ¾±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ’Ú¬[µsŽ‘°¬]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®c‘ÿ}'opyŽ‘(õ¬(‘ª¨);Ž¤ ‘°gŽ¡‘­elseŽ‘5Øâ°fŽ¡‘(±c‘ÿ}'errŽ‘A è°‘T>´"ERROR!® ´In® ´Solid::geŽ‘oTt_shape_ptr():\n"Ž’Ïnu°‘T>´"s® ´("Ž‘'nÕ°Ž¡‘<µsŽ‘FÅî°‘è´")® ´>® ´reg_polygons.siŽ‘o¬ze()® ´("Ž’šqç°‘è±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘< 8µ:±sizeŽ‘\¬(‘ª¨)‘è°Ž¡‘<´")\nReturning® ´a® ´nullŽ’¤ÿÊ® ´pointer® ´(0).\n\n"Ž’Í°‘DZ ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾staticu½‰™šs4Ž‘ÔwcastŽ’€d`°h­ShapQÇeŽ‘"Ab°Ž‘'Aci¬(0Ž‘);Ž¡‘°gŽ¡‘gŽ¡‘­elseŽ‘+Øá°fŽ¡‘±c‘ÿ}'errŽ‘3ÓK°‘¢´"ERROR!® ´In® ´Solid::geŽ‘lft_shape_ptr():\n"Ž’É=°‘¢´"Invalid® ´value® ´for® ´sŽ‘lfhape_type:® ´"Ž’®ÁL°Ž¡‘2±shap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘b›ß°‘DZend‘‚ØlŽ‘ò°‘Ç´"Returning® ´a® ´null® ´poŽ‘kÆÜinter® ´(0).\n\n"Ž’½Ô/°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½staticu½‰™šs4Ž‘ÔwcastŽ‘vd_°h­ShapQÇeŽ‘"Ab°Ž‘'Aci¬(0Ž‘);Ž¡‘°gŽ¡‘ +gŽ©­1358.‘ üGet–ÕTCircle“pQÇoin®9ter.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.04.11.¬]Ž‘Y;Added–UUthis“function.Ž¡‘ +[²LDF‘T2003.04.30.¬]Ž‘Y;Changed–UUthis“function,“so“that“it“no“longer“uses“±get‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ‘<ö¹¬(‘ª®).Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°ŽŸ ‘ +­virtualŽ‘/ÔconstŽ‘M¸vCircleŽ‘op÷°Ž‘tpø±get‘‰ffŽ–®cir‘ÿ}'cle‘‰ffŽ“ptrŽ’­°7¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµsŽ‘pÜS¬)‘UU­constŽ‘*¢¬;Ž¦­1359.Ž¡°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¤ ‘ +­constŽ‘(*£CircleŽ‘Iã$°Ž‘Nã%­SolidŽ‘ia¬::‘±get‘‰ffŽ–®cir‘ÿ}'cle‘‰ffŽ“ptrŽ‘:?C¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµsŽ‘pÜS¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­ifŽ‘´ú¬(±cir‘ÿ}'clesŽ‘Œdµ:±sizeŽ‘\¬(‘ª¨)–ǵ>“sŽ‘w¬)‘°fŽ¡‘­returnŽ‘Aæ½±cir‘ÿ}'clesŽ‘^s!¬[µsŽ‘°¬];Ž¡‘°gŽ¡‘­elseŽ‘+Øá°fŽ¡‘­returnŽ‘Aæ½staticu½‰™šs4Ž‘ÔwcastŽ‘vd_°h­constŽ‘*¢CircleŽ‘?ã#°Ž‘Dã$i¬(0Ž‘);Ž¡‘°gŽ¡‘ +gŽ¦­1360.‘ üGet–ÕTEllipse“pQÇoin®9ter.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.04.11.¬]Ž‘Y;Added–UUthis“function.Ž¡‘ +[²LDF‘T2003.04.30.¬]Ž‘Y;Changed–UUthis“function,“so“that“it“no“longer“uses“±get‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ‘<ö¹¬(‘ª®).Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°ŽŸ ‘ +­virtualŽ‘/ÔconstŽ‘M¸vEllipseŽ‘rö¤°Ž‘wö¥±get‘‰ffŽ–®el‘‚Ølipse‘‰ffŽ“ptrŽ’µ+ñ¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµsŽ‘pÜS¬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹”¶n Šn ý‘ì¬404›¯GET–ÕX­ELLIPSE“¯POINTER’傆3DLDF-1.1.5.1˜°x¬1361Ž €n ý•@P­1361.Ž©°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¤ ‘ +­constŽ‘(*£EllipseŽ‘MhÑ°Ž‘RhÒ­SolidŽ‘læ­¬::‘±get‘‰ffŽ–®el‘‚Ølipse‘‰ffŽ“ptrŽ‘>5P¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµsŽ‘pÜS¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­ifŽ‘´ú¬(±el‘‚ØlipsesŽ‘ ‚qµ:±sizeŽ‘\¬(‘ª¨)–ǵ>“sŽ‘w¬)‘°fŽ¡‘­returnŽ‘Aæ½±el‘‚ØlipsesŽ‘bi.¬[µsŽ‘°¬];Ž¡‘°gŽ¡‘­elseŽ‘+Øá°fŽ¡‘­returnŽ‘Aæ½staticu½‰™šs4Ž‘ÔwcastŽ‘vd_°h­constŽ‘*¢EllipseŽ‘ChаŽ‘HhÑi¬(0Ž‘);Ž¡‘°gŽ¡‘ +gŽŸ­1362.‘ üGet–ÕTPš®9ath“pQÇoin˜ter.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.04.11.¬]Ž‘Y;Added–UUthis“function.Ž¡‘ +[²LDF‘T2003.04.30.¬]Ž‘Y;Changed–UUthis“function,“so“that“it“no“longer“uses“±get‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ‘<ö¹¬(‘ª®).Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔconstŽ‘M¸vP®9athŽ‘iŸ/°Ž‘nŸ0±get‘‰ffŽ–®p‘ÿ}'ath‘‰ffŽ“ptrŽ’¢â¸¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµsŽ‘pÜS¬)‘UU­constŽ‘*¢¬;ŽŸ­1363.Ž¦°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¡‘ +­constŽ‘(*£P®9athŽ‘D\°Ž‘I]­SolidŽ‘c8¬::‘±get‘‰ffŽ–®p‘ÿ}'ath‘‰ffŽ“ptrŽ‘5CŒ¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµsŽ‘pÜS¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­ifŽ‘´ú¬(±p‘ÿ}'athsŽ‘­µ:±sizeŽ‘\¬(‘ª¨)–ǵ>“sŽ‘w¬)‘°fŽ¡‘­returnŽ‘Aæ½±p‘ÿ}'athsŽ‘Ywj¬[µsŽ‘°¬];Ž¡‘°gŽ¡‘­elseŽ‘+Øá°fŽ¡‘­returnŽ‘Aæ½staticu½‰™šs4Ž‘ÔwcastŽ‘vd_°h­constŽ‘*¢P®9athŽ‘:[°Ž‘?\i¬(0Ž‘);Ž¡‘°gŽ¡‘ +gŽŸ­1364.‘ üGet–ÕTRectangle“pQÇoin®9ter.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.04.11.¬]Ž‘Y;Added–UUthis“function.Ž¡‘ +[²LDF‘T2003.04.30.¬]Ž‘Y;Changed–UUthis“function,“so“that“it“no“longer“uses“±get‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ‘<ö¹¬(‘ª®).Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔconstŽ‘M¸vRectangleŽ’ƒM`°Ž’ˆMa±get‘‰ffŽ›®r–ÿ}'e“ctangle‘‰ffŽ˜ptrŽ’Р¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµsŽ‘pÜS¬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹•ÁŠ Šn ý‘ì°x¬1365›¯3DLDF-1.1.5.1’ÌTVGET–ÕX­RECT‘ÿ +«ANGLE“¯POINTER˜¬405Ž €n ý•@P­1365.Ž©°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¤ ‘ +­constŽ‘(*£RectangleŽ‘]¿°Ž‘b¿Ž­SolidŽ‘}=i¬::‘±get‘‰ffŽ›®r–ÿ}'e“ctangle‘‰ffŽ˜ptrŽ‘IS$¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµsŽ‘pÜS¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­ifŽ‘´ú¬(±r–ÿ}'e“ctanglesŽ‘+ Eµ:±sizeŽ‘\¬(‘ª¨)–ǵ>“sŽ‘w¬)‘°fŽ¡‘­returnŽ‘Aæ½±r–ÿ}'e“ctanglesŽ‘m‡¬[µsŽ‘°¬];Ž¡‘°gŽ¡‘­elseŽ‘+Øá°fŽ¡‘­returnŽ‘Aæ½staticu½‰™šs4Ž‘ÔwcastŽ‘vd_°h­constŽ‘*¢RectangleŽ‘S¿Œ°Ž‘X¿i¬(0Ž‘);Ž¡‘°gŽ¡‘ +gŽŸ­1366.‘ üGet–ÕTReg‘°¡‰ffs4Ž‘#ÕPš®9olygon“pQÇoin˜ter.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.04.11.¬]Ž‘Y;Added–UUthis“function.Ž¡‘ +[²LDF‘T2003.04.30.¬]Ž‘Y;Changed–UUthis“function,“so“that“it“no“longer“uses“±get‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ‘<ö¹¬(‘ª®).Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔconstŽ‘M¸vRegu½‰™šs4Ž‘ÔwP®9olygonŽ’’Œ°Ž’—Œ€±get‘‰ffŽ›®r–ÿ}'e“g‘‰ffŽ˜p“olygon‘‰ffŽ˜ptrŽ’ê2«¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµsŽ‘pÜS¬)‘UU­constŽ‘*¢¬;ŽŸ­1367.Ž¦°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¡‘ +­constŽ‘(*£Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘lþ¬°Ž‘qþ­­SolidŽ’Œ|ˆ¬::‘±get‘‰ffŽ›®r–ÿ}'e“g‘‰ffŽ˜p“olygon‘‰ffŽ˜ptrŽ‘S¦/¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµsŽ‘pÜS¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­ifŽ‘´ú¬(±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óPµ:±sizeŽ‘\¬(‘ª¨)–ǵ>“sŽ‘w¬)‘°fŽ¡‘­returnŽ‘Aæ½±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘wÚ ¬[µsŽ‘°¬];Ž¡‘°gŽ¡‘­elseŽ‘+Øá°fŽ¡‘­returnŽ‘Aæ½staticu½‰™šs4Ž‘ÔwcastŽ‘vd_°h­constŽ‘*¢Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘bþ«°Ž‘gþ¬i¬(0Ž‘);Ž¡‘°gŽ¡‘ +gŽŸ­1368.› üGetting– ÍShapQÇe“cen®9ters.˜¬[²LDF‘T2003.04.30.¬]Ž‘[—TO–cèDO:›d.I“think˜it˜migh¸ãt˜b•Ge˜p“ossible˜to˜co“de˜theŽ¡functions–UUin“this“section“more“succinctly‘ÿ*ª.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.04.11.¬]Ž‘Y;Added–UUthis“section.Ž¦ŸüÈ„`ÕÁGŽŽŽŽŒ‹–Ê´ Šn ý‘ì¬406›¯GET–ÕXSHAPE“CENTER’û”Ù3DLDF-1.1.5.1˜°x¬1369Ž €n ý•@P­1369.› üGet–7•ShapQÇe“cen®9ter.˜¬This–‰afunction“returns“the“cen¸ãter“of“the“­CircleŽ‘"ì¬,‘Öd­EllipseŽ‘&¿=¬,‘Öd­RectangleŽ‘7ù¬,‘ÖdorŽ¤ ­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘E¼ž¬n•¸ãum“bšGer‘=êµsŽ‘ +Ô¬in‘=ê±cir‘ÿ}'clesŽ‘ ÊN¬,‘x±el‘‚ØlipsesŽ‘$ú¬,‘x±r–ÿ}'e“ctanglesŽ‘0S¬,–xor‘=ê±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:1:¬,“resp˜ectiv¸ãely‘ÿ*ª.‘+…If‘=êµsŽ‘ +Ô¬is–=êlarger“thanŽ¡°h±ve‘ÿ}'ctor‘°iµ:‘UU±sizeŽ‘p±¬(‘ª®),–UUan“error“message“is“issued“and“´INVALID_POINTŽ‘Kpë¬is“returned.Ž¡‘ +One–q)of“the“folloš¸ãwing“­publicŽ‘& 'staticŽ‘E„ÔconstŽ‘cËJ¬data“mem˜bšGers“of“­SolidŽ‘ `)¬can“(and“probably“should)“b˜e“used“asŽ¡the‘UU±shap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘4l¬argumen¸ãt:‘qÇ´CIRCLEŽ‘$x¬,‘UU´ELLIPSEŽ‘(›¨¬,‘UU´RECTANGLEŽ‘3¢¬,–UUand“´REG_POLYGONŽ‘=›œ¬.Ž¡‘ +!!‘ZNote–¢Æthat“this“function“will“ha•¸ãv“e–¢Æto“bGe“cš¸ãhanged,‘¶"if“new“v˜ectors“of“­ShapQÇeŽ‘&1™¬pGoin˜ters“are“added“to“­classŽŽ¡SolidŽ‘}׬!ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.10.16.¬]Ž‘Y;Added–UUthis“function.Ž¡‘ +[²LDF‘T2003.04.09.¬]Ž‘Y;Mo•¸ãv“ed–UUthis“function“from“­P®9olyhedronŽ‘@¸w¬to“­SolidŽ‘Ó,¬.Ž¡‘ +[²LDF‘T2003.04.11.¬]Ž‘X-ŸChanged–z¹this“function“from“±get‘‰ffŽ–®p›ÿ}'olygon‘‰ffŽ“c˜enterŽ‘RÚ¤¬(›ª®)“to“±get‘‰ffŽ–®shap›ÿ}'e‘‰ffŽ“c˜enterŽ‘Ièá¬(˜).‘(éAdded“the“­c®9harŽŽ¡¬argumenš¸ãt‘Á„±shap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘5Wʬto–Á„indicate“whether“it“should“return“the“cen˜ter“of“a“­CircleŽ‘"$°¬,‘Ü­EllipseŽ‘%Åi¬,‘Ü­RectangleŽ‘6%¬,‘ÜorŽ¡­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘A~´¬.Ž¡‘ +[²LDF‘T2003.04.11.¬]Ž‘Y;Changed–UUthe“±shap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘4l¬argumen¸ãt“from“­c®9harŽ‘¿ž¬to“­constŽ‘!÷unsignedŽ‘Q·shortŽ‘l,S¬.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°Ž¤ ‘ +­virtualŽ‘/˜;constŽ‘MÍDP•®9oin“tŽ‘lÇH¬&Ž‘tŽf±get‘‰ffŽ–®shap›ÿ}'e‘‰ffŽ“c˜enterŽ’»üŽ¬(­constŽ‘5 unsignedŽ‘Nv~shortŽ‘lKˆ±shap–ÿ}'e‘‰ffŽ‘®typ“eŽ’š Jµ;‘ª¨­constŽ‘ß±unsignedŽ‘P!&shortŽ‘mö0µsŽ‘r¦0¬)Ž¡‘­constŽ‘8ÕP¬;ŽŽŽŒ‹—Ó¸ Šn ý‘ì°x¬1370›¯3DLDF-1.1.5.1’û”ÙGET–ÕXSHAPE“CENTER˜¬407Ž €n ý•@P­1370.ŽŸ°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¤ ‘ +­constŽ‘(F(P•®9oin“tŽ‘GQJ¬&Ž‘Oh­SolidŽ‘i–C¬::‘±get‘‰ffŽ–®shap›ÿ}'e‘‰ffŽ“c˜enterŽ‘Hn,¬(­constŽ‘F'unsignedŽ‘N˜ºshortŽ‘l~â±shap–ÿ}'e‘‰ffŽ‘®typ“eŽ’šS¤µ;‘ª¨­constŽ‘ðÏunsignedŽ‘PCbshortŽ‘n)ŠµsŽ‘rÙŠ¬)Ž¡‘2­constŽŽ¡‘ +°fŽ¡‘­ifŽ‘´ú¬(±shap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘0›Ú°‘Ç´CIRCLEŽ‘"Ín¬)‘°fŽ¡‘­ifŽ‘)´û¬(µsŽ‘w<‘DZcir‘ÿ}'clesŽ‘S|µ:±sizeŽ‘\¬(–ª¨))‘­returnŽ‘(溱cir‘ÿ}'clesŽ‘Es¬[µsŽ‘°¬]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘0=H¬(“);Ž¡‘­elseŽ‘5Øâ°fŽ¡‘(±c‘ÿ}'errŽ‘@ W°‘S­´"ERROR!® ´In® ´Solid::geŽ‘nSqt_shape_center():\n"Ž’Ý-J°‘S­´"s® ´("Ž‘%m³°‘S­µsŽ‘WZ°Ž¡‘<´")® ´>® ´circles.size()® Ž’¤ÿÊ´("Ž’³>Ù°‘8­±cir‘ÿ}'clesŽ‘ŵ:±sizeŽ‘\¬(‘ª¨)–8­°“´")\nReturning® ´INVALIŽ‘l8qD_POINT.\n\n"Ž’´7_°Ž¡‘<± ushŽ‘Q¹¬;Ž¡‘(­returnŽ‘Kæ¾´INVALID_POINTŽ’¬ÿ¬;Ž¡‘°gŽ¡‘gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±shap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘0›Ú°‘Ç´ELLIPSEŽ‘( k¬)‘°fŽ¡‘­ifŽ‘)´û¬(µsŽ‘w<‘DZel‘‚ØlipsesŽ‘#I‰µ:±sizeŽ‘\¬(–ª¨))‘­returnŽ‘(溱el‘‚ØlipsesŽ‘Ii+¬[µsŽ‘°¬]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘0=H¬(“);Ž¡‘­elseŽ‘5Øâ°fŽ¡‘(±c‘ÿ}'errŽ‘@ W°‘S­´"ERROR!® ´In® ´Solid::geŽ‘nSqt_shape_center():\n"Ž’Ý-J°‘S­´"s® ´("Ž‘%m³°‘S­µsŽ‘WZ°Ž¡‘<´")® ´>® ´ellipses.size()Ž’¤ÿÊ® ´("Ž’¸ES°‘ÿ*±el‘‚ØlipsesŽ‘#›µ:±sizeŽ‘\¬(‘ª¨)–ÿ*°“´")\nReturning® ´INVALIŽ‘kþîD_POINT.\n\n"Ž’³ÄY°Ž¡‘<± ushŽ‘Q¹¬;Ž¡‘(­returnŽ‘Kæ¾´INVALID_POINTŽ’¬ÿ¬;Ž¡‘°gŽ¡‘gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±shap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘0›Ú°‘Ç´RECTANGLEŽ‘2e¬)‘°fŽ¡‘­ifŽ‘)´û¬(µsŽ‘w<‘DZr–ÿ}'e“ctanglesŽ‘.g]µ:±sizeŽ‘\¬(–ª¨))‘­returnŽ‘(溱r–ÿ}'e“ctanglesŽ‘T†ÿ¬[µsŽ‘°¬]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘0=H¬(“);Ž¡‘­elseŽ‘5Øâ°fŽ¡‘(±c‘ÿ}'errŽ‘@§‘°‘ñç´"ERROR!® ´In® ´Solid::geŽ‘nñ«t_shape_center():\n"Ž’Þi¾°‘ñç´"s® ´("Ž‘&ª'°Ž¡‘<µsŽ‘GGô°‘—î´")® ´>® ´rectangles.sizeŽ‘o—²()® ´("Ž’õù°‘—î±r–ÿ}'e“ctanglesŽ‘283µ:±sizeŽ‘\¬(‘ª¨)‘—î°Ž¡‘<´")\nReturning® ´INVALIŽ’¤ÿÊD_POINT.\n\n"Ž’ì#°‘DZ ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾´INVALID_POINTŽ’¬ÿ¬;Ž¡‘°gŽ¡‘gŽ¡‘­elseŽ‘*.6ifŽ‘5ã.¬(±shap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘0›Ú°‘Ç´REG_POLYGONŽ‘= _¬)‘°fŽ¡‘­ifŽ‘)´û¬(µsŽ‘w<‘DZr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºhµ:±sizeŽ‘\¬(–ª¨))‘­returnŽ‘(溱r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘^Ú +¬[µsŽ‘°¬]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘0=H¬(“);Ž¡‘­elseŽ‘5Øâ°fŽ¡‘(±c‘ÿ}'errŽ‘@§‘°‘ñç´"ERROR!® ´In® ´Solid::geŽ‘nñ«t_shape_center():\n"Ž’Þi¾°‘ñç´"s® ´("Ž‘&ª'°Ž¡‘<µsŽ‘FÅî°‘è´")® ´>® ´reg_polygons.siŽ‘o¬ze()® ´("Ž’šqç°‘è±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘< 8µ:±sizeŽ‘\¬(‘ª¨)‘è°Ž¡‘<´")\nReturning® ´INVALIŽ’¤ÿÊD_POINT.\n\n"Ž’ì#°‘DZ ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾´INVALID_POINTŽ’¬ÿ¬;Ž¡‘°gŽ¡‘gŽ¡‘­elseŽ‘+Øá°fŽ¡‘±c‘ÿ}'errŽ‘8(¢°‘rù´"ERROR!® ´In® ´Solid::geŽ‘pr½t_shape_center():\n"Ž’ákâ°Ž¡‘2´"Invalid® ´argument® ´foŽ’šÿÉr® ´shape_type:® ´"Ž’𯰑ث±shap–ÿ}'e‘‰ffŽ‘®typ“eŽ‘9†°‘Ø«±end‘‚ØlŽ‘£°Ž¡‘2´"Returning® ´INVALID_PŽ’šÿÉOINT.\n\n"Ž’ÒÍ+°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘Aæ½´INVALID_POINTŽ’†¬þ¬;Ž¡‘°gŽ¡‘ +gŽŽŽŒ‹˜ܹ Šn ý‘ì¬408›¯GET–ÕXCIRÃŽCLE“CENTER’ø'S3DLDF-1.1.5.1˜°x¬1371Ž €n ý•@P­1371.‘ üGet–ÕTCircle“cen®9ter.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ© ‘ +¬[²LDF‘T2003.04.11.¬]Ž‘Y;Added–UUthis“function.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°Ž¦‘ +­virtualŽ‘/ÔconstŽ‘M¸vP•®9oin“tŽ‘l¨¬&Ž‘to1±get‘‰ffŽ–®cir›ÿ}'cle‘‰ffŽ“c˜enterŽ’»{4¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµsŽ‘pÜS¬)‘UU­constŽ‘*¢¬;ŽŸ­1372.Ž¡°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¦‘ +­constŽ‘(*£P•®9oin“tŽ‘G@¬&Ž‘Ná^­SolidŽ‘i_9¬::‘±get‘‰ffŽ–®cir›ÿ}'cle‘‰ffŽ“c˜enterŽ‘H ¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµsŽ‘pÜS¬)‘UU­constŽŽ¦‘ +°fŽ¦‘­returnŽ‘7æ¼±get‘‰ffŽ–®shap›ÿ}'e‘‰ffŽ“c˜enterŽ‘Tä¬(´CIRCLEŽ‘ Vµ;‘ª¨sŽ‘Z¨¬);Ž¦‘ +°gŽŸ­1373.‘ üGet–ÕTEllipse“cen®9ter.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ +¬[²LDF‘T2003.04.11.¬]Ž‘Y;Added–UUthis“function.Ž¡ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°Ž¦‘ +­virtualŽ‘/ÔconstŽ‘M¸vP•®9oin“tŽ‘l¨¬&Ž‘to1±get‘‰ffŽ–®el‘‚Ølipse‘‰ffŽ“c‘ÿ}'enterŽ’¿qA¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµsŽ‘pÜS¬)‘UU­constŽ‘*¢¬;ŽŸ­1374.Ž¡°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¦‘ +­constŽ‘(*£P•®9oin“tŽ‘G@¬&Ž‘Ná^­SolidŽ‘i_9¬::‘±get‘‰ffŽ–®el‘‚Ølipse‘‰ffŽ“c‘ÿ}'enterŽ‘L¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµsŽ‘pÜS¬)‘UU­constŽŽ¦‘ +°fŽ¦‘­returnŽ‘7æ¼±get‘‰ffŽ–®shap›ÿ}'e‘‰ffŽ“c˜enterŽ‘Tä¬(´ELLIPSEŽ‘%FSµ;‘ª¨sŽ‘Z¨¬);Ž¦‘ +°gŽŸ­1375.‘ üGet–ÕTRectangle“cen®9ter.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¦‘ +¬[²LDF‘T2003.04.11.¬]Ž‘Y;Added–UUthis“function.Ž¡ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°Ž¦‘ +­virtualŽ‘/ÔconstŽ‘M¸vP•®9oin“tŽ‘l¨¬&Ž‘to1±get‘‰ffŽ›®r–ÿ}'e“ctangle‘‰ffŽ˜c“enterŽ’ʬ(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµsŽ‘pÜS¬)‘UU­constŽ‘*¢¬;ŽŸ­1376.Ž¡°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¦‘ +­constŽ‘(*£P•®9oin“tŽ‘G@¬&Ž‘Ná^­SolidŽ‘i_9¬::‘±get‘‰ffŽ›®r–ÿ}'e“ctangle‘‰ffŽ˜c“enterŽ‘Wè¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµsŽ‘pÜS¬)‘UU­constŽŽ¦‘ +°fŽ¦‘­returnŽ‘7æ¼±get‘‰ffŽ–®shap›ÿ}'e‘‰ffŽ“c˜enterŽ‘Tä¬(´RECTANGLEŽ‘/ÆMµ;‘ª¨sŽ‘Z¨¬);Ž¦‘ +°gŽŽŽŒ‹™꘠Šn ý‘ì°x¬1377›¯3DLDF-1.1.5.1’ÁgJGET–ÕX­REG‘°¡‰ffs4Ž‘#ÕPOL‘ÿ +«YGON“¯CENTER˜¬409Ž €n ý•@P­1377.‘ üGet–ÕTReg‘°¡‰ffs4Ž‘#ÕPš®9olygon“cen˜ter.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ© ‘ +¬[²LDF‘T2003.04.11.¬]Ž‘Y;Added–UUthis“function.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°Ž¦‘ +­virtualŽ‘/ÔconstŽ‘M¸vP•®9oin“tŽ‘l¨¬&Ž‘to1±get‘‰ffŽ›®r–ÿ}'e“g‘‰ffŽ˜p“olygon‘‰ffŽ˜c“enterŽ’Ôâ ¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµsŽ‘pÜS¬)‘UU­constŽ‘*¢¬;ŽŸ­1378.Ž¡°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¦‘ +­constŽ‘(*£P•®9oin“tŽ‘G@¬&Ž‘Ná^­SolidŽ‘i_9¬::‘±get‘‰ffŽ›®r–ÿ}'e“g‘‰ffŽ˜p“olygon‘‰ffŽ˜c“enterŽ‘aró¬(­constŽ‘*¢unsignedŽ‘Na°shortŽ‘l,SµsŽ‘pÜS¬)‘UU­constŽŽ¦‘ +°fŽ¦‘­returnŽ‘7æ¼±get‘‰ffŽ–®shap›ÿ}'e‘‰ffŽ“c˜enterŽ‘Tä¬(´REG_POLYGONŽ‘:FGµ;‘ª¨sŽ‘Z¨¬);Ž¦‘ +°gŽŸ­1379.‘ üIs–ÕTon“free“store.Ž¡°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°Ž¦‘ +­virtualŽ‘/Ôb•QÇo“olŽ‘I/:±is‘‰ffŽ–®on‘‰ffŽ“fr–ÿ}'e“e‘‰ffŽ‘®stor“eŽ’‹ª¬(‘ª®)‘UU­constŽ‘*¢¬;ŽŸ­1380.Ž¡°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¦‘ +­b•QÇo“olŽ‘#¡gSolidŽ‘>B¬::‘±is‘‰ffŽ–®on‘‰ffŽ“fr–ÿ}'e“e‘‰ffŽ‘®stor“eŽ‘CzÙ¬(‘ª®)‘UU­constŽŽ¦‘ +°fŽ¦‘­b•QÇo“olŽ‘-¡hµbŽ‘4³*¬=‘DZtrueŽ‘‹°¬;Ž¡‘­returnŽ‘7æ¼µbŽ‘<1f¬;Ž¦‘ +°gŽŸ­1381.‘ üSho®9w.Ž¡°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°Ž¦‘ +­virtualŽ‘/Õ[v®9oidŽ‘Iº±showŽ‘_¥¹¬(­stringŽ‘!lÔ±textŽ‘6î¬=‘>N´""Ž‘D°µ;‘ª¨­c®9harŽ‘\x±c–ÿ}'o“or“dsŽ‘:¤R¬=‘>N´'w'Ž‘„­µ;‘ª¨­constŽ‘ Ñb•QÇo“olŽ‘:¾±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘bíD¬=‘>N±trueŽ‘æµ;‘ª¨­constŽ‘ Ñb•QÇo“olŽŽ¦‘±do‘‰ffŽ‘®applyŽ‘Gd¬=‘Œ±trueŽ‘Ó$µ;‘ª¨­F‘ÿ +«oQÇcusŽ‘" )°Ž‘' *µfŽ‘0'œ¬=‘Œ0Ž‘µ;‘ª¨­constŽ‘ *unsignedŽ‘PbshortŽ‘nW›±pr‘ÿ}'ojŽ’„Yê¬=‘Œ­Pro‘£ŽjectionsŽ‘=Úð¬::Ž‘Di.´PERSPŽ‘_/‡µ;‘ª¨­constŽ‘ *realŽŽ¦‘±factorŽ‘;Êù¬=‘Ç1Ž‘Ç)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹šô£ Šn ý‘ì¬410–¯SHOÃŽW’;¯3DLDF-1.1.5.1“°x¬1382Ž €n ý•@P­1382.Ž©°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘#ŒhSolidŽ‘> +C¬::‘±showŽ‘‹¬(­stringŽ‘!³Ü±textŽ‘3 ¨µ;‘ª¨­c®9harŽ‘£€±c–ÿ}'o“or“dsŽ‘7­ µ;‘ª¨­constŽ‘ cÙb•QÇo“olŽ‘:“αdo‘‰ffŽ‘®p‘ÿ}'erspŽ‘`=µ;‘ª¨­constŽ‘ cÙb•QÇo“olŽ‘:“αdo‘‰ffŽ‘®applyŽ‘`ž£µ;‘ª¨­F‘ÿ +«oQÇcusŽŽ¡‘2°Ž‘7µfŽ‘<øì;‘ª¨­constŽ‘ÕJunsignedŽ‘P XshortŽ‘mÖû±pr‘ÿ}'ojŽ’€Ê¾µ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±factorŽ‘QŒV¬)‘UU­constŽŽ¡‘ +°fŽ¡‘­ifŽ‘´ú¬(±textŽ‘ä°‘Ç´""Ž‘ Íz¬)‘±textŽ‘ä¬=‘Ç´"Solid:"Ž‘-Mh¬;Ž¡‘±c‘ÿ}'outŽ‘* Q°‘DZtextŽ‘åü°‘DZend‘‚ØlŽ‘¸Ú¬;Ž¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"on_free_store® ´==® ´"Ž‘iÔ_°‘DZon‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘=3"°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¦‘­stringstreamŽ‘W,¹µgŽ‘\Mœ¬;Ž¡‘­in®9tŽ‘%¤ùµiŽ‘)í¬;Ž¦‘­ifŽ‘´ú¬(±p‘ÿ}'athsŽ‘­µ:±sizeŽ‘\¬(‘ª¨)–ǵ>“¬0Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"Showing® ´paths.\n"Ž‘aÍJ¬;Ž¡‘µiŽ‘$9¬=‘Ç0Ž‘Ç;Ž¡‘­forŽ‘/艬(­v®9ectorŽ‘ªH°h­P®9athŽ‘æ¹°Ž‘ æºi‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘DZp‘ÿ}'athsŽ–Wŵ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZp‘ÿ}'athsŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘(µgŽ‘/çÿ°‘Ç´"Path® ´"Ž‘*Ôƒ°‘ǵiŽ‘¹ Ÿÿ³+‘ÿ+ŽŽ‘GD°‘Ç´":"Ž‘ w¬;Ž¡‘((°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±showŽ‘Šÿ¬(µgŽ‘ ã:±strŽ‘ 7¬(–ª¨)µ;“±c–ÿ}'o“or“dsŽ‘´4µ;“±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘'Sàµ;“±do‘‰ffŽ‘®applyŽ‘'µ}µ;“fŽ‘£Ž;“±pr‘ÿ}'ojŽ‘žkµ;“±factorŽ‘®†¬);Ž¡‘(µgŽ‘- ç:±strŽ‘ 7¬(´""Ž‘ b¬);Ž¡‘°gŽ¡‘gŽ¡‘­elseŽ‘+Øá±c‘ÿ}'outŽ‘Aù0°‘Ç´"paths® ´is® ´empty.\n"Ž‘g G¬;Ž¡‘­ifŽ‘´ú¬(±cir‘ÿ}'clesŽ‘Œdµ:±sizeŽ‘\¬(‘ª¨)–ǵ>“¬0Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"Showing® ´circles.\n"Ž‘lMD¬;Ž¡‘µiŽ‘$9¬=‘Ç0Ž‘Ç;Ž¡‘­forŽ‘/艬(­v®9ectorŽ‘ªH°h­CircleŽ‘!¸°Ž‘&¸‚i‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘DZcir‘ÿ}'clesŽ–S|µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZcir‘ÿ}'clesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘(µgŽ‘/çÿ°‘Ç´"Circle® ´"Ž‘5T}°‘ǵiŽ‘¹ Ÿÿ³+‘ÿ+ŽŽ‘GD°‘Ç´":"Ž‘ w¬;Ž¡‘((°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±showŽ‘Šÿ¬(µgŽ‘ ã:±strŽ‘ 7¬(–ª¨)µ;“±c–ÿ}'o“or“dsŽ‘´4µ;“±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘'Sàµ;“±do‘‰ffŽ‘®applyŽ‘'µ}µ;“fŽ‘£Ž;“±pr‘ÿ}'ojŽ‘žkµ;“±factorŽ‘®†¬);Ž¡‘(µgŽ‘- ç:±strŽ‘ 7¬(´""Ž‘ b¬);Ž¡‘°gŽ¡‘gŽ¡‘­elseŽ‘+Øá±c‘ÿ}'outŽ‘Aù0°‘Ç´"circles® ´is® ´empty.\nŽ‘kÆÜ"Ž‘qA¬;Ž¡‘­ifŽ‘´ú¬(±el‘‚ØlipsesŽ‘ ‚qµ:±sizeŽ‘\¬(‘ª¨)–ǵ>“¬0Ž‘Ç)‘°fŽ¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"Showing® ´ellipses.\nŽ‘kÆÜ"Ž‘qA¬;Ž¡‘µiŽ‘$9¬=‘Ç0Ž‘Ç;Ž¡‘­forŽ‘/艬(­v®9ectorŽ‘ªH°h­EllipseŽ‘%>.°Ž‘*>/i‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘DZel‘‚ØlipsesŽ–#I‰µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZel‘‚ØlipsesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘(µgŽ‘/çÿ°‘Ç´"Ellipse® ´"Ž‘:”z°‘ǵiŽ‘¹ Ÿÿ³+‘ÿ+ŽŽ‘GD°‘Ç´":"Ž‘ w¬;Ž¡‘((°Ž‘Ž‘ 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´empŽ‘kÆÜty.\n"Ž’‹Í2¬;ŽŽŽŒ‹›ýQ Šn ý‘ì°x¬1382–¯3DLDF-1.1.5.1’;¯SHOÃŽW“¬411Ž €n ý•@P‘­ifŽ‘´ú¬(±r–ÿ}'e“ctanglesŽ‘+ Eµ:±sizeŽ‘\¬(‘ª¨)–ǵ>“¬0Ž‘Ç)‘°fŽ¤ ‘±c‘ÿ}'outŽ‘4 R°‘Ç´"Showing® ´rectangles.Ž‘kÆÜ\n"Ž‘| ;¬;Ž¡‘µiŽ‘$9¬=‘Ç0Ž‘Ç;Ž¡‘­forŽ‘0Q»¬(­v®9ectorŽ‘ªH°h­RectangleŽ‘5þ°Ž‘:þi‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘WÄd¬=‘vk±r–ÿ}'e“ctanglesŽ–/°µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘i/±iterŽ‘ª˜°6¬=‘vk±r–ÿ}'e“ctanglesŽ“µ:±endŽ‘ಬ(˜);Ž¡‘<€Ÿÿ³+‘ÿ+ŽŽ‘HG&±iterŽ‘Y$¬)‘°fŽ¡‘(µgŽ‘/çÿ°‘Ç´"Rectangle® ´"Ž‘Et°‘ǵiŽ‘¹ Ÿÿ³+‘ÿ+ŽŽ‘GD°‘Ç´":"Ž‘ w¬;Ž¡‘((°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±showŽ‘Šÿ¬(µgŽ‘ ã:±strŽ‘ 7¬(–ª¨)µ;“±c–ÿ}'o“or“dsŽ‘´4µ;“±do‘‰ffŽ‘®p‘ÿ}'erspŽ‘'Sàµ;“±do‘‰ffŽ‘®applyŽ‘'µ}µ;“fŽ‘£Ž;“±pr‘ÿ}'ojŽ‘žkµ;“±factorŽ‘®†¬);Ž¡‘(µgŽ‘- ç:±strŽ‘ 7¬(´""Ž‘ b¬);Ž¡‘°gŽ¡‘gŽ¡‘­elseŽ‘+Øá±c‘ÿ}'outŽ‘Aù0°‘Ç´"rectangles® ´is® ´emptyŽ‘kÆÜ.\n"Ž’M8¬;Ž¡‘±c‘ÿ}'outŽ‘* Q°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘4‘g¬;Ž¡‘ +°gŽ©­1383.– üClear.“¬[²LDF‘T2002.10.07.¬]Ž‘ZÑôReplaced–Ÿdummš¸ãy“de nition“with“a“real“one.‘ONo˜w,‘±ƒ±cle‘ÿ}'arŽ‘Ú\¬(‘ª®)“is“called“forŽ¡all–UUof“the“ob‘Ž8jects“in“the“­SolidŽ‘Ó,¬.ŽŸ°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/Ôv®9oidŽ‘H‹¬±cle‘ÿ}'arŽ‘^´…¬(‘ª®);Ž¦­1384.Ž©°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙSolidŽ‘={´¬::‘±cle‘ÿ}'arŽ‘(ݬ(‘ª®)Ž¡‘ +°fŽ¡‘­b•QÇo“olŽ‘-¡h´DEBUGŽ‘K.Ù¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¦‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Entering® ´Solid::cleŽ‘kÆÜar().\n"Ž’™D°‘DZ ushŽ‘€¬;Ž¡‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­P®9athŽ‘æ¹°Ž‘ æºi‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZp‘ÿ}'athsŽ–Wŵ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZp‘ÿ}'athsŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±cle‘ÿ}'arŽ‘(Ù¬(˜);Ž¡‘±p‘ÿ}'athsŽ‘+¯µ:±cle‘ÿ}'arŽ‘(Ù¬(‘ª¨);Ž¡‘­forŽ‘%åì¬(­v®9ectorŽ‘ªH°h­CircleŽ‘!µå°Ž‘&µæi‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZcir‘ÿ}'clesŽ–S|µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ýa±iterŽ‘w°6¬=‘DZcir‘ÿ}'clesŽ“µ:±endŽ‘ಬ(˜);‘}aŸÿ³+‘ÿ+ŽŽ‘D±iterŽ‘"¬)‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±cle‘ÿ}'arŽ‘(Ù¬(˜);Ž¡‘±cir‘ÿ}'clesŽ‘0Œfµ:±cle‘ÿ}'arŽ‘(Ù¬(‘ª¨);Ž¡‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­EllipseŽ‘%>.°Ž‘*>/i‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZel‘‚ØlipsesŽ–#I‰µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZel‘‚ØlipsesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)Ž¡‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±cle‘ÿ}'arŽ‘(Ù¬(‘ª¨);Ž¡‘±el‘‚ØlipsesŽ‘4‚sµ:±cle‘ÿ}'arŽ‘(Ù¬(‘ª¨);Ž¡‘­forŽ‘&Qˬ(­v®9ectorŽ‘ªH°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘E=L°Ž‘J=Mi‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=Ú¼¬=‘v‡±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ–9i×µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘i@±iterŽ‘ªÅ°6¬=‘v‡±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ“µ:±endŽ‘ಬ(˜);Ž¡‘2€Ÿÿ³+‘ÿ+ŽŽ‘>G%±iterŽ‘O#¬)‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±cle‘ÿ}'arŽ‘(Ù¬(‘ª¨);Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘IóRµ:±cle‘ÿ}'arŽ‘(Ù¬(‘ª¨);Ž¡‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­RectangleŽ‘5”ê°Ž‘:”ëi‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZr–ÿ}'e“ctanglesŽ–.g]µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZr–ÿ}'e“ctanglesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)Ž¡‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±cle‘ÿ}'arŽ‘(Ù¬(‘ª¨);Ž¡‘±r–ÿ}'e“ctanglesŽ‘? Gµ:±cle‘ÿ}'arŽ‘(Ù¬(‘ª¨);Ž¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Exiting® ´Solid::cleaŽ‘kÆÜr().\n"Ž’“ÔG°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘4‘g¬;Ž¡‘ +°gŽ¤­1385.‘ üT‘ÿ +«ransformations.Ž¡1386.‘ üMultiplying–ÕTb®9y“a“T‘ÿ +«ransform.Ž¦°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°ŽŸ ‘ +­virtualŽ‘/ÔT‘ÿ +«ransformŽ‘gV¦opQÇeratorŽ’’í[°¬=ŽŽŽ’Ÿ´z(­constŽ‘*¢T‘ÿ +«ransformŽ‘Uót¬&Ž‘]º’µtŽ‘aW¬);ŽŽŽŒ‹œv Šn ý‘ì¬412›¯MUL–ÿJªTIPL“YING–ÕXBY“A“­TRANSF®9ORM’±va¯3DLDF-1.1.5.1˜°x¬1387Ž €n ý•@P­1387.Ž©°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¤ ‘ +­T‘ÿ +«ransformŽ‘AÈÓSolidŽ‘\F®¬::Ž‘bÔì­opQÇeratorŽ’Žk¡°¬=ŽŽŽ’›2À(­constŽ‘*¢T‘ÿ +«ransformŽ‘Uót¬&Ž‘]º’µtŽ‘aW¬)Ž¡‘ +°fŽ¡‘±c‘ÿ}'enterŽ‘2Ð¥°¬=ŽŽ‘B^ܵtŽ‘EûN¬;Ž¡‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­P®9athŽ‘æ¹°Ž‘ æºi‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZp‘ÿ}'athsŽ–Wŵ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZp‘ÿ}'athsŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°Ž‘ +Ž‘±iterŽ‘"’°¬=ŽŽ‘2 OµtŽ‘5¼Á¬;Ž¡‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­EllipseŽ‘%>.°Ž‘*>/i‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZel‘‚ØlipsesŽ–#I‰µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZel‘‚ØlipsesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°Ž‘ +Ž‘±iterŽ‘"’°¬=ŽŽ‘2 OµtŽ‘5¼Á¬;Ž¡‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­CircleŽ‘!¸°Ž‘&¸‚i‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZcir‘ÿ}'clesŽ–S|µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZcir‘ÿ}'clesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°Ž‘ +Ž‘±iterŽ‘"’°¬=ŽŽ‘2 OµtŽ‘5¼Á¬;Ž¡‘­forŽ‘&Qˬ(­v®9ectorŽ‘ªH°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘E=L°Ž‘J=Mi‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=Ú¼¬=‘v‡±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ–9i×µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘i@±iterŽ‘ªÅ°6¬=‘v‡±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ“µ:±endŽ‘ಬ(˜);Ž¡‘2€Ÿÿ³+‘ÿ+ŽŽ‘>G%±iterŽ‘O#¬)‘°Ž‘ +Ž‘±iterŽ‘"’°¬=ŽŽ‘2 OµtŽ‘5¼Á¬;Ž¡‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­RectangleŽ‘5”ê°Ž‘:”ëi‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZr–ÿ}'e“ctanglesŽ–.g]µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZr–ÿ}'e“ctanglesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)Ž¡‘°Ž‘#Ž‘(±iterŽ‘;’°¬=ŽŽ‘K RµtŽ‘N¼Ä¬;Ž¡‘­returnŽ‘7æ¼µtŽ‘;ƒ.¬;Ž¡‘ +°gŽŸ­1388.‘ üApplying–ÕTa“transformation.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.01.05.¬]Ž‘Z‡{Added–Ô•this“function.‘ï†It's“noš¸ãw“needed“bGecause“I'v˜e“made“±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Jôt¬(‘ª®)“a“pureŽ¡­virtualŽ‘$Þ2¬function–¥´in“­classŽ‘ÖdShapQÇeŽ‘;Âq¬.‘7.°Ž‘*>/i‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZel‘‚ØlipsesŽ–#I‰µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZel‘‚ØlipsesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)Ž¡‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¡‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­CircleŽ‘!¸°Ž‘&¸‚i‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZcir‘ÿ}'clesŽ–S|µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZcir‘ÿ}'clesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)Ž¡‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¡‘­forŽ‘&Qˬ(­v®9ectorŽ‘ªH°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘E=L°Ž‘J=Mi‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=Ú¼¬=‘v‡±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ–9i×µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘i@±iterŽ‘ªÅ°6¬=‘v‡±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ“µ:±endŽ‘ಬ(˜);Ž¡‘2€Ÿÿ³+‘ÿ+ŽŽ‘>G%±iterŽ‘O#¬)‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¡‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­RectangleŽ‘5”ê°Ž‘:”ëi‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZr–ÿ}'e“ctanglesŽ–.g]µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZr–ÿ}'e“ctanglesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)Ž¡‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¡‘ +°gŽŸ­1390.‘ üScale.Ž¦°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔT‘ÿ +«ransformŽ‘gV¦±sc‘ÿ}'aleŽ‘} ˜¬(­realŽ‘³.±xxŽ‘!±fµ;‘ª¨­realŽ‘]Ö±yyŽ‘&@K¬=‘Ç0Ž–ǵ;‘ª¨­realŽ‘]Ö±zzŽ‘%ó¬=‘Ç0Ž“);ŽŽŽŒ‹ Šn ý‘ì°x¬1391–¯3DLDF-1.1.5.1’8þ­SCALE“¬413Ž €n ý•@P­1391.Ž©°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¤ ‘ +­T‘ÿ +«ransformŽ‘AÈÓSolidŽ‘\F®¬::‘±sc‘ÿ}'aleŽ‘´ö¬(­realŽ‘³.±xxŽ‘!±fµ;‘ª¨­realŽ‘]Ö±yyŽ‘#y3µ;‘ª¨­realŽ‘]Ö±zzŽ‘"HÛ¬)Ž¡‘ +°fŽ¡‘­T‘ÿ +«ransformŽ‘KÈÔµtŽ‘OeF¬;Ž¦‘µtŽ‘œt:±sc‘ÿ}'aleŽ‘´ò¬(±xxŽ‘ +þ8µ;‘ª¨±yyŽ‘ Ƶ;‘ª¨±zzŽ‘ •­¬);Ž¡‘°Ž‘±thisŽ‘,²Ñ°¬=ŽŽ‘¬(­realŽ‘³.±xyŽ‘!—µ;‘ª¨­realŽ‘]Ö±xzŽ‘"Õ¨µ;‘ª¨­realŽ‘]Ö±yxŽ‘#“„µ;‘ª¨­realŽ‘]Ö±yzŽ‘# µ;‘ª¨­realŽ‘]Ö±zxŽ‘"ÏAµ;‘ª¨­realŽ‘]Ö±zyŽ‘"´ð¬)Ž¡‘ +°fŽ¡‘­T‘ÿ +«ransformŽ‘KÈÔµtŽ‘OeF¬;Ž¦‘µtŽ‘œt:±she‘ÿ}'arŽ‘4:¬(±xyŽ‘ +ãçµ;‘ª¨±xzŽ‘ "zµ;‘ª¨±yxŽ‘ àVµ;‘ª¨±yzŽ‘ Yðµ;‘ª¨±zxŽ‘ µ;‘ª¨±zyŽ‘ ¬);Ž¡‘°Ž‘±thisŽ‘,²Ñ°¬=ŽŽ‘¬(±xxŽ‘ +þ8µ;‘ª¨±yyŽ‘ Ƶ;‘ª¨±zzŽ‘ •­¬);Ž¡‘°Ž‘±thisŽ‘,²Ñ°¬=ŽŽ‘Äç¬&Ž‘FŒ±p1Ž‘R¢Åµ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±angleŽ‘Qã¬=‘Ç180ŽŽ‘Ç);ŽŸ­1402.Ž¦°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¡‘ +­T‘ÿ +«ransformŽ‘AÈÓSolidŽ‘\F®¬::‘±r‘ÿ}'otateŽ‘oB¬(­constŽ‘*¢P•®9oin“tŽ‘=?¬&Ž‘Dá]±p0Ž‘Pøµ;‘ª¨­constŽ‘ÕJP•®9oin“tŽ‘>Äç¬&Ž‘FŒ±p1Ž‘R¢Åµ;‘ª¨­constŽ‘ÕJrealŽ‘6ˆx±angleŽ‘NHˬ)Ž¡‘ +°fŽ¡‘­T‘ÿ +«ransformŽ‘KÈÔµtŽ‘OeF¬;Ž¦‘µtŽ‘œt:±r‘ÿ}'otateŽ‘o>¬(±p0Ž‘ Àµ;‘ª¨±p1Ž‘ Áhµ;‘ª¨±angleŽ‘jû¬);Ž¡‘°Ž‘±thisŽ‘,²Ñ°¬=ŽŽ‘uC¬&Ž‘FuC¬&Ž‘F›°‘ån´"WARNING!® ´In® ´Solid::Ž‘lå2extract():\n"Ž’µá°‘ån´"Path® ´cannot® ´be® ´projŽ‘lå2ected.® ´"Ž’›Pð°Ž¡‘<´"Returning® ´empty® ´vecŽ’¤ÿÊtor® ´.\n"Ž’üM°‘DZ ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾µvŽ‘Q{¬;Ž¡‘(­breakŽ‘D¡h¬;Ž¡‘°gŽ¡‘gŽ¡‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­EllipseŽ‘%>.°Ž‘*>/i‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZel‘‚ØlipsesŽ–#I‰µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZel‘‚ØlipsesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘¬(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¡‘­ifŽ‘)´û¬(°:¬(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±pr–ÿ}'oje“ctŽ‘w¬(µfŽ‘øæ;‘ª¨±pr‘ÿ}'ojŽ‘žkµ;‘ª¨±factorŽ‘®†¬))‘°fŽ¡‘(±c‘ÿ}'errŽ‘>8Á°‘ƒ´"WARNING!® ´In® ´Solid::Ž‘l‚Ûextract():\n"Ž’´Ì3°‘ƒ´"Ellipse® ´cannot® ´be® ´pŽ‘l‚Ûrojected.® ´"Ž’ªL9°Ž¡‘<´"Returning® ´empty® ´vecŽ’¤ÿÊtor® ´.\n"Ž’üM°‘DZ ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾µvŽ‘Q{¬;Ž¡‘(­breakŽ‘D¡h¬;Ž¡‘°gŽ¡‘gŽ¡‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­CircleŽ‘!¸°Ž‘&¸‚i‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZcir‘ÿ}'clesŽ–S|µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZcir‘ÿ}'clesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘¬(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¡‘­ifŽ‘)´û¬(°:¬(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±pr–ÿ}'oje“ctŽ‘w¬(µfŽ‘øæ;‘ª¨±pr‘ÿ}'ojŽ‘žkµ;‘ª¨±factorŽ‘®†¬))‘°fŽ¡‘(±c‘ÿ}'errŽ‘>Y‰°‘£ß´"WARNING!® ´In® ´Solid::Ž‘l££extract():\n"Ž’µ ð‘£ß´"Circle® ´cannot® ´be® ´prŽ‘l££ojected.® ´"Ž’¥MÌ°Ž¡‘<´"Returning® ´empty® ´vecŽ’¤ÿÊtor® ´.\n"Ž’üM°‘DZ ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾µvŽ‘Q{¬;Ž¡‘(­breakŽ‘D¡h¬;Ž¡‘°gŽ¡‘gŽ¡‘­forŽ‘&Qˬ(­v®9ectorŽ‘ªH°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘E=L°Ž‘J=Mi‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=Ú¼¬=‘v‡±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ–9i×µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘i@±iterŽ‘ªÅ°6¬=‘v‡±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ“µ:±endŽ‘ಬ(˜);Ž¡‘2€Ÿÿ³+‘ÿ+ŽŽ‘>G%±iterŽ‘O#¬)‘°fŽ¡‘¬(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¡‘­ifŽ‘)´û¬(°:¬(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±pr–ÿ}'oje“ctŽ‘w¬(µfŽ‘øæ;‘ª¨±pr‘ÿ}'ojŽ‘žkµ;‘ª¨±factorŽ‘®†¬))‘°fŽ¡‘(±c‘ÿ}'errŽ‘>8Á°‘ƒ´"WARNING!® ´In® ´Solid::Ž‘l‚Ûextract():\n"Ž’´Ì3°‘ƒ´"Polygon® ´cannot® ´be® ´pŽ‘l‚Ûrojected.® ´"Ž’ªL9°Ž¡‘<´"Returning® ´empty® ´vecŽ’¤ÿÊtor® ´.\n"Ž’üM°‘DZ ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾µvŽ‘Q{¬;Ž¡‘(­breakŽ‘D¡h¬;Ž¡‘°gŽ¡‘gŽ¡‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­RectangleŽ‘5”ê°Ž‘:”ëi‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZr–ÿ}'e“ctanglesŽ–.g]µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZr–ÿ}'e“ctanglesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘¬(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬(‘ª¨);Ž¡‘­ifŽ‘)´û¬(°:¬(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±pr–ÿ}'oje“ctŽ‘w¬(µfŽ‘øæ;‘ª¨±pr‘ÿ}'ojŽ‘žkµ;‘ª¨±factorŽ‘®†¬))‘°fŽ¡‘(±c‘ÿ}'errŽ‘=÷2°‘Aˆ´"WARNING!® ´In® ´Solid::Ž‘lALextract():\n"Ž—´I°‘Aˆ´"Rectangle® ´cannot® ´beŽ‘lAL® ´projected.® ´"Ž“°Ž¡‘<´"Returning® ´empty® ´vecŽ’¤ÿÊtor® ´.\n"Ž’üM°‘DZ ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾µvŽ‘Q{¬;Ž¡‘(­breakŽ‘D¡h¬;Ž¡‘°gŽ¡‘gŽ¡‘µvŽ‘4¿:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(±thisŽ‘붬);ŽŽŽŒ‹ Fô Šn ý‘ì¬416–¯EXTRAÃŽCT’*]33DLDF-1.1.5.1“°x¬1405Ž €n ý•@P‘­returnŽ‘7æ¼µvŽ‘=y¬;Ž¤ ‘ +°gŽŸ­1406.‘ üSet‘ÕTextremes.ŽŸ°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/Ôb•QÇo“olŽ‘I/:±set‘‰ffŽ‘®extr‘ÿ}'emesŽ‘ðì(‘ª®);ŽŽŽŒ‹¡XQ Šn ý‘ì°x¬1407–¯3DLDF-1.1.5.1’:ùSET‘ÕXEXTREMES“¬417Ž €n ý•@P­1407.Ž©°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¤ ‘ +­b•QÇo“olŽ‘#¡gSolidŽ‘>B¬::‘±set‘‰ffŽ‘®extr‘ÿ}'emesŽ‘7Á¬(‘ª®)Ž¡‘ +°fŽ¡‘­b•QÇo“olŽ‘-¡h´DEBUGŽ‘K.Ù¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¦‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Entering® ´Solid::setŽ‘kÆÜ_extremes()"Ž’®8°‘Ç´"\n"Ž‘Œ°‘DZ ushŽ‘€¬;Ž¦‘­v‘ÿ\ralarra®9yŽ‘=ZC°h­realŽ‘]Ù°i‘UUµvŽ‘Š¬;Ž¦‘µvŽ‘4¿:±r‘ÿ}'esizeŽ‘i¬(6Ž‘µ;‘ª¨¬0Ž‘ª©);‘µ=°‘Ó¬LDF›X*2002.12.13.–zHAdded.“Needed–X+for“compiling“under“GNU/Lin¸ãux“using“GCC˜onŽ¡‘(the–UUIn¸ãtel“i686“computer“gwdu101.gwdg.de.‘o°µ=Ž¡‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­P®9athŽ‘æ¹°Ž‘ æºi‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZp‘ÿ}'athsŽ–Wŵ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZp‘ÿ}'athsŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘­ifŽ‘)´û¬(°:¬(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ‘®extr‘ÿ}'emesŽ‘6Á‰¬(‘ª¨))‘°fŽ¡‘(±c‘ÿ}'errŽ‘Bp×°‘»-´"ERROR!® ´In® ´Solid::seŽ‘pºñt_extremes():\n"Ž’ÌüV°Ž¡‘<´"Path::set_extremes(Ž’¤ÿÊ)® ´returned® ´false.® ´"Ž’ °‘Ç´"Returning® ´false.\n\Ž‘kÆÜn"Ž‘y”V°‘DZ ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾±falseŽ‘`–¬;Ž¡‘°gŽ¡‘µvŽ‘%ûج=‘Ç(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±get‘‰ffŽ‘®extr‘ÿ}'emesŽ‘7D`¬(‘ª¨);Ž¡‘­forŽ‘/艬(­in®9tŽ‘¤÷µiŽ‘Þ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ3Ž“;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘µ=°‘ÿý¬Minima.‘o°µ=Ž¡‘°fŽ¡‘(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘|U¬[µiŽ›qô¬]–Ç=“±minŽ‘ì-¬(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ¬[µiŽ˜¬]µ;‘ª¨vŽ‘ße¬[µiŽ˜¬]);Ž¡‘°gŽ¡‘­forŽ‘/艬(­in®9tŽ‘¤÷µiŽ‘Þ¬=‘Ç3Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ6Ž“;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘µ=°‘ÿý¬Maxima.‘o°µ=Ž¡‘°fŽ¡‘(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘|U¬[µiŽ›qô¬]–Ç=“±maxŽ‘k³¬(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ¬[µiŽ˜¬]µ;‘ª¨vŽ‘ße¬[µiŽ˜¬]);Ž¡‘°gŽ¡‘gŽ¡‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­EllipseŽ‘%>.°Ž‘*>/i‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZel‘‚ØlipsesŽ–#I‰µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZel‘‚ØlipsesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘­ifŽ‘)´û¬(°:¬(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ‘®extr‘ÿ}'emesŽ‘6Á‰¬(‘ª¨))‘°fŽ¡‘(±c‘ÿ}'errŽ‘Bp×°‘»-´"ERROR!® ´In® ´Solid::seŽ‘pºñt_extremes():\n"Ž’ÌüV°Ž¡‘<´"Path::set_extremes(Ž’¤ÿÊ)® ´returned® ´false.® ´"Ž’ °‘Ç´"Returning® ´false.\n\Ž‘kÆÜn"Ž‘y”V°‘DZ ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾±falseŽ‘`–¬;Ž¡‘°gŽ¡‘µvŽ‘%ûج=‘Ç(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±get‘‰ffŽ‘®extr‘ÿ}'emesŽ‘7D`¬(‘ª¨);Ž¡‘­forŽ‘/艬(­in®9tŽ‘¤÷µiŽ‘Þ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ3Ž“;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘µ=°‘ÿý¬Minima.‘o°µ=Ž¡‘°fŽ¡‘(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘|U¬[µiŽ›qô¬]–Ç=“±minŽ‘ì-¬(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ¬[µiŽ˜¬]µ;‘ª¨vŽ‘ße¬[µiŽ˜¬]);Ž¡‘°gŽ¡‘­forŽ‘/艬(­in®9tŽ‘¤÷µiŽ‘Þ¬=‘Ç3Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ6Ž“;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘µ=°‘ÿý¬Maxima.‘o°µ=Ž¡‘°fŽ¡‘(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘|U¬[µiŽ›qô¬]–Ç=“±maxŽ‘k³¬(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ¬[µiŽ˜¬]µ;‘ª¨vŽ‘ße¬[µiŽ˜¬]);Ž¡‘°gŽ¡‘gŽ¡‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­CircleŽ‘!¸°Ž‘&¸‚i‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZcir‘ÿ}'clesŽ–S|µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZcir‘ÿ}'clesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘­ifŽ‘)´û¬(°:¬(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ‘®extr‘ÿ}'emesŽ‘6Á‰¬(‘ª¨))‘°fŽ¡‘(±c‘ÿ}'errŽ‘Bp×°‘»-´"ERROR!® ´In® ´Solid::seŽ‘pºñt_extremes():\n"Ž’ÌüV°Ž¡‘<´"Path::set_extremes(Ž’¤ÿÊ)® ´returned® ´false.® ´"Ž’ °‘Ç´"Returning® ´false.\n\Ž‘kÆÜn"Ž‘y”V°‘DZ ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾±falseŽ‘`–¬;Ž¡‘°gŽ¡‘µvŽ‘%ûج=‘Ç(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±get‘‰ffŽ‘®extr‘ÿ}'emesŽ‘7D`¬(‘ª¨);Ž¡‘­forŽ‘/艬(­in®9tŽ‘¤÷µiŽ‘Þ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ3Ž“;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘µ=°‘ÿý¬Minima.‘o°µ=Ž¡‘°fŽ¡‘(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘|U¬[µiŽ›qô¬]–Ç=“±minŽ‘ì-¬(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ¬[µiŽ˜¬]µ;‘ª¨vŽ‘ße¬[µiŽ˜¬]);ŽŽŽŒ‹¢Y¥ Šn ý‘ì¬418–¯SET‘ÕXEXTREMES’:ù3DLDF-1.1.5.1“°x¬1407Ž €n ý•@P‘°gŽ¤ ‘­forŽ‘/艬(­in®9tŽ‘¤÷µiŽ‘Þ¬=‘Ç3Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ6Ž“;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘µ=°‘ÿý¬Maxima.‘o°µ=Ž¡‘°fŽ¡‘(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘|U¬[µiŽ›qô¬]–Ç=“±maxŽ‘k³¬(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ¬[µiŽ˜¬]µ;‘ª¨vŽ‘ße¬[µiŽ˜¬]);Ž¡‘°gŽ¡‘gŽ¡‘­forŽ‘&Qˬ(­v®9ectorŽ‘ªH°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘E=L°Ž‘J=Mi‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=Ú¼¬=‘v‡±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ–9i×µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘i@±iterŽ‘ªÅ°6¬=‘v‡±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ“µ:±endŽ‘ಬ(˜);Ž¡‘2€Ÿÿ³+‘ÿ+ŽŽ‘>G%±iterŽ‘O#¬)‘°fŽ¡‘­ifŽ‘)´û¬(°:¬(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ‘®extr‘ÿ}'emesŽ‘6Á‰¬(‘ª¨))‘°fŽ¡‘(±c‘ÿ}'errŽ‘Bp×°‘»-´"ERROR!® ´In® ´Solid::seŽ‘pºñt_extremes():\n"Ž’ÌüV°Ž¡‘<´"Path::set_extremes(Ž’¤ÿÊ)® ´returned® ´false.® ´"Ž’ °‘Ç´"Returning® ´false.\n\Ž‘kÆÜn"Ž‘y”V°‘DZ ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾±falseŽ‘`–¬;Ž¡‘°gŽ¡‘µvŽ‘%ûج=‘Ç(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±get‘‰ffŽ‘®extr‘ÿ}'emesŽ‘7D`¬(‘ª¨);Ž¡‘­forŽ‘/艬(­in®9tŽ‘¤÷µiŽ‘Þ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ3Ž“;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘µ=°‘ÿý¬Minima.‘o°µ=Ž¡‘°fŽ¡‘(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘|U¬[µiŽ›qô¬]–Ç=“±minŽ‘ì-¬(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ¬[µiŽ˜¬]µ;‘ª¨vŽ‘ße¬[µiŽ˜¬]);Ž¡‘°gŽ¡‘­forŽ‘/艬(­in®9tŽ‘¤÷µiŽ‘Þ¬=‘Ç3Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ6Ž“;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘µ=°‘ÿý¬Maxima.‘o°µ=Ž¡‘°fŽ¡‘(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘|U¬[µiŽ›qô¬]–Ç=“±maxŽ‘k³¬(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ¬[µiŽ˜¬]µ;‘ª¨vŽ‘ße¬[µiŽ˜¬]);Ž¡‘°gŽ¡‘gŽ¡‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­RectangleŽ‘5”ê°Ž‘:”ëi‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZr–ÿ}'e“ctanglesŽ–.g]µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZr–ÿ}'e“ctanglesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘­ifŽ‘)´û¬(°:¬(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ‘®extr‘ÿ}'emesŽ‘6Á‰¬(‘ª¨))‘°fŽ¡‘(±c‘ÿ}'errŽ‘Bp×°‘»-´"ERROR!® ´In® ´Solid::seŽ‘pºñt_extremes():\n"Ž’ÌüV°Ž¡‘<´"Path::set_extremes(Ž’¤ÿÊ)® ´returned® ´false.® ´"Ž’ °‘Ç´"Returning® ´false.\n\Ž‘kÆÜn"Ž‘y”V°‘DZ ushŽ‘€¬;Ž¡‘(­returnŽ‘Kæ¾±falseŽ‘`–¬;Ž¡‘°gŽ¡‘µvŽ‘%ûج=‘Ç(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±get‘‰ffŽ‘®extr‘ÿ}'emesŽ‘7D`¬(‘ª¨);Ž¡‘­forŽ‘/艬(­in®9tŽ‘¤÷µiŽ‘Þ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ3Ž“;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘µ=°‘ÿý¬Minima.‘o°µ=Ž¡‘°fŽ¡‘(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘|U¬[µiŽ›qô¬]–Ç=“±minŽ‘ì-¬(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ¬[µiŽ˜¬]µ;‘ª¨vŽ‘ße¬[µiŽ˜¬]);Ž¡‘°gŽ¡‘­forŽ‘/艬(­in®9tŽ‘¤÷µiŽ‘Þ¬=‘Ç3Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ6Ž“;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘µ=°‘ÿý¬Maxima.‘o°µ=Ž¡‘°fŽ¡‘(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘|U¬[µiŽ›qô¬]–Ç=“±maxŽ‘k³¬(±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ¬[µiŽ˜¬]µ;‘ª¨vŽ‘ße¬[µiŽ˜¬]);Ž¡‘°gŽ¡‘gŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Exiting® ´Solid::set_Ž‘kÆÜextremes()"Ž’¨Ô;°‘Ç´"\n"Ž‘Œ°‘DZ ushŽ‘€¬;Ž¡‘­returnŽ‘7æ¼±trueŽ‘J«T¬;Ž¡‘ +°gŽ©­1408.‘ üGet‘ÕTextremes.ŽŸ°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°Ž¡‘ +­inlineŽ‘)ŠIvirtualŽ‘OconstŽ‘mB¾v‘ÿ\ralarra®9yŽ’–œÿ°h­realŽ‘]Ù°i‘UU±get‘‰ffŽ‘®extr‘ÿ}'emesŽ‘:™µ¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7æ¼±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ’‹ë ¬;Ž¡‘ +°gŽ¦­1409.‘ üGet–ÕTminim®9um“z.ŽŸ°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°ŽŽŽŒ‹£k{ Šn ý‘ì°x¬1409›¯3DLDF-1.1.5.1’ ¨GET–ÕXMINIMUM“Z˜¬419Ž €n ý•@P‘ +­virtualŽ‘/ÔrealŽ‘FA±get‘‰ffŽ–®minimum‘‰ffŽ“zŽ’‰žÚ¬(‘ª®)‘UU­constŽ‘*¢¬;ŽŸ­1410.Ž©°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¤ ‘ +­realŽ‘ ³/SolidŽ‘;1 +¬::‘±get‘‰ffŽ–®minimum‘‰ffŽ“zŽ‘D]ܬ(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­b•QÇo“olŽ‘-¡h´DEBUGŽ‘K.Ù¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¦‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"Entering® ´Solid::getŽ‘kÆÜ_minimum_z()"Ž’³T5°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"projective_extremesŽ‘kÆÜ[4]® ´==® ´"Ž’™D°‘DZpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘VËi¬[4Ž‘]–Ç°“±end‘‚ØlŽ‘ò°“± ushŽ‘€¬;Ž¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"Exiting® ´Solid::get_Ž‘kÆÜminimum_z()"Ž’®8°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘°gŽ¡‘­returnŽ‘7æ¼±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ’‹ë ¬[4Ž‘];Ž¡‘ +°gŽŸ­1411.‘ üGet–ÕTmaxim®9um“z.Ž¦°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔrealŽ‘FA±get‘‰ffŽ–®maximum‘‰ffŽ“zŽ’Š®¬(‘ª®)‘UU­constŽ‘*¢¬;ŽŸ­1412.Ž¦°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¡‘ +­realŽ‘ ³/SolidŽ‘;1 +¬::‘±get‘‰ffŽ–®maximum‘‰ffŽ“zŽ‘Em¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­b•QÇo“olŽ‘-¡h´DEBUGŽ‘K.Ù¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¦‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"Entering® ´Solid::getŽ‘kÆÜ_maximum_z()"Ž’³T5°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"projective_extremesŽ‘kÆÜ[5]® ´==® ´"Ž’™D°‘DZpr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘VËi¬[5Ž‘]–Ç°“±end‘‚ØlŽ‘ò°“± ushŽ‘€¬;Ž¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"Exiting® ´Solid::get_Ž‘kÆÜmaximum_z()"Ž’®8°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘°gŽ¡‘­returnŽ‘7æ¼±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ’‹ë ¬[5Ž‘];Ž¡‘ +°gŽŸ­1413.› üGet–ÕTmean“z.˜¬[²LDF‘T2003.05.16.¬]Ž‘Zˆ6Added–UUthis“function.Ž¦°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/ÔrealŽ‘FA±get‘‰ffŽ–®me‘ÿ}'an‘‰ffŽ“zŽ‘v÷ ¬(‘ª®)‘UU­constŽ‘*¢¬;ŽŸ­1414.Ž¦°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¡‘ +­realŽ‘ ³/SolidŽ‘;1 +¬::‘±get‘‰ffŽ–®me‘ÿ}'an‘‰ffŽ“zŽ‘1¶¬(‘ª®)‘UU­constŽŽ¡‘ +°fŽ¡‘­returnŽ‘7漬((±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘TQ¬[4Ž›]–8à+“±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘V=1¬[5Ž˜])µ=¬2Ž˜);Ž¡‘ +°gŽŸ­1415.‘ üSuppress‘ÕToutput.Ž¦°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/Ôv®9oidŽ‘H‹¬±suppr‘ÿ}'ess‘‰ffŽ‘®outputŽ’r.¬(‘ª®);ŽŽŽŒ‹¤zÈ Šn ý‘ì¬420–¯SUPPRESS‘ÕXOUTPUT’òa3DLDF-1.1.5.1“°x¬1416Ž €n ý•@P­1416.Ž©°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘"ýÙSolidŽ‘={´¬::‘±suppr‘ÿ}'ess‘‰ffŽ‘®outputŽ‘E憬(‘ª®)Ž¡‘ +°fŽ¡‘±do‘‰ffŽ‘®outputŽ‘A½M¬=‘DZfalseŽ‘v\¬;Ž¡‘­returnŽ‘4‘g¬;Ž¡‘ +°gŽŸ­1417.‘ üUnsuppress‘ÕToutput.Ž¦°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/Ôv®9oidŽ‘H‹¬±unsuppr‘ÿ}'ess‘‰ffŽ‘®outputŽ’˜oR¬(‘ª®);ŽŸ­1418.Ž¦°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¡‘ +­v®9oidŽ‘"ýÙSolidŽ‘={´¬::‘±unsuppr‘ÿ}'ess‘‰ffŽ‘®outputŽ‘P㪬(‘ª®)Ž¡‘ +°fŽ¡‘±do‘‰ffŽ‘®outputŽ‘A½M¬=‘DZtrueŽ‘‹°¬;Ž¡‘­returnŽ‘4‘g¬;Ž¡‘ +°gŽŸ­1419.– üOutput.“¬[²LDF‘T2002.10.02.¬]Ž‘Zˆ6In‘UU­PictureŽ‘)ñf¬::‘±outputŽ‘D¬(‘ª®),‘UU±shap‘ÿ}'esŽ‘#™3¬is–UUsorted“according“to“the“v‘ÿqÇalues“inŽ¡±pr–ÿ}'oje“ctive‘‰ffŽ‘®extr“emesŽ‘W¸á¬for–´eacš¸ãh“­ShapQÇeŽ‘" ¬.‘wHo˜w˜ev˜er,‘Ì^it's“pGossible“(and“ev˜en“lik˜ely)“that“the“individual“­P®9athsŽ‘$ƒÀ¬inŽ¡a‘Ü +­SolidŽ‘!5ë¬are–Ü +not“ordered“in“sucš¸ãh“a“w˜a˜y“that“they“will“bGe“output“in“the“correct“order.‘åTherefore,‘ý·I‘ÛçdeclareŽ¡a‘™­v®9ectorŽ‘#ºá°h­ShapQÇeŽ‘"ü¦°Ž‘'ü§i‘™µsŽ‘ Ñ2¬and–™put“the“­P®9athsŽ‘%;Ò¬from“±p‘ÿ}'athsŽ‘¡F¬,‘?j±cir‘ÿ}'clesŽ‘ Ëά,‘?j±el‘‚ØlipsesŽ‘$ÁÛ¬,‘?j±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:2º¬,‘?jand“±r–ÿ}'e“ctanglesŽ‘3Áw¬on¸ãtoŽ¡it.›FôThen–ñ¹I‘ñ‘sort“µsŽ‘ “r¬and“call“±outputŽ‘!ù¬(‘ª®)“for“eac¸ãh“­ShapQÇeŽ‘"ÝƬ.˜Currenš¸ãtly‘ÿ*ª,‘Ò±outputŽ‘!(¬(‘ª®)“will“resolv˜e“to“­P®9athŽ‘ƒ!¬::‘±outputŽ‘D¬(‘ª®),Ž¡bšGecause‘z±outputŽ‘ º¬(‘ª®)–zhasn't“b˜een“o•¸ãv“erloaded–zfor“­CircleŽ‘!d¦¬,‘?­EllipseŽ‘$û¬,‘?­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘Dó¬,‘?or“­RectangleŽ‘8B‰¬(and“probablyŽ¡w¸ãon't‘UUbGe).Ž¡‘ +The›Àin•¸ãv“oGcation˜of˜±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.j¬(‘ª®)˜in˜eac“h˜of˜the˜four˜lo•Gops˜dep“ends˜on˜the˜fact˜that˜­P®9athŽ‘£(¬::‘±extr‘ÿ}'actŽ‘Âs¬(‘ª®)˜returnsŽ¡a‘{:­v®9ectorŽ‘( ¼¬conš¸ãtaining–{:only“one“elemen˜t.‘ãuThat's“wh˜y“I‘zîuse“±fr‘ÿ}'ontŽ‘Äˬ(‘ª®).‘ãuThere“is“no“opGerator“or“function“forŽ¡concatenating‘UU­v®9ectorsŽ‘'ˆÙ¬,–UUat“least“I“couldn't“ nd“one“in“Stroustrup.‘qÇTO“DO:“Get“reference!Ž¦°h–ª¨¬Declare‘UU­SolidŽ‘ (¬functions‘@¯1336“°i‘Ǭ+°Ž¡‘ +­virtualŽ‘/Ôv®9oidŽ‘H‹¬±outputŽ‘ešì¬(‘ª®);ŽŽŽŒ‹¥†  Šn ý‘ì°x¬1420–¯3DLDF-1.1.5.1’/è™OUTPUT“¬421Ž €n ý•@P­1420.Ž©°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘"ýÙSolidŽ‘={´¬::‘±outputŽ‘D¬(‘ª®)Ž¡‘ +°fŽ¡‘­b•QÇo“olŽ‘-¡h´DEBUGŽ‘K.Ù¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¦‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Entering® ´Solid::outŽ‘kÆÜput().\n"Ž’›)¬;Ž¦‘­v®9ectorŽ‘3ªJ°h­ShapQÇeŽ‘"Ab°Ž‘'Aci‘UUµsŽ‘U¬;Ž¦‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­P®9athŽ‘æ¹°Ž‘ æºi‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZp‘ÿ}'athsŽ–Wŵ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZp‘ÿ}'athsŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)Ž¡‘µsŽ‘"°:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬((°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±get‘‰ffŽ‘®c‘ÿ}'opyŽ‘$ô¬(‘ª¨));Ž¡‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­CircleŽ‘!¸°Ž‘&¸‚i‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZcir‘ÿ}'clesŽ–S|µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZcir‘ÿ}'clesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)Ž¡‘µsŽ‘"°:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬((°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±get‘‰ffŽ‘®c‘ÿ}'opyŽ‘$ô¬(‘ª¨));Ž¡‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­EllipseŽ‘%>.°Ž‘*>/i‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZel‘‚ØlipsesŽ–#I‰µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZel‘‚ØlipsesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)Ž¡‘µsŽ‘"°:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬((°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±get‘‰ffŽ‘®c‘ÿ}'opyŽ‘$ô¬(‘ª¨));Ž¡‘­forŽ‘&Qˬ(­v®9ectorŽ‘ªH°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘E=L°Ž‘J=Mi‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=Ú¼¬=‘v‡±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ–9i×µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘i@±iterŽ‘ªÅ°6¬=‘v‡±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ“µ:±endŽ‘ಬ(˜);Ž¡‘2€Ÿÿ³+‘ÿ+ŽŽ‘>G%±iterŽ‘O#¬)‘µsŽ‘ °:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬((°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±get‘‰ffŽ‘®c‘ÿ}'opyŽ‘$ô¬(‘ª¨));Ž¡‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­RectangleŽ‘5”ê°Ž‘:”ëi‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZr–ÿ}'e“ctanglesŽ–.g]µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZr–ÿ}'e“ctanglesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)Ž¡‘µsŽ‘"°:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬((°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±get‘‰ffŽ‘®c‘ÿ}'opyŽ‘$ô¬(‘ª¨));Ž¡‘±sortŽ‘&2Ô¬(µsŽ‘°:±b–ÿ}'e“ginŽ‘¾¨¬(–ª¨)µ;“sŽ‘Z¨:±endŽ‘ಬ(“)µ;“­Compareu½‰™šs4Ž–Ôwmaxim®9umu½‰™šs4Ž“zŽ‘pOŠ¬(“));Ž¡‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­ShapQÇeŽ‘"Ab°Ž‘'Aci‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘ǵsŽ–w:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘ǵsŽ“:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘¬(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±outputŽ‘@¬(‘ª¨);Ž¡‘­deleteŽ‘?ƽ¬(°Ž‘±iterŽ‘Êÿ¬);Ž¡‘°gŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Exiting® ´Solid::outpŽ‘kÆÜut().\n"Ž’–M,¬;Ž¡‘ +°gŽŸ­1421.‘ üDra®9wing–ÕTand“ lling.ŽŽŽŒ‹¦ Šn ý‘ì¬422›¯DRA‘ÿ8WING–ÕXAND“FILLING’î¯3DLDF-1.1.5.1˜°x¬1422Ž €n ý•@P­1422.‘ ü¬ProGcess–èËvš¸ãectors“for“±dr‘ÿ}'aw‘¬().‘M™[²LDF‘T2002.10.09.¬]Ž‘RéIAdded“this“section.‘M™The“same“things“are“done“to“eac˜hŽ¤ of– ¦the“­ShapQÇeŽ‘'-Y°Ž‘0N¬v¸ãectors“±p‘ÿ}'athsŽ‘±S¬,‘Sz±el‘‚ØlipsesŽ‘$Õë¬,‘Sz±cir‘ÿ}'clesŽ‘ ßÞ¬,‘Sz±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:Fʬ,›Szand“±r–ÿ}'e“ctanglesŽ‘/Àë¬,˜so“I'v¸ãe“put“the“coGde“in“thisŽ¡named–UUsection.‘qÇEacš¸ãh“time“it“it's“used,“±iterŽ‘u¨¬is“an“iterator“for“a“di eren˜t“v˜ector.Ž©°h›ª¨¬ProGcess–UUv¸ãectors“for“±dr‘ÿ}'awŽ‘~0¬(‘ª®)‘@¯1422˜°i‘ÇŽ¡‘ +fŽ¡‘ +­ifŽ‘´ù¬(±c‘‰ffŽ‘®iterŽ‘ÙÀ°6¬=‘ǵvŽ‘ûÕ:±endŽ‘ಬ(‘ª¨))‘°fŽ¡‘±c‘ÿ}'olor‘‰ffŽ‘®ptrŽ‘=Ç?¬=‘Ç°Ž‘DZc‘‰ffŽ‘®iterŽ‘!YÁŸÿ³+‘ÿ+ŽŽ‘- á¬;Ž¡‘ +°gŽ¡‘ +¬(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–® l‘‚Øl‘‰ffŽ“dr‘ÿ}'aw‘‰ffŽ“valueŽ‘N\ö¬(´DRAWŽ‘†\¬);‘µ=°‘ÿý¬LDF–UU2002.10.09.‘qÇAdded“coGde“for“handling“±dr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘2AŽ¬.‘o°µ=Ž¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"color_ptr->get_use_Ž‘kÆÜname()® ´==® ´"Ž’¨Ô;°‘DZc‘ÿ}'olor‘‰ffŽ‘®ptrŽ‘'Ç=Ÿµ~ŽŽ‘-Ç>±get‘‰ffŽ–®use‘‰ffŽ“nameŽ‘h}D¬(‘ª¨)–Ç°“±end‘‚ØlŽ‘ò°“± ushŽ‘€¬;Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(±c‘ÿ}'olor‘‰ffŽ‘®ptrŽ‘%%Ÿµ~ŽŽ‘+&±get‘‰ffŽ–®use‘‰ffŽ“nameŽ‘e¶,¬(‘ª¨)–Ç°“±falseŽ‘v\¬)‘UU°fŽ¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Allocating® ´memory® ´fŽ‘kÆÜor® ´Color.\n"Ž’®8°‘DZ ushŽ‘€¬;Ž¡‘ +­ColorŽ‘)¤ô°Ž‘.¤õµcŽ‘6N%¬=‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­ColorŽ‘"l µ>‘Ǭ(0Ž‘);Ž¦‘ +°Ž‘µcŽ‘õ¬=‘Ç°Ž‘DZc‘ÿ}'olor‘‰ffŽ‘®ptrŽ‘.Ç>¬;Ž¡‘ +(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–®dr›ÿ}'aw‘‰ffŽ“c˜olorŽ‘>¬(µcŽ‘SÛ¬);‘UU°gŽ¡‘ +­elseŽ‘!Øà°fŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"color_ptr->get_nameŽ‘kÆÜ()® ´==® ´"Ž’“ÔG°‘DZc‘ÿ}'olor‘‰ffŽ‘®ptrŽ‘'Ç=Ÿµ~ŽŽ‘-Ç>±get‘‰ffŽ‘®nameŽ‘VÀþ¬(‘ª¨)–Ç°“±end‘‚ØlŽ‘ò°“± ushŽ‘€¬;Ž¡‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–®dr›ÿ}'aw‘‰ffŽ“c˜olorŽ‘>¬(±c‘ÿ}'olor‘‰ffŽ‘®ptrŽ‘'%¬);Ž¡‘ +°gŽ¡‘ +¬(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–® l‘‚Øl‘‰ffŽ“c‘ÿ}'olorŽ‘5I:¬(­staticu½‰™šs4Ž‘ÔwcastŽ‘4}¢°h­ColorŽ‘¤ó°Ž‘$¤ôi¬(0Ž‘));Ž¡‘ +(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–®dash‘‰ffŽ“p‘ÿ}'atternŽ‘FÝ–¬(±ddashe‘ÿ}'dŽ‘#G¬);Ž¡‘ +(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ‘®p‘ÿ}'enŽ‘ʘ¬(±pp‘ÿ}'enŽ‘6#¬);‘UU°gŽŸ ¯This–ÕXco(i°h­constŽ‘~!ColorŽ‘>v“°Ž‘Cv”i‘¨ÔµvŽ‘ /Ѭ=‘R@­ColorsŽ‘%+¬::Ž‘+¹\±default‘‰ffŽ–®c›ÿ}'olor‘‰ffŽ“ve˜ctorŽ’€Ó–µ;‘ª¨­constŽ‘ (ÉstringŽŽ¡‘±ddashe‘ÿ}'dŽ‘D,¬=‘Ç´""Ž– Ízµ;‘ª¨­constŽ‘ÕJstringŽ‘@ú—±pp‘ÿ}'enŽ‘X÷Ò¬=‘Ç´""Ž“µ;‘ª¨­PictureŽ‘*œ +¬&Ž‘2c(±pictur‘ÿ}'eŽ‘T3¬=‘DZcurr–ÿ}'ent‘‰ffŽ‘®pictur“eŽ‘Dì߬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹§œ7 Šn ý‘ì°x¬1424–¯3DLDF-1.1.5.1’:k{DRA‘ÿ8W“¬423Ž €n ý•@P­1424.Ž©°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘"Î:SolidŽ‘=L¬::‘±dr‘ÿ}'awŽ‘(߬(­constŽ‘ûv®9ectorŽ‘=¥K°h­constŽ‘ûColorŽ‘=pW°Ž‘BpXi‘%¶µvŽ‘Zs;‘ª¨­constŽ‘¥«stringŽ‘@›Y±ddashe‘ÿ}'dŽ‘câjµ;‘ª¨­constŽ‘¥«stringŽ‘@›Y±pp‘ÿ}'enŽ‘UÑ|µ;‘ª¨­PictureŽŽ¡‘2¬&Ž‘9Ç#±pictur‘ÿ}'eŽ‘XÏù¬)‘UU­constŽ‘*¢°f‘UU­b•QÇo“olŽ‘ö»´DEBUGŽ‘:„,¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¦‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Entering® ´Solid::draŽ‘kÆÜw():"Ž’‰TM°‘Ç´"\n"Ž‘Œ°‘DZ ushŽ‘€¬;Ž¡‘­SolidŽ‘:Ó/°Ž‘?Ó0µsŽ‘GØ…¬=‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­SolidŽ‘šDµ>‘Ǭ(0Ž‘);Ž¦‘°Ž‘#µsŽ‘*w¬=‘Ç°Ž‘DZthisŽ‘²Ï¬;Ž¦‘­constŽ‘<*¥ColorŽ‘[Ϙ°Ž‘`Ï™±c‘ÿ}'olor‘‰ffŽ‘®ptrŽ’Š–Ö¬=‘Ç­ColorsŽ‘$Ÿö¬::Ž‘+.4±default‘‰ffŽ‘®c‘ÿ}'olorŽ‘bª¬;Ž¦‘­v®9ectorŽ‘=ªK°h­constŽ‘*¢ColorŽ‘=Ï•°Ž‘BÏ–i‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûc‘‰ffŽ‘®iterŽ‘_\»¬=‘ǵvŽ‘ûÕ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¡‘­forŽ‘/艬(­v®9ectorŽ‘ªH°h­P®9athŽ‘æ¹°Ž‘ æºi‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±p‘ÿ}'athsŽ–#Ƶ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±p‘ÿ}'athsŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘(h›ª¨¬ProGcess–UUv¸ãectors“for“±dr‘ÿ}'awŽ‘~0¬(‘ª®)‘@¯1422˜°iŽ¡‘gŽ¡‘±c‘‰ffŽ‘®iterŽ‘9Ùì=‘ǵvŽ‘ûÕ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¡‘­forŽ‘/艬(­v®9ectorŽ‘ªH°h­CircleŽ‘!¸°Ž‘&¸‚i‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±cir‘ÿ}'clesŽ–(}µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±cir‘ÿ}'clesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘(h›ª¨¬ProGcess–UUv¸ãectors“for“±dr‘ÿ}'awŽ‘~0¬(‘ª®)‘@¯1422˜°iŽ¡‘gŽ¡‘±c‘‰ffŽ‘®iterŽ‘9Ùì=‘ǵvŽ‘ûÕ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¡‘­forŽ‘/艬(­v®9ectorŽ‘ªH°h­EllipseŽ‘%>.°Ž‘*>/i‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±el‘‚ØlipsesŽ–+ùŠµ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±el‘‚ØlipsesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘(h›ª¨¬ProGcess–UUv¸ãectors“for“±dr‘ÿ}'awŽ‘~0¬(‘ª®)‘@¯1422˜°iŽ¡‘g‘µ=°‘ÿý­forŽ‘“+°µ=Ž¡‘±c‘‰ffŽ‘®iterŽ‘9Ùì=‘ǵvŽ‘ûÕ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¡‘­forŽ‘1ƒö¬(­v®9ectorŽ‘ªH°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘Fov°Ž‘Kowi‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘YÂì=‘tʵsŽ‘$ÊŸ~ŽŽ‘$˱r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘Dµ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¡‘<±iterŽ‘O’°6¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘Ajiµ:±endŽ‘ಬ(‘ª¨);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘(h›ª¨¬ProGcess–UUv¸ãectors“for“±dr‘ÿ}'awŽ‘~0¬(‘ª®)‘@¯1422˜°iŽ¡‘gŽ¡‘­forŽ‘0ã¬(­v®9ectorŽ‘ªH°h­RectangleŽ‘5¾D°Ž‘:¾Ei‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘WYû¬=‘ µsŽ‘¼Ÿ~ŽŽ‘ ¼±r–ÿ}'e“ctanglesŽ–7\Hµ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘)W±iterŽ‘W°6¬=‘ µsŽ‘¼Ÿ~ŽŽ‘ ¼±r–ÿ}'e“ctanglesŽ“µ:±endŽ‘ಬ(˜);Ž¡‘<€Ÿÿ³+‘ÿ+ŽŽ‘HG&±iterŽ‘Y$¬)‘°fŽ¡‘(h›ª¨¬ProGcess–UUv¸ãectors“for“±dr‘ÿ}'awŽ‘~0¬(‘ª®)‘@¯1422˜°iŽ¡‘gŽ¡‘±pictur‘ÿ}'eŽ‘?Ïñ¬+=ŽŽ‘R%E­dynamicu½‰™šs4Ž‘ÔwcastŽ’•–°h­ShapQÇeŽ‘"Ab°Ž‘'Aci¬(µsŽ‘°¬);Ž¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘(±c‘ÿ}'outŽ‘> S°‘Ç´"Exiting® ´Solid::drawŽ‘kÆÜ():"Ž’„P°‘Ç´"\n"Ž‘Œ°‘DZ ushŽ‘€¬;Ž¡‘°gŽ¡‘gŽŽŽŒ‹¨©š Šn ý‘ì¬424–¯DRA‘ÿ8W’:k{3DLDF-1.1.5.1“°x¬1425Ž €n ý•@P­1425.‘ ü¬ProGcess–Ž:vš¸ãectors“for“± l‘‚Øl‘‰¬().‘v[²LDF‘T2002.10.09.¬]Ž‘T]•Added“this“section.‘vThe“same“things“are“done“to“eac˜hŽ¤ of– ¦the“­ShapQÇeŽ‘'-Y°Ž‘0N¬v¸ãectors“±p‘ÿ}'athsŽ‘±S¬,‘Sz±el‘‚ØlipsesŽ‘$Õë¬,‘Sz±cir‘ÿ}'clesŽ‘ ßÞ¬,‘Sz±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:Fʬ,›Szand“±r–ÿ}'e“ctanglesŽ‘/Àë¬,˜so“I'v¸ãe“put“the“coGde“in“thisŽ¡named–UUsection.‘qÇEacš¸ãh“time“it“it's“used,“±iterŽ‘u¨¬is“an“iterator“for“a“di eren˜t“v˜ector.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2003.08.10.¬]Ž‘Y;No¸ãw–UUsetting“pšGen“to“´""Ž‘[·¬,“b˜ecause“I'vš¸ãe“remo˜v˜ed“the“pGen“argumen˜t“from“± l‘‚ØlŽ‘H¬(‘ª®).Ž¤ŸüÈ„`ÕÁGŽŽ¡°h›ª¨¬ProGcess–UUv¸ãectors“for“± l‘‚ØlŽ‘H¬(‘ª®)‘@¯1425˜°i‘ÇŽ¤ ‘ +fŽ¡‘ +­ifŽ‘´ù¬(±c‘‰ffŽ‘®iterŽ‘ÙÀ°6¬=‘ǵvŽ‘ûÕ:±endŽ‘ಬ(‘ª¨))‘°fŽ¡‘±c‘ÿ}'olor‘‰ffŽ‘®ptrŽ‘=Ç?¬=‘Ç°Ž‘DZc‘‰ffŽ‘®iterŽ‘!YÁŸÿ³+‘ÿ+ŽŽ‘- á¬;Ž¡‘ +°gŽ¡‘ +¬(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–® l‘‚Øl‘‰ffŽ“dr‘ÿ}'aw‘‰ffŽ“valueŽ‘N\ö¬(´FILLŽ‘†\¬);Ž¡‘µ=°‘ÿý¬LDF–UU2002.10.09.‘qÇAdded“coGde“for“handling“±dr–ÿ}'aw‘‰ffŽ‘®c“olorŽ‘5–ã¬and“± l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘(íª¬.‘o°µ=Ž¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"color_ptr->get_use_Ž‘kÆÜname()® ´==® ´"Ž’¨Ô;°‘DZc‘ÿ}'olor‘‰ffŽ‘®ptrŽ‘'Ç=Ÿµ~ŽŽ‘-Ç>±get‘‰ffŽ–®use‘‰ffŽ“nameŽ‘h}D¬(‘ª¨)–Ç°“±end‘‚ØlŽ‘ò°“± ushŽ‘€¬;Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(±c‘ÿ}'olor‘‰ffŽ‘®ptrŽ‘%%Ÿµ~ŽŽ‘+&±get‘‰ffŽ–®use‘‰ffŽ“nameŽ‘e¶,¬(‘ª¨)–Ç°“±falseŽ‘v\¬)‘UU°fŽ¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Allocating® ´memory® ´fŽ‘kÆÜor® ´Color.\n"Ž’®8°‘DZ ushŽ‘€¬;Ž¡‘ +­ColorŽ‘)¤ô°Ž‘.¤õµcŽ‘6N%¬=‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­ColorŽ‘"l µ>‘Ǭ(0Ž‘);Ž©‘ +°Ž‘µcŽ‘õ¬=‘Ç°Ž‘DZc‘ÿ}'olor‘‰ffŽ‘®ptrŽ‘.Ç>¬;Ž¡‘ +(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–® l‘‚Øl‘‰ffŽ“c‘ÿ}'olorŽ‘5I:¬(µcŽ‘SÛ¬);‘UU°gŽ¡‘ +­elseŽ‘!Øà°fŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"color_ptr->get_nameŽ‘kÆÜ()® ´==® ´"Ž’“ÔG°‘DZc‘ÿ}'olor‘‰ffŽ‘®ptrŽ‘'Ç=Ÿµ~ŽŽ‘-Ç>±get‘‰ffŽ‘®nameŽ‘VÀþ¬(‘ª¨)–Ç°“±end‘‚ØlŽ‘ò°“± ushŽ‘€¬;Ž¡‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–® l‘‚Øl‘‰ffŽ“c‘ÿ}'olorŽ‘5I:¬(±c‘ÿ}'olor‘‰ffŽ‘®ptrŽ‘'%¬);Ž¡‘ +°gŽ¡‘ +¬(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–®dr›ÿ}'aw‘‰ffŽ“c˜olorŽ‘>¬(­staticu½‰™šs4Ž‘ÔwcastŽ‘4}¢°h­ColorŽ‘¤ó°Ž‘$¤ôi¬(0Ž‘));Ž¡‘ +(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–®dash‘‰ffŽ“p‘ÿ}'atternŽ‘FÝ–¬(´""Ž‘ b¬);Ž¡‘ +(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ‘®p‘ÿ}'enŽ‘ʘ¬(´""Ž‘ b¬);‘UU°gŽŸ ¯This–ÕXcožÏ°h­constŽ‘ô‡ColorŽ‘?c_°Ž‘Dc`i‘:µvŽ‘ kŠ¬=‘“­ColorsŽ‘%ðq¬::Ž‘,~¯±default‘‰ffŽ–®c›ÿ}'olor‘‰ffŽ“ve˜ctorŽ’˜éµ;‘ª¨­PictureŽŽ¡‘¬&Ž‘%Ç!±pictur‘ÿ}'eŽ‘G—¬=‘DZcurr–ÿ}'ent‘‰ffŽ‘®pictur“eŽ‘Dì߬)‘UU­constŽ‘*¢¬;ŽŽŽŒ‹©¸† Šn ý‘ì°x¬1427–¯3DLDF-1.1.5.1’BãFILL“¬425Ž €n ý•@P­1427.Ž©°h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘"ýÙSolidŽ‘={´¬::‘± l‘‚ØlŽ‘ É÷¬(­constŽ‘*¢v®9ectorŽ‘=Ôê°h­constŽ‘*¢ColorŽ‘=Ï•°Ž‘BÏ–i‘UUµvŽ‘Š;‘ª¨­PictureŽ‘*œ +¬&Ž‘2c(±pictur‘ÿ}'eŽ‘Qkþ¬)‘UU­constŽ‘*¢°f‘UU­b•QÇo“olŽ‘ö»´DEBUGŽ‘:„,¬=‘DZfalseŽ‘v\¬;Ž¡‘(µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¦‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Entering® ´Solid::filŽ‘kÆÜl():"Ž’‰TM°‘Ç´"\n"Ž‘Œ°‘DZ ushŽ‘€¬;Ž¡‘­SolidŽ‘:Ó/°Ž‘?Ó0µsŽ‘GØ…¬=‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­SolidŽ‘šDµ>‘Ǭ(0Ž‘);Ž¦‘°Ž‘#µsŽ‘*w¬=‘Ç°Ž‘DZthisŽ‘²Ï¬;Ž¦‘­constŽ‘<*¥ColorŽ‘[Ϙ°Ž‘`Ï™±c‘ÿ}'olor‘‰ffŽ‘®ptrŽ’Š–Ö¬=‘Ç­ColorsŽ‘$Ÿö¬::Ž‘+.4±default‘‰ffŽ‘®c‘ÿ}'olorŽ‘bª¬;Ž¦‘­v®9ectorŽ‘=ªK°h­constŽ‘*¢ColorŽ‘=Ï•°Ž‘BÏ–i‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûc‘‰ffŽ‘®iterŽ‘_\»¬=‘ǵvŽ‘ûÕ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¡‘­forŽ‘/艬(­v®9ectorŽ‘ªH°h­P®9athŽ‘æ¹°Ž‘ æºi‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±p‘ÿ}'athsŽ–#Ƶ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±p‘ÿ}'athsŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘(h›ª¨¬ProGcess–UUv¸ãectors“for“± l‘‚ØlŽ‘H¬(‘ª®)‘@¯1425˜°iŽ¡‘gŽ¡‘±c‘‰ffŽ‘®iterŽ‘9Ùì=‘ǵvŽ‘ûÕ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¡‘­forŽ‘/艬(­v®9ectorŽ‘ªH°h­CircleŽ‘!¸°Ž‘&¸‚i‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±cir‘ÿ}'clesŽ–(}µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±cir‘ÿ}'clesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘(h›ª¨¬ProGcess–UUv¸ãectors“for“± l‘‚ØlŽ‘H¬(‘ª®)‘@¯1425˜°iŽ¡‘gŽ¡‘±c‘‰ffŽ‘®iterŽ‘9Ùì=‘ǵvŽ‘ûÕ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¡‘­forŽ‘/艬(­v®9ectorŽ‘ªH°h­EllipseŽ‘%>.°Ž‘*>/i‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±el‘‚ØlipsesŽ–+ùŠµ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±el‘‚ØlipsesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘(h›ª¨¬ProGcess–UUv¸ãectors“for“± l‘‚ØlŽ‘H¬(‘ª®)‘@¯1425˜°iŽ¡‘gŽ¡‘±c‘‰ffŽ‘®iterŽ‘9Ùì=‘ǵvŽ‘ûÕ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¡‘­forŽ‘1ƒö¬(­v®9ectorŽ‘ªH°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘Fov°Ž‘Kowi‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘YÂì=‘tʵsŽ‘$ÊŸ~ŽŽ‘$˱r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘Dµ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¡‘<±iterŽ‘O’°6¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘Ajiµ:±endŽ‘ಬ(‘ª¨);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘(h›ª¨¬ProGcess–UUv¸ãectors“for“± l‘‚ØlŽ‘H¬(‘ª®)‘@¯1425˜°iŽ¡‘gŽ¡‘±c‘‰ffŽ‘®iterŽ‘9Ùì=‘ǵvŽ‘ûÕ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¡‘­forŽ‘0ã¬(­v®9ectorŽ‘ªH°h­RectangleŽ‘5¾D°Ž‘:¾Ei‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘WYû¬=‘ µsŽ‘¼Ÿ~ŽŽ‘ ¼±r–ÿ}'e“ctanglesŽ–7\Hµ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘)W±iterŽ‘W°6¬=‘ µsŽ‘¼Ÿ~ŽŽ‘ ¼±r–ÿ}'e“ctanglesŽ“µ:±endŽ‘ಬ(˜);Ž¡‘<€Ÿÿ³+‘ÿ+ŽŽ‘HG&±iterŽ‘Y$¬)‘°fŽ¡‘(h›ª¨¬ProGcess–UUv¸ãectors“for“± l‘‚ØlŽ‘H¬(‘ª®)‘@¯1425˜°iŽ¡‘gŽ¡‘±pictur‘ÿ}'eŽ‘?Ïñ¬+=ŽŽ‘R%E­dynamicu½‰™šs4Ž‘ÔwcastŽ’•–°h­ShapQÇeŽ‘"Ab°Ž‘'Aci¬(µsŽ‘°¬);Ž¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘(±c‘ÿ}'outŽ‘> S°‘Ç´"Exiting® ´Solid::fillŽ‘kÆÜ():"Ž’„P°‘Ç´"\n"Ž‘Œ°‘DZ ushŽ‘€¬;Ž¡‘°gŽ¡‘gŽŽŽŒ‹ªÇ Šn ý‘ì¬426–¯FILL’Bã3DLDF-1.1.5.1“°x¬1428Ž €n ý•@P­1428.‘ ü¬ProGcess–­õv¸ãectors“for“± l‘‚Øldr‘ÿ}'aw‘¬().‘{¨[²LDF‘T2002.10.09.¬]Ž‘TÜ‚Added“this“section.‘{¨The“same“things“are“done“toŽ¤ eacš¸ãh–ö‘of“the“­ShapQÇeŽ‘&Ù/°Ž‘/ÏÁ¬v˜ectors“±p‘ÿ}'athsŽ‘‡>¬,‘ß±el‘‚ØlipsesŽ‘$¡P¬,‘ß±cir‘ÿ}'clesŽ‘ «C¬,‘ß±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:/¬,›ßand“±r–ÿ}'e“ctanglesŽ‘/–Ö¬,˜so“I'v¸ãe“put“the“coGde“inŽ¡this–UUnamed“section.‘qÇEacš¸ãh“time“it“it's“used,“±iterŽ‘u¨¬is“an“iterator“for“a“di eren˜t“v˜ector.Ž©°h›ª¨¬ProGcess–UUv¸ãectors“for“± l‘‚Øldr‘ÿ}'awŽ‘$¼À¬(‘ª®)‘@¯1428˜°i‘ÇŽ¡‘ +fŽ¡‘ +­ifŽ‘´ù¬(±dr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜iterŽ‘D•û°6¬=‘DZdr–ÿ}'aw‘‰ffŽ‘®c“olorsŽ‘5ˆ¥µ:±endŽ‘ಬ(‘ª¨))‘°fŽ¡‘±dr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜ptrŽ‘VƬ=‘Ç°Ž‘DZdr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜iterŽ‘JüŸÿ³+‘ÿ+ŽŽ‘Uݬ;Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(± l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“iterŽ‘;B°6¬=‘DZ l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorsŽ‘,4Áµ:±endŽ‘ಬ(‘ª¨))‘°fŽ¡‘± l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“ptrŽ‘L³â¬=‘Ç°Ž‘DZ l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“iterŽ‘@Ÿÿ³+‘ÿ+ŽŽ‘L‰8¬;Ž¡‘ +°gŽ¡‘ +¬(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–® l‘‚Øl‘‰ffŽ“dr‘ÿ}'aw‘‰ffŽ“valueŽ‘N\ö¬(´FILLDRAWŽ‘*†P¬);Ž¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"draw_color_ptr->getŽ‘kÆÜ_use_name()® ´==® ´"Ž’Ã,°‘DZdr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜ptrŽ‘@ÄŸµ~ŽŽ‘Fűget‘‰ffŽ–®use‘‰ffŽ“nameŽ’€½Ë¬(‘ª¨)–Ç°“±end‘‚ØlŽ‘ò°“± ushŽ‘€¬;Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(±dr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜ptrŽ‘=@¬Ÿµ~ŽŽ‘C@­±get‘‰ffŽ–®use‘‰ffŽ“nameŽ‘}ö³¬(‘ª¨)–Ç°“±falseŽ‘v\¬)‘UU°fŽ¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Allocating® ´memory® ´fŽ‘kÆÜor® ´Color.\n"Ž’®8°‘DZ ushŽ‘€¬;Ž¡‘ +­ColorŽ‘)¤ô°Ž‘.¤õµcŽ‘6N%¬=‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­ColorŽ‘"l µ>‘Ǭ(0Ž‘);Ž¦‘ +°Ž‘µcŽ‘õ¬=‘Ç°Ž‘DZdr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜ptrŽ‘GŬ;Ž¡‘ +(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–®dr›ÿ}'aw‘‰ffŽ“c˜olorŽ‘>¬(µcŽ‘SÛ¬);‘UU°gŽ¡‘ +­elseŽ‘!Øà°fŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)Ž¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"draw_color_ptr->getŽ‘kÆÜ_name()® ´==® ´"Ž’®8°‘DZdr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜ptrŽ‘@ÄŸµ~ŽŽ‘Fűget‘‰ffŽ‘®nameŽ‘o…¬(‘ª¨)–Ç°“±end‘‚ØlŽ‘ò°“± ushŽ‘€¬;Ž¡‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–®dr›ÿ}'aw‘‰ffŽ“c˜olorŽ‘>¬(±dr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜ptrŽ‘?@¬¬);Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘±c‘ÿ}'outŽ‘* Q°‘Ç´"fill_color_ptr->getŽ‘kÆÜ_use_name()® ´==® ´"Ž’Ã,°‘DZ l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“ptrŽ‘6³àŸµ~ŽŽ‘<³á±get‘‰ffŽ–®use‘‰ffŽ“nameŽ‘wiç¬(‘ª¨)–Ç°“±end‘‚ØlŽ‘ò°“± ushŽ‘€¬;Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(± l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“ptrŽ‘3ìÈŸµ~ŽŽ‘9ìɱget‘‰ffŽ–®use‘‰ffŽ“nameŽ‘t¢Ï¬(‘ª¨)–Ç°“±falseŽ‘v\¬)‘UU°fŽ¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Allocating® ´memory® ´fŽ‘kÆÜor® ´Color.\n"Ž’®8°‘DZ ushŽ‘€¬;Ž¡‘ +­ColorŽ‘)¤ô°Ž‘.¤õµcŽ‘6N%¬=‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­ColorŽ‘"l µ>‘Ǭ(0Ž‘);Ž¦‘ +°Ž‘µcŽ‘õ¬=‘Ç°Ž‘DZ l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“ptrŽ‘=³á¬;Ž¡‘ +(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–® l‘‚Øl‘‰ffŽ“c‘ÿ}'olorŽ‘5I:¬(µcŽ‘SÛ¬);‘UU°gŽ¡‘ +­elseŽ‘!Øà°fŽ¡‘­ifŽ‘´ú¬(´DEBUGŽ‘ÆY¬)Ž¡‘±c‘ÿ}'outŽ‘4 R°‘Ç´"fill_color_ptr->getŽ‘kÆÜ_name()® ´==® ´"Ž’®8°‘DZ l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“ptrŽ‘6³àŸµ~ŽŽ‘<³á±get‘‰ffŽ‘®nameŽ‘e­¡¬(‘ª¨)–Ç°“±end‘‚ØlŽ‘ò°“± ushŽ‘€¬;Ž¡‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–® l‘‚Øl‘‰ffŽ“c‘ÿ}'olorŽ‘5I:¬(± l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“ptrŽ‘5ìȬ);Ž¡‘ +°gŽ¡‘ +¬(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ‘®p‘ÿ}'enŽ‘ʘ¬(±pp‘ÿ}'enŽ‘6#¬);Ž¡‘ +(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–®dash‘‰ffŽ“p‘ÿ}'atternŽ‘FÝ–¬(±ddashe‘ÿ}'dŽ‘#G¬);‘UU°gŽŸ ¯This–ÕXcoQU°h­constŽ‘§ ColorŽ‘>Èk°Ž–CÈli‘ÑÀ±dr–ÿ}'aw‘‰ffŽ‘®c“olorsŽ‘6“Mµ;‘ª¨­constŽ‘ Qµv®9ectorŽ‘?ûý°h­constŽ‘§ ColorŽ‘>Èk°Ž“iŽ¡‘2± l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorsŽ‘[m®µ;‘ª¨­constŽ‘ dVstringŽ‘B¯±ddashe‘ÿ}'dŽ‘e_Àµ;‘ª¨­constŽ‘ dVstringŽ‘B¯±pp‘ÿ}'enŽ‘WNÒµ;‘ª¨­PictureŽ‘++¬&Ž‘2ò4±pictur‘ÿ}'eŽ‘Qû +¬)‘äa­constŽ‘¹®°f‘äa­b•QÇo“olŽŽ¡‘2´DEBUGŽ‘Ov¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¦‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Entering® ´Solid::filŽ‘kÆÜldraw():"Ž’žTA°‘Ç´"\n"Ž‘Œ°‘DZ ushŽ‘€¬;Ž¡‘­SolidŽ‘:Ó/°Ž‘?Ó0µsŽ‘GØ…¬=‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­SolidŽ‘šDµ>‘Ǭ(0Ž‘);Ž¦‘°Ž‘#µsŽ‘*w¬=‘Ç°Ž‘DZthisŽ‘²Ï¬;Ž¦‘­constŽ‘<*¥ColorŽ‘[Ϙ°Ž‘`Ï™±dr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜ptrŽ’ E¬;Ž¡‘­constŽ‘<*¥ColorŽ‘[Ϙ°Ž‘`Ï™± l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“ptrŽ’–¼a¬;Ž¦‘­v®9ectorŽ‘=ªK°h­constŽ‘*¢ColorŽ‘=Ï•°Ž‘BÏ–i‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûdr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜iterŽ’ˆö¬=‘DZdr–ÿ}'aw‘‰ffŽ‘®c“olorsŽ‘5ˆ¥µ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¡‘­v®9ectorŽ‘=ªK°h­constŽ‘*¢ColorŽ‘=Ï•°Ž‘BÏ–i‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚û l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“iterŽ‘~Ŭ=‘DZ l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorsŽ‘,4Áµ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¡‘­forŽ‘/艬(­v®9ectorŽ‘ªH°h­P®9athŽ‘æ¹°Ž‘ æºi‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±p‘ÿ}'athsŽ–#Ƶ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±p‘ÿ}'athsŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘(h›ª¨¬ProGcess–UUv¸ãectors“for“± l‘‚Øldr‘ÿ}'awŽ‘$¼À¬(‘ª®)‘@¯1428˜°iŽ¡‘gŽ¡‘±dr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜iterŽ‘b•þ¬=‘DZdr–ÿ}'aw‘‰ffŽ‘®c“olorsŽ‘5ˆ¥µ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¡‘± l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“iterŽ‘YB¬=‘DZ l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorsŽ‘,4Áµ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¡‘­forŽ‘/艬(­v®9ectorŽ‘ªH°h­CircleŽ‘!¸°Ž‘&¸‚i‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±cir‘ÿ}'clesŽ–(}µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±cir‘ÿ}'clesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘(h›ª¨¬ProGcess–UUv¸ãectors“for“± l‘‚Øldr‘ÿ}'awŽ‘$¼À¬(‘ª®)‘@¯1428˜°iŽ¡‘gŽ¡‘±dr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜iterŽ‘b•þ¬=‘DZdr–ÿ}'aw‘‰ffŽ‘®c“olorsŽ‘5ˆ¥µ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¡‘± l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“iterŽ‘YB¬=‘DZ l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorsŽ‘,4Áµ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¡‘­forŽ‘/艬(­v®9ectorŽ‘ªH°h­EllipseŽ‘%>.°Ž‘*>/i‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±el‘‚ØlipsesŽ–+ùŠµ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±el‘‚ØlipsesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘(h›ª¨¬ProGcess–UUv¸ãectors“for“± l‘‚Øldr‘ÿ}'awŽ‘$¼À¬(‘ª®)‘@¯1428˜°iŽ¡‘gŽ¡‘±dr–ÿ}'aw‘‰ffŽ›®c“olor‘‰ffŽ˜iterŽ‘b•þ¬=‘DZdr–ÿ}'aw‘‰ffŽ‘®c“olorsŽ‘5ˆ¥µ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¡‘± l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“iterŽ‘YB¬=‘DZ l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorsŽ‘,4Áµ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¡‘­forŽ‘1ƒö¬(­v®9ectorŽ‘ªH°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘Fov°Ž‘Kowi‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘YÂì=‘tʵsŽ‘$ÊŸ~ŽŽ‘$˱r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘Dµ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¡‘<±iterŽ‘O’°6¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘Ajiµ:±endŽ‘ಬ(‘ª¨);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘(h›ª¨¬ProGcess–UUv¸ãectors“for“± l‘‚Øldr‘ÿ}'awŽ‘$¼À¬(‘ª®)‘@¯1428˜°iŽ¡‘gŽ¡‘­forŽ‘0ã¬(­v®9ectorŽ‘ªH°h­RectangleŽ‘5¾D°Ž‘:¾Ei‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘WYû¬=‘ µsŽ‘¼Ÿ~ŽŽ‘ ¼±r–ÿ}'e“ctanglesŽ–7\Hµ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘)W±iterŽ‘W°6¬=‘ µsŽ‘¼Ÿ~ŽŽ‘ ¼±r–ÿ}'e“ctanglesŽ“µ:±endŽ‘ಬ(˜);Ž¡‘<€Ÿÿ³+‘ÿ+ŽŽ‘HG&±iterŽ‘Y$¬)‘°fŽ¡‘(h›ª¨¬ProGcess–UUv¸ãectors“for“± l‘‚Øldr‘ÿ}'awŽ‘$¼À¬(‘ª®)‘@¯1428˜°iŽ¡‘gŽ¡‘±pictur‘ÿ}'eŽ‘?Ïñ¬+=ŽŽ‘R%E­dynamicu½‰™šs4Ž‘ÔwcastŽ’•–°h­ShapQÇeŽ‘"Ab°Ž‘'Aci¬(µsŽ‘°¬);Ž¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘(±c‘ÿ}'outŽ‘> S°‘Ç´"Exiting® ´Solid::fillŽ‘kÆÜdraw():"Ž’™D°‘Ç´"\n"Ž‘Œ°‘DZ ushŽ‘€¬;Ž¡‘°gŽ¡‘gŽŽŽŒ‹¬êÉ Šn ý‘ì¬428–¯FILLDRA‘ÿ8W’'2…3DLDF-1.1.5.1“°x¬1431Ž €n ý•@P­1431.‘ ü¬ProGcess–±Îv¸ãectors“for“±undr‘ÿ}'aw‘¬().‘‡3[²LDF‘T2002.10.09.¬]Ž‘TëæAdded“this“section.‘‡3The“same“things“are“done“toŽ¤ eacš¸ãh–ö‘of“the“­ShapQÇeŽ‘&Ù/°Ž‘/ÏÁ¬v˜ectors“±p‘ÿ}'athsŽ‘‡>¬,‘ß±el‘‚ØlipsesŽ‘$¡P¬,‘ß±cir‘ÿ}'clesŽ‘ «C¬,‘ß±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:/¬,›ßand“±r–ÿ}'e“ctanglesŽ‘/–Ö¬,˜so“I'v¸ãe“put“the“coGde“inŽ¡this–UUnamed“section.‘qÇEacš¸ãh“time“it“it's“used,“±iterŽ‘u¨¬is“an“iterator“for“a“di eren˜t“v˜ector.Ž©°h›ª¨¬ProGcess–UUv¸ãectors“for“±undr‘ÿ}'awŽ‘${T¬(‘ª®)‘@¯1431˜°i‘ÇŽ¡‘ +fŽ¡‘¬(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–® l‘‚Øl‘‰ffŽ“dr‘ÿ}'aw‘‰ffŽ“valueŽ‘N\ö¬(´UNDRAWŽ‘ V¬);Ž¡‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–®dr›ÿ}'aw‘‰ffŽ“c˜olorŽ‘>¬(­staticu½‰™šs4Ž‘ÔwcastŽ‘4}¢°h­ColorŽ‘¤ó°Ž‘$¤ôi¬(0Ž‘));Ž¡‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–® l‘‚Øl‘‰ffŽ“c‘ÿ}'olorŽ‘5I:¬(­staticu½‰™šs4Ž‘ÔwcastŽ‘4}¢°h­ColorŽ‘¤ó°Ž‘$¤ôi¬(0Ž‘));Ž¡‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–®dash‘‰ffŽ“p‘ÿ}'atternŽ‘FÝ–¬(±ddashe‘ÿ}'dŽ‘#G¬);Ž¡‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ‘®p‘ÿ}'enŽ‘ʘ¬(±pp‘ÿ}'enŽ‘6#¬);Ž¡‘ +°gŽŸ ¯This–ÕXco‘Ǭ(0Ž‘);Ž¦‘°Ž‘#µsŽ‘*w¬=‘Ç°Ž‘DZthisŽ‘²Ï¬;Ž¡‘­forŽ‘/艬(­v®9ectorŽ‘ªH°h­P®9athŽ‘æ¹°Ž‘ æºi‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±p‘ÿ}'athsŽ–#Ƶ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±p‘ÿ}'athsŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘(h›ª¨¬ProGcess–UUv¸ãectors“for“±undr‘ÿ}'awŽ‘${T¬(‘ª®)‘@¯1431˜°iŽ¡‘gŽ¡‘­forŽ‘/艬(­v®9ectorŽ‘ªH°h­CircleŽ‘!¸°Ž‘&¸‚i‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±cir‘ÿ}'clesŽ–(}µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±cir‘ÿ}'clesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘(h›ª¨¬ProGcess–UUv¸ãectors“for“±undr‘ÿ}'awŽ‘${T¬(‘ª®)‘@¯1431˜°iŽ¡‘gŽ¡‘­forŽ‘/艬(­v®9ectorŽ‘ªH°h­EllipseŽ‘%>.°Ž‘*>/i‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±el‘‚ØlipsesŽ–+ùŠµ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±el‘‚ØlipsesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘(h›ª¨¬ProGcess–UUv¸ãectors“for“±undr‘ÿ}'awŽ‘${T¬(‘ª®)‘@¯1431˜°iŽ¡‘gŽ¡‘­forŽ‘1ƒö¬(­v®9ectorŽ‘ªH°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘Fov°Ž‘Kowi‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘YÂì=‘tʵsŽ‘$ÊŸ~ŽŽ‘$˱r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘Dµ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¡‘<±iterŽ‘O’°6¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘Ajiµ:±endŽ‘ಬ(‘ª¨);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘(h›ª¨¬ProGcess–UUv¸ãectors“for“±undr‘ÿ}'awŽ‘${T¬(‘ª®)‘@¯1431˜°iŽ¡‘gŽ¡‘­forŽ‘0ã¬(­v®9ectorŽ‘ªH°h­RectangleŽ‘5¾D°Ž‘:¾Ei‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘WYû¬=‘ µsŽ‘¼Ÿ~ŽŽ‘ ¼±r–ÿ}'e“ctanglesŽ–7\Hµ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘)W±iterŽ‘W°6¬=‘ µsŽ‘¼Ÿ~ŽŽ‘ ¼±r–ÿ}'e“ctanglesŽ“µ:±endŽ‘ಬ(˜);Ž¡‘<€Ÿÿ³+‘ÿ+ŽŽ‘HG&±iterŽ‘Y$¬)‘°fŽ¡‘(h›ª¨¬ProGcess–UUv¸ãectors“for“±undr‘ÿ}'awŽ‘${T¬(‘ª®)‘@¯1431˜°iŽ¡‘gŽ¡‘±pictur‘ÿ}'eŽ‘?Ïñ¬+=ŽŽ‘R%E­dynamicu½‰™šs4Ž‘ÔwcastŽ’•–°h­ShapQÇeŽ‘"Ab°Ž‘'Aci¬(µsŽ‘°¬);Ž¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘(±c‘ÿ}'outŽ‘> S°‘Ç´"Exiting® ´Solid::undrŽ‘kÆÜaw():"Ž’Ž”J°‘Ç´"\n"Ž‘Œ°‘DZ ushŽ‘€¬;Ž¡‘°gŽ¡‘gŽŽŽŒ‹­þE Šn ý‘ì°x¬1434–¯3DLDF-1.1.5.1’-¯³UNDRA‘ÿ8W“¬429Ž €n ý•@P­1434.‘ ü¬ProGcess–UUv¸ãectors“for“±un l‘‚Øl‘‰¬().ŽŸN9Ÿû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¤ ‘ +¬[²LDF‘T2002.10.09.¬]Ž‘Y‡Added–Ü¡this“section.‘ªThe“same“things“are“done“to“eacš¸ãh“of“the“­ShapQÇeŽ‘&¥O°Ž‘/ñ¬v˜ectors“±p‘ÿ}'athsŽ‘mN¬,Ž¡±el‘‚ØlipsesŽ‘ ‚q¬,‘­±cir‘ÿ}'clesŽ‘ 9l¬,‘­±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘9 X¬,–­and‘›~±r–ÿ}'e“ctanglesŽ‘/;ì,“so–›~I'vš¸ãe“put“the“coGde“in“this“named“section.‘DAEac˜h“time“it“it'sŽ¡used,‘UU±iterŽ‘u¨¬is–UUan“iterator“for“a“di erenš¸ãt“v˜ector.Ž¡‘ +[²LDF‘T2003.08.10.¬]Ž‘Y;Noš¸ãw–UUsetting“pGen“to“´""Ž‘[·¬,“since“I'v˜e“remo˜v˜ed“the“pGen“argumen˜t“to“±un l‘‚ØlŽ‘l¬(‘ª®).Ž¤ŸüÈ„`ÕÁGŽŽ¡°h›ª¨¬ProGcess–UUv¸ãectors“for“±un l‘‚ØlŽ‘l¬(‘ª®)‘@¯1434˜°i‘ÇŽ¤ ‘ +fŽ¡‘¬(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–® l‘‚Øl‘‰ffŽ“dr‘ÿ}'aw‘‰ffŽ“valueŽ‘N\ö¬(´UNFILLŽ‘ V¬);Ž¡‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–®dr›ÿ}'aw‘‰ffŽ“c˜olorŽ‘>¬(­staticu½‰™šs4Ž‘ÔwcastŽ‘4}¢°h­ColorŽ‘¤ó°Ž‘$¤ôi¬(0Ž‘));Ž¡‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–® l‘‚Øl‘‰ffŽ“c‘ÿ}'olorŽ‘5I:¬(­staticu½‰™šs4Ž‘ÔwcastŽ‘4}¢°h­ColorŽ‘¤ó°Ž‘$¤ôi¬(0Ž‘));Ž¡‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–®dash‘‰ffŽ“p‘ÿ}'atternŽ‘FÝ–¬(´""Ž‘ b¬);Ž¡‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ‘®p‘ÿ}'enŽ‘ʘ¬(´""Ž‘ b¬);Ž¡‘ +°gŽŸ ¯This–ÕXco‘Ǭ(0Ž‘);Ž¡‘°Ž‘#µsŽ‘*w¬=‘Ç°Ž‘DZthisŽ‘²Ï¬;Ž¦‘­forŽ‘/艬(­v®9ectorŽ‘ªH°h­P®9athŽ‘æ¹°Ž‘ æºi‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±p‘ÿ}'athsŽ–#Ƶ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±p‘ÿ}'athsŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¦‘(h›ª¨¬ProGcess–UUv¸ãectors“for“±un l‘‚ØlŽ‘l¬(‘ª®)‘@¯1434˜°iŽ¦‘gŽ¦‘­forŽ‘/艬(­v®9ectorŽ‘ªH°h­CircleŽ‘!¸°Ž‘&¸‚i‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±cir‘ÿ}'clesŽ–(}µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±cir‘ÿ}'clesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¦‘(h›ª¨¬ProGcess–UUv¸ãectors“for“±un l‘‚ØlŽ‘l¬(‘ª®)‘@¯1434˜°iŽ¦‘gŽ¦‘­forŽ‘/艬(­v®9ectorŽ‘ªH°h­EllipseŽ‘%>.°Ž‘*>/i‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±el‘‚ØlipsesŽ–+ùŠµ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±el‘‚ØlipsesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¦‘(h›ª¨¬ProGcess–UUv¸ãectors“for“±un l‘‚ØlŽ‘l¬(‘ª®)‘@¯1434˜°iŽ¦‘gŽ¦‘­forŽ‘1ƒö¬(­v®9ectorŽ‘ªH°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘Fov°Ž‘Kowi‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘YÂì=‘tʵsŽ‘$ÊŸ~ŽŽ‘$˱r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘Dµ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¦‘<±iterŽ‘O’°6¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘Ajiµ:±endŽ‘ಬ(‘ª¨);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¦‘(h›ª¨¬ProGcess–UUv¸ãectors“for“±un l‘‚ØlŽ‘l¬(‘ª®)‘@¯1434˜°iŽ¦‘gŽ¦‘­forŽ‘0ã¬(­v®9ectorŽ‘ªH°h­RectangleŽ‘5¾D°Ž‘:¾Ei‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘WYû¬=‘ µsŽ‘¼Ÿ~ŽŽ‘ ¼±r–ÿ}'e“ctanglesŽ–7\Hµ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘)W±iterŽ‘W°6¬=‘ µsŽ‘¼Ÿ~ŽŽ‘ ¼±r–ÿ}'e“ctanglesŽ“µ:±endŽ‘ಬ(˜);Ž¦‘<€Ÿÿ³+‘ÿ+ŽŽ‘HG&±iterŽ‘Y$¬)‘°fŽ¦‘(h›ª¨¬ProGcess–UUv¸ãectors“for“±un l‘‚ØlŽ‘l¬(‘ª®)‘@¯1434˜°iŽ¦‘gŽ¦‘±pictur‘ÿ}'eŽ‘?Ïñ¬+=ŽŽ‘R%E­dynamicu½‰™šs4Ž‘ÔwcastŽ’•–°h­ShapQÇeŽ‘"Ab°Ž‘'Aci¬(µsŽ‘°¬);Ž¦‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘°fŽ¦‘(±c‘ÿ}'outŽ‘> S°‘Ç´"Exiting® ´Solid::unfiŽ‘kÆÜll():"Ž’Ž”J°‘Ç´"\n"Ž‘Œ°‘DZ ushŽ‘€¬;Ž¦‘°gŽ¦‘gŽŸ­1437.‘ ü¬ProGcess–Ç;v¸ãectors“for“±un l‘‚Øldr‘ÿ}'aw‘¬().‘Çz[²LDF‘T2002.10.09.¬]Ž‘UAšAdded“this“section.‘ÇzThe“same“things“are“doneŽ¦to–J^eacš¸ãh“of“the“­ShapQÇeŽ‘%€É°Ž‘-Ë(¬v˜ectors“±p‘ÿ}'athsŽ‘Û ¬,‘L±el‘‚ØlipsesŽ‘#Ϭ,‘L±cir‘ÿ}'clesŽ‘Øô¬,‘L±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘9?à¬,›Land“±r–ÿ}'e“ctanglesŽ‘.꣬,˜so“I'v¸ãe“put“the“coGde“inŽ¦this–UUnamed“section.‘qÇEacš¸ãh“time“it“it's“used,“±iterŽ‘u¨¬is“an“iterator“for“a“di eren˜t“v˜ector.Ž¡°h›ª¨¬ProGcess–UUv¸ãectors“for“±un l‘‚Øldr‘ÿ}'awŽ‘/¹ä¬(‘ª®)‘@¯1437˜°i‘ÇŽ¦‘ +fŽ¦‘¬(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–® l‘‚Øl‘‰ffŽ“dr‘ÿ}'aw‘‰ffŽ“valueŽ‘N\ö¬(´UNFILLDRAWŽ‘5J¬);Ž¦‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–®dr›ÿ}'aw‘‰ffŽ“c˜olorŽ‘>¬(­staticu½‰™šs4Ž‘ÔwcastŽ‘4}¢°h­ColorŽ‘¤ó°Ž‘$¤ôi¬(0Ž‘));Ž¦‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–® l‘‚Øl‘‰ffŽ“c‘ÿ}'olorŽ‘5I:¬(­staticu½‰™šs4Ž‘ÔwcastŽ‘4}¢°h­ColorŽ‘¤ó°Ž‘$¤ôi¬(0Ž‘));Ž¦‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ–®dash‘‰ffŽ“p‘ÿ}'atternŽ‘FÝ–¬(±ddashe‘ÿ}'dŽ‘#G¬);Ž¦‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±set‘‰ffŽ‘®p‘ÿ}'enŽ‘ʘ¬(±pp‘ÿ}'enŽ‘6#¬);Ž¦‘ +°gŽŸ ¯This–ÕXco‘Ǭ(0Ž‘);Ž¦‘°Ž‘#µsŽ‘*w¬=‘Ç°Ž‘DZthisŽ‘²Ï¬;Ž¡‘­forŽ‘/艬(­v®9ectorŽ‘ªH°h­P®9athŽ‘æ¹°Ž‘ æºi‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±p‘ÿ}'athsŽ–#Ƶ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±p‘ÿ}'athsŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘(h›ª¨¬ProGcess–UUv¸ãectors“for“±un l‘‚Øldr‘ÿ}'awŽ‘/¹ä¬(‘ª®)‘@¯1437˜°iŽ¡‘g‘µ=°‘ÿý­forŽ‘“+°µ=Ž¡‘­forŽ‘/艬(­v®9ectorŽ‘ªH°h­CircleŽ‘!¸°Ž‘&¸‚i‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±cir‘ÿ}'clesŽ–(}µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±cir‘ÿ}'clesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘(h›ª¨¬ProGcess–UUv¸ãectors“for“±un l‘‚Øldr‘ÿ}'awŽ‘/¹ä¬(‘ª®)‘@¯1437˜°iŽ¡‘gŽ¡‘­forŽ‘/艬(­v®9ectorŽ‘ªH°h­EllipseŽ‘%>.°Ž‘*>/i‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘W¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±el‘‚ØlipsesŽ–+ùŠµ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±el‘‚ØlipsesŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘(h›ª¨¬ProGcess–UUv¸ãectors“for“±un l‘‚Øldr‘ÿ}'awŽ‘/¹ä¬(‘ª®)‘@¯1437˜°iŽ¡‘gŽ¡‘­forŽ‘1ƒö¬(­v®9ectorŽ‘ªH°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘Fov°Ž‘Kowi‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘YÂì=‘tʵsŽ‘$ÊŸ~ŽŽ‘$˱r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘Dµ:±b–ÿ}'e“ginŽ‘¾¨¬(‘ª¨);Ž¡‘<±iterŽ‘O’°6¬=‘ǵsŽ‘wŸ~ŽŽ‘ w±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘Ajiµ:±endŽ‘ಬ(‘ª¨);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘(h›ª¨¬ProGcess–UUv¸ãectors“for“±un l‘‚Øldr‘ÿ}'awŽ‘/¹ä¬(‘ª®)‘@¯1437˜°iŽ¡‘gŽ¡‘­forŽ‘0ã¬(­v®9ectorŽ‘ªH°h­RectangleŽ‘5¾D°Ž‘:¾Ei‘¬::Ž‘ŽB±c–ÿ}'onst‘‰ffŽ‘®iter“atorŽ‘C‚ûiterŽ‘WYû¬=‘ µsŽ‘¼Ÿ~ŽŽ‘ ¼±r–ÿ}'e“ctanglesŽ–7\Hµ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘)W±iterŽ‘W°6¬=‘ µsŽ‘¼Ÿ~ŽŽ‘ ¼±r–ÿ}'e“ctanglesŽ“µ:±endŽ‘ಬ(˜);Ž¡‘<€Ÿÿ³+‘ÿ+ŽŽ‘HG&±iterŽ‘Y$¬)‘°fŽ¡‘(h›ª¨¬ProGcess–UUv¸ãectors“for“±un l‘‚Øldr‘ÿ}'awŽ‘/¹ä¬(‘ª®)‘@¯1437˜°iŽ¡‘gŽ¡‘±pictur‘ÿ}'eŽ‘?Ïñ¬+=ŽŽ‘R%E­dynamicu½‰™šs4Ž‘ÔwcastŽ’•–°h­ShapQÇeŽ‘"Ab°Ž‘'Aci¬(µsŽ‘°¬);Ž¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘(±c‘ÿ}'outŽ‘> S°‘Ç´"Exiting® ´Solid::unfiŽ‘kÆÜlldraw():"Ž’£”>°‘Ç´"\n"Ž‘Œ°‘DZ ushŽ‘€¬;Ž¡‘°gŽ¡‘gŽ¤­1440.‘ üPutting–ÕTSolid“together.Ž¡1441.‘ ü¬This–UUis“what's“compiled.Ž¦‘ +°h–ª¨¬Include‘UU les‘@¯6“°iŽ¤ ‘ +h‘ª¨¬V‘ÿ*ªersion–UUconš¸ãtrol“iden˜ti er‘@¯5‘ª¨°iŽ¡‘ +h–ª¨¬De ne‘UU­classŽ‘5¦SolidŽ‘;ó¯1333“°iŽ¡‘ +h–ª¨¬De ne‘UU­staticŽ‘"ž.constŽ‘@ÈÐSolidŽ‘]›ü¬data‘UUmem¸ãbGers‘@¯1334“°iŽ¡‘ +h–ª¨¬De ne‘UU­SolidŽ‘ (¬functions‘@¯1337“°iŽ¡‘ +h›ª¨¬Declare–UUnon-mem¸ãbGer“template“functions“for“­SolidŽ‘!0¯1341˜°iŽŽŽŒ‹°/F Šn ý‘ì¬432›¯PUTTING–ÕX­SOLID“¯TOGETHER’ÒB¾3DLDF-1.1.5.1˜°x¬1442Ž €n ý•@P­1442.‘ ü¬This–UUis“what's“written“to“®solids.h¬.Ž©áX°h‘ª¨´solids.hŽ‘5°ù¯1442‘ª¨°i‘ÇŽ¤ ‘ +h–ª¨¬De ne‘UU­classŽ‘5¦SolidŽ‘;ó¯1333“°iŽ¡‘ 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-«etrahedronŽ‘Ck«is–Ïconstructed.‘ÞøIn“addition,‘-inš¸ãtersections“can't“alw˜a˜ys“bšGe“found,‘-b˜ecause“of“inaccuraciesŽ¡caused–UUb¸ãy“rotating“the“triangles.‘qÇ[¬LDF‘T2002.08.12.«]ŽŽ¡‘ -Therefore,‘xgI'vš¸ãe–qccalculated“distance“using“the“commen˜ted-out“cošGde“b˜eloš¸ãw,‘xgand“no˜w“simply“use“the“v‘ÿqÇalue“IŽ¡found.‘qÇ[¬LDF‘T2002.08.12.«]ŽŽ©·h–ª¨«De ne‘UUÂT‘ÿ -«etrahedronŽ‘EF®«functions‘@­1440“·i‘Ç«+·Ž¡‘ -ÂrealŽ‘ ³/Ïdistanc‘ÿ}'eŽ‘GÀD«=‘Ç0±:«74997889995574951171875ŽŽ‘}ŽM;Ž¡#ÂifŽ‘ ´ø«0ŽŽ¡‘ -ÂP•®9oin“tŽ‘(ïžÝP0Ž‘6½«=‘ÇÂP•®9oin“tŽ‘ad«::Ž‘%ï¢Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘s†x«(ÏptsŽ‘ Ú¦«[0Ž–]±;‘ª¨ÏptsŽ›…N«[6Ž“]±;‘ª¨ÏptsŽ˜«[1Ž“]±;‘ª¨ÏptsŽ˜«[5Ž“])±:ÏptŽ‘ ä«;Ž¦‘ -ÝP0Ž‘c±:ÏshowŽ‘Šÿ«(Ý"P0È Ý=È Ý0,È Ý6,È Ý1,È Ý5:"Ž‘_2«);Ž¡‘ -ÂP•®9oin“tŽ‘&šM«::Ž‘-(‹Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘z¿a«(ÏptsŽ‘ Ú¦«[0Ž–]±;‘ª¨ÏptsŽ›…N«[6Ž“]±;‘ª¨ÏptsŽ˜«[2Ž“]±;‘ª¨ÏptsŽ˜«[4Ž“])±:ÏptŽ‘ ä±:ÏshowŽ‘Šÿ«(Ý"0,È Ý6,È Ý2,È Ý4:"Ž‘DÆA«);Ž¡‘ -ÂP•®9oin“tŽ‘&šM«::Ž‘-(‹Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘z¿a«(ÏptsŽ‘ Ú¦«[0Ž–]±;‘ª¨ÏptsŽ›…N«[6Ž“]±;‘ª¨ÏptsŽ˜«[3Ž“]±;‘ª¨ÏptsŽ˜«[7Ž“])±:ÏptŽ‘ ä±:ÏshowŽ‘Šÿ«(Ý"0,È Ý6,È Ý3,È Ý7:"Ž‘DÆA«);Ž¡‘ -ÂP•®9oin“tŽ‘&šM«::Ž‘-(‹Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘z¿a«(ÏptsŽ‘ Ú¦«[1Ž–]±;‘ª¨ÏptsŽ›…N«[5Ž“]±;‘ª¨ÏptsŽ˜«[2Ž“]±;‘ª¨ÏptsŽ˜«[4Ž“])±:ÏptŽ‘ ä±:ÏshowŽ‘Šÿ«(Ý"1,È Ý5,È Ý2,È Ý4:"Ž‘DÆA«);Ž¡‘ -ÂP•®9oin“tŽ‘&šM«::Ž‘-(‹Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘z¿a«(ÏptsŽ‘ Ú¦«[1Ž–]±;‘ª¨ÏptsŽ›…N«[5Ž“]±;‘ª¨ÏptsŽ˜«[3Ž“]±;‘ª¨ÏptsŽ˜«[7Ž“])±:ÏptŽ‘ ä±:ÏshowŽ‘Šÿ«(Ý"1,È Ý5,È Ý3,È Ý7:"Ž‘DÆA«);Ž¡‘ -ÂP•®9oin“tŽ‘&šM«::Ž‘-(‹Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘z¿a«(ÏptsŽ‘ Ú¦«[2Ž–]±;‘ª¨ÏptsŽ›…N«[4Ž“]±;‘ª¨ÏptsŽ˜«[3Ž“]±;‘ª¨ÏptsŽ˜«[7Ž“])±:ÏptŽ‘ ä±:ÏshowŽ‘Šÿ«(Ý"2,È Ý4,È Ý3,È Ý7:"Ž‘DÆA«);Ž¦‘ -ÂP•®9oin“tŽ‘(ïžÝP1Ž‘6½«=‘ÇÏptsŽ‘¡¾«[5Ž›]–8à·“ÏptsŽ‘†«[1Ž˜];Ž¡‘ -ÂP•®9oin“tŽ‘(ïžÝP2Ž‘6½«=‘ÇÝP0Ž‘Z·‘8àÏptsŽ‘†«[1Ž‘];Ž¦‘ -ÝP1Ž‘c±:ÏshowŽ‘Šÿ«(Ý"P1"Ž‘†\«);Ž¡‘ -Ïc‘ÿ}'outŽ‘ P·‘ÇÝ"È ÝP1.magnitude()È Ý==Ž‘kÆÜÈ Ý"Ž‘y”V·‘ÇÝP1Ž‘ Íz±:ÏmagnitudeŽ‘.=r«(‘ª¨)–Ç·“Ïend‘‚ØlŽ‘ò·“Ï ushŽ‘€«;Ž¡‘ -ÝP2Ž‘c±:ÏshowŽ‘Šÿ«(Ý"P2"Ž‘†\«);Ž¡‘ -Ïc‘ÿ}'outŽ‘ P·‘ÇÝ"P2.magnitude()È Ý==È Ý"Ž‘o\·‘ÇÝP2Ž‘ Íz±:ÏmagnitudeŽ‘.=r«(‘ª¨)–Ç·“Ïend‘‚ØlŽ‘ò·“Ï ushŽ‘€«;Ž¡‘ -Ïdistanc‘ÿ}'eŽ‘1 «=‘Ç(ÝP2Ž– b±:ÏmagnitudeŽ›.=r«(‘ª¨)±=ÝP1Ž“±:ÏmagnitudeŽ˜«(‘ª¨));Ž¡‘ -Ïc‘ÿ}'outŽ‘Y8±:Ïpr–ÿ}'e“cisionŽ‘'½6«(25ŽŽ‘ +¬[²LDF‘T2002.11.12.¬]Ž‘Y;Added–UUthis“section.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬De ne‘UU­staticŽ‘"ž.constŽ‘@ÈÐT‘ÿ +«etrahedronŽ’‚º)¬data‘UUmem¸ãbGers‘@¯1478“°i‘ÇŽ¡‘ +­constŽ‘(*£realŽ‘>ÝÑT‘ÿ +«etrahedronŽ‘~yÙ¬::‘±dihe–ÿ}'dr“al‘‰ffŽ‘®angleŽ‘Aä¬=‘Ç´PIŽ‘Z°–8à¬(70ŽŽ› 8â+“32ŽŽ˜µ=¬60µ:¬0ŽŽ‘Ç )µ=¬180µ:¬0ŽŽ‘Ç!;ŽŽŽŒ‹º• Šn ý‘ì¬442‘¯DEFINE›ÕX­ST–ÿ +«A“TIC–ÕTCONST“TETRAHEDR®9ON˜¯DÃŽA–ÿJªT“A˜MEMBERS‘1îü3DLDF-1.1.5.1‘°x¬1478Ž €n ý•@P¯This–ÕXcoK&¬.‘o°µ=Ž¦‘±vertic‘ÿ}'esŽ‘8±X¬=‘Ç4Ž‘Ç;Ž¦‘±e‘ÿ}'dgesŽ‘.™1¬=‘Ç6Ž‘Ç;Ž¦‘±c‘ÿ}'enterŽ‘2Ð¥¬=‘Ç´INVALID_POINTŽ‘GY¬;‘µ=°‘ÿý¬from‘UU­P®9olyhedronŽ‘=c"¬.‘o°µ=Ž¦‘±numb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜olygon‘‰ffŽ“typ˜esŽ’R9¬=‘Ç1Ž‘Ç;Ž¦‘±fac–ÿ}'e‘‰ffŽ‘®r“adiusŽ‘G%¬=‘DZe–ÿ}'dge‘‰ffŽ‘®r“adiusŽ‘7j¬=‘DZvertex‘‰ffŽ‘®r‘ÿ}'adiusŽ‘>þ¨¬=‘Ç´INVALID_REALŽ‘BM\¬;Ž¦‘±triangle‘‰ffŽ‘®r‘ÿ}'adiusŽ‘WUn¬=‘Ç´INVALID_REALŽ‘BM\¬;‘µ=°‘ÿý¬F‘ÿ*ªrom‘UU­T‘ÿ +«etrahedronŽ‘AñY¬.‘o°µ=Ž¦‘ +°gŽ¡¯See–ÕXalso“sections“1484,“1485,“1486,“1488,“1490,“and“1492.Ž¡This–ÕXcoë¬&Ž‘EÜ µpŽ‘Jä ;‘ª¨­constŽ‘ R realŽ‘7ƒ$±triangle‘‰ffŽ‘®diameterŽ’„Jµ;‘ª¨­realŽ‘Û,±angle‘‰ffŽ‘®xŽ‘9aµ;‘ª¨­realŽŽ¡‘2±angle‘‰ffŽ‘®yŽ‘Rkµ;‘ª¨­realŽ‘]Ö±angle‘‰ffŽ‘®zŽ‘8]L¬)°f‘UU­b•QÇo“olŽ‘ö»´DEBUGŽ‘:„,¬=‘DZtrueŽ‘‹°¬;‘µ=°–ÿý¬false“°µ=Ž¦‘±on‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘Xl ¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý¬from‘UU­SolidŽ‘Ó,¬.‘o°µ=Ž¡‘±do‘‰ffŽ‘®outputŽ‘K½N¬=‘DZtrueŽ‘‹°¬;Ž¡‘±fac‘ÿ}'esŽ‘7«¬=‘Ç4Ž‘Ç;‘µ=°‘ÿý¬from‘UU­Solidu½‰™šs4Ž‘ÔwF‘ÿ +«acedŽ‘>K&¬.‘o°µ=Ž¡‘±vertic‘ÿ}'esŽ‘B±Y¬=‘Ç4Ž‘Ç;Ž¡‘±e‘ÿ}'dgesŽ‘8™2¬=‘Ç6Ž‘Ç;Ž¡‘±numb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜olygon‘‰ffŽ“typ˜esŽ’‹R:¬=‘Ç1Ž‘Ç;Ž¡#­ifŽ‘ ´ø¬0Ž‘$´úµ=°‘ÿý¬ST–ÿ*ªAR“T–UUHERE.“TO“DO:“Must“calculate“these!‘o°µ=Ž¡‘±fac–ÿ}'e‘‰ffŽ‘®r“adiusŽ‘Q&¬=‘Ç0Ž‘Ç;Ž¡‘±e–ÿ}'dge‘‰ffŽ‘®r“adiusŽ‘R£­¬=‘Ç0Ž‘Ç;Ž¡‘±vertex‘‰ffŽ‘®r‘ÿ}'adiusŽ‘Z7“¬=‘Ç0Ž‘Ç;Ž¡#­endifŽŽ¡‘±triangle‘‰ffŽ‘®r‘ÿ}'adiusŽ‘aUo¬=‘DZtriangle‘‰ffŽ‘®diameterŽ‘OX>µ=¬2µ:¬0ŽŽ‘ Ç;Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘Vºk¬=‘DZget‘‰ffŽ‘®netŽ‘!ûà¬(±triangle‘‰ffŽ‘®diameterŽ‘L‘&¬);Ž¦‘­realŽ‘4³1±angleŽ‘O:œ¬=‘Ç180ŽŽ‘ÿû°–8à¬(±dihe–ÿ}'dr“al‘‰ffŽ‘®angleŽ‘?ƒ¨°“¬180ŽŽ‘8ãµ=´PIŽ‘ b¬);Ž¡‘­P•®9oin“tŽ‘<ï ±ptsŽ‘JÊF¬[11ŽŽ‘ +];Ž¡‘­in®9tŽ‘/¤úµiŽ‘3î¬;Ž¦‘­forŽ‘/艬(µiŽ‘9 ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ3Ž“;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘±ptsŽ‘Ú¦¬[µiŽ›qô¬]–Ç=“±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh¬[0Ž‘]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(µiŽ˜¬);Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS¬[1Ž–]‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(±ptsŽ‘ Ú¦¬[0Ž“]µ;‘ª¨±ptsŽ‘…N¬[1Ž“]µ;‘ª¨±angleŽ‘jû¬);Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS¬[2Ž–]‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(±ptsŽ‘ Ú¦¬[2Ž“]µ;‘ª¨±ptsŽ‘…N¬[0Ž“]µ;‘ª¨±angleŽ‘jû¬);Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS¬[3Ž–]‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(±ptsŽ‘ Ú¦¬[1Ž“]µ;‘ª¨±ptsŽ‘…N¬[2Ž“]µ;‘ª¨°Ž‘ qƱangleŽ‘!2¬);Ž¡#­ifŽ‘ ´ø¬0ŽŽ¡‘­forŽ‘/艬(µiŽ‘9 ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ3Ž“;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘±ptsŽ‘Ú¦¬[µiŽ–qô¬]µ:±lab‘ÿ}'elŽ‘t˜¬(µiŽ“;‘ª¨´""Ž‘ ± +¬);Ž¡#­endifŽŽ¡‘forŽ‘/艬(µiŽ‘9 ¬=‘Ç3Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ7Ž“;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘°fŽ¡‘(±ptsŽ‘5Úª¬[µiŽ‘qô¬]–Ç=“±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh¬[µiŽ‘ªÔ°‘8à¬3Ž‘8á]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘0=H¬(‘ª¨);Ž¡#­ifŽ‘ ´ø¬0ŽŽ¡‘(±ptsŽ‘5Úª¬[µiŽ–qô¬]µ:±lab‘ÿ}'elŽ‘t˜¬(µiŽ“;‘ª¨´""Ž‘ ± +¬);Ž¡#­endifŽŽ¡‘°gŽ¡‘±ptsŽ‘+Ú©¬[7Ž›]–Ç=“±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh¬[3Ž˜]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(0Ž˜);Ž¡#­ifŽ‘ ´ø¬0ŽŽ¡‘±ptsŽ‘+Ú©¬[7Ž–]µ:±lab‘ÿ}'elŽ‘t˜¬(7Ž“µ;‘ª¨´""Ž‘ ± +¬);Ž¡#­endifŽŽ¡‘±ptsŽ‘+Ú©¬[8Ž›]–Ç=“±ptsŽ‘¡¾¬[0Ž˜]µ:±me‘ÿ}'diateŽ‘"½u¬(±ptsŽ‘ Ú¦¬[1Ž˜]);Ž¡‘±ptsŽ‘+Ú©¬[9Ž›]–Ç=“±ptsŽ‘¡¾¬[1Ž˜]µ:±me‘ÿ}'diateŽ‘"½u¬(±ptsŽ‘ Ú¦¬[2Ž˜]);Ž¡‘±ptsŽ‘+Ú©¬[10ŽŽ‘ +]–Ç=“±ptsŽ‘¡¾¬[2Ž–]µ:±me‘ÿ}'diateŽ‘"½u¬(±ptsŽ‘ Ú¦¬[0Ž“]);Ž¡#­ifŽ‘ ´ø¬0ŽŽ¡‘­forŽ‘/艬(µiŽ‘9 ¬=‘Ç8Ž‘Ç;‘ÿýµiŽ‘ 9 <‘Ǭ11ŽŽ‘ Ç;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)‘±ptsŽ‘Ú¦¬[µiŽ–qô¬]µ:±lab‘ÿ}'elŽ‘t˜¬(µiŽ“¬);Ž¡#­endifŽŽ¦‘usingŽ‘ù¬is“the“distance“along“one“of“these“line“segmen˜ts“to“the“in˜tersectionŽ¡pGoinš¸ãt–UUdivided“b˜y“the“length“of“the“en˜tire“line“segmen˜t.‘qÇ[²LDF‘T2002.08.12.¬]ŽŽ¡‘ +Since–Ú/this“ratio“should“bGe“the“same“for“all“±T‘ÿ;¼etr–ÿ}'ahe“dr“aŽ‘4b¿¬,‘;ethere's“no“need“to“recalculate“it“eac¸ãh“time“aŽ¡­T‘ÿ +«etrahedronŽ‘Ck¬is–Ïconstructed.‘ÞøIn“addition,‘-inš¸ãtersections“can't“alw˜a˜ys“bšGe“found,‘-b˜ecause“of“inaccuraciesŽ¡caused–UUb¸ãy“rotating“the“triangles.‘qÇ[²LDF‘T2002.08.12.¬]ŽŽ¡‘ +Therefore,‘xgI'vš¸ãe–qccalculated“distance“using“the“commen˜ted-out“cošGde“b˜eloš¸ãw,‘xgand“no˜w“simply“use“the“v‘ÿqÇalue“IŽ¡found.‘qÇ[²LDF‘T2002.08.12.¬]ŽŽ©°h–ª¨¬De ne‘UU­T‘ÿ +«etrahedronŽ‘EF®¬functions‘@¯1481“°i‘Ǭ+°Ž¡‘ +­realŽ‘ ³/±distanc‘ÿ}'eŽ‘GÀD¬=‘Ç0µ:¬74997889995574951171875ŽŽ‘}ŽM;Ž¡#­ifŽ‘ ´ø¬0ŽŽ¡‘ +­P•®9oin“tŽ‘(ïž´P0Ž‘6½¬=‘Ç­P•®9oin“tŽ‘ad¬::Ž‘%interse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘s†x¬(±ptsŽ‘ Ú¦¬[0Ž–]µ;‘ª¨±ptsŽ›…N¬[6Ž“]µ;‘ª¨±ptsŽ˜¬[1Ž“]µ;‘ª¨±ptsŽ˜¬[5Ž“])µ:±ptŽ‘ ä¬;Ž¦‘ +´P0Ž‘cµ:±showŽ‘Šÿ¬(´"P0® ´=® ´0,® ´6,® ´1,® ´5:"Ž‘_2¬);Ž¡‘ +­P•®9oin“tŽ‘&šM¬::Ž‘-(‹±interse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘z¿a¬(±ptsŽ‘ Ú¦¬[0Ž–]µ;‘ª¨±ptsŽ›…N¬[6Ž“]µ;‘ª¨±ptsŽ˜¬[2Ž“]µ;‘ª¨±ptsŽ˜¬[4Ž“])µ:±ptŽ‘ äµ:±showŽ‘Šÿ¬(´"0,® ´6,® ´2,® ´4:"Ž‘DÆA¬);Ž¡‘ +­P•®9oin“tŽ‘&šM¬::Ž‘-(‹±interse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘z¿a¬(±ptsŽ‘ Ú¦¬[0Ž–]µ;‘ª¨±ptsŽ›…N¬[6Ž“]µ;‘ª¨±ptsŽ˜¬[3Ž“]µ;‘ª¨±ptsŽ˜¬[7Ž“])µ:±ptŽ‘ äµ:±showŽ‘Šÿ¬(´"0,® ´6,® ´3,® ´7:"Ž‘DÆA¬);Ž¡‘ +­P•®9oin“tŽ‘&šM¬::Ž‘-(‹±interse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘z¿a¬(±ptsŽ‘ Ú¦¬[1Ž–]µ;‘ª¨±ptsŽ›…N¬[5Ž“]µ;‘ª¨±ptsŽ˜¬[2Ž“]µ;‘ª¨±ptsŽ˜¬[4Ž“])µ:±ptŽ‘ äµ:±showŽ‘Šÿ¬(´"1,® ´5,® ´2,® ´4:"Ž‘DÆA¬);Ž¡‘ +­P•®9oin“tŽ‘&šM¬::Ž‘-(‹±interse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘z¿a¬(±ptsŽ‘ Ú¦¬[1Ž–]µ;‘ª¨±ptsŽ›…N¬[5Ž“]µ;‘ª¨±ptsŽ˜¬[3Ž“]µ;‘ª¨±ptsŽ˜¬[7Ž“])µ:±ptŽ‘ äµ:±showŽ‘Šÿ¬(´"1,® ´5,® ´3,® ´7:"Ž‘DÆA¬);Ž¡‘ +­P•®9oin“tŽ‘&šM¬::Ž‘-(‹±interse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘z¿a¬(±ptsŽ‘ Ú¦¬[2Ž–]µ;‘ª¨±ptsŽ›…N¬[4Ž“]µ;‘ª¨±ptsŽ˜¬[3Ž“]µ;‘ª¨±ptsŽ˜¬[7Ž“])µ:±ptŽ‘ äµ:±showŽ‘Šÿ¬(´"2,® ´4,® ´3,® ´7:"Ž‘DÆA¬);Ž¦‘ +­P•®9oin“tŽ‘(ïž´P1Ž‘6½¬=‘DZptsŽ‘¡¾¬[5Ž›]–8à°“±ptsŽ‘†¬[1Ž˜];Ž¡‘ +­P•®9oin“tŽ‘(ïž´P2Ž‘6½¬=‘Ç´P0Ž‘Z°‘8à±ptsŽ‘†¬[1Ž‘];Ž¦‘ +´P1Ž‘cµ:±showŽ‘Šÿ¬(´"P1"Ž‘†\¬);Ž¡‘ +±c‘ÿ}'outŽ‘ P°‘Ç´"® ´P1.magnitude()® ´==Ž‘kÆÜ® ´"Ž‘y”V°‘Ç´P1Ž‘ Ízµ:±magnitudeŽ‘.=r¬(‘ª¨)–Ç°“±end‘‚ØlŽ‘ò°“± ushŽ‘€¬;Ž¡‘ +´P2Ž‘cµ:±showŽ‘Šÿ¬(´"P2"Ž‘†\¬);Ž¡‘ +±c‘ÿ}'outŽ‘ P°‘Ç´"P2.magnitude()® ´==® ´"Ž‘o\°‘Ç´P2Ž‘ Ízµ:±magnitudeŽ‘.=r¬(‘ª¨)–Ç°“±end‘‚ØlŽ‘ò°“± ushŽ‘€¬;Ž¡‘ +±distanc‘ÿ}'eŽ‘1 ¬=‘Ç(´P2Ž– bµ:±magnitudeŽ›.=r¬(‘ª¨)µ=´P1Ž“µ:±magnitudeŽ˜¬(‘ª¨));Ž¡‘ +±c‘ÿ}'outŽ‘Y8µ:±pr–ÿ}'e“cisionŽ‘'½6¬(25ŽŽ‘ );Ž¡‘ -Ïc‘ÿ}'outŽ‘ P·‘ÇÝ"distanceÈ Ý==È Ý"Ž‘O”n·‘ÇÏdistanc‘ÿ}'eŽ‘)Ô-·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘ -Ïc‘ÿ}'outŽ‘Y8±:Ïpr–ÿ}'e“cisionŽ‘'½6«(6Ž‘);Ž¡#ÂendifŽŽŸ1445.Ž¦·h–ª¨«De ne‘UUÂT‘ÿ -«etrahedronŽ‘EF®«functions‘@­1440“·i‘Ç«+·Ž¡‘ -Ïc‘ÿ}'enterŽ‘(Ф«=‘ÇÏptsŽ‘¡¾«[1Ž–]±:Ïme‘ÿ}'diateŽ‘"½u«(ÏptsŽ‘ Ú¦«[5Ž“]±;‘ª¨Ïdistanc‘ÿ}'eŽ‘%ð¥«);Ž¡‘ -ÂforŽ‘臫(±iŽ‘9 «=‘Ç0Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«4Ž“;‘ýŸÿ®+‘ÿ+ŽŽ‘G±iŽ‘¹«)‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:óP«[±iŽ‘qô«]‘þŸ±~ŽŽ‘ÏshiftŽ‘~«(·Ž‘ÇÏc‘ÿ}'enterŽ‘#Щ«);Ž¡‘ -Ïc‘ÿ}'enterŽ‘& Œ±:ÏshiftŽ‘}«(·Ž‘ÇÏc‘ÿ}'enterŽ‘#Щ«);Ž¡‘ -ÂifŽ‘´ù«(Ïangle‘‰ffŽ‘®xŽ‘#Lô·6«=‘Ç0Ž– ÿù·_‘8àÏangle‘‰ffŽ‘®yŽ‘%kƒ·6«=‘Ç0Ž“·_‘8àÏangle‘‰ffŽ‘®zŽ‘$ÿn·6«=‘Ç0Ž‘Ç)‘·fŽ¡‘ÂforŽ‘%舫(±iŽ‘9 «=‘Ç0Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«4Ž“;‘ýŸÿ®+‘ÿ+ŽŽ‘G±iŽ‘¹«)‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:óP«[±iŽ‘qô«]‘þŸ±~ŽŽ‘Ïr‘ÿ}'otateŽ‘o?«(Ïangle‘‰ffŽ‘®xŽ‘ …ܱ;‘ª¨Ïangle‘‰ffŽ‘®yŽ‘"3±;‘ª¨Ïangle‘‰ffŽ‘®zŽ‘!ª«);Ž¡‘ -·gŽ¡‘ -ÂifŽ‘´ù«(±pŽ‘Ï·6«=‘ÇÏoriginŽ‘½9«)‘·fŽ¡‘Ïc‘ÿ}'enterŽ‘2Ð¥«=‘DZpŽ‘Ï«;Ž¡‘ÂforŽ‘%舫(±iŽ‘9 «=‘Ç0Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«4Ž“;‘ýŸÿ®+‘ÿ+ŽŽ‘G±iŽ‘¹«)‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:óP«[±iŽ‘qô«]‘þŸ±~ŽŽ‘ÏshiftŽ‘~«(±pŽ‘«);Ž¡‘ -·gŽ¡‘ -ÂreturnŽ‘*‘f«;‘qÇ·gŽŽŽŒ‹¸ÏQ Šn ý‘ì«440–­SETTING‘ÕXFUNCTION’u=3DLDFPRÃŽG“·x«1446Ž €n ý•@PÂ1446.– üSetting‘ª'function.“«[¬LDF‘T2002.11.12.«]Ž‘[AG!!‘œùThis–fwš¸ãorks,‘<ªbut“it“fails“to“assign“to“the“data“mem˜bGersŽ¤ of‘ÏâÂT‘ÿ -«etrahedronŽ›F;È«that–Ïâare“de ned“in“its“o¸ãwn“ÂclassŽ‘*À«declaration.‘ámThat's“bGecause“neither“ÂT‘ÿ -«etrahedronŽ˜«norŽ¡ÂP®9olyhedronŽ‘=c"«has–UUan“assignmenš¸ãt“opGerator“y˜et.‘qÇTO“DO:“W‘ÿ*ªrite“assignmen˜t“opGerators“for“ÂP®9olyhedraŽ‘6Ö±«!ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.11.12.«]Ž‘Y;Added–UUthis“function.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂT‘ÿ -«etrahedronŽ‘EF®«functions‘@­1439“·i‘Ç«+·Ž¤ ‘ -Âv®9oidŽ‘#=²ÏsetŽ‘0¶6«(ÂconstŽ‘j{P•®9oin“tŽ‘=™ñ«&Ž‘Ea±pŽ‘Ji;‘ª¨ÂconstŽ‘ #realŽ‘7*Ïdiameter‘‰ffŽ–®of‘‰ffŽ“triangleŽ’!±±;‘ª¨ÂrealŽ‘¯Ïangle‘‰ffŽ‘®xŽ‘«(ÏptsŽ‘ Ú¦«[6Ž–]±;‘ª¨ÏptsŽ‘…N«[8Ž“]±;‘ª¨·Ž‘ qÆ«110ŽŽ‘qÉ);Ž¡‘ÏptsŽ‘!Ú¨«[11ŽŽ‘ -]±:Ïr‘ÿ}'otateŽ‘o>«(ÏptsŽ‘ Ú¦«[7Ž–]±;‘ª¨ÏptsŽ‘…N«[9Ž“]±;‘ª¨«110ŽŽ‘ª«);Ž¡‘ÏptsŽ‘!Ú¨«[10ŽŽ› -]–Ç=“ÏptsŽ‘¡¾«[6Ž‘]±:Ïme‘ÿ}'diateŽ‘"½u«(ÏptsŽ‘ Ú¦«[10ŽŽ˜]±;‘ª¨«1±:«5ŽŽ‘qÇ);Ž¡‘ÏptsŽ‘!Ú¨«[11ŽŽ› -]–Ç=“ÏptsŽ‘¡¾«[7Ž‘]±:Ïme‘ÿ}'diateŽ‘"½u«(ÏptsŽ‘ Ú¦«[11ŽŽ˜]±;‘ª¨«1±:«5ŽŽ‘qÇ);Ž¡#ÂifŽ‘ ´ø«0ŽŽ¡‘ÂforŽ‘%舫(±iŽ‘9 «=‘Ç0Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«8Ž“;‘ÿý±iŽ‘ññŸÿ®+‘ÿ+ŽŽ‘¹«)‘ÏptsŽ‘Ú¦«[±iŽ–qô«]±:Ïdotlab‘ÿ}'elŽ‘!ÿó«(±iŽ“«);Ž¡‘ÏptsŽ‘!Ú¨«[10ŽŽ– -]±:Ïdotlab‘ÿ}'elŽ‘!ÿó«(10ŽŽ“);Ž¡‘ÏptsŽ‘!Ú¨«[11ŽŽ– -]±:Ïdotlab‘ÿ}'elŽ‘!ÿó«(11ŽŽ“);Ž¡#ÂendifŽŽ¦‘P®9athŽ‘/æ»±pŽ‘4[6Ž‘];Ž¦‘±pŽ‘«[0Ž–]±:ÏsetŽ‘ x„«(Ý"--"Ž‘†\±;‘ª¨ÏtrueŽ‘o@±;‘ª¨«&Ž‘ qÆÏptsŽ›Ll«[6Ž“]±;‘ª¨«&Ž‘ qÆÏptsŽ˜«[10ŽŽ– -]±;‘ª¨«&Ž‘ qÆÏptsŽ˜«[11ŽŽ“]±;‘ª¨«&Ž‘ qÆÏptsŽ˜«[7Ž‘]±;‘ª¨«0Ž‘ª©);Ž¡‘±pŽ‘«[0Ž‘]±:Ïdr‘ÿ}'awŽ‘(Û«(‘ª¨);Ž¡‘ÏptsŽ‘!Ú¨«[12ŽŽ‘ -]–Ç=“ÏptsŽ‘¡¾«[6Ž–]±:Ïme‘ÿ}'diateŽ‘"½u«(ÏptsŽ‘ Ú¦«[7Ž“]);Ž¡‘ÏptsŽ‘!Ú¨«[13ŽŽ› -]–Ç=“ÏptsŽ‘¡¾«[10ŽŽ˜]±:Ïme‘ÿ}'diateŽ‘"½u«(ÏptsŽ‘ Ú¦«[11ŽŽ˜]);Ž¡#ÂifŽ‘ ´ø«0ŽŽ¡‘ÏptsŽ‘!Ú¨«[12ŽŽ– -]±:Ïdotlab‘ÿ}'elŽ‘!ÿó«(12ŽŽ“);Ž¡‘ÏptsŽ‘!Ú¨«[13ŽŽ– -]±:Ïdotlab‘ÿ}'elŽ‘!ÿó«(13ŽŽ“);Ž¡#ÂendifŽŽ¡‘±pŽ‘«[1Ž‘]±:ÏsetŽ‘ x„«(ÏptsŽ‘ Ú¦«[12ŽŽ– -]±;‘ª¨ÏptsŽ‘…N«[13ŽŽ“]);Ž¡#ÂifŽ‘ ´ø«0ŽŽ¡‘±pŽ‘«[1Ž–]±:Ïdr‘ÿ}'aw‘‰ffŽ‘®helpŽ‘*Ũ«(·Ž“ÂColorsŽ‘&Øß«::Ž‘-gÏhelp‘‰ffŽ‘®c‘ÿ}'olorŽ‘Y!‘±;‘ª¨Ý""Ž‘ ± -«);Ž¡#ÂendifŽŽ¡‘ÏptsŽ‘!Ú¨«[14ŽŽ› -]–Ç=“ÏptsŽ‘¡¾«[12ŽŽ˜]±:Ïme‘ÿ}'diateŽ‘"½u«(ÏptsŽ‘ Ú¦«[13ŽŽ˜]);Ž¡#ÂifŽ‘ ´ø«0ŽŽ¡‘ÏptsŽ‘!Ú¨«[14ŽŽ– -]±:Ïdotlab‘ÿ}'elŽ‘!ÿó«(14ŽŽ“);ŽŽŽŒ‹»øü Šn ý‘ì·x«1451–­3DLDFPRÃŽG’-ÀiDRA‘ÿ8W‘ÕXNET“«443Ž €n ý•@P#ÂendifŽŽ¤ ‘ÏptsŽ‘!Ú¨«[15ŽŽ‘ -]–Ç=“ÏptsŽ‘¡¾«[6Ž–]±:Ïme‘ÿ}'diateŽ‘"½u«(ÏptsŽ‘ Ú¦«[7Ž“]±;‘ª¨:«25ŽŽ‘qÇ);Ž¡#ÂifŽ‘ ´ø«0ŽŽ¡‘ÏptsŽ‘!Ú¨«[15ŽŽ– -]±:Ïdotlab‘ÿ}'elŽ‘!ÿó«(15ŽŽ“);Ž¡#ÂendifŽŽ¡‘ÏptsŽ‘!Ú¨«[16ŽŽ› -]–Ç=“ÏptsŽ‘¡¾«[14ŽŽ˜];Ž¡‘ÏptsŽ‘!Ú¨«[16ŽŽ– 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-]–Ç=“ÏptsŽ‘¡¾«[17ŽŽ˜]±:Ïme‘ÿ}'diateŽ‘"½u«(ÏptsŽ‘ Ú¦«[18ŽŽ˜]±;‘ª¨iŽ‘œ=«16±:«0ŽŽ‘Ç );Ž¡‘ÏptsŽ‘+Ú©«[19ŽŽ‘ -]±:Ïdr‘ÿ}'awdotŽ‘#“«(·Ž‘ÂColorsŽ‘&Øß«::Ž‘-gÏdefault‘‰ffŽ‘®c‘ÿ}'olorŽ‘dâø±;‘ª¨Ý"pencircleÈ ÝscaledÈ Ý.5Ž‘jªlmm"Ž‘zðË«);Ž¡‘·gŽ¡‘ÏptsŽ‘!Ú¨«[20ŽŽ› -]–Ç=“ÏptsŽ‘¡¾«[17ŽŽ˜];Ž¡‘ÏptsŽ‘!Ú¨«[21ŽŽ› -]–Ç=“ÏptsŽ‘¡¾«[18ŽŽ˜];Ž¡‘±pŽ‘«[3Ž›]–Ç=“±pŽ‘Ï«[0Ž˜];Ž¤‘ÂT‘ÿ -«ransformŽ‘KÈÔ±tŽ‘OeF«;Ž¡‘±tŽ‘œt:ÏshiftŽ‘}«(ÏptsŽ‘ Ú¦«[4Ž›]–8à·“ÏptsŽ‘†«[5Ž˜]);Ž¤ ‘±tŽ‘œt:Ïr‘ÿ}'otateŽ‘o>«(ÏptsŽ‘ Ú¦«[4Ž–]±;‘ª¨ÏptsŽ‘…N«[5Ž“]);Ž¡‘ÏptsŽ‘!Ú¨«[20ŽŽ– -]‘Ç·«=ŽŽ‘UOÏptsŽ‘ /õ«[21ŽŽ“]‘Ç·«=ŽŽ‘UO±pŽ‘]O«[3Ž‘]‘Ç·«=ŽŽ‘UO±tŽ‘ñÁ«;Ž¡‘±pŽ‘«[3Ž‘]±:Ïdr‘ÿ}'awŽ‘(Û«(‘ª¨);Ž¡‘ÂforŽ‘%舫(±iŽ‘9 «=‘Ç1Ž‘Ç;‘ÿý±iŽ‘ 9 <‘Ç«16ŽŽ‘ Ç;‘ýŸÿ®+‘ÿ+ŽŽ‘G±iŽ‘¹«)‘·fŽ¡‘ÏptsŽ‘+Ú©«[19ŽŽ› -]–Ç=“ÏptsŽ‘¡¾«[20ŽŽ˜]±:Ïme‘ÿ}'diateŽ‘"½u«(ÏptsŽ‘ Ú¦«[21ŽŽ˜]±;‘ª¨iŽ‘œ=«16±:«0ŽŽ‘Ç );Ž¡‘ÏptsŽ‘+Ú©«[19ŽŽ‘ -]±:Ïdr‘ÿ}'awdotŽ‘#“«(·Ž‘ÂColorsŽ‘&Øß«::Ž‘-gÏdefault‘‰ffŽ‘®c‘ÿ}'olorŽ‘dâø±;‘ª¨Ý"pencircleÈ ÝscaledÈ 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ne‘UUÂDoQÇdecahedronŽ‘Oj8«functions‘@­1457“·i‘Ç«+·Ž¤ ‘ -Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQ«[1Ž–]‘þŸ±~ŽŽ‘Ïr‘ÿ}'otateŽ‘o?«(ÏptsŽ‘ Ú¦«[0Ž“]±;‘ª¨ÏptsŽ‘…N«[1Ž“]±;‘ª¨ÏangleŽ‘jû«);Ž¡‘ -Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQ«[2Ž–]‘þŸ±~ŽŽ‘Ïr‘ÿ}'otateŽ‘o?«(ÏptsŽ‘ Ú¦«[4Ž“]±;‘ª¨ÏptsŽ‘…N«[0Ž“]±;‘ª¨ÏangleŽ‘jû«);Ž¡‘ -Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQ«[3Ž–]‘þŸ±~ŽŽ‘Ïr‘ÿ}'otateŽ‘o?«(ÏptsŽ‘ Ú¦«[3Ž“]±;‘ª¨ÏptsŽ‘…N«[4Ž“]±;‘ª¨ÏangleŽ‘jû«);Ž¡‘ -Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQ«[4Ž–]‘þŸ±~ŽŽ‘Ïr‘ÿ}'otateŽ‘o?«(ÏptsŽ‘ Ú¦«[3Ž“]±;‘ª¨ÏptsŽ‘…N«[2Ž“]±;‘ª¨ÏangleŽ‘jû«);Ž¡‘ -Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQ«[5Ž–]‘þŸ±~ŽŽ‘Ïr‘ÿ}'otateŽ‘o?«(ÏptsŽ‘ Ú¦«[1Ž“]±;‘ª¨ÏptsŽ‘…N«[2Ž“]±;‘ª¨ÏangleŽ‘jû«);Ž¡#ÂifŽ‘ ´ø«0ŽŽ¦‘ -ÂusingŽ‘(S‡namespaceŽ‘a÷ColorsŽ’‚ÏÛ«;Ž¡‘ -Âv®9ectorŽ‘)ªI·hÂconstŽ‘*¢ColorŽ‘=Ï•·Ž‘BÏ–i‘UUÏc–ÿ}'ol‘‰ffŽ‘®ve“cŽ‘!"J«;Ž¦‘ -Ïc–ÿ}'ol‘‰ffŽ‘®ve“cŽ‘'Ìö±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(&Ž‘ÇÏblackŽ‘Ôò«);Ž¡‘ -Ïc–ÿ}'ol‘‰ffŽ‘®ve“cŽ‘'Ìö±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(&Ž‘ÇÏr–ÿ}'e“dŽ‘:K«);Ž¡‘ 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-ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘ÂforŽ‘%舫(±iŽ‘9 «=‘Ç6Ž‘Ç;‘ÿý±iŽ‘ 9 <‘Ç«12ŽŽ‘ Ç;‘ýŸÿ®+‘ÿ+ŽŽ‘G±iŽ‘¹«)‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:óP«[±iŽ‘qô«]‘þŸ±~ŽŽ‘Ïdr‘ÿ}'awŽ‘(Ü«(·Ž‘«(Ïc–ÿ}'ol‘‰ffŽ‘®ve“cŽ‘Ìõ«[±iŽ‘ªÔ·‘8à«6Ž‘8á]));Ž¡‘ -·gŽ¡«#ÂendifŽŽ¦‘ -P•®9oin“tŽ‘(ïžÏc‘ÿ}'enter‘‰ffŽ‘®0Ž‘PÒ=«=‘ÇÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh«[0Ž‘]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®c‘ÿ}'enterŽ‘0=H«(‘ª¨);Ž¡‘ -ÂP•®9oin“tŽ‘(ïžÏc‘ÿ}'enter‘‰ffŽ‘®6Ž‘PÒ=«=‘ÇÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh«[6Ž‘]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®c‘ÿ}'enterŽ‘0=H«(‘ª¨);Ž¦‘ -Ïc‘ÿ}'enterŽ‘(Ф«=‘ÇÏc‘ÿ}'enter‘‰ffŽ‘®0Ž‘'⟱:Ïme‘ÿ}'diateŽ‘"½u«(Ïc‘ÿ}'enter‘‰ffŽ‘®6Ž‘%‡«);Ž¦‘ -ÂT‘ÿ -«ransformŽ‘AÈÓ±tŽ‘H,]«=‘ÇÏc‘ÿ}'enterŽ‘У±:ÏshiftŽ‘}«(·Ž‘ÇÏc‘ÿ}'enterŽ‘#Щ«);ŽŽŽŒ‹À>. Šn ý‘ì«448›­CONSTR•ÃŽUCTOR’By3DLDFPR“G˜·x«1461Ž €n ý•@P‘ -ÂifŽ‘´ù«(Ïangle‘‰ffŽ‘®xŽ‘#Lô·6«=‘Ç0Ž– ÿù·_‘8àÏangle‘‰ffŽ‘®yŽ‘%kƒ·6«=‘Ç0Ž“·_‘8àÏangle‘‰ffŽ‘®zŽ‘$ÿn·6«=‘Ç0Ž‘Ç)‘±tŽ‘œr:Ïr‘ÿ}'otateŽ‘o>«(Ïangle‘‰ffŽ‘®xŽ‘ …ܱ;‘ª¨Ïangle‘‰ffŽ‘®yŽ‘"3±;‘ª¨Ïangle‘‰ffŽ‘®zŽ‘!ª«);Ž¤ ‘ -ÂifŽ‘´ù«(±pŽ‘Ï·6«=‘ÇÏoriginŽ‘½9«)‘Ïc‘ÿ}'enterŽ‘#У·«=ŽŽ‘3^Ú±tŽ‘6ûL:ÏshiftŽ‘}«(±pŽ‘«);Ž¡‘ -ÂforŽ‘臫(Âv®9ectorŽ‘ªH·hÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘DÔ ·Ž‘IÔ -i‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘ÇÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ–8ºh±:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘ÇÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ“±:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)‘Ç·«=ŽŽ‘UO±tŽ‘ñÁ«;Ž¡‘ -ÂifŽ‘´ù«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ExitingÈ ÝDodecahedroŽ‘kÆÜn::Dodecahedron().\nŽ’ÔÆ "Ž’ÝT·‘ÇÏ ushŽ‘€«;Ž¡‘ -ÂreturnŽ‘*‘f«;‘qÇ·gŽŸÂ1462.– üGet‘íunet.“«[¬LDF‘T2002.09.29.«]Ž‘Y¾•Changed–‹´this“function.‘.’TO‘‹DO.“I'vš¸ãe“remo˜v˜ed“Ïr‘ÿ}'otateŽ‘úò«(‘ª®)“and“no˜w“rotateŽ¡the–èpGenš¸ãtagons“in“the“x-z“plane“only“in“order“to“a˜v˜oid“ha˜ving“the“y-cošGordinates“b˜e“o “bš¸ãy“small“amoun˜ts.‘MVThisŽ¡mighš¸ãt–÷bnot“happGen“with“Ïr‘ÿ}'otateŽ‘f «(‘ª®)“once“I‘÷Jimplemen˜t“the“routine“in“Salomon“(“!!›RvGet“reference!)˜for“calculatingŽ¡sine–UUand“cosine“using“in¸ãtegers.Ž¡‘ 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ªª);Ž¡‘·Ž‘Ïp‘ÿ}'entsŽ‘0¯«[5Ž›]–Ç=“·Ž‘ÇÏp‘ÿ}'entsŽ‘WÅ«[4Ž˜]“=“·Ž‘ÇÏp‘ÿ}'entsŽ‘WÅ«[3Ž˜]“=“·Ž‘ÇÏp‘ÿ}'entsŽ‘WÅ«[2Ž˜]“=“·Ž‘ÇÏp‘ÿ}'entsŽ‘WÅ«[1Ž˜];Ž¡‘ÂforŽ‘%舫(±iŽ‘9 «=‘Ç5Ž‘Ç;‘ÿý±iŽ‘ 9 <‘Ç«10ŽŽ‘ Ç;‘ÿý±iŽ‘ññŸÿ®+‘ÿ+ŽŽ‘¹«)‘ÏptsŽ‘Ú¦«[±iŽ‘qô«]–Ç=“Ïp‘ÿ}'entsŽ‘WÄ«[1Ž‘]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI«(±iŽ‘ªÔ·‘8à«5Ž‘8á);Ž¡‘Ïp‘ÿ}'entsŽ‘+®«[1Ž–]‘þŸ±~ŽŽ‘ÏshiftŽ‘~«(ÏptsŽ‘ Ú¦«[0Ž“]–8à·“ÏptsŽ‘†«[8Ž‘]);Ž¡‘Ïp‘ÿ}'entsŽ‘+®«[2Ž–]‘þŸ±~ŽŽ‘ÏshiftŽ‘~«(ÏptsŽ‘ Ú¦«[0Ž“]–8à·“ÏptsŽ‘†«[6Ž‘]);Ž¡‘Ïp‘ÿ}'entsŽ‘+®«[3Ž–]‘þŸ±~ŽŽ‘ÏshiftŽ‘~«(ÏptsŽ‘ Ú¦«[4Ž“]–8à·“ÏptsŽ‘†«[5Ž‘]);Ž¡‘Ïp‘ÿ}'entsŽ‘+®«[4Ž–]‘þŸ±~ŽŽ‘ÏshiftŽ‘~«(ÏptsŽ‘ Ú¦«[3Ž“]–8à·“ÏptsŽ‘†«[9Ž‘]);Ž¡‘Ïp‘ÿ}'entsŽ‘+®«[5Ž–]‘þŸ±~ŽŽ‘ÏshiftŽ‘~«(ÏptsŽ‘ Ú¦«[1Ž“]–8à·“ÏptsŽ‘†«[9Ž‘]);Ž¡‘ÂifŽ‘´ú«(Ïdo‘‰ffŽ‘®halfŽ‘#'¡·‘ÇÏtrueŽ‘‹°«)Ž¡‘±=·‘ «[¬LDF‘T2002.09.29.«]Ž‘TH_W‘ÿ*ªe–uionly“need“half“of“the“net,‘}nif“wš¸ãe're“using“it“to“mak˜e“a“pGolyhedron.‘ÒIn“thatŽ¡‘(case,–UUwš¸ãe“cop˜y“and“transform“the“half“w˜e'v˜e“already“got“and“the“cop˜y“on“top“of“the“ rst“half.‘o·±=Ž¡‘·fŽ¡‘ÂforŽ‘/艫(±iŽ‘9 «=‘Ç0Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«6Ž“;‘ýŸÿ®+‘ÿ+ŽŽ‘G±iŽ‘¹«)‘·fŽ¡‘(ÂforŽ‘9芫(Âin®9tŽ‘¤÷±jŽ‘Ó«=‘Ç0Ž–Ç;‘ÿý±jŽ‘ wÙ<‘Ç«5Ž“;‘ÿý±jŽ‘ -0ÁŸÿ®+‘ÿ+ŽŽ‘÷á«)Ž¡‘2ÂifŽ‘=´ý«(Ïp‘ÿ}'entsŽ‘¬«[±iŽ‘qô«]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI«(±jŽ‘°Ä«)±:Ïget‘‰ffŽ‘®yŽ‘t«(‘ª¨)–Ç·6«=“0Ž‘Ç)‘·fŽ¡‘<Ïc‘ÿ}'errŽ‘R?·‘‰UÝ"ERROR!È ÝInÈ ÝDodecahedŽ‘l‰ron::get_net():\n"Ž’Ï ·‘‰UÝ"y-coordinateÈ Ý!=È Ý0!\Ž‘l‰n"Ž‘{зŽ¡‘PÝ"You'dÈ ÝbetterÈ ÝfixÈ ÝthŽ’¸ÿÌis!\n\n"Ž’æM4·‘ÇÏ ushŽ‘€«;Ž¡‘2·gŽ¡‘gŽ¡‘ÂreturnŽ‘Aæ½Ïp‘ÿ}'entsŽ‘Ywi«;Ž¡‘·gŽ¡‘ÂforŽ‘%舫(±iŽ‘9 «=‘Ç6Ž‘Ç;‘ÿý±iŽ‘ 9 <‘Ç«12ŽŽ‘ Ç;‘ÿý±iŽ‘ññŸÿ®+‘ÿ+ŽŽ‘¹«)‘·fŽ¡‘Ïp‘ÿ}'entsŽ‘5¯±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘B~¸«::Ž‘I öÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“r–ÿ}'e“g‘‰ffŽ‘®p“olygonŽ’¬ƒ8«(‘ª¨));Ž¡‘·Ž‘#Ïp‘ÿ}'entsŽ‘:°«[±iŽ‘qô«]–Ç=“·Ž‘ÇÏp‘ÿ}'entsŽ‘WÅ«[±iŽ‘ªÔ·‘8à«6Ž‘8á];Ž¡‘Ïp‘ÿ}'entsŽ‘5¯«[±iŽ‘qô«]‘þŸ±~ŽŽ‘Ïr‘ÿ}'otateŽ‘o?«(0Ž‘±;‘ª¨«180ŽŽ‘ª«);Ž¡‘·gŽ¡‘ÏptsŽ‘!Ú¨«[0Ž›]–Ç=“Ïp‘ÿ}'entsŽ‘WÄ«[11ŽŽ‘ -]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI«(0Ž˜);Ž¡‘ÏptsŽ‘!Ú¨«[1Ž›]–Ç=“Ïp‘ÿ}'entsŽ‘WÄ«[5Ž˜]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI«(1Ž˜);Ž¡‘ÂforŽ‘%舫(±iŽ‘9 «=‘Ç6Ž‘Ç;‘ÿý±iŽ‘ 9 <‘Ç«12ŽŽ‘ Ç;‘ýŸÿ®+‘ÿ+ŽŽ‘G±iŽ‘¹«)‘Ïp‘ÿ}'entsŽ‘¬«[±iŽ‘qô«]‘þŸ±~ŽŽ‘ÏshiftŽ‘~«(ÏptsŽ‘ Ú¦«[1Ž›]–8à·“ÏptsŽ‘†«[0Ž˜]);Ž¡‘ÂforŽ‘%舫(±iŽ‘9 «=‘Ç0Ž‘Ç;‘ÿý±iŽ‘ 9 <‘Ç«12ŽŽ‘ Ç;‘ýŸÿ®+‘ÿ+ŽŽ‘G±iŽ‘¹«)‘·fŽ¡‘ÂforŽ‘/艫(Âin®9tŽ‘¤÷±jŽ‘Ó«=‘Ç0Ž–Ç;‘ÿý±jŽ‘ wÙ<‘Ç«5Ž“;‘ÿý±jŽ‘ -0ÁŸÿ®+‘ÿ+ŽŽ‘÷á«)Ž¡‘(ÂifŽ‘3´ü«(Ïp‘ÿ}'entsŽ‘¬«[±iŽ‘qô«]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI«(±jŽ‘°Ä«)±:Ïget‘‰ffŽ‘®yŽ‘t«(‘ª¨)–Ç·6«=“0Ž‘Ç)‘·fŽ¡‘2Ïc‘ÿ}'errŽ‘H}q·‘ÇÆÝ"ERROR!È ÝInÈ ÝDodecahedŽ‘lÇŠron::get_net():\n"Ž’Ï•‚·‘ÇÆÝ"y-coordinateÈ Ý!=È Ý0!\Ž‘lÇŠn"Ž‘{•²·Ž¡‘FÝ"You'dÈ ÝbetterÈ ÝfixÈ ÝthŽ’®ÿËis!\n\n"Ž’ÜM3·‘ÇÏ ushŽ‘€«;Ž¡‘(·gŽ¡‘gŽ¡‘ÂreturnŽ‘7æ¼Ïp‘ÿ}'entsŽ‘Owh«;Ž¡‘ -·gŽŽŽŒ‹Â\/ Šn ý‘ì«450–­DRA‘ÿ8W‘ÕXNET’-Ài3DLDFPRÃŽG“·x«1464Ž €n ý•@PÂ1464.– üDra®9w‘¾—net.“«[¬LDF‘T2002.11.10.«]Ž‘Y•ÔThis–bófunction“is“for“dra¸ãwing“the“net“of“a“ÂDoQÇdecahedronŽ‘K"«.‘ üNormally‘ÿ*ª,Ž¤ this–m)will“bšGe“done“in“order“to“mak¸ãe“a“cardb˜oard“mo˜del,‘³whic¸ãh“will“require“tabs“for“gluing“the“p˜en¸ãtagonsŽ¡together.‘qÇIf–UUno“tabs“are“desired,“passing“ÏfalseŽ‘Yî«as“the“Ïmake‘‰ffŽ‘®tabsŽ‘3J«argumen¸ãt“will“suppress“the“tabs.Ž¡‘ -[¬LDF‘T2002.11.10.«]Ž‘Y¬0TO‘ùDO:–ùJThe“arraš¸ãys“ÂP•®9oin“tŽ‘#ŒÜÏptsŽ‘5`Ì«and“ÂP®9athŽ‘ ƒø±pŽ‘)…B«ha˜v˜e“toGo“man˜y“mem˜bGers.‘]¥In“w˜orking“onŽ¡this–:êfunction,‘@2I‘:ãended“up“getting“rid“of“some“of“the“memš¸ãbGers“of“these“arra˜ys“after“I'd“already“used“mem˜bGersŽ¡folloš¸ãwing–UUthem.‘qÇI“should“go“through“and“reassign“the“n˜um˜bGers,“so“that“no“mem˜bšGers“are“skipp˜ed.Ž¡‘ -[¬LDF‘T2002.11.10.«]Ž‘Y;TO–UUDO:“Add“the“usual“argumenš¸ãts“for“dra˜wing“and“ lling“commands.Ž¡‘ -[¬LDF‘T2002.11.10.«]Ž‘XûåTO‘HüDO:‘HÿÏp–ÿ}'ortr“aitŽ‘(|>«doGesn't–Hÿwš¸ãork“righ˜t.›mªFix“it!˜!!˜KLUDGE:“Ïp–ÿ}'ortr“aitŽ‘(|>«is“set“to“ÏfalseŽ‘AB«at“theŽ¡bGeginning–UUof“this“function“and“a“w¸ãarning“is“issued.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8ÂLogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.11.10.«]Ž‘Y;Added–UUthis“function.Ž¡‘ -[¬LDF‘T2002.11.10.«]Ž‘Y;T‘ÿ*ªried–UUto“get“output“in“pšGortrait“format“to“w¸ãork,“but“it“do˜esn't“y¸ãet.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂDoQÇdecahedronŽ‘Oj8«functions‘@­1456“·i‘Ç«+·ŽŸ ‘ -ÂstaticŽ‘)HÚv®9oidŽ‘BF²Ïdr‘ÿ}'aw‘‰ffŽ‘®netŽ‘iˆE«(ÂconstŽ‘*¢realŽ‘4ÝÐÏp‘ÿ}'entagon‘‰ffŽ‘®diameterŽ’†íˆ±;‘ª¨Âb•QÇo“olŽ‘LÏp–ÿ}'ortr“aitŽ‘?ýf«=‘ÇÏtrueŽ–‹°±;‘ª¨Âb•QÇo“olŽ‘LÏmake‘‰ffŽ‘®tabsŽ‘J²”«=‘ÇÏtrueŽ“«);ŽŽŽŒ‹Ãp‰ Šn ý‘ì·x«1465–­3DLDFPRÃŽG’-ÀiDRA‘ÿ8W‘ÕXNET“«451Ž €n ý•@PÂ1465.Ž©:¤·h–ª¨«De ne‘UUÂDoQÇdecahedronŽ‘Oj8«functions‘@­1457“·i‘Ç«+·Ž¤ ‘ -Âv®9oidŽ‘"ýÙDoQÇdecahedronŽ‘l½k«::‘Ïdr‘ÿ}'aw‘‰ffŽ‘®netŽ‘(A—«(ÂconstŽ‘*¢realŽ‘4ÝÐÏp‘ÿ}'entagon‘‰ffŽ‘®diameterŽ’†íˆ±;‘ª¨Âb•QÇo“olŽ‘LÏp–ÿ}'ortr“aitŽ‘=6N±;‘ª¨Âb•QÇo“olŽ‘LÏmake‘‰ffŽ‘®tabsŽ‘Gë|«)Ž¡‘ -·fŽ¡‘Âv®9ectorŽ‘3ªJ·hÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘DÔ ·Ž‘IÔ -i‘UU±vŽ‘ Q*«=‘ÇÏget‘‰ffŽ‘®netŽ‘!ûà«(Ïp‘ÿ}'entagon‘‰ffŽ‘®diameterŽ‘R¸«);Ž¦‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘DÔ ·Ž‘IÔ -i‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘DZvŽ–ûÕ:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘DZvŽ“:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘ÂifŽ‘)´û«(Ïp–ÿ}'ortr“aitŽ‘!ê@«)‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïr‘ÿ}'otateŽ‘o>«(0Ž‘±;‘ª¨«90ŽŽ‘ ªª);Ž¡#ÂifŽ‘ ´ø«0ŽŽ¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïr‘ÿ}'otateŽ‘o>«(90ŽŽ‘ -);Ž¡#ÂendifŽŽ¡‘·gŽ¦‘ÂP•®9oin“tŽ‘2pŽ‘7÷Ÿ«[32ŽŽ‘ -];Ž¡‘Âin®9tŽ‘%¤ù±iŽ‘)í«;Ž¦‘ÂforŽ‘%舫(±iŽ‘9 «=‘Ç0Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«5Ž“;‘ÿý±iŽ‘ññŸÿ®+‘ÿ+ŽŽ‘¹«)‘·fŽ¡‘±pŽ‘#«[±iŽ›qô«]–Ç=“±vŽ‘ûÕ«[3Ž‘]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI«(±iŽ˜«);Ž¡#ÂifŽ‘ ´ø«0ŽŽ¡‘±pŽ‘#«[±iŽ–qô«]±:Ïdotlab‘ÿ}'elŽ‘!ÿó«(±iŽ“«);Ž¡#ÂendifŽŽ¡‘·g‘±=·›ÿý«ST–ÿ*ªAR“T‘UUHERE.˜·±=Ž¡‘iŽ‘9«=‘Ç0Ž‘Ç;Ž¡‘ÂforŽ‘%舫(Âv®9ectorŽ‘ªH·hÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘DÔ ·Ž‘IÔ -i‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘DZvŽ–ûÕ:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘DZvŽ“:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘«(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïdr‘ÿ}'awŽ‘(Û«(‘ª¨);Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïget‘‰ffŽ‘®c‘ÿ}'enterŽ‘,=G«(–ª¨)±:Ïlab‘ÿ}'elŽ‘t˜«(±iŽ‘ñôŸÿ®+‘ÿ+ŽŽ‘¹±;“Ý""Ž‘ ± -«);Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(·:Ïmake‘‰ffŽ‘®tabsŽ‘,Ÿn«)‘ÂreturnŽ‘%‘e«;Ž¡‘ÂreturnŽ‘4‘g«;Ž¡‘ -·gŽ¤Â1466.‘ üIcosahedron.Ž¡1467.‘ üIcosahedron–ÕTclass“de nition.Ž¦·h–ª¨«De ne‘UUÂclassŽ‘5¦IcosahedronŽ‘_Ny­1467“·i‘ÇŽ¤ ‘ -ÂclassŽ‘$àRIcosahedronŽ‘ev«:‘qÇÂpublicŽ‘'ñP®9olyhedronŽ‘dh·fŽ¡‘ -ÂprotectedŽ‘:o™«:‘ÂstaticŽ‘$HÙconstŽ‘Bs{realŽ‘Y&©Ïdihe–ÿ}'dr“al‘‰ffŽ‘®angleŽ’–qq«;‘±=·‘ÿý«In‘UUradians!‘o·±=Ž¡‘ÂrealŽ‘*³0Ïtriangle‘‰ffŽ‘®r‘ÿ}'adiusŽ‘kA„«;Ž¦‘ -ÂpublicŽ‘)=Ö«:‘·h–ª¨«Declare‘UUÂIcosahedronŽ‘Cƒy«functions‘@­1470“·iŽ¡‘ -g«;ŽŸ :¤­This–ÕXcoÝÑIcosahedronŽ‘|¶¤«::‘Ïdihe–ÿ}'dr“al‘‰ffŽ‘®angleŽ‘Aä«=‘ÇÝPIŽ‘Z·‘8àÏasinŽ‘c¥«(2±:«0ŽŽ– DZ=«3±:«0ŽŽ“);ŽŸ :¤­This–ÕXcoK&«.‘o·±=Ž¡‘Ïvertic‘ÿ}'esŽ‘8±X«=‘Ç12ŽŽ‘ Ç;Ž¡‘Ïe‘ÿ}'dgesŽ‘.™1«=‘Ç30ŽŽ‘ Ç;Ž¡‘Ïc‘ÿ}'enterŽ‘2Ð¥«=‘ÇÝINVALID_POINTŽ‘GY«;‘±=·‘ÿý«from‘UUÂP®9olyhedronŽ‘=c"«.‘o·±=Ž¡‘Ïnumb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜olygon‘‰ffŽ“typ˜esŽ’R9«=‘Ç1Ž‘Ç;Ž¡‘Ïfac–ÿ}'e‘‰ffŽ‘®r“adiusŽ‘G%«=‘ÇÏe–ÿ}'dge‘‰ffŽ‘®r“adiusŽ‘7j«=‘ÇÏvertex‘‰ffŽ‘®r‘ÿ}'adiusŽ‘>þ¨«=‘ÇÝINVALID_REALŽ‘BM\«;Ž¡‘Ïtriangle‘‰ffŽ‘®r‘ÿ}'adiusŽ‘WUn«=‘ÇÝINVALID_REALŽ‘BM\«;Ž¡‘ -·gŽ¤ ­See–ÕXalso“sections“1474,“1476,“and“1478.Ž¡This–ÕXco0¯«&Ž‘E÷ͱpŽ‘JÿÍ;‘ª¨ÂconstŽ‘ `‚realŽ‘7žèÏtriangle‘‰ffŽ‘®diameterŽ’„0±;‘ª¨ÂrealŽ‘éÏangle‘‰ffŽ‘®xŽ‘9nê±;‘ª¨ÂrealŽŽ¡‘2Ïangle‘‰ffŽ‘®yŽ‘Rk±;‘ª¨ÂrealŽ‘]ÖÏangle‘‰ffŽ‘®zŽ‘8]L«)Ž¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EnteringÈ ÝIcosahedroŽ‘kÆÜn::Icosahedron().\n"Ž’Ø ·‘ÇÏ ushŽ‘€«;Ž¡‘Ïon‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘Nl «=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿý«from‘UUÂSolidŽ‘Ó,«.‘o·±=Ž¡‘Ïdo‘‰ffŽ‘®outputŽ‘A½M«=‘ÇÏtrueŽ‘‹°«;Ž¡‘Ïfac‘ÿ}'esŽ‘-ª«=‘Ç20ŽŽ‘ Ç;‘±=·‘ÿý«from‘UUÂSolidu½‰™šs4Ž‘ÔwF‘ÿ -«acedŽ‘>K&«.‘o·±=Ž¡‘Ïvertic‘ÿ}'esŽ‘8±X«=‘Ç12ŽŽ‘ Ç;Ž¡‘Ïe‘ÿ}'dgesŽ‘.™1«=‘Ç30ŽŽ‘ Ç;Ž¡‘Ïnumb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜olygon‘‰ffŽ“typ˜esŽ’R9«=‘Ç1Ž‘Ç;Ž¡#ÂifŽ‘ ´ø«0Ž‘$´ú±=·‘ÿý«ST–ÿ*ªAR“T–UUHERE.“TO“DO:“Must“calculate“these!‘o·±=Ž¡‘Ïfac–ÿ}'e‘‰ffŽ‘®r“adiusŽ‘G%«=‘Ç0Ž‘Ç;Ž¡‘Ïe–ÿ}'dge‘‰ffŽ‘®r“adiusŽ‘H£¬«=‘Ç0Ž‘Ç;Ž¡‘Ïvertex‘‰ffŽ‘®r‘ÿ}'adiusŽ‘P7’«=‘Ç0Ž‘Ç;Ž¡#ÂendifŽŽ¡‘Ïtriangle‘‰ffŽ‘®r‘ÿ}'adiusŽ‘WUn«=‘ÇÏtriangle‘‰ffŽ‘®diameterŽ‘OX>±=«2±:«0ŽŽ‘ Ç;Ž¦‘Âin®9tŽ‘%¤ù±iŽ‘)í«;Ž¦‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘IóR±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘B~¸«::Ž‘I öÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“r–ÿ}'e“g‘‰ffŽ‘®p“olygonŽ’¬ƒ8«(‘ª¨));Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘IóR±:Ïfr‘ÿ}'ontŽ‘I‘«(–ª¨)‘þŸ±~ŽŽ‘ÏsetŽ‘x…«(ÏoriginŽ‘ö!±;“«3Ž‘ª©±;“Ïtriangle‘‰ffŽ‘®diameterŽ‘N;Ϋ);Ž¦‘ÂP•®9oin“tŽ‘2ïŸÏptsŽ‘@ÊE«[7Ž‘];Ž¦‘ÂforŽ‘%舫(±iŽ‘9 «=‘Ç0Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«3Ž“;‘ýŸÿ®+‘ÿ+ŽŽ‘G±iŽ‘¹«)‘ÏptsŽ‘Ú¦«[±iŽ›qô«]–Ç=“Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh±:Ïfr‘ÿ}'ontŽ‘I‘«(‘ª¨)‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI«(±iŽ˜«);Ž¡‘ÂforŽ‘%舫(±iŽ‘9 «=‘Ç1Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«6Ž“;‘ýŸÿ®+‘ÿ+ŽŽ‘G±iŽ‘¹«)‘·fŽ¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘B~¸«::Ž‘I öÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“r–ÿ}'e“g‘‰ffŽ‘®p“olygonŽ’¬ƒ8«(Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP±:Ïfr‘ÿ}'ontŽ‘I‘«(‘ª¨)));Ž¡‘·gŽ¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘IóR«[1Ž–]‘þŸ±~ŽŽ‘ÏshiftŽ‘~«(ÏptsŽ‘ Ú¦«[2Ž“]–8à·“ÏptsŽ‘†«[1Ž‘]);Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘IóR«[2Ž–]‘þŸ±~ŽŽ‘ÏshiftŽ‘~«(ÏptsŽ‘ Ú¦«[1Ž“]–8à·“ÏptsŽ‘†«[2Ž‘]);Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘IóR«[3Ž–]‘þŸ±~ŽŽ‘ÏshiftŽ‘~«(ÏptsŽ‘ Ú¦«[0Ž“]–8à·“ÏptsŽ‘†«[2Ž‘]);Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘IóR«[4Ž–]‘þŸ±~ŽŽ‘ÏshiftŽ‘~«(ÏptsŽ‘ Ú¦«[0Ž“]–8à·“ÏptsŽ‘†«[1Ž‘]);Ž¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘ÏoriginŽ‘ö!±:Ïlab‘ÿ}'elŽ‘t˜«(Ý"O"Ž‘F_±;‘ª¨Ý""Ž‘ ± -«);Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘IóR«[5Ž–]‘þŸ±~ŽŽ‘Ïr‘ÿ}'otateŽ‘o?«(0Ž“±;‘ª¨«180ŽŽ‘ª«);Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘IóR«[5Ž–]‘þŸ±~ŽŽ‘ÏshiftŽ‘~«(ÏptsŽ‘ Ú¦«[1Ž“]–8à·“Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8,0«[5Ž–]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI«(0Ž“));Ž¡‘ÂforŽ‘%舫(±iŽ‘9 «=‘Ç6Ž‘Ç;‘ÿý±iŽ‘ 9 <‘Ç«10ŽŽ‘ 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«=‘Ç10ŽŽ– Ç;‘ÿý±iŽ‘ 9 <‘Ç«20ŽŽ“;‘ýŸÿ®+‘ÿ+ŽŽ‘G±iŽ‘¹«)‘·fŽ¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘B~¸«::Ž‘I öÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“r–ÿ}'e“g‘‰ffŽ‘®p“olygonŽ’¬ƒ8«(Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP«[±iŽ‘ªÔ·‘8à«10ŽŽ‘ 8â]));Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS±:Ïb‘ÿ}'ackŽ‘üë(‘ª¨)‘þŸ±~ŽŽ‘Ïr‘ÿ}'otateŽ‘o?«(180ŽŽ‘);Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS±:Ïb‘ÿ}'ackŽ‘üë(–ª¨)‘þŸ±~ŽŽ‘ÏshiftŽ‘~«(0Ž‘±;“«12ŽŽ‘ ªª);Ž¡‘·gŽ¡‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS«[4Ž‘]‘þŸ±~ŽŽ‘Ïdotlab‘ÿ}'elŽ‘%ÿô«(‘ª¨);Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS«[19ŽŽ‘ -]‘þŸ±~ŽŽ‘Ïdotlab‘ÿ}'elŽ‘%ÿô«(‘ª¨);Ž¡‘·gŽ¤‘ÂrealŽ‘*³0Ïy‘‰ffŽ‘®shiftŽ‘J Û«=‘ÇÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh«[4Ž–]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ›+bI«(0Ž“)±:Ïget‘‰ffŽ‘®yŽ‘t«(‘ª¨)–8à·“Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8,0«[19ŽŽ‘ -]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ˜«(0Ž‘)±:Ïget‘‰ffŽ‘®yŽ‘t«(‘ª¨);Ž¡‘ÂforŽ‘%舫(±iŽ‘9 «=‘Ç10ŽŽ– Ç;‘ÿý±iŽ‘ 9 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-i‘«::Ž‘ŽBÏiter‘ÿ}'atorŽ‘)™7iterŽ‘=+M«=‘DZvŽ–ûÕ:Ïb–ÿ}'e“ginŽ‘¾¨«(›ª¨);‘ÿýÏiterŽ‘’·6«=‘DZvŽ“:ÏendŽ‘ಫ(˜);‘ýŸÿ®+‘ÿ+ŽŽ‘GÏiterŽ‘"«)‘·fŽ¡‘ÂifŽ‘)´û«(Ïp–ÿ}'ortr“aitŽ‘!ê@«)‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïr‘ÿ}'otateŽ‘o>«(0Ž‘±;‘ª¨«90ŽŽ‘ ªª);Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïget‘‰ffŽ‘®c‘ÿ}'enterŽ‘,=G«(–ª¨)±:Ïlab‘ÿ}'elŽ‘t˜«(±iŽ‘ñôŸÿ®+‘ÿ+ŽŽ‘¹±;“Ý""Ž‘ ± -«);Ž¡‘(·Ž‘Ž‘ -ÏiterŽ‘Ë«)±:Ïdr‘ÿ}'awŽ‘(Û«(‘ª¨);Ž¡‘·gŽ¡‘ÂreturnŽ‘4‘g«;‘±=·‘ÿý«Delete,–UUwhen“I“start“writing“coGde“for“tabs.‘qÇ[¬LDF‘T2002.08.12.«]Ž‘U$©·±=Ž¡‘ÂifŽ‘´ú«(·:Ïmake‘‰ffŽ‘®tabsŽ‘,Ÿn«)‘ÂreturnŽ‘%‘e«;Ž¦‘ÂP®9athŽ‘/æ»±pŽ‘4[11ŽŽ‘ -];Ž¡‘ÂP•®9oin“tŽ‘2ïŸÏptsŽ‘@ÊE«[11ŽŽ‘ -];Ž¡#ÂifŽ‘ ´ø«0ŽŽ¦‘±vŽ‘4¿«[0Ž‘]‘þŸ±~ŽŽ‘Ïdotlab‘ÿ}'elŽ‘%ÿô«(‘ª¨);Ž¡#ÂendifŽŽ¡‘ÏptsŽ‘!Ú¨«[0Ž›]–Ç=“±vŽ‘ûÕ«[0Ž˜]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI«(0Ž˜);Ž¡‘ÏptsŽ‘!Ú¨«[1Ž›]–Ç=“±vŽ‘ûÕ«[0Ž˜]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI«(1Ž˜);Ž¡‘ÏptsŽ‘!Ú¨«[2Ž›]–Ç=“±vŽ‘ûÕ«[0Ž˜]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI«(2Ž˜);Ž¡‘ÏptsŽ‘!Ú¨«[3Ž›]–Ç=“ÏptsŽ‘¡¾«[0Ž˜]±:Ïme‘ÿ}'diateŽ‘"½u«(ÏptsŽ‘ Ú¦«[1Ž˜]±;‘ª¨:«1ŽŽ‘ 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-]–Ç=“ÏptsŽ‘¡¾«[6Ž–]±:Ïme‘ÿ}'diateŽ‘"½u«(ÏptsŽ‘ Ú¦«[5Ž“]±;‘ª¨:«1ŽŽ‘ qÆ);Ž¡#ÂifŽ‘ ´ø«0ŽŽ¡‘ÏptsŽ‘!Ú¨«[9Ž–]±:Ïdotlab‘ÿ}'elŽ‘!ÿó«(8Ž“);Ž¡‘ÏptsŽ‘!Ú¨«[10ŽŽ‘ -]±:Ïdotlab‘ÿ}'elŽ‘!ÿó«(9Ž‘);Ž¡#ÂendifŽŽ¡‘±pŽ‘«[0Ž–]±:ÏsetŽ‘ x„«(Ý"--"Ž‘†\±;‘ª¨ÏtrueŽ‘o@±;‘ª¨«&Ž‘ qÆÏptsŽ›Ll«[3Ž“]±;‘ª¨«&Ž‘ qÆÏptsŽ˜«[9Ž“]±;‘ª¨«&Ž‘ qÆÏptsŽ˜«[10ŽŽ‘ -]±;‘ª¨«&Ž‘ qÆÏptsŽ˜«[4Ž“]±;‘ª¨«0Ž‘ª©);Ž¡‘±pŽ‘«[1Ž›]–Ç=“±pŽ‘Ï«[2Ž˜]“=“±pŽ‘Ï«[3Ž˜]“=“±pŽ‘Ï«[4Ž˜]“=“±pŽ‘Ï«[5Ž˜]“=“±pŽ‘Ï«[0Ž˜];Ž¡‘±pŽ‘«[1Ž–]±:ÏshiftŽ‘}«(±vŽ‘4½«[4Ž“]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI«(1Ž“)–8à·“ÏptsŽ‘†«[1Ž‘]);Ž¡‘±pŽ‘«[2Ž–]±:ÏshiftŽ‘}«(±vŽ‘4½«[8Ž“]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI«(1Ž“)–8à·“ÏptsŽ‘†«[1Ž‘]);Ž¡‘±pŽ‘«[3Ž–]±:ÏshiftŽ‘}«(±vŽ‘4½«[12ŽŽ‘ -]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI«(1Ž“)–8à·“ÏptsŽ‘†«[1Ž‘]);Ž¡‘±pŽ‘«[4Ž–]±:ÏshiftŽ‘}«(±vŽ‘4½«[16ŽŽ‘ -]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI«(1Ž“)–8à·“ÏptsŽ‘†«[1Ž‘]);ŽŽŽŒ‹ÊØž Šn ý‘ì«458–­DRA‘ÿ8W‘ÕXNET’-Ài3DLDFPRÃŽG“·x«1478Ž €n ý•@P‘±pŽ‘«[5Ž–]±:ÏshiftŽ‘}«(±vŽ‘4½«[18ŽŽ‘ 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-·gŽ¤Â1479.‘ üSemi-Regular–ÕTArcš®9himedean“P˜olyhedra.Ž¡1480.‘ üT‘ÿ -«runcated‘ÕTOctahedron.Ž¡1481.‘ üT‘ÿ -«runc‘°¡‰ffs4Ž‘#ÕOctahedron–ÕTclass“de nition.Ž©·h–ª¨«De ne‘UUÂclassŽ‘5¦T‘ÿ -«runcu½‰™šs4Ž‘ÔwOctahedronŽ’€DT­1481“·i‘ÇŽ¤ ‘ -ÂclassŽ‘$àRT‘ÿ -«runcu½‰™šs4Ž‘ÔwOctahedronŽ’†Q«:‘qÇÂpublicŽ‘'ñP®9olyhedronŽ‘dh·fŽ¡‘ -ÂprotectedŽ‘:o™«:‘ÂstaticŽ‘$HÙconstŽ‘Bs{realŽ‘Y&©Ïangle‘‰ffŽ–®hex‘‰ffŽ“squar‘ÿ}'eŽ’¢Œ«;‘±=·‘ÿý«In‘UUradians!‘o·±=Ž¡‘ÂstaticŽ‘3HÛconstŽ‘Qs}realŽ‘h&«Ïangle‘‰ffŽ–®hex‘‰ffŽ“hexŽ’¤j5«;‘±=·‘ÿý«In‘UUradians!‘o·±=Ž¡‘ÂrealŽ‘*³0Ïhexagon‘‰ffŽ‘®r‘ÿ}'adiusŽ‘lô¹«;Ž¦‘ -ÂpublicŽ‘)=Ö«:‘·h–ª¨«Declare‘UUÂT‘ÿ -«runcu½‰™šs4Ž‘ÔwOctahedronŽ‘dyT«functions‘@­1484“·iŽ¡‘ -g«;ŽŸ ­This–ÕXcoÝÑT‘ÿ -«runcu½‰™šs4Ž‘ÔwOctahedronŽ’¬«::‘Ïangle‘‰ffŽ–®hex‘‰ffŽ“squar‘ÿ}'eŽ‘Lµÿ«=‘Ç(125ŽŽ‘8ã+›8à(16±:«0ŽŽ–Ç ±=«60±:«0ŽŽ“))˜·˜«(ÝPIŽ‘ b±=«180±:«0ŽŽ‘Ç!);Ž¡‘ -ÂconstŽ‘(*£realŽ‘>ÝÑT‘ÿ -«runcu½‰™šs4Ž‘ÔwOctahedronŽ’¬«::‘Ïangle‘‰ffŽ–®hex‘‰ffŽ“hexŽ‘@ -¦«=‘Ç(109ŽŽ‘8ã+›8à(28±:«0ŽŽ–Ç ±=«60±:«0ŽŽ“))˜·˜«(ÝPIŽ‘ b±=«180±:«0ŽŽ‘Ç!);ŽŸ ­This–ÕXcoi|«.‘ÌÈ[¬LDF‘T2002.10.29.«]Ž‘SóXT‘ÿ*ªruncated–s«oGctahedrons“consist“of“6“squaresŽ¡‘(and–UU8“hexagons.‘o·±=Ž¡‘Ïvertic‘ÿ}'esŽ‘8±X«=‘Ç24ŽŽ‘ Ç;Ž¡‘Ïe‘ÿ}'dgesŽ‘.™1«=‘Ç36ŽŽ‘ Ç;Ž¡‘Ïc‘ÿ}'enterŽ‘2Ð¥«=‘ÇÝINVALID_POINTŽ‘GY«;‘±=·‘ÿý«from‘UUÂP®9olyhedronŽ‘=c"«.‘o·±=Ž¡‘Ïnumb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜olygon‘‰ffŽ“typ˜esŽ’R9«=‘Ç2Ž‘Ç;Ž¡‘Ïfac–ÿ}'e‘‰ffŽ‘®r“adiusŽ‘G%«=‘ÇÏe–ÿ}'dge‘‰ffŽ‘®r“adiusŽ‘7j«=‘ÇÏvertex‘‰ffŽ‘®r‘ÿ}'adiusŽ‘>þ¨«=‘ÇÝINVALID_REALŽ‘BM\«;Ž¡‘Ïhexagon‘‰ffŽ‘®r‘ÿ}'adiusŽ‘Y£«=‘ÇÝINVALID_REALŽ‘BM\«;Ž¡‘ -·gŽ¤ ­See–ÕXalso“sections“1488,“1490,“and“1491.Ž¡This–ÕXco@«&Ž‘F%±pŽ‘K%;‘ª¨ÂconstŽ‘ h.realŽ‘7®@Ïdiameter‘‰ffŽ–®of‘‰ffŽ“hexagonŽ’‘±;‘ª¨ÂrealŽ‘ðºÏangle‘‰ffŽ‘®xŽ‘=2~«=‘»è0Ž‘»é±;‘ª¨ÂrealŽŽ¡‘Ïangle‘‰ffŽ‘®yŽ‘A2¦«=‘Ç0Ž–DZ;‘ª¨ÂrealŽ‘]ÖÏangle‘‰ffŽ‘®zŽ‘;$d«=‘Ç0Ž“);Ž¡#ÂendifŽŽŽŽŒ‹Ìú Šn ý‘ì«460›­CONSTR•ÃŽUCTOR’By3DLDFPR“G˜·x«1488Ž €n ý•@PÂ1488.Ž©·h–ª¨«De ne‘UUÂT‘ÿ -«runcu½‰™šs4Ž‘ÔwOctahedronŽ‘dyT«functions‘@­1485“·i‘Ç«+·Ž¤ «#ÂifŽ‘ ´ø«0ŽŽ¡‘ -ÂT‘ÿ -«runcu½‰™šs4Ž‘ÔwOctahedronŽ‘hί«::‘ÂT‘ÿ -«runcu½‰™šs4Ž‘ÔwOctahedronŽ‘^ή«(ÂconstŽ‘˜7P•®9oin“tŽ‘=õi«&Ž‘E¼‡±pŽ‘Jć;‘ª¨ÂconstŽ‘ BßrealŽ‘7c¢Ïhexagon‘‰ffŽ‘®diameterŽ’…§ý±;‘ª¨ÂrealŽŽ¡‘2Ïangle‘‰ffŽ‘®xŽ‘R…á±;‘ª¨ÂrealŽ‘]ÖÏangle‘‰ffŽ‘®yŽ‘8Éa±;‘ª¨ÂrealŽ‘]ÖÏangle‘‰ffŽ‘®zŽ‘8]L«)Ž¡‘ -·fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘ÂifŽ‘´ú«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"EnteringÈ ÝTrunc_OctaŽ‘kÆÜhedron::Trunc_OctaheŽ’ÔÆ dron().\n"Ž’ ”·‘ÇÏ ushŽ‘€«;Ž¡‘Ïc‘ÿ}'enterŽ‘2Ð¥«=‘DZpŽ‘Ï«;Ž¡‘Ïon‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘Nl «=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿý«from‘UUÂSolidŽ‘Ó,«.‘o·±=Ž¡‘Ïdo‘‰ffŽ‘®outputŽ‘A½M«=‘ÇÏtrueŽ‘‹°«;‘±=·‘ÿý«ST–ÿ*ªAR“T–UUHERE.“TO“DO:“Must“calculate“these!‘o·±=Ž¡‘Ïfac–ÿ}'e‘‰ffŽ‘®r“adiusŽ‘G%«=‘Ç0Ž‘Ç;Ž¡‘Ïe–ÿ}'dge‘‰ffŽ‘®r“adiusŽ‘H£¬«=‘Ç0Ž‘Ç;Ž¡‘Ïvertex‘‰ffŽ‘®r‘ÿ}'adiusŽ‘P7’«=‘Ç0Ž‘Ç;Ž¡‘Ïfac‘ÿ}'esŽ‘-C9«=‘ù§14ŽŽ‘ ù©;‘±=·‘S«from‘s«ÂSolidu½‰™šs4Ž‘ÔwF‘ÿ -«acedŽ‘>i|«.‘ÌÈ[¬LDF‘T2002.10.29.«]Ž‘SóXT‘ÿ*ªruncated–s«oGctahedrons“consist“of“6“squaresŽ¡‘(and–UU8“hexagons.‘o·±=Ž¡‘Ïvertic‘ÿ}'esŽ‘8±X«=‘Ç24ŽŽ‘ Ç;Ž¡‘Ïe‘ÿ}'dgesŽ‘.™1«=‘Ç36ŽŽ‘ Ç;Ž¡‘Ïnumb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜olygon‘‰ffŽ“typ˜esŽ’R9«=‘Ç2Ž‘Ç;Ž¡‘Ïhexagon‘‰ffŽ‘®r‘ÿ}'adiusŽ‘Y£«=‘ÇÏhexagon‘‰ffŽ‘®diameterŽ‘Q s±=«2±:«0ŽŽ‘ Ç;Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘Lºj«=‘ÇÏget‘‰ffŽ‘®netŽ‘!ûà«(Ïhexagon‘‰ffŽ‘®diameterŽ‘ND[±;‘ª¨ÏtrueŽ‘o@«);Ž¦‘ÂP•®9oin“tŽ‘2ïŸÏptsŽ‘@ÊE«[24ŽŽ‘ -];Ž¡‘Âin®9tŽ‘%¤ù±iŽ‘)í«;Ž¦‘ÂforŽ‘%舫(±iŽ‘9 «=‘Ç0Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«6Ž“;‘ÿý±iŽ‘ññŸÿ®+‘ÿ+ŽŽ‘¹«)‘ÏptsŽ‘Ú¦«[±iŽ›qô«]–Ç=“Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh«[0Ž‘]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI«(±iŽ˜«);Ž¡#ÂifŽ‘ ´ø«0ŽŽ¡‘ÏptsŽ‘!Ú¨«[0Ž–]±:Ïdotlab‘ÿ}'elŽ‘!ÿó«(0Ž“);Ž¡‘ÏptsŽ‘!Ú¨«[1Ž–]±:Ïdotlab‘ÿ}'elŽ‘!ÿó«(1Ž“±;‘ª¨Ý"lft"Ž‘q«);Ž¡‘ÏptsŽ‘!Ú¨«[2Ž–]±:Ïdotlab‘ÿ}'elŽ‘!ÿó«(2Ž“±;‘ª¨Ý"bot"Ž‘q«);Ž¡‘ÏptsŽ‘!Ú¨«[3Ž–]±:Ïdotlab‘ÿ}'elŽ‘!ÿó«(3Ž“±;‘ª¨Ý"bot"Ž‘q«);Ž¡‘ÏptsŽ‘!Ú¨«[4Ž–]±:Ïdotlab‘ÿ}'elŽ‘!ÿó«(4Ž“±;‘ª¨Ý"rt"Ž‘1«);Ž¡‘ÏptsŽ‘!Ú¨«[5Ž–]±:Ïdotlab‘ÿ}'elŽ‘!ÿó«(5Ž“);Ž¡#ÂendifŽŽ¦‘realŽ‘*³0Ïangle‘‰ffŽ–®h‘‰ffŽ“hŽ‘VÓ©«=‘Ç180±:«0ŽŽ‘Ç·–8à«(Ïangle‘‰ffŽ–®hex‘‰ffŽ“hexŽ‘>|j·“«180±:«0ŽŽ‘±=ÝPIŽ‘ b«);Ž¦‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘IóR«[1Ž–]‘þŸ±~ŽŽ‘Ïr‘ÿ}'otateŽ‘o?«(ÏptsŽ‘ Ú¦«[4Ž“]±;‘ª¨ÏptsŽ‘…N«[5Ž“]±;‘ª¨Ïangle‘‰ffŽ–®h‘‰ffŽ“hŽ‘+ «);Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘IóR«[2Ž–]‘þŸ±~ŽŽ‘Ïr‘ÿ}'otateŽ‘o?«(ÏptsŽ‘ Ú¦«[3Ž“]±;‘ª¨ÏptsŽ‘…N«[2Ž“]±;‘ª¨·Ž‘ qÆÏangle‘‰ffŽ–®h‘‰ffŽ“hŽ‘2Ë'«);Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘IóR«[3Ž–]‘þŸ±~ŽŽ‘Ïr‘ÿ}'otateŽ‘o?«(ÏptsŽ‘ Ú¦«[0Ž“]±;‘ª¨ÏptsŽ‘…N«[1Ž“]±;‘ª¨Ïangle‘‰ffŽ–®h‘‰ffŽ“hŽ‘+ «);Ž¦‘ÂrealŽ‘*³0Ïangle‘‰ffŽ–®h‘‰ffŽ“sŽ‘UÛ·«=‘Ç180±:«0ŽŽ‘Ç·–8à«(Ïangle‘‰ffŽ–®hex‘‰ffŽ“squar‘ÿ}'eŽ‘K'÷“«180±:«0ŽŽ‘±=ÝPIŽ‘ b«);Ž¦‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘IóR«[4Ž–]‘þŸ±~ŽŽ‘Ïr‘ÿ}'otateŽ‘o?«(ÏptsŽ‘ Ú¦«[0Ž“]±;‘ª¨ÏptsŽ‘…N«[5Ž“]±;‘ª¨Ïangle‘‰ffŽ–®h‘‰ffŽ“sŽ‘* «);Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘IóR«[5Ž–]‘þŸ±~ŽŽ‘Ïr‘ÿ}'otateŽ‘o?«(ÏptsŽ‘ Ú¦«[1Ž“]±;‘ª¨ÏptsŽ‘…N«[2Ž“]±;‘ª¨Ïangle‘‰ffŽ–®h‘‰ffŽ“sŽ‘* «);Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘IóR«[6Ž–]‘þŸ±~ŽŽ‘Ïr‘ÿ}'otateŽ‘o?«(ÏptsŽ‘ Ú¦«[3Ž“]±;‘ª¨ÏptsŽ‘…N«[4Ž“]±;‘ª¨Ïangle‘‰ffŽ–®h‘‰ffŽ“sŽ‘* «);Ž¡‘±=·‘ÿý«[¬LDF‘T2002.11.07.«]Ž‘T7Do–UUsomething“abGout“these“commen¸ãts!‘o·±=‘=·–ÿý«7“·±=Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘IóR±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘B~¸«::Ž‘I öÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“r–ÿ}'e“g‘‰ffŽ‘®p“olygonŽ’¬ƒ8«(Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP«[0Ž‘]));‘±=·–ÿý«8“·±=Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘IóR±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘B~¸«::Ž‘I öÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“r–ÿ}'e“g‘‰ffŽ‘®p“olygonŽ’¬ƒ8«(Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP«[1Ž‘]));‘±=·–ÿý«9“·±=Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘IóR±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘B~¸«::Ž‘I öÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“r–ÿ}'e“g‘‰ffŽ‘®p“olygonŽ’¬ƒ8«(Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP«[2Ž‘]));‘±=·–ÿý«10“·±=Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘IóR±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘B~¸«::Ž‘I 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üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2002.11.08.«]Ž‘Y;Added–UUthis“function.Ž¡‘ -[¬LDF‘T2002.08.12.«]Ž‘Y;Remo•¸ãv“ed‘UUÏc‘ÿ}'enter‘‰ffŽ‘®0Ž‘+Æ1«argumen“t.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h–ª¨«Declare‘UUÂT‘ÿ -«runcu½‰™šs4Ž‘ÔwOctahedronŽ‘dyT«functions‘@­1484“·i‘Ç«+·Ž¤ «#ÂifŽ‘ ´ø«0ŽŽ¡‘ -ÂstaticŽ‘)HÚv®9ectorŽ‘Hó"·hÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘DÔ ·Ž‘IÔ -i‘UUÏget‘‰ffŽ‘®netŽ‘"Š«(ÂconstŽ‘*¢realŽ‘4ÝÐÏhexagon‘‰ffŽ‘®diameterŽ’ƒ"+±;‘ª¨Âb•QÇo“olŽ‘LÏdo‘‰ffŽ‘®halfŽ‘>s¯«=‘ÇÏfalseŽ‘v\«);Ž¡#ÂendifŽŽŽŽŒ‹Îe Šn ý‘ì«462–­GET‘ÕXNET’6O3DLDFPRÃŽG“·x«1490Ž €n ý•@PÂ1490.Ž©·h–ª¨«De ne‘UUÂT‘ÿ -«runcu½‰™šs4Ž‘ÔwOctahedronŽ‘dyT«functions‘@­1485“·i‘Ç«+·Ž¤ «#ÂifŽ‘ ´ø«0ŽŽ¡‘ -Âv®9ectorŽ‘)ªI·hÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘D䦷Ž‘Iä§i‘eòÂT‘ÿ -«runcu½‰™šs4Ž‘ÔwOctahedronŽ‘b4 «::‘Ïget‘‰ffŽ‘®netŽ‘ 4Ì«(ÂconstŽ‘;?realŽ‘4ÿ -Ïhexagon‘‰ffŽ‘®diameterŽ’ƒCe±;‘ª¨Âb•QÇo“olŽ‘\«Ïdo‘‰ffŽ‘®halfŽ‘;½4«)·fŽ¡‘2Âb•QÇo“olŽ‘K¡kÝDEBUGŽ‘i.Ü«=‘ÇÏfalseŽ‘v\«;‘±=·‘ÿýÏtrueŽ‘Ä’·±=Ž¦‘Âv®9ectorŽ‘=ªK·hÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘DÔ ·Ž‘IÔ -i‘UUÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘9H¥«;Ž¡‘Âin®9tŽ‘/¤ú±iŽ‘3î«;Ž¦‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘B~¸«::Ž‘I öÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“r–ÿ}'e“g‘‰ffŽ‘®p“olygonŽ’¬ƒ8«(‘ª¨));Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS«[0Ž‘]‘þŸ±~ŽŽ‘ÏsetŽ‘x…«(ÏoriginŽ‘ö!±;‘ª¨«6Ž‘ª©±;‘ª¨Ïhexagon‘‰ffŽ‘®diameterŽ‘Oï«);Ž¦‘ÂP•®9oin“tŽ‘<ï ÏptsŽ‘JÊF«[24ŽŽ‘ -];Ž¦‘ÂforŽ‘/艫(±iŽ‘9 «=‘Ç0Ž–Ç;‘ÿý±iŽ‘ 9 <‘Ç«6Ž“;‘ÿý±iŽ‘ññŸÿ®+‘ÿ+ŽŽ‘¹«)‘ÏptsŽ‘Ú¦«[±iŽ›qô«]–Ç=“Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh«[0Ž‘]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI«(±iŽ˜«);Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘B~¸«::Ž‘I öÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“r–ÿ}'e“g‘‰ffŽ‘®p“olygonŽ’¬ƒ8«(Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP«[0Ž‘]));Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS«[1Ž–]‘þŸ±~ŽŽ‘ÏshiftŽ‘~«(ÏptsŽ‘ Ú¦«[4Ž“]–8à·“ÏptsŽ‘†«[2Ž‘]);Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘B~¸«::Ž‘I öÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“r–ÿ}'e“g‘‰ffŽ‘®p“olygonŽ’¬ƒ8«(Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP«[0Ž‘]));Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS«[2Ž–]‘þŸ±~ŽŽ‘ÏshiftŽ‘~«(ÏptsŽ‘ Ú¦«[3Ž“]–8à·“ÏptsŽ‘†«[5Ž‘]);Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘B~¸«::Ž‘I öÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“r–ÿ}'e“g‘‰ffŽ‘®p“olygonŽ’¬ƒ8«(Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP«[0Ž‘]));Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS«[3Ž–]‘þŸ±~ŽŽ‘ÏshiftŽ‘~«(ÏptsŽ‘ Ú¦«[1Ž“]–8à·“ÏptsŽ‘†«[3Ž‘]);Ž¦‘ÂrealŽ‘4³1Ïside‘‰ffŽ‘®lengthŽ‘g «=‘ÇÏptsŽ‘¡¾«[5Ž›]±:Ïget‘‰ffŽ‘®xŽ‘Žg«(‘ª¨)–8à·“ÏptsŽ‘†«[0Ž˜]±:Ïget‘‰ffŽ‘®xŽ‘Žg«(‘ª¨);Ž¦‘ÏptsŽ‘+Ú©«[6Ž›]–Ç=“ÏptsŽ‘¡¾«[0Ž˜];Ž¡‘ÏptsŽ‘+Ú©«[6Ž–]±:ÏshiftŽ‘}«(0Ž“±;‘ª¨«0Ž‘ª©±;‘ª¨Ïside‘‰ffŽ‘®lengthŽ‘1Mh«);Ž¡‘ÏptsŽ‘+Ú©«[7Ž›]–Ç=“ÏptsŽ‘¡¾«[5Ž˜];Ž¡‘ÏptsŽ‘+Ú©«[7Ž–]±:ÏshiftŽ‘}«(0Ž“±;‘ª¨«0Ž‘ª©±;‘ª¨Ïside‘‰ffŽ‘®lengthŽ‘1Mh«);Ž¦‘ÂRectangleŽ‘S”í±rŽ‘X_«(ÏptsŽ‘ Ú¦«[0Ž–]±;‘ª¨ÏptsŽ›…N«[5Ž“]±;‘ª¨ÏptsŽ˜«[7Ž“]±;‘ª¨ÏptsŽ˜«[6Ž“]);Ž¦‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘B~¸«::Ž‘I öÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“r–ÿ}'e“g‘‰ffŽ‘®p“olygonŽ’¬ƒ8«(±rŽ‘Ê«));Ž¡‘ÏptsŽ‘+Ú©«[8Ž›]–Ç=“ÏptsŽ‘¡¾«[2Ž˜];Ž¡‘ÏptsŽ‘+Ú©«[9Ž›]–Ç=“ÏptsŽ‘¡¾«[1Ž˜];Ž¡‘ÏptsŽ‘+Ú©«[9Ž–]±:ÏshiftŽ‘}«(0Ž“±;‘ª¨«1Ž‘ª©);Ž¡‘ÏptsŽ‘+Ú©«[8Ž–]±:Ïr‘ÿ}'otateŽ‘o>«(ÏptsŽ‘ Ú¦«[9Ž“]±;‘ª¨ÏptsŽ‘…N«[1Ž“]±;‘ª¨·Ž‘ qÆ«90ŽŽ‘qÈ);Ž¡‘ÏptsŽ‘+Ú©«[10ŽŽ‘ -]–Ç=“ÏptsŽ‘¡¾«[8Ž‘];Ž¡‘ÏptsŽ‘+Ú©«[10ŽŽ‘ -]±:ÏshiftŽ‘}«(ÏptsŽ‘ Ú¦«[2Ž›]–8à·“ÏptsŽ‘†«[1Ž˜]);Ž¡‘±rŽ‘"Ê:ÏsetŽ‘ x„«(ÏptsŽ‘ Ú¦«[10ŽŽ‘ -]±;‘ª¨ÏptsŽ–…N«[2Ž›]±;‘ª¨ÏptsŽ“«[1Ž˜]±;‘ª¨ÏptsŽ“«[8Ž˜]);Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘B~¸«::Ž‘I öÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“r–ÿ}'e“g‘‰ffŽ‘®p“olygonŽ’¬ƒ8«(±rŽ‘Ê«));Ž¡‘ÏptsŽ‘+Ú©«[11ŽŽ‘ -]–Ç=“ÏptsŽ‘¡¾«[3Ž‘];Ž¡‘ÏptsŽ‘+Ú©«[12ŽŽ‘ -]–Ç=“ÏptsŽ‘¡¾«[4Ž‘];Ž¡‘ÏptsŽ‘+Ú©«[12ŽŽ‘ -]±:ÏshiftŽ‘}«(0Ž‘±;‘ª¨«1Ž‘ª©);Ž¡‘ÏptsŽ‘+Ú©«[11ŽŽ– -]±:Ïr‘ÿ}'otateŽ‘o>«(ÏptsŽ‘ Ú¦«[4Ž‘]±;‘ª¨ÏptsŽ‘…N«[12ŽŽ“]±;‘ª¨«90ŽŽ‘ ªª);Ž¡‘ÏptsŽ‘+Ú©«[13ŽŽ› -]–Ç=“ÏptsŽ‘¡¾«[11ŽŽ˜];Ž¡‘ÏptsŽ‘+Ú©«[13ŽŽ‘ -]±:ÏshiftŽ‘}«(ÏptsŽ‘ Ú¦«[3Ž›]–8à·“ÏptsŽ‘†«[4Ž˜]);Ž¡‘±rŽ‘"Ê:ÏsetŽ‘ x„«(ÏptsŽ‘ Ú¦«[11ŽŽ‘ -]±;‘ª¨ÏptsŽ–…N«[4Ž›]±;‘ª¨ÏptsŽ“«[3Ž˜]±;‘ª¨ÏptsŽ“«[13ŽŽ‘ -]);Ž¡‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘B~¸«::Ž‘I öÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“r–ÿ}'e“g‘‰ffŽ‘®p“olygonŽ’¬ƒ8«(±rŽ‘Ê«));Ž¡‘ÂifŽ‘)´û«(Ïdo‘‰ffŽ‘®halfŽ‘ `‰«)‘ÂreturnŽ‘(æºÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘^Ú -«;Ž¡#ÂendifŽŽŽŽŒ‹Ï%> Šn ý‘ì·x«1491–­3DLDFPRÃŽG’6OGET‘ÕXNET“«463Ž €n ý•@PÂ1491.‘ ü«[¬LDF‘T2002.11.08.«]Ž‘[ÇÓIf–”òwš¸ãe“just“w˜an˜t“the“net,‘äÙÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:Ø)«[5Ž›]“and“Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:ˆB«[6Ž˜]“mš¸ãust“bGe“c˜hanged,Ž¤ bGecause–âQI'vš¸ãe“made“the“net“a“bit“di eren˜tly“from“the“w˜a˜y“it's“done“in“Cundy‘ÿ*ª.›¼Get“reference!!˜P¸ãage“104.˜IŽ¡made›UUt•¸ãw“o˜of˜the˜squares˜slan“ted,˜in˜order˜to˜a“v“oid˜ha“ving˜to˜rotate˜them˜t“wice.Ž©·h–ª¨«De ne‘UUÂT‘ÿ -«runcu½‰™šs4Ž‘ÔwOctahedronŽ‘dyT«functions‘@­1485“·i‘Ç«+·Ž¡«#ÂifŽ‘ ´ø«0ŽŽ¡‘ -·Ž‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘DóR«[6Ž›]–Ç=“·Ž‘ÇÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘=ºi«[5Ž˜]“=“·Ž‘ÇÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘=ºi«[4Ž˜];Ž¡‘ -ÏptsŽ‘Ú§«[14ŽŽ‘ -]–Ç=“Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh«[4Ž–]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI«(2Ž“);Ž¡‘ -ÏptsŽ‘Ú§«[15ŽŽ‘ -]–Ç=“Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh«[4Ž–]‘þŸ±~ŽŽ‘Ïget‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI«(3Ž“);Ž¡‘ -Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQ«[5Ž–]‘þŸ±~ŽŽ‘ÏshiftŽ‘~«(ÏptsŽ‘ Ú¦«[1Ž“]–8à·“ÏptsŽ‘†«[14ŽŽ‘ -]);Ž¡‘ -Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQ«[6Ž–]‘þŸ±~ŽŽ‘ÏshiftŽ‘~«(ÏptsŽ‘ Ú¦«[4Ž“]–8à·“ÏptsŽ‘†«[15ŽŽ‘ +±c‘ÿ}'outŽ‘ P°‘Ç´"distance® ´==® ´"Ž‘O”n°‘DZdistanc‘ÿ}'eŽ‘)Ô-°‘DZend‘‚ØlŽ‘ò°‘DZ ushŽ‘€¬;Ž¡‘ +±c‘ÿ}'outŽ‘Y8µ:±pr–ÿ}'e“cisionŽ‘'½6¬(6Ž‘);Ž¡#­endifŽŽŸ1486.Ž¦°h–ª¨¬De ne‘UU­T‘ÿ +«etrahedronŽ‘EF®¬functions‘@¯1481“°i‘Ǭ+°Ž¡‘ +±c‘ÿ}'enterŽ‘(Ф¬=‘DZptsŽ‘¡¾¬[1Ž–]µ:±me‘ÿ}'diateŽ‘"½u¬(±ptsŽ‘ Ú¦¬[5Ž“]µ;‘ª¨±distanc‘ÿ}'eŽ‘%ð¥¬);Ž¡‘ +­forŽ‘臬(µiŽ‘9 ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ4Ž“;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:óP¬[µiŽ‘qô¬]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(°Ž‘DZc‘ÿ}'enterŽ‘#Щ¬);Ž¡‘ +±c‘ÿ}'enterŽ‘& Œµ:±shiftŽ‘}¬(°Ž‘DZc‘ÿ}'enterŽ‘#Щ¬);Ž¡‘ +­ifŽ‘´ù¬(±angle‘‰ffŽ‘®xŽ‘#Lô°6¬=‘Ç0Ž– ÿù°_‘8à±angle‘‰ffŽ‘®yŽ‘%kƒ°6¬=‘Ç0Ž“°_‘8à±angle‘‰ffŽ‘®zŽ‘$ÿn°6¬=‘Ç0Ž‘Ç)‘°fŽ¡‘­forŽ‘%般(µiŽ‘9 ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ4Ž“;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:óP¬[µiŽ‘qô¬]‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(±angle‘‰ffŽ‘®xŽ‘ …ܵ;‘ª¨±angle‘‰ffŽ‘®yŽ‘"3µ;‘ª¨±angle‘‰ffŽ‘®zŽ‘!ª¬);Ž¡‘ +°gŽ¡‘ +­ifŽ‘´ù¬(µpŽ‘Ï°6¬=‘DZoriginŽ‘½9¬)‘°fŽ¡‘±c‘ÿ}'enterŽ‘2Ð¥¬=‘ǵpŽ‘Ϭ;Ž¡‘­forŽ‘%般(µiŽ‘9 ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ4Ž“;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:óP¬[µiŽ‘qô¬]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(µpŽ‘¬);Ž¡‘ +°gŽ¡‘ +­returnŽ‘*‘f¬;‘qÇ°gŽŽŽŒ‹½½} Šn ý‘ì°x¬1487–¯3DLDF-1.1.5.1’ý§SETTING‘ÕXFUNCTION“¬445Ž €n ý•@P­1487.– üSetting‘ª'function.“¬[²LDF‘T2002.11.12.¬]Ž‘[AG!!‘œùThis–fwš¸ãorks,‘<ªbut“it“fails“to“assign“to“the“data“mem˜bGersŽ¤ of‘Ïâ­T‘ÿ +«etrahedronŽ›F;Ȭthat–Ïâare“de ned“in“its“o¸ãwn“­classŽ‘*À¬declaration.‘ámThat's“bGecause“neither“­T‘ÿ +«etrahedronŽ˜¬norŽ¡­P®9olyhedronŽ‘=c"¬has–UUan“assignmenš¸ãt“opGerator“y˜et.‘qÇTO“DO:“W‘ÿ*ªrite“assignmen˜t“opGerators“for“­P®9olyhedraŽ‘6Ö±¬!ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.11.12.¬]Ž‘Y;Added–UUthis“function.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­T‘ÿ +«etrahedronŽ‘EF®¬functions‘@¯1480“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘#=²±setŽ‘0¶6¬(­constŽ‘j{P•®9oin“tŽ‘=™ñ¬&Ž‘EaµpŽ‘Ji;‘ª¨­constŽ‘ #realŽ‘7*±diameter‘‰ffŽ–®of‘‰ffŽ“triangleŽ’!±µ;‘ª¨­realŽ‘¯±angle‘‰ffŽ‘®xŽ‘‘Ǭ(0Ž‘)–UU)“;Ž¡‘±trianglesŽ‘DƒÜ¬[0Ž‘]‘þŸµ~ŽŽ‘±setŽ‘x…¬(±originŽ‘ö!µ;‘ª¨¬3Ž–ª©µ;‘ª¨±triangle‘‰ffŽ‘®diameterŽ‘N;ε;‘ª¨¬0Ž“µ;‘ª¨¬180ŽŽ‘ª«);Ž¡‘±trianglesŽ‘DƒÜ¬[1Ž‘]‘þŸµ~ŽŽ‘±setŽ‘x…¬(±originŽ‘ö!µ;‘ª¨¬3Ž‘ª©µ;‘ª¨±triangle‘‰ffŽ‘®diameterŽ‘N;ά);Ž¦‘­P•®9oin“tŽ‘<ï ±ptsŽ‘JÊF¬[6Ž‘];Ž¦‘­forŽ‘/艬(µiŽ‘9 ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ3Ž“;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘°fŽ¡‘(±ptsŽ‘5Úª¬[µiŽ›qô¬]–Ç=“±trianglesŽ‘)Jñ¬[0Ž‘]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(µiŽ˜¬);Ž¡‘°gŽ¡‘­forŽ‘/艬(µiŽ‘9 ¬=‘Ç3Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ6Ž“;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘°fŽ¡‘(±ptsŽ‘5Úª¬[µiŽ‘qô¬]–Ç=“±trianglesŽ‘)Jñ¬[1Ž‘]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(µiŽ‘ªÔ°‘8à¬3Ž‘8á);Ž¡‘°gŽ¡‘Ž‘#±trianglesŽ‘IƒÝ¬[2Ž›]–Ç=“°Ž‘DZtrianglesŽ‘.Jò¬[3Ž˜]“=“°Ž‘DZtrianglesŽ‘.Jò¬[1Ž˜];Ž¡‘±trianglesŽ‘DƒÜ¬[1Ž–]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[0Ž“]–8à°“±ptsŽ‘†¬[4Ž‘]);Ž¡‘±trianglesŽ‘DƒÜ¬[2Ž–]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[0Ž“]–8à°“±ptsŽ‘†¬[5Ž‘]);Ž¡‘±trianglesŽ‘DƒÜ¬[3Ž–]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[2Ž“]–8à°“±ptsŽ‘†¬[4Ž‘]);Ž¡‘­returnŽ‘Aæ½±trianglesŽ‘hj–¬;‘qÇ°gŽŸ­1491.– üDra®9w‘Ânet.“¬[²LDF‘T2002.11.12.¬]Ž‘[VAs–#$of“this“date“it's“necessary“to“rotate“the“triangles“in¸ãto“the“x-yŽ¡plane,‘YbGecause‘XS­P•®9oin“tŽ‘òŸ¬::‘±interse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘N–Ú¬(‘ª®)–XShas“a“bug“that“I›XRdisco•¸ãv“ered–XSwhen“I˜tried“to“call“it“on“­P•®9oin“tsŽ‘&Ô*¬inŽ¡the–C +x-z“plane.‘k®It's“not“so“terrible,‘F³bGecause“as“of“this“date“it's“necessary“to“put“the“­PictureŽ‘,"!¬in“the“x-y“planeŽ¡in–‚order“to“use“the“parallel“pro‘Ž8jection.‘ MThe“latter“currenš¸ãtly“only“w˜orks“for“the“x-y“plane.‘ MTO‘sDO:“Fix“theŽ¡bug–UUand“get“parallel“pro›Ž8jection“on¸ãto“other“ma˜jor“planes“to“w¸ãork!ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.11.12.¬]Ž‘Y;Added–UUthis“function.Ž¦ŸüÈ„`ÕÁGŽŽ¦°h–ª¨¬Declare‘UU­T‘ÿ +«etrahedronŽ‘EF®¬functions‘@¯1480“°i‘Ǭ+°Ž¡‘ +­staticŽ‘)HÚv®9oidŽ‘BF²±dr‘ÿ}'aw‘‰ffŽ‘®netŽ‘iˆE¬(­constŽ‘*¢realŽ‘4Ýбtriangle‘‰ffŽ‘®diameterŽ’nöµ;‘ª¨­b•QÇo“olŽ‘L±make‘‰ffŽ‘®tabsŽ‘J²”¬=‘DZtrueŽ‘‹°¬);ŽŽŽŒ‹¿Úe Šn ý‘ì°x¬1492–¯3DLDF-1.1.5.1’%LÓDRA‘ÿ8W‘ÕXNET“¬447Ž €n ý•@P­1492.Ž©°h–ª¨¬De ne‘UU­T‘ÿ +«etrahedronŽ‘EF®¬functions‘@¯1481“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘"ýÙT‘ÿ +«etrahedronŽ‘b™á¬::‘±dr‘ÿ}'aw‘‰ffŽ‘®netŽ‘(A—¬(­constŽ‘*¢realŽ‘4Ýбtriangle‘‰ffŽ‘®diameterŽ’nöµ;‘ª¨­b•QÇo“olŽ‘L±make‘‰ffŽ‘®tabsŽ‘Gë|¬)Ž¡‘ +°fŽ¡‘­v®9ectorŽ‘3ªJ°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘DÔ °Ž‘IÔ +i‘UUµvŽ‘ Q*¬=‘DZget‘‰ffŽ‘®netŽ‘!ûà¬(±triangle‘‰ffŽ‘®diameterŽ‘L‘&¬);Ž¡‘­in®9tŽ‘%¤ùµiŽ‘)í¬;Ž¦‘­forŽ‘%般(µiŽ‘9 ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ4Ž“;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)‘°fŽ¡‘µvŽ‘#4À¬[µiŽ‘qô¬]‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(90ŽŽ‘ +);Ž¡‘µvŽ‘#4À¬[µiŽ‘qô¬]‘þŸµ~ŽŽ‘±dr‘ÿ}'awŽ‘(ܬ(‘ª¨);Ž¡‘µvŽ‘#4À¬[µiŽ–qô¬]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘0=H¬(›ª¨)µ:±lab‘ÿ}'elŽ‘t˜¬(µiŽ“;˜´""Ž‘ ± +¬);Ž¡‘°gŽ¡‘­ifŽ‘´ú¬(°:±make‘‰ffŽ‘®tabsŽ‘,Ÿn¬)‘­returnŽ‘%‘e¬;Ž¦‘­P•®9oin“tŽ‘2ptsŽ‘@ÊE¬[32ŽŽ‘ +];Ž¦‘±ptsŽ‘!Ú¨¬[0Ž›]–Ç=“µvŽ‘ûÕ¬[2Ž˜]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(1Ž˜);Ž¡‘±ptsŽ‘!Ú¨¬[1Ž›]–Ç=“µvŽ‘ûÕ¬[2Ž˜]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(2Ž˜);Ž¡‘±ptsŽ‘!Ú¨¬[2Ž›]–Ç=“µvŽ‘ûÕ¬[1Ž˜]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(2Ž˜);Ž¡‘±ptsŽ‘!Ú¨¬[3Ž›]–Ç=“µvŽ‘ûÕ¬[1Ž˜]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(0Ž˜);Ž¡‘±ptsŽ‘!Ú¨¬[4Ž›]–Ç=“µvŽ‘ûÕ¬[3Ž˜]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(0Ž˜);Ž¡‘±ptsŽ‘!Ú¨¬[5Ž›]–Ç=“µvŽ‘ûÕ¬[3Ž˜]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(1Ž˜);Ž¡‘±ptsŽ‘!Ú¨¬[6Ž›]–Ç=“±ptsŽ‘¡¾¬[0Ž˜]µ:±me‘ÿ}'diateŽ‘"½u¬(±ptsŽ‘ Ú¦¬[5Ž˜]µ;‘ª¨:¬075ŽŽ‘qÈ);Ž¡‘±ptsŽ‘!Ú¨¬[7Ž›]–Ç=“±ptsŽ‘¡¾¬[5Ž˜]µ:±me‘ÿ}'diateŽ‘"½u¬(±ptsŽ‘ Ú¦¬[0Ž˜]µ;‘ª¨:¬075ŽŽ‘qÈ);Ž¡‘±ptsŽ‘!Ú¨¬[8Ž›]–Ç=“±ptsŽ‘¡¾¬[6Ž˜];Ž¡‘±ptsŽ‘!Ú¨¬[9Ž›]–Ç=“±ptsŽ‘¡¾¬[7Ž˜];Ž¡‘±ptsŽ‘!Ú¨¬[8Ž–]‘Ç°¬=ŽŽ‘UO±ptsŽ‘ /õ¬[9Ž“]µ:±shiftŽ‘}¬(0Ž“µ;‘ª¨¬0Ž–ª©µ;‘ª¨¬1Ž“);Ž¡‘±ptsŽ‘!Ú¨¬[10ŽŽ‘ +]–Ç=“±ptsŽ‘¡¾¬[0Ž‘];Ž¡‘±ptsŽ‘!Ú¨¬[11ŽŽ‘ +]–Ç=“±ptsŽ‘¡¾¬[5Ž‘];Ž¡‘±ptsŽ‘!Ú¨¬[10ŽŽ‘ +]µ:±r‘ÿ}'otateŽ‘o>¬(±ptsŽ‘ Ú¦¬[6Ž–]µ;‘ª¨±ptsŽ‘…N¬[8Ž“]µ;‘ª¨°Ž‘ qƬ110ŽŽ‘qÉ);Ž¡‘±ptsŽ‘!Ú¨¬[11ŽŽ‘ +]µ:±r‘ÿ}'otateŽ‘o>¬(±ptsŽ‘ Ú¦¬[7Ž–]µ;‘ª¨±ptsŽ‘…N¬[9Ž“]µ;‘ª¨¬110ŽŽ‘ª«);Ž¡‘±ptsŽ‘!Ú¨¬[10ŽŽ› +]–Ç=“±ptsŽ‘¡¾¬[6Ž‘]µ:±me‘ÿ}'diateŽ‘"½u¬(±ptsŽ‘ Ú¦¬[10ŽŽ˜]µ;‘ª¨¬1µ:¬5ŽŽ‘qÇ);Ž¡‘±ptsŽ‘!Ú¨¬[11ŽŽ› +]–Ç=“±ptsŽ‘¡¾¬[7Ž‘]µ:±me‘ÿ}'diateŽ‘"½u¬(±ptsŽ‘ Ú¦¬[11ŽŽ˜]µ;‘ª¨¬1µ:¬5ŽŽ‘qÇ);Ž¡#­ifŽ‘ ´ø¬0ŽŽ¡‘­forŽ‘%般(µiŽ‘9 ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ8Ž“;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)‘±ptsŽ‘Ú¦¬[µiŽ–qô¬]µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(µiŽ“¬);Ž¡‘±ptsŽ‘!Ú¨¬[10ŽŽ– +]µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(10ŽŽ“);Ž¡‘±ptsŽ‘!Ú¨¬[11ŽŽ– +]µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(11ŽŽ“);Ž¡#­endifŽŽ¦‘P®9athŽ‘/滵pŽ‘4[6Ž‘];Ž¦‘µpŽ‘¬[0Ž–]µ:±setŽ‘ x„¬(´"--"Ž‘†\µ;‘ª¨±trueŽ‘o@µ;‘ª¨¬&Ž‘ qƱptsŽ›Ll¬[6Ž“]µ;‘ª¨¬&Ž‘ qƱptsŽ˜¬[10ŽŽ– +]µ;‘ª¨¬&Ž‘ qƱptsŽ˜¬[11ŽŽ“]µ;‘ª¨¬&Ž‘ qƱptsŽ˜¬[7Ž‘]µ;‘ª¨¬0Ž‘ª©);Ž¡‘µpŽ‘¬[0Ž‘]µ:±dr‘ÿ}'awŽ‘(Û¬(‘ª¨);Ž¡‘±ptsŽ‘!Ú¨¬[12ŽŽ‘ +]–Ç=“±ptsŽ‘¡¾¬[6Ž–]µ:±me‘ÿ}'diateŽ‘"½u¬(±ptsŽ‘ Ú¦¬[7Ž“]);Ž¡‘±ptsŽ‘!Ú¨¬[13ŽŽ› +]–Ç=“±ptsŽ‘¡¾¬[10ŽŽ˜]µ:±me‘ÿ}'diateŽ‘"½u¬(±ptsŽ‘ Ú¦¬[11ŽŽ˜]);Ž¡#­ifŽ‘ ´ø¬0ŽŽ¡‘±ptsŽ‘!Ú¨¬[12ŽŽ– +]µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(12ŽŽ“);Ž¡‘±ptsŽ‘!Ú¨¬[13ŽŽ– +]µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(13ŽŽ“);Ž¡#­endifŽŽ¡‘µpŽ‘¬[1Ž‘]µ:±setŽ‘ x„¬(±ptsŽ‘ Ú¦¬[12ŽŽ– +]µ;‘ª¨±ptsŽ‘…N¬[13ŽŽ“]);Ž¡#­ifŽ‘ ´ø¬0ŽŽ¡‘µpŽ‘¬[1Ž–]µ:±dr‘ÿ}'aw‘‰ffŽ‘®helpŽ‘*Ũ¬(°Ž“­ColorsŽ‘&Ø߬::Ž‘-g±help‘‰ffŽ‘®c‘ÿ}'olorŽ‘Y!‘µ;‘ª¨´""Ž‘ ± +¬);Ž¡#­endifŽŽ¡‘±ptsŽ‘!Ú¨¬[14ŽŽ› +]–Ç=“±ptsŽ‘¡¾¬[12ŽŽ˜]µ:±me‘ÿ}'diateŽ‘"½u¬(±ptsŽ‘ Ú¦¬[13ŽŽ˜]);Ž¡#­ifŽ‘ ´ø¬0ŽŽ¡‘±ptsŽ‘!Ú¨¬[14ŽŽ– +]µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(14ŽŽ“);ŽŽŽŒ‹Àæþ Šn ý‘ì¬448–¯DRA‘ÿ8W‘ÕXNET’%LÓ3DLDF-1.1.5.1“°x¬1492Ž €n ý•@P#­endifŽŽ¤ ‘±ptsŽ‘!Ú¨¬[15ŽŽ‘ +]–Ç=“±ptsŽ‘¡¾¬[6Ž–]µ:±me‘ÿ}'diateŽ‘"½u¬(±ptsŽ‘ Ú¦¬[7Ž“]µ;‘ª¨:¬25ŽŽ‘qÇ);Ž¡#­ifŽ‘ ´ø¬0ŽŽ¡‘±ptsŽ‘!Ú¨¬[15ŽŽ– +]µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(15ŽŽ“);Ž¡#­endifŽŽ¡‘±ptsŽ‘!Ú¨¬[16ŽŽ› +]–Ç=“±ptsŽ‘¡¾¬[14ŽŽ˜];Ž¡‘±ptsŽ‘!Ú¨¬[16ŽŽ– +]µ:±shiftŽ‘}¬(±ptsŽ‘ Ú¦¬[15ŽŽ“]–8à°“±ptsŽ‘†¬[12ŽŽ‘ +]);Ž¡#­ifŽ‘ ´ø¬0ŽŽ¡‘±ptsŽ‘!Ú¨¬[16ŽŽ– +]µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(16ŽŽ“);Ž¡#­endifŽŽ¤‘b•QÇo“olu½‰™šs4Ž‘Ôwp“oin®9tŽ‘L§±bpŽ‘ZI.¬=‘Ç­P•®9oin“tŽ‘ad¬::Ž‘%interse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘s†x¬(±ptsŽ‘ Ú¦¬[14ŽŽ– +]µ;‘ª¨±ptsŽ›…N¬[16ŽŽ“]µ;‘ª¨±ptsŽ˜¬[6Ž‘]µ;‘ª¨±ptsŽ˜¬[10ŽŽ“]);Ž¡‘±ptsŽ‘!Ú¨¬[17ŽŽ‘ +]–Ç=“±bpŽ‘ ¡‘µ:±ptŽ‘ ä¬;Ž¤ #­ifŽ‘ ´ø¬0ŽŽ¡‘±ptsŽ‘!Ú¨¬[17ŽŽ– +]µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(17ŽŽ“);Ž¡#­endifŽŽ¡‘±bpŽ‘!¡“¬=‘Ç­P•®9oin“tŽ‘ad¬::Ž‘%interse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘s†x¬(±ptsŽ‘ Ú¦¬[14ŽŽ– +]µ;‘ª¨±ptsŽ›…N¬[16ŽŽ“]µ;‘ª¨±ptsŽ˜¬[7Ž‘]µ;‘ª¨±ptsŽ˜¬[11ŽŽ“]);Ž¡‘±ptsŽ‘!Ú¨¬[18ŽŽ‘ +]–Ç=“±bpŽ‘ ¡‘µ:±ptŽ‘ ä¬;Ž¡#­ifŽ‘ ´ø¬0ŽŽ¡‘±ptsŽ‘!Ú¨¬[18ŽŽ– +]µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(18ŽŽ“);Ž¡#­endifŽŽ¡‘µpŽ‘¬[2Ž‘]µ:±setŽ‘ x„¬(±ptsŽ‘ Ú¦¬[17ŽŽ– +]µ;‘ª¨±ptsŽ‘…N¬[18ŽŽ“]);Ž¡#­ifŽ‘ ´ø¬0ŽŽ¡‘µpŽ‘¬[2Ž–]µ:±dr‘ÿ}'aw‘‰ffŽ‘®helpŽ‘*Ũ¬(°Ž“­ColorsŽ‘&Ø߬::Ž‘-g±help‘‰ffŽ‘®c‘ÿ}'olorŽ‘Y!‘µ;‘ª¨´""Ž‘ ± +¬);Ž¡#­endifŽŽ¡‘forŽ‘%般(µiŽ‘9 ¬=‘Ç1Ž‘Ç;‘ÿýµiŽ‘ 9 <‘Ǭ16ŽŽ‘ Ç;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘°fŽ¡‘±ptsŽ‘+Ú©¬[19ŽŽ› +]–Ç=“±ptsŽ‘¡¾¬[17ŽŽ˜]µ:±me‘ÿ}'diateŽ‘"½u¬(±ptsŽ‘ Ú¦¬[18ŽŽ˜]µ;‘ª¨iŽ‘œ=¬16µ:¬0ŽŽ‘Ç );Ž¡‘±ptsŽ‘+Ú©¬[19ŽŽ‘ +]µ:±dr‘ÿ}'awdotŽ‘#“¬(°Ž‘­ColorsŽ‘&Ø߬::Ž‘-g±default‘‰ffŽ‘®c‘ÿ}'olorŽ‘dâøµ;‘ª¨´"pencircle® ´scaled® ´.5Ž‘jªlmm"Ž‘zðˬ);Ž¡‘°gŽ¡‘±ptsŽ‘!Ú¨¬[20ŽŽ› +]–Ç=“±ptsŽ‘¡¾¬[17ŽŽ˜];Ž¡‘±ptsŽ‘!Ú¨¬[21ŽŽ› +]–Ç=“±ptsŽ‘¡¾¬[18ŽŽ˜];Ž¡‘µpŽ‘¬[3Ž›]–Ç=“µpŽ‘Ϭ[0Ž˜];Ž¤‘­T‘ÿ +«ransformŽ‘KÈÔµtŽ‘OeF¬;Ž¡‘µtŽ‘œt:±shiftŽ‘}¬(±ptsŽ‘ Ú¦¬[4Ž›]–8à°“±ptsŽ‘†¬[5Ž˜]);Ž¤ ‘µtŽ‘œt:±r‘ÿ}'otateŽ‘o>¬(±ptsŽ‘ Ú¦¬[4Ž–]µ;‘ª¨±ptsŽ‘…N¬[5Ž“]);Ž¡‘±ptsŽ‘!Ú¨¬[20ŽŽ– +]‘Ç°¬=ŽŽ‘UO±ptsŽ‘ /õ¬[21ŽŽ“]‘Ç°¬=ŽŽ‘UOµpŽ‘]O¬[3Ž‘]‘Ç°¬=ŽŽ‘UOµtŽ‘ñÁ¬;Ž¡‘µpŽ‘¬[3Ž‘]µ:±dr‘ÿ}'awŽ‘(Û¬(‘ª¨);Ž¡‘­forŽ‘%般(µiŽ‘9 ¬=‘Ç1Ž‘Ç;‘ÿýµiŽ‘ 9 <‘Ǭ16ŽŽ‘ Ç;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘°fŽ¡‘±ptsŽ‘+Ú©¬[19ŽŽ› +]–Ç=“±ptsŽ‘¡¾¬[20ŽŽ˜]µ:±me‘ÿ}'diateŽ‘"½u¬(±ptsŽ‘ Ú¦¬[21ŽŽ˜]µ;‘ª¨iŽ‘œ=¬16µ:¬0ŽŽ‘Ç );Ž¡‘±ptsŽ‘+Ú©¬[19ŽŽ‘ 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<‘Ǭ16ŽŽ‘ Ç;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘°fŽ¡‘±ptsŽ‘+Ú©¬[19ŽŽ› +]–Ç=“±ptsŽ‘¡¾¬[20ŽŽ˜]µ:±me‘ÿ}'diateŽ‘"½u¬(±ptsŽ‘ Ú¦¬[21ŽŽ˜]µ;‘ª¨iŽ‘œ=¬16µ:¬0ŽŽ‘Ç );Ž¡‘±ptsŽ‘+Ú©¬[19ŽŽ‘ +]µ:±dr‘ÿ}'awdotŽ‘#“¬(°Ž‘­ColorsŽ‘&Ø߬::Ž‘-g±default‘‰ffŽ‘®c‘ÿ}'olorŽ‘dâøµ;‘ª¨´"pencircle® ´scaled® ´.5Ž‘jªlmm"Ž‘zðˬ);Ž¡‘°gŽ¡‘µtŽ‘œt:±r‘ÿ}'esetŽ‘Æ·¬(‘ª¨);Ž¡‘±ptsŽ‘!Ú¨¬[22ŽŽ‘ +]–Ç=“µvŽ‘ûÕ¬[2Ž‘]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘0=H¬(‘ª¨);Ž¡‘±ptsŽ‘!Ú¨¬[23ŽŽ› +]–Ç=“±ptsŽ‘¡¾¬[22ŽŽ˜];Ž¡‘±ptsŽ‘!Ú¨¬[23ŽŽ‘ +]µ:±shiftŽ‘}¬(0Ž‘µ;‘ª¨¬0Ž–ª©µ;‘ª¨¬1Ž“);Ž¡‘µtŽ‘œt:±r‘ÿ}'otateŽ‘o>¬(±ptsŽ‘ Ú¦¬[22ŽŽ– +]µ;‘ª¨±ptsŽ‘…N¬[23ŽŽ“]µ;‘ª¨¬120ŽŽ‘ª«);Ž¡‘±ptsŽ‘!Ú¨¬[20ŽŽ› +]–Ç=“±ptsŽ‘¡¾¬[17ŽŽ˜];Ž¡‘±ptsŽ‘!Ú¨¬[21ŽŽ› +]–Ç=“±ptsŽ‘¡¾¬[18ŽŽ˜];Ž¡‘µpŽ‘¬[3Ž›]–Ç=“µpŽ‘Ϭ[0Ž˜];Ž¡‘±ptsŽ‘!Ú¨¬[20ŽŽ– +]‘Ç°¬=ŽŽ‘UO±ptsŽ‘ /õ¬[21ŽŽ“]‘Ç°¬=ŽŽ‘UOµpŽ‘]O¬[3Ž‘]‘Ç°¬=ŽŽ‘UOµtŽ‘ñÁ¬;Ž¡‘µpŽ‘¬[3Ž‘]µ:±dr‘ÿ}'awŽ‘(Û¬(‘ª¨);Ž¡‘­forŽ‘%般(µiŽ‘9 ¬=‘Ç1Ž‘Ç;‘ÿýµiŽ‘ 9 <‘Ǭ16ŽŽ‘ Ç;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘°fŽ¡‘±ptsŽ‘+Ú©¬[19ŽŽ› +]–Ç=“±ptsŽ‘¡¾¬[20ŽŽ˜]µ:±me‘ÿ}'diateŽ‘"½u¬(±ptsŽ‘ Ú¦¬[21ŽŽ˜]µ;‘ª¨iŽ‘œ=¬16µ:¬0ŽŽ‘Ç );Ž¡‘±ptsŽ‘+Ú©¬[19ŽŽ‘ +]µ:±dr‘ÿ}'awdotŽ‘#“¬(°Ž‘­ColorsŽ‘&Ø߬::Ž‘-g±default‘‰ffŽ‘®c‘ÿ}'olorŽ‘dâøµ;‘ª¨´"pencircle® ´scaled® ´.5Ž‘jªlmm"Ž‘zðˬ);Ž¡‘°gŽ¡‘µtŽ‘œt:±r‘ÿ}'otateŽ‘o>¬(±ptsŽ‘ Ú¦¬[4Ž–]µ;‘ª¨±ptsŽ‘…N¬[1Ž“]);Ž¡‘µtŽ‘œt:±r‘ÿ}'otateŽ‘o>¬(±ptsŽ‘ Ú¦¬[0Ž–]µ;‘ª¨±ptsŽ‘…N¬[2Ž“]);Ž¡‘±ptsŽ‘!Ú¨¬[20ŽŽ› +]–Ç=“±ptsŽ‘¡¾¬[17ŽŽ˜];Ž¡‘±ptsŽ‘!Ú¨¬[21ŽŽ› +]–Ç=“±ptsŽ‘¡¾¬[18ŽŽ˜];Ž¡‘µpŽ‘¬[3Ž›]–Ç=“µpŽ‘Ϭ[0Ž˜];Ž¡‘±ptsŽ‘!Ú¨¬[20ŽŽ– +]‘Ç°¬=ŽŽ‘UO±ptsŽ‘ /õ¬[21ŽŽ“]‘Ç°¬=ŽŽ‘UOµpŽ‘]O¬[3Ž‘]‘Ç°¬=ŽŽ‘UOµtŽ‘ñÁ¬;Ž¡‘µpŽ‘¬[3Ž‘]µ:±dr‘ÿ}'awŽ‘(Û¬(‘ª¨);Ž¡‘­forŽ‘%般(µiŽ‘9 ¬=‘Ç1Ž‘Ç;‘ÿýµiŽ‘ 9 <‘Ǭ16ŽŽ‘ Ç;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘°fŽ¡‘±ptsŽ‘+Ú©¬[19ŽŽ› +]–Ç=“±ptsŽ‘¡¾¬[20ŽŽ˜]µ:±me‘ÿ}'diateŽ‘"½u¬(±ptsŽ‘ Ú¦¬[21ŽŽ˜]µ;‘ª¨iŽ‘œ=¬16µ:¬0ŽŽ‘Ç );Ž¡‘±ptsŽ‘+Ú©¬[19ŽŽ‘ +]µ:±dr‘ÿ}'awdotŽ‘#“¬(°Ž‘­ColorsŽ‘&Ø߬::Ž‘-g±default‘‰ffŽ‘®c‘ÿ}'olorŽ‘dâøµ;‘ª¨´"pencircle® ´scaled® ´.5Ž‘jªlmm"Ž‘zðˬ);Ž¡‘°gŽ¡‘ +gŽ¤­1493.‘ üDoQÇdecahedron.Ž¡1494.‘ üDoQÇdecahedron–ÕTclass“de nition.Ž¤‘ +formatŽ‘3c(±Do–ÿ}'de“c“ahe“dr“onŽ‘xLhPolyhe–ÿ}'dr“onŽŽ¡°h–ª¨¬De ne‘UU­classŽ‘5¦DoQÇdecahedronŽ‘k58¯1494“°i‘ÇŽ¤ ‘ +­classŽ‘$àRDoQÇdecahedronŽ‘põ5¬:‘qÇ­publicŽ‘'ñP®9olyhedronŽ‘dh°fŽ¡‘ +­protectedŽ‘:o™¬:‘­staticŽ‘$HÙconstŽ‘Bs{realŽ‘Y&©±dihe–ÿ}'dr“al‘‰ffŽ‘®angleŽ’–qq¬;‘µ=°‘ÿý¬In‘UUradians!‘o°µ=Ž¡‘­realŽ‘*³0±p–ÿ}'entagon‘‰ffŽ‘®r“adiusŽ‘pÀ¬;Ž©‘ +­publicŽ‘)=Ö¬:‘°h–ª¨¬Declare‘UU­DoQÇdecahedronŽ‘Oj8¬functions‘@¯1497“°iŽ¡‘ +g¬;ŽŸ ¯This–ÕXcoÝÑDoQÇdecahedronŽ’ˆc¬::‘±dihe–ÿ}'dr“al‘‰ffŽ‘®angleŽ‘Aä¬=‘Ç´PIŽ‘Z°‘8à±atanŽ‘ªÀ¬(2µ:¬0ŽŽ‘ Ç);ŽŸ ¯This–ÕXcoK&¬.‘o°µ=Ž¦‘±vertic‘ÿ}'esŽ‘8±X¬=‘Ç20ŽŽ‘ Ç;Ž¦‘±e‘ÿ}'dgesŽ‘.™1¬=‘Ç30ŽŽ‘ Ç;Ž¦‘±c‘ÿ}'enterŽ‘2Ð¥¬=‘Ç´INVALID_POINTŽ‘GY¬;‘µ=°‘ÿý¬from‘UU­P®9olyhedronŽ‘=c"¬.‘o°µ=Ž¦‘±numb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜olygon‘‰ffŽ“typ˜esŽ’R9¬=‘Ç1Ž‘Ç;Ž¦‘±fac–ÿ}'e‘‰ffŽ‘®r“adiusŽ‘G%¬=‘DZe–ÿ}'dge‘‰ffŽ‘®r“adiusŽ‘7j¬=‘DZvertex‘‰ffŽ‘®r‘ÿ}'adiusŽ‘>þ¨¬=‘Ç´INVALID_REALŽ‘BM\¬;Ž¦‘±p–ÿ}'entagon‘‰ffŽ‘®r“adiusŽ‘\Ô¬=‘Ç´INVALID_REALŽ‘BM\¬;‘µ=°‘ÿý¬F‘ÿ*ªrom‘UU­DoQÇdecahedronŽ‘Lã¬.‘o°µ=Ž¦‘ +°gŽ¡¯See–ÕXalso“sections“1501,“1502,“1504,“and“1506.Ž¡This–ÕXcoK&¬.‘o°µ=Ž¡‘±vertic‘ÿ}'esŽ‘B±Y¬=‘Ç20ŽŽ‘ Ç;Ž¡‘±e‘ÿ}'dgesŽ‘8™2¬=‘Ç30ŽŽ‘ Ç;Ž¡‘±numb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜olygon‘‰ffŽ“typ˜esŽ’‹R:¬=‘Ç1Ž‘Ç;Ž¡#­ifŽ‘ ´ø¬0Ž‘$´úµ=°‘ÿý¬ST–ÿ*ªAR“T–UUHERE.“TO“DO:“Must“calculate“these!‘o°µ=Ž¡‘±fac–ÿ}'e‘‰ffŽ‘®r“adiusŽ‘Q&¬=‘Ç0Ž‘Ç;Ž¡‘±e–ÿ}'dge‘‰ffŽ‘®r“adiusŽ‘R£­¬=‘Ç0Ž‘Ç;Ž¡‘±vertex‘‰ffŽ‘®r‘ÿ}'adiusŽ‘Z7“¬=‘Ç0Ž‘Ç;Ž¡#­endifŽŽ¡‘±p–ÿ}'entagon‘‰ffŽ‘®r“adiusŽ‘fÔ¬=‘DZp‘ÿ}'entagon‘‰ffŽ‘®diameterŽ‘TÖе=¬2µ:¬0ŽŽ‘ Ç;Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘Vºk¬=‘DZget‘‰ffŽ‘®netŽ‘!ûà¬(±p‘ÿ}'entagon‘‰ffŽ‘®diameterŽ‘R¸µ;‘ª¨±trueŽ‘o@¬);Ž¦‘­P•®9oin“tŽ‘<ï ±ptsŽ‘JÊF¬[8Ž‘];Ž¡‘­in®9tŽ‘/¤úµiŽ‘5Þ¬=‘Ç0Ž‘Ç;Ž¦‘­forŽ‘/艬(µiŽ‘9 ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ5Ž“;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘°fŽ¡‘(±ptsŽ‘5Úª¬[µiŽ›qô¬]–Ç=“±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh¬[0Ž‘]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(µiŽ˜¬);Ž¡‘°gŽ¦‘­realŽ‘4³1±angleŽ‘O:œ¬=‘Ç180ŽŽ‘ÿû°–8à¬(±dihe–ÿ}'dr“al‘‰ffŽ‘®angleŽ‘?ƒ¨°“¬180µ:¬0ŽŽ‘µ=´PIŽ‘ b¬);ŽŽŽŒ‹Ä#J Šn ý‘ì¬452–¯CONSTRÃŽUCTOR’Îã3DLDF-1.1.5.1“°x¬1502Ž €n ý•@P­1502.‘ ü¬[²LDF‘T2003.08.10.¬]Ž‘Zˆ6Checš¸ãk–UUthis,“as“noted“abGo˜v˜e.Ž©°h–ª¨¬De ne‘UU­DoQÇdecahedronŽ‘Oj8¬functions‘@¯1498“°i‘Ǭ+°Ž¤ ‘ +±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQ¬[1Ž–]‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(±ptsŽ‘ Ú¦¬[0Ž“]µ;‘ª¨±ptsŽ‘…N¬[1Ž“]µ;‘ª¨±angleŽ‘jû¬);Ž¡‘ +±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQ¬[2Ž–]‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(±ptsŽ‘ Ú¦¬[4Ž“]µ;‘ª¨±ptsŽ‘…N¬[0Ž“]µ;‘ª¨±angleŽ‘jû¬);Ž¡‘ +±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQ¬[3Ž–]‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(±ptsŽ‘ Ú¦¬[3Ž“]µ;‘ª¨±ptsŽ‘…N¬[4Ž“]µ;‘ª¨±angleŽ‘jû¬);Ž¡‘ +±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQ¬[4Ž–]‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(±ptsŽ‘ Ú¦¬[3Ž“]µ;‘ª¨±ptsŽ‘…N¬[2Ž“]µ;‘ª¨±angleŽ‘jû¬);Ž¡‘ +±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQ¬[5Ž–]‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(±ptsŽ‘ Ú¦¬[1Ž“]µ;‘ª¨±ptsŽ‘…N¬[2Ž“]µ;‘ª¨±angleŽ‘jû¬);Ž¡#­ifŽ‘ ´ø¬0ŽŽ¦‘ +­usingŽ‘(S‡namespaceŽ‘a÷ColorsŽ’‚ÏÛ¬;Ž¡‘ +­v®9ectorŽ‘)ªI°h­constŽ‘*¢ColorŽ‘=Ï•°Ž‘BÏ–i‘UU±c–ÿ}'ol‘‰ffŽ‘®ve“cŽ‘!"J¬;Ž¦‘ +±c–ÿ}'ol‘‰ffŽ‘®ve“cŽ‘'Ìöµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(&Ž‘DZblackŽ‘Ôò¬);Ž¡‘ +±c–ÿ}'ol‘‰ffŽ‘®ve“cŽ‘'Ìöµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(&Ž‘DZr–ÿ}'e“dŽ‘:K¬);Ž¡‘ +±c–ÿ}'ol‘‰ffŽ‘®ve“cŽ‘'Ìöµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(&Ž‘DZgr–ÿ}'e“enŽ‘¬+¬);Ž¡‘ +±c–ÿ}'ol‘‰ffŽ‘®ve“cŽ‘'Ìöµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(&Ž‘DZblueŽ‘)•¬);Ž¡‘ +±c–ÿ}'ol‘‰ffŽ‘®ve“cŽ‘'Ìöµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(&Ž‘DZcyanŽ‘>­¬);Ž¡‘ +±c–ÿ}'ol‘‰ffŽ‘®ve“cŽ‘'Ìöµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(&Ž‘DZmagentaŽ‘-™¬¬);Ž¡‘ +±c–ÿ}'ol‘‰ffŽ‘®ve“cŽ‘'Ìöµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬(&Ž‘DZor‘ÿ}'angeŽ‘%ÊE¬);Ž¡#­endifŽŽ¡‘ +ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘µiŽ‘9¬=‘Ç0Ž‘Ç;Ž¡‘­forŽ‘&Qˬ(­v®9ectorŽ‘ªH°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘E=L°Ž‘J=Mi‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=Ú¼¬=‘v‡±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ–9i×µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘i@±iterŽ‘ªÅ°6¬=‘v‡±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ“µ:±endŽ‘ಬ(˜);Ž¡‘(€Ÿÿ³+‘ÿ+ŽŽ‘4G$±iterŽ‘E"¬)‘°fŽ¡¬#­ifŽ‘ ´ø¬0ŽŽ¡‘(°Ž‘Ž‘ 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+­forŽ‘臬(µiŽ‘9 ¬=‘Ç6Ž‘Ç;‘ÿýµiŽ‘ 9 <‘Ǭ12ŽŽ‘ Ç;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:óP¬[µiŽ‘qô¬]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[7Ž‘]);Ž¡#­ifŽ‘ ´ø¬0ŽŽ¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘­forŽ‘%般(µiŽ‘9 ¬=‘Ç6Ž‘Ç;‘ÿýµiŽ‘ 9 <‘Ǭ12ŽŽ‘ Ç;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:óP¬[µiŽ‘qô¬]‘þŸµ~ŽŽ‘±dr‘ÿ}'awŽ‘(ܬ(°Ž‘¬(±c–ÿ}'ol‘‰ffŽ‘®ve“cŽ‘Ìõ¬[µiŽ‘ªÔ°‘8à¬6Ž‘8á]));Ž¡‘ +°gŽ¡¬#­endifŽŽ¦‘ +P•®9oin“tŽ‘(ïž±c‘ÿ}'enter‘‰ffŽ‘®0Ž‘PÒ=¬=‘DZr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh¬[0Ž‘]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘0=H¬(‘ª¨);Ž¡‘ +­P•®9oin“tŽ‘(ïž±c‘ÿ}'enter‘‰ffŽ‘®6Ž‘PÒ=¬=‘DZr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh¬[6Ž‘]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘0=H¬(‘ª¨);Ž¦‘ +±c‘ÿ}'enterŽ‘(Ф¬=‘DZc‘ÿ}'enter‘‰ffŽ‘®0Ž‘'⟵:±me‘ÿ}'diateŽ‘"½u¬(±c‘ÿ}'enter‘‰ffŽ‘®6Ž‘%‡¬);Ž¦‘ +­T‘ÿ +«ransformŽ‘AÈÓµtŽ‘H,]¬=‘DZc‘ÿ}'enterŽ‘Уµ:±shiftŽ‘}¬(°Ž‘DZc‘ÿ}'enterŽ‘#Щ¬);Ž¦‘ +­ifŽ‘´ù¬(±angle‘‰ffŽ‘®xŽ‘#Lô°6¬=‘Ç0Ž– ÿù°_‘8à±angle‘‰ffŽ‘®yŽ‘%kƒ°6¬=‘Ç0Ž“°_‘8à±angle‘‰ffŽ‘®zŽ‘$ÿn°6¬=‘Ç0Ž‘Ç)‘µtŽ‘œr:±r‘ÿ}'otateŽ‘o>¬(±angle‘‰ffŽ‘®xŽ‘ …ܵ;‘ª¨±angle‘‰ffŽ‘®yŽ‘"3µ;‘ª¨±angle‘‰ffŽ‘®zŽ‘!ª¬);Ž¡‘ +­ifŽ‘´ù¬(µpŽ‘Ï°6¬=‘DZoriginŽ‘½9¬)‘±c‘ÿ}'enterŽ‘#У°¬=ŽŽ‘3^ÚµtŽ‘6ûL:±shiftŽ‘}¬(µpŽ‘¬);ŽŽŽŒ‹Å,< Šn ý‘ì°x¬1502–¯3DLDF-1.1.5.1’ÎãCONSTRÃŽUCTOR“¬453Ž €n ý•@P‘ +­forŽ‘臬(­v®9ectorŽ‘ªH°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘DÔ °Ž‘IÔ +i‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘DZr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ–8ºhµ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘DZr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ“µ:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)Ž¤ ‘(°Ž‘Ž‘ +±iterŽ‘ˬ)‘Ç°¬=ŽŽ‘UOµtŽ‘ñÁ¬;Ž¡‘ +­ifŽ‘´ù¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Exiting® ´DodecahedroŽ‘kÆÜn::Dodecahedron().\nŽ’ÔÆ "Ž’ÝT°‘DZ ushŽ‘€¬;Ž¡‘ +­returnŽ‘*‘f¬;‘qÇ°gŽŸ­1503.– üGet‘íunet.“¬[²LDF‘T2002.09.29.¬]Ž‘Y¾•Changed–‹´this“function.‘.’TO‘‹DO.“I'vš¸ãe“remo˜v˜ed“±r‘ÿ}'otateŽ‘úò¬(‘ª®)“and“no˜w“rotateŽ¡the–èpGenš¸ãtagons“in“the“x-z“plane“only“in“order“to“a˜v˜oid“ha˜ving“the“y-cošGordinates“b˜e“o 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+i‘UU±get‘‰ffŽ‘®netŽ‘"Š¬(­constŽ‘*¢realŽ‘4Ýбp‘ÿ}'entagon‘‰ffŽ‘®diameterŽ’†íˆµ;‘ª¨­b•QÇo“olŽ‘L±do‘‰ffŽ‘®halfŽ‘>s¯¬=‘DZfalseŽ‘v\¬);ŽŽŽŒ‹ÆAk Šn ý‘ì¬454–¯GET‘ÕXNET’-š¹3DLDF-1.1.5.1“°x¬1504Ž €n ý•@P­1504.Ž©°h–ª¨¬De ne‘UU­DoQÇdecahedronŽ‘Oj8¬functions‘@¯1498“°i‘Ǭ+°Ž¤ ‘ +­v®9ectorŽ‘)ªI°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘DxŒ°Ž‘Ixi‘ùØ­DoQÇdecahedronŽ‘L¹j¬::‘±get‘‰ffŽ‘®netŽ‘ 4̬(­constŽ‘Ï%realŽ‘4&Ö±p‘ÿ}'entagon‘‰ffŽ‘®diameterŽ’†6Žµ;‘ª¨­b•QÇo“olŽ‘ð‘±do‘‰ffŽ‘®halfŽ‘;Q¬)°f‘ùØ­in®9tŽ‘CRµiŽ‘µF¬;Ž¡‘­v®9ectorŽ‘=ªK°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘Euk°Ž‘Juli‘ö·±p‘ÿ}'entsŽ›‡c¬;‘Uî­forŽ‘ßÖ¬(µiŽ‘F¬=‘Ô0Ž–Ô;‘¡_µiŽ‘ çc<‘Ô¬6Ž“;‘!_Ÿÿ³+‘ÿ+ŽŽ‘èµiŽ‘Zs¬)‘ö·±p‘ÿ}'entsŽ˜µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘/O ¬(‘ö·±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘7}2µ<Ž¡‘2­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘vEѵ>‘Ǭ(0Ž‘)–UU)“;Ž¡‘±p‘ÿ}'entsŽ‘5¯¬[0Ž‘]‘þŸµ~ŽŽ‘±setŽ‘x…¬(±originŽ‘ö!µ;‘ª¨¬5Ž–ª©µ;‘ª¨±p‘ÿ}'entagon‘‰ffŽ‘®diameterŽ‘Sº`µ;‘ª¨¬0Ž“µ;‘ª¨¬180ŽŽ‘ª«);‘µ=°‘ÿý¬The–UUmiddle“pGen¸ãtagon.‘o°µ=Ž¦‘­P•®9oin“tŽ‘<ï ±ptsŽ‘JÊF¬[10ŽŽ‘ +];Ž¦‘­forŽ‘/艬(µiŽ‘9 ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ5Ž“;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)‘°fŽ¡‘(±ptsŽ‘5Úª¬[µiŽ›qô¬]–Ç=“±p‘ÿ}'entsŽ‘WĬ[0Ž‘]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(µiŽ˜¬);Ž¡‘°gŽ¡‘Ž‘#±p‘ÿ}'entsŽ‘:°¬[1Ž›]–Ç=“°Ž‘DZp‘ÿ}'entsŽ‘WŬ[0Ž˜];Ž¡‘±p‘ÿ}'entsŽ‘5¯¬[1Ž–]‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(0Ž“µ;‘ª¨¬36ŽŽ‘ ªª);Ž¡‘°Ž‘#±p‘ÿ}'entsŽ‘:°¬[5Ž›]–Ç=“°Ž‘DZp‘ÿ}'entsŽ‘WŬ[4Ž˜]“=“°Ž‘DZp‘ÿ}'entsŽ‘WŬ[3Ž˜]“=“°Ž‘DZp‘ÿ}'entsŽ‘WŬ[2Ž˜]“=“°Ž‘DZp‘ÿ}'entsŽ‘WŬ[1Ž˜];Ž¡‘­forŽ‘/艬(µiŽ‘9 ¬=‘Ç5Ž‘Ç;‘ÿýµiŽ‘ 9 <‘Ǭ10ŽŽ‘ Ç;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)‘±ptsŽ‘Ú¦¬[µiŽ‘qô¬]–Ç=“±p‘ÿ}'entsŽ‘WĬ[1Ž‘]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(µiŽ‘ªÔ°‘8à¬5Ž‘8á);Ž¡‘±p‘ÿ}'entsŽ‘5¯¬[1Ž–]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[0Ž“]–8à°“±ptsŽ‘†¬[8Ž‘]);Ž¡‘±p‘ÿ}'entsŽ‘5¯¬[2Ž–]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[0Ž“]–8à°“±ptsŽ‘†¬[6Ž‘]);Ž¡‘±p‘ÿ}'entsŽ‘5¯¬[3Ž–]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[4Ž“]–8à°“±ptsŽ‘†¬[5Ž‘]);Ž¡‘±p‘ÿ}'entsŽ‘5¯¬[4Ž–]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[3Ž“]–8à°“±ptsŽ‘†¬[9Ž‘]);Ž¡‘±p‘ÿ}'entsŽ‘5¯¬[5Ž–]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[1Ž“]–8à°“±ptsŽ‘†¬[9Ž‘]);Ž¡‘­ifŽ‘)´û¬(±do‘‰ffŽ‘®halfŽ‘#'¡°‘DZtrueŽ‘‹°¬)Ž¡‘(µ=°‘*¬[²LDF‘T2002.09.29.¬]Ž‘T‘W‘ÿ*ªe–U‚only“need“half“of“the“net,‘UŽif“wš¸ãe're“using“it“to“mak˜e“a“pGolyhedron.‘rOIn“thatŽ¡‘2case,‘Szw•¸ãe›Scop“y˜and˜transform˜the˜half˜w“e'v“e˜already˜got˜and˜the˜cop“y˜on˜top˜of˜the˜ rst˜half.‘©°µ=Ž¡‘°fŽ¡‘(­forŽ‘9芬(µiŽ‘9 ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ6Ž“;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘°fŽ¡‘2­forŽ‘C苬(­in®9tŽ‘¤÷µjŽ‘Ó¬=‘Ç0Ž–Ç;‘ÿýµjŽ‘ wÙ<‘Ǭ5Ž“;‘ÿýµjŽ‘ +0ÁŸÿ³+‘ÿ+ŽŽ‘÷á¬)Ž¡‘<­ifŽ‘G´þ¬(±p‘ÿ}'entsŽ‘¬¬[µiŽ‘qô¬]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(µjŽ‘°Ä¬)µ:±get‘‰ffŽ‘®yŽ‘t¬(‘ª¨)–Ç°6¬=“0Ž‘Ç)‘°fŽ¡‘F±c‘ÿ}'errŽ‘\’°‘Jå´"ERROR!® ´In® ´DodecahedŽ‘lJ©ron::get_net():\n"Ž’ΛÀ°‘Jå´"y-coordinate® ´!=® ´0!\Ž‘lJ©n"Ž‘z›ð°Ž¡‘Z ´"You'd® ´better® ´fix® ´thŽ’ÂÿÍis!\n\n"Ž’ðM5°‘DZ ushŽ‘€¬;Ž¡‘<°gŽ¡‘(gŽ¡‘(­returnŽ‘Kæ¾±p‘ÿ}'entsŽ‘cwj¬;Ž¡‘°gŽ¡‘­forŽ‘/艬(µiŽ‘9 ¬=‘Ç6Ž‘Ç;‘ÿýµiŽ‘ 9 <‘Ǭ12ŽŽ‘ Ç;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)–UU°f“±p‘ÿ}'entsŽ‘æµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(“±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<“­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘G›!µ>‘Ǭ(0Ž‘)“)“;Ž¡‘°Ž‘#±p‘ÿ}'entsŽ‘:°¬[µiŽ‘qô¬]–Ç=“°Ž‘DZp‘ÿ}'entsŽ‘WŬ[µiŽ‘ªÔ°‘8à¬6Ž‘8á];Ž¡‘±p‘ÿ}'entsŽ‘5¯¬[µiŽ‘qô¬]‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(0Ž›µ;‘ª¨¬180ŽŽ‘ª«);–UU°g“±ptsŽ‘/û¬[0Ž˜]–Ç=“±p‘ÿ}'entsŽ‘WĬ[11ŽŽ‘ +]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(0Ž˜);Ž¡‘±ptsŽ‘+Ú©¬[1Ž›]–Ç=“±p‘ÿ}'entsŽ‘WĬ[5Ž˜]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(1Ž˜);Ž¡‘­forŽ‘/艬(µiŽ‘9 ¬=‘Ç6Ž‘Ç;‘ÿýµiŽ‘ 9 <‘Ǭ12ŽŽ‘ Ç;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘±p‘ÿ}'entsŽ‘¬¬[µiŽ‘qô¬]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[1Ž›]–8à°“±ptsŽ‘†¬[0Ž˜]);Ž¡‘­forŽ‘/艬(µiŽ‘9 ¬=‘Ç0Ž‘Ç;‘ÿýµiŽ‘ 9 <‘Ǭ12ŽŽ‘ Ç;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘°fŽ¡‘(­forŽ‘9芬(­in®9tŽ‘¤÷µjŽ‘Ó¬=‘Ç0Ž–Ç;‘ÿýµjŽ‘ wÙ<‘Ǭ5Ž“;‘ÿýµjŽ‘ +0ÁŸÿ³+‘ÿ+ŽŽ‘÷á¬)Ž¡‘2­ifŽ‘=´ý¬(±p‘ÿ}'entsŽ‘¬¬[µiŽ‘qô¬]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(µjŽ‘°Ä¬)µ:±get‘‰ffŽ‘®yŽ‘t¬(‘ª¨)–Ç°6¬=“0Ž‘Ç)‘°fŽ¡‘<±c‘ÿ}'errŽ‘R?°‘‰U´"ERROR!® ´In® ´DodecahedŽ‘l‰ron::get_net():\n"Ž’Ï °‘‰U´"y-coordinate® ´!=® ´0!\Ž‘l‰n"Ž‘{аŽ¡‘P´"You'd® ´better® ´fix® ´thŽ’¸ÿÌis!\n\n"Ž’æM4°‘DZ ushŽ‘€¬;Ž¡‘2°gŽ¡‘gŽ¡‘­returnŽ‘Aæ½±p‘ÿ}'entsŽ‘Ywi¬;‘qÇ°gŽŸ­1505.– üDra®9w‘¾—net.“¬[²LDF‘T2002.11.10.¬]Ž‘Y•ÔThis–bófunction“is“for“dra¸ãwing“the“net“of“a“­DoQÇdecahedronŽ‘K"¬.‘ üNormally‘ÿ*ª,Ž¡this–m)will“bšGe“done“in“order“to“mak¸ãe“a“cardb˜oard“mo˜del,‘³whic¸ãh“will“require“tabs“for“gluing“the“p˜en¸ãtagonsŽ¡together.‘qÇIf–UUno“tabs“are“desired,“passing“±falseŽ‘Yî¬as“the“±make‘‰ffŽ‘®tabsŽ‘3J¬argumen¸ãt“will“suppress“the“tabs.ŽŽŽŒ‹ÇJ Šn ý‘ì°x¬1505–¯3DLDF-1.1.5.1’%LÓDRA‘ÿ8W‘ÕXNET“¬455Ž €n ý•@P‘ +[²LDF‘T2002.11.10.¬]Ž‘Y¬0TO‘ùDO:–ùJThe“arraš¸ãys“­P•®9oin“tŽ‘#ŒÜ±ptsŽ‘5`̬and“­P®9athŽ‘ ƒøµpŽ‘)…B¬ha˜v˜e“toGo“man˜y“mem˜bGers.‘]¥In“w˜orking“onŽ¤ this–:êfunction,‘@2I‘:ãended“up“getting“rid“of“some“of“the“memš¸ãbGers“of“these“arra˜ys“after“I'd“already“used“mem˜bGersŽ¡folloš¸ãwing–UUthem.‘qÇI“should“go“through“and“reassign“the“n˜um˜bGers,“so“that“no“mem˜bšGers“are“skipp˜ed.Ž¡‘ +[²LDF‘T2002.11.10.¬]Ž‘Y;TO–UUDO:“Add“the“usual“argumenš¸ãts“for“dra˜wing“and“ lling“commands.Ž¡‘ +[²LDF‘T2002.11.10.¬]Ž‘XûåTO‘HüDO:‘Hÿ±p–ÿ}'ortr“aitŽ‘(|>¬doGesn't–Hÿwš¸ãork“righ˜t.›mªFix“it!˜!!˜KLUDGE:“±p–ÿ}'ortr“aitŽ‘(|>¬is“set“to“±falseŽ‘AB¬at“theŽ¡bGeginning–UUof“this“function“and“a“w¸ãarning“is“issued.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.11.10.¬]Ž‘Y;Added–UUthis“function.Ž¡‘ +[²LDF‘T2002.11.10.¬]Ž‘Y;T‘ÿ*ªried–UUto“get“output“in“pšGortrait“format“to“w¸ãork,“but“it“do˜esn't“y¸ãet.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­DoQÇdecahedronŽ‘Oj8¬functions‘@¯1497“°i‘Ǭ+°ŽŸ ‘ +­staticŽ‘)HÚv®9oidŽ‘BF²±dr‘ÿ}'aw‘‰ffŽ‘®netŽ‘iˆE¬(­constŽ‘*¢realŽ‘4Ýбp‘ÿ}'entagon‘‰ffŽ‘®diameterŽ’†íˆµ;‘ª¨­b•QÇo“olŽ‘L±p–ÿ}'ortr“aitŽ‘?ýf¬=‘DZtrueŽ–‹°µ;‘ª¨­b•QÇo“olŽ‘L±make‘‰ffŽ‘®tabsŽ‘J²”¬=‘DZtrueŽ“¬);ŽŽŽŒ‹È_“ Šn ý‘ì¬456–¯DRA‘ÿ8W‘ÕXNET’%LÓ3DLDF-1.1.5.1“°x¬1506Ž €n ý•@P­1506.Ž©:¤°h–ª¨¬De ne‘UU­DoQÇdecahedronŽ‘Oj8¬functions‘@¯1498“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘"ýÙDoQÇdecahedronŽ‘l½k¬::‘±dr‘ÿ}'aw‘‰ffŽ‘®netŽ‘(A—¬(­constŽ‘*¢realŽ‘4Ýбp‘ÿ}'entagon‘‰ffŽ‘®diameterŽ’†íˆµ;‘ª¨­b•QÇo“olŽ‘L±p–ÿ}'ortr“aitŽ‘=6Nµ;‘ª¨­b•QÇo“olŽ‘L±make‘‰ffŽ‘®tabsŽ‘Gë|¬)Ž¡‘ +°fŽ¡‘­v®9ectorŽ‘3ªJ°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘DÔ °Ž‘IÔ +i‘UUµvŽ‘ Q*¬=‘DZget‘‰ffŽ‘®netŽ‘!ûà¬(±p‘ÿ}'entagon‘‰ffŽ‘®diameterŽ‘R¸¬);Ž¦‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘DÔ °Ž‘IÔ +i‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘ǵvŽ–ûÕ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘ǵvŽ“:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘­ifŽ‘)´û¬(±p–ÿ}'ortr“aitŽ‘!ê@¬)‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±r‘ÿ}'otateŽ‘o>¬(0Ž‘µ;‘ª¨¬90ŽŽ‘ ªª);Ž¡#­ifŽ‘ ´ø¬0ŽŽ¡‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±r‘ÿ}'otateŽ‘o>¬(90ŽŽ‘ +);Ž¡#­endifŽŽ¡‘°gŽ¦‘­P•®9oin“tŽ‘2pŽ‘7÷Ÿ¬[32ŽŽ‘ +];Ž¡‘­in®9tŽ‘%¤ùµiŽ‘)í¬;Ž¦‘­forŽ‘%般(µiŽ‘9 ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ5Ž“;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)‘°fŽ¡‘µpŽ‘#¬[µiŽ›qô¬]–Ç=“µvŽ‘ûÕ¬[3Ž‘]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(µiŽ˜¬);Ž¡#­ifŽ‘ ´ø¬0ŽŽ¡‘µpŽ‘#¬[µiŽ–qô¬]µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(µiŽ“¬);Ž¡#­endifŽŽ¡‘°g‘µ=°›ÿý¬ST–ÿ*ªAR“T‘UUHERE.˜°µ=Ž¡‘iŽ‘9¬=‘Ç0Ž‘Ç;Ž¡‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘DÔ °Ž‘IÔ +i‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘ǵvŽ–ûÕ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘ǵvŽ“:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘¬(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±dr‘ÿ}'awŽ‘(Û¬(‘ª¨);Ž¡‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘,=G¬(–ª¨)µ:±lab‘ÿ}'elŽ‘t˜¬(µiŽ‘ñôŸÿ³+‘ÿ+ŽŽ‘¹µ;“´""Ž‘ ± +¬);Ž¡‘°gŽ¡‘­ifŽ‘´ú¬(°:±make‘‰ffŽ‘®tabsŽ‘,Ÿn¬)‘­returnŽ‘%‘e¬;Ž¡‘­returnŽ‘4‘g¬;Ž¡‘ +°gŽ¤­1507.‘ üIcosahedron.Ž¡1508.‘ üIcosahedron–ÕTclass“de nition.Ž¦°h–ª¨¬De ne‘UU­classŽ‘5¦IcosahedronŽ‘_Ny¯1508“°i‘ÇŽ¤ ‘ +­classŽ‘$àRIcosahedronŽ‘ev¬:‘qÇ­publicŽ‘'ñP®9olyhedronŽ‘dh°fŽ¡‘ +­protectedŽ‘:o™¬:‘­staticŽ‘$HÙconstŽ‘Bs{realŽ‘Y&©±dihe–ÿ}'dr“al‘‰ffŽ‘®angleŽ’–qq¬;‘µ=°‘ÿý¬In‘UUradians!‘o°µ=Ž¡‘­realŽ‘*³0±triangle‘‰ffŽ‘®r‘ÿ}'adiusŽ‘kA„¬;Ž¦‘ +­publicŽ‘)=Ö¬:‘°h–ª¨¬Declare‘UU­IcosahedronŽ‘Cƒy¬functions‘@¯1511“°iŽ¡‘ +g¬;ŽŸ :¤¯This–ÕXcoÝÑIcosahedronŽ‘|¶¤¬::‘±dihe–ÿ}'dr“al‘‰ffŽ‘®angleŽ‘Aä¬=‘Ç´PIŽ‘Z°‘8à±asinŽ‘c¥¬(2µ:¬0ŽŽ– ǵ=¬3µ:¬0ŽŽ“);ŽŸ :¤¯This–ÕXcoK&¬.‘o°µ=Ž¡‘±vertic‘ÿ}'esŽ‘8±X¬=‘Ç12ŽŽ‘ Ç;Ž¡‘±e‘ÿ}'dgesŽ‘.™1¬=‘Ç30ŽŽ‘ Ç;Ž¡‘±c‘ÿ}'enterŽ‘2Ð¥¬=‘Ç´INVALID_POINTŽ‘GY¬;‘µ=°‘ÿý¬from‘UU­P®9olyhedronŽ‘=c"¬.‘o°µ=Ž¡‘±numb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜olygon‘‰ffŽ“typ˜esŽ’R9¬=‘Ç1Ž‘Ç;Ž¡‘±fac–ÿ}'e‘‰ffŽ‘®r“adiusŽ‘G%¬=‘DZe–ÿ}'dge‘‰ffŽ‘®r“adiusŽ‘7j¬=‘DZvertex‘‰ffŽ‘®r‘ÿ}'adiusŽ‘>þ¨¬=‘Ç´INVALID_REALŽ‘BM\¬;Ž¡‘±triangle‘‰ffŽ‘®r‘ÿ}'adiusŽ‘WUn¬=‘Ç´INVALID_REALŽ‘BM\¬;Ž¡‘ +°gŽ¤ ¯See–ÕXalso“sections“1515,“1517,“and“1519.Ž¡This–ÕXco0¯¬&Ž‘E÷͵pŽ‘JÿÍ;‘ª¨­constŽ‘ `‚realŽ‘7žè±triangle‘‰ffŽ‘®diameterŽ’„0µ;‘ª¨­realŽ‘é±angle‘‰ffŽ‘®xŽ‘9nêµ;‘ª¨­realŽŽ¡‘2±angle‘‰ffŽ‘®yŽ‘Rkµ;‘ª¨­realŽ‘]Ö±angle‘‰ffŽ‘®zŽ‘8]L¬)°f‘UU­b•QÇo“olŽ‘ö»´DEBUGŽ‘:„,¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¦‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Entering® ´IcosahedroŽ‘kÆÜn::Icosahedron().\n"Ž’Ø °‘DZ ushŽ‘€¬;Ž¡‘±on‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘Xl ¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý¬from‘UU­SolidŽ‘Ó,¬.‘o°µ=Ž¡‘±do‘‰ffŽ‘®outputŽ‘K½N¬=‘DZtrueŽ‘‹°¬;Ž¡‘±fac‘ÿ}'esŽ‘7«¬=‘Ç20ŽŽ‘ Ç;‘µ=°‘ÿý¬from‘UU­Solidu½‰™šs4Ž‘ÔwF‘ÿ +«acedŽ‘>K&¬.‘o°µ=Ž¡‘±vertic‘ÿ}'esŽ‘B±Y¬=‘Ç12ŽŽ‘ Ç;Ž¡‘±e‘ÿ}'dgesŽ‘8™2¬=‘Ç30ŽŽ‘ Ç;Ž¡‘±numb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜olygon‘‰ffŽ“typ˜esŽ’‹R:¬=‘Ç1Ž‘Ç;Ž¡#­ifŽ‘ ´ø¬0Ž‘$´úµ=°‘ÿý¬ST–ÿ*ªAR“T–UUHERE.“TO“DO:“Must“calculate“these!‘o°µ=Ž¡‘±fac–ÿ}'e‘‰ffŽ‘®r“adiusŽ‘Q&¬=‘Ç0Ž‘Ç;Ž¡‘±e–ÿ}'dge‘‰ffŽ‘®r“adiusŽ‘R£­¬=‘Ç0Ž‘Ç;Ž¡‘±vertex‘‰ffŽ‘®r‘ÿ}'adiusŽ‘Z7“¬=‘Ç0Ž‘Ç;Ž¡#­endifŽŽ¡‘±triangle‘‰ffŽ‘®r‘ÿ}'adiusŽ‘aUo¬=‘DZtriangle‘‰ffŽ‘®diameterŽ‘OX>µ=¬2µ:¬0ŽŽ‘ Ç;Ž¦‘­in®9tŽ‘/¤úµiŽ‘3î¬;‘qDZr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:eµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘G›!µ>‘Ǭ(0Ž‘)–UU)“;Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóSµ:±fr‘ÿ}'ontŽ‘I‘¬(–ª¨)‘þŸµ~ŽŽ‘±setŽ‘x…¬(±originŽ‘ö!µ;“¬3Ž‘ª©µ;“±triangle‘‰ffŽ‘®diameterŽ‘N;ά);Ž¦‘­P•®9oin“tŽ‘<ï ±ptsŽ‘JÊF¬[7Ž‘];Ž¦‘­forŽ‘/艬(µiŽ‘9 ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ3Ž“;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘±ptsŽ‘Ú¦¬[µiŽ›qô¬]–Ç=“±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºhµ:±fr‘ÿ}'ontŽ‘I‘¬(‘ª¨)‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(µiŽ˜¬);Ž¡‘­forŽ‘2(¬(µiŽ‘ Ág¬=‘Os1Ž– Ot;‘œµiŽ‘à<‘Os¬6Ž“;‘žœŸÿ³+‘ÿ+ŽŽ‘e¼µiŽ‘×°¬)–sô°f“±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘;gDµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘0ÌF¬(“±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘:w¬µ<Ž¡‘2­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘vEѵ>‘Ǭ(±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óPµ:±fr‘ÿ}'ontŽ‘I‘¬(‘ª¨))–UU)“;‘qÇ°g“±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘9H¥¬[1Ž–]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[2Ž“]–8à°“±ptsŽ‘†¬[1Ž‘]);Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS¬[2Ž–]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[1Ž“]–8à°“±ptsŽ‘†¬[2Ž‘]);Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS¬[3Ž–]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[0Ž“]–8à°“±ptsŽ‘†¬[2Ž‘]);Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS¬[4Ž–]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[0Ž“]–8à°“±ptsŽ‘†¬[1Ž‘]);Ž¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±originŽ‘ö!µ:±lab‘ÿ}'elŽ‘t˜¬(´"O"Ž‘F_µ;‘ª¨´""Ž‘ ± +¬);Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS¬[5Ž–]‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(0Ž“µ;‘ª¨¬180ŽŽ‘ª«);Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS¬[5Ž–]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[1Ž“]–Óc°“±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8Ƴ¬[5Ž–]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(0Ž“));‘=­forŽ‘ e¬(µiŽ‘»R¬=‘I^6Ž‘ I_;‘çµiŽ‘ £<‘I^¬10ŽŽ‘I`;‘gŸÿ³+‘ÿ+ŽŽ‘.âµiŽ‘ Ö¬)‘=°fŽ¡‘2±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘góUµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘/°Ó¬(‘X±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘8@Ƶ<‘X­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘JN@µ>‘w ¬(±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP¬[5Ž‘])–X)“;‘{L°gŽ¡‘2±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘góU¬[6Ž–]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[2Ž“]–8à°“±ptsŽ‘†¬[1Ž‘]);Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS¬[7Ž–]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[1Ž“]–8à°“±ptsŽ‘†¬[0Ž‘]);Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS¬[8Ž–]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[2Ž“]–8à°“±ptsŽ‘†¬[0Ž‘]);Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS¬[9Ž–]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[2Ž“]–8à°“±ptsŽ‘†¬[0Ž‘]);Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS¬[9Ž–]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[2Ž“]–8à°“±ptsŽ‘†¬[1Ž‘]);Ž¡‘±ptsŽ‘+Ú©¬[3Ž›]–Ç=“±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh¬[2Ž˜]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(1Ž˜);Ž¡‘±ptsŽ‘+Ú©¬[4Ž›]–Ç=“±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh¬[2Ž˜]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(0Ž˜);Ž¡‘±ptsŽ‘+Ú©¬[5Ž›]–Ç=“±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh¬[1Ž˜]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(2Ž˜);Ž¡‘±ptsŽ‘+Ú©¬[6Ž›]–Ç=“±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh¬[1Ž˜]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(0Ž˜);Ž¦‘­realŽ‘4³1±angleŽ‘O:œ¬=‘Ç180µ:¬0ŽŽ‘Ç°–8à¬(±dihe–ÿ}'dr“al‘‰ffŽ‘®angleŽ‘?ƒ¨°“¬180µ:¬0ŽŽ‘µ=´PIŽ‘ b¬);Ž¦‘°Ž‘#±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘XóT¬[9Ž–]‘Ç°¬=ŽŽ‘UO°Ž‘UP±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘MH ¬[8Ž“]‘Ç°¬=ŽŽ‘UO±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘HHŸ¬[7Ž“]‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(±ptsŽ‘ Ú¦¬[3Ž“]µ;‘ª¨±ptsŽ‘…N¬[5Ž“]µ;‘ª¨°Ž‘ qƱangleŽ‘!2¬);Ž¡‘°Ž‘#±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘XóT¬[3Ž–]‘Ç°¬=ŽŽ‘UO±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘HHŸ¬[4Ž“]‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(±ptsŽ‘ Ú¦¬[4Ž“]µ;‘ª¨±ptsŽ‘…N¬[6Ž“]µ;‘ª¨±angleŽ‘jû¬);Ž¡‘°Ž‘#±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘XóT¬[2Ž–]‘Ç°¬=ŽŽ‘UO±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘HHŸ¬[7Ž“]‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(±ptsŽ‘ Ú¦¬[1Ž“]µ;‘ª¨±ptsŽ‘…N¬[4Ž“]µ;‘ª¨°Ž‘ qƱangleŽ‘!2¬);Ž¡‘°Ž‘#±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘XóT¬[7Ž–]‘Ç°¬=ŽŽ‘UO°Ž‘UP±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ›MH ¬[2Ž“]‘Ç°¬=ŽŽ‘UO°Ž‘UP±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ˜¬[3Ž“]‘Ç°¬=ŽŽ‘UO±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘HHŸ¬[5Ž“]‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(±ptsŽ‘ Ú¦¬[1Ž“]µ;‘ª¨±ptsŽ‘…N¬[0Ž“]µ;Ž¡‘2°Ž‘9Ç#±angleŽ‘Q‡v¬);Ž¡‘°Ž‘#±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘XóT¬[1Ž–]‘Ç°¬=ŽŽ‘UO±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘HHŸ¬[9Ž“]‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(±ptsŽ‘ Ú¦¬[2Ž“]µ;‘ª¨±ptsŽ‘…N¬[6Ž“]µ;‘ª¨±angleŽ‘jû¬);Ž¡‘°Ž‘#±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘XóT¬[9Ž–]‘Ç°¬=ŽŽ‘UO°Ž‘UP±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ›MH ¬[1Ž“]‘Ç°¬=ŽŽ‘UO°Ž‘UP±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ˜¬[6Ž“]‘Ç°¬=ŽŽ‘UO±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘HHŸ¬[4Ž“]‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(±ptsŽ‘ Ú¦¬[2Ž“]µ;Ž¡‘2±ptsŽ‘?Ú«¬[0Ž‘]µ;‘ª¨±angleŽ‘jû¬);‘3z­forŽ‘ú%¬(µiŽ‘«H¬=‘9T10ŽŽ–9V;‘Þ"µiŽ‘ ‰j<‘9T¬20ŽŽ“;‘^"Ÿÿ³+‘ÿ+ŽŽ‘%BµiŽ‘—6¬)–3z°f“±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:&ʵ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘/‹Ì¬(“±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘7ö¸µ<Ž¡‘2­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘vEѵ>‘Ǭ(±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP¬[µiŽ‘ªÔ°‘8à¬10ŽŽ‘ 8â])–UU)“;Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóSµ:±b‘ÿ}'ackŽ‘üì(‘ª¨)‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(180ŽŽ‘);ŽŽŽŒ‹Ëzª Šn ý‘ì°x¬1515–¯3DLDF-1.1.5.1’ÎãCONSTRÃŽUCTOR“¬459Ž €n ý•@P‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóSµ:±b‘ÿ}'ackŽ‘üì(–ª¨)‘þŸµ~ŽŽ‘±shiftŽ‘~¬(0Ž‘µ;“¬12ŽŽ‘ ªª);‘UU°gŽ¤ ‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘(±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘]óT¬[4Ž‘]‘þŸµ~ŽŽ‘±dotlab‘ÿ}'elŽ‘%ÿô¬(‘ª¨);Ž¡‘(±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘]óT¬[19ŽŽ‘ +]‘þŸµ~ŽŽ‘±dotlab‘ÿ}'elŽ‘%ÿô¬(‘ª¨);Ž¡‘°gŽ¤‘­realŽ‘4³1±y‘‰ffŽ‘®shiftŽ‘T ܬ=‘DZr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh¬[4Ž–]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ›+bI¬(0Ž“)µ:±get‘‰ffŽ‘®yŽ‘t¬(‘ª¨)–8à°“±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8,0¬[19ŽŽ‘ +]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ˜¬(0Ž‘)µ:±get‘‰ffŽ‘®yŽ‘t¬(‘ª¨);Ž¡‘­forŽ‘/艬(µiŽ‘9 ¬=‘Ç10ŽŽ– Ç;‘ÿýµiŽ‘ 9 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<‘Ǭ4Ž“;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘±ptsŽ‘Ú¦¬[µiŽ–qô¬]µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(µiŽ“¬);Ž¡‘­ifŽ‘)´û¬(±do‘‰ffŽ‘®halfŽ‘#'¡°‘DZtrueŽ‘‹°¬)‘°fŽ¡‘(Ž‘-±trianglesŽ‘SƒÞ¬[8Ž›]–Ç=“°Ž‘DZtrianglesŽ‘.Jò¬[4Ž˜];Ž¡‘(°Ž‘-±trianglesŽ‘SƒÞ¬[9Ž›]–Ç=“°Ž‘DZtrianglesŽ‘.Jò¬[5Ž˜];Ž¡‘(°Ž‘-±trianglesŽ‘SƒÞ¬[8Ž–]‘Ç°¬=ŽŽ‘UO±trianglesŽ‘8Ù(¬[9Ž“]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[1Ž“]–8à°“±ptsŽ‘†¬[2Ž‘]);Ž¡‘(­forŽ‘9芬(µiŽ‘9 ¬=‘Ç0Ž‘Ç;‘ÿýµiŽ‘ 9 <‘Ǭ10ŽŽ‘ Ç;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘°fŽ¡‘2­forŽ‘C苬(­in®9tŽ‘¤÷µjŽ‘Ó¬=‘Ç0Ž–Ç;‘ÿýµjŽ‘ wÙ<‘Ǭ3Ž“;‘ÿýµjŽ‘ +0ÁŸÿ³+‘ÿ+ŽŽ‘÷á¬)Ž¡‘<­ifŽ‘G´þ¬(±trianglesŽ‘&ƒÙ¬[µiŽ‘qô¬]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(µjŽ‘°Ä¬)µ:±get‘‰ffŽ‘®yŽ‘t¬(‘ª¨)–Ç°6¬=“0Ž‘Ç)‘°fŽ¡‘F±c‘ÿ}'errŽ‘\!Z°‘k­´"ERROR!® ´In® ´IcosahedrŽ‘lkqon::get_net():\n"Ž’ÉS°‘k­´"y-coordinate® ´!=® ´0!\Ž‘lkqn"Ž‘zÝ€°Ž¡‘Z ´"You'd® ´better® ´fix® ´thŽ’ÂÿÍis!\n\n"Ž’ðM5°‘DZ ushŽ‘€¬;Ž¡‘<°gŽ¡‘(gŽ¡‘(­returnŽ‘Kæ¾±trianglesŽ‘rj—¬;Ž¡‘°g‘µ=°‘ÿý¬Do–UUthe“second“half.‘o°µ=Ž¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Doing® ´the® ´second® ´haŽ‘kÆÜlf.\n"Ž’‹Í2¬;Ž¡‘­forŽ‘/艬(µiŽ‘9 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¬=‘Ç0Ž‘Ç;‘ÿýµiŽ‘ 9 <‘Ǭ20ŽŽ‘ Ç;‘ýŸÿ³+‘ÿ+ŽŽ‘GµiŽ‘¹¬)‘°fŽ¤ ‘(­forŽ‘9芬(­in®9tŽ‘¤÷µjŽ‘Ó¬=‘Ç0Ž–Ç;‘ÿýµjŽ‘ wÙ<‘Ǭ3Ž“;‘ÿýµjŽ‘ +0ÁŸÿ³+‘ÿ+ŽŽ‘÷á¬)Ž¡‘2­ifŽ‘=´ý¬(±trianglesŽ‘&ƒÙ¬[µiŽ‘qô¬]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(µjŽ‘°Ä¬)µ:±get‘‰ffŽ‘®yŽ‘t¬(‘ª¨)–Ç°6¬=“0Ž‘Ç)‘°fŽ¡‘<±c‘ÿ}'errŽ‘R_É°‘ª´"ERROR!® ´In® ´IcosahedrŽ‘l©áon::get_net():\n"Ž’Ê3°‘ª´"y-coordinate® ´!=® ´0!\Ž‘l©án"Ž‘{Z`°Ž¡‘P´"You'd® ´better® ´fix® ´thŽ’¸ÿÌis!\n\n"Ž’æM4°‘DZ ushŽ‘€¬;Ž¡‘2°gŽ¡‘gŽ¡‘­returnŽ‘Aæ½±trianglesŽ‘hj–¬;‘qÇ°gŽŸ­1518.– üDra®9w‘ÕTnet.“¬TO–UUDO:“Add“parallel“pro‘Ž8jections“on¸ãto“planes“other“than“the“x-y“plane.ŽŸÀŸû9ŸüÈ„`Ö+U‘ üŸî8­LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.11.10.¬]Ž‘Y¾”Added– ®this“function.‘”ѱp–ÿ}'ortr“aitŽ‘,Š¿¬w•¸ãorks,‘9Dunlik“e‘ ®­DoQÇdecahedronŽ‘MË@¬::Ž‘TY~±dr‘ÿ}'aw‘‰ffŽ‘®netŽ‘{›¬(‘ª¨)±p–ÿ}'olyhe“dŽ‘ úCµ:±webŽŽ¡¬(as–UUof“this“date).Ž¡‘ +[²LDF‘T2002.08.12.¬]Ž‘Y;Changed,–UUso“that“net“is“dra¸ãwn“in“x-z“plane.Ž¡‘ +[²LDF‘T2002.08.12.¬]Ž‘X›¤This–è¾function“no¸ãw“returns“bšGefore“the“co˜de“for“making“the“tabs“can“b˜e“executed,‘þvb˜ecauseŽ¡it–UUdoGesn't“wš¸ãork“y˜et.‘qÇTO“DO:“W‘ÿ*ªrite“coGde“for“tabs.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­IcosahedronŽ‘Cƒy¬functions‘@¯1511“°i‘Ǭ+°ŽŸ ‘ +­staticŽ‘)HÚv®9oidŽ‘BF²±dr‘ÿ}'aw‘‰ffŽ‘®netŽ‘iˆE¬(­constŽ‘*¢realŽ‘4Ýбtriangle‘‰ffŽ‘®diameterŽ’nöµ;‘ª¨­b•QÇo“olŽ‘L±p–ÿ}'ortr“aitŽ‘?ýf¬=‘DZtrueŽ–‹°µ;‘ª¨­b•QÇo“olŽ‘L±make‘‰ffŽ‘®tabsŽ‘J²”¬=‘DZtrueŽ“¬);ŽŽŽŒ‹Î½Ø Šn ý‘ì¬462–¯DRA‘ÿ8W‘ÕXNET’%LÓ3DLDF-1.1.5.1“°x¬1519Ž €n ý•@P­1519.Ž©°h–ª¨¬De ne‘UU­IcosahedronŽ‘Cƒy¬functions‘@¯1512“°i‘Ǭ+°Ž¤ ‘ +­v®9oidŽ‘"ýÙIcosahedronŽ‘`Ö¬¬::‘±dr‘ÿ}'aw‘‰ffŽ‘®netŽ‘(A—¬(­constŽ‘*¢realŽ‘4Ýбtriangle‘‰ffŽ‘®diameterŽ’nöµ;‘ª¨­b•QÇo“olŽ‘L±p–ÿ}'ortr“aitŽ‘=6Nµ;‘ª¨­b•QÇo“olŽ‘L±make‘‰ffŽ‘®tabsŽ‘Gë|¬)Ž¡‘ +°fŽ¡‘­v®9ectorŽ‘3ªJ°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘DÔ °Ž‘IÔ +i‘UUµvŽ‘ Q*¬=‘DZget‘‰ffŽ‘®netŽ‘!ûà¬(±triangle‘‰ffŽ‘®diameterŽ‘L‘&¬);Ž¡‘­in®9tŽ‘%¤ùµiŽ‘+Þ¬=‘Ç0Ž‘Ç;Ž¦‘­forŽ‘%般(­v®9ectorŽ‘ªH°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘DÔ °Ž‘IÔ +i‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=+M¬=‘ǵvŽ–ûÕ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘ÿý±iterŽ‘’°6¬=‘ǵvŽ“:±endŽ‘ಬ(˜);‘ýŸÿ³+‘ÿ+ŽŽ‘G±iterŽ‘"¬)‘°fŽ¡‘­ifŽ‘)´û¬(±p–ÿ}'ortr“aitŽ‘!ê@¬)‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±r‘ÿ}'otateŽ‘o>¬(0Ž‘µ;‘ª¨¬90ŽŽ‘ ªª);Ž¡‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘,=G¬(–ª¨)µ:±lab‘ÿ}'elŽ‘t˜¬(µiŽ‘ñôŸÿ³+‘ÿ+ŽŽ‘¹µ;“´""Ž‘ ± +¬);Ž¡‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±dr‘ÿ}'awŽ‘(Û¬(‘ª¨);Ž¡‘°gŽ¡‘­returnŽ‘4‘g¬;‘µ=°‘ÿý¬Delete,–UUwhen“I“start“writing“coGde“for“tabs.‘qÇ[²LDF‘T2002.08.12.¬]Ž‘U$©°µ=Ž¡‘­ifŽ‘´ú¬(°:±make‘‰ffŽ‘®tabsŽ‘,Ÿn¬)‘­returnŽ‘%‘e¬;Ž¦‘­P®9athŽ‘/滵pŽ‘4[11ŽŽ‘ +];Ž¡‘­P•®9oin“tŽ‘2ptsŽ‘@ÊE¬[11ŽŽ‘ +];Ž¡#­ifŽ‘ ´ø¬0ŽŽ¦‘µvŽ‘4¿¬[0Ž‘]‘þŸµ~ŽŽ‘±dotlab‘ÿ}'elŽ‘%ÿô¬(‘ª¨);Ž¡#­endifŽŽ¡‘±ptsŽ‘!Ú¨¬[0Ž›]–Ç=“µvŽ‘ûÕ¬[0Ž˜]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(0Ž˜);Ž¡‘±ptsŽ‘!Ú¨¬[1Ž›]–Ç=“µvŽ‘ûÕ¬[0Ž˜]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(1Ž˜);Ž¡‘±ptsŽ‘!Ú¨¬[2Ž›]–Ç=“µvŽ‘ûÕ¬[0Ž˜]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(2Ž˜);Ž¡‘±ptsŽ‘!Ú¨¬[3Ž›]–Ç=“±ptsŽ‘¡¾¬[0Ž˜]µ:±me‘ÿ}'diateŽ‘"½u¬(±ptsŽ‘ Ú¦¬[1Ž˜]µ;‘ª¨:¬1ŽŽ‘ qÆ);Ž¡‘±ptsŽ‘!Ú¨¬[4Ž›]–Ç=“±ptsŽ‘¡¾¬[1Ž˜]µ:±me‘ÿ}'diateŽ‘"½u¬(±ptsŽ‘ Ú¦¬[0Ž˜]µ;‘ª¨:¬1ŽŽ‘ qÆ);Ž¡#­ifŽ‘ ´ø¬0ŽŽ¡‘±ptsŽ‘!Ú¨¬[3Ž–]µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(2Ž“);Ž¡‘±ptsŽ‘!Ú¨¬[4Ž–]µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(3Ž“);Ž¡#­endifŽŽ¡‘±ptsŽ‘!Ú¨¬[5Ž›]–Ç=“±ptsŽ‘¡¾¬[0Ž˜]µ:±me‘ÿ}'diateŽ‘"½u¬(±ptsŽ‘ Ú¦¬[3Ž˜]µ;‘ª¨:¬1ŽŽ‘ qÆ);Ž¡‘±ptsŽ‘!Ú¨¬[6Ž›]–Ç=“±ptsŽ‘¡¾¬[1Ž˜]µ:±me‘ÿ}'diateŽ‘"½u¬(±ptsŽ‘ Ú¦¬[4Ž˜]µ;‘ª¨:¬1ŽŽ‘ qÆ);Ž¡‘±ptsŽ‘!Ú¨¬[7Ž›]–Ç=“±ptsŽ‘¡¾¬[3Ž˜];Ž¡‘±ptsŽ‘!Ú¨¬[7Ž–]µ:±shiftŽ‘}¬(0Ž“µ;‘ª¨¬0Ž–ª©µ;‘ª¨¬1Ž“);Ž¡‘±ptsŽ‘!Ú¨¬[8Ž›]–Ç=“±ptsŽ‘¡¾¬[4Ž˜];Ž¡‘±ptsŽ‘!Ú¨¬[8Ž–]µ:±shiftŽ‘}¬(0Ž“µ;‘ª¨¬0Ž–ª©µ;‘ª¨¬1Ž“);Ž¡‘±ptsŽ‘!Ú¨¬[5Ž–]µ:±r‘ÿ}'otateŽ‘o>¬(±ptsŽ‘ Ú¦¬[3Ž“]µ;‘ª¨±ptsŽ‘…N¬[7Ž“]µ;‘ª¨¬90ŽŽ‘ ªª);Ž¡‘±ptsŽ‘!Ú¨¬[6Ž–]µ:±r‘ÿ}'otateŽ‘o>¬(±ptsŽ‘ Ú¦¬[8Ž“]µ;‘ª¨±ptsŽ‘…N¬[4Ž“]µ;‘ª¨¬90ŽŽ‘ ªª);Ž¡#­ifŽ‘ ´ø¬0ŽŽ¡‘±ptsŽ‘!Ú¨¬[5Ž–]µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(4Ž“);Ž¡‘±ptsŽ‘!Ú¨¬[6Ž–]µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(5Ž“);Ž¡#­endifŽŽ¡‘±ptsŽ‘!Ú¨¬[9Ž›]–Ç=“±ptsŽ‘¡¾¬[5Ž˜]µ:±me‘ÿ}'diateŽ‘"½u¬(±ptsŽ‘ Ú¦¬[6Ž˜]µ;‘ª¨:¬1ŽŽ‘ qÆ);Ž¡‘±ptsŽ‘!Ú¨¬[10ŽŽ‘ +]–Ç=“±ptsŽ‘¡¾¬[6Ž–]µ:±me‘ÿ}'diateŽ‘"½u¬(±ptsŽ‘ Ú¦¬[5Ž“]µ;‘ª¨:¬1ŽŽ‘ qÆ);Ž¡#­ifŽ‘ ´ø¬0ŽŽ¡‘±ptsŽ‘!Ú¨¬[9Ž–]µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(8Ž“);Ž¡‘±ptsŽ‘!Ú¨¬[10ŽŽ‘ +]µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(9Ž‘);Ž¡#­endifŽŽ¡‘µpŽ‘¬[0Ž–]µ:±setŽ‘ x„¬(´"--"Ž‘†\µ;‘ª¨±trueŽ‘o@µ;‘ª¨¬&Ž‘ qƱptsŽ›Ll¬[3Ž“]µ;‘ª¨¬&Ž‘ qƱptsŽ˜¬[9Ž“]µ;‘ª¨¬&Ž‘ qƱptsŽ˜¬[10ŽŽ‘ +]µ;‘ª¨¬&Ž‘ qƱptsŽ˜¬[4Ž“]µ;‘ª¨¬0Ž‘ª©);Ž¡‘µpŽ‘¬[1Ž›]–Ç=“µpŽ‘Ϭ[2Ž˜]“=“µpŽ‘Ϭ[3Ž˜]“=“µpŽ‘Ϭ[4Ž˜]“=“µpŽ‘Ϭ[5Ž˜]“=“µpŽ‘Ϭ[0Ž˜];Ž¡‘µpŽ‘¬[1Ž–]µ:±shiftŽ‘}¬(µvŽ‘4½¬[4Ž“]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(1Ž“)–8à°“±ptsŽ‘†¬[1Ž‘]);Ž¡‘µpŽ‘¬[2Ž–]µ:±shiftŽ‘}¬(µvŽ‘4½¬[8Ž“]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(1Ž“)–8à°“±ptsŽ‘†¬[1Ž‘]);Ž¡‘µpŽ‘¬[3Ž–]µ:±shiftŽ‘}¬(µvŽ‘4½¬[12ŽŽ‘ +]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(1Ž“)–8à°“±ptsŽ‘†¬[1Ž‘]);Ž¡‘µpŽ‘¬[4Ž–]µ:±shiftŽ‘}¬(µvŽ‘4½¬[16ŽŽ‘ +]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(1Ž“)–8à°“±ptsŽ‘†¬[1Ž‘]);ŽŽŽŒ‹ÏÅ Šn ý‘ì°x¬1519–¯3DLDF-1.1.5.1’%LÓDRA‘ÿ8W‘ÕXNET“¬463Ž €n ý•@P‘µpŽ‘¬[5Ž–]µ:±shiftŽ‘}¬(µvŽ‘4½¬[18ŽŽ‘ +]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(1Ž“)–8à°“±ptsŽ‘†¬[1Ž‘]);Ž¤ ‘µpŽ‘¬[6Ž›]–Ç=“µpŽ‘Ϭ[0Ž˜];Ž¡‘µpŽ‘¬[6Ž–]µ:±r‘ÿ}'otateŽ‘o>¬(0Ž“µ;‘ª¨¬0Ž‘ª©µ;‘ª¨¬240ŽŽ‘ª«);Ž¡‘µpŽ‘¬[6Ž–]µ:±r‘ÿ}'otateŽ‘o>¬(±ptsŽ‘ Ú¦¬[0Ž“]µ;‘ª¨±ptsŽ‘…N¬[2Ž“]);Ž¡#­ifŽ‘ ´ø¬0ŽŽ¡‘µvŽ‘4¿¬[3Ž‘]‘þŸµ~ŽŽ‘±dotlab‘ÿ}'elŽ‘%ÿô¬(‘ª¨);Ž¡#­endifŽŽ¡‘µpŽ‘¬[7Ž›]–Ç=“µpŽ‘Ϭ[8Ž˜]“=“µpŽ‘Ϭ[9Ž˜]“=“µpŽ›Ï¬[10ŽŽ‘ +]“=“µpŽ˜¬[6Ž‘];Ž¡‘µpŽ‘¬[6Ž–]µ:±shiftŽ‘}¬(µvŽ‘4½¬[3Ž“]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(0Ž“)–8à°“±ptsŽ‘†¬[2Ž‘]);Ž¡‘µpŽ‘¬[7Ž–]µ:±shiftŽ‘}¬(µvŽ‘4½¬[7Ž“]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(0Ž“)–8à°“±ptsŽ‘†¬[2Ž‘]);Ž¡‘µpŽ‘¬[8Ž–]µ:±shiftŽ‘}¬(µvŽ‘4½¬[11ŽŽ‘ +]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(0Ž“)–8à°“±ptsŽ‘†¬[2Ž‘]);Ž¡‘µpŽ‘¬[9Ž–]µ:±shiftŽ‘}¬(µvŽ‘4½¬[15ŽŽ‘ +]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(0Ž“)–8à°“±ptsŽ‘†¬[2Ž‘]);Ž¡‘µpŽ‘¬[10ŽŽ– +]µ:±shiftŽ‘}¬(µvŽ‘4½¬[19ŽŽ“]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(0Ž›)–8à°“±ptsŽ‘†¬[2Ž˜]);Ž¡‘­forŽ‘%般(µiŽ‘9 ¬=‘Ç0Ž‘Ç;‘ÿýµiŽ‘ 9 <‘Ǭ11ŽŽ‘ Ç;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)‘µpŽ‘ +¬[µiŽ‘qô¬]µ:±dr‘ÿ}'awŽ‘(Û¬(‘ª¨);Ž¡‘­returnŽ‘4‘g¬;Ž¡‘ +°gŽ¤­1520.‘ üSemi-Regular–ÕTArcš®9himedean“P˜olyhedra.Ž¡1521.‘ üT‘ÿ +«runcated‘ÕTOctahedron.Ž¡1522.‘ üT‘ÿ +«runc‘°¡‰ffs4Ž‘#ÕOctahedron–ÕTclass“de nition.Ž©°h–ª¨¬De ne‘UU­classŽ‘5¦T‘ÿ +«runcu½‰™šs4Ž‘ÔwOctahedronŽ’€DT¯1522“°i‘ÇŽ¤ ‘ +­classŽ‘$àRT‘ÿ +«runcu½‰™šs4Ž‘ÔwOctahedronŽ’†Q¬:‘qÇ­publicŽ‘'ñP®9olyhedronŽ‘dh°fŽ¡‘ +­protectedŽ‘:o™¬:‘­staticŽ‘$HÙconstŽ‘Bs{realŽ‘Y&©±angle‘‰ffŽ–®hex‘‰ffŽ“squar‘ÿ}'eŽ’¢Œ¬;‘µ=°‘ÿý¬In‘UUradians!‘o°µ=Ž¡‘­staticŽ‘3HÛconstŽ‘Qs}realŽ‘h&«±angle‘‰ffŽ–®hex‘‰ffŽ“hexŽ’¤j5¬;‘µ=°‘ÿý¬In‘UUradians!‘o°µ=Ž¡‘­realŽ‘*³0±hexagon‘‰ffŽ‘®r‘ÿ}'adiusŽ‘lô¹¬;Ž¦‘ +­publicŽ‘)=Ö¬:‘°h–ª¨¬Declare‘UU­T‘ÿ +«runcu½‰™šs4Ž‘ÔwOctahedronŽ‘dyT¬functions‘@¯1525“°iŽ¡‘ +g¬;ŽŸ ¯This–ÕXcoÝÑT‘ÿ +«runcu½‰™šs4Ž‘ÔwOctahedronŽ’¬¬::‘±angle‘‰ffŽ–®hex‘‰ffŽ“squar‘ÿ}'eŽ‘Lµÿ¬=‘Ç(125ŽŽ‘8ã+›8à(16µ:¬0ŽŽ–Ç µ=¬60µ:¬0ŽŽ“))˜°˜¬(´PIŽ‘ bµ=¬180µ:¬0ŽŽ‘Ç!);Ž¡‘ +­constŽ‘(*£realŽ‘>ÝÑT‘ÿ +«runcu½‰™šs4Ž‘ÔwOctahedronŽ’¬¬::‘±angle‘‰ffŽ–®hex‘‰ffŽ“hexŽ‘@ +¦¬=‘Ç(109ŽŽ‘8ã+›8à(28µ:¬0ŽŽ–Ç µ=¬60µ:¬0ŽŽ“))˜°˜¬(´PIŽ‘ bµ=¬180µ:¬0ŽŽ‘Ç!);ŽŸ ¯This–ÕXcoi|¬.‘ÌÈ[²LDF‘T2002.10.29.¬]Ž‘SóXT‘ÿ*ªruncated–s«oGctahedrons“consist“of“6“squaresŽ¡‘(and–UU8“hexagons.‘o°µ=Ž¡‘±vertic‘ÿ}'esŽ‘8±X¬=‘Ç24ŽŽ‘ Ç;Ž¡‘±e‘ÿ}'dgesŽ‘.™1¬=‘Ç36ŽŽ‘ Ç;Ž¡‘±c‘ÿ}'enterŽ‘2Ð¥¬=‘Ç´INVALID_POINTŽ‘GY¬;‘µ=°‘ÿý¬from‘UU­P®9olyhedronŽ‘=c"¬.‘o°µ=Ž¡‘±numb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜olygon‘‰ffŽ“typ˜esŽ’R9¬=‘Ç2Ž‘Ç;Ž¡‘±fac–ÿ}'e‘‰ffŽ‘®r“adiusŽ‘G%¬=‘DZe–ÿ}'dge‘‰ffŽ‘®r“adiusŽ‘7j¬=‘DZvertex‘‰ffŽ‘®r‘ÿ}'adiusŽ‘>þ¨¬=‘Ç´INVALID_REALŽ‘BM\¬;Ž¡‘±hexagon‘‰ffŽ‘®r‘ÿ}'adiusŽ‘Y£¬=‘Ç´INVALID_REALŽ‘BM\¬;Ž¡‘ +°gŽ¤ ¯See–ÕXalso“sections“1529,“1531,“and“1532.Ž¡This–ÕXco@¬&Ž‘F%µpŽ‘K%;‘ª¨­constŽ‘ h.realŽ‘7®@±diameter‘‰ffŽ–®of‘‰ffŽ“hexagonŽ’‘µ;‘ª¨­realŽ‘ðº±angle‘‰ffŽ‘®xŽ‘=2~¬=‘»è0Ž‘»éµ;‘ª¨­realŽŽ¡‘±angle‘‰ffŽ‘®yŽ‘A2¦¬=‘Ç0Ž–ǵ;‘ª¨­realŽ‘]Ö±angle‘‰ffŽ‘®zŽ‘;$d¬=‘Ç0Ž“);Ž¡#­endifŽŽŽŽŒ‹Ñæ~ Šn ý‘ì°x¬1529–¯3DLDF-1.1.5.1’ÎãCONSTRÃŽUCTOR“¬465Ž €n ý•@P­1529.Ž©°h–ª¨¬De ne‘UU­T‘ÿ +«runcu½‰™šs4Ž‘ÔwOctahedronŽ‘dyT¬functions‘@¯1526“°i‘Ǭ+°Ž¤ ¬#­ifŽ‘ ´ø¬0ŽŽ¡‘ +­T‘ÿ +«runcu½‰™šs4Ž‘ÔwOctahedronŽ‘hί¬::‘­T‘ÿ +«runcu½‰™šs4Ž‘ÔwOctahedronŽ‘^ή¬(­constŽ‘˜7P•®9oin“tŽ‘=õi¬&Ž‘E¼‡µpŽ‘Jć;‘ª¨­constŽ‘ BßrealŽ‘7c¢±hexagon‘‰ffŽ‘®diameterŽ’…§ýµ;‘ª¨­realŽŽ¡‘2±angle‘‰ffŽ‘®xŽ‘R…áµ;‘ª¨­realŽ‘]Ö±angle‘‰ffŽ‘®yŽ‘8Éaµ;‘ª¨­realŽ‘]Ö±angle‘‰ffŽ‘®zŽ‘8]L¬)°f‘UU­b•QÇo“olŽ‘ö»´DEBUGŽ‘:„,¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¦‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘±c‘ÿ}'outŽ‘ O°‘Ç´"Entering® ´Trunc_OctaŽ‘kÆÜhedron::Trunc_OctaheŽ’ÔÆ dron().\n"Ž’ ”°‘DZ ushŽ‘€¬;Ž¡‘±c‘ÿ}'enterŽ‘<Ц¬=‘ǵpŽ‘Ϭ;Ž¡‘±on‘‰ffŽ›®fr–ÿ}'e“e‘‰ffŽ˜stor“eŽ‘Xl ¬=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý¬from‘UU­SolidŽ‘Ó,¬.‘o°µ=Ž¡‘±do‘‰ffŽ‘®outputŽ‘K½N¬=‘DZtrueŽ‘‹°¬;‘µ=°‘ÿý¬ST–ÿ*ªAR“T–UUHERE.“TO“DO:“Must“calculate“these!‘o°µ=Ž¡‘±fac–ÿ}'e‘‰ffŽ‘®r“adiusŽ‘Q&¬=‘Ç0Ž‘Ç;Ž¡‘±e–ÿ}'dge‘‰ffŽ‘®r“adiusŽ‘R£­¬=‘Ç0Ž‘Ç;Ž¡‘±vertex‘‰ffŽ‘®r‘ÿ}'adiusŽ‘Z7“¬=‘Ç0Ž‘Ç;Ž¡‘±fac‘ÿ}'esŽ‘7«¬=‘Ç14ŽŽ‘ Ç;‘µ=°‘îc¬from‘C»­Solidu½‰™šs4Ž‘ÔwF‘ÿ +«acedŽ‘>9Œ¬.‘ké[²LDF‘T2002.10.29.¬]Ž‘Sb‰T‘ÿ*ªruncated–C»oGctahedrons“consist“of“6“squaresŽ¡‘2and–UU8“hexagons.‘o°µ=Ž¡‘±vertic‘ÿ}'esŽ‘B±Y¬=‘Ç24ŽŽ‘ Ç;Ž¡‘±e‘ÿ}'dgesŽ‘8™2¬=‘Ç36ŽŽ‘ Ç;Ž¡‘±numb›ÿ}'er‘‰ffŽ–®of‘‰ffŽ“p˜olygon‘‰ffŽ“typ˜esŽ’‹R:¬=‘Ç2Ž‘Ç;Ž¡‘±hexagon‘‰ffŽ‘®r‘ÿ}'adiusŽ‘c¤¬=‘DZhexagon‘‰ffŽ‘®diameterŽ‘Q sµ=¬2µ:¬0ŽŽ‘ Ç;Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘Vºk¬=‘DZget‘‰ffŽ‘®netŽ‘!ûà¬(±hexagon‘‰ffŽ‘®diameterŽ‘ND[µ;‘ª¨±trueŽ‘o@¬);Ž¦‘­P•®9oin“tŽ‘<ï ±ptsŽ‘JÊF¬[24ŽŽ‘ +];Ž¡‘­in®9tŽ‘/¤úµiŽ‘3î¬;Ž¦‘­forŽ‘/艬(µiŽ‘9 ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ6Ž“;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)‘±ptsŽ‘Ú¦¬[µiŽ›qô¬]–Ç=“±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh¬[0Ž‘]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(µiŽ˜¬);Ž¡#­ifŽ‘ ´ø¬0ŽŽ¡‘±ptsŽ‘+Ú©¬[0Ž–]µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(0Ž“);Ž¡‘±ptsŽ‘+Ú©¬[1Ž–]µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(1Ž“µ;‘ª¨´"lft"Ž‘q¬);Ž¡‘±ptsŽ‘+Ú©¬[2Ž–]µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(2Ž“µ;‘ª¨´"bot"Ž‘q¬);Ž¡‘±ptsŽ‘+Ú©¬[3Ž–]µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(3Ž“µ;‘ª¨´"bot"Ž‘q¬);Ž¡‘±ptsŽ‘+Ú©¬[4Ž–]µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(4Ž“µ;‘ª¨´"rt"Ž‘1¬);Ž¡‘±ptsŽ‘+Ú©¬[5Ž–]µ:±dotlab‘ÿ}'elŽ‘!ÿó¬(5Ž“);Ž¡#­endifŽŽ¦‘realŽ‘4³1±angle‘‰ffŽ–®h‘‰ffŽ“hŽ‘`Óª¬=‘Ç180µ:¬0ŽŽ‘Ç°–8à¬(±angle‘‰ffŽ–®hex‘‰ffŽ“hexŽ‘>|j°“¬180µ:¬0ŽŽ‘µ=´PIŽ‘ b¬);Ž¦‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS¬[1Ž–]‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(±ptsŽ‘ Ú¦¬[4Ž“]µ;‘ª¨±ptsŽ‘…N¬[5Ž“]µ;‘ª¨±angle‘‰ffŽ–®h‘‰ffŽ“hŽ‘+ ¬);Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS¬[2Ž–]‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(±ptsŽ‘ Ú¦¬[3Ž“]µ;‘ª¨±ptsŽ‘…N¬[2Ž“]µ;‘ª¨°Ž‘ qƱangle‘‰ffŽ–®h‘‰ffŽ“hŽ‘2Ë'¬);Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS¬[3Ž–]‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(±ptsŽ‘ Ú¦¬[0Ž“]µ;‘ª¨±ptsŽ‘…N¬[1Ž“]µ;‘ª¨±angle‘‰ffŽ–®h‘‰ffŽ“hŽ‘+ ¬);Ž¦‘­realŽ‘4³1±angle‘‰ffŽ–®h‘‰ffŽ“sŽ‘_Û¸¬=‘Ç180µ:¬0ŽŽ‘Ç°–8à¬(±angle‘‰ffŽ–®hex‘‰ffŽ“squar‘ÿ}'eŽ‘K'ð“¬180µ:¬0ŽŽ‘µ=´PIŽ‘ b¬);Ž¦‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS¬[4Ž–]‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(±ptsŽ‘ Ú¦¬[0Ž“]µ;‘ª¨±ptsŽ‘…N¬[5Ž“]µ;‘ª¨±angle‘‰ffŽ–®h‘‰ffŽ“sŽ‘* ¬);Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS¬[5Ž–]‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(±ptsŽ‘ Ú¦¬[1Ž“]µ;‘ª¨±ptsŽ‘…N¬[2Ž“]µ;‘ª¨±angle‘‰ffŽ–®h‘‰ffŽ“sŽ‘* ¬);Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS¬[6Ž–]‘þŸµ~ŽŽ‘±r‘ÿ}'otateŽ‘o?¬(±ptsŽ‘ Ú¦¬[3Ž“]µ;‘ª¨±ptsŽ‘…N¬[4Ž“]µ;‘ª¨±angle‘‰ffŽ–®h‘‰ffŽ“sŽ‘* ¬);Ž¡‘(µ=°‘ÿý¬[²LDF‘T2002.11.07.¬]Ž‘T7Do–UUsomething“abGout“these“commen¸ãts!‘o°µ=‘=°–ÿý¬7“°µ=Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóSµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘G›!µ>‘Ǭ(±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP¬[0Ž‘])–UU)“;‘µ=°–ÿý¬8“°µ=Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóSµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘G›!µ>‘Ǭ(±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP¬[1Ž‘])–UU)“;‘µ=°–ÿý¬9“°µ=Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóSµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘G›!µ>‘Ǭ(±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP¬[2Ž‘])–UU)“;‘µ=°–ÿý¬10“°µ=Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóSµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘G›!µ>‘Ǭ(±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP¬[3Ž‘])–UU)“;‘µ=°–ÿý¬11“°µ=Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóSµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘G›!µ>‘Ǭ(±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP¬[4Ž‘])–UU)“;‘µ=°–ÿý¬12“°µ=Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóSµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘G›!µ>‘Ǭ(±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP¬[5Ž‘])–UU)“;‘µ=°–ÿý¬13“°µ=Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóSµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘G›!µ>‘Ǭ(±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP¬[6Ž‘])–UU)“;Ž¦‘­T‘ÿ +«ransformŽ‘UÈÕµtŽ‘YeG¬;Ž¦‘µtŽ‘!œu:±r‘ÿ}'otateŽ‘o>¬(180ŽŽ‘);Ž¡‘µtŽ‘!œu:±shiftŽ‘}¬(0Ž‘µ;‘ª¨¬15ŽŽ‘ ªª);Ž¡‘­forŽ‘/艬(µiŽ‘9 ¬=‘Ç7Ž‘Ç;‘ÿýµiŽ‘ 9 <‘Ǭ14ŽŽ‘ Ç;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)‘°Ž‘ +±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQ¬[µiŽ‘qô¬]‘Ç°¬=ŽŽ‘UOµtŽ‘ñÁ¬;ŽŽŽŒ‹ÒîÌ Šn ý‘ì¬466–¯CONSTRÃŽUCTOR’Îã3DLDF-1.1.5.1“°x¬1529Ž €n ý•@P‘µtŽ‘!œu:±r‘ÿ}'esetŽ‘Æ·¬(‘ª¨);Ž¤ ‘µtŽ‘!œu:±shiftŽ‘}¬(±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP¬[2Ž–]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ›+bI¬(2Ž“)–8à°“±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8,0¬[11ŽŽ‘ +]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ˜¬(3Ž‘));Ž¡‘­forŽ‘/艬(µiŽ‘9 ¬=‘Ç7Ž‘Ç;‘ÿýµiŽ‘ 9 <‘Ǭ14ŽŽ‘ Ç;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)‘°Ž‘ +±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQ¬[µiŽ‘qô¬]‘Ç°¬=ŽŽ‘UOµtŽ‘ñÁ¬;Ž¡‘µiŽ‘$9¬=‘Ç0Ž‘Ç;Ž¡‘­forŽ‘0- ¬(­v®9ectorŽ‘ªH°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘E°Ž‘JŽi‘¬::Ž‘ŽB±iter‘ÿ}'atorŽ‘)™7iterŽ‘=~¬=‘9I±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ–9,™µ:±b–ÿ}'e“ginŽ‘¾¨¬(›ª¨);‘D±iterŽ‘HÈ°6¬=‘9I±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ“µ:±endŽ‘ಬ(˜);Ž¡‘<€Ÿÿ³+‘ÿ+ŽŽ‘HG&±iterŽ‘Y$¬)‘°fŽ¡‘(­ifŽ‘3´ü¬(±c‘ÿ}'enterŽ‘У°6¬=‘DZoriginŽ‘½9¬)‘(°Ž‘Ž‘ +±iterŽ‘ˬ)µ:±shiftŽ‘}¬(±c‘ÿ}'enterŽ‘ ‹¬);Ž¡‘°gŽ¡‘­ifŽ‘)´û¬(´DEBUGŽ‘ÆY¬)‘°fŽ¡‘(±c‘ÿ}'outŽ‘> S°‘Ç´"Exiting® ´Trunc_OctahŽ‘kÆÜedron::Trunc_OctahedŽ’ÔÆ ron()."Ž’üÔ °‘DZend‘‚ØlŽ–ò°‘DZend‘‚ØlŽ“°‘DZ ushŽ‘€¬;Ž¡‘°gŽ¡‘­returnŽ‘>‘h¬;‘qÇ°gŽ¡¬#­endifŽŽŸ1530.‘ üGet‘ÕTnet.ŽŸŸû9ŸüÈ„`Ö+U‘ üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ +¬[²LDF‘T2002.11.08.¬]Ž‘Y;Added–UUthis“function.Ž¡‘ +[²LDF‘T2002.08.12.¬]Ž‘Y;Remo•¸ãv“ed‘UU±c‘ÿ}'enter‘‰ffŽ‘®0Ž‘+Æ1¬argumen“t.Ž¤ŸüÈ„`ÕÁGŽŽ¡°h–ª¨¬Declare‘UU­T‘ÿ +«runcu½‰™šs4Ž‘ÔwOctahedronŽ‘dyT¬functions‘@¯1525“°i‘Ǭ+°Ž¤ ¬#­ifŽ‘ ´ø¬0ŽŽ¡‘ +­staticŽ‘)HÚv®9ectorŽ‘Hó"°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘DÔ °Ž‘IÔ +i‘UU±get‘‰ffŽ‘®netŽ‘"Š¬(­constŽ‘*¢realŽ‘4Ýбhexagon‘‰ffŽ‘®diameterŽ’ƒ"+µ;‘ª¨­b•QÇo“olŽ‘L±do‘‰ffŽ‘®halfŽ‘>s¯¬=‘DZfalseŽ‘v\¬);Ž¡#­endifŽŽŽŽŒ‹Ó­ Šn ý‘ì°x¬1531–¯3DLDF-1.1.5.1’-š¹GET‘ÕXNET“¬467Ž €n ý•@P­1531.Ž©°h–ª¨¬De ne‘UU­T‘ÿ +«runcu½‰™šs4Ž‘ÔwOctahedronŽ‘dyT¬functions‘@¯1526“°i‘Ǭ+°Ž¤ ¬#­ifŽ‘ ´ø¬0ŽŽ¡‘ +­v®9ectorŽ‘)ªI°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘D䦰Ž‘Iä§i‘eò­T‘ÿ +«runcu½‰™šs4Ž‘ÔwOctahedronŽ‘b4 ¬::‘±get‘‰ffŽ‘®netŽ‘ 4̬(­constŽ‘;?realŽ‘4ÿ +±hexagon‘‰ffŽ‘®diameterŽ’ƒCeµ;‘ª¨­b•QÇo“olŽ‘\«±do‘‰ffŽ‘®halfŽ‘;½4¬)°fŽ¡‘2­b•QÇo“olŽ‘K¡k´DEBUGŽ‘i.ܬ=‘DZfalseŽ‘v\¬;‘µ=°‘ÿý±trueŽ‘Ä’°µ=Ž¦‘­v®9ectorŽ‘=ªK°h­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘DÔ °Ž‘IÔ +i‘UU±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘9H¥¬;Ž¡‘­in®9tŽ‘/¤úµiŽ‘3î¬;‘qDZr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:eµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘G›!µ>‘Ǭ(0Ž‘)–UU)“;Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS¬[0Ž‘]‘þŸµ~ŽŽ‘±setŽ‘x…¬(±originŽ‘ö!µ;‘ª¨¬6Ž‘ª©µ;‘ª¨±hexagon‘‰ffŽ‘®diameterŽ‘Oï¬);Ž¦‘­P•®9oin“tŽ‘<ï ±ptsŽ‘JÊF¬[24ŽŽ‘ +];Ž¦‘­forŽ‘/艬(µiŽ‘9 ¬=‘Ç0Ž–Ç;‘ÿýµiŽ‘ 9 <‘Ǭ6Ž“;‘ÿýµiŽ‘ññŸÿ³+‘ÿ+ŽŽ‘¹¬)‘±ptsŽ‘Ú¦¬[µiŽ›qô¬]–Ç=“±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh¬[0Ž‘]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(µiŽ˜¬);Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóSµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘G›!µ>‘Ǭ(±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP¬[0Ž‘])–UU)“;Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS¬[1Ž–]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[4Ž“]–P°“±ptsŽ‘*Ŭ[2Ž‘]);‘ø6±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:놵:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘0Pˆ¬(‘ø6±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘9€0µ<Ž¡‘2­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘vEѵ>‘Ǭ(±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP¬[0Ž‘])–UU)“;Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS¬[2Ž–]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[3Ž“]–P°“±ptsŽ‘*Ŭ[5Ž‘]);‘ø6±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:놵:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘0Pˆ¬(‘ø6±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘9€0µ<Ž¡‘2­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘vEѵ>‘Ǭ(±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP¬[0Ž‘])–UU)“;Ž¡‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘SóS¬[3Ž–]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[1Ž“]–8à°“±ptsŽ‘†¬[3Ž‘]);Ž¦‘­realŽ‘4³1±side‘‰ffŽ‘®lengthŽ‘g ¬=‘DZptsŽ‘¡¾¬[5Ž›]µ:±get‘‰ffŽ‘®xŽ‘Žg¬(‘ª¨)–8à°“±ptsŽ‘†¬[0Ž˜]µ:±get‘‰ffŽ‘®xŽ‘Žg¬(‘ª¨);Ž¦‘±ptsŽ‘+Ú©¬[6Ž›]–Ç=“±ptsŽ‘¡¾¬[0Ž˜];Ž¡‘±ptsŽ‘+Ú©¬[6Ž–]µ:±shiftŽ‘}¬(0Ž“µ;‘ª¨¬0Ž‘ª©µ;‘ª¨±side‘‰ffŽ‘®lengthŽ‘1Mh¬);Ž¡‘±ptsŽ‘+Ú©¬[7Ž›]–Ç=“±ptsŽ‘¡¾¬[5Ž˜];Ž¡‘±ptsŽ‘+Ú©¬[7Ž–]µ:±shiftŽ‘}¬(0Ž“µ;‘ª¨¬0Ž‘ª©µ;‘ª¨±side‘‰ffŽ‘®lengthŽ‘1Mh¬);Ž¦‘­RectangleŽ‘SεrŽ‘WÞâ¬(±ptsŽ‘ Ú¦¬[0Ž–]µ;‘ª¨±ptsŽ›…N¬[5Ž“]µ;‘ª¨±ptsŽ˜¬[7Ž“]µ;‘ª¨±ptsŽ˜¬[6Ž“]);‘Õ6±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8Ȇµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.-ˆ¬(‘Õ6±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘5:0µ<‘Õ6­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘Gµ>‘Ǭ(µrŽ‘ʬ)Ž¡‘2)‘UU;Ž¡‘±ptsŽ‘+Ú©¬[8Ž›]–Ç=“±ptsŽ‘¡¾¬[2Ž˜];Ž¡‘±ptsŽ‘+Ú©¬[9Ž›]–Ç=“±ptsŽ‘¡¾¬[1Ž˜];Ž¡‘±ptsŽ‘+Ú©¬[9Ž–]µ:±shiftŽ‘}¬(0Ž“µ;‘ª¨¬1Ž‘ª©);Ž¡‘±ptsŽ‘+Ú©¬[8Ž–]µ:±r‘ÿ}'otateŽ‘o>¬(±ptsŽ‘ Ú¦¬[9Ž“]µ;‘ª¨±ptsŽ‘…N¬[1Ž“]µ;‘ª¨°Ž‘ qƬ90ŽŽ‘qÈ);Ž¡‘±ptsŽ‘+Ú©¬[10ŽŽ‘ +]–Ç=“±ptsŽ‘¡¾¬[8Ž‘];Ž¡‘±ptsŽ‘+Ú©¬[10ŽŽ‘ +]µ:±shiftŽ‘}¬(±ptsŽ‘ Ú¦¬[2Ž›]–8à°“±ptsŽ‘†¬[1Ž˜]);Ž¡‘µrŽ‘"Ê:±setŽ‘ x„¬(±ptsŽ‘ Ú¦¬[10ŽŽ‘ +]µ;‘ª¨±ptsŽ–…N¬[2Ž›]µ;‘ª¨±ptsŽ“¬[1Ž˜]µ;‘ª¨±ptsŽ“¬[8Ž˜]);‘UU±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘9H¥µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘G›!µ>‘Ǭ(µrŽ‘ʬ)–UU)“;Ž¡‘±ptsŽ‘+Ú©¬[11ŽŽ‘ +]–Ç=“±ptsŽ‘¡¾¬[3Ž‘];Ž¡‘±ptsŽ‘+Ú©¬[12ŽŽ‘ +]–Ç=“±ptsŽ‘¡¾¬[4Ž‘];Ž¡‘±ptsŽ‘+Ú©¬[12ŽŽ‘ +]µ:±shiftŽ‘}¬(0Ž‘µ;‘ª¨¬1Ž‘ª©);Ž¡‘±ptsŽ‘+Ú©¬[11ŽŽ– +]µ:±r‘ÿ}'otateŽ‘o>¬(±ptsŽ‘ Ú¦¬[4Ž‘]µ;‘ª¨±ptsŽ‘…N¬[12ŽŽ“]µ;‘ª¨¬90ŽŽ‘ ªª);Ž¡‘±ptsŽ‘+Ú©¬[13ŽŽ› +]–Ç=“±ptsŽ‘¡¾¬[11ŽŽ˜];Ž¡‘±ptsŽ‘+Ú©¬[13ŽŽ‘ +]µ:±shiftŽ‘}¬(±ptsŽ‘ Ú¦¬[3Ž›]–8à°“±ptsŽ‘†¬[4Ž˜]);Ž¡‘µrŽ‘"Ê:±setŽ‘ x„¬(±ptsŽ‘ Ú¦¬[11ŽŽ‘ +]µ;‘ª¨±ptsŽ–…N¬[4Ž›]µ;‘ª¨±ptsŽ“¬[3Ž˜]µ;‘ª¨±ptsŽ“¬[13ŽŽ‘ +]);‘UU±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘9H¥µ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘G›!µ>‘Ǭ(µrŽ‘ʬ)–UU)“;Ž¡‘­ifŽ‘)´û¬(±do‘‰ffŽ‘®halfŽ‘ `‰¬)‘­returnŽ‘(溱r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘^Ú +¬;Ž¡#­endifŽŽŽŽŒ‹Ô‹ Šn ý‘ì¬468–¯GET‘ÕXNET’-š¹3DLDF-1.1.5.1“°x¬1532Ž €n ý•@P­1532.‘ ü¬[²LDF‘T2002.11.08.¬]Ž‘[ÇÓIf–”òwš¸ãe“just“w˜an˜t“the“net,‘äÙ±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:Ø)¬[5Ž›]“and“±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:ˆB¬[6Ž˜]“mš¸ãust“bGe“c˜hanged,Ž¤ bGecause–âQI'vš¸ãe“made“the“net“a“bit“di eren˜tly“from“the“w˜a˜y“it's“done“in“Cundy‘ÿ*ª.›¼Get“reference!!˜P¸ãage“104.˜IŽ¡made›UUt•¸ãw“o˜of˜the˜squares˜slan“ted,˜in˜order˜to˜a“v“oid˜ha“ving˜to˜rotate˜them˜t“wice.Ž©°h–ª¨¬De ne‘UU­T‘ÿ +«runcu½‰™šs4Ž‘ÔwOctahedronŽ‘dyT¬functions‘@¯1526“°i‘Ǭ+°Ž¡¬#­ifŽ‘ ´ø¬0ŽŽ¡‘ +°Ž‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘DóR¬[6Ž›]–Ç=“°Ž‘DZr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘=ºi¬[5Ž˜]“=“°Ž‘DZr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘=ºi¬[4Ž˜];Ž¡‘ +±ptsŽ‘Ú§¬[14ŽŽ‘ +]–Ç=“±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh¬[4Ž–]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(2Ž“);Ž¡‘ +±ptsŽ‘Ú§¬[15ŽŽ‘ +]–Ç=“±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘8ºh¬[4Ž–]‘þŸµ~ŽŽ‘±get‘‰ffŽ‘®p‘ÿ}'ointŽ‘+bI¬(3Ž“);Ž¡‘ +±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQ¬[5Ž–]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[1Ž“]–8à°“±ptsŽ‘†¬[14ŽŽ‘ ]);Ž¡‘ -Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQ±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘B~¸«::Ž‘I öÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“r–ÿ}'e“g‘‰ffŽ‘®p“olygonŽ’¬ƒ8«(Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP«[0Ž‘]));‘±=·–ÿý«7“·±=Ž¡‘ -Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQ±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘B~¸«::Ž‘I öÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“r–ÿ}'e“g‘‰ffŽ‘®p“olygonŽ’¬ƒ8«(Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP«[4Ž‘]));‘±=·–ÿý«8“·±=Ž¡‘ -·Ž‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘DóR«[7Ž–]‘Ç·«=ŽŽ‘UOÏr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘HHŸ«[8Ž“]‘þŸ±~ŽŽ‘ÏshiftŽ‘~«(ÏptsŽ‘ Ú¦«[1Ž“]–8à+“ÏptsŽ›†«[2Ž‘]“·“ÏptsŽ˜«[3Ž‘]“·“ÏptsŽ˜«[4Ž‘]);Ž¡‘ -Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQ±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘B~¸«::Ž‘I öÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“r–ÿ}'e“g‘‰ffŽ‘®p“olygonŽ’¬ƒ8«(Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP«[0Ž‘]));‘±=·–ÿý«9“·±=Ž¡‘ -Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQ«[9Ž–]‘þŸ±~ŽŽ‘ÏshiftŽ‘~«(ÏptsŽ‘ Ú¦«[4Ž“]–8à+“ÏptsŽ›†«[0Ž‘]“·“«(2Ž‘8á·“ÏptsŽ˜«[2Ž‘]));Ž¡‘ -Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQ±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘B~¸«::Ž‘I öÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“r–ÿ}'e“g‘‰ffŽ‘®p“olygonŽ’¬ƒ8«(Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP«[4Ž‘]));‘±=·–ÿý«10“·±=Ž¡‘ -Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQ±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘B~¸«::Ž‘I öÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“r–ÿ}'e“g‘‰ffŽ‘®p“olygonŽ’¬ƒ8«(Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP«[0Ž‘]));‘±=·–ÿý«11“·±=Ž¡‘ -Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQ±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘B~¸«::Ž‘I öÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“r–ÿ}'e“g‘‰ffŽ‘®p“olygonŽ’¬ƒ8«(Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP«[1Ž‘]));‘±=·–ÿý«12“·±=Ž¡‘ -Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQ±:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘B~¸«::Ž‘I öÏcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“r–ÿ}'e“g‘‰ffŽ‘®p“olygonŽ’¬ƒ8«(Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP«[6Ž‘]));‘±=·–ÿý«13“·±=Ž¡‘ -·Ž‘Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘DóR«[10ŽŽ– +±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQ¬[6Ž–]‘þŸµ~ŽŽ‘±shiftŽ‘~¬(±ptsŽ‘ Ú¦¬[4Ž“]–wN°“±ptsŽ‘Qô¬[15ŽŽ‘ 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Ú¦¬[4Ž“]–ã¨+“±ptsŽ›¾N¬[0Ž‘]“°“¬(2Ž‘ã©°“±ptsŽ˜¬[2Ž‘]));‘Uƒ±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘:HÓµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘/­Õ¬(‘Uƒ±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘8:ʵ<Ž¡‘­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘bEϵ>‘Ǭ(±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP¬[4Ž‘])–UU)“;‘µ=°–ÿý¬10“°µ=Ž¡‘ +±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘G›!µ>‘Ǭ(±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP¬[0Ž‘])–UU)“;‘µ=°–ÿý¬11“°µ=Ž¡‘ +±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘G›!µ>‘Ǭ(±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP¬[1Ž‘])–UU)“;‘µ=°–ÿý¬12“°µ=Ž¡‘ +±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘?óQµ:±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘.­§¬(‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘6:nµ<‘UU­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘G›!µ>‘Ǭ(±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘5óP¬[6Ž‘])–UU)“;‘µ=°–ÿý¬13“°µ=Ž¡‘ +°Ž‘±r–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ‘DóR¬[10ŽŽ– ]‘D -·«=ŽŽ‘O3·Ž‘ O4Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ›VB„«[11ŽŽ“]‘D -·«=ŽŽ‘O3·Ž‘ O4Ïr–ÿ}'e“g‘‰ffŽ‘®p“olygonsŽ˜«[12ŽŽ“]‘D 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-±vŽ‘4¾:Ïpush‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR«(&Ž‘ÇÏviolet‘‰ffŽ‘®r–ÿ}'e“dŽ‘1)¿«);Ž¡#ÂendifŽŽ¡«#ÂendifŽŽ¤ ­See–ÕXalso“section“1506.Ž¡This–ÕXco{Added–‹•coGde“for“handling“the“\È--silent«"“option,‘³ïincluding“the“constan¸ãt“ÝSILENT_INDEXŽ‘BÙ«.Ž¤ŸüÈ„`ÕÁGŽŽ¡·h›ª¨«GCC–UUcommand“line“option“proGcessing‘@­1508˜·i‘ÇŽ¤ ‘ -fŽ¡‘Âb•QÇo“olŽ‘-¡hÝDEBUGŽ‘K.Ù«=‘ÇÏfalseŽ‘v\«;‘±=·–ÿý«true“·±=Ž¡‘Âin®9tŽ‘%¤ùÏoption‘‰ffŽ‘®ctrŽ‘Re«;Ž¡‘Âin®9tŽ‘%¤ùÏdigit‘‰ffŽ‘®optindŽ‘\(L«=‘Ç0Ž‘Ç;Ž¡‘ÂconstŽ‘2*¤unsignedŽ‘ba²shortŽ’€,UÝHELP_INDEXŽ’·ù·«=‘Ç0Ž‘Ç;Ž¡‘ÂconstŽ‘2*¤unsignedŽ‘ba²shortŽ’€,UÝSILENT_INDEXŽ’Ây±«=‘Ç1Ž‘Ç;Ž¡‘ÂconstŽ‘2*¤unsignedŽ‘ba²shortŽ’€,UÝVERBOSE_INDEXŽ’ǹ®«=‘Ç2Ž‘Ç;Ž¡‘ÂconstŽ‘2*¤unsignedŽ‘ba²shortŽ’€,UÝVERSION_INDEXŽ’ǹ®«=‘Ç3Ž‘Ç;Ž¡‘ÂstaticŽ‘3HÛstructŽ‘TèÒÏoptionŽ‘t݇long‘‰ffŽ‘®optionsŽ’«2ÿ«[‘ª®]–Ç=“·ffÝ"help"Ž‘ V±;‘ª¨«0Ž–ª©±;‘ª¨«0Ž“±;‘ª¨«0Ž“·g±;–ª¨·fÝ"silent"Ž‘*†P±;“«0Ž›ª©±;“«0Ž˜±;“«0Ž˜·g±;“·fÝ"verbose"Ž‘/ÆM±;“«0Ž˜±;“«0Ž˜±;“«0Ž˜·g±;Ž¡‘(·fÝ"version"Ž‘/ÆM±;‘ª¨«0Ž–ª©±;‘ª¨«0Ž“±;‘ª¨«0Ž“·g±;–ª¨·f«0Ž‘±;“«0Ž›ª©±;“«0Ž˜±;“«0Ž˜·gg«;Ž¡‘Âin®9tŽ‘%¤ùÏoption‘‰ffŽ‘®indexŽ‘`3Q«=‘Ç0Ž‘Ç;Ž¡‘Âin®9tŽ‘%¤ùÏthis‘‰ffŽ–®option‘‰ffŽ“optindŽ‘wš›«=‘ÇÏoptindŽ–"q¶«?‘ÇÏoptindŽ“«:‘Ç1Ž‘Ç;ŽŸ‘ÂwhileŽ‘2C.«(1Ž‘)‘·fŽ¡‘Ïoption‘‰ffŽ‘®ctrŽ‘M‡?«=‘ÇÏgetopt‘‰ffŽ–®long‘‰ffŽ“onlyŽ‘I¢«(Ïar‘ÿ}'gcŽ‘ʱ;‘ª¨Ïar‘ÿ}'gvŽ‘EI±;‘ª¨Ý"hv"Ž‘1±;‘ª¨Ïlong‘‰ffŽ‘®optionsŽ‘8 ±;‘ª¨«&Ž‘ qÆÏoption‘‰ffŽ‘®indexŽ‘A9«);Ž¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÝ"option_ctrÈ Ý==È Ý"Ž‘Zh·‘ÇÏoption‘‰ffŽ‘®ctrŽ‘2NT·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÝ"option_indexÈ Ý==È Ý"Ž‘d”b·‘ÇÏoption‘‰ffŽ‘®indexŽ‘=Up·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘(Ïc‘ÿ}'outŽ‘> S·‘ÇÝ"optargÈ Ý==È Ý"Ž‘Et·‘ÇÏoptar‘ÿ}'gŽ‘!é…·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¡‘ÂifŽ‘)´û«(Ïoption‘‰ffŽ‘®ctrŽ‘/‡<·‘ÇŽ‘ -Ž6«1Ž‘Ž7)‘·fŽ¡‘(ÂifŽ‘3´ü«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"NoÈ ÝmoreÈ Ýoptions."Ž‘d”b·‘ÇÏend‘‚ØlŽ–ò·‘ÇÏend‘‚ØlŽ“·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂbreakŽ‘D¡h«;Ž¡‘·gŽ¡‘ÂifŽ‘)´û«(Ïoption‘‰ffŽ‘®ctrŽ‘/‡<·‘Ç«0Ž‘Ç)‘·fŽ¡‘(ÂifŽ‘3´ü«(ÝDEBUGŽ‘ÆY«)‘·fŽ¡‘2Ïc‘ÿ}'outŽ‘H T·‘ÇÝ"optionÈ Ý"Ž‘5T}·‘ÇÏlong‘‰ffŽ‘®optionsŽ‘9«[Ïoption‘‰ffŽ‘®indexŽ‘7Ç@«]±:ÏnameŽ‘Æ«;Ž¡‘2ÂifŽ‘=´ý«(Ïoptar‘ÿ}'gŽ‘[U«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"È ÝwithÈ ÝargÈ Ý"Ž‘Et·‘ÇÏoptar‘ÿ}'gŽ‘"m«;Ž¡‘2Ïc‘ÿ}'outŽ‘H T·‘ÇÏend‘‚ØlŽ‘¸Ú«;Ž¡‘(·gŽ¡‘(ÂifŽ‘3´ü«(Ïoption‘‰ffŽ‘®indexŽ‘:ŽX·‘ÇÝHELP_INDEXŽ‘7Íb«)‘·fŽ¡‘2Ïc‘ÿ}'outŽ‘Iµý·‘\ÁÝ"3DLDFÈ ÝVersionÈ Ý"Ž‘]?º·‘\ÁÝVERSION_3DLDFŽ‘M÷‘\ÁÝ".È Ý"Ž‘?Þ·‘\ÁÝCOPYRIGHT_3DLDFŽ‘Wÿ½·Ž¡‘FÏend‘‚ØlŽ‘`“·‘¡RÝ"ValidÈ ÝoptionsÈ ÝforÈ Ý3Ž‘o¡DLDFÈ Ýare:"Ž’«H²·‘¡RÏend‘‚ØlŽ‘!4f·Ž¡‘FÝ"--help:È ÝPrintsŽ’®ÿËÈ ÝthisÈ ÝmessageÈ ÝandÈ ÝexŽ’ÿitsÈ Ý"Ž’6@·‘AXÝ"withÈ ÝreturnÈ ÝvalueÈ Ý0Ž‘lA."Ž‘zˆÖ·Ž¡‘FÏend‘‚ØlŽ‘]>×·‘MÏend‘‚ØlŽ‘‹Þ·‘MÝ"--silent:È ÝSuppreŽ‘lLÒssesÈ ÝsomeÈ ÝoutputÈ ÝtoÈ Ž’ÕL–ÝstandardÈ Ýoutput"Ž’-Ü·Ž¡‘FÏend‘‚ØlŽ‘]Áõ·‘Ð,Ý"È ÝandÈ ÝstŽ‘lÏðandardÈ ÝerrorÈ ÝwhenÈ Ý3dŽ’ÕÏ´ldfÈ ÝisÈ Ýrun."Ž’&$·‘Ð,Ïend‘‚ØlŽ‘’·Ž¡‘FÏend‘‚ØlŽ‘^Q0·‘_gÝ"--verbose:È ÝCausesŽ‘m_+È ÝstatusÈ ÝinformationÈ Ž’Ö^ïÝtoÈ ÝbeÈ ÝprintedÈ Ý"Ž’*‘·Ž¡‘FÝ"toÈ ÝstandardÈ Ýoutput"Ž’³®Ø·‘(¥Ïend‘‚ØlŽ‘C ·‘(¥Ý"È ÝwhenÈ Ý3Ž‘m(idldfÈ ÝisÈ Ýrun."Ž’¶O·Ž¡‘FÏend‘‚ØlŽ‘]@ ·‘NDÏend‘‚ØlŽ–ŽJ·‘NDÝ"--version:È ÝPrintsŽ‘lNÈ ÝtheÈ ÝversionÈ ÝnumberÈ Ž’ÕMÌÝofÈ Ý3DLDF"Ž’b]·‘NDÏend‘‚ØlŽ“·Ž¡‘FÝ"È ÝtoÈ ÝstaŽ’®ÿËndardÈ ÝoutputÈ ÝandÈ Ý"Ž’iË·‘cÎÝ"exitsÈ ÝwithÈ ÝreturnÈ ÝvŽ‘lc’alueÈ Ý0."Ž’šM°·Ž¡‘FÏend‘‚ØlŽ‘\¸á·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘2ÂifŽ‘=´ý«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ExitingÈ ÝwithÈ ÝreturnŽ‘kÆÜÈ ÝvalueÈ Ý0."Ž’£”>·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘2ÏexitŽ‘Cf«(0Ž‘);Ž¡‘(·gŽ¡‘(ÂelseŽ‘>.8ifŽ‘Iã0«(Ïoption‘‰ffŽ‘®indexŽ‘:ŽX·‘ÇÝSILENT_INDEXŽ‘BM\«)‘·fŽ¡‘2ÂifŽ‘=´ý«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"SettingÈ ÝSILENT_GLOBŽ‘kÆÜALÈ ÝtoÈ Ýtrue."Ž’®8·‘ÇÏend‘‚ØlŽ‘¸Ú«;ŽŽŽŒ‹ÖwÚ Šn ý‘ì«470‘­PRšÃŽOCESS–ÕXCOMMAND“LINE“OPTIONS’Â$G3DLDFPR˜G‘·x«1508Ž €n ý•@P‘2ÝSILENT_GLOBALŽ‘y^«=‘ÇÏtrueŽ‘‹°«;Ž¤ ‘(·gŽ¡‘(ÂelseŽ‘>.8ifŽ‘Iã0«(Ïoption‘‰ffŽ‘®indexŽ‘:ŽX·‘ÇÝVERBOSE_INDEXŽ‘GY«)‘·fŽ¡‘2ÂifŽ‘=´ý«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"SettingÈ ÝVERBOSE_GLOŽ‘kÆÜBALÈ ÝtoÈ Ýtrue."Ž’³T5·‘ÇÏend‘‚ØlŽ‘¸Ú«;Ž¡‘2ÝVERBOSE_GLOBALŽ‘~Í[«=‘ÇÏtrueŽ‘‹°«;Ž¡‘(·gŽ¡‘(ÂelseŽ‘>.8ifŽ‘Iã0«(Ïoption‘‰ffŽ‘®indexŽ‘:ŽX·‘ÇÝVERSION_INDEXŽ‘GY«)‘·fŽ¡‘2Ïc‘ÿ}'outŽ‘H T·‘ÇÝ"3DLDFÈ ÝVersionÈ Ý"Ž‘Zh·‘ÇÝVERSION_3DLDFŽ‘JTq·‘ÇÝ".È Ý"Ž‘Œ·‘ÇÝCOPYRIGHT_3DLDFŽ‘TÔk·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘2ÂifŽ‘=´ý«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"ExitingÈ ÝwithÈ ÝreturnŽ‘kÆÜÈ ÝvalueÈ Ý0."Ž’£”>·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘2ÏexitŽ‘Cf«(0Ž‘);Ž¡‘(·gŽ¡‘(ÂelseŽ‘?Øã·fŽ¡‘2Ïc‘ÿ}'errŽ‘G|÷‘ÇÝ"ThisÈ Ýcan'tÈ Ýhappen!È Ž‘kÆÜÝ"Ž‘tTY·‘ÇÝ"option_indexÈ ÝhasÈ ÝinŽ‘kÆÜvalidÈ Ývalue:È Ý"Ž’¸”2·‘ÇÏoption‘‰ffŽ‘®indexŽ‘=Up·Ž¡‘FÏend‘‚ØlŽ‘\¸á·‘ÇÝ"WillÈ ÝtryÈ ÝtoÈ ÝcontinuŽ‘kÆÜe."Ž‘~ÔS·‘ÇÏend‘‚ØlŽ–ò·‘ÇÏend‘‚ØlŽ“·‘ÇÏ ushŽ‘€«;Ž¡‘(·gŽ¡‘gŽ¡‘ÂelseŽ‘4.7ifŽ‘?ã/«(Ïoption‘‰ffŽ‘®ctrŽ‘/‡<·‘ÇÝ'?'Ž‘ w«)‘·fŽ¡‘(Ïc‘ÿ}'errŽ‘=|·‘ÇÝ"getopt_long()È ÝreturŽ‘kÆÜnedÈ ÝambiguousÈ Ýmatch.Ž’ÔÆ È ÝBreaking."Ž’Óÿ·‘ÇÏend‘‚ØlŽ–ò·‘ÇÏend‘‚ØlŽ“·‘ÇÏ ushŽ‘€«;Ž¡‘(ÂbreakŽ‘D¡h«;Ž¡‘·gŽ¡‘ÂelseŽ‘5Øâ·fŽ¡‘(Ïc‘ÿ}'errŽ‘=|·‘ÇÝ"getopt_long()È ÝreturŽ‘kÆÜnedÈ ÝinvalidÈ Ýoption."Ž’Ø ·‘ÇÏend‘‚ØlŽ‘ò·‘ÇÏ ushŽ‘€«;Ž¡‘·gŽ¡‘ÂifŽ‘)´û«(ÝDEBUGŽ‘ÆY«)‘Ïc‘ÿ}'outŽ‘ O·‘ÇÝ"*******************Ž‘kÆÜ**\n\n"Ž’‘ /«;Ž¡‘·g‘±=·‘ÿýÂwhileŽ‘$íÑ·±=Ž¡‘ÂifŽ‘´ú«(ÏoptindŽ‘ªž±<‘ÇÏar‘ÿ}'gcŽ‘Þâ«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘4 R·‘ÇÝ"non-optionÈ ÝARGV-eleŽ‘kÆÜments:È Ý"Ž’–M,«;Ž¡‘ÂwhileŽ‘ŸÓVEŽ‘ãxXŽ‘Gsection‘UUabGo•¸ãv“e.‘o·±=Ž¤ ­See–ÕXalso“sections“1515,“1516,“1517,“1518,“and“1519.Ž¡This–ÕXco¸Þ·‘ÇÝ"ExitingÈ ÝwithÈ ÝreturnŽ‘kÆÜÈ ÝvalueÈ Ý1."Ž’£”>·‘ÇÏend‘‚ØlŽ–ò·‘ÇÏend‘‚ØlŽ“·‘ÇÏ ushŽ‘€«;Ž¦‘ÏexitŽ‘%c«(1Ž‘);Ž¦‘ -·gŽŽŽŒ‹Ù  Šn ý‘ì·x«1516–­3DLDFPRÃŽG’$ËÁMAIN‘ÕXITSELF“«473Ž €n ý•@PÂ1516.‘ ü«This–„—tests“whether“ÝMAX_REALŽ‘1~«has“a“reasonable“v‘ÿqÇalue.‘ÿŒThis“is“system“depGendenš¸ãt,‘gso“it“ma˜y“need“toŽ¤ bšGe–UU ddled“with“when“3DLDF“is“p˜orted.‘qÇ[¬LDF‘T2003.12.08.«]ŽŽ¡‘ -TO–UUDO:“If“ÝLDF_REAL_DOUBLEŽ‘R›«,“Ïthr‘ÿ}'esholdŽ‘.ís«m¸ãust“bGe“set“to“a“smaller“v‘ÿqÇalue.‘qÇ[¬LDF‘T2003.12.08.«]ŽŽ©·h–ª¨«Main‘@­1514“·i‘Ç«+·Ž¡«#ÂifdefŽ‘áeÝWORDS_BIGENDIANŽŽ¡‘ -·fŽ¡‘Ïc‘ÿ}'errŽ‘,ªI·‘ô¡Ý"ERROR!È ÝInÈ Ýmain():\nŽ‘nôeThisÈ ÝisÈ ÝaÈ Ýbig-endianŽ’×ô)È Ýcomputer.\n"Ž’"¯ ·Ž¡‘(Ý"YouÈ ÝwillÈ ÝhaveÈ ÝtoÈ ÝchŽ’ÿÈangeÈ ÝtheÈ ÝwayÈ ÝMAX_REAŽ’ùÿŒLÈ ÝisÈ Ýcalculated\n"Ž’^Óm·Ž¡‘(Ý"inÈ Ýpspglb.webÈ ÝandÈ ÝrŽ’ÿÈecompile.È ÝSorryÈ ÝabouŽ’ùÿŒtÈ Ýthis.\n"Ž’5ö·Ž¡‘(Ý"ExitingÈ ÝwithÈ ÝreturnŽ’ÿÈÈ ÝvalueÈ Ý1\n\n"Ž’Ø!·‘ÇÏ ushŽ‘€«;Ž¡‘ÏexitŽ‘%c«(1Ž‘);Ž¡‘ -·gŽ¡«#ÂendifŽŽ¡‘ -·fŽ¡‘ÂrealŽ‘*³0Ïthr‘ÿ}'esholdŽ‘U½«=‘Ç1–8à·“«10Ÿü^ÿ®35ŽŽŽ‘!xÞ«;Ž¡#ÂifŽ‘ ´øÝLDF_REAL_DOUBLEŽŽ¦‘Ïc‘ÿ}'errŽ‘)•8·‘ßÝ"WARNING!È ÝInÈ Ýmain()Ž‘kßT:"Ž‘yÅF·‘ßÏend‘‚ØlŽ‘°â·‘ßÝ"thresholdÈ ÝmustÈ ÝbeÈ ÝsŽ‘kßTetÈ ÝtoÈ ÝaÈ ÝsmallerÈ ÝvaluŽ’Ôße,È Ý"Ž’íE·Ž¡‘(Ý"becauseÈ ÝrealÈ ÝisÈ ÝaÈ ÝsŽ’ÿÈynonymÈ ÝforÈ Ýdouble."Ž’ü‘¨·‘K±Ïend‘‚ØlŽ‘"‰$·Ž¡‘(Ý"ProcedingÈ ÝwithÈ ÝfingŽ’ÿÈersÈ Ýcrossed."Ž’Ø!·‘ÇÏend‘‚ØlŽ–ò·‘ÇÏend‘‚ØlŽ“·‘ÇÏ 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üŸî8LogŽ‘)jœ„`Ö+UŽŽŽ¡‘ -«[¬LDF‘T2003.08.29.«]Ž‘Y<žChanged–‰¸the“string“that's“passed“to“Ïinitialize‘‰ffŽ‘®ioŽ‘6¿«(‘ª®)“as“the“name“of“the“input“ le.‘ñIt's“aŽ¡dummš¸ãy–æname,‘Ésince“I'v˜e“c˜hanged“Ïinitialize‘‰ffŽ‘®ioŽ‘5 í«(‘ª®)“toGda˜y‘ÿ*ª,›Éso“that“no“Ïin‘‰ffŽ‘®str–ÿ}'e“amŽ‘0Cù«isn't“opGened.‘Z¢Also,˜commen¸ãted-Ž¡out–UUthe“line“where“Ïin‘‰ffŽ‘®str–ÿ}'e“amŽ‘0Î׫is“closed.Ž¡‘ -[¬LDF‘T2003.11.28.«]Ž‘WëÉRemo•¸ãv“ed‘8ãT‘þU>ŸÓVEŽ‘ãxXŽ‘#text›8ãabGo“v“e,‘qÇthat˜referred˜to˜the˜precision˜used˜when˜prin“ting˜out˜ÝVERSION_3DLDFŽ‘Fÿ$«.Ÿ€„ -Ž¡This–UUis“no“longer“relev‘ÿqÇanš¸ãt,“bGecause“ÝVERSION_3DLDFŽ‘Kpë«is“no˜w“a“ÂstringŽ‘$z¢«rather“than“a“ÂrealŽ‘³.«.Ž¦ŸüÈ„`ÕÁGŽŽ¦·h–ª¨«Main‘@­1514“·i‘Ç«+·Ž¡‘ -h‘ª¨«Prin•¸ãt›UUv“ersion,˜cop“yrigh“t,˜and˜license˜information‘@­1511‘ª¨·i«;ŽŽŽŒ‹Ú­ Šn ý‘ì«474–­MAIN‘U>ITSELF’$KÛ3DLDFPRÃŽG“·x«1519Ž €n ý•@PÂ1519.Ž©·h–ª¨«Main‘@­1514“·i‘Ç«+·Ž¤ ‘ -Ïinitialize‘‰ffŽ‘®ioŽ‘<‘«(Ý"3DLDFin.ldf"Ž‘DÆA±;‘ª¨Ý"3DLDFput.mp"Ž‘Fpé±;‘ª¨Ý"3DLDFput.tex"Ž‘K°æ±;‘ª¨Ïar‘ÿ}'gvŽ‘EI«[0Ž‘]);Ž¡‘ -ÂColorŽ‘'O£«::‘Ïinitialize‘‰ffŽ‘®c‘ÿ}'olorsŽ‘DÀ«(‘ª®);Ž¡‘ -·h›ª¨«Actions–UUin“main‘@­1505˜·i«;Ž¡‘ -Ïwrite‘‰ffŽ‘®fo‘ÿ}'otersŽ‘AÝü«(‘ª®);Ž¡#ÂifŽ‘ ´ø«0ŽŽ¡‘ -Ïin‘‰ffŽ‘®str–ÿ}'e“amŽ‘4$.±:ÏcloseŽ‘7Ë«(‘ª¨);Ž¡#ÂendifŽŽ¡‘ -Ïout‘‰ffŽ‘®str–ÿ}'e“amŽ‘9@±:ÏcloseŽ‘7Ë«(‘ª¨);Ž¡‘ -Ïtex‘‰ffŽ‘®str–ÿ}'e“amŽ‘8u±:ÏcloseŽ‘7Ë«(‘ª¨);Ž¡‘ -ÂifŽ‘´ù«(·:ÝSILENT_GLOBALŽ‘DÆA«)‘·fŽ¡‘Ïc‘ÿ}'outŽ‘* Q·‘ÇÝ"ExitingÈ Ý3DLDFÈ ÝVersiŽ‘kÆÜonÈ Ý"Ž’„P·‘ÇÝVERSION_3DLDFŽ‘JTq·‘ÇÝ".\n\n"Ž‘*Ôƒ·‘ÇÏ ushŽ‘€«;Ž¡‘ -·gŽ¡‘ -ÂreturnŽ‘-滫(0Ž‘);‘qÇ·gŽŸÂ1520.› üPutting–ÕTMain“together.˜«This–UUis“what's“compiled.Ž¦‘ -·h–ª¨«Include‘UU les‘@­11“·iŽ¡‘ -h‘ª¨«V‘ÿ*ªersion–UUconš¸ãtrol“iden˜ti er‘@­10‘ª¨·iŽ¡‘ -h–ª¨«Main‘@­1514“·iŽ¡«#ÂendifŽŽ¤1521.‘ üAppQÇendices.Ž¡1522.‘ üReferences.Ž¤«Cundy›ÿ*ª,–U>H.“Mart¸ãyn“and“A.P˜.“Rollet.‘ÏMathematic›ÿ}'al“Mo˜dels«.›Oxford“1961.˜Oxford“Univ•¸ãersit“y‘U>Press.Ž¦‘sçUnfortunately–U>out“of“prin¸ãt.Ž¡Finston,–U>Laurence“D.“Ï3DLDF“User“and“R–ÿ}'efer“enc“e–U>Manual«.‘G‘úÿÿottingen“2003.Ž¡Fisc¸ãher,–U>Gerd.‘ÏEb›ÿ}'ene“algebr˜aische“Kurven«.›View¸ãeg“Studium.˜Aufbaukurs“Mathematik.˜F‘ÿ*ªriedr.“View¸ãegŽ© ‘ÂSŽ‘öÁ«ohn–U>V‘ÿ*ªerlagsgesellscš¸ãhaft“m˜bH.“Braunsc˜h˜w˜eig/Wiesbaden“1994.Ž¡Hobb¸ãy›ÿ*ª,–U>John“D.“ÏA“User's“Manual“for“MetaPost«.‘A˜TÂTŽ‘ èp«Bell“LabGoratories.‘Murra¸ãy“Hill,“NJ.“No“date.Ž¡Jones,–U>Hu¸ãw.‘ÏComputer“Gr›ÿ}'aphics“thr˜ough“Key“Mathematics«.‘Springer-V‘ÿ*ªerlag“London“Limited“2001.Ž¦‘ISBN‘U>1-85233-422-3.ŽŽ¡Kn¸ãuth,–U>Donald“Ervin.–ÏMetafont:“The›U>Pr–ÿ}'o“gr“am«.‘Computers˜and˜T¸ãypGesetting;˜D.˜Addison˜W‘ÿ*ªesley˜Publish-Ž¦‘ing–U>Companš¸ãy‘ÿ*ª,“Inc.‘Reading,“Massac˜h˜usetts“1986.Ž¦‘ISBN‘U>0-201-13438-1.ŽŽ¡Kn¸ãuth,–U>Donald“Ervin.›ÏThe“MET‘ÿ;¼AF¾“ONTb–ÿ}'o“ok«.˜Computers–U>and“T¸ãypGesetting;“C.“Addison“W‘ÿ*ªesley“PublishingŽ¦‘Companš¸ãy‘ÿ*ª,–U>Inc.‘Reading,“Massac˜h˜usetts“1986.Ž¡Kn¸ãuth,–U>Donald“Ervin.›ÏT‘ÿ;¼eX:“The“Pr–ÿ}'o“gr“am«.˜Computers–U>and“T¸ãypGesetting;“B.“Addison“W‘ÿ*ªesley“PublishingŽ¦‘Companš¸ãy‘ÿ*ª,–U>Inc.‘Reading,“Massac˜h˜usetts“1986.Ž¦‘ISBN‘U>0-201-13437-3.ŽŽ¡Knš¸ãuth,–U>Donald“E.“ÏThe“T‘þKßÓVEŽ‘Í-XŽ‘¹&b–ÿ}'o“ok«.‘Computers–U>and“T˜ypGesetting;“A.“Addison“W‘ÿ*ªesley“Publishing“Compan˜y‘ÿ*ª,Ž¦‘Inc.‘Reading,›U>Massac•¸ãh“usetts˜1986.Ž¡Kn¸ãuth,–U>Donald“E.“and“Silvio“Levy‘ÿ*ª.‘ÏThe“ÂCWEB“ÏSystem“of“Structur–ÿ}'e“d‘U>Do“cumentation«.Ž¦‘V–ÿ*ªersion›U>3.64|F“ebruary˜2002.ŽŽŽŽŒ‹Û»- Šn ý‘ì·x«1522–­3DLDFPRÃŽG’#\ÑREFERENCES“«475Ž €n ý•@PSalomon,–U>Da¸ãvid.‘ÏComputer“Gr›ÿ}'aphics“and“Ge˜ometric“Mo˜deling«.›Berlin“1999.˜Springer-V‘ÿ*ªerlag.Ž¤ ‘ISBN:‘U>0-387-98682-0.ŽŽ©StoGer,–U>Josef.›ÏNumerische“Mathematik“1«.˜Ac•¸ãh“te,–U>neu“b•Gearb“eitete–U>und“erw¸ãeiterte“Au age.˜Springer-V‘ÿ*ªerlag.Ž¡‘Berlin–U>1999.‘ISBN“3-540-66154-9.ŽŽ¦Stroustrup,–U>Bjarne.›ÏThe“¬C‘€Ÿÿ®+‘ÿ+ŽŽ‘œ^ÏPr–ÿ}'o“gr“amming‘U>L“anguage«.˜SpGecial–U>Edition.˜Reading,“Massac•¸ãh“usetts‘U>2000.Ž¡‘Addison-W–ÿ*ªesley“.Ž¡‘ISBN‘U>0-201-70073-5.ŽŽ¦Stroustrup,–U>Bjarne.›ÏThe“Design“and“Evolution“of“¬C‘€Ÿÿ®+‘ÿ+ŽŽ‘ G «.˜Reading,“Massac•¸ãh“usetts‘U>1994.˜Addison-W‘ÿ*ªesleyŽ¡‘Publishing‘U>Compan¸ãy‘ÿ*ª.Ž¡‘ISBN‘U>0-201-54330-3.ŽŽ©Â1523.› üGNU‘‚^F‘ÿ -«ree–‚‹DoQÇcumen®9tation“License.˜«The–ëôGNU‘ëÍF‘ÿ*ªree“DoGcumenš¸ãtation“License,‘›whic˜h“follo˜ws,Ž¡applies–UUto“this“doGcumen¸ãt.Ž¦’Ÿ»GGNU–UUF‘ÿ*ªree“DoGcumen¸ãtation“LicenseŽ¡’­ýV‘ÿ*ªersion–UU1.2,“No•¸ãv“em“bGer‘UU2002Ž©Cop•¸ãyrigh“t‘rž²×cŽŽŽ‘UU· 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üPutting–ÕTMain“together.˜¬This–UUis“what's“compiled.Ž¦‘ +°h–ª¨¬Include‘UU les‘@¯6“°iŽ¡‘ +h‘ª¨¬V‘ÿ*ªersion–UUconš¸ãtrol“iden˜ti er‘@¯5‘ª¨°iŽ¡‘ +h–ª¨¬Main‘@¯1555“°iŽ¤­1559.‘ üAppQÇendices.Ž¡1560.‘ üReferences.Ž¤¬Cundy›ÿ*ª,–U>H.“Mart¸ãyn“and“A.P˜.“Rollet.‘±Mathematic›ÿ}'al“Mo˜dels¬.›Oxford“1961.˜Oxford“Univ•¸ãersit“y‘U>Press.Ž¦‘sçUnfortunately–U>out“of“prin¸ãt.Ž¡Finston,–U>Laurence“D.“±3DLDF“User“and“R–ÿ}'efer“enc“e–U>Manual¬.‘G‘úÿÿottingen“2003.Ž¡Fisc¸ãher,–U>Gerd.‘±Eb›ÿ}'ene“algebr˜aische“Kurven¬.›View¸ãeg“Studium.˜Aufbaukurs“Mathematik.˜F‘ÿ*ªriedr.“View¸ãegŽ© ‘­SŽ‘öÁ¬ohn–U>V‘ÿ*ªerlagsgesellscš¸ãhaft“m˜bH.“Braunsc˜h˜w˜eig/Wiesbaden“1994.Ž¡Harbison,–U>Sam¸ãuel“P‘ÿ*ª.,“and“Guy“L.“Steele“Jr.›±C,“A“R–ÿ}'efer“enc“e–U>Manual¬.˜Pren¸ãtice“Hall.˜Englew¸ão•Go“d–U>Cli s,“NewŽ¦‘Jersey–U>1995.‘ISBN“0-13-326232-4“°f¬Case°g¬.ŽŽ¦‘ISBN–U>0-13-326224-3“°f¬P•¸ãapGerbac“k°g¬.ŽŽ¡Hobb¸ãy›ÿ*ª,–U>John“D.“±A“User's“Manual“for“MetaPost¬.‘A˜T­TŽ‘ èp¬Bell“LabGoratories.‘Murra¸ãy“Hill,“NJ.“No“date.Ž¡Jones,–U>Hu¸ãw.‘±Computer“Gr›ÿ}'aphics“thr˜ough“Key“Mathematics¬.‘Springer-V‘ÿ*ªerlag“London“Limited“2001.Ž¦‘ISBN‘U>1-85233-422-3.ŽŽ¡Kn¸ãuth,–U>Donald“Ervin.–±Metafont:“The›U>Pr–ÿ}'o“gr“am¬.‘Computers˜and˜T¸ãypGesetting;˜D.˜Addison˜W‘ÿ*ªesley˜Publish-Ž¦‘ing–U>Companš¸ãy‘ÿ*ª,“Inc.‘Reading,“Massac˜h˜usetts“1986.Ž¦‘ISBN‘U>0-201-13438-1.ŽŽ¡Kn¸ãuth,–U>Donald“Ervin.›±The“MET‘ÿ;¼AF¾“ONTb–ÿ}'o“ok¬.˜Computers–U>and“T¸ãypGesetting;“C.“Addison“W‘ÿ*ªesley“PublishingŽ¦‘Companš¸ãy‘ÿ*ª,–U>Inc.‘Reading,“Massac˜h˜usetts“1986.Ž¡Kn¸ãuth,–U>Donald“Ervin.›±T‘ÿ;¼eX:“The“Pr–ÿ}'o“gr“am¬.˜Computers–U>and“T¸ãypGesetting;“B.“Addison“W‘ÿ*ªesley“PublishingŽ¦‘Companš¸ãy‘ÿ*ª,–U>Inc.‘Reading,“Massac˜h˜usetts“1986.Ž¦‘ISBN‘U>0-201-13437-3.ŽŽ¡Knš¸ãuth,–U>Donald“E.“±The“T‘þKßÓVEŽ‘Í-XŽ‘¹&b–ÿ}'o“ok¬.‘Computers–U>and“T˜ypGesetting;“A.“Addison“W‘ÿ*ªesley“Publishing“Compan˜y‘ÿ*ª,Ž¦‘Inc.‘Reading,›U>Massac•¸ãh“usetts˜1986.ŽŽŽŒ‹ß” Šn ý‘ì°x¬1560–¯3DLDF-1.1.5.1’é;REFERENCES“¬479Ž €n ý•@PKn¸ãuth,–U>Donald“E.“and“Silvio“Levy‘ÿ*ª.‘±The“­CWEB“±System“of“Structur–ÿ}'e“d‘U>Do“cumentation¬.Ž¤ ‘V–ÿ*ªersion›U>3.64|F“ebruary˜2002.ŽŽ©Salomon,–U>Da¸ãvid.‘±Computer“Gr›ÿ}'aphics“and“Ge˜ometric“Mo˜deling¬.›Berlin“1999.˜Springer-V‘ÿ*ªerlag.Ž¡‘ISBN:‘U>0-387-98682-0.ŽŽ¦StoGer,–U>Josef.›±Numerische“Mathematik“1¬.˜Ac•¸ãh“te,–U>neu“b•Gearb“eitete–U>und“erw¸ãeiterte“Au age.˜Springer-V‘ÿ*ªerlag.Ž¡‘Berlin–U>1999.‘ISBN“3-540-66154-9.ŽŽ¦Stroustrup,–U>Bjarne.›±The“²C‘€Ÿÿ³+‘ÿ+ŽŽ‘œ^±Pr–ÿ}'o“gr“amming‘U>L“anguage¬.˜SpGecial–U>Edition.˜Reading,“Massac•¸ãh“usetts‘U>2000.Ž¡‘Addison-W–ÿ*ªesley“.Ž¡‘ISBN‘U>0-201-70073-5.ŽŽ¦Stroustrup,–U>Bjarne.›±The“Design“and“Evolution“of“²C‘€Ÿÿ³+‘ÿ+ŽŽ‘ G ¬.˜Reading,“Massac•¸ãh“usetts‘U>1994.˜Addison-W‘ÿ*ªesleyŽ¡‘Publishing‘U>Compan¸ãy‘ÿ*ª.Ž¡‘ISBN‘U>0-201-54330-3.ŽŽ©­1561.› üGNU‘‚^F‘ÿ +«ree–‚‹DoQÇcumen®9tation“License.˜¬The–ëôGNU‘ëÍF‘ÿ*ªree“DoGcumenš¸ãtation“License,‘›whic˜h“follo˜ws,Ž¡applies–UUto“this“doGcumen¸ãt.Ž¦’Ÿ»GGNU–UUF‘ÿ*ªree“DoGcumen¸ãtation“LicenseŽ¡’­ýV‘ÿ*ªersion–UU1.2,“No•¸ãv“em“bGer‘UU2002Ž©Cop•¸ãyrigh“t‘rž²×cŽŽŽ‘UU° ŽŽŽŽ‘ª«¬2000,2001,2002–UUF›ÿ*ªree“Soft•¸ãw“are–UUF˜oundation,“Inc.Ž¡59–UUT‘ÿ*ªemple“Place,“Suite“330,“Boston,“MA“02111-1307“USAŽ¡Ev•¸ãery“one–áois“pGermitted“to“copš¸ãy“and“distribute“v˜erbatim“copies“of“this“license“doGcumen˜t,‘ubut“c˜hanging“it“isŽ¡not‘UUallo•¸ãw“ed.Ž¡’ÇàŸ0.‘qÇPREAMBLEŽ¦‘ The–ÀRpurpGose“of“this“License“is“to“makš¸ãe“a“man˜ual,›Þtextb•Go“ok,˜or–ÀRother“functional“and“useful“doGcumen¸ãt“\free"Ž¡in–øthe“sense“of“freedom:‘C\to“assure“ev•¸ãery“one–øthe“e ectivš¸ãe“freedom“to“cop˜y“and“redistribute“it,‘ with“or“withoutŽ¡moGdifying–Ý¥it,›õ•either“commercially“or“noncommercially–ÿ*ª.‘IâSecondarily“,˜this–Ý¥License“preserv¸ães“for“the“author“andŽ¡publisher–~a“w•¸ãa“y–~to“get“credit“for“their“w¸ãork,‘ˆIwhile“not“bšGeing“considered“resp˜onsible“for“mo˜di cations“madeŽ¡b¸ãy‘UUothers.Ž¦‘ 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The›Eð\In•¸ãv‘ÿqÇarian“t˜Sections"˜are˜certain˜Secondary˜Sections˜whose˜titles˜are˜designated,‘‚as˜bGeing˜those˜ofŽ¡In•¸ãv‘ÿqÇarian“t–ЕSections,‘ë"in“the“notice“that“saš¸ãys“that“the“DoGcumen˜t“is“released“under“this“License.‘E‡If“a“section“doGesŽ¡not–úQ t“the“abšGo•¸ãv“e–úQde nition“of“Secondary“then“it“is“not“allo•¸ãw“ed–úQto“b˜e“designated“as“In•¸ãv‘ÿqÇarian“t.‘SpThe‘úQDo˜cumen“tŽ¡ma•¸ãy›Ñ6con“tain˜zero˜In“v‘ÿqÇarian“t˜Sections.‘åjIf˜the˜DoGcumen“t˜doGes˜not˜iden“tify˜an“y˜In“v‘ÿqÇarian“t˜Sections˜then˜thereŽ¡are‘UUnone.Ž¦‘ The›O\Co•¸ãv“er˜T–ÿ*ªexts"˜are˜certain˜short˜passages˜of˜text˜that˜are˜listed,‘PYas˜F“ron•¸ãt-Co“v“er˜T‘ÿ*ªexts˜or˜Bac“k-Co“v“erŽ¡T‘ÿ*ªexts,‘£in–¶the“notice“that“saš¸ãys“that“the“DoGcumen˜t“is“released“under“this“License.‘W=A‘¢F‘ÿ*ªron˜t-Co˜v˜er“T‘ÿ*ªext“ma˜y“bGeŽ¡at–UUmost“5“wš¸ãords,“and“a“Bac˜k-Co˜v˜er“T‘ÿ*ªext“ma˜y“bGe“at“most“25“w˜ords.Ž¦‘ A‘Ø\T‘ÿ*ªransparen•¸ãt"›Ø)cop“y˜of˜the˜DoGcumen“t˜means˜a˜mac“hine-readable˜cop“y‘ÿ*ª,‘øÞrepresen“ted˜in˜a˜format˜whoseŽ¡spšGeci cation–°ºis“a¸ãv‘ÿqÇailable“to“the“general“public,‘Ç“that“is“suitable“for“revising“the“do˜cumenš¸ãt“straigh˜tforw˜ardlyŽ¡with–„ôgeneric“text“editors“or“(for“images“compGosed“of“pixels)“generic“painš¸ãt“programs“or“(for“dra˜wings)“someŽ¡widely–ç!aš¸ãv‘ÿqÇailable“dra˜wing“editor,‘ý,and“that“is“suitable“for“input“to“text“formatters“or“for“automatic“translationŽ¡to–\ƒa“v‘ÿqÇarietš¸ãy“of“formats“suitable“for“input“to“text“formatters.‘‡RA‘\?cop˜y“made“in“an“otherwise“T‘ÿ*ªransparen˜tŽ¡ le–M%format“whose“markup,›‹or“absence“of“markup,˜has“bGeen“arranged“to“th•¸ãw“art–M%or“discourage“subsequen¸ãtŽ¡moGdi cation–X(bš¸ãy“readers“is“not“T‘ÿ*ªransparen˜t.‘z@An“image“format“is“not“T‘ÿ*ªransparen˜t“if“used“for“an˜y“substan˜tialŽ¡amounš¸ãt–UUof“text.‘qÇA“cop˜y“that“is“not“\T‘ÿ*ªransparen˜t"“is“called“\Opaque".Ž¦‘ @@ -5857,14 +6051,14 @@ A›^section–q\En¸ãtitled“XYZ"˜means“a“named“subunit“of“the“DoGcumen¸ãt“whose“title“either“is“precisely“XYZ˜orŽ¡conš¸ãtains–àXYZ‘Ñin“paren˜theses“follo˜wing“text“that“translates“XYZ›Ñin“another“language.‘^K(Here“XYZ˜stands“forŽ¡a–W3spšGeci c“section“name“men¸ãtioned“b˜elo•¸ãw,›W«suc“h–W3as“\Ac•¸ãkno“wledgemen“ts",˜\Dedications",˜\Endorsemen“ts",˜orŽ¡\History".)‘Q&T‘ÿ*ªo–óp\Preservš¸ãe“the“Title"“of“suc˜h“a“section“when“y˜ou“mošGdify“the“Do˜cumen¸ãt“means“that“it“remainsŽ¡a–UUsection“\En¸ãtitled“XYZ"“according“to“this“de nition.Ž¦‘ The–ËsDoGcumenš¸ãt“ma˜y“include“W‘ÿ*ªarran˜t˜y“Disclaimers“next“to“the“notice“whic˜h“states“that“this“License“appliesŽ¡to–Ísthe“DoGcumenš¸ãt.‘Ú!These“W‘ÿ*ªarran˜t˜y“Disclaimers“are“considered“to“bGe“included“b˜y“reference“in“this“License,Ž¡but–Ùonly“as“regards“disclaiming“w•¸ãarran“ties:‘3©an“y–Ùother“implication“that“these“W‘ÿ*ªarran•¸ãt“y–ÙDisclaimers“maš¸ãy“ha˜v˜eŽ¡is–UUv¸ãoid“and“has“no“e ect“on“the“meaning“of“this“License.Ž¤’¯Bd2.‘qÇVERBA‘ÿ*ªTIM‘UUCOPYINGŽ¡‘ Y‘ÿ*ªou–v°maš¸ãy“cop˜y“and“distribute“the“DoGcumen˜t“in“an˜y“medium,‘¿either“commercially“or“noncommercially‘ÿ*ª,Ž¤ proš¸ãvided–äêthat“this“License,‘Ïthe“cop˜yrigh˜t“notices,‘Ïand“the“license“notice“sa˜ying“this“License“applies“to“theŽ¡DošGcumen¸ãt–æare“repro˜duced“in“all“copies,‘ -Gand“that“y¸ãou“add“no“other“conditions“whatso˜ev¸ãer“to“those“of“thisŽ¡License.‘$Y‘ÿ*ªou–ßmaš¸ãy“not“use“tec˜hnical“measures“to“obstruct“or“con˜trol“the“reading“or“further“cop˜ying“of“theŽ¡copies–»Xyš¸ãou“mak˜e“or“distribute.‘£ÑHo˜w˜ev˜er,‘Ùy˜ou“ma˜y“accept“compGensation“in“exc˜hange“for“copies.‘£ÑIf“y˜ouŽ¡distribute–UUa“large“enough“n•¸ãum“bGer–UUof“copies“yš¸ãou“m˜ust“also“follo˜w“the“conditions“in“section“3.ŽŽŽŒ‹Ýו Šn ý‘ì·x«1523›­3DLDFPRÃŽG’¶ŠGGNU–ÕXFREE“DOCUMENT–ÿJªA“TION‘ÕXLICENSE˜«477Ž €n ý•@P‘ +Gand“that“y¸ãou“add“no“other“conditions“whatso˜ev¸ãer“to“those“of“thisŽ¡License.‘$Y‘ÿ*ªou–ßmaš¸ãy“not“use“tec˜hnical“measures“to“obstruct“or“con˜trol“the“reading“or“further“cop˜ying“of“theŽŽŽŒ‹á°o Šn ý‘ì°x¬1561›¯3DLDF-1.1.5.1’®±GNU–ÕXFREE“DOCUMENT–ÿJªA“TION‘ÕXLICENSE˜¬481Ž €n ý•@Pcopies–»Xyš¸ãou“mak˜e“or“distribute.‘£ÑHo˜w˜ev˜er,‘Ùy˜ou“ma˜y“accept“compGensation“in“exc˜hange“for“copies.‘£ÑIf“y˜ouŽ© distribute–UUa“large“enough“n•¸ãum“bGer–UUof“copies“yš¸ãou“m˜ust“also“follo˜w“the“conditions“in“section“3.ŽŸ‘ Y‘ÿ*ªou–UUmaš¸ãy“also“lend“copies,“under“the“same“conditions“stated“abGo˜v˜e,“and“y˜ou“ma˜y“publicly“displa˜y“copies.Ž¤’§Ô+3.‘qÇCOPYING–UUIN“QUANTITYŽ¡‘ -If–Ê»yš¸ãou“publish“prin˜ted“copies“(or“copies“in“media“that“commonly“ha˜v˜e“prin˜ted“co˜v˜ers)“of“the“DoGcumen˜t,Ž¤ n•¸ãum“bšGering–úmore“than“100,‘#Land“the“Do˜cumenš¸ãt's“license“notice“requires“Co˜v˜er“T‘ÿ*ªexts,‘#Ly˜ou“m˜ust“enclose“theŽ¡copies–_Åin“co•¸ãv“ers–_Åthat“carry›ÿ*ª,‘baclearly“and“legibly˜,‘baall“these“Co•¸ãv“er‘_ÅT˜exts:‘†§F˜ron“t-Co“v“er–_ÅT˜exts“on“the“fronš¸ãt“co˜v˜er,Ž¡and›p¶Bac•¸ãk-Co“v“er˜T‘ÿ*ªexts˜on˜the˜bac“k˜co“v“er.‘ÃêBoth˜co“v“ers˜m“ust˜also˜clearly˜and˜legibly˜iden“tify˜y“ou˜as˜theŽ¡publisher–zof“these“copies.‘ö6The“fronš¸ãt“co˜v˜er“m˜ust“presen˜t“the“full“title“with“all“w˜ords“of“the“title“equallyŽ¡prominenš¸ãt–ôëand“visible.‘Q¤Y‘ÿ*ªou“ma˜y“add“other“material“on“the“co˜v˜ers“in“addition.‘Q¤Cop˜ying“with“c˜hanges“limitedŽ¡to– the“co•¸ãv“ers,‘as– long“as“they“preservš¸ãe“the“title“of“the“DoGcumen˜t“and“satisfy“these“conditions,‘can“bGe“treatedŽ¡as–UUvš¸ãerbatim“cop˜ying“in“other“respGects.Ž©‘ -If–]„the“required“texts“for“either“co•¸ãv“er–]„are“toGo“vš¸ãoluminous“to“ t“legibly‘ÿ*ª,‘_y˜ou“should“put“the“ rst“ones“listedŽ¡(as–UUmanš¸ãy“as“ t“reasonably)“on“the“actual“co˜v˜er,“and“con˜tin˜ue“the“rest“on˜to“adjacen˜t“pages.Ž¦‘ -If–¿¼yš¸ãou“publish“or“distribute“Opaque“copies“of“the“DoGcumen˜t“n˜um˜bGering“more“than“100,‘ÚVy˜ou“m˜ust“eitherŽ¡include–üIa“macš¸ãhine-readable“T‘ÿ*ªransparen˜t“cop˜y“along“with“eac˜h“Opaque“cop˜y‘ÿ*ª,‘or“state“in“or“with“eac˜h“OpaqueŽ¡copš¸ãy–Å'a“computer-net˜w˜ork“loGcation“from“whic˜h“the“general“net˜w˜ork-using“public“has“access“to“do˜wnload“usingŽ¡public-standard›znet•¸ãw“ork˜protoGcols˜a˜complete˜T‘ÿ*ªransparen“t˜cop“y˜of˜the˜DoGcumen“t,‘' free˜of˜added˜material.‘^~IfŽ¡yš¸ãou–†õuse“the“latter“option,‘“]y˜ou“m˜ust“tak˜e“reasonably“pruden˜t“steps,‘“]when“y˜ou“bGegin“distribution“of“OpaqueŽ¡copies–áßin“quan•¸ãtit“y›ÿ*ª,‘to–áßensure“that“this“T˜ransparenš¸ãt“cop˜y“will“remain“th˜us“accessible“at“the“stated“loGcationŽ¡unš¸ãtil–"Ýat“least“one“y˜ear“after“the“last“time“y˜ou“distribute“an“Opaque“cop˜y“(directly“or“through“y˜our“agen˜ts“orŽ¡retailers)–UUof“that“edition“to“the“public.Ž¦‘ -It–(Fis“requested,›1Ibut“not“required,˜that“yš¸ãou“con˜tact“the“authors“of“the“DoGcumen˜t“w˜ell“bGefore“redistributingŽ¡anš¸ãy–ûlarge“n˜um˜bGer“of“copies,‘Ato“giv˜e“them“a“c˜hance“to“pro˜vide“y˜ou“with“an“upGdated“v˜ersion“of“the“DoGcumen˜t.Ž¤’ºÒe4.‘qÇMODIFICA‘ÿ*ªTIONSŽ¡‘ -Y‘ÿ*ªou–V¦maš¸ãy“cop˜y“and“distribute“a“MošGdi ed“V‘ÿ*ªersion“of“the“Do˜cumen¸ãt“under“the“conditions“of“sections“2“andŽ¤ 3›i!abGo•¸ãv“e,‘®pro“vided˜that˜y“ou˜release˜the˜Mo•Gdi ed˜V‘ÿ*ªersion˜under˜precisely˜this˜License,‘®with˜the˜Mo“di edŽ¡V‘ÿ*ªersion–ã lling“the“role“of“the“DošGcumen•¸ãt,‘ùèth“us–ã licensing“distribution“and“mo˜di cation“of“the“Mo˜di ed“V‘ÿ*ªersionŽ¡to–UUwhošGev¸ãer“p˜ossesses“a“copš¸ãy“of“it.‘qÇIn“addition,“y˜ou“m˜ust“do“these“things“in“the“MoGdi ed“V‘ÿ*ªersion:Ž¦‘ -A.–V Use“in“the“Title“Pš¸ãage“(and“on“the“co˜v˜ers,‘V9if“an˜y)“a“title“distinct“from“that“of“the“DoGcumen˜t,‘V9and“fromŽ¡those–Êof“previous“vš¸ãersions“(whic˜h“should,‘åÞif“there“w˜ere“an˜y‘ÿ*ª,‘åÞbšGe“listed“in“the“History“section“of“the“Do˜cumen¸ãt).Ž¡Y‘ÿ*ªou–¦amaš¸ãy“use“the“same“title“as“a“previous“v˜ersion“if“the“original“publisher“of“that“v˜ersion“giv˜es“pGermission.Ž¡B.–6List“on“the“Title“P¸ãage,›Ì.as“authors,˜one“or“more“pšGersons“or“en¸ãtities“resp˜onsible“for“authorship“of“theŽ¡mošGdi cations–‡Iin“the“Mo˜di ed“V‘ÿ*ªersion,‘“Ætogether“with“at“least“ v¸ãe“of“the“principal“authors“of“the“Do˜cumen¸ãtŽ¡(all–êTof“its“principal“authors,‘ÿ»if“it“has“fewš¸ãer“than“ v˜e),‘ÿ»unless“they“release“y˜ou“from“this“requiremen˜t.‘NC.“StateŽ¡on–±¾the“Title“page“the“name“of“the“publisher“of“the“MoGdi ed“V‘ÿ*ªersion,‘ÈÙas“the“publisher.‘‡D.“Preserv¸ãe“all“theŽ¡cop•¸ãyrigh“t–@œnotices“of“the“DoGcumenš¸ãt.‘jßE.“Add“an“appropriate“cop˜yrigh˜t“notice“for“y˜our“moGdi cations“adjacen˜tŽ¡to–Éœthe“other“cop•¸ãyrigh“t–Éœnotices.‘ÎœF.“Include,›æ­immediately“after“the“cop•¸ãyrigh“t–Éœnotices,˜a“license“notice“givingŽ¡the–9public“pšGermission“to“use“the“Mo˜di ed“V‘ÿ*ªersion“under“the“terms“of“this“License,‘>¯in“the“form“sho¸ãwn“in“theŽ¡Addendum–›„bGeloš¸ãw.‘DTG.“Preserv˜e“in“that“license“notice“the“full“lists“of“In˜v‘ÿqÇarian˜t“Sections“and“required“Co˜v˜erŽ¡T‘ÿ*ªexts–zùgivš¸ãen“in“the“DoGcumen˜t's“license“notice.‘â²H.“Include“an“unaltered“cop˜y“of“this“License.‘â²I.“Preserv˜e“theŽ¡section–J‰Enš¸ãtitled“\History",‘‡ÖPreserv˜e“its“Title,›‡Öand“add“to“it“an“item“stating“at“least“the“title,˜y¸ãear,˜newŽ¡authors,‘ ‘and–çpublisher“of“the“MoGdi ed“V‘ÿ*ªersion“as“givš¸ãen“on“the“Title“P˜age.‘'$If“there“is“no“section“En˜titledŽ¡\History"–êOin“the“DoGcumen¸ãt,›Žcreate“one“stating“the“title,˜y¸ãear,˜authors,˜and“publisher“of“the“DoGcumen¸ãt“asŽ¡givš¸ãen–õon“its“Title“P˜age,‘\then“add“an“item“describing“the“MoGdi ed“V‘ÿ*ªersion“as“stated“in“the“previous“sen˜tence.Ž¡J.–R%Preservš¸ãe“the“net˜w˜ork“loGcation,‘‘Xif“an˜y‘ÿ*ª,‘‘Xgiv˜en“in“the“DoGcumen˜t“for“public“access“to“a“T‘ÿ*ªransparen˜t“cop˜yŽ¡of–;$the“DoGcumenš¸ãt,‘t˜and“lik˜ewise“the“net˜w˜ork“loGcations“giv˜en“in“the“DoGcumen˜t“for“previous“v˜ersions“it“w˜asŽ¡based–W¥on.›x¶These“ma¸ãy“bGe“placed“in“the“\History"“section.˜Y‘ÿ*ªou“maš¸ãy“omit“a“net˜w˜ork“loGcation“for“a“w˜orkŽŽŽŒ‹Þìü Šn ý‘ì«478›­GNU–ÕXFREE“DOCUMENT–ÿJªA“TION‘ÕXLICENSE’¶ŠG3DLDFPRÃŽG˜·x«1523Ž €n ý•@Pthat–n¸wš¸ãas“published“at“least“four“y˜ears“bšGefore“the“Do˜cumenš¸ãt“itself,‘uor“if“the“original“publisher“of“the“v˜ersionŽ¤ it–Ͷrefers“to“givš¸ães“pGermission.‘ÚéK.“F‘ÿ*ªor“an˜y“section“En˜titled“\Ac˜kno˜wledgemen˜ts"“or“\Dedications",‘ëÎPreserv˜eŽ¡the–ú„Title“of“the“section,‘#Ïand“preservš¸ãe“in“the“section“all“the“substance“and“tone“of“eac˜h“of“the“con˜tributorŽ¡ac•¸ãkno“wledgemen“ts–ï]and/or“dedications“givš¸ãen“therein.‘OÊL.“Preserv˜e“all“the“In˜v‘ÿqÇarian˜t“Sections“of“the“DoGcumen˜t,Ž¡unaltered–pÃin“their“text“and“in“their“titles.‘ÄSection“n•¸ãum“bGers–pÃor“the“equiv‘ÿqÇalen¸ãt“are“not“considered“part“of“theŽ¡section–²ætitles.‘ŠyM.“Delete“anš¸ãy“section“En˜titled“\Endorsemen˜ts".‘ŠySuc˜h“a“section“ma˜y“not“bGe“included“in“theŽ¡MošGdi ed–ÿ1V‘ÿ*ªersion.‘UN.“Do“not“retitle“an¸ãy“existing“section“to“b˜e“Enš¸ãtitled“\Endorsemen˜ts"“or“to“con ict“in“titleŽ¡with–UUanš¸ãy“In˜v‘ÿqÇarian˜t“Section.‘qÇO.“Preserv˜e“an˜y“W‘ÿ*ªarran˜t˜y“Disclaimers.Ž©‘ +If–Ê»yš¸ãou“publish“prin˜ted“copies“(or“copies“in“media“that“commonly“ha˜v˜e“prin˜ted“co˜v˜ers)“of“the“DoGcumen˜t,Ž¦n•¸ãum“bšGering–úmore“than“100,‘#Land“the“Do˜cumenš¸ãt's“license“notice“requires“Co˜v˜er“T‘ÿ*ªexts,‘#Ly˜ou“m˜ust“enclose“theŽ¦copies–_Åin“co•¸ãv“ers–_Åthat“carry›ÿ*ª,‘baclearly“and“legibly˜,‘baall“these“Co•¸ãv“er‘_ÅT˜exts:‘†§F˜ron“t-Co“v“er–_ÅT˜exts“on“the“fronš¸ãt“co˜v˜er,Ž¦and›p¶Bac•¸ãk-Co“v“er˜T‘ÿ*ªexts˜on˜the˜bac“k˜co“v“er.‘ÃêBoth˜co“v“ers˜m“ust˜also˜clearly˜and˜legibly˜iden“tify˜y“ou˜as˜theŽ¦publisher–zof“these“copies.‘ö6The“fronš¸ãt“co˜v˜er“m˜ust“presen˜t“the“full“title“with“all“w˜ords“of“the“title“equallyŽ¦prominenš¸ãt–ôëand“visible.‘Q¤Y‘ÿ*ªou“ma˜y“add“other“material“on“the“co˜v˜ers“in“addition.‘Q¤Cop˜ying“with“c˜hanges“limitedŽ¦to– the“co•¸ãv“ers,‘as– long“as“they“preservš¸ãe“the“title“of“the“DoGcumen˜t“and“satisfy“these“conditions,‘can“bGe“treatedŽ¦as–UUvš¸ãerbatim“cop˜ying“in“other“respGects.Ž¤‘ +If–]„the“required“texts“for“either“co•¸ãv“er–]„are“toGo“vš¸ãoluminous“to“ t“legibly‘ÿ*ª,‘_y˜ou“should“put“the“ rst“ones“listedŽ¦(as–UUmanš¸ãy“as“ t“reasonably)“on“the“actual“co˜v˜er,“and“con˜tin˜ue“the“rest“on˜to“adjacen˜t“pages.Ž¡‘ +If–¿¼yš¸ãou“publish“or“distribute“Opaque“copies“of“the“DoGcumen˜t“n˜um˜bGering“more“than“100,‘ÚVy˜ou“m˜ust“eitherŽ¦include–üIa“macš¸ãhine-readable“T‘ÿ*ªransparen˜t“cop˜y“along“with“eac˜h“Opaque“cop˜y‘ÿ*ª,‘or“state“in“or“with“eac˜h“OpaqueŽ¦copš¸ãy–Å'a“computer-net˜w˜ork“loGcation“from“whic˜h“the“general“net˜w˜ork-using“public“has“access“to“do˜wnload“usingŽ¦public-standard›znet•¸ãw“ork˜protoGcols˜a˜complete˜T‘ÿ*ªransparen“t˜cop“y˜of˜the˜DoGcumen“t,‘' free˜of˜added˜material.‘^~IfŽ¦yš¸ãou–†õuse“the“latter“option,‘“]y˜ou“m˜ust“tak˜e“reasonably“pruden˜t“steps,‘“]when“y˜ou“bGegin“distribution“of“OpaqueŽ¦copies–áßin“quan•¸ãtit“y›ÿ*ª,‘to–áßensure“that“this“T˜ransparenš¸ãt“cop˜y“will“remain“th˜us“accessible“at“the“stated“loGcationŽ¦unš¸ãtil–"Ýat“least“one“y˜ear“after“the“last“time“y˜ou“distribute“an“Opaque“cop˜y“(directly“or“through“y˜our“agen˜ts“orŽ¦retailers)–UUof“that“edition“to“the“public.Ž¡‘ +It–(Fis“requested,›1Ibut“not“required,˜that“yš¸ãou“con˜tact“the“authors“of“the“DoGcumen˜t“w˜ell“bGefore“redistributingŽ¦anš¸ãy–ûlarge“n˜um˜bGer“of“copies,‘Ato“giv˜e“them“a“c˜hance“to“pro˜vide“y˜ou“with“an“upGdated“v˜ersion“of“the“DoGcumen˜t.Ž¤’ºÒe4.‘qÇMODIFICA‘ÿ*ªTIONSŽ¡‘ +Y‘ÿ*ªou–V¦maš¸ãy“cop˜y“and“distribute“a“MošGdi ed“V‘ÿ*ªersion“of“the“Do˜cumen¸ãt“under“the“conditions“of“sections“2“andŽ¦3›i!abGo•¸ãv“e,‘®pro“vided˜that˜y“ou˜release˜the˜Mo•Gdi ed˜V‘ÿ*ªersion˜under˜precisely˜this˜License,‘®with˜the˜Mo“di edŽ¦V‘ÿ*ªersion–ã lling“the“role“of“the“DošGcumen•¸ãt,‘ùèth“us–ã licensing“distribution“and“mo˜di cation“of“the“Mo˜di ed“V‘ÿ*ªersionŽ¦to–UUwhošGev¸ãer“p˜ossesses“a“copš¸ãy“of“it.‘qÇIn“addition,“y˜ou“m˜ust“do“these“things“in“the“MoGdi ed“V‘ÿ*ªersion:ŽŸ‘ +A.–V Use“in“the“Title“Pš¸ãage“(and“on“the“co˜v˜ers,‘V9if“an˜y)“a“title“distinct“from“that“of“the“DoGcumen˜t,‘V9and“fromŽ¦those–Êof“previous“vš¸ãersions“(whic˜h“should,‘åÞif“there“w˜ere“an˜y‘ÿ*ª,‘åÞbšGe“listed“in“the“History“section“of“the“Do˜cumen¸ãt).Ž¦Y‘ÿ*ªou–¦amaš¸ãy“use“the“same“title“as“a“previous“v˜ersion“if“the“original“publisher“of“that“v˜ersion“giv˜es“pGermission.Ž¦B.–6List“on“the“Title“P¸ãage,›Ì.as“authors,˜one“or“more“pšGersons“or“en¸ãtities“resp˜onsible“for“authorship“of“theŽ¦mošGdi cations–‡Iin“the“Mo˜di ed“V‘ÿ*ªersion,‘“Ætogether“with“at“least“ v¸ãe“of“the“principal“authors“of“the“Do˜cumen¸ãtŽ¦(all–êTof“its“principal“authors,‘ÿ»if“it“has“fewš¸ãer“than“ v˜e),‘ÿ»unless“they“release“y˜ou“from“this“requiremen˜t.‘NC.“StateŽ¦on–±¾the“Title“page“the“name“of“the“publisher“of“the“MoGdi ed“V‘ÿ*ªersion,‘ÈÙas“the“publisher.‘‡D.“Preserv¸ãe“all“theŽ¦cop•¸ãyrigh“t–@œnotices“of“the“DoGcumenš¸ãt.‘jßE.“Add“an“appropriate“cop˜yrigh˜t“notice“for“y˜our“moGdi cations“adjacen˜tŽ¦to–Éœthe“other“cop•¸ãyrigh“t–Éœnotices.‘ÎœF.“Include,›æ­immediately“after“the“cop•¸ãyrigh“t–Éœnotices,˜a“license“notice“givingŽ¦the–9public“pšGermission“to“use“the“Mo˜di ed“V‘ÿ*ªersion“under“the“terms“of“this“License,‘>¯in“the“form“sho¸ãwn“in“theŽ¦Addendum–›„bGeloš¸ãw.‘DTG.“Preserv˜e“in“that“license“notice“the“full“lists“of“In˜v‘ÿqÇarian˜t“Sections“and“required“Co˜v˜erŽ¦T‘ÿ*ªexts–zùgivš¸ãen“in“the“DoGcumen˜t's“license“notice.‘â²H.“Include“an“unaltered“cop˜y“of“this“License.‘â²I.“Preserv˜e“theŽ¦section–J‰Enš¸ãtitled“\History",‘‡ÖPreserv˜e“its“Title,›‡Öand“add“to“it“an“item“stating“at“least“the“title,˜y¸ãear,˜newŽ¦authors,‘ ‘and–çpublisher“of“the“MoGdi 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based–W¥on.›x¶These“ma¸ãy“bGe“placed“in“the“\History"“section.˜Y‘ÿ*ªou“maš¸ãy“omit“a“net˜w˜ork“loGcation“for“a“w˜orkŽ¡that–n¸wš¸ãas“published“at“least“four“y˜ears“bšGefore“the“Do˜cumenš¸ãt“itself,‘uor“if“the“original“publisher“of“the“v˜ersionŽ¡it–Ͷrefers“to“givš¸ães“pGermission.‘ÚéK.“F‘ÿ*ªor“an˜y“section“En˜titled“\Ac˜kno˜wledgemen˜ts"“or“\Dedications",‘ëÎPreserv˜eŽ¡the–ú„Title“of“the“section,‘#Ïand“preservš¸ãe“in“the“section“all“the“substance“and“tone“of“eac˜h“of“the“con˜tributorŽ¡ac•¸ãkno“wledgemen“ts–ï]and/or“dedications“givš¸ãen“therein.‘OÊL.“Preserv˜e“all“the“In˜v‘ÿqÇarian˜t“Sections“of“the“DoGcumen˜t,Ž¡unaltered–pÃin“their“text“and“in“their“titles.‘ÄSection“n•¸ãum“bGers–pÃor“the“equiv‘ÿqÇalen¸ãt“are“not“considered“part“of“theŽ¡section–²ætitles.‘ŠyM.“Delete“anš¸ãy“section“En˜titled“\Endorsemen˜ts".‘ŠySuc˜h“a“section“ma˜y“not“bGe“included“in“theŽ¡MošGdi ed–ÿ1V‘ÿ*ªersion.‘UN.“Do“not“retitle“an¸ãy“existing“section“to“b˜e“Enš¸ãtitled“\Endorsemen˜ts"“or“to“con ict“in“titleŽ¡with–UUanš¸ãy“In˜v‘ÿqÇarian˜t“Section.‘qÇO.“Preserv˜e“an˜y“W‘ÿ*ªarran˜t˜y“Disclaimers.Ž©‘ If–vîthe“MošGdi ed“V‘ÿ*ªersion“includes“new“fron¸ãt-matter“sections“or“app˜endices“that“qualify“as“Secondary“SectionsŽ¡and–‚—conš¸ãtain“no“material“copied“from“the“DoGcumen˜t,‘çy˜ou“ma˜y“at“y˜our“option“designate“some“or“all“of“theseŽ¡sections–¢Jas“in•¸ãv›ÿqÇarian“t.‘X§T‘ÿ*ªo–¢Jdo“this,‘µˆadd“their“titles“to“the“list“of“In•¸ãv˜arian“t–¢JSections“in“the“MoGdi ed“V‘ÿ*ªersion'sŽ¡license–UUnotice.‘qÇThese“titles“mš¸ãust“bGe“distinct“from“an˜y“other“section“titles.Ž¦‘ Y‘ÿ*ªou–zÕmaš¸ãy“add“a“section“En˜titled“\Endorsemen˜ts",‘„5pro˜vided“it“con˜tains“nothing“but“endorsemen˜ts“of“y˜ourŽ¡MoGdi ed–UOV‘ÿ*ªersion“bš¸ãy“v‘ÿqÇarious“parties{for“example,‘ˆ„statemen˜ts“of“pšGeer“review“or“that“the“text“has“b˜een“appro•¸ãv“edŽ¡bš¸ãy–UUan“organization“as“the“authoritativ˜e“de nition“of“a“standard.Ž¦‘ Y‘ÿ*ªou–êQmaš¸ãy“add“a“passage“of“up“to“ 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and–î­replace“the“individual“copies“of“this“License“in“the“v‘ÿqÇarious“doGcumenš¸ãts“with“a“single“cop˜y“that“is“includedŽ¡in–sthe“collection,‘Ýúproš¸ãvided“that“y˜ou“follo˜w“the“rules“of“this“License“for“v˜erbatim“cop˜ying“of“eac˜h“of“theŽ¡došGcumen¸ãts–UUin“all“other“resp˜ects.ŽŽŽŒ‹ãÜÝ Šn ý‘ì°x¬1561›¯3DLDF-1.1.5.1’®±GNU–ÕXFREE“DOCUMENT–ÿJªA“TION‘ÕXLICENSE˜¬483Ž €n ý•@P‘ +Y‘ÿ*ªou–~Dmaš¸ãy“extract“a“single“doGcumen˜t“from“suc˜h“a“collection,‘©Gand“distribute“it“individually“under“this“License,Ž¤ pro•¸ãvided›sey“ou˜insert˜a˜cop“y˜of˜this˜License˜in“to˜the˜extracted˜doGcumen“t,‘zéand˜follo“w˜this˜License˜in˜all˜otherŽ¡respGects–UUregarding“vš¸ãerbatim“cop˜ying“of“that“doGcumen˜t.Ž¤‘qt%7.‘qÇAš¸ãGGREGA‘ÿ*ªTION–UUWITH“INDEPENDENT“W˜ORKSŽ¡‘ +A‘vbcompilation–všof“the“DoGcumenš¸ãt“or“its“deriv‘ÿqÇativ˜es“with“other“separate“and“indepGenden˜t“doGcumen˜ts“or“w˜orks,Ž¤ in–­or“on“a“vš¸ãolume“of“a“storage“or“distribution“medium,‘θis“called“an“\aggregate"“if“the“cop˜yrigh˜t“resulting“fromŽ¡the–Àæcompilation“is“not“used“to“limit“the“legal“righš¸ãts“of“the“compilation's“users“bGey˜ond“what“the“individualŽ¡w¸ãorks–öÒpšGermit.‘V=When“the“Do˜cumen¸ãt“is“included“in“an“aggregate,‘1this“License“do˜es“not“apply“to“the“otherŽ¡wš¸ãorks–UUin“the“aggregate“whic˜h“are“not“themselv˜es“deriv‘ÿqÇativ˜e“w˜orks“of“the“DoGcumen˜t.Ž©‘ +If–‡Ethe“Co•¸ãv“er–‡ET‘ÿ*ªext“requiremenš¸ãt“of“section“3“is“applicable“to“these“copies“of“the“DoGcumen˜t,‘ÓÀthen“if“theŽ¡DoGcumenš¸ãt–çˆis“less“than“one“half“of“the“en˜tire“aggregate,‘ý~the“DoGcumen˜t's“Co˜v˜er“T‘ÿ*ªexts“ma˜y“bGe“placed“on“co˜v˜ersŽ¡that›¿Mbrac•¸ãk“et˜the˜DoGcumen“t˜within˜the˜aggregate,‘ÙËor˜the˜electronic˜equiv‘ÿqÇalen“t˜of˜co“v“ers˜if˜the˜DoGcumen“t˜isŽ¡in–UUelectronic“form.‘qÇOtherwise“they“mš¸ãust“appGear“on“prin˜ted“co˜v˜ers“that“brac˜k˜et“the“whole“aggregate.Ž¤’¿®Ø8.‘qÇTRANSLA‘ÿ*ªTIONŽ¡‘ +T‘ÿ*ªranslation–¢Áis“considered“a“kind“of“moGdi cation,‘öso“yš¸ãou“ma˜y“distribute“translations“of“the“DoGcumen˜tŽ¤ under–Ú¿the“terms“of“section“4.‘HëReplacing“In•¸ãv‘ÿqÇarian“t–Ú¿Sections“with“translations“requires“spšGecial“p˜ermission“fromŽ¡their›cop•¸ãyrigh“t˜holders,‘½but˜y“ou˜ma“y˜include˜translations˜of˜some˜or˜all˜In“v‘ÿqÇarian“t˜Sections˜in˜addition˜to˜theŽ¡original–°vš¸ãersions“of“these“In˜v‘ÿqÇarian˜t“Sections.‘:ÚY‘ÿ*ªou“ma˜y“include“a“translation“of“this“License,‘Ñ‚and“all“the“licenseŽ¡notices–in“the“DoGcumenš¸ãt,‘Šand“an˜y“W‘ÿ*ªarran˜t˜y“Disclaimers,‘Špro˜vided“that“y˜ou“also“include“the“original“EnglishŽ¡vš¸ãersion–~/of“this“License“and“the“original“v˜ersions“of“those“notices“and“disclaimers.‘ìVIn“case“of“a“disagreemen˜tŽ¡bGet•¸ãw“een–úÐthe“translation“and“the“original“vš¸ãersion“of“this“License“or“a“notice“or“disclaimer,‘ ëthe“original“v˜ersionŽ¡will‘UUprev‘ÿqÇail.Ž¦‘ +If–®]a“section“in“the“DoGcumenš¸ãt“is“En˜titled“\Ac˜kno˜wledgemen˜ts",–ÄŸ\Dedications",“or›®]\History",“the˜require-Ž¡menš¸ãt–UU(section“4)“to“Preserv˜e“its“Title“(section“1)“will“t˜ypically“require“c˜hanging“the“actual“title.Ž¤’¿‹J9.‘qÇTERMINA‘ÿ*ªTIONŽ¡‘ +Y‘ÿ*ªou–1Úmaš¸ãy“not“cop˜y–ÿ*ª,›8òmoGdify“,˜sublicense,˜or–1Údistribute“the“DoGcumenš¸ãt“except“as“expressly“pro˜vided“for“underŽ¤ this–ULicense.‘xÆAnš¸ãy“other“attempt“to“cop˜y–ÿ*ª,›-•moGdify“,˜sublicense–Uor“distribute“the“DoGcumenš¸ãt“is“v˜oid,‘-•and“willŽ¡automatically–öterminate“yš¸ãour“righ˜ts“under“this“License.‘A=Ho˜w˜ev˜er,‘àÖparties“who“ha˜v˜e“receiv˜ed“copies,‘àÖor“righ˜ts,Ž¡from– ´yš¸ãou“under“this“License“will“not“ha˜v˜e“their“licenses“terminated“so“long“as“suc˜h“parties“remain“in“fullŽ¡compliance.Ž¤’‡³10.‘qÇFUTURE–UUREVISIONS“OF“THIS“LICENSEŽ¡‘ +The–ÓÒF›ÿ*ªree“Soft•¸ãw“are–ÓÒF˜oundation“maš¸ãy“publish“new,‘íºrevised“v˜ersions“of“the“GNU‘Ó²F‘ÿ*ªree“DoGcumen˜tation“LicenseŽ¤ from–ªtime“to“time.‘^9Sucš¸ãh“new“v˜ersions“will“bGe“similar“in“spirit“to“the“presen˜t“v˜ersion,‘&fbut“ma˜y“di er“in“detailŽ¡to–UUaddress“new“problems“or“concerns.‘qÇSee“®http://www.gnu.org/copyleft/¬.Ž¦‘ +Eac•¸ãh›Êv“ersion˜of˜the˜License˜is˜giv“en˜a˜distinguishing˜v“ersion˜n“um“b•Ger.‘³%If˜the˜Do“cumen¸ãt˜sp“eci es˜that˜aŽ¡particular›š¦n•¸ãum“bGered˜v“ersion˜of˜this˜License˜\or˜an“y˜later˜v“ersion"˜applies˜to˜it,‘ëúy“ou˜ha“v“e˜the˜option˜ofŽ¡folloš¸ãwing–¥the“terms“and“conditions“either“of“that“spGeci ed“v˜ersion“or“of“an˜y“later“v˜ersion“that“has“bGeenŽ¡published–#ü(not“as“a“draft)“bš¸ãy“the“F‘ÿ*ªree“Soft˜w˜are“F‘ÿ*ªoundation.‘ݼIf“the“DoGcumen˜t“došGes“not“sp˜ecify“a“v¸ãersionŽ¡n•¸ãum“bGer–ú7of“this“License,‘#oyš¸ãou“ma˜y“c˜hoGose“an˜y“v˜ersion“ev˜er“published“(not“as“a“draft)“b˜y“the“F‘ÿ*ªree“Soft˜w˜areŽ¡F‘ÿ*ªoundation.ŽŸ‘i9zADDENDUM:–UUHoš¸ãw“to“use“this“License“for“y˜our“doGcumen˜tsŽŽŽŒ‹äñs Šn ý‘ì¬484›¯GNU–ÕXFREE“DOCUMENT–ÿJªA“TION‘ÕXLICENSE’®±3DLDF-1.1.5.1˜°x¬1561Ž €n ý•@P‘ +T‘ÿ*ªo–§fuse“this“License“in“a“doGcumenš¸ãt“y˜ou“ha˜v˜e“written,‘»êinclude“a“cop˜y“of“the“License“in“the“doGcumen˜t“andŽ¤ put–UUthe“folloš¸ãwing“cop˜yrigh˜t“and“license“notices“just“after“the“title“page:Ž©Cop•¸ãyrigh“t‘ä]ž²×cŽŽŽ‘@° ŽŽŽŽ‘:¬YEAR–1YOUR“NAME.–@Pš¸ãermission“is“gran˜ted“to“cop˜y‘ÿ*ª,‘(wdistribute“and/or“mošGdify“this“do˜cumen¸ãtŽ¡under–:…the“terms“of“the“GNU‘:~F›ÿ*ªree“DoGcumen¸ãtation“License,‘?âV˜ersion“1.2“or“anš¸ãy“later“v˜ersion“published“b˜y“theŽ¡F‘ÿ*ªree› ESoft•¸ãw“are˜F‘ÿ*ªoundation;‘žwith˜no˜In“v‘ÿqÇarian“t˜Sections,‘³no˜F‘ÿ*ªron“t-Co“v“er˜T‘ÿ*ªexts,‘³and˜no˜Bac“k-Co“v“er˜T‘ÿ*ªexts.‘R˜AŽ¡copš¸ãy–UUof“the“license“is“included“in“the“section“en˜titled“\GNU“F‘ÿ*ªree“DoGcumen˜tation“License".Ž¦‘ If–pyš¸ãou“ha˜v˜e“In˜v‘ÿqÇarian˜t“Sections,‘v®F‘ÿ*ªron˜t-Co˜v˜er“T‘ÿ*ªexts“and“Bac˜k-Co˜v˜er“T›ÿ*ªexts,‘v®replace“the“\with...T˜exts."‘ÁÑlineŽ¡with‘UUthis:Ž¦with–Aøthe“In•¸ãv‘ÿqÇarian“t–AøSections“bGeing“LIST–AóTHEIR“TITLES,–Aøwith“the“F›ÿ*ªron•¸ãt-Co“v“er–AøT˜exts“bGeing“LIST,“and“withŽ¡the›UUBac•¸ãk-Co“v“er˜T‘ÿ*ªexts˜bGeing˜LIST.Ž¦‘ If–\¹yš¸ãou“ha˜v˜e“In˜v‘ÿqÇarian˜t“Sections“without“Co˜v˜er“T‘ÿ*ªexts,‘^’or“some“other“com˜bination“of“the“three,‘^’merge“thoseŽ¡t•¸ãw“o›UUalternativ“es˜to˜suit˜the˜situation.Ž¦‘ -If–h2yš¸ãour“doGcumen˜t“con˜tains“non˜trivial“examples“of“program“coGde,‘léw˜e“recommend“releasing“these“examplesŽ¡in–÷Šparallel“under“yš¸ãour“c˜hoice“of“free“soft˜w˜are“license,‘ suc˜h“as“the“GNU‘÷`General“Public“License,‘ to“pGermitŽ¡their–UUuse“in“free“soft•¸ãw“are.ŽŸ·h›ª¨«GNU–UUF‘ÿ*ªree“DoGcumen¸ãtation“License‘@­1523˜·i‘ǑDZ=·‘ÿý«This“section“con¸ãtains“no“¬C‘€Ÿÿ®+‘ÿ+ŽŽ‘œu«coGde.‘o·±=ŽŸ ­This–ÕXcolicenses“for“most“soft•¸ãw“are–¯>are“designed“to“takš¸ãe“a˜w˜a˜y“y˜our“freedom“to“share“and“c˜hange“it.‘:jBy“con˜trast,Ž¡the–âLGNU‘â/General“Public“License“is“inš¸ãtended“to“guaran˜tee“y˜our“freedom“to“share“and“c˜hange“free“soft˜w˜are{toŽ¡makš¸ãe–R+sure“the“soft˜w˜are“is“free“for“all“its“users.‘hJThis“General“Public“License“applies“to“most“of“the“F‘ÿ*ªreeŽ¡Soft•¸ãw“are–¬ÒF‘ÿ*ªoundation's“soft•¸ãw“are–¬Òand“to“an¸ãy“other“program“whose“authors“commit“to“using“it.‘x=(Some“otherŽ¡F‘ÿ*ªree›ë?Soft•¸ãw“are˜F‘ÿ*ªoundation˜soft“w“are˜is˜co“v“ered˜b“y˜the˜GNU‘ë$Library˜General˜Public˜License˜instead.)‘NjY‘ÿ*ªou˜canŽ¡apply–UUit“to“y¸ãour“programs,“toGo.Ž¦‘ When–y­wš¸ãe“spGeak“of“free“soft˜w˜are,‘‚Âw˜e“are“referring“to“freedom,‘‚Ânot“price.‘ÞÎOur“General“Public“Licenses“areŽ¡designed–¼æto“makš¸ãe“sure“that“y˜ou“ha˜v˜e“the“freedom“to“distribute“copies“of“free“soft˜w˜are“(and“c˜harge“for“thisŽ¡service–¢òif“yš¸ãou“wish),‘Æ that“y˜ou“receiv˜e“source“coGde“or“can“get“it“if“y˜ou“w˜an˜t“it,‘Æ that“y˜ou“can“c˜hange“the“soft˜w˜areŽ¡or–UUuse“pieces“of“it“in“new“free“programs;“and“that“yš¸ãou“kno˜w“y˜ou“can“do“these“things.Ž¦‘ T‘ÿ*ªo–(aprotect“yš¸ãour“righ˜ts,‘1^w˜e“need“to“mak˜e“restrictions“that“forbid“an˜y˜one“to“den˜y“y˜ou“these“righ˜ts“or“to“askŽ¡yš¸ãou–˜Sto“surrender“the“righ˜ts.‘:ÀThese“restrictions“translate“to“certain“respGonsibilities“for“y˜ou“if“y˜ou“distributeŽ¡copies–UUof“the“soft•¸ãw“are,–UUor“if“y¸ãou“moGdify“it.Ž¦‘ F‘ÿ*ªor–~example,‘,ˆif“yš¸ãou“distribute“copies“of“suc˜h“a“program,›,ˆwhether“gratis“or“for“a“fee,˜yš¸ãou“m˜ust“giv˜e“theŽ¡recipienš¸ãts–all“the“righ˜ts“that“y˜ou“ha˜v˜e.‘zÜY‘ÿ*ªou“m˜ust“mak˜e“sure“that“they‘ÿ*ª,–.stoGo,“receiv˜e–or“can“get“the“sourceŽ¡coGde.‘qÇAnd–UUyš¸ãou“m˜ust“sho˜w“them“these“terms“so“they“kno˜w“their“righ˜ts.Ž¦‘ -W‘ÿ*ªe–˜protect“yš¸ãour“righ˜ts“with“t˜w˜o“steps:‘êM(1)“cop˜yrigh˜t“the“soft˜w˜are,‘@¨and“(2)“o er“y˜ou“this“license“whic˜hŽ¡giv•¸ães›UUy“ou˜legal˜pGermission˜to˜cop“y‘ÿ*ª,˜distribute˜and/or˜moGdify˜the˜soft“w“are.Ž¦‘ -Also,›ìºfor–Ò“eac¸ãh“author's“protection“and“ours,˜wš¸ãe“w˜an˜t“to“mak˜e“certain“that“ev˜ery˜one“understands“that“thereŽ¡is–@óno“w•¸ãarran“t“y–@ófor“this“free“soft•¸ãw“are.‘jüIf–@óthe“soft•¸ãw“are–@óis“moGdi ed“bš¸ãy“someone“else“and“passed“on,‘Ew˜e“w˜an˜t“itsŽ¡recipienš¸ãts–Ýto“kno˜w“that“what“they“ha˜v˜e“is“not“the“original,‘°so“that“an˜y“problems“in˜troGduced“b˜y“others“willŽ¡not–UUre 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is–@óno“w•¸ãarran“t“y–@ófor“this“free“soft•¸ãw“are.‘jüIf–@óthe“soft•¸ãw“are–@óis“moGdi ed“bš¸ãy“someone“else“and“passed“on,‘Ew˜e“w˜an˜t“itsŽ¡recipienš¸ãts–Ýto“kno˜w“that“what“they“ha˜v˜e“is“not“the“original,‘°so“that“an˜y“problems“in˜troGduced“b˜y“others“willŽ¡not–UUre ect“on“the“original“authors'“reputations.Ž©‘ +Finally‘ÿ*ª,‘¾anš¸ãy–uöfree“program“is“threatened“constan˜tly“b˜y“soft˜w˜are“paten˜ts.‘ÓªW‘ÿ*ªe“wish“to“a˜v˜oid“the“dangerŽ¡that–¢Wredistributors“of“a“free“program“will“individually“obtain“paten¸ãt“licenses,‘µ—in“e ect“making“the“programŽ¡proprietary–ÿ*ª.‘l®T“o›F +prev•¸ãen“t˜this,‘Iw“e˜ha“v“e˜made˜it˜clear˜that˜an“y˜paten“t˜m“ust˜bGe˜licensed˜for˜ev“ery“one's˜free˜useŽ¡or–UUnot“licensed“at“all.Ž¦‘ The–UUprecise“terms“and“conditions“for“copš¸ãying,“distribution“and“moGdi cation“follo˜w.ŽŸ’˜NÓGNU–UUGENERAL“PUBLIC“LICENSEŽ¡‘$”TERMS–UUAND“CONDITIONS“F¸ãOR“COPYING,“DISTRIBUTION“AND“MODIFICA‘ÿ*ªTIONŽ¦‘ 0.‘$This– ÉLicense“applies“to“anš¸ãy“program“or“other“w˜ork“whic˜h“con˜tains“a“notice“placed“b˜y“the“cop˜yrigh˜tŽ¡holder–.+saš¸ãying“it“ma˜y“bšGe“distributed“under“the“terms“of“this“General“Public“License.‘d¹The“\Program",‘6b˜elo¸ãw,Ž¡refers–u»to“anš¸ãy“suc˜h“program“or“w˜ork,‘½Õand“a“\w˜ork“based“on“the“Program"“means“either“the“Program“orŽ¡an•¸ãy›£²deriv‘ÿqÇativ“e˜w“ork˜under˜cop“yrigh“t˜la“w:‘€that˜is˜to˜sa“y‘ÿ*ª,‘·Ia˜w“ork˜con“taining˜the˜Program˜or˜a˜pGortion˜of˜it,Ž¡either–ŽKvš¸ãerbatim“or“with“moGdi cations“and/or“translated“in˜to“another“language.‘©(Hereinafter,‘œ‰translation“isŽ¡included–UUwithout“limitation“in“the“term“\moGdi cation".)‘qÇEacš¸ãh“licensee“is“addressed“as“\y˜ou".Ž¦‘ Activities–xother“than“copš¸ãying,‘ÀÏdistribution“and“moGdi cation“are“not“co˜v˜ered“b˜y“this“License;‘ ‚they“areŽ¡outside–óÃits“scopGe.‘MThe“act“of“running“the“Program“is“not“restricted,‘^and“the“output“from“the“Program“isŽ¡co•¸ãv“ered–™ÿonly“if“its“con•¸ãten“ts–™ÿconstitute“a“wš¸ãork“based“on“the“Program“(indepGenden˜t“of“ha˜ving“bGeen“made“b˜yŽ¡running–UUthe“Program).‘qÇWhether“that“is“true“depšGends“on“what“the“Program“do˜es.Ž¦‘ 1.‘ ÍY‘ÿ*ªou–ÞWmaš¸ãy“cop˜y“and“distribute“v˜erbatim“copies“of“the“Program's“source“coGde“as“y˜ou“receiv˜e“it,‘—in“an˜yŽ¡medium,‘C,proš¸ãvided–>¢that“y˜ou“conspicuously“and“appropriately“publish“on“eac˜h“cop˜y“an“appropriate“cop˜yrigh˜tŽ¡notice–¡and“disclaimer“of“w•¸ãarran“t“y;‘/ˆk“eep›¡in“tact˜all˜the˜notices˜that˜refer˜to˜this˜License˜and˜to˜the˜absence˜ofŽ¡an•¸ãy›UUw“arran“t“y;˜and˜giv“e˜an“y˜other˜recipien“ts˜of˜the˜Program˜a˜cop“y˜of˜this˜License˜along˜with˜the˜Program.Ž¦‘ Y‘ÿ*ªou–ºthe“recipien˜t“automaticallyŽ¡receivš¸ães– za“license“from“the“original“licensor“to“cop˜y‘ÿ*ª,‘sdistribute“or“moGdify“the“Program“sub‘Ž8ject“to“these“termsŽ¡and–vconditions.‘UÒY‘ÿ*ªou“maš¸ãy“not“impGose“an˜y“further“restrictions“on“the“recipien˜ts'“exercise“of“the“righ˜ts“gran˜tedŽ¡herein.‘qÇY‘ÿ*ªou–UUare“not“respGonsible“for“enforcing“compliance“b¸ãy“third“parties“to“this“License.Ž¦‘ -7.‘1|If,‘»as–”sa“consequence“of“a“court“judgmenš¸ãt“or“allegation“of“paten˜t“infringemen˜t“or“for“an˜y“other“reason“(notŽ¡limited–ŸDto“patenš¸ãt“issues),‘±Àconditions“are“impGosed“on“y˜ou“(whether“b˜y“court“order,‘±Àagreemen˜t“or“otherwise)Ž¡that–Êâconš¸ãtradict“the“conditions“of“this“License,‘èEthey“do“not“excuse“y˜ou“from“the“conditions“of“this“License.Ž¡If–ä‚yš¸ãou“cannot“distribute“so“as“to“satisfy“sim˜ultaneously“y˜our“obligations“under“this“License“and“an˜y“otherŽ¡pGertinenš¸ãt–¬.obligations,‘Áäthen“as“a“consequence“y˜ou“ma˜y“not“distribute“the“Program“at“all.‘vQF‘ÿ*ªor“example,‘Áäif“aŽ¡patenš¸ãt–Õglicense“w˜ould“not“pGermit“ro˜y˜alt˜y-free“redistribution“of“the“Program“b˜y“all“those“who“receiv˜e“copiesŽ¡directly–@5or“indirectly“through“yš¸ãou,‘Dnthen“the“only“w˜a˜y“y˜ou“could“satisfy“bGoth“it“and“this“License“w˜ould“bGe“toŽ¡refrain–UUen¸ãtirely“from“distribution“of“the“Program.ŽŽŽŒ‹ãQR Šn ý‘ì·x«1524›­3DLDFPRÃŽG’Ñ}GNU–ÕXGENERAL“PUBLIC“LICENSE˜«483Ž €n ý•@P‘ -If–nanš¸ãy“pGortion“of“this“section“is“held“in˜v‘ÿqÇalid“or“unenforceable“under“an˜y“particular“circumstance,‘œQthe“balanceŽ¤ of–UUthe“section“is“inš¸ãtended“to“apply“and“the“section“as“a“whole“is“in˜tended“to“apply“in“other“circumstances.Ž©‘ +7.‘1|If,‘»as–”sa“consequence“of“a“court“judgmenš¸ãt“or“allegation“of“paten˜t“infringemen˜t“or“for“an˜y“other“reason“(notŽ¡limited–ŸDto“patenš¸ãt“issues),‘±Àconditions“are“impGosed“on“y˜ou“(whether“b˜y“court“order,‘±Àagreemen˜t“or“otherwise)Ž¡that–Êâconš¸ãtradict“the“conditions“of“this“License,‘èEthey“do“not“excuse“y˜ou“from“the“conditions“of“this“License.ŽŽŽŒ‹ç)ª Šn ý‘ì°x¬1562›¯3DLDF-1.1.5.1’É çGNU–ÕXGENERAL“PUBLIC“LICENSE˜¬487Ž €n ý•@PIf–ä‚yš¸ãou“cannot“distribute“so“as“to“satisfy“sim˜ultaneously“y˜our“obligations“under“this“License“and“an˜y“otherŽ¤ pGertinenš¸ãt–¬.obligations,‘Áäthen“as“a“consequence“y˜ou“ma˜y“not“distribute“the“Program“at“all.‘vQF‘ÿ*ªor“example,‘Áäif“aŽ¡patenš¸ãt–Õglicense“w˜ould“not“pGermit“ro˜y˜alt˜y-free“redistribution“of“the“Program“b˜y“all“those“who“receiv˜e“copiesŽ¡directly–@5or“indirectly“through“yš¸ãou,‘Dnthen“the“only“w˜a˜y“y˜ou“could“satisfy“bGoth“it“and“this“License“w˜ould“bGe“toŽ¡refrain–UUen¸ãtirely“from“distribution“of“the“Program.Ž©‘ +If–nanš¸ãy“pGortion“of“this“section“is“held“in˜v‘ÿqÇalid“or“unenforceable“under“an˜y“particular“circumstance,‘œQthe“balanceŽ¡of–UUthe“section“is“inš¸ãtended“to“apply“and“the“section“as“a“whole“is“in˜tended“to“apply“in“other“circumstances.Ž¦‘ It– þis“not“the“purpGose“of“this“section“to“induce“yš¸ãou“to“infringe“an˜y“paten˜ts“or“other“propGert˜y“righ˜t“claimsŽ¡or–oGto“conš¸ãtest“v‘ÿqÇalidit˜y“of“an˜y“suc˜h“claims;‘|Athis“section“has“the“sole“purpGose“of“protecting“the“in˜tegrit˜y“of“theŽ¡free›Òsoft•¸ãw“are˜distribution˜system,‘¹whic“h˜is˜implemen“ted˜b“y˜public˜license˜practices.‘WFMan“y˜pGeople˜ha“v“e˜madeŽ¡generous–ƒÝconš¸ãtributions“to“the“wide“range“of“soft˜w˜are“distributed“through“that“system“in“reliance“on“consisten˜tŽ¡application–í@of“that“system;‘òit“is“up“to“the“author/donor“to“decide“if“he“or“she“is“willing“to“distribute“soft•¸ãw“areŽ¡through–UUanš¸ãy“other“system“and“a“licensee“cannot“impGose“that“c˜hoice.Ž¦‘ This–Ogsection“is“inš¸ãtended“to“mak˜e“thoroughly“clear“what“is“bGeliev˜ed“to“bGe“a“consequence“of“the“rest“of“thisŽ¡License.Ž¦‘ 8.‘Ö5If–vÏthe“distribution“and/or“use“of“the“Program“is“restricted“in“certain“counš¸ãtries“either“b˜y“paten˜ts“or“b˜yŽ¡cop•¸ãyrigh“ted›Šin“terfaces,‘!the˜original˜cop“yrigh“t˜holder˜who˜places˜the˜Program˜under˜this˜License˜ma“y˜add˜anŽ¡explicit–vgeographical“distribution“limitation“excluding“those“coun¸ãtries,‘Öso“that“distribution“is“pGermitted“onlyŽ¡in–Aor“among“counš¸ãtries“not“th˜us“excluded.‘k0In“suc˜h“case,‘E…this“License“incorpGorates“the“limitation“as“if“writtenŽ¡in–UUthe“b•Go“dy–UUof“this“License.Ž¦‘ @@ -5919,2795 +6113,2778 @@ Eac•¸ãh›–ùv“ersion˜is˜giv“en˜a˜distinguishing˜v“ersion˜n“um“b•Ger.‘6²If˜the˜Program˜sp“eci es˜a˜v•¸ãersion˜n“um“bGer˜of˜thisŽ¡License–¶Êwhicš¸ãh“applies“to“it“and“\an˜y“later“v˜ersion",‘Ö€y˜ou“ha˜v˜e“the“option“of“follo˜wing“the“terms“and“conditionsŽ¡either– 'of“that“vš¸ãersion“or“of“an˜y“later“v˜ersion“published“b˜y“the“F‘ÿ*ªree“Soft˜w˜are“F‘ÿ*ªoundation.‘™>If“the“ProgramŽ¡došGes–Â~not“sp˜ecify“a“vš¸ãersion“n˜um˜bGer“of“this“License,‘ÝÉy˜ou“ma˜y“c˜hoGose“an˜y“v˜ersion“ev˜er“published“b˜y“the“F‘ÿ*ªreeŽ¡Soft•¸ãw“are‘UUF‘ÿ*ªoundation.Ž¦‘ 10.‘D If–Ì yš¸ãou“wish“to“incorpGorate“parts“of“the“Program“in˜to“other“free“programs“whose“distribution“conditionsŽ¡are–¢:di erenš¸ãt,‘õswrite“to“the“author“to“ask“for“pGermission.‘XvF‘ÿ*ªor“soft˜w˜are“whic˜h“is“cop˜yrigh˜ted“b˜y“the“F‘ÿ*ªreeŽ¡Soft•¸ãw“are–¯fF›ÿ*ªoundation,‘Åêwrite“to“the“F˜ree“Soft•¸ãw“are‘¯fF˜oundation;‘Üow“e–¯fsometimes“mak¸ãe“exceptions“for“this.‘úOurŽ¡decision–¶³will“bGe“guided“bš¸ãy“the“t˜w˜o“goals“of“preserving“the“free“status“of“all“deriv‘ÿqÇativ˜es“of“our“free“soft˜w˜areŽ¡and–UUof“promoting“the“sharing“and“reuse“of“soft•¸ãw“are‘UUgenerally‘ÿ*ª.ŽŸ’Ã.NO‘UUW‘þãARRANTYŽ¦‘ 11.‘—BECAš¸ãUSE–R‚THE“PR˜OGRAM“IS“LICENSED“FREE“OF“CHAR˜GE,‘RÄTHERE“IS“NO“W‘þãARRANTY“F˜ORŽ¡THE–ö PR¸ãOGRAM,›ö6TO“THE“EXTENT“PERMITTED“BY“APPLICABLE“LA‘þãW.˜EX¸ãCEPT“WHEN“OTH-Ž¡ER‘þãWISE›àÒST–ÿ*ªA“TED˜IN˜WRITING˜THE˜COPYRIGHT˜HOLDERS˜AND/OR˜OTHER˜P“AR“TIES˜PR•¸ãO“VIDEŽ¡THE–ePR¸ãOGRAM“\AS“IS"“WITHOUT“W‘þãARRANTY“OF“ANY“KIND,‘eaEITHER“EXPRESSED“OR“IM-Ž¡PLIED,–-JINCLUDING,“BUT–-@NOT“LIMITED“TO,‘-JTHE“IMPLIED“W‘þãARRANTIES“OF“MER¸ãCHANT‘ÿ*ªABIL-Ž¡ITY–sßAND“FITNESS“F¸ãOR“A“P–ÿ*ªAR“TICULAR–sßPURPOSE.‘tTHE“ENTIRE“RISK“AS“TO“THE“QUALITY“ANDŽ¡PERFš¸ãORMANCE–;OF“THE“PR˜OGRAM“IS“WITH“YOU.‘nSHOULD“THE“PR˜OGRAM“PR˜O˜VE“DEFEC-Ž¡TIVE,–UUYOU“ASSUME“THE“COST“OF“ALL“NECESSAR›ÿ*ªY“SER‘þãVICING,“REP˜AIR“OR“CORRECTION.Ž¦‘ -12.‘LIN– þNO“EVENT“UNLESS“REQUIRED“BY“APPLICABLE“LA‘þãW“OR“A¸ãGREED“TO“IN“WRITINGŽ¡WILL–JqANY“COPYRIGHT“HOLDER,‘J°OR“ANY“OTHER“P–ÿ*ªAR“TY–JqWHO“MA‘ÿ*ªY“MODIFY“AND/OR“RE-Ž¡DISTRIBUTE–¬¬THE“PRš¸ãOGRAM“AS“PERMITTED“ABO˜VE,‘­BE“LIABLE“TO“YOU“F˜OR“D˜AMA˜GES,Ž¡INCLUDING–QéANY“GENERAL,–QêSPECIAL,“INCIDENT‘ÿ*ªAL–QéOR“CONSEQUENTIAL“D•¸ãAMA“GES‘QéARISINGŽ¡OUT–P×OF“THE“USE“OR“INABILITY“TO“USE“THE“PR¸ãOGRAM“(INCLUDING“BUT“NOT“LIMITED“TOŽ¡LOSS–YFOF“Dš¸ãA–ÿ*ªT“A–YFOR“D˜A–ÿ*ªT“A–YFBEING“RENDERED“INA˜CCURA›ÿ*ªTE“OR“LOSSES“SUST˜AINED“BY“YOUŽ¡OR–,THIRD“P–ÿ*ªAR“TIES–,OR“A“F‘þãAILURE“OF“THE“PRš¸ãOGRAM“TO“OPERA‘ÿ*ªTE“WITH“ANY“OTHER“PR˜O-Ž¡GRAMS),‘ ?EVEN– IF“SUCH“HOLDER“OR“OTHER“P–ÿ*ªAR“TY– HAS“BEEN“AD¸ãVISED“OF“THE“POSSIBILITYŽ¡OF–UUSUCH“D•¸ãAMA“GES.ŽŽŽŒ‹äf’ Šn ý‘ì«484›­GNU–ÕXGENERAL“PUBLIC“LICENSE’Ñ}3DLDFPRÃŽG˜·x«1524Ž €n ý•@P’”šEND–UUOF“TERMS“AND“CONDITIONSŽŸ‘z+DHo¸ãw–UUto“Apply“These“T›ÿ*ªerms“to“Y˜our“New“ProgramsŽ¤‘ +12.‘LIN– þNO“EVENT“UNLESS“REQUIRED“BY“APPLICABLE“LA‘þãW“OR“A¸ãGREED“TO“IN“WRITINGŽ¡WILL–JqANY“COPYRIGHT“HOLDER,‘J°OR“ANY“OTHER“P–ÿ*ªAR“TY–JqWHO“MA‘ÿ*ªY“MODIFY“AND/OR“RE-Ž¡DISTRIBUTE–¬¬THE“PRš¸ãOGRAM“AS“PERMITTED“ABO˜VE,‘­BE“LIABLE“TO“YOU“F˜OR“D˜AMA˜GES,Ž¡INCLUDING–QéANY“GENERAL,–QêSPECIAL,“INCIDENT‘ÿ*ªAL–QéOR“CONSEQUENTIAL“D•¸ãAMA“GES‘QéARISINGŽ¡OUT–P×OF“THE“USE“OR“INABILITY“TO“USE“THE“PR¸ãOGRAM“(INCLUDING“BUT“NOT“LIMITED“TOŽŽŽŒ‹è>º Šn ý‘ì¬488›¯GNU–ÕXGENERAL“PUBLIC“LICENSE’É ç3DLDF-1.1.5.1˜°x¬1562Ž €n ý•@PLOSS–YFOF“Dš¸ãA–ÿ*ªT“A–YFOR“D˜A–ÿ*ªT“A–YFBEING“RENDERED“INA˜CCURA›ÿ*ªTE“OR“LOSSES“SUST˜AINED“BY“YOUŽ¤ OR–,THIRD“P–ÿ*ªAR“TIES–,OR“A“F‘þãAILURE“OF“THE“PRš¸ãOGRAM“TO“OPERA‘ÿ*ªTE“WITH“ANY“OTHER“PR˜O-Ž¡GRAMS),‘ ?EVEN– IF“SUCH“HOLDER“OR“OTHER“P–ÿ*ªAR“TY– HAS“BEEN“AD¸ãVISED“OF“THE“POSSIBILITYŽ¡OF–UUSUCH“D•¸ãAMA“GES.Ž¤’”šEND–UUOF“TERMS“AND“CONDITIONSŽ¡‘z+DHo¸ãw–UUto“Apply“These“T›ÿ*ªerms“to“Y˜our“New“ProgramsŽ¤‘ If––ßyš¸ãou“dev˜elop“a“new“program,‘§Aand“y˜ou“w˜an˜t“it“to“bšGe“of“the“greatest“p˜ossible“use“to“the“public,‘§Athe“b˜estŽ© w•¸ãa“y–Ëéto“ac•¸ãhiev“e–Ëéthis“is“to“makš¸ãe“it“free“soft˜w˜are“whic˜h“ev˜ery˜one“can“redistribute“and“c˜hange“under“these“terms.Ž¡‘ -T‘ÿ*ªo–³ùdo“so,‘Ô?attacš¸ãh“the“follo˜wing“notices“to“the“program.‘;þIt“is“safest“to“attac˜h“them“to“the“start“of“eac˜h“sourceŽ¦ le–’Xto“most“e ectivš¸ãely“con˜v˜ey“the“exclusion“of“w˜arran˜t˜y;‘°Úand“eac˜h“ le“should“ha˜v˜e“at“least“the“\cop˜yrigh˜t"Ž¦line–UUand“a“pGoin¸ãter“to“where“the“full“notice“is“found.Ž¡·h«one–UUline“to“giv¸ãe“the“program's“name“and“a“brief“idea“of“what“it“doGes.·iŽ¦«Cop•¸ãyrigh“t–UU(C)“·h«y¸ãear·i“h«name“of“author·iŽ¡«This–\program“is“free“soft•¸ãw“are;‘&¯y“ou–\can“redistribute“it“and/or“moGdify“it“under“the“terms“of“the“GNU‘JGeneralŽ¦Public–ù¦License“as“published“bš¸ãy“the“F‘ÿ*ªree“Soft˜w˜are“F‘ÿ*ªoundation;‘KÏeither“v˜ersion“2“of“the“License,‘"»or“(at“y˜ourŽ¦option)–UUanš¸ãy“later“v˜ersion.Ž¡This–(fprogram“is“distributed“in“the“hopšGe“that“it“will“b˜e“useful,‘1cbut“WITHOUT–([ANY“W‘þãARRANTY;‘(fwithoutŽ¦evš¸ãen–ƒªthe“implied“w˜arran˜t˜y“of“MER˜CHANT‘ÿ*ªABILITY›ƒžor“FITNESS˜F¸ãOR˜A˜P–ÿ*ªAR“TICULAR˜PURPOSE.‘ƒªSeeŽ¦the–UUGNU“General“Public“License“for“more“details.Ž¡Y‘ÿ*ªou–qÖshould“ha•¸ãv“e›qÖreceiv“ed˜a˜cop“y˜of˜the˜GNU‘qÏGeneral˜Public˜License˜along˜with˜this˜program;‘€if˜not,‘xöwriteŽ¦to–UUthe“F›ÿ*ªree“Soft•¸ãw“are–UUF˜oundation,“Inc.,“59“T˜emple“Place,“Suite“330,“Boston,“MA“02111-1307“USAŽ¡‘ +T‘ÿ*ªo–³ùdo“so,‘Ô?attacš¸ãh“the“follo˜wing“notices“to“the“program.‘;þIt“is“safest“to“attac˜h“them“to“the“start“of“eac˜h“sourceŽ¦ le–’Xto“most“e ectivš¸ãely“con˜v˜ey“the“exclusion“of“w˜arran˜t˜y;‘°Úand“eac˜h“ le“should“ha˜v˜e“at“least“the“\cop˜yrigh˜t"Ž¦line–UUand“a“pGoin¸ãter“to“where“the“full“notice“is“found.Ž¡°h¬one–UUline“to“giv¸ãe“the“program's“name“and“a“brief“idea“of“what“it“doGes.°iŽ¦¬Cop•¸ãyrigh“t–UU(C)“°h¬y¸ãear°i“h¬name“of“author°iŽ¡¬This–\program“is“free“soft•¸ãw“are;‘&¯y“ou–\can“redistribute“it“and/or“moGdify“it“under“the“terms“of“the“GNU‘JGeneralŽ¦Public–ù¦License“as“published“bš¸ãy“the“F‘ÿ*ªree“Soft˜w˜are“F‘ÿ*ªoundation;‘KÏeither“v˜ersion“2“of“the“License,‘"»or“(at“y˜ourŽ¦option)–UUanš¸ãy“later“v˜ersion.Ž¡This–(fprogram“is“distributed“in“the“hopšGe“that“it“will“b˜e“useful,‘1cbut“WITHOUT–([ANY“W‘þãARRANTY;‘(fwithoutŽ¦evš¸ãen–ƒªthe“implied“w˜arran˜t˜y“of“MER˜CHANT‘ÿ*ªABILITY›ƒžor“FITNESS˜F¸ãOR˜A˜P–ÿ*ªAR“TICULAR˜PURPOSE.‘ƒªSeeŽ¦the–UUGNU“General“Public“License“for“more“details.Ž¡Y‘ÿ*ªou–qÖshould“ha•¸ãv“e›qÖreceiv“ed˜a˜cop“y˜of˜the˜GNU‘qÏGeneral˜Public˜License˜along˜with˜this˜program;‘€if˜not,‘xöwriteŽ¦to–UUthe“F›ÿ*ªree“Soft•¸ãw“are–UUF˜oundation,“Inc.,“59“T˜emple“Place,“Suite“330,“Boston,“MA“02111-1307“USAŽ¡‘ Also–UUadd“information“on“hoš¸ãw“to“con˜tact“y˜ou“b˜y“electronic“and“papGer“mail.Ž¡‘ -If–2the“program“is“in•¸ãteractiv“e,‘ lmak“e–2it“output“a“short“notice“likš¸ãe“this“when“it“starts“in“an“in˜teractiv˜e“moGde:Ž¡Gnomo•¸ãvision›UUv“ersion˜69,˜Cop“yrigh“t‘rž²×cŽŽŽ˜· ŽŽŽŽ‘ª««y“ear˜name˜of˜authorŽ¦Gnomoš¸ãvision–UUcomes“with“ABSOLUTEL‘ÿ*ªY“NO“W‘þãARRANTY;“for“details“t˜ypGe“`sho˜w“w'.Ž¦This–r=is“free“soft•¸ãw“are,‘¹wand›r=y“ou˜are˜w“elcome˜to˜redistribute˜it˜under˜certain˜conditions;‘±t“ypGe˜`sho“w˜c'˜forŽ¦details.Ž¡‘ +If–2the“program“is“in•¸ãteractiv“e,‘ lmak“e–2it“output“a“short“notice“likš¸ãe“this“when“it“starts“in“an“in˜teractiv˜e“moGde:Ž¡Gnomo•¸ãvision›UUv“ersion˜69,˜Cop“yrigh“t‘rž²×cŽŽŽ˜° ŽŽŽŽ‘ª«¬y“ear˜name˜of˜authorŽ¦Gnomoš¸ãvision–UUcomes“with“ABSOLUTEL‘ÿ*ªY“NO“W‘þãARRANTY;“for“details“t˜ypGe“`sho˜w“w'.Ž¦This–r=is“free“soft•¸ãw“are,‘¹wand›r=y“ou˜are˜w“elcome˜to˜redistribute˜it˜under˜certain˜conditions;‘±t“ypGe˜`sho“w˜c'˜forŽ¦details.Ž¡‘ The–…ÿhš¸ãypGothetical“commands“`sho˜w“w'“and“`sho˜w“c'“should“sho˜w“the“appropriate“parts“of“the“GeneralŽ¦Public–ƒLicense.‘üyOf“course,‘the“commands“yš¸ãou“use“ma˜y“bGe“called“something“other“than“`sho˜w“w'“and“`sho˜wŽ¦c';–UUthey“could“evš¸ãen“bGe“mouse-clic˜ks“or“men˜u“items{whatev˜er“suits“y˜our“program.Ž¡‘ Y‘ÿ*ªou–u+should“also“get“yš¸ãour“emplo˜y˜er“(if“y˜ou“w˜ork“as“a“programmer)“or“y˜our“sc˜hoGol,‘¢if“an˜y‘ÿ*ª,‘¢to“sign“a“\cop˜yrigh˜tŽ¦disclaimer"–UUfor“the“program,“if“necessary‘ÿ*ª.‘qÇHere“is“a“sample;“alter“the“names:Ž¡‘ Y‘ÿ*ªo•¸ãy“oGdyne,– Inc.,“herebš¸ãy–ùµdisclaims“all“cop˜yrigh˜t“in˜terest“in“the“program“`Gnomo˜vision'“(whic˜h“mak˜es“passesŽ¦at–UUcompilers)“written“bš¸ãy“James“Hac˜k˜er.Ž¡‘ -·h«signature–UUof“Tš¸ãy“CoGon·i«,“1“April“1989“T˜y“CoGon,“Presiden˜t“of“ViceŽ¡‘ -This–9iGeneral“Public“License“došGes“not“p˜ermit“incorp˜orating“yš¸ãour“program“in˜to“proprietary“programs.‘$If“y˜ourŽ¦program–l·is“a“subroutine“library‘ÿ*ª,‘ryš¸ãou“ma˜y“consider“it“more“useful“to“pGermit“linking“proprietary“applicationsŽ¦with–Cthe“library‘ÿ*ª.‘ZÁIf“this“is“what“yš¸ãou“w˜an˜t“to“do,‘use“the“GNU‘2Library“General“Public“License“instead“of“thisŽ¦License.ŽŸ·h›ª¨«GNU–UUGeneral“Public“License‘@­1524˜·i‘ǑDZ=·‘ÿý«This“section“con¸ãtains“no“¬C‘€Ÿÿ®+‘ÿ+ŽŽ‘œu«coGde.‘o·±=ŽŸ ­This–ÕXcoŸÓVEŽ‘ãxXŽ‘•macros“that“I‘|use“forŽŽŽŒ‹åy Šn ý‘ì·x«1525–­3DLDFPRÃŽG’A²ùINDEX“«485Ž €n ýý2Ÿ˜9formatting–ùthe“index“enš¸ãtries,‘"‰so“the“order“of“the“en˜tries“is“a“bit“pGeculiar.‘^EF‘ÿ*ªor“example,‘"‰È\cfunc{z}“«w˜ouldŽ¤ come–'GbšGefore“È\ofunc{a}“«(È\cfunc“«is“for“class“functions,‘0}and“È\ofunc“«is“for“op˜erators“that“aren't“mem¸ãb˜ers“of“aŽ¡class).Ž¡‘ +°h¬signature–UUof“Tš¸ãy“CoGon°i¬,“1“April“1989“T˜y“CoGon,“Presiden˜t“of“ViceŽ¡‘ 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First–"‘come“the“index“enš¸ãtries“whic˜h“start“with“\??"›`Ûand“\!!".˜These“are“follo•¸ãw“ed›"‘b“y˜the˜non-opGerator˜classŽ¡memš¸ãbGer–ßfunctions“for“all“of“the“classes.‘J_Then“come“the“class“mem˜bšGer“op˜erators“for“all“of“the“classes,‘öÁfollo•¸ãw“edŽ¡bš¸ãy–æWthe“non-class“opGerators.‘$ÎCurren˜tly‘ÿ*ª,‘ ˜I'm“only“putting“index“en˜tries“in“b˜y“hand“where“the“class“mem˜bGerŽ¡functions–UUand“opGerators“are“declared.Ž¡‘ -[¬LDF‘T2002.10.11.«]Ž‘Yq¢Another–¾¼problem“is“that“\Ïop–ÿ}'er“ator&Ž‘,칫"“and“\Ïop–ÿ}'er“ator&=Ž‘4H•«"“use“the“italic“ampGersand.‘­ûItŽ¡w¸ãould–UUbšGe“p˜ossible“to“ x“this,“but“slighš¸ãtly“tric˜ky‘ÿ*ª.‘qÇTO“DO:“Fix“this!ŽŽ Íé þ2‘²wÂBUG‘²>FIX«:‘ -15,–E²150,“173,“404,“549,“656,“658,Ž¤ ‘828,– ³1348,“1475.Ž© Â!!«:‘ -56,–®•60,“111,“112,“114,“122,“130,“148,“162,“163,Ž¡‘181,–Ò311,“404,“436,“458,“502,“503,“515,“528,“685,Ž¡‘791,–~l800,“863,“874,“896,“926,“1080,“1120,“1234,Ž¡‘1283,–<„1329,“1398,“1423,“1432,“1446,“1462,“1491.Ž¦Â!!‘÷¾BUG«:‘ -379,–» 537,“677.Ž¦Â!!‘TKLUDGE«:‘ 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-1010.Ž¡ÂP®9olygonŽ‘)î«::Ïshe‘ÿ}'arŽ‘4:«:‘ -1012.Ž¡ÂP®9olygonŽ‘)î«::Ïshift‘‰ffŽ‘®timesŽ‘.ì;«:‘ -1020,‘:Ò1022.Ž¡ÂP®9olygonŽ‘)î«::ÏshiftŽ‘}«:‘ -1015,‘“1017.ŽŽ ý•@P’ôà¤ÂP®9olyhedronŽ’.îq«::Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘QŒß«:‘ -1432.Ž¤ #þ’ôà¤ÂRectangleŽ’' 9«::Ï~R–ÿ}'e“ctangleŽ‘/¨«:‘ -1078.Ž¡’ôà¤ÂRectangleŽ’' 9«::Ïc‘ÿ}'ornerŽ‘q^«:‘ -1085.Ž¡’ôà¤ÂRectangleŽ’' 9«::Ïcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“r–ÿ}'e“ctangleŽ‘Y/«:‘ -1074,‘‘†1076.Ž¡’ôà¤ÂRectangleŽ’' 9«::Ïis‘‰ffŽ‘®r–ÿ}'e“ctangularŽ‘<¸þ«:‘ -1082.Ž¡’ôà¤ÂRectangleŽ’' 9«::Ïmid‘‰ffŽ‘®p‘ÿ}'ointŽ‘+7Ÿ«:‘ -1087.Ž¡’ôà¤ÂRectangleŽ’' 9«::ÏR–ÿ}'e“ctangleŽ‘*‹¨«:‘ -1061,–ÓF1064,“1069.Ž¡’ôà¤ÂRectangleŽ’' 9«::ÏsetŽ‘ x„«:‘ -1066,‘Š1071.Ž¡’ôà¤ÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ’]Ø<«::Ïangle‘‰ffŽ‘®p‘ÿ}'ointŽ‘1Y½«:‘ -950.Ž¡’ôà¤ÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ’]Ø<«::Ïget‘‰ffŽ‘®c–ÿ}'o“ecientsŽ‘@ðr«:‘ -946.Ž¡’ôà¤ÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ’]Ø<«::ÏhalfŽ‘y–«:‘ -969.Ž¡’ôà¤ÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ’]Ø<«::Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘QŒß«:‘ -953,Ž© ’à¦964.Ž¡’ôà¤ÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ’]Ø<«::Ïis‘‰ffŽ‘®cubicŽ‘"%$«:‘ -944.Ž¡’ôà¤ÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ’]Ø<«::Ïis‘‰ffŽ‘®quadr‘ÿ}'aticŽ‘3çô«:‘ -943.Ž¡’ôà¤ÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ’]Ø<«::Ïis‘‰ffŽ‘®quarticŽ‘*1í«:‘ -945.Ž¡’ôà¤ÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ’]Ø<«::Ïlo–ÿ}'c“ationŽ‘"Á}«:‘ -948.Ž¡’ôà¤ÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ’]Ø<«::ÏquarterŽ‘!F«:‘ -970.Ž¡’ôà¤ÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ’]Ø<«::Ïse‘ÿ}'gmentŽ‘#õ¡«:‘ -967.Ž¡’ôà¤ÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ’]Ø<«::ÏsolveŽ‘7Ë«:‘ -947.Ž¡’ôà¤ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ’6_X«::Ïcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“r–ÿ}'e“g‘‰ffŽ‘®p“olygonŽ‘cvB«:‘ -1039.Ž¡’ôà¤ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ’6_X«::Ïcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“R–ÿ}'e“g‘‰ffŽ‘®PolygonŽ‘h¹«:‘ -1041.Ž¡’ôà¤ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ’6_X«::Ïdr›ÿ}'aw‘‰ffŽ–®in‘‰ffŽ“cir˜cleŽ‘=Ы:‘ -1049,–±t1050,“1272,Ž¦’à¦1273.Ž¡’ôà¤ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ’6_X«::Ïdr›ÿ}'aw‘‰ffŽ–®out‘‰ffŽ“cir˜cleŽ‘B?«:‘ -1053,–Kú1054,“1275,Ž¦’à¦1276,‘VÕ1277.Ž¡’ôà¤ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ’6_X«::Ïget‘‰ffŽ‘®r‘ÿ}'adiusŽ‘+ûß«:‘ -1045.Ž¡’ôà¤ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ’6_X«::Ïin‘‰ffŽ‘®cir‘ÿ}'cleŽ‘$ÂI«:‘ -1047,‘ µ1270.Ž¡’ôà¤ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ’6_X«::Ïout‘‰ffŽ‘®cir‘ÿ}'cleŽ‘)Þ¸«:‘ -1051,‘úâ1274.Ž¡’ôà¤ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ’6_X«::ÏR–ÿ}'e“g‘‰ffŽ‘®PolygonŽ‘7ª«:‘ -1029,‘Ïo1032.Ž¡’ôà¤ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ’6_X«::ÏsetŽ‘ x„«:‘ -1035.Ž¡’ôà¤ÂSolidŽ’^{«::Ï~SolidŽ‘C«:‘ -1305.Ž¡’ôà¤ÂSolidŽ’^{«::Ïapply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘Fß«:‘ -1348.Ž¡’ôà¤ÂSolidŽ’^{«::Ïcle‘ÿ}'arŽ‘(Ù«:‘ -1343.Ž¡’ôà¤ÂSolidŽ’^{«::Ïcr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“solidŽ‘G!»«:‘ -1303.Ž¡’ôà¤ÂSolidŽ’^{«::Ïdr‘ÿ}'awŽ‘(Û«:‘ -1383.Ž¡’ôà¤ÂSolidŽ’^{«::Ïextr‘ÿ}'actŽ‘Âo«:‘ -1364.Ž¡’ôà¤ÂSolidŽ’^{«::Ï l‘‚ØlŽ‘ Éó«:‘ -1386.Ž¡’ôà¤ÂSolidŽ’^{«::Ï l‘‚Øldr‘ÿ}'awŽ‘!gk«:‘ 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-«runcu½‰™šs4Ž‘ÔwOctahedronŽ‘]Ϊ«::ÏT‘ÿ;¼runc‘‰ffŽ‘®Octahe–ÿ}'dr“onŽ‘Pš'«:‘ -1484,ŽŸ ‘1487.Ž¡ÂCircleŽ‘c,«::Ïop–ÿ}'er“ator=Ž‘,í«:‘ -1253,‘ei1255.Ž¡ÂColorŽ‘Ož«::Ïop–ÿ}'er“ator!=Ž‘/®ý«:‘ -77.Ž¡ÂColorŽ‘Ož«::Ïop–ÿ}'er“ator==Ž‘4H•«:‘ -75.Ž¡ÂColorŽ‘Ož«::Ïop–ÿ}'er“ator=Ž‘,í«:‘ -73.Ž¡ÂCubQÇoidŽ‘%Oš«::Ïop–ÿ}'er“ator=Ž‘,í«:‘ -1425.Ž¡ÂEllipseŽ‘!èÙ«::Ïop–ÿ}'er“ator*=Ž‘1º]«:‘ -1194.Ž¡ÂEllipseŽ‘!èÙ«::Ïop–ÿ}'er“ator=Ž‘,í«:‘ -1119.Ž¡ÂEllipseŽ‘!èÙ«::Ïop–ÿ}'er“ator“do‘‰ffŽ‘®tr“ansformŽ‘\Þe«:‘ -1192.Ž¡ÂLineŽ‘Xƒ«::Ïop–ÿ}'er“ator=Ž‘,í«:‘ -599.Ž¡ÂP®9athŽ‘‘d«::Ïop–ÿ}'er“ator*=Ž‘1º]«:‘ -738.Ž¡ÂP®9athŽ‘‘d«::Ïop–ÿ}'er“ator+=Ž‘4H•«:‘ -754,‘€@758.Ž¡ÂP®9athŽ‘‘d«::Ïop–ÿ}'er“ator+Ž‘,S«:‘ -756.ŽŽ ý•@P’ôà¤ÂP®9athŽ’ r«::Ïop–ÿ}'er“ator==Ž‘4H•«:‘ -917.Ž¤ %’ôà¤ÂP®9athŽ’ r«::Ïop–ÿ}'er“ator=Ž‘,í«:‘ -656.Ž¡’ôà¤ÂP®9athŽ’ r«::Ïop–ÿ}'er“ator&=Ž‘4H•«:‘ -762.Ž¡’ôà¤ÂP®9athŽ’ r«::Ïop–ÿ}'er“ator&Ž‘,칫:‘ -767.Ž¡’ôà¤ÂPictureŽ’|±«::Ïop–ÿ}'er“ator*=Ž‘1º]«:‘ -246.Ž¡’ôà¤ÂPictureŽ’|±«::Ïop–ÿ}'er“ator+=Ž‘4H•«:‘ -224,–Çd225,“227,“545.Ž¡’ôà¤ÂPictureŽ’|±«::Ïop–ÿ}'er“ator=Ž‘,í«:‘ -222.Ž¡’ôà¤ÂP•®9oin“tŽ’zì«::Ïop–ÿ}'er“ator!=Ž‘/®ý«:‘ -525.Ž¡’ôà¤ÂP•®9oin“tŽ’zì«::Ïop–ÿ}'er“ator*=Ž‘1º]«:‘ -474,‘~¬485.Ž¡’ôà¤ÂP•®9oin“tŽ’zì«::Ïop–ÿ}'er“ator*Ž‘*ä2«:‘ -488.Ž¡’ôà¤ÂP•®9oin“tŽ’zì«::Ïop–ÿ}'er“ator+=Ž‘4H•«:‘ -479.Ž¡’ôà¤ÂP•®9oin“tŽ’zì«::Ïop–ÿ}'er“ator+Ž‘,S«:‘ -477.Ž¡’ôà¤ÂP•®9oin“tŽ’zì«::Ïop–ÿ}'er“ator-=Ž‘01Ô«:‘ -483.Ž¡’ôà¤ÂP•®9oin“tŽ’zì«::Ïop–ÿ}'er“ator-Ž‘(&&«:‘ -481,‘ž5492.Ž¡’ôà¤ÂP•®9oin“tŽ’zì«::Ïop–ÿ}'er“ator/=Ž‘1º]«:‘ -494.Ž¡’ôà¤ÂP•®9oin“tŽ’zì«::Ïop–ÿ}'er“ator/Ž‘+ç«:‘ -496.Ž¡’ôà¤ÂP•®9oin“tŽ’zì«::Ïop–ÿ}'er“ator==Ž‘4H•«:‘ -515,–-ú516,“523.Ž¡’ôà¤ÂP•®9oin“tŽ’zì«::Ïop–ÿ}'er“ator=Ž‘,í«:‘ -299.Ž¡’ôà¤ÂP®9olygonŽ’å’«::Ïop–ÿ}'er“ator*=Ž‘1º]«:‘ -1001.Ž¡’ôà¤ÂRectangleŽ’' 9«::Ïop–ÿ}'er“ator=Ž‘,í«:‘ -1079.Ž¡’ôà¤ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ’6_X«::Ïop–ÿ}'er“ator=Ž‘,í«:‘ -1026.Ž¡’ôà¤ÂSolidŽ’^{«::Ïop–ÿ}'er“ator*=Ž‘1º]«:‘ -1346.Ž¡’ôà¤ÂSolidŽ’^{«::Ïop–ÿ}'er“ator=Ž‘,í«:‘ -1307.Ž¡’ôà¤ÂT‘ÿ -«ransformŽ’)T!«::Ïop–ÿ}'er“ator*=Ž‘1º]«:‘ -171,‘,à173.Ž¡’ôà¤ÂT‘ÿ -«ransformŽ’)T!«::Ïop–ÿ}'er“ator*Ž‘*ä2«:‘ -176,‘Ca178.Ž¡’ôà¤ÂT‘ÿ -«ransformŽ’)T!«::Ïop–ÿ}'er“ator=Ž‘,í«:‘ -130.Ž¡’ôà¤Ïop–ÿ}'er“ator·Ž’#*‰«:‘ -103,‘÷&436.Ž¡’ôà¤Ïop–ÿ}'er“ator*Ž’ÄÖ«:‘ -490.Ž¡’ôà¤Ý__CXXL_PIŽ’$¦ñ«:‘ -36.Ž¡’ôà¤Ý__DECCXXŽ’fô«:‘ -6,–Z²7,“16,“23,“25,“36,“44,“278,“399,“1507.Ž¡’ôà¤Ý__GNUC__Ž’fô«:‘ -7,–u21,“26,“44,“278,“399,“1503,“1507.Ž¡’ôà¤Ý__USE_STD_IOSTREAMŽ’SæÖ«:‘ +[²LDF‘T2002.10.11.¬]Ž‘Yq¢Another–¾¼problem“is“that“\±op–ÿ}'er“ator&Ž‘,칬"“and“\±op–ÿ}'er“ator&=Ž‘4H•¬"“use“the“italic“ampGersand.‘­ûItŽ¡w¸ãould–UUbšGe“p˜ossible“to“ x“this,“but“slighš¸ãtly“tric˜ky‘ÿ*ª.‘qÇTO“DO:“Fix“this!ŽŽ ºÍé þO2‘²w­BUG‘²>FIX¬:‘ +18,–E²195,“218,“448,“593,“700,“702,Ž¤ ‘871,– ³1388,“1516.Ž© ”­!!¬:‘ +95,–®•99,“155,“156,“158,“166,“174,“193,“207,“208,Ž¡‘226,–Ò354,“448,“480,“502,“546,“547,“559,“572,“727,Ž¡‘834,–~l843,“906,“918,“940,“970,“1120,“1158,“1273,Ž¡‘1320,–<„1369,“1438,“1464,“1473,“1487,“1503,“1532.Ž¦­!!‘÷¾BUG¬:‘ +423,–» 581,“721.Ž¦­!!‘ù KLUDGE¬:‘ +19,–¥y310,“317,“445,“475,“1505.Ž¦­!!‘ „»LOOK‘M UP¬:‘ +441.Ž¦­!!‘ +úNOTE¬:‘ +1317.Ž¦­!!‘(TO‘Ù7DO¬:‘ +6,–Y24,“31,“49,“182,“184,“226,“267,“309,Ž¡‘350,–Ò398,“423,“439,“441,“444,“445,“453,“475,“505,Ž¡‘507,–Ò509,“591,“600,“601,“635,“647,“648,“687,“698,Ž¡‘728,–Ò751,“763,“766,“785,“961,“967,“992,“994,“996,Ž¡‘1011,–<„1039,“1068,“1101,“1122,“1129,“1171,“1201,Ž¡‘1203,–<„1212,“1265,“1269,“1270,“1299,“1320,“1323,Ž¡‘1331,–<„1368,“1419,“1438,“1470,“1472,“1487,“1491,Ž¡‘1497,–<„1500,“1503,“1505,“1518,“1524,“1543,“1563.Ž¦­!!‘ ¬mUR®9GENT¬:‘ +700.Ž¦­??¬:‘ +158,–Ù244,“353,“354,“530,“538,“590,“688,“700,Ž¡‘711,–ñS721,“728,“835,“882,“1080,“1081.Ž¦­CircleŽ‘c,¬::±Cir‘ÿ}'cleŽ‘ò¬:‘ +1278,‘Ÿ–1281.Ž¦­CircleŽ‘c,¬::±cr–ÿ}'e“ate‘‰ffŽ–®new‘‰ffŽ“cir‘ÿ}'cleŽ‘J N¬:‘ +1286.Ž¦­CircleŽ‘c,¬::±get‘‰ffŽ‘®diameterŽ‘7þ±¬:‘ +1298.Ž¦­CircleŽ‘c,¬::±get‘‰ffŽ‘®r‘ÿ}'adiusŽ‘+û߬:‘ +1297.Ž¦­CircleŽ‘c,¬::±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘QŒß¬:‘ +1300,–•1302,“1304.Ž¦­CircleŽ‘c,¬::±is‘‰ffŽ‘®cir‘ÿ}'cularŽ‘-¥¬:‘ +1295.Ž¦­CircleŽ‘c,¬::±setŽ‘ x„¬:‘ +1283.Ž¦­ColorŽ‘Ož¬::±ColorŽ‘¼Ã¬:‘ +97,–Z‡99,“102,“107.Ž¦­ColorŽ‘Ož¬::±de ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ‘Dn¬:‘ +149.Ž¦­ColorŽ‘Ož¬::±get‘‰ffŽ–®blue‘‰ffŽ“p‘ÿ}'artŽ‘7¶º¬:‘ +143.Ž¦­ColorŽ‘Ož¬::±get‘‰ffŽ›®gr–ÿ}'e“en‘‰ffŽ˜p“artŽ‘=5H¬:‘ +142.Ž¦­ColorŽ‘Ož¬::±get‘‰ffŽ‘®nameŽ‘(ùÀ¬:‘ +146.Ž¦­ColorŽ‘Ož¬::±get‘‰ffŽ›®r–ÿ}'e“d‘‰ffŽ˜p“artŽ‘3B¬:‘ +141.Ž¦­ColorŽ‘Ož¬::±get‘‰ffŽ–®use‘‰ffŽ“nameŽ‘:¶¬:‘ +144.Ž¦­ColorŽ‘Ož¬::±initialize‘‰ffŽ‘®c‘ÿ}'olorsŽ‘CÀ¬:‘ +151.Ž¦­ColorŽ‘Ož¬::±is‘‰ffŽ–®on‘‰ffŽ“fr–ÿ}'e“e‘‰ffŽ‘®stor“eŽ‘BzÕ¬:‘ +138.ŽŽ þO2’ôभColorŽ’0B¬::±mo‘ÿ}'difyŽ‘F¬:‘ +127.Ž¤ ¸’ôभColorŽ’0B¬::±set‘‰ffŽ–®blue‘‰ffŽ“p‘ÿ}'artŽ‘73ã¬:‘ +133.Ž¡’ôभColorŽ’0B¬::±set‘‰ffŽ›®gr–ÿ}'e“en‘‰ffŽ˜p“artŽ‘<²q¬:‘ +131.Ž¡’ôभColorŽ’0B¬::±set‘‰ffŽ‘®nameŽ‘(vé¬:‘ +123.Ž¡’ôभColorŽ’0B¬::±set‘‰ffŽ–®on‘‰ffŽ“fr–ÿ}'e“e‘‰ffŽ‘®stor“eŽ‘GU׬:‘ +121.Ž¡’ôभColorŽ’0B¬::±set‘‰ffŽ›®r–ÿ}'e“d‘‰ffŽ˜p“artŽ‘2ük¬:‘ +129.Ž¡’ôभColorŽ’0B¬::±set‘‰ffŽ–®use‘‰ffŽ“nameŽ‘:3/¬:‘ +125.Ž¡’ôभColorŽ’0B¬::±setŽ‘ x„¬:‘ +104,‘ó²109.Ž¡’ôभColorŽ’0B¬::±showŽ‘Šÿ¬:‘ +135.Ž¡’ôभCubQÇoidŽ’0>¬::±~Cub‘ÿ}'oidŽ‘$Ž,¬:‘ +1464.Ž¡’ôभCubQÇoidŽ’0>¬::±Cub‘ÿ}'oidŽ‘q¼¬:‘ +1455,–!g1457,“1459.Ž¡’ôभDoQÇdecahedronŽ’= 2¬::±Do–ÿ}'de“c“ahe“dr“onŽ‘<“ë¬:‘ +1497,‘¥l1500.Ž¡’ôभDoQÇdecahedronŽ’= 2¬::±dr‘ÿ}'aw‘‰ffŽ‘®netŽ‘'A“¬:‘ +1505.Ž¡’ôभDoQÇdecahedronŽ’= 2¬::±get‘‰ffŽ‘®netŽ‘4Ȭ:‘ +1503.Ž¡’ôभEllipseŽ’É}¬::±~El‘‚ØlipseŽ‘#¥J¬:‘ +1156.Ž¡’ôभEllipseŽ’É}¬::±angle‘‰ffŽ‘®p‘ÿ}'ointŽ‘1Y½¬:‘ +1201.Ž¡’ôभEllipseŽ’É}¬::±dotlab‘ÿ}'elŽ‘!ÿó¬:‘ +1162.Ž¡’ôभEllipseŽ’É}¬::±dr›ÿ}'aw‘‰ffŽ–®out‘‰ffŽ“r˜e˜ctangleŽ‘Q3 ¬:‘ +1261.Ž¡’ôभEllipseŽ’É}¬::±El‘‚ØlipseŽ‘ˆÚ¬:‘ +1146,‘ˆ-1149.Ž¡’ôभEllipseŽ’É}¬::±get‘‰ffŽ–®axis‘‰ffŽ“hŽ‘+-I¬:‘ +1197,‘^1199.Ž¡’ôभEllipseŽ’É}¬::±get‘‰ffŽ–®axis‘‰ffŽ“vŽ‘*ùš¬:‘ +1192,‘_91194.Ž¡’ôभEllipseŽ’É}¬::±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘,=G¬:‘ +1177,‘[1179.Ž¡’ôभEllipseŽ’É}¬::±get‘‰ffŽ‘®c–ÿ}'o“ecientsŽ‘@ðr¬:‘ +1174.Ž¡’ôभEllipseŽ’É}¬::±get‘‰ffŽ‘®fo‘ÿ}'cusŽ‘'A‘¬:‘ +1182,‘kw1184.Ž¡’ôभEllipseŽ’É}¬::±in‘‰ffŽ‘®r–ÿ}'e“ctangleŽ‘3Ö*¬:‘ +1259.Ž¡’ôभEllipseŽ’É}¬::±interse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘QŒß¬:‘ +1208,–‰›1210,“1212.Ž¡’ôभEllipseŽ’É}¬::±is‘‰ffŽ‘®cubicŽ‘"%$¬:‘ +1167.Ž¡’ôभEllipseŽ’É}¬::±is‘‰ffŽ‘®el‘‚Øliptic‘ÿ}'alŽ‘0ì–¬:‘ +1164.Ž¡’ôभEllipseŽ’É}¬::±is‘‰ffŽ‘®quadr‘ÿ}'aticŽ‘3çô¬:‘ +1166.Ž¡’ôभEllipseŽ’É}¬::±is‘‰ffŽ‘®quarticŽ‘*1í¬:‘ +1169.Ž¡’ôभEllipseŽ’É}¬::±lab‘ÿ}'elŽ‘t˜¬:‘ +1160.Ž¡’ôभEllipseŽ’É}¬::±lo–ÿ}'c“ationŽ‘"Á}¬:‘ +1205.Ž¡’ôभEllipseŽ’É}¬::±out‘‰ffŽ‘®r–ÿ}'e“ctangleŽ‘8ò™¬:‘ +1257.Ž¡’ôभEllipseŽ’É}¬::±r‘ÿ}'otateŽ‘o>¬:‘ +1235,–<¾1252,“1254.Ž¡’ôभEllipseŽ’É}¬::±sc‘ÿ}'aleŽ‘´ò¬:‘ +1237.Ž¡’ôभEllipseŽ’É}¬::±setŽ‘ x„¬:‘ +1151.Ž¡’ôभEllipseŽ’É}¬::±she‘ÿ}'arŽ‘4:¬:‘ +1239.ŽŽŽŽŽŒ‹êb¹ Šn ý‘ì¬490–¯INDEX’9?c3DLDF-1.1.5.1“°x¬1563Ž €n ý•@P­EllipseŽ‘!èÙ¬::±shift‘‰ffŽ‘®timesŽ‘.ì;¬:‘ +1247,‘R:1249.Ž¤ !à­EllipseŽ‘!èÙ¬::±shiftŽ‘}¬:‘ +1242,‘ªz1244.Ž¡­EllipseŽ‘!èÙ¬::±solveŽ‘7ˬ:‘ +1171.Ž¡­F‘ÿ +«oQÇcusŽ‘õL¬::±F‘ÿ;¼o‘ÿ}'cusŽ‘¿š¬:‘ +602,–Ñ604,“609.Ž¡­F‘ÿ +«oQÇcusŽ‘õL¬::±get‘‰ffŽ‘®dir–ÿ}'e“ctionŽ‘7,­¬:‘ +621.Ž¡­F‘ÿ +«oQÇcusŽ‘õL¬::±get‘‰ffŽ‘®distanc‘ÿ}'eŽ‘4y¹¬:‘ +622.Ž¡­F‘ÿ +«oQÇcusŽ‘õL¬::±get‘‰ffŽ–®p‘ÿ}'ersp‘‰ffŽ“elementŽ‘Mo”¬:‘ +628.Ž¡­F‘ÿ +«oQÇcusŽ‘õL¬::±get‘‰ffŽ‘®p‘ÿ}'erspŽ‘'ö¬:‘ +627.Ž¡­F‘ÿ +«oQÇcusŽ‘õL¬::±get‘‰ffŽ‘®p‘ÿ}'ositionŽ‘3x¬:‘ +620.Ž¡­F‘ÿ +«oQÇcusŽ‘õL¬::±get‘‰ffŽ–®tr‘ÿ}'ansform‘‰ffŽ“elementŽ‘a=Ŭ:‘ +625.Ž¡­F‘ÿ +«oQÇcusŽ‘õL¬::±get‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘;æý¬:‘ +624.Ž¡­F‘ÿ +«oQÇcusŽ‘õL¬::±get‘‰ffŽ‘®upŽ‘Òz¬:‘ +623.Ž¡­F‘ÿ +«oQÇcusŽ‘õL¬::±r‘ÿ}'eset‘‰ffŽ‘®angleŽ‘/¿k¬:‘ +615.Ž¡­F‘ÿ +«oQÇcusŽ‘õL¬::±setŽ‘ x„¬:‘ +606,‘ñ‘611.Ž¡­F‘ÿ +«oQÇcusŽ‘õL¬::±showŽ‘Šÿ¬:‘ +617.Ž¡­IcosahedronŽ‘<ØϬ::±dr‘ÿ}'aw‘‰ffŽ‘®netŽ‘'A“¬:‘ +1518.Ž¡­IcosahedronŽ‘<ØϬ::±get‘‰ffŽ‘®netŽ‘4Ȭ:‘ +1516.Ž¡­IcosahedronŽ‘<ØϬ::±Ic–ÿ}'osahe“dr“onŽ‘4H‘¬:‘ +1511,‘çç1514.Ž¡­LabQÇelŽ‘Ac¬::±get‘‰ffŽ‘®c‘ÿ}'opyŽ‘$ô¬:‘ +515.Ž¡­LabQÇelŽ‘Ac¬::±outputŽ‘@¬:‘ +516.Ž¡­LineŽ‘Xƒ¬::±get‘‰ffŽ‘®distanc‘ÿ}'eŽ‘4y¹¬:‘ +648.Ž¡­LineŽ‘Xƒ¬::±get‘‰ffŽ‘®p‘ÿ}'athŽ‘#Ÿë¬:‘ +646,‘¾h978.Ž¡­LineŽ‘Xƒ¬::±LineŽ‘ÒѬ:‘ +639,‘ï!641.Ž¡­LineŽ‘Xƒ¬::±showŽ‘Šÿ¬:‘ +652.Ž¡­P®9athŽ‘‘d¬::±~PathŽ‘·Ž¬:‘ 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+1091,–±t1092,“1309,Ž¦’à¦1310.Ž¡’ôभRegu½‰™šs4Ž‘ÔwP®9olygonŽ’6_X¬::±dr›ÿ}'aw‘‰ffŽ–®out‘‰ffŽ“cir˜cleŽ‘B?¬:‘ +1095,–Kú1096,“1312,Ž¦’à¦1313,‘VÕ1314.Ž¡’ôभRegu½‰™šs4Ž‘ÔwP®9olygonŽ’6_X¬::±get‘‰ffŽ‘®r‘ÿ}'adiusŽ‘+û߬:‘ +1087.Ž¡’ôभRegu½‰™šs4Ž‘ÔwP®9olygonŽ’6_X¬::±in‘‰ffŽ‘®cir‘ÿ}'cleŽ‘$ÂI¬:‘ +1089,‘ µ1307.Ž¡’ôभRegu½‰™šs4Ž‘ÔwP®9olygonŽ’6_X¬::±out‘‰ffŽ‘®cir‘ÿ}'cleŽ‘)Þ¸¬:‘ +1093,‘úâ1311.Ž¡’ôभRegu½‰™šs4Ž‘ÔwP®9olygonŽ’6_X¬::±R–ÿ}'e“g‘‰ffŽ‘®PolygonŽ‘7ª¬:‘ +1073,‘Ïo1076.Ž¡’ôभRegu½‰™šs4Ž‘ÔwP®9olygonŽ’6_X¬::±setŽ‘ x„¬:‘ +1079.Ž¡’ôभSolidŽ’^{¬::±~SolidŽ‘C¬:‘ +1343.Ž¡’ôभSolidŽ’^{¬::±apply‘‰ffŽ‘®tr‘ÿ}'ansformŽ‘F߬:‘ +1388.Ž¡’ôभSolidŽ’^{¬::±cle‘ÿ}'arŽ‘(Ù¬:‘ +1383.Ž¡’ôभSolidŽ’^{¬::±dr‘ÿ}'awŽ‘(Û¬:‘ +1423.Ž¡’ôभSolidŽ’^{¬::±extr‘ÿ}'actŽ‘Âo¬:‘ +1404.Ž¡’ôभSolidŽ’^{¬::± l‘‚ØlŽ‘ Éó¬:‘ +1426.Ž¡’ôभSolidŽ’^{¬::± l‘‚Øldr‘ÿ}'awŽ‘!gk¬:‘ +1429.Ž¡’ôभSolidŽ’^{¬::±get‘‰ffŽ‘®c‘ÿ}'enterŽ‘,=G¬:‘ +1353.Ž¡’ôभSolidŽ’^{¬::±get‘‰ffŽ–®cir›ÿ}'cle‘‰ffŽ“c˜enterŽ‘G ¬:‘ +1371.Ž¡’ôभSolidŽ’^{¬::±get‘‰ffŽ–®cir‘ÿ}'cle‘‰ffŽ“ptrŽ‘9??¬:‘ +1358.Ž¡’ôभSolidŽ’^{¬::±get‘‰ffŽ‘®c‘ÿ}'opyŽ‘$ô¬:‘ +1348.Ž¡’ôभSolidŽ’^{¬::±get‘‰ffŽ–®el‘‚Ølipse‘‰ffŽ“c‘ÿ}'enterŽ‘K¬:‘ +1373.Ž¡’ôभSolidŽ’^{¬::±get‘‰ffŽ–®el‘‚Ølipse‘‰ffŽ“ptrŽ‘=5L¬:‘ +1360.Ž¡’ôभSolidŽ’^{¬::±get‘‰ffŽ‘®extr‘ÿ}'emesŽ‘7D`¬:‘ +1408.Ž¡’ôभSolidŽ’^{¬::±get‘‰ffŽ–®maximum‘‰ffŽ“zŽ‘Dm}¬:‘ +1411.Ž¡’ôभSolidŽ’^{¬::±get‘‰ffŽ–®me‘ÿ}'an‘‰ffŽ“zŽ‘0¶ +¬:‘ +1413.Ž¡’ôभSolidŽ’^{¬::±get‘‰ffŽ–®minimum‘‰ffŽ“zŽ‘C]ج:‘ +1409.ŽŽŽŽŽŒ‹ìš Šn ý‘ì¬492–¯INDEX’9?c3DLDF-1.1.5.1“°x¬1563Ž €n ý•@P­SolidŽ‘}׬::±get‘‰ffŽ–®p‘ÿ}'ath‘‰ffŽ“ptrŽ‘4Cˆ¬:‘ +1362.Ž¤ "Ž­SolidŽ‘}׬::±get‘‰ffŽ›®r–ÿ}'e“ctangle‘‰ffŽ˜c“enterŽ‘Vä¬:‘ +1375.Ž¡­SolidŽ‘}׬::±get‘‰ffŽ›®r–ÿ}'e“ctangle‘‰ffŽ˜ptrŽ‘HS ¬:‘ +1364.Ž¡­SolidŽ‘}׬::±get‘‰ffŽ›®r–ÿ}'e“g‘‰ffŽ˜p“olygon‘‰ffŽ˜c“enterŽ‘`rï¬:‘ +1377.Ž¡­SolidŽ‘}׬::±get‘‰ffŽ›®r–ÿ}'e“g‘‰ffŽ˜p“olygon‘‰ffŽ˜ptrŽ‘R¦+¬:‘ +1366.Ž¡­SolidŽ‘}׬::±get‘‰ffŽ–®shap›ÿ}'e‘‰ffŽ“c˜enterŽ‘Gn(¬:‘ +1369.Ž¡­SolidŽ‘}׬::±get‘‰ffŽ–®shap‘ÿ}'e‘‰ffŽ“ptrŽ‘9¡d¬:‘ +1356.Ž¡­SolidŽ‘}׬::±is‘‰ffŽ–®on‘‰ffŽ“fr–ÿ}'e“e‘‰ffŽ‘®stor“eŽ‘BzÕ¬:‘ +1379.Ž¡­SolidŽ‘}׬::±outputŽ‘@¬:‘ +1419.Ž¡­SolidŽ‘}׬::±r‘ÿ}'otateŽ‘o>¬:‘ +1399,‘±b1401.Ž¡­SolidŽ‘}׬::±sc‘ÿ}'aleŽ‘´ò¬:‘ +1390.Ž¡­SolidŽ‘}׬::±set‘‰ffŽ‘®extr‘ÿ}'emesŽ‘6Á‰¬:‘ +1406.Ž¡­SolidŽ‘}׬::±set‘‰ffŽ–®on‘‰ffŽ“fr–ÿ}'e“e‘‰ffŽ‘®stor“eŽ‘GU׬:‘ +1350.Ž¡­SolidŽ‘}׬::±she‘ÿ}'arŽ‘4:¬:‘ +1392.Ž¡­SolidŽ‘}׬::±shiftŽ‘}¬:‘ +1395,‘Æ01397.Ž¡­SolidŽ‘}׬::±showŽ‘Šÿ¬:‘ +1381.Ž¡­SolidŽ‘}׬::±SolidŽ‘Ó¬:‘ +1336,‘¼§1338.Ž¡­SolidŽ‘}׬::±suppr‘ÿ}'ess‘‰ffŽ‘®outputŽ‘D悬:‘ +1415.Ž¡­SolidŽ‘}׬::±undr‘ÿ}'awŽ‘!%ÿ¬:‘ +1432.Ž¡­SolidŽ‘}׬::±un l‘‚ØlŽ‘Ǭ:‘ +1435.Ž¡­SolidŽ‘}׬::±un l‘‚Øldr‘ÿ}'awŽ‘,d¬:‘ +1438.Ž¡­SolidŽ‘}׬::±unsuppr‘ÿ}'ess‘‰ffŽ‘®outputŽ‘O㦬:‘ +1417.Ž¡­T‘ÿ +«etrahedronŽ‘>œ¬::±dr‘ÿ}'aw‘‰ffŽ‘®netŽ‘'A“¬:‘ +1491.Ž¡­T‘ÿ +«etrahedronŽ‘>œ¬::±get‘‰ffŽ‘®netŽ‘4Ȭ:‘ +1489.Ž¡­T‘ÿ +«etrahedronŽ‘>œ¬::±setŽ‘ x„¬:‘ +1487.Ž¡­T‘ÿ +«etrahedronŽ‘>œ¬::±T‘ÿ;¼etr–ÿ}'ahe“dr“onŽ‘5'ج:‘ +1480,‘ß;1483.Ž¡­T‘ÿ +«ransformŽ‘4s}¬::±align‘‰ffŽ–®with‘‰ffŽ“axisŽ‘@²x¬:‘ +213,‘û™423.Ž¡­T‘ÿ +«ransformŽ‘4s}¬::±cle‘ÿ}'anŽ‘A‚¬:‘ +180.Ž¡­T‘ÿ +«ransformŽ‘4s}¬::±epsilonŽ‘o¬:‘ +182.Ž¡­T‘ÿ +«ransformŽ‘4s}¬::±get‘‰ffŽ‘®elementŽ‘3#®¬:‘ +190.Ž¡­T‘ÿ +«ransformŽ‘4s}¬::±inverseŽ‘ ‡¬:‘ +226,‘g 232.Ž¡­T‘ÿ +«ransformŽ‘4s}¬::±is‘‰ffŽ‘®identityŽ‘-2¢¬:‘ +185,‘;É187.Ž¡­T‘ÿ +«ransformŽ‘4s}¬::±r‘ÿ}'esetŽ‘Æ·¬:‘ +176.Ž¡­T‘ÿ +«ransformŽ‘4s}¬::±r‘ÿ}'otateŽ‘o>¬:‘ +205,–¥ô211,“212,“439,“759.Ž¡­T‘ÿ +«ransformŽ‘4s}¬::±sc‘ÿ}'aleŽ‘´ò¬:‘ +195.Ž¡­T‘ÿ +«ransformŽ‘4s}¬::±set‘‰ffŽ‘®elementŽ‘2 ×¬:‘ +178.Ž¡­T‘ÿ +«ransformŽ‘4s}¬::±she‘ÿ}'arŽ‘4:¬:‘ +197.Ž¡­T‘ÿ +«ransformŽ‘4s}¬::±shiftŽ‘}¬:‘ +200,–ÿ202,“203,“416.Ž¡­T‘ÿ +«ransformŽ‘4s}¬::±showŽ‘Šÿ¬:‘ +192.Ž¡­T‘ÿ +«ransformŽ‘4s}¬::±T‘ÿ;¼r‘ÿ}'ansformŽ‘.ÄQ¬:‘ +168,–ï&170,“172.Ž¡­T‘ÿ +«runcu½‰™šs4Ž‘ÔwOctahedronŽ‘]Ϊ¬::±get‘‰ffŽ‘®netŽ‘4Ȭ:‘ +1530.Ž¡­T‘ÿ +«runcu½‰™šs4Ž‘ÔwOctahedronŽ‘]Ϊ¬::±T‘ÿ;¼runc‘‰ffŽ‘®Octahe–ÿ}'dr“onŽ‘Pš'¬:‘ +1525,ŽŸ ‘1528.Ž¡­CircleŽ‘c,¬::±op–ÿ}'er“ator=Ž‘,í¬:‘ +1290,‘ei1292.Ž¡­ColorŽ‘Ož¬::±op–ÿ}'er“ator!=Ž‘/®ý¬:‘ +118.Ž¡­ColorŽ‘Ož¬::±op–ÿ}'er“ator==Ž‘4H•¬:‘ +116.Ž¡­ColorŽ‘Ož¬::±op–ÿ}'er“ator=Ž‘,í¬:‘ +114.Ž¡­CubQÇoidŽ‘%Oš¬::±op–ÿ}'er“ator=Ž‘,í¬:‘ +1466.Ž¡­EllipseŽ‘!èÙ¬::±op–ÿ}'er“ator*=Ž‘1º]¬:‘ +1233.Ž¡­EllipseŽ‘!èÙ¬::±op–ÿ}'er“ator=Ž‘,í¬:‘ +1157.Ž¡­EllipseŽ‘!èÙ¬::±op–ÿ}'er“ator“do‘‰ffŽ‘®tr“ansformŽ‘\Þe¬:‘ +1231.Ž¡­LineŽ‘Xƒ¬::±op–ÿ}'er“ator=Ž‘,í¬:‘ +643.ŽŽ ý•@P’ôभP®9athŽ’ r¬::±op–ÿ}'er“ator*=Ž‘1º]¬:‘ +781.Ž¤ %’ôभP®9athŽ’ r¬::±op–ÿ}'er“ator+=Ž‘4H•¬:‘ +797,‘€@801.Ž¡’ôभP®9athŽ’ r¬::±op–ÿ}'er“ator+Ž‘,S¬:‘ +799.Ž¡’ôभP®9athŽ’ r¬::±op–ÿ}'er“ator==Ž‘4H•¬:‘ +961.Ž¡’ôभP®9athŽ’ r¬::±op–ÿ}'er“ator=Ž‘,í¬:‘ +700.Ž¡’ôभP®9athŽ’ r¬::±op–ÿ}'er“ator&=Ž‘4H•¬:‘ +805.Ž¡’ôभP®9athŽ’ r¬::±op–ÿ}'er“ator&Ž‘,칬:‘ +810.Ž¡’ôभPictureŽ’|±¬::±op–ÿ}'er“ator*=Ž‘1º]¬:‘ +291.Ž¡’ôभPictureŽ’|±¬::±op–ÿ}'er“ator+=Ž‘4H•¬:‘ +269,–Çd270,“272,“589.Ž¡’ôभPictureŽ’|±¬::±op–ÿ}'er“ator=Ž‘,í¬:‘ +267.Ž¡’ôभP•®9oin“tŽ’zì¬::±op–ÿ}'er“ator!=Ž‘/®ý¬:‘ +569.Ž¡’ôभP•®9oin“tŽ’zì¬::±op–ÿ}'er“ator*=Ž‘1º]¬:‘ +518,‘~¬529.Ž¡’ôभP•®9oin“tŽ’zì¬::±op–ÿ}'er“ator*Ž‘*ä2¬:‘ +532.Ž¡’ôभP•®9oin“tŽ’zì¬::±op–ÿ}'er“ator+=Ž‘4H•¬:‘ 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-1032Ž‘ -Ÿ™”‰feŽ‘,‘&1033Ž‘&Ÿ™”‰feŽ–&,‘&1035Ž‘&Ÿ™”‰feŽ“,‘&1036Ž‘&Ÿ™”‰feŽ“,–&1037,“1242Ž“Ÿ™”‰feŽ‘&,Ž¦‘1243Ž‘Ÿ™”‰feŽ‘(,‘ûs1244Ž‘ûsŸ™”‰feŽ–ûw,‘ûs1245Ž‘ûsŸ™”‰feŽ“.ŽŽ ý•@P’ôà¤Ïddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ’(éM«:‘ -419Ž‘ -Ÿ™”‰feŽ‘,‘3420Ž‘3Ÿ™”‰feŽ–3‚,‘3422Ž‘3Ÿ™”‰feŽ“,‘3423Ž‘3Ÿ™”‰feŽ“,‘3428Ž‘3Ÿ™”‰feŽ“,‘3429Ž‘3Ÿ™”‰feŽ“,‘3775Ž‘3Ÿ™”‰feŽ“,Ž¤ ’à¦776Ž’ট™”‰feŽ’à©,‘>l777Ž‘>lŸ™”‰feŽ–>o,‘>l778Ž‘>lŸ™”‰feŽ“,‘>l780Ž‘>lŸ™”‰feŽ“,‘>l781Ž‘>lŸ™”‰feŽ“,‘>l784Ž‘>lŸ™”‰feŽ“,‘>l785Ž‘>lŸ™”‰feŽ“,‘>l786Ž‘>lŸ™”‰feŽ“,‘>l787Ž‘>lŸ™”‰feŽ“,Ž¡’à¦789Ž’ট™”‰feŽ’à©,‘>l790Ž‘>lŸ™”‰feŽ–>o,‘>l793Ž‘>lŸ™”‰feŽ“,‘>l794Ž‘>lŸ™”‰feŽ“,‘>l795Ž‘>lŸ™”‰feŽ“,‘>l796Ž‘>lŸ™”‰feŽ“,‘>l798Ž‘>lŸ™”‰feŽ“,‘>l799Ž‘>lŸ™”‰feŽ“,‘>l805,Ž¡’à¦806Ž’ট™”‰feŽ’à©,‘>l807Ž‘>lŸ™”‰feŽ–>o,‘>l808Ž‘>lŸ™”‰feŽ“,‘>l809Ž‘>lŸ™”‰feŽ“,‘>l823Ž‘>lŸ™”‰feŽ“,‘>l824Ž‘>lŸ™”‰feŽ“,‘>l825Ž‘>lŸ™”‰feŽ“,‘>l826Ž‘>lŸ™”‰feŽ“,‘>l924Ž‘>lŸ™”‰feŽ“,Ž¡’à¦925Ž’ট™”‰feŽ’à©,–Y©928,“929Ž“Ÿ™”‰feŽ›Y¬,“930Ž“Ÿ™”‰feŽ˜,“1049Ž“Ÿ™”‰feŽ›Y­,“1050Ž“Ÿ™”‰feŽ˜,“1053Ž“Ÿ™”‰feŽ˜,“1054Ž“Ÿ™”‰feŽ˜,Ž¡’à¦1097Ž’ট™”‰feŽ’àª,‘<„1098Ž‘<„Ÿ™”‰feŽ–<ˆ,‘<„1222Ž‘<„Ÿ™”‰feŽ“,‘<„1223Ž‘<„Ÿ™”‰feŽ“,‘<„1224Ž‘<„Ÿ™”‰feŽ“,‘<„1225Ž‘<„Ÿ™”‰feŽ“,‘<„1230Ž‘<„Ÿ™”‰feŽ“,‘<„1231Ž‘<„Ÿ™”‰feŽ“,Ž¡’à¦1272Ž’ট™”‰feŽ’àª,‘¢[1273Ž‘¢[Ÿ™”‰feŽ–¢_,‘¢[1276Ž‘¢[Ÿ™”‰feŽ“,‘¢[1277Ž‘¢[Ÿ™”‰feŽ“.Ž¤ RE’ôà¤Ïddr–ÿ}'awdot‘‰ffŽ‘®c“olorŽ’6t¨«:‘ -409,‘á¿410Ž‘á¿Ÿ™”‰feŽ–áÂ,‘á¿411Ž‘á¿Ÿ™”‰feŽ“,‘á¿412Ž‘á¿Ÿ™”‰feŽ“,‘á¿413Ž‘á¿Ÿ™”‰feŽ“.Ž¡’ôà¤ÝDEBUGŽ’¦ý«:‘ -72Ž‘ -Ÿ™”‰fe -Ž‘,‘„'159Ž‘„'Ÿ™”‰feŽ–„*,‘„'161Ž‘„'Ÿ™”‰feŽ“,‘„'174Ž‘„'Ÿ™”‰feŽ“,‘„'182Ž‘„'Ÿ™”‰feŽ“,–„'183,“184,“185,“186,Ž¤ ’à¦188Ž’ট™”‰feŽ’à©,‘Ò346Ž‘ÒŸ™”‰feŽ–Õ,‘Ò350Ž‘ÒŸ™”‰feŽ“,‘Ò380Ž‘ÒŸ™”‰feŽ“,–Ò381,“382,“385,“387,“388,“389,Ž¡’à¦395Ž’ট™”‰feŽ’à©,‘Ò399Ž‘ÒŸ™”‰feŽ›Õ,–Ò400,“401,“405Ž“Ÿ™”‰feŽ˜,“411Ž“Ÿ™”‰feŽ˜,“432Ž“Ÿ™”‰feŽ˜,“443Ž“Ÿ™”‰feŽ˜,“446Ž“Ÿ™”‰feŽ˜,“448Ž“Ÿ™”‰feŽ˜,Ž¡’à¦452Ž’ট™”‰feŽ’à©,‘Ò458Ž‘ÒŸ™”‰feŽ–Õ,‘Ò462Ž‘ÒŸ™”‰feŽ“,‘Ò464Ž‘ÒŸ™”‰feŽ“,‘Ò505Ž‘ÒŸ™”‰feŽ“,‘Ò517Ž‘ÒŸ™”‰feŽ“,–Ò518,“519,“520,“521,Ž¡’à¦522,‘Ò530Ž‘ÒŸ™”‰feŽ‘Õ,–Ò531,“532,“533,“534,“535,“536,“537,“538,Ž¡’à¦540,–Ò541,“546Ž“Ÿ™”‰feŽ›Õ,“548Ž“Ÿ™”‰feŽ˜,“549,“550,“551,“552,“553,“561Ž“Ÿ™”‰feŽ˜,Ž¡’à¦603Ž’ট™”‰feŽ’à©,‘Ò605Ž‘ÒŸ™”‰feŽ›Õ,–Ò606,“607,“644Ž“Ÿ™”‰feŽ˜,“661Ž“Ÿ™”‰feŽ˜,“664Ž“Ÿ™”‰feŽ˜,“669Ž“Ÿ™”‰feŽ˜,“674Ž“Ÿ™”‰feŽ˜,“678Ž“Ÿ™”‰feŽ˜,Ž¡’à¦681Ž’ট™”‰feŽ’à©,‘Ò683Ž‘ÒŸ™”‰feŽ–Õ,‘Ò685Ž‘ÒŸ™”‰feŽ“,‘Ò687Ž‘ÒŸ™”‰feŽ“,‘Ò726Ž‘ÒŸ™”‰feŽ“,‘Ò776Ž‘ÒŸ™”‰feŽ“,‘Ò802Ž‘ÒŸ™”‰feŽ“,‘Ò807Ž‘ÒŸ™”‰feŽ“,‘Ò824Ž‘ÒŸ™”‰feŽ“,‘Ò830Ž‘ÒŸ™”‰feŽ“,Ž¡’à¦840Ž’ট™”‰feŽ’à©,‘Ò842Ž‘ÒŸ™”‰feŽ›Õ,–Ò843,“844,“847Ž“Ÿ™”‰feŽ˜,“849Ž“Ÿ™”‰feŽ˜,“857Ž“Ÿ™”‰feŽ˜,“859,“861,“862,Ž¡’à¦863,–Ò864,“873Ž“Ÿ™”‰feŽ›Õ,“875Ž“Ÿ™”‰feŽ˜,“882Ž“Ÿ™”‰feŽ˜,“886,“897Ž“Ÿ™”‰feŽ˜,“900,“904Ž“Ÿ™”‰feŽ˜,“906,Ž¡’à¦912Ž’ট™”‰feŽ’à©,–Ò914,“949Ž“Ÿ™”‰feŽ›Õ,“954Ž“Ÿ™”‰feŽ˜,“955,“957,“958,“959,“960,“961,Ž¡’à¦963,‘Ò985Ž‘ÒŸ™”‰feŽ›Õ,–Ò986,“988,“990,“991,“992,“996Ž“Ÿ™”‰feŽ˜,“997,“999,Ž¡’à¦1033Ž’ট™”‰feŽ’àª,–<„1034,“1036Ž“Ÿ™”‰feŽ›<ˆ,“1037,“1127Ž“Ÿ™”‰feŽ˜,“1168Ž“Ÿ™”‰feŽ˜,“1176Ž“Ÿ™”‰feŽ˜,“1177,Ž¡’à¦1178,–<„1179,“1180,“1182,“1183,“1184,“1185,“1186,Ž¡’à¦1188,‘<„1193Ž‘<„Ÿ™”‰feŽ–<ˆ,‘<„1259Ž‘<„Ÿ™”‰feŽ“,‘<„1268Ž‘<„Ÿ™”‰feŽ“,‘<„1284Ž‘<„Ÿ™”‰feŽ“,‘<„1287Ž‘<„Ÿ™”‰feŽ“,‘<„1290Ž‘<„Ÿ™”‰feŽ“,‘<„1308Ž‘<„Ÿ™”‰feŽ“,Ž¡’à¦1317Ž’ট™”‰feŽ’àª,‘<„1344Ž‘<„Ÿ™”‰feŽ–<ˆ,‘<„1367Ž‘<„Ÿ™”‰feŽ“,‘<„1370Ž‘<„Ÿ™”‰feŽ“,‘<„1372Ž‘<„Ÿ™”‰feŽ“,‘<„1380Ž‘<„Ÿ™”‰feŽ“,–<„1382,“1384Ž“Ÿ™”‰feŽ‘<ˆ,Ž¡’à¦1385,‘<„1387Ž‘<„Ÿ™”‰feŽ›<ˆ,–<„1388,“1390Ž“Ÿ™”‰feŽ˜,“1393Ž“Ÿ™”‰feŽ˜,“1396Ž“Ÿ™”‰feŽ˜,“1399Ž“Ÿ™”‰feŽ˜,“1420Ž“Ÿ™”‰feŽ˜,Ž¡’à¦1443Ž’ট™”‰feŽ’àª,‘<„1460Ž‘<„Ÿ™”‰feŽ›<ˆ,–<„1461,“1474Ž“Ÿ™”‰feŽ˜,“1476Ž“Ÿ™”‰feŽ˜,“1488Ž“Ÿ™”‰feŽ˜,“1490Ž“Ÿ™”‰feŽ˜,“1508Ž“Ÿ™”‰feŽ˜.Ž¤ RE’ôà¤Ïde‘ÿ}'cimalŽ’"«:‘ -96,‘Ëù97Ž‘ËùŸ™”‰fe -Ž–Ëû,‘Ëù98Ž‘ËùŸ™”‰fe -Ž“,‘Ëù99Ž‘ËùŸ™”‰fe -Ž“.Ž¡’ôà¤Ïdefault‘‰ffŽ‘®b–ÿ}'ackgr“oundŽ’G&ë:‘ -108,‘8F112Ž‘8FŸ™”‰feŽ–8I,‘8F113Ž‘8FŸ™”‰feŽ“.Ž¡’ôà¤Ïdefault‘‰ffŽ‘®c‘ÿ}'olorŽ’,\«:‘ -112Ž‘ -Ÿ™”‰feŽ‘,‘n113Ž‘nŸ™”‰feŽ‘q,–n115,“410,“412,“419,“420,Ž¤ ’à¦422,–>l423,“458,“775,“777,“784,“786,“801,“803,Ž¡’à¦806,–¾l808,“859,“861,“862,“863,“924,“1049,“1050,Ž¡’à¦1053,–<„1054,“1097,“1098,“1222,“1224,“1283,“1284,Ž¡’à¦1287,–¢[1384,“1387,“1451.Ž© RE’ôà¤Ïdefault‘‰ffŽ–®c›ÿ}'olor‘‰ffŽ“ve˜ctorŽ’IúÞ«:‘ -115Ž‘ -Ÿ™”‰feŽ‘,‘ñº116Ž‘ñºŸ™”‰feŽ‘ñ½,–ñº1286,“1289,“1383,Ž¡’à¦1386,‘VÕ1389.Ž¦’ôà¤Ïdefault‘‰ffŽ‘®fo‘ÿ}'cusŽ’,¾¢«:‘ -313,–üû318,“397,“402,“403,“431,“443,Ž¡’à¦457,–â‹554,“586Ž“Ÿ™”‰feŽ›âŽ,“587Ž“Ÿ™”‰feŽ˜.Ž¦’ôà¤ÝDEFAULT_NUMBER_OF_POINTSŽ’sfÄ«:‘ -1103Ž‘ -Ÿ™”‰feŽ‘,‘¶1104Ž‘¶Ÿ™”‰feŽ‘º,‘¶1109,Ž¡’à¦1110,–¢[1111,“1242,“1244.Ž¦’ôà¤Ïde ne‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“mpŽ’9N¥«:‘ -105Ž‘ -Ÿ™”‰feŽ‘,‘eE106Ž‘eEŸ™”‰feŽ‘eH,‘eE108.Ž¦’ôà¤Ïdelta‘‰ffŽ‘®xŽ’œŒ«:‘ -522Ž‘ -Ÿ™”‰feŽ‘.Ž¦’ôà¤Ïdelta‘‰ffŽ–®x‘‰ffŽ“pŽ’Ôc«:‘ -532Ž‘ -Ÿ™”‰feŽ‘,‘M533.Ž¦’ôà¤Ïdelta‘‰ffŽ–®x‘‰ffŽ“qŽ’’o«:‘ -532Ž‘ -Ÿ™”‰feŽ‘,‘&534.Ž¦’ôà¤Ïdelta‘‰ffŽ‘®yŽ’‚;«:‘ -522Ž‘ -Ÿ™”‰feŽ‘.Ž¦’ôà¤Ïdelta‘‰ffŽ–®y‘‰ffŽ“pŽ’ Ù«:‘ -532Ž‘ -Ÿ™”‰feŽ‘,‘–533.Ž¦’ôà¤Ïdelta‘‰ffŽ–®y‘‰ffŽ“qŽ’Éå«:‘ -532Ž‘ -Ÿ™”‰feŽ‘,‘p534.Ž¦’ôà¤Ïdelta‘‰ffŽ‘®zŽ’&«:‘ -522Ž‘ -Ÿ™”‰feŽ‘.Ž¦’ôà¤Ïdelta‘‰ffŽ–®z‘‰ffŽ“pŽ’G–«:‘ -532Ž‘ -Ÿ™”‰feŽ‘,‘533.Ž¦’ôà¤Ïdelta‘‰ffŽ–®z‘‰ffŽ“qŽ’¢«:‘ -532Ž‘ -Ÿ™”‰feŽ‘,‘ö534.Ž¦’ôà¤ÏdenominatorŽ’-‰r«:‘ -641Ž‘ -Ÿ™”‰feŽ‘,‘Ä1183Ž‘ÄŸ™”‰feŽ‘Ä‘.Ž¦’ôà¤ÏdepthŽ’ iC«:‘ -1413Ž‘ -Ÿ™”‰feŽ‘,–Ã/1420,“1426.Ž¦’ôà¤Ïdiameter‘‰ffŽ‘®innerŽ’7zX«:‘ -1283Ž‘ -Ÿ™”‰feŽ‘,‘yÂ1284Ž‘yŸ™”‰feŽ–yÆ,‘yÂ1286Ž‘yŸ™”‰feŽ“,‘yÂ1287Ž‘yŸ™”‰feŽ“,‘yÂ1289Ž‘yŸ™”‰feŽ“,ŽŽŽŽŽŒ‹íƒ  Šn ý‘ì·x«1525–­3DLDFPRÃŽG’A²ùINDEX“«493Ž €n ý•@P‘1290Ž‘Ÿ™”‰feŽ‘(.Ž¤ 5þÏdiameter‘‰ffŽ‘®midd‘‚ØleŽ‘HGí«:‘ -1283Ž‘ -Ÿ™”‰feŽ‘,‘€ª1284Ž‘€ªŸ™”‰feŽ‘€®.Ž¡Ïdiameter‘‰ffŽ–®of‘‰ffŽ“hexagonŽ‘YÐÄ«:‘ -1487Ž‘ -Ÿ™”‰feŽ‘.Ž¡Ïdiameter‘‰ffŽ–®of‘‰ffŽ“triangleŽ‘X‡«:‘ -1442Ž‘ 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-1284Ž‘ -Ÿ™”‰feŽ‘.Ž¡Ïi‘‰ffŽ‘®minŽ‘ä8«:‘ -1284Ž‘ -Ÿ™”‰feŽ‘.Ž¡ÂIcosahedronŽ‘<ØÏ«:‘ -658,–J1429,“1467Ž“Ÿ™”‰feŽ›N,“1468,“1470,“1471Ž“Ÿ™”‰feŽ˜,Ž¦‘1473,‘¢[1474Ž‘¢[Ÿ™”‰feŽ‘¢_,–¢[1476,“1478.Ž¡ÝIDENTITY_TRANSFORMŽ‘_2«:‘ -191Ž‘ -Ÿ™”‰feŽ‘,‘V·192Ž‘V·Ÿ™”‰feŽ‘Vº.Ž¡ÂifstreamŽ‘)xÖ«:‘ -39,‘'í40.Ž¡Ïin‘‰ffŽ‘®angleŽ‘$¾«:‘ -1185Ž‘ -Ÿ™”‰feŽ‘.Ž¡Ïin‘‰ffŽ‘®cir‘ÿ}'cleŽ‘$ÂI«:‘ -1024,‘C1047Ž‘CŸ™”‰feŽ–C”,‘C1270Ž‘CŸ™”‰feŽ“,‘C1272.Ž¡Ïin‘‰ffŽ‘®distanc‘ÿ}'eŽ‘0¤h«:‘ -1228Ž‘ -Ÿ™”‰feŽ‘.Ž¡Ïin‘‰ffŽ‘®el‘‚ØlipseŽ‘(¸V«:‘ -1096Ž‘ -Ÿ™”‰feŽ‘,‘Ž”1229Ž‘Ž”Ÿ™”‰feŽ‘Ž˜,‘Ž”1231.Ž¡Ïin‘‰ffŽ‘®r–ÿ}'e“ctangleŽ‘3Ö*«:‘ -1220Ž‘ -Ÿ™”‰feŽ‘,‘js1221Ž‘jsŸ™”‰feŽ‘jw,‘js1225.Ž¡Ïin‘‰ffŽ‘®str–ÿ}'e“amŽ‘*$-«:‘ -39Ž‘ +Ž‘,‘ý83.Ž¡´DBL_MAXŽ‘%FS¬:‘ +19,–ÚÇ66,“1546.Ž¡´DBL_SIZEŽ‘*†P¬:‘ +68Ž‘ Ÿ™”‰fe -Ž‘,‘ž40Ž‘žŸ™”‰fe -Ž‘ ,–ž42,“44,“1518,“1519.Ž¡Ïin‘‰ffŽ›®str–ÿ}'e“am‘‰ffŽ˜nameŽ‘EQ«:‘ -42Ž‘ -Ÿ™”‰fe -Ž‘,‘“$43Ž‘“$Ÿ™”‰fe -Ž‘“&,‘“$44.Ž¡Ïinitialize‘‰ffŽ‘®c‘ÿ}'olorsŽ‘CÀ«:‘ -107Ž‘ -Ÿ™”‰feŽ‘,‘=108Ž‘=Ÿ™”‰feŽ‘@,–=112,“1519.Ž¡Ïinitialize‘‰ffŽ‘®ioŽ‘2‘«:‘ -42Ž‘ -Ÿ™”‰fe -Ž‘,‘Wp43Ž‘WpŸ™”‰fe -Ž‘Wr,–Wp1518,“1519.Ž¡Ïinner‘‰ffŽ‘®cir‘ÿ}'cleŽ‘32«:‘ -1287Ž‘ -Ÿ™”‰feŽ‘,‘Æ1290Ž‘ÆŸ™”‰feŽ‘Æ.Ž¡Ïinternal‘‰ffŽ‘®angleŽ‘=Œ5«:‘ -1025Ž‘ -Ÿ™”‰feŽ‘,–ô1027,“1033,“1034.Ž¡Ïinterse‘ÿ}'ction‘‰ffŽ‘®ctrŽ‘D"8«:‘ -1185Ž‘ -Ÿ™”‰feŽ‘,‘ŽQ1186.Ž¡Ïinterse‘ÿ}'ction‘‰ffŽ‘®lineŽ‘Gƒ¦«:‘ -594,‘¿643Ž‘¿Ÿ™”‰feŽ–¿,‘¿644Ž‘¿Ÿ™”‰feŽ“,–¿999,“1188.Ž¡Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointŽ‘M–Ö«:‘ -33,–Hï272,“527,“528Ž“Ÿ™”‰feŽ›Hò,“529Ž“Ÿ™”‰feŽ˜,“530Ž“Ÿ™”‰feŽ˜,Ž¦‘603Ž‘Ÿ™”‰feŽ‘#,–>l604,“640Ž“Ÿ™”‰feŽ›>o,“641Ž“Ÿ™”‰feŽ˜,“642Ž“Ÿ™”‰feŽ˜,“920Ž“Ÿ™”‰feŽ˜,“921Ž“Ÿ™”‰feŽ˜,“922Ž“Ÿ™”‰feŽ˜,“953,Ž¦‘963,–áÜ988,“990,“997,“1444,“1450,“1451.Ž¡Ïinterse–ÿ}'ction‘‰ffŽ‘®p“ointsŽ‘QŒß«:‘ -268,–Áþ528,“644,“952,“953Ž“Ÿ™”‰feŽ›Â,“954Ž“Ÿ™”‰feŽ˜,Ž¦‘964Ž‘Ÿ™”‰feŽ‘#,‘Ò965Ž‘ÒŸ™”‰feŽ–Õ,‘Ò984Ž‘ÒŸ™”‰feŽ“,‘Ò985Ž‘ÒŸ™”‰feŽ“,–Ò991,“993Ž“Ÿ™”‰feŽ›Õ,“994Ž“Ÿ™”‰feŽ˜,“995Ž“Ÿ™”‰feŽ˜,“996Ž“Ÿ™”‰feŽ˜,“999,Ž¦‘1164,‘<„1170Ž‘<„Ÿ™”‰feŽ–<ˆ,‘<„1171Ž‘<„Ÿ™”‰feŽ“,‘<„1172Ž‘<„Ÿ™”‰feŽ“,‘<„1173Ž‘<„Ÿ™”‰feŽ“,–<„1174,“1175Ž“Ÿ™”‰feŽ›<ˆ,“1176Ž“Ÿ™”‰feŽ˜,Ž¦‘1179,–<„1188,“1189,“1221,“1228,“1262,“1263Ž“Ÿ™”‰feŽ›<ˆ,“1264Ž“Ÿ™”‰feŽ˜,Ž¦‘1265Ž‘Ÿ™”‰feŽ‘(,‘ö¶1266Ž‘ö¶Ÿ™”‰feŽ–öº,‘ö¶1267Ž‘ö¶Ÿ™”‰feŽ“,‘ö¶1268Ž‘ö¶Ÿ™”‰feŽ“,‘ö¶1432Ž‘ö¶Ÿ™”‰feŽ“,‘ö¶1433Ž‘ö¶Ÿ™”‰feŽ“.Ž¡ÏintsŽ‘nŽ«:‘ -667.ŽŽ ý•@P’ôà¤ÝINVALID_BOOL_POINTŽ’SæÖ«:‘ -271,–Bú273,“274Ž“Ÿ™”‰feŽ›Bý,“275Ž“Ÿ™”‰feŽ˜,“536,Ž¤ ’à¦540,–T£541,“603,“641,“921,“922.Ž© ?ý’ôà¤ÝINVALID_BOOL_POINT_PAIRŽ’n&Ç«:‘ -274Ž‘ -Ÿ™”‰feŽ‘,‘û275Ž‘ûŸ™”‰feŽ‘û",–û954,“955,Ž¡’à¦962,–¾9963,“965,“985,“986,“989,“994,“1173.Ž¦’ôà¤ÝINVALID_BOOL_POINT_QUADRUPLEŽ’ˆf¸«:‘ -274Ž‘ -Ÿ™”‰feŽ‘,‘275Ž‘Ÿ™”‰feŽ‘ ,‘1176,Ž¡’à¦1179,–£ÿ1182,“1184,“1185,“1186,“1187,“1268.Ž¦’ôà¤ÝINVALID_BOOL_REAL_POINTŽ’n&Ç«:‘ -274Ž‘ -Ÿ™”‰feŽ‘,‘¹…275Ž‘¹…Ÿ™”‰feŽ‘¹ˆ,‘¹…606.Ž¦’ôà¤ÝINVALID_LINEŽ’4fè«:‘ -610Ž‘ -Ÿ™”‰feŽ‘,‘èA611Ž‘èAŸ™”‰feŽ‘èD,–èA644,“932,“933.Ž¦’ôà¤ÝINVALID_PATHŽ’4fè«:‘ -883.Ž¦’ôà¤ÝINVALID_PLANEŽ’9¦å«:‘ -619,–‚a623,“646,“647Ž“Ÿ™”‰feŽ›‚d,“648Ž“Ÿ™”‰feŽ˜,“903,Ž¡’à¦904,‘wÁ949.Ž¦’ôà¤ÝINVALID_POINTŽ’9¦å«:‘ -24,–Œ…269,“273,“274Ž“Ÿ™”‰feŽ›Œˆ,“275Ž“Ÿ™”‰feŽ˜,“350,“432,Ž¡’à¦462,–>l507,“508,“518,“527,“536,“541,“603,“605,Ž¡’à¦607,–>l610,“623,“624,“641,“647,“873,“889,“891,Ž¡’à¦893,–>l896,“897,“898,“900,“901,“903,“951,“952,Ž¡’à¦955,–>l958,“959,“960,“961,“979,“981,“986,“988,Ž¡’à¦999,–1086,“1088,“1126,“1127,“1145,“1147,“1163,Ž¡’à¦1164,–<„1179,“1184,“1188,“1192,“1221,“1329,“1330,Ž¡’à¦1440,–Kx1456,“1457,“1471,“1485.Ž¦’ôà¤ÝINVALID_REALŽ’4fè«:‘ -12,–òe15,“16Ž“Ÿ™”‰fe -Ž› òg,“24,“25,“27Ž“Ÿ™”‰fe -Ž˜,“30,“191,“273,Ž¡’à¦274,–Ò318,“346,“347,“349,“350,“351,“355,“382,“385,Ž¡’à¦387,–Ò401,“452,“503,“505,“518,“533,“534,“535,“536,Ž¡’à¦538,–Ò539,“540,“541,“623,“624,“842,“844,“879,“880,Ž¡’à¦946,–¾l947,“949,“958,“959,“960,“961,“1152,“1155,Ž¡’à¦1157,–<„1160,“1162,“1168,“1183,“1184,“1192,“1193,Ž¡’à¦1440,–<„1456,“1457,“1471,“1485,“1514,“1515,“1516.Ž¦’ôà¤ÝINVALID_REAL_PAIRŽ’N¦Ù«:‘ -25Ž‘ +Ž‘.Ž¡±ddŽ‘ ÄC¬:‘ +1222Ž‘ +Ÿ™”‰feŽ‘.ŽŽ ý•@P’ôऱddashe‘ÿ}'dŽ’'µ¬:‘ +463Ž‘ +Ÿ™”‰feŽ‘,‘í!464Ž‘í!Ÿ™”‰feŽ–í$,‘í!466Ž‘í!Ÿ™”‰feŽ“,‘í!467Ž‘í!Ÿ™”‰feŽ“,‘í!469Ž‘í!Ÿ™”‰feŽ“,‘í!470Ž‘í!Ÿ™”‰feŽ“,‘í!472Ž‘í!Ÿ™”‰feŽ“,‘í!473Ž‘í!Ÿ™”‰feŽ“,Ž¤ ’à¦818Ž’ট™”‰feŽ’à©,‘>l819Ž‘>lŸ™”‰feŽ–>o,‘>l820Ž‘>lŸ™”‰feŽ“,‘>l821Ž‘>lŸ™”‰feŽ“,‘>l823Ž‘>lŸ™”‰feŽ“,‘>l824Ž‘>lŸ™”‰feŽ“,‘>l827Ž‘>lŸ™”‰feŽ“,‘>l828Ž‘>lŸ™”‰feŽ“,‘>l829Ž‘>lŸ™”‰feŽ“,Ž¡’à¦830Ž’ট™”‰feŽ’à©,‘>l832Ž‘>lŸ™”‰feŽ–>o,‘>l833Ž‘>lŸ™”‰feŽ“,‘>l836Ž‘>lŸ™”‰feŽ“,‘>l837Ž‘>lŸ™”‰feŽ“,‘>l838Ž‘>lŸ™”‰feŽ“,‘>l839Ž‘>lŸ™”‰feŽ“,‘>l841Ž‘>lŸ™”‰feŽ“,‘>l842Ž‘>lŸ™”‰feŽ“,Ž¡’à¦849Ž’ট™”‰feŽ’à©,‘>l850Ž‘>lŸ™”‰feŽ–>o,‘>l851Ž‘>lŸ™”‰feŽ“,‘>l852Ž‘>lŸ™”‰feŽ“,‘>l855Ž‘>lŸ™”‰feŽ“,‘>l856Ž‘>lŸ™”‰feŽ“,‘>l857Ž‘>lŸ™”‰feŽ“,‘>l858Ž‘>lŸ™”‰feŽ“,‘>l860Ž‘>lŸ™”‰feŽ“,Ž¡’à¦861Ž’ট™”‰feŽ’à©,‘>l866Ž‘>lŸ™”‰feŽ–>o,‘>l867Ž‘>lŸ™”‰feŽ“,‘>l868Ž‘>lŸ™”‰feŽ“,‘>l869Ž‘>lŸ™”‰feŽ“,–>l967,“968Ž“Ÿ™”‰feŽ›>o,“969Ž“Ÿ™”‰feŽ˜,“972,Ž¡’à¦973Ž’ট™”‰feŽ’à©,‘Òí974Ž‘Òퟙ”‰feŽ‘Òð,‘Òí1091Ž‘Òퟙ”‰feŽ–Òñ,‘Òí1092Ž‘Òퟙ”‰feŽ“,‘Òí1095Ž‘Òퟙ”‰feŽ“,‘Òí1096Ž‘Òퟙ”‰feŽ“,‘Òí1137Ž‘Òퟙ”‰feŽ“,‘Òí1138Ž‘Òퟙ”‰feŽ“,Ž¡’à¦1261Ž’ট™”‰feŽ’àª,‘<„1262Ž‘<„Ÿ™”‰feŽ–<ˆ,‘<„1263Ž‘<„Ÿ™”‰feŽ“,‘<„1264Ž‘<„Ÿ™”‰feŽ“,‘<„1269Ž‘<„Ÿ™”‰feŽ“,‘<„1270Ž‘<„Ÿ™”‰feŽ“,‘<„1309Ž‘<„Ÿ™”‰feŽ“,‘<„1310Ž‘<„Ÿ™”‰feŽ“,Ž¡’à¦1313Ž’ট™”‰feŽ’àª,‘<„1314Ž‘<„Ÿ™”‰feŽ›<ˆ,–<„1422,“1423Ž“Ÿ™”‰feŽ˜,“1424Ž“Ÿ™”‰feŽ˜,“1428,“1429Ž“Ÿ™”‰feŽ˜,“1430Ž“Ÿ™”‰feŽ˜,Ž¡’à¦1431,‘ö¶1432Ž‘ö¶Ÿ™”‰feŽ–öº,‘ö¶1433Ž‘ö¶Ÿ™”‰feŽ“,–ö¶1437,“1438Ž“Ÿ™”‰feŽ›öº,“1439Ž“Ÿ™”‰feŽ˜.Ž© ’ôऱddiameterŽ’!È ¬:‘ +1076Ž‘ +Ÿ™”‰feŽ‘,‘&1077Ž‘&Ÿ™”‰feŽ–&,‘&1079Ž‘&Ÿ™”‰feŽ“,‘&1080Ž‘&Ÿ™”‰feŽ“,–&1081,“1281Ž“Ÿ™”‰feŽ‘&,Ž¡’à¦1282Ž’ট™”‰feŽ’àª,‘ûs1283Ž‘ûsŸ™”‰feŽ–ûw,‘ûs1284Ž‘ûsŸ™”‰feŽ“.Ž¦’ôऱddr–ÿ}'aw‘‰ffŽ‘®c“olorŽ’(éM¬:‘ +463Ž‘ 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_ü±l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘(ʬ:‘ +844Ž‘ +Ÿ™”‰feŽ‘,‘Ój845Ž‘ÓjŸ™”‰feŽ–Óm,‘Ój846Ž‘ÓjŸ™”‰feŽ“,‘Ój847Ž‘ÓjŸ™”‰feŽ“,–Ój848,“849Ž“Ÿ™”‰feŽ›Óm,“850Ž“Ÿ™”‰feŽ˜,Ž¡‘851Ž‘Ÿ™”‰feŽ‘#,‘wÁ852Ž‘wÁŸ™”‰feŽ‘wÄ.Ž¦± g‘‰ffŽ‘®numŽ‘"XÓ¬:‘ +78Ž‘ +Ÿ™”‰fe +Ž‘,‘Ë®79Ž‘Ë®Ÿ™”‰fe +Ž‘Ë°,–Ë®87,“89.Ž¦± l‘‚ØlŽ‘ Éó¬:‘ +597,‘•e844Ž‘•eŸ™”‰feŽ–•h,‘•e845Ž‘•eŸ™”‰feŽ“,‘•e846Ž‘•eŸ™”‰feŽ“,‘•e847Ž‘•eŸ™”‰feŽ“,–•e848,“1013,“1014,Ž¡‘1321,–¢[1425,“1426Ž“Ÿ™”‰feŽ›¢_,“1427Ž“Ÿ™”‰feŽ˜.Ž¦´FILLŽ‘†\¬:‘ +244Ž‘ +Ÿ™”‰feŽ‘,‘]ˆ246Ž‘]ˆŸ™”‰feŽ‘]‹,–]ˆ845,“902,“1425.Ž¦± l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorŽ‘%˜U¬:‘ +698Ž‘ +Ÿ™”‰feŽ‘,–Ù701,“705,“708,“710,“713,“715,Ž¡‘718,–>l720,“727,“728,“729,“744,“746,“818,“819,Ž¡‘844,–>l845,“849,“850,“856,“864,“867,“902,“907,Ž¡‘912,– ³1321,“1425.Ž¦± l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“innerŽ‘@g¬:‘ +1320Ž‘ +Ÿ™”‰feŽ‘,‘šš1321Ž‘ššŸ™”‰feŽ‘šž.Ž¦± l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“iterŽ‘8zÿ¬:‘ +1428,‘´®1430.Ž¦± l›‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“midd˜leŽ‘FM¬:‘ +1320Ž‘ +Ÿ™”‰feŽ‘,‘‡æ1321Ž‘‡æŸ™”‰feŽ‘‡ê.Ž¦± l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“outerŽ‘?ä;¬:‘ +1320Ž‘ +Ÿ™”‰feŽ‘,‘œH1321Ž‘œHŸ™”‰feŽ‘œL.Ž¦± l‘‚Øl‘‰ffŽ–®c‘ÿ}'olor‘‰ffŽ“ptrŽ‘5ìȬ:‘ +1428,‘½1430Ž‘½Ÿ™”‰feŽ‘½.Ž¦± l‘‚Øl‘‰ffŽ‘®c‘ÿ}'olorsŽ‘)m©¬:‘ +1428,‘ŒG1429Ž‘ŒGŸ™”‰feŽ–ŒK,‘ŒG1430Ž‘ŒGŸ™”‰feŽ“.Ž¦± l‘‚Øl‘‰ffŽ–®dr‘ÿ}'aw‘‰ffŽ“valueŽ‘>¬¬:‘ +698Ž‘ +Ÿ™”‰feŽ‘,–œ3701,“705,“708,“710,“713,“715,Ž¡‘718,–>l720,“736,“819,“845,“850,“856,“864,“867,Ž¡‘902,–T£904,“905,“906,“909,“910.Ž¦± l›‚Øl‘‰ffŽ–®out‘‰ffŽ“el˜lipseŽ‘<Áh¬:‘ +1265.Ž¦± l‘‚Øldr‘ÿ}'awŽ‘!gk¬:‘ +597,–£848,“849Ž“Ÿ™”‰feŽ›¦,“850Ž“Ÿ™”‰feŽ˜,“851Ž“Ÿ™”‰feŽ˜,“852Ž“Ÿ™”‰feŽ˜,“1013,“1014,Ž¡‘1321,‘Kx1429Ž‘KxŸ™”‰feŽ–K|,‘Kx1430Ž‘KxŸ™”‰feŽ“,–Kx1438,“1547.Ž¦´FILLDRAWŽ‘*†P¬:‘ +244Ž‘ +Ÿ™”‰feŽ‘,‘ø246Ž‘øŸ™”‰feŽ‘û,–ø850,“902,“1428.Ž¦± rstŽ‘µª¬:‘ 16Ž‘ Ÿ™”‰fe -Ž‘.Ž¦’ôà¤Ïis‘‰ffŽ‘®cir‘ÿ}'cularŽ’"…Á«:‘ -1258Ž‘ -Ÿ™”‰feŽ‘,‘ØY1259Ž‘ØYŸ™”‰feŽ‘Ø].Ž¦’ôà¤Ïis‘‰ffŽ‘®cubicŽ’È«:‘ -944Ž‘ -Ÿ™”‰feŽ‘,‘´31129Ž‘´3Ÿ™”‰feŽ–´7,‘´31130Ž‘´3Ÿ™”‰feŽ“.Ž¦’ôà¤Ïis‘‰ffŽ‘®cycleŽ’/¼«:‘ -763,–ŽÓ864,“877Ž“Ÿ™”‰feŽ‘ŽÖ,“912.Ž¦’ôà¤Ïis‘‰ffŽ‘®el‘‚ØlipseŽ’r«:‘ -1152.Ž¦’ôà¤Ïis‘‰ffŽ‘®el‘‚Øliptic‘ÿ}'alŽ’%Í:«:‘ -1126Ž‘ -Ÿ™”‰feŽ‘,‘é‰1127Ž‘鉟™”‰feŽ‘é,–é‰1155,“1157,“1160,“1162,Ž¡’à¦1192,–ûs1193,“1194.Ž¦’ôà¤Ïis‘‰ffŽ‘®identityŽ’"F«:‘ -140Ž‘ -Ÿ™”‰feŽ‘,‘”¸141Ž‘”¸Ÿ™”‰feŽ–”»,‘”¸142Ž‘”¸Ÿ™”‰feŽ“,‘”¸143Ž‘”¸Ÿ™”‰feŽ“,–”¸174,“283,“307Ž“Ÿ™”‰feŽ‘”»,Ž¡’à¦399,–š¶405,“472,“549,“553.Ž¦’ôà¤Ïis‘‰ffŽ–®in‘‰ffŽ“triangleŽ’.pE«:‘ -357Ž‘ -Ÿ™”‰feŽ‘,‘ˆ˜904Ž‘ˆ˜Ÿ™”‰feŽ‘ˆ›,‘ˆ˜991.Ž¦’ôà¤Ïis‘‰ffŽ‘®lineŽ’Ñã«:‘ -876,‘3‹879.Ž¦’ôà¤Ïis‘‰ffŽ‘®line‘ÿ}'arŽ’ö!«:‘ -716,–ÔÊ721,“722,“749,“750,“874Ž“Ÿ™”‰feŽ›ÔÍ,“875Ž“Ÿ™”‰feŽ˜,“876,Ž¡’à¦879,–þl880,“920,“921,“922,“933,“965,“994,“1009,Ž¡’à¦1172,–ûs1173,“1216.Ž¦’ôà¤Ïis‘‰ffŽ–®on‘‰ffŽ“fr–ÿ}'e“e‘‰ffŽ‘®stor“eŽ’7[y«:‘ -95Ž‘ +Ž‘,–+b32,“315Ž“Ÿ™”‰feŽ‘+e,“316,“399,“585,“647,“677,“992,Ž¡‘993,–1002,“1003,“1004,“1005,“1007,“1032,“1034,Ž¡‘1035,–<„1043,“1173,“1174,“1175,“1201,“1202,“1218,Ž¡‘1223,–ö¶1225,“1227,“1260,“1267,“1305.Ž¦± rst‘‰ffŽ–®p‘ÿ}'oint‘‰ffŽ“ptrŽ‘<‘¿¬:‘ +711Ž‘ +Ÿ™”‰feŽ‘,–­716,“717Ž“Ÿ™”‰feŽ›­ ,“718Ž“Ÿ™”‰feŽ˜,“719Ž“Ÿ™”‰feŽ˜,“720Ž“Ÿ™”‰feŽ˜.Ž¦± rst‘‰ffŽ‘®r‘ÿ}'owŽ‘%úv¬:‘ +1320Ž‘ +Ÿ™”‰feŽ‘,‘ñ–1321Ž‘ñ–Ÿ™”‰feŽ‘ñš.ŽŽ ý•@P’ôऱ xe‘ÿ}'dŽ’ â +¬:‘ +83,–ÿh907,“1553.Ž¤ e¡’ôऱ o‘ÿ}'at eldŽ’8ì:‘ +83,‘M1553.Ž¡’ôऱ o‘ÿ}'atsŽ’ 5”¬:‘ +15,–˺27,“182,“546.Ž¡’ôऱ o‘ÿ}'orŽ’ +E:¬:‘ +1224,‘(/1293.Ž¡’ôऴFLT_EXPŽ’&÷¬:‘ +70.Ž¡’ôऴFLT_MAXŽ’&÷¬:‘ +7,–²<19,“66,“1546.Ž¡’ôऴFLT_SIZEŽ’fô¬:‘ +68Ž‘ +Ÿ™”‰fe +Ž‘.Ž¡’ôऱ ushŽ’ +™ ¬:‘ +37,–îë68,“69,“70,“87,“89,“150,“152,“193,“196,Ž¤ 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e¡’ôऱfmo‘ÿ}'dŽ’ `ž¬:‘ +1012,‘$Š1327.Ž¡’ôऱfmt agsŽ’t$¬:‘ +1553.Ž¡’ôऱfo‘ÿ}'cusŽ’ îy¬:‘ +899.Ž¡’ôभF‘ÿ +«oQÇcusŽ’Õð¬:‘ +49Ž‘ Ÿ™”‰fe -Ž‘,‘­(200Ž‘­(Ÿ™”‰feŽ–­+,‘­(344Ž‘­(Ÿ™”‰feŽ“,–­(685,“687,“698,“703,Ž¡’à¦871Ž’ট™”‰feŽ’à©,‘ ³1339Ž‘ ³Ÿ™”‰feŽ– ·,‘ ³1340Ž‘ ³Ÿ™”‰feŽ“.Ž¦’ôà¤Ïis‘‰ffŽ–®on‘‰ffŽ“lineŽ’;®«:‘ -349,‘º354Ž‘ºŸ™”‰feŽ–º,‘º355Ž‘ºŸ™”‰feŽ“.ŽŽŽŽŽŒ‹ò`Ú Šn ý‘ì«498–­INDEX’A²ù3DLDFPRÃŽG“·x«1525Ž €n ý•@PÏis‘‰ffŽ–®on‘‰ffŽ“planeŽ‘1‚Ú«:‘ -356Ž‘ -Ÿ™”‰feŽ‘,‘JÇ637Ž‘JÇŸ™”‰feŽ‘JÊ,–JÇ904,“1168.Ž¤ 4[Ïis‘‰ffŽ–®on‘‰ffŽ“se‘ÿ}'gmentŽ‘=5O«:‘ -349Ž‘ -Ÿ™”‰feŽ‘,‘±350Ž‘±Ÿ™”‰feŽ–±,‘±352Ž‘±Ÿ™”‰feŽ“,‘±353Ž‘±Ÿ™”‰feŽ“,–±355,“541,“603,Ž© ‘961,–T£963,“988,“990,“991,“999.Ž¡Ïis‘‰ffŽ‘®op‘ÿ}'enŽ‘ «:‘ -106,‘&108.Ž¡Ïis‘‰ffŽ‘®p–ÿ}'ar“al‘‚ØlelŽ‘+¯p«:‘ -1082.Ž¡Ïis‘‰ffŽ‘®planarŽ‘(&«:‘ -872Ž‘ -Ÿ™”‰feŽ‘,‘+873Ž‘+Ÿ™”‰feŽ‘.,–+901,“942,“1044,“1083,“1258,Ž¦‘1259,–ûs1270,“1274.Ž¡Ïis‘‰ffŽ‘®quadr‘ÿ}'aticŽ‘3çô«:‘ -943Ž‘ -Ÿ™”‰feŽ‘,–Š¹960,“1128Ž“Ÿ™”‰feŽ‘Š½.Ž¡Ïis‘‰ffŽ‘®quarticŽ‘*1í«:‘ -945Ž‘ -Ÿ™”‰feŽ‘,‘š 1131Ž‘š Ÿ™”‰feŽ–š ,‘š 1132Ž‘š 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+977,–×21032,“1034,“1041,“1419,“1515.ŽŽŽŽŽŒ‹ôì Šn ý‘ì¬500–¯INDEX’9?c3DLDF-1.1.5.1“°x¬1563Ž €n ý•@PµgŽ‘ ã¬:‘ +102Ž‘ +Ÿ™”‰feŽ‘,‘Y9103Ž‘Y9Ÿ™”‰feŽ–Y<,‘Y9104Ž‘Y9Ÿ™”‰feŽ“,‘Y9105Ž‘Y9Ÿ™”‰feŽ“,‘Y9107Ž‘Y9Ÿ™”‰feŽ“,‘Y9108Ž‘Y9Ÿ™”‰feŽ“,‘Y9109Ž‘Y9Ÿ™”‰feŽ“,‘Y9110Ž‘Y9Ÿ™”‰feŽ“,‘Y9127Ž‘Y9Ÿ™”‰feŽ“,Ž© ‘128Ž‘Ÿ™”‰feŽ‘#,‘Ò131Ž‘ÒŸ™”‰feŽ–Ò‚,‘Ò132Ž‘ÒŸ™”‰feŽ“,‘Ò1382Ž‘ÒŸ™”‰feŽ‘Òƒ.Ž¤ 5þ±get‘‰ffŽ–®al‘‚Øl‘‰ffŽ“c–ÿ}'o“or“dsŽ‘:§¬:‘ +355Ž‘ +Ÿ™”‰feŽ‘,‘³356Ž‘³Ÿ™”‰feŽ–³ ,‘³357Ž‘³Ÿ™”‰feŽ“,‘³358Ž‘³Ÿ™”‰feŽ“,–³476,“910.Ž¡±get‘‰ffŽ–®axis‘‰ffŽ“hŽ‘+-I¬:‘ +1130Ž‘ +Ÿ™”‰feŽ‘,‘@1131Ž‘@Ÿ™”‰feŽ‘@,–@1171,“1172,“1174,“1175,Ž¦‘1190,‘¿ 1197Ž‘¿ Ÿ™”‰feŽ–¿ ,‘¿ 1198Ž‘¿ Ÿ™”‰feŽ“,‘¿ 1199Ž‘¿ Ÿ™”‰feŽ“,‘¿ 1200Ž‘¿ Ÿ™”‰feŽ“,–¿ 1201,“1202,Ž¦‘1206,–¢[1216,“1222,“1293.Ž¡±get‘‰ffŽ–®axis‘‰ffŽ“vŽ‘*ùš¬:‘ +1132Ž‘ +Ÿ™”‰feŽ‘,‘C 1133Ž‘C Ÿ™”‰feŽ‘C$,–C 1171,“1172,“1174,“1175,Ž¦‘1190,‘¿ 1192Ž‘¿ Ÿ™”‰feŽ–¿ ,‘¿ 1193Ž‘¿ Ÿ™”‰feŽ“,‘¿ 1194Ž‘¿ Ÿ™”‰feŽ“,‘¿ 1195Ž‘¿ Ÿ™”‰feŽ“,–¿ 1201,“1202,Ž¦‘1206,–¢[1216,“1222,“1293.Ž¡±get‘‰ffŽ–®blue‘‰ffŽ“p‘ÿ}'artŽ‘7¶º¬:‘ 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+Ÿ™”‰feŽ‘,–=255,“313Ž“Ÿ™”‰feŽ›@,“314,“315,“317Ž“Ÿ™”‰feŽ˜,“318,“352Ž“Ÿ™”‰feŽ˜,“455Ž“Ÿ™”‰feŽ˜,Ž¡’à¦459Ž’ট™”‰feŽ’à©,‘Ò469Ž‘ÒŸ™”‰feŽ–Õ,‘Ò470Ž‘ÒŸ™”‰feŽ“,‘Ò472Ž‘ÒŸ™”‰feŽ“,‘Ò473Ž‘ÒŸ™”‰feŽ“,–Ò506,“514,“515,“516,“585,Ž¡’à¦589,–>l590,“597,“645Ž“Ÿ™”‰feŽ‘>o,“647,“649,“650,“651,“685,Ž¡’à¦797Ž’ট™”‰feŽ’à©,‘þl798Ž‘þlŸ™”‰feŽ–þo,‘þl799Ž‘þlŸ™”‰feŽ“,‘þl800Ž‘þlŸ™”‰feŽ“,‘þl841Ž‘þlŸ™”‰feŽ“,‘þl842Ž‘þlŸ™”‰feŽ“,‘þl860Ž‘þlŸ™”‰feŽ“,‘þl861Ž‘þlŸ™”‰feŽ“,‘þl1002,Ž¡’à¦1003,–<„1004,“1005,“1007,“1032,“1034,“1035,“1041,Ž¡’à¦1043,–<„1201,“1202,“1218,“1223,“1225,“1227,“1260,Ž¡’à¦1267,–ö¶1305,“1397Ž“Ÿ™”‰feŽ›öº,“1398Ž“Ÿ™”‰feŽ˜,“1485,“1492.Ž¦’ôऱpt‘‰ffŽ‘®c4Ž’ ‘‰¬:‘ +993Ž‘ +Ÿ™”‰feŽ‘.Ž¦’ôऱpt‘‰ffŽ‘®iterŽ’È ¬:‘ +1474.Ž¦’ôऱpt‘‰ffŽ–®on‘‰ffŽ“x‘‰ffŽ“axisŽ’)õÕ¬:‘ +426Ž‘ +Ÿ™”‰feŽ‘.Ž¦’ôऱpt‘‰ffŽ–®on‘‰ffŽ“z‘‰ffŽ“axisŽ’)i¬:‘ +427Ž‘ +Ÿ™”‰feŽ‘,–˜ð428,“430.Ž¦’ôऱpt‘‰ffŽ‘®ve‘ÿ}'ctorŽ’„U¬:‘ +997,‘ÇT998Ž‘ÇTŸ™”‰feŽ‘ÇW,–ÇT999,“1000,“1007,“1029Ž“Ÿ™”‰feŽ‘ÇX,“1030,Ž¡’à¦1031,‘VÕ1034.Ž¦’ôऱptrŽ’k¬:‘ +1041Ž‘ +Ÿ™”‰feŽ‘,‘?¾1352Ž‘?¾Ÿ™”‰feŽ‘?Â.ŽŽŽŽŽŒ‹û © Šn ý‘ì°x¬1563–¯3DLDF-1.1.5.1’9?cINDEX“¬507Ž €n ý•@P±ptsŽ‘ Ú¦¬:‘ +1460Ž‘ +Ÿ™”‰feŽ‘,‘`¸1484Ž‘`¸Ÿ™”‰feŽ›`¼,–`¸1485,“1486,“1490Ž“Ÿ™”‰feŽ˜,“1492Ž“Ÿ™”‰feŽ˜,“1501Ž“Ÿ™”‰feŽ˜,Ž¤ ‘1502,‘¿ 1504Ž‘¿ Ÿ™”‰feŽ–¿ ,‘¿ 1505Ž‘¿ Ÿ™”‰feŽ“,‘¿ 1515Ž‘¿ Ÿ™”‰feŽ“,‘¿ 1517Ž‘¿ Ÿ™”‰feŽ“,‘¿ 1519Ž‘¿ Ÿ™”‰feŽ“,‘¿ 1529Ž‘¿ Ÿ™”‰feŽ“,Ž¡‘1531Ž‘Ÿ™”‰feŽ‘(,‘VÕ1532.Ž© ;“±pt0Ž‘i;¬:‘ +194Ž‘ +Ÿ™”‰feŽ‘,‘.²760Ž‘.²Ÿ™”‰feŽ–.µ,‘.²992Ž‘.²Ÿ™”‰feŽ“,‘.²993Ž‘.²Ÿ™”‰feŽ“,‘.²998Ž‘.²Ÿ™”‰feŽ“,–.²1001,“1005,“1007,Ž¡‘1028Ž‘Ÿ™”‰feŽ‘(,‘¿ 1029Ž‘¿ Ÿ™”‰feŽ›¿ ,–¿ 1032,“1034,“1035,“1111Ž“Ÿ™”‰feŽ˜,“1112Ž“Ÿ™”‰feŽ˜,Ž¡‘1113Ž‘Ÿ™”‰feŽ‘(,‘¿ 1114Ž‘¿ Ÿ™”‰feŽ›¿ ,–¿ 1201,“1202Ž“Ÿ™”‰feŽ˜,“1209Ž“Ÿ™”‰feŽ˜,“1218Ž“Ÿ™”‰feŽ˜,“1227Ž“Ÿ™”‰feŽ˜,Ž¡‘1258Ž‘Ÿ™”‰feŽ‘(,‘¢[1300Ž‘¢[Ÿ™”‰feŽ–¢_,‘¢[1301Ž‘¢[Ÿ™”‰feŽ“,‘¢[1321Ž‘¢[Ÿ™”‰feŽ“.Ž¦±pt0‘‰ffŽ‘®hŽ‘¬:‘ +993Ž‘ +Ÿ™”‰feŽ‘,‘}Ì1001Ž‘}ÌŸ™”‰feŽ‘}Ð,–}Ì1003,“1004.Ž¦±pt0‘‰ffŽ‘®vŽ‘il¬:‘ +993Ž‘ +Ÿ™”‰feŽ‘,‘~r1001Ž‘~rŸ™”‰feŽ‘~v,–~r1002,“1004.Ž¦±pt1Ž‘i;¬:‘ +194Ž‘ +Ÿ™”‰feŽ‘,‘ëT760Ž‘ëTŸ™”‰feŽ–ëW,‘ëT993Ž‘ëTŸ™”‰feŽ“,‘ëT998Ž‘ëTŸ™”‰feŽ“,–ëT1001,“1005,“1007,“1028Ž“Ÿ™”‰feŽ‘ëX,Ž¡‘1029Ž‘Ÿ™”‰feŽ‘(,–<„1032,“1034,“1035,“1111Ž“Ÿ™”‰feŽ›<ˆ,“1112Ž“Ÿ™”‰feŽ˜,“1113Ž“Ÿ™”‰feŽ˜,“1114Ž“Ÿ™”‰feŽ˜,Ž¡‘1209Ž‘Ÿ™”‰feŽ‘(,‘Kx1218Ž‘KxŸ™”‰feŽ–K|,‘Kx1258Ž‘KxŸ™”‰feŽ“,‘Kx1300Ž‘KxŸ™”‰feŽ“,‘Kx1301Ž‘KxŸ™”‰feŽ“.Ž¦±pt1‘‰ffŽ‘®hŽ‘¬:‘ +1001Ž‘ +Ÿ™”‰feŽ‘,‘ à1003.Ž¦±pt1‘‰ffŽ‘®vŽ‘il¬:‘ +1001Ž‘ +Ÿ™”‰feŽ‘.Ž¦±pt2Ž‘i;¬:‘ +194Ž‘ +Ÿ™”‰feŽ‘,‘š"1111Ž‘š"Ÿ™”‰feŽ–š&,‘š"1112Ž‘š"Ÿ™”‰feŽ“,‘š"1113Ž‘š"Ÿ™”‰feŽ“,‘š"1114Ž‘š"Ÿ™”‰feŽ“,‘š"1218Ž‘š"Ÿ™”‰feŽ“,‘š"1258Ž‘š"Ÿ™”‰feŽ“.Ž¦±pt20Ž‘…«¬:‘ +1222Ž‘ +Ÿ™”‰feŽ‘,‘+ 1223.Ž¦±pt21Ž‘…«¬:‘ +1222Ž‘ +Ÿ™”‰feŽ‘,‘+ 1223.Ž¦±pt22Ž‘…«¬:‘ +1222Ž‘ +Ÿ™”‰feŽ‘,‘+ 1223.Ž¦±pt23Ž‘…«¬:‘ +1222Ž‘ +Ÿ™”‰feŽ‘,‘+ 1223.Ž¦±pt3Ž‘i;¬:‘ +1111Ž‘ +Ÿ™”‰feŽ‘,‘Ý1112Ž‘ÝŸ™”‰feŽ–Ý,‘Ý1113Ž‘ÝŸ™”‰feŽ“,‘Ý1114Ž‘ÝŸ™”‰feŽ“,‘Ý1218Ž‘ÝŸ™”‰feŽ“,‘Ý1258Ž‘ÝŸ™”‰feŽ“.Ž¦±pt4Ž‘i;¬:‘ +1112Ž‘ +Ÿ™”‰feŽ‘,‘;à1258Ž‘;àŸ™”‰feŽ‘;ä.Ž¦±pt5Ž‘i;¬:‘ +1112Ž‘ +Ÿ™”‰feŽ‘,‘;à1258Ž‘;àŸ™”‰feŽ‘;ä.Ž¦±pt6Ž‘i;¬:‘ +1112Ž‘ +Ÿ™”‰feŽ‘,‘;à1258Ž‘;àŸ™”‰feŽ‘;ä.Ž¦±pt7Ž‘i;¬:‘ +1112Ž‘ +Ÿ™”‰feŽ‘,‘;à1258Ž‘;àŸ™”‰feŽ‘;ä.Ž¦±pt8Ž‘i;¬:‘ +1112Ž‘ +Ÿ™”‰feŽ‘,‘;à1258Ž‘;àŸ™”‰feŽ‘;ä.Ž¦±pt9Ž‘i;¬:‘ +1258Ž‘ +Ÿ™”‰feŽ‘.Ž¦±purpleŽ‘95¬:‘ +152,‘çò156Ž‘çòŸ™”‰feŽ–çõ,‘çò157Ž‘çòŸ™”‰feŽ“.Ž¦±push‘‰ffŽ‘®b‘ÿ}'ackŽ‘+XR¬:‘ +271,–€n273,“487,“587,“589,“593,“701,“708,Ž¡‘710,–Ò713,“715,“718,“720,“752,“798,“800,“802,“807,Ž¡‘808,–þl809,“813,“814,“883,“929,“930,“957,“1041,Ž¡‘1043,–<„1078,“1107,“1112,“1150,“1324,“1339,“1347,Ž¡‘1405,–<„1419,“1420,“1458,“1460,“1474,“1490,“1502,Ž¡‘1504,–£ÿ1515,“1517,“1529,“1531,“1532,“1546.Ž¦±p0Ž‘ À¬:‘ 211Ž‘ -Ÿ™”‰feŽ‘,‘u6212Ž‘u6Ÿ™”‰feŽ‘u9,‘u6400.Ž¡ÝPARALLEL_Z_YŽ‘?†D«:‘ +Ÿ™”‰feŽ‘,‘!213Ž‘!Ÿ™”‰feŽ–$,‘!288Ž‘!Ÿ™”‰feŽ“,‘!393Ž‘!Ÿ™”‰feŽ“,‘!394Ž‘!Ÿ™”‰feŽ“,–!395,“396Ž“Ÿ™”‰feŽ›$,“397Ž“Ÿ™”‰feŽ˜,“398Ž“Ÿ™”‰feŽ˜,Ž¡‘399Ž‘Ÿ™”‰feŽ‘#,‘Ò401Ž‘ÒŸ™”‰feŽ›Õ,–Ò423,“424Ž“Ÿ™”‰feŽ˜,“425,“433,“436Ž“Ÿ™”‰feŽ˜,“437Ž“Ÿ™”‰feŽ˜,“439Ž“Ÿ™”‰feŽ˜,“440Ž“Ÿ™”‰feŽ˜,Ž¡‘520,‘>l573Ž‘>lŸ™”‰feŽ–>o,‘>l574Ž‘>lŸ™”‰feŽ“,–>l575,“585,“684Ž“Ÿ™”‰feŽ›>o,“685Ž“Ÿ™”‰feŽ˜,“707Ž“Ÿ™”‰feŽ˜,“708Ž“Ÿ™”‰feŽ˜,Ž¡‘709Ž‘Ÿ™”‰feŽ‘#,‘>l710Ž‘>lŸ™”‰feŽ–>o,‘>l762Ž‘>lŸ™”‰feŽ“,‘>l763Ž‘>lŸ™”‰feŽ“,‘>l764Ž‘>lŸ™”‰feŽ“,‘>l791Ž‘>lŸ™”‰feŽ“,‘>l794Ž‘>lŸ™”‰feŽ“,‘>l795Ž‘>lŸ™”‰feŽ“,‘>l944Ž‘>lŸ™”‰feŽ“,Ž¡‘948Ž‘Ÿ™”‰feŽ‘#,‘Òí997Ž‘Òퟙ”‰feŽ‘Òð,‘Òí1050Ž‘Òퟙ”‰feŽ–Òñ,‘Òí1051Ž‘Òퟙ”‰feŽ“,‘Òí1128Ž‘Òퟙ”‰feŽ“,‘Òí1165Ž‘Òퟙ”‰feŽ“,‘Òí1208Ž‘Òퟙ”‰feŽ“,‘Òí1252Ž‘Òퟙ”‰feŽ“,Ž¡‘1253Ž‘Ÿ™”‰feŽ‘(,‘ö¶1267Ž‘ö¶Ÿ™”‰feŽ–öº,‘ö¶1324Ž‘ö¶Ÿ™”‰feŽ“,‘ö¶1327Ž‘ö¶Ÿ™”‰feŽ“,‘ö¶1401Ž‘ö¶Ÿ™”‰feŽ“,‘ö¶1402Ž‘ö¶Ÿ™”‰feŽ“.Ž¦´P0Ž‘ b¬:‘ +1485Ž‘ +Ÿ™”‰feŽ‘.Ž¦±p0‘‰ffŽ‘®xŽ‘Až¬:‘ +575Ž‘ +Ÿ™”‰feŽ‘,–+Ô576,“579,“580,“582,“584.Ž¦±p0‘‰ffŽ‘®yŽ‘'M¬:‘ +575Ž‘ +Ÿ™”‰feŽ‘,–q¹576,“579,“580,“583.Ž¦±p0‘‰ffŽ‘®zŽ‘»8¬:‘ +575Ž‘ +Ÿ™”‰feŽ‘,–s576,“580,“582,“584.Ž¦±p1Ž‘ À¬:‘ 211Ž‘ -Ÿ™”‰feŽ‘,‘u6212Ž‘u6Ÿ™”‰feŽ‘u9,‘u6400.Ž¡ÂP®9athŽ‘‘d«:‘ -33Ž‘ +Ÿ™”‰feŽ‘,‘!213Ž‘!Ÿ™”‰feŽ–$,‘!288Ž‘!Ÿ™”‰feŽ“,‘!393Ž‘!Ÿ™”‰feŽ“,‘!394Ž‘!Ÿ™”‰feŽ“,–!395,“396Ž“Ÿ™”‰feŽ›$,“397Ž“Ÿ™”‰feŽ˜,“398Ž“Ÿ™”‰feŽ˜,Ž¡‘399Ž‘Ÿ™”‰feŽ‘#,‘Ò401Ž‘ÒŸ™”‰feŽ›Õ,–Ò423,“424Ž“Ÿ™”‰feŽ˜,“425,“426,“427,“429,“430,“431,Ž¡‘432,–>l433,“436Ž“Ÿ™”‰feŽ›>o,“437Ž“Ÿ™”‰feŽ˜,“439Ž“Ÿ™”‰feŽ˜,“440Ž“Ÿ™”‰feŽ˜,“573Ž“Ÿ™”‰feŽ˜,“574Ž“Ÿ™”‰feŽ˜,“575,Ž¡‘585,‘>l684Ž‘>lŸ™”‰feŽ–>o,‘>l685Ž‘>lŸ™”‰feŽ“,‘>l707Ž‘>lŸ™”‰feŽ“,‘>l708Ž‘>lŸ™”‰feŽ“,‘>l709Ž‘>lŸ™”‰feŽ“,‘>l710Ž‘>lŸ™”‰feŽ“,‘>l762Ž‘>lŸ™”‰feŽ“,‘>l763Ž‘>lŸ™”‰feŽ“,Ž¡‘764,‘¾l791Ž‘¾lŸ™”‰feŽ–¾o,‘¾l794Ž‘¾lŸ™”‰feŽ“,‘¾l795Ž‘¾lŸ™”‰feŽ“,‘¾l944Ž‘¾lŸ™”‰feŽ“,‘¾l948Ž‘¾lŸ™”‰feŽ“,‘¾l997Ž‘¾lŸ™”‰feŽ“,‘¾l1050Ž‘¾lŸ™”‰feŽ–¾p,‘¾l1051Ž‘¾lŸ™”‰feŽ“,Ž¡‘1128Ž‘Ÿ™”‰feŽ‘(,‘ö¶1208Ž‘ö¶Ÿ™”‰feŽ–öº,‘ö¶1252Ž‘ö¶Ÿ™”‰feŽ“,‘ö¶1253Ž‘ö¶Ÿ™”‰feŽ“,‘ö¶1401Ž‘ö¶Ÿ™”‰feŽ“,‘ö¶1402Ž‘ö¶Ÿ™”‰feŽ“.Ž¦´P1Ž‘ b¬:‘ +1485Ž‘ +Ÿ™”‰feŽ‘.Ž¦±p1‘‰ffŽ‘®xŽ‘Až¬:‘ +575Ž‘ +Ÿ™”‰feŽ‘,–¸·576,“580,“584.Ž¦±p1‘‰ffŽ‘®yŽ‘'M¬:‘ +575Ž‘ +Ÿ™”‰feŽ‘,–,576,“580.ŽŽ ý•@P’ôऱp1‘‰ffŽ‘®zŽ’›Ü¬:‘ +575Ž‘ +Ÿ™”‰feŽ‘,–ºf576,“580,“584.Ž¤ 9—’ôऱp2Ž’÷d¬:‘ +401Ž‘ +Ÿ™”‰feŽ‘,‘k—944Ž‘k—Ÿ™”‰feŽ–kš,‘k—948Ž‘k—Ÿ™”‰feŽ“,‘k—1128Ž‘k—Ÿ™”‰feŽ–k›,‘k—1324Ž‘k—Ÿ™”‰feŽ“.Ž¡’ôऴP2Ž’ÿç¬:‘ +1485Ž‘ +Ÿ™”‰feŽ‘.Ž¡’ôवqŽ’ù³N¬:‘ +557Ž‘ +Ÿ™”‰feŽ‘,‘ø¾560Ž‘ø¾Ÿ™”‰feŽ–øÁ,‘ø¾930Ž‘ø¾Ÿ™”‰feŽ“,‘ø¾945Ž‘ø¾Ÿ™”‰feŽ“,‘ø¾948Ž‘ø¾Ÿ™”‰feŽ“,‘ø¾1206Ž‘ø¾Ÿ™”‰feŽ–øÂ,‘ø¾1547Ž‘ø¾Ÿ™”‰feŽ“.Ž¡’ôऱq‘‰ffŽ‘®plŽ’^Y¬:‘ +948Ž‘ +Ÿ™”‰feŽ‘.Ž¡’ôऱqq0Ž’"¬:‘ +572Ž‘ +Ÿ™”‰feŽ‘,‘ZF647Ž‘ZFŸ™”‰feŽ‘ZI.Ž¡’ôऱqq1Ž’"¬:‘ +572Ž‘ +Ÿ™”‰feŽ‘,‘ZF647Ž‘ZFŸ™”‰feŽ‘ZI.Ž¡’ôऱQuaderŽ’‰{¬:‘ +1451.Ž¡’ôऱquarterŽ’åê¬:‘ +49,–È1010,“1014Ž“Ÿ™”‰feŽ‘È.Ž¡’ôऱq0Ž’t‹¬:‘ +573Ž‘ +Ÿ™”‰feŽ‘,‘}574Ž‘}Ÿ™”‰feŽ‘},–}575,“585,“1032Ž“Ÿ™”‰feŽ‘}.Ž¡’ôऱq0‘‰ffŽ‘®xŽ’Ÿi¬:‘ +575Ž‘ +Ÿ™”‰feŽ‘,–-n576,“579,“580,“582,“584.Ž¡’ôऱq0‘‰ffŽ‘®yŽ’…¬:‘ +575Ž‘ +Ÿ™”‰feŽ‘,–º¯576,“579,“580.Ž¡’ôऱq0‘‰ffŽ‘®zŽ’¬:‘ +575Ž‘ +Ÿ™”‰feŽ‘,–t¯576,“580,“582,“584.Ž¡’ôऱq1Ž’t‹¬:‘ +573Ž‘ +Ÿ™”‰feŽ‘,‘}574Ž‘}Ÿ™”‰feŽ‘},–}575,“585,“1032Ž“Ÿ™”‰feŽ‘}.Ž¡’ôऱq1‘‰ffŽ‘®xŽ’Ÿi¬:‘ +575Ž‘ 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«:‘ -268Ž‘ -Ÿ™”‰feŽ‘,‘^#272Ž‘^#Ÿ™”‰feŽ‘^&.Ž¡Ïpp0Ž‘30«:‘ -528Ž‘ -Ÿ™”‰feŽ‘,‘Vè603Ž‘V蟙”‰feŽ‘Vë.Ž¡Ïpp1Ž‘30«:‘ -528Ž‘ -Ÿ™”‰feŽ‘,‘Vè603Ž‘V蟙”‰feŽ‘Vë.Ž¡Ïpr–ÿ}'e“cisionŽ‘'½6«:‘ -1444,–‘Ä1512,“1513.Ž¡Ïpr–ÿ}'o“gr“am‘‰ffŽ‘®nameŽ‘?vÝ«:‘ -42Ž‘ +Ž‘,–s¿16,“18,“19,“21,“23,“26,“27,“28,“29,“31,“32,Ž¦’à¦52,–èÔ66,“95,“106,“107,“108,“109,“110,“127,“128,Ž¦’à¦129,–Ò130,“131,“132,“133,“134,“140,“141,“142,“143,Ž¦’à¦170,–Ò171,“172,“173,“178,“179,“181,“182,“183,“190,Ž¦’à¦191,–Ò195,“196,“197,“198,“200,“201,“203,“204,“205,Ž¦’à¦206,–Ò211,“212,“216,“217,“221,“222,“226,“227,“245,Ž¦’à¦255,–Ò280,“281,“283,“284,“286,“287,“288,“297,“298,Ž¦’à¦299,–Ò309,“310,“317,“327,“328,“329,“330,“347,“350,Ž¦’à¦351,–Ò355,“356,“357,“358,“360,“361,“362,“363,“365,Ž¦’à¦366,–Ò367,“368,“370,“371,“372,“373,“375,“376,“377,Ž¦’à¦378,–Ò380,“381,“382,“383,“389,“390,“393,“394,“395,Ž¦’à¦404,–Ò405,“406,“407,“408,“409,“412,“413,“419,“420,Ž¦’à¦423,–Ò424,“433,“436,“437,“438,“439,“440,“442,“443,ŽŽŽŽŽŒ‹ü 2 Šn ý‘ì¬508–¯INDEX’9?c3DLDF-1.1.5.1“°x¬1563Ž €n ý•@P‘445,–Ò446,“447,“449,“475,“476,“486,“487,“488,“489,Ž¤ ‘490,–Ò491,“492,“493,“494,“509,“516,“529,“530,“532,Ž¡‘533,–Ò534,“535,“538,“539,“540,“541,“542,“543,“546,Ž¡‘547,–Ò548,“549,“552,“555,“556,“561,“566,“575,“576,Ž¡‘577,–Ò578,“579,“580,“582,“592,“594,“595,“598,“600,Ž¡‘603,–Ò604,“605,“606,“607,“609,“610,“611,“612,“615,Ž¡‘616,–Ò622,“625,“626,“628,“629,“650,“661,“677,“678,Ž¡‘680,–Ò685,“688,“698,“756,“757,“759,“760,“762,“763,Ž¡‘764,–Ò765,“766,“767,“768,“769,“771,“772,“776,“777,Ž¡‘785,–>l786,“882,“883,“886,“888,“889,“890,“891,Ž¡‘892,–>l893,“894,“909,“910,“923,“924,“940,“948,Ž¡‘950,–>l968,“969,“973,“974,“990,“991,“992,“993,Ž¡‘994,–Òí995,“1001,“1004,“1011,“1012,“1013,“1014,Ž¡‘1040,–<„1047,“1048,“1050,“1051,“1052,“1053,“1054,Ž¡‘1055,–<„1056,“1057,“1059,“1060,“1064,“1065,“1069,Ž¡‘1076,–<„1077,“1079,“1080,“1087,“1101,“1106,“1107,Ž¡‘1108,–<„1109,“1130,“1131,“1132,“1133,“1143,“1149,Ž¡‘1150,–<„1151,“1152,“1165,“1171,“1172,“1174,“1175,Ž¡‘1186,–<„1187,“1188,“1189,“1192,“1193,“1194,“1195,Ž¡‘1197,–<„1198,“1199,“1200,“1201,“1202,“1206,“1214,Ž¡‘1215,–<„1216,“1220,“1222,“1224,“1232,“1235,“1236,Ž¡‘1237,–<„1238,“1239,“1240,“1242,“1243,“1247,“1248,Ž¡‘1252,–<„1253,“1254,“1255,“1267,“1268,“1276,“1281,Ž¡‘1282,–<„1283,“1284,“1293,“1295,“1296,“1297,“1298,Ž¡‘1304,–<„1305,“1307,“1320,“1321,“1323,“1324,“1326,Ž¡‘1327,–<„1333,“1381,“1382,“1390,“1391,“1392,“1393,Ž¡‘1395,–<„1396,“1399,“1400,“1401,“1402,“1404,“1405,Ž¡‘1407,–<„1408,“1409,“1410,“1411,“1412,“1413,“1414,Ž¡‘1453,–<„1459,“1460,“1472,“1477,“1478,“1483,“1484,Ž¡‘1485,–<„1487,“1488,“1489,“1490,“1491,“1492,“1494,Ž¡‘1495,–<„1500,“1501,“1503,“1504,“1505,“1506,“1508,Ž¡‘1509,–<„1514,“1515,“1516,“1517,“1518,“1519,“1522,Ž¡‘1523,–ö¶1528,“1529,“1530,“1531,“1556.Ž¤ 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+206Ž‘ +Ÿ™”‰feŽ‘,‘P209.Ž¡±t‘‰ffŽ‘®inverseŽ‘'¬:‘ +1005Ž‘ +Ÿ™”‰feŽ‘,‘æ1218Ž‘柙”‰feŽ‘æ“,–æ1221,“1223,“1225.Ž¡±t‘‰ffŽ‘®xŽ‘ [9¬:‘ +206Ž‘ +Ÿ™”‰feŽ‘,–|207,“209,“561Ž“Ÿ™”‰feŽ‘,“562,“563,“564,“565,Ž¦‘566,‘,4948Ž‘,4Ÿ™”‰feŽ‘,7,‘,4950.Ž¡±t‘‰ffŽ–®x‘‰ffŽ“signŽ‘!ú¬:‘ +565Ž‘ +Ÿ™”‰feŽ‘.Ž¡±t‘‰ffŽ‘®yŽ‘ @è¬:‘ +206Ž‘ +Ÿ™”‰feŽ‘,–ñ9208,“209,“561Ž“Ÿ™”‰feŽ‘ñ<,“562,“563,“564,“565,“566,Ž¦‘948Ž‘Ÿ™”‰feŽ‘#,–,4949,“950.Ž¡±t‘‰ffŽ–®y‘‰ffŽ“signŽ‘"1¬:‘ +565Ž‘ +Ÿ™”‰feŽ‘.Ž¡±t‘‰ffŽ‘®zŽ‘ ÔÓ¬:‘ +206Ž‘ +Ÿ™”‰feŽ‘,–209,“561Ž“Ÿ™”‰feŽ‘’,“562,“563,“564,“565,“566,Ž¦‘948Ž‘Ÿ™”‰feŽ‘#,–,4949,“950.Ž¡±t‘‰ffŽ–®z‘‰ffŽ“signŽ‘!mM¬:‘ +565Ž‘ +Ÿ™”‰feŽ‘.Ž¡±tempŽ‘Zt¬:‘ +547Ž‘ +Ÿ™”‰feŽ‘,‘±ü948Ž‘±üŸ™”‰feŽ‘±ÿ,–±ü949,“950.Ž¡±temp‘‰ffŽ‘®b–ÿ}'o“olŽ‘*Êu¬:‘ +1227Ž‘ +Ÿ™”‰feŽ‘,‘á¿1228.Ž¡±temp‘‰ffŽ‘®cir‘ÿ}'cleŽ‘1Gó¬:‘ +1324Ž‘ +Ÿ™”‰feŽ‘.Ž¡±temp‘‰ffŽ–®cir›ÿ}'cle‘‰ffŽ“c˜enterŽ‘O¼\¬:‘ +1324Ž‘ +Ÿ™”‰feŽ‘.Ž¡±temp‘‰ffŽ–®cir‘ÿ}'cle‘‰ffŽ“normalŽ‘T ‰¬:‘ +1324Ž‘ +Ÿ™”‰feŽ‘.Ž¡±temp‘‰ffŽ‘®c–ÿ}'o“or“dinatesŽ‘J¦{¬:‘ +441,‘Q 443Ž‘Q Ÿ™”‰feŽ‘Q,‘Q 445.Ž¡±temp‘‰ffŽ‘®matrixŽ‘7#°¬:‘ +219Ž‘ +Ÿ™”‰feŽ‘.Ž¡±temp‘‰ffŽ‘®ptŽ‘"Ȳ¬:‘ +649Ž‘ +Ÿ™”‰feŽ‘.Ž¡±temp‘‰ffŽ‘®stringŽ‘34 ¬:‘ +1227Ž‘ +Ÿ™”‰feŽ‘,‘Æ 1228.Ž¡±temp1Ž‘0R¬:‘ +206Ž‘ +Ÿ™”‰feŽ‘,–ŸA207,“208,“209.Ž¡±temp2Ž‘0R¬:‘ +206Ž‘ +Ÿ™”‰feŽ‘,–ŸA207,“208,“209.Ž¡±test‘‰ffŽ‘®angleŽ‘*ó¬:‘ +1224Ž‘ +Ÿ™”‰feŽ‘.Ž¡±test‘‰ffŽ‘®p‘ÿ}'ointsŽ‘.'õ¬:‘ +401,‘÷–948.Ž¡±T‘ÿ;¼etr–ÿ}'ahe“dr“aŽ‘/ˆ¬:‘ +1485.Ž¡­T‘ÿ +«etrahedronŽ‘>œ¬:‘ +1470,‘¹1477Ž‘¹Ÿ™”‰feŽ›¹¡,–¹1478,“1480,“1481Ž“Ÿ™”‰feŽ˜,Ž¦‘1483,‘<„1484Ž‘<„Ÿ™”‰feŽ‘<ˆ,–<„1485,“1487,“1488,“1489,“1490,“1492.ŽŽ ý•@P’ôऱtex‘‰ffŽ‘®str–ÿ}'e“amŽ’"ä¬:‘ +78Ž‘ +Ÿ™”‰fe +Ž‘,‘Î79Ž‘Ο™”‰fe +Ž‘Ð,–Î83,“84,“85,“1557.Ž¤ Zî’ôऱtex‘‰ffŽ›®str–ÿ}'e“am‘‰ffŽ˜nameŽ’>ò¬:‘ +81Ž‘ +Ÿ™”‰fe +Ž‘,‘†Ž82Ž‘†ŽŸ™”‰fe +Ž‘†,‘†Ž83.Ž¡’ôऱtextŽ’8p¬:‘ +135Ž‘ +Ÿ™”‰feŽ‘,‘ÞÅ136Ž‘ÞÅŸ™”‰feŽ–ÞÈ,‘ÞÅ192Ž‘ÞÅŸ™”‰feŽ“,‘ÞÅ193Ž‘ÞÅŸ™”‰feŽ“,‘ÞÅ245Ž‘ÞÅŸ™”‰feŽ“,‘ÞÅ253Ž‘ÞÅŸ™”‰feŽ“,‘ÞÅ293Ž‘ÞÅŸ™”‰feŽ“,‘ÞÅ294Ž‘ÞÅŸ™”‰feŽ“,Ž¤ ’à¦295Ž’ট™”‰feŽ’à©,‘>l296Ž‘>lŸ™”‰feŽ–>o,‘>l475Ž‘>lŸ™”‰feŽ“,‘>l476Ž‘>lŸ™”‰feŽ“,‘>l477Ž‘>lŸ™”‰feŽ“,‘>l478Ž‘>lŸ™”‰feŽ“,–>l506,“515,“516,Ž¡’à¦652Ž’ট™”‰feŽ’à©,‘>l653Ž‘>lŸ™”‰feŽ–>o,‘>l689Ž‘>lŸ™”‰feŽ“,‘>l690Ž‘>lŸ™”‰feŽ“,‘>l909Ž‘>lŸ™”‰feŽ“,‘>l910Ž‘>lŸ™”‰feŽ“,‘>l916Ž‘>lŸ™”‰feŽ“,‘>l917Ž‘>lŸ™”‰feŽ“,‘>l918Ž‘>lŸ™”‰feŽ“,Ž¡’à¦919Ž’ট™”‰feŽ’à©,‘ ³1381Ž‘ ³Ÿ™”‰feŽ– ·,‘ ³1382Ž‘ ³Ÿ™”‰feŽ“.Ž© Zî’ôऱtext‘‰ffŽ‘®shortŽ’À¬:‘ +507Ž‘ +Ÿ™”‰feŽ‘,‘†Ë508Ž‘†ËŸ™”‰feŽ–†Î,‘†Ë512Ž‘†ËŸ™”‰feŽ“,‘†Ë513Ž‘†ËŸ™”‰feŽ“,‘†Ë871Ž‘†ËŸ™”‰feŽ“,‘†Ë872Ž‘†ËŸ™”‰feŽ“,‘†Ë873Ž‘†ËŸ™”‰feŽ“,‘†Ë874Ž‘†ËŸ™”‰feŽ“,Ž¡’à¦875Ž’ট™”‰feŽ’à©,‘š¶877Ž‘š¶Ÿ™”‰feŽ–š¹,‘š¶878Ž‘š¶Ÿ™”‰feŽ“,‘š¶879Ž‘š¶Ÿ™”‰feŽ“,‘š¶880Ž‘š¶Ÿ™”‰feŽ“.Ž¦’ôऱtext‘‰ffŽ‘®strŽ’§è¬:‘ +505Ž‘ +Ÿ™”‰feŽ‘,‘Ÿ506Ž‘ŸŸ™”‰feŽ–¢,‘Ÿ510Ž‘ŸŸ™”‰feŽ“,‘Ÿ511Ž‘ŸŸ™”‰feŽ“,‘Ÿ617Ž‘ŸŸ™”‰feŽ“,‘Ÿ618Ž‘ŸŸ™”‰feŽ“.Ž¦’ôऱthetaŽ’ ŸN¬:‘ +1324Ž‘ +Ÿ™”‰feŽ‘,‘#¼1327Ž‘#¼Ÿ™”‰feŽ‘#À.Ž¦’ôऱtheta‘‰ffŽ‘®totalŽ’"ý•¬:‘ +1327Ž‘ +Ÿ™”‰feŽ‘.Ž¦’ôऱthir‘ÿ}'dŽ’ +½¬:‘ +16Ž‘ Ÿ™”‰fe -Ž‘,‘ÿc93Ž‘ÿcŸ™”‰fe -Ž‘ ÿe,‘ÿc147Ž‘ÿcŸ™”‰feŽ–ÿf,‘ÿc148Ž‘ÿcŸ™”‰feŽ“,‘ÿc200Ž‘ÿcŸ™”‰feŽ“,‘ÿc208Ž‘ÿcŸ™”‰feŽ“,‘ÿc248Ž‘ÿcŸ™”‰feŽ“,‘ÿc249Ž‘ÿcŸ™”‰feŽ“,‘ÿc250Ž‘ÿcŸ™”‰feŽ“,‘ÿc251Ž‘ÿcŸ™”‰feŽ“,Ž¦‘431Ž‘Ÿ™”‰feŽ‘#,‘Ò432Ž‘ÒŸ™”‰feŽ–Õ,‘Ò433Ž‘ÒŸ™”‰feŽ“,‘Ò434Ž‘ÒŸ™”‰feŽ“,–Ò462,“471,“472,“608Ž“Ÿ™”‰feŽ›Õ,“609Ž“Ÿ™”‰feŽ˜,“645Ž“Ÿ™”‰feŽ˜,Ž¦‘646Ž‘Ÿ™”‰feŽ‘#,‘n!866Ž‘n!Ÿ™”‰feŽ–n$,‘n!867Ž‘n!Ÿ™”‰feŽ“,‘n!872Ž‘n!Ÿ™”‰feŽ“,‘n!873Ž‘n!Ÿ™”‰feŽ“,‘n!874Ž‘n!Ÿ™”‰feŽ“,‘n!875Ž‘n!Ÿ™”‰feŽ“,‘n!1341Ž‘n!Ÿ™”‰feŽ–n%,‘n!1342Ž‘n!Ÿ™”‰feŽ“.Ž¡Ïtext‘‰ffŽ‘®shortŽ‘*ßo«:‘ -463Ž‘ -Ÿ™”‰feŽ‘,‘†Ë464Ž‘†ËŸ™”‰feŽ–†Î,‘†Ë468Ž‘†ËŸ™”‰feŽ“,‘†Ë469Ž‘†ËŸ™”‰feŽ“,‘†Ë828Ž‘†ËŸ™”‰feŽ“,‘†Ë829Ž‘†ËŸ™”‰feŽ“,‘†Ë830Ž‘†ËŸ™”‰feŽ“,‘†Ë831Ž‘†ËŸ™”‰feŽ“,Ž¦‘832Ž‘Ÿ™”‰feŽ‘#,‘š¶834Ž‘š¶Ÿ™”‰feŽ–š¹,‘š¶835Ž‘š¶Ÿ™”‰feŽ“,‘š¶836Ž‘š¶Ÿ™”‰feŽ“,‘š¶837Ž‘š¶Ÿ™”‰feŽ“.Ž¡Ïtext‘‰ffŽ‘®strŽ‘ ÇD«:‘ -461Ž‘ -Ÿ™”‰feŽ‘,‘Ÿ462Ž‘ŸŸ™”‰feŽ–¢,‘Ÿ466Ž‘ŸŸ™”‰feŽ“,‘Ÿ467Ž‘ŸŸ™”‰feŽ“,‘Ÿ573Ž‘ŸŸ™”‰feŽ“,‘Ÿ574Ž‘ŸŸ™”‰feŽ“.Ž¡ÏthetaŽ‘¾ª«:‘ -1287Ž‘ -Ÿ™”‰feŽ‘,‘#¼1290Ž‘#¼Ÿ™”‰feŽ‘#À.Ž¡Ïtheta‘‰ffŽ‘®totalŽ‘.ñ«:‘ -1290Ž‘ -Ÿ™”‰feŽ‘.Ž¡Ïthir‘ÿ}'dŽ‘Üj«:‘ -13Ž‘ -Ÿ™”‰fe -Ž‘,‘Rf270Ž‘RfŸ™”‰feŽ‘Ri,–Rf271,“960,“1136,“1137,“1184,Ž¦‘1186,‘VÕ1188.Ž¡ÏthisŽ‘붫:‘ -78,–H143,“149,“151,“153,“156,“159,“164,“171,Ž¦‘173,–Ò174,“177,“179,“188,“224,“239,“284,“285,“287,Ž¦‘289,–Ò315,“320,“343,“345,“346,“349,“350,“351,“353,Ž¦‘356,–Ò357,“388,“392,“393,“395,“409,“411,“415,“418,Ž¦‘431,–Ò432,“442,“443,“462,“463,“478,“482,“489,“493,Ž¦‘497,–Ò499,“501,“503,“504,“507,“508,“510,“512,“523,Ž¦‘524,–Ò526,“544,“545,“557,“563,“566,“568,“570,“601,Ž¦‘622,–Ò626,“637,“646,“657,“677,“678,“689,“714,“716,Ž¦‘720,–Ò724,“726,“729,“750,“751,“752,“754,“757,“762,Ž¦‘764,–Ò768,“770,“771,“776,“780,“789,“798,“802,“807,Ž¦‘813,–Ò817,“821,“824,“840,“872,“874,“881,“886,“896Ž“Ÿ™”‰feŽ‘Õ,Ž¦‘901,–>l904,“912,“914,“915,“916,“920,“932,“948,Ž¦‘949,–953,“957,“967,“999,“1004,“1007,“1011,“1013,Ž¦‘1016,–<„1027,“1037,“1067,“1072,“1080,“1112,“1120,Ž¦‘1126,–<„1127,“1152,“1167,“1176,“1178,“1179,“1192,Ž¦‘1196,–<„1198,“1199,“1200,“1201,“1203,“1213,“1243,Ž¦‘1245,–<„1253,“1254,“1255,“1256,“1258,“1308,“1310,Ž¦‘1351,–<„1353,“1356,“1358,“1360,“1362,“1365,“1384,Ž¦‘1387,–£ÿ1390,“1393,“1396,“1399,“1426,“1447.Ž¡Ïthis‘‰ffŽ–®axis‘‰ffŽ“orientationŽ‘YMí«:‘ 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-Ÿ™”‰feŽ‘,‘–ƒ153Ž‘–ƒŸ™”‰feŽ––†,‘–ƒ200Ž‘–ƒŸ™”‰feŽ“,‘–ƒ364Ž‘–ƒŸ™”‰feŽ“,‘–ƒ365Ž‘–ƒŸ™”‰feŽ“,‘–ƒ725Ž‘–ƒŸ™”‰feŽ“,‘–ƒ726Ž‘–ƒŸ™”‰feŽ“,‘–ƒ1012Ž‘–ƒŸ™”‰feŽ––‡,‘–ƒ1013Ž‘–ƒŸ™”‰feŽ“,Ž¡’à¦1200Ž’ট™”‰feŽ’àª,‘¢[1201Ž‘¢[Ÿ™”‰feŽ–¢_,‘¢[1352Ž‘¢[Ÿ™”‰feŽ“,‘¢[1353Ž‘¢[Ÿ™”‰feŽ“.Ž¡’ôà¤ÏzzŽ’þË©«:‘ -1203Ž‘ -Ÿ™”‰feŽ‘,‘Ùí1204Ž‘Ùퟙ”‰feŽ–Ùñ,‘Ùí1350Ž‘Ùퟙ”‰feŽ“,‘Ùí1351Ž‘Ùퟙ”‰feŽ“,‘Ùí1355Ž‘Ùퟙ”‰feŽ“,‘Ùí1356Ž‘Ùퟙ”‰feŽ“,‘Ùí1359Ž‘Ùퟙ”‰feŽ“,‘Ùí1360Ž‘Ùퟙ”‰feŽ“.Ž¡’ôà¤Ïz0Ž’ÿñ´«:‘ -928Ž‘ -Ÿ™”‰feŽ‘.Ž¡’ôà¤Ïz1Ž’ÿñ´«:‘ -928Ž‘ -Ÿ™”‰feŽ‘.ŽŽŽŽŽŒ‹þRM Šn ý‘ì«510‘­NAMES–ÕXOF“THE“SECTIONS’´*3DLDFPRÃŽGŽ €n ý•@P·h›ª¨«Actions–UUin“main‘@­1505,–ÕX1506˜·i‘ -­Used“in“section“1519.Ž¤ 5þ·h–ª¨«All‘UUÂColorsŽ‘(n3­0“·i‘ -­Cited–ÕXin“sections“109“and“114.Ž¡·h‘ª¨«Chec•¸ãk›UUin“tersection˜pGoin“t˜loGcations‘@­1189‘ª¨·i‘ -­Used–ÕXin“section“1188.Ž¡·h›ª¨«DEC–UUcommand“line“option“proGcessing‘@­1510˜·i‘ -­Used–ÕXin“section“1507.Ž¡·h›ª¨«Declarations–Ü¡for“the“header“ le‘@­18,–e20,“23,“27,“190,“192,“258,“275,“587,“611,“648˜·i‘ -­Cited–HYin“section“21.‘­Used“inŽ© ‘sections–ÕX36,“195,“261,“590,“614,“and“651.Ž¡·h›ª¨«Declare–UUI/O“functions‘@­42,–ÕX45,“47,“49˜·i‘ -­Used“in“section“53.Ž¡·h›ª¨«Declare–UUP¸ãattern“functions‘@­1283,–ÕX1286,“1289˜·i‘ -­Used“in“sections“1292“and“1293.Ž¡·h›ª¨«Declare–UUnamespace“ÂPro‘£ŽjectionsŽ‘Aa¹­211˜·i‘ -­Used–ÕXin“section“260.Ž¡·h›ª¨«Declare–UUnamespace“ÂSortingŽ‘,ÿŸ­213˜·i‘ -­Used–ÕXin“section“260.Ž¡·h›ª¨«Declare–UUnon-mem¸ãbGer“functions“for“ÂColorŽ‘#ä÷­103˜·i‘ -­Used–ÕXin“section“119.Ž¡·h›ª¨«Declare–UUnon-mem¸ãbGer“functions“for“ÂP•®9oin“tsŽ‘'¸Ý­436,–ÕX490˜·i‘ -­Used“in“section“590.Ž¡·h›ª¨«Declare–UUparser“functions‘@­1497˜·i‘ -­Used–ÕXin“section“1501.Ž¡·h›ª¨«Declare–UUutilit¸ãy“functions‘@­21,–ÕX29,“31˜·i‘ -­Cited“in“section“21.‘qÈUsed“in“section“36.Ž¡·h›ª¨«Declare‘FÂCircleŽ‘&•¸«functions‘@­1239,–¥‰1242,“1244,“1247,“1249,“1253,“1255,“1258,“1260,“1261,“1263,“1265,“1267˜·i‘ -­Used‘{æinŽ¦‘section‘ÕX1237.Ž¡·h‘ª¨«Declare‘«rÂColorŽ‘#¦‚«functions‘@­58,–0×60,“63,“65,“68,“70,“72,“73,“75,“77,“80,“82,“84,“86,“88,“90,“92,“95,“97,“98,“99,“100,“102,“105,Ž¦‘107‘ª¨·i‘ -­Used–ÕXin“section“56.Ž¡·h›ª¨«Declare‘UUÂCubQÇoidŽ‘+úD«functions‘@­1415,–ÕX1417,“1419,“1421,“1423,“1425˜·i‘ -­Used“in“section“1413.Ž¡·h›ª¨«Declare‘UUÂDoQÇdecahedronŽ‘Oj8«functions‘@­1456,–ÕX1459,“1462,“1464˜·i‘ -­Used“in“section“1453.Ž¡·h‘ª¨«Declare‘Ü•ÂEllipseŽ‘)¢«functions‘@­1106,–e 1109,“1111,“1114,“1116,“1119,“1122,“1124,“1126,“1128,“1129,“1131,“1133,“1136,“1139,Ž¦‘1141,–‹1144,“1146,“1148,“1150,“1154,“1156,“1159,“1161,“1163,“1165,“1167,“1170,“1172,“1175,“1192,“1194,“1196,“1198,“1200,Ž¦‘1203,–ÕX1205,“1208,“1210,“1213,“1215,“1218,“1220,“1222,“1224‘ª¨·i‘ -­Used“in“section“1103.Ž¡·h›ª¨«Declare‘ZÂF‘ÿ -«oQÇcusŽ‘%.«functions‘@­558,–¨Î560,“562,“565,“567,“569,“571,“573,“576,“577,“578,“579,“580,“581,“583,“584˜·i‘ -­Used‘~ƒinŽ¦‘section‘ÕX556.Ž¡·h›ª¨«Declare‘UUÂIcosahedronŽ‘Cƒy«functions‘@­1470,–ÕX1473,“1475,“1477˜·i‘ -­Used“in“section“1467.Ž¡·h–ª¨«Declare‘UUÂLabQÇelŽ‘"ì «functions‘@­210“·i‘ -­Used–ÕXin“section“208.Ž¡·h–ª¨«Declare‘UUÂLineŽ‘-«constructors‘@­595,›ÕX597“·i‘ -­Used˜in˜section˜593.Ž¡·h›ª¨«Declare‘UUÂLineŽ‘-«functions‘@­599,–ÕX602,“604,“608˜·i‘ -­Used“in“section“593.Ž¡·h‘ª¨«Declare‘VÆÂP®9athŽ‘>ð«functions‘@­656,–Öà660,“663,“665,“668,“670,“673,“675,“677,“680,“682,“684,“686,“688,“690,“692,“695,“697,“700,“702,Ž¦‘704,–ð706,“708,“713,“719,“721,“723,“725,“728,“730,“733,“735,“738,“740,“742,“747,“749,“751,“754,“756,“758,“762,“767,“769,“775,Ž¦‘777,–ð784,“786,“793,“795,“801,“803,“806,“808,“812,“814,“820,“823,“825,“829,“831,“834,“836,“839,“841,“845,“846,“848,“850,“852,Ž¦‘854,–Vw856,“866,“868,“871,“872,“874,“876,“877,“878,“879,“881,“888,“890,“892,“894,“896,“902,“908,“911,“915,“917,“920,“932‘ª¨·iŽ¦‘­Used–ÕXin“section“654.Ž¡·h‘ª¨«Declare‘yÂPictureŽ‘,-«functions‘@­218,–û×220,“222,“224,“225,“227,“229,“230,“231,“235,“238,“240,“241,“243,“244,“246,“248,“250,“253,Ž¦‘254,–ÕX255,“256‘ª¨·i‘ -­Used“in“section“216.Ž¡·h›ª¨«Declare‘UUÂPlaneŽ‘#Œ «functions‘@­619,–ÕX621,“623,“625,“628,“630,“633,“635,“640,“642,“643,“645˜·i‘ -­Used“in“section“617.Ž¡·h›ª¨«Declare‘UUÂP•®9oin“tŽ‘"Dò«constructors‘@­279,–ÕX282,“286˜·i‘ -­Used“in“section“264.Ž¡·h‘ª¨«Declare‘$ÛÂP•®9oin“tŽ‘!ãþ«functions‘@­284,–´b288,“291,“293,“295,“297,“299,“301,“302,“304,“307,“308,“309,“312,“314,“317,“319,“322,“324,“327,Ž¦‘329,–ð332,“334,“337,“339,“341,“342,“344,“345,“349,“352,“354,“356,“357,“360,“362,“364,“368,“370,“375,“377,“392,“394,“398,“402,Ž¦‘404,–ð406,“410,“412,“414,“416,“419,“420,“422,“423,“425,“426,“428,“429,“431,“433,“438,“440,“442,“444,“445,“447,“449,“451,“457,Ž¦‘461,–ð463,“466,“468,“474,“477,“479,“481,“483,“485,“488,“492,“494,“496,“498,“500,“502,“504,“507,“509,“511,“513,“516,“523,“525,Ž¦‘528,–ÕX529‘ª¨·i‘ -­Used“in“section“264.Ž¡·h›ª¨«Declare‘K¶ÂP®9olygonŽ‘/œZ«functions‘@­978,–ÎÍ980,“984,“993,“995,“1001,“1003,“1006,“1008,“1010,“1012,“1015,“1017,“1020,“1022˜·i‘ -­UsedŽ¦‘in–ÕXsection“975.Ž¡·h–ª¨«Declare‘UUÂP®9olyhedronŽ‘@¸w«functions‘@­1432“·i‘ -­Used–ÕXin“section“1431.Ž¡·h‘ª¨«Declare‘Y]ÂRectangleŽ‘8òO«functions‘@­1061,–Ù 1064,“1066,“1069,“1071,“1074,“1076,“1079,“1082,“1085,“1087,“1090,“1092,“1095,“1096,Ž¦‘1097,–ÕX1098‘ª¨·i‘ -­Used“in“section“1059.Ž¡·h›ª¨«Declare‘SÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘q >«functions‘@­943,– G944,“945,“946,“947,“948,“950,“953,“964,“967,“969,“970˜·i‘ -­Used‘w±inŽ¦‘section‘ÕX941.Ž¡·h›ª¨«Declare‘(¿ÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘GÐ2«functions‘@­1026,–·1029,“1032,“1035,“1039,“1041,“1045,“1047,“1049,“1050,“1051,“1053,“1054˜·i‘ -­UsedŽ¦‘in–ÕXsection“1025.ŽŽŽŒ‹ÿ‚ý Šn ý‘ì­3DLDFPRÃŽG’´*NAMES–ÕXOF“THE“SECTIONS‘«511Ž €n ý•@P·h–ª¨«Declare‘UUÂSolidu½‰™šs4Ž‘ÔwF‘ÿ -«acedŽ‘A {«functions‘@­1406“·i‘ -­Used–ÕXin“section“1405.Ž© •þ·h‘ª¨«Declare‘m%ÂSolidŽ‘ X!«functions‘@­1299,–î¥1301,“1303,“1305,“1307,“1309,“1311,“1313,“1316,“1318,“1320,“1322,“1324,“1326,“1329,“1331,Ž¤ ‘1333,–‹1335,“1337,“1339,“1341,“1343,“1346,“1348,“1350,“1352,“1355,“1357,“1359,“1361,“1364,“1366,“1368,“1369,“1371,“1373,Ž¡‘1375,–ÕX1377,“1379,“1383,“1386,“1389,“1392,“1395,“1398‘ª¨·i‘ -­Used“in“section“1296.Ž¦·h›ª¨«Declare‘UUÂT‘ÿ -«etrahedronŽ‘EF®«functions‘@­1439,–ÕX1442,“1446,“1448,“1450˜·i‘ -­Used“in“section“1436.Ž¦·h‘ª¨«Declare‘‘QÂT‘ÿ -«ransformŽ‘;–«functions‘@­124,–126,“128,“130,“132,“134,“136,“138,“140,“142,“145,“147,“150,“152,“155,“157,“158,“160,Ž¡‘166,–ÕX167,“168,“171,“173,“176,“178,“181,“187‘ª¨·i‘ -­Used“in“section“122.Ž¦·h›ª¨«Declare‘UUÂT‘ÿ -«runcu½‰™šs4Ž‘ÔwOctahedronŽ‘dyT«functions‘@­1484,–ÕX1487,“1489˜·i‘ -­Used“in“section“1481.Ž¦·h–ª¨«Declare‘UUÏdr‘ÿ}'aw‘‰ffŽ‘®axesŽ‘/[+«(‘ª®)‘@­924,›ÕX929“·i‘ -­Used˜in˜section˜937.Ž¦·h–ª¨«Declare‘UUÂnamespaceŽ‘<øÏColorsŽ‘b­­109“·i‘ -­Cited–ÕXin“section“109.‘qÈUsed“in“section“118.Ž¦·h›ª¨«De ne–UUI/O“functions‘@­43,–ÕX44,“46,“48,“50˜·i‘ -­Used“in“section“52.Ž¦·h›ª¨«De ne–UUP¸ãattern“functions‘@­1284,–ÕX1287,“1290˜·i‘ -­Used“in“section“1292.Ž¦·h–ª¨«De ne‘UUclasses‘@­208,›ÕX216“·i‘ -­Used˜in˜sections˜260˜and˜261.Ž¦·h›ª¨«De ne–UUcomparison“classes‘@­454,–ÕX455,“456˜·i‘ -­Cited“in“section“552.‘qÈUsed“in“sections“589“and“590.Ž¦·h›ª¨«De ne–UUnon-mem¸ãbGer“functions“for“ÂColorŽ‘#ä÷­104˜·i‘ -­Used–ÕXin“section“118.Ž¦·h›ª¨«De ne–UUnon-mem¸ãbGer“functions“for“ÂP•®9oin“tsŽ‘'¸Ý­437,–ÕX491˜·i‘ -­Used“in“section“589.Ž¦·h›ª¨«De ne–UUparser“functions‘@­1498˜·i‘ -­Used–ÕXin“section“1500.Ž¦·h›ª¨«De ne–UUutilit¸ãy“functions‘@­22,–ÕX30,“32˜·i‘ -­Cited“in“section“22.‘qÈUsed“in“section“35.Ž¦·h›ª¨«De ne‘UUÂCircleŽ‘% Ö«functions‘@­1240,–ÕX1243,“1245,“1248,“1250,“1254,“1256,“1259,“1264,“1266,“1268˜·i‘ -­Used“in“section“1278.Ž¦·h›ª¨«De ne‘RÂColorŽ‘"ó¬«functions‘@­59,–Ó61,“64,“66,“69,“71,“74,“76,“78,“81,“83,“85,“87,“89,“91,“93,“101,“106,“108˜·i‘ -­Used–Ò‰in“section“118.Ž¦·h›ª¨«De ne‘UUÂCubQÇoidŽ‘+úD«functions‘@­1416,–ÕX1418,“1420,“1422,“1424,“1426˜·i‘ -­Used“in“section“1427.Ž¦·h›ª¨«De ne‘UUÂDoQÇdecahedronŽ‘Oj8«functions‘@­1457,–ÕX1460,“1461,“1463,“1465˜·i‘ -­Used“in“section“1493.Ž¦·h‘ª¨«De ne‘N{ÂEllipseŽ‘(…Ï«functions‘@­1107,–Я1110,“1112,“1115,“1117,“1120,“1123,“1127,“1130,“1132,“1134,“1135,“1137,“1140,“1142,“1145,Ž¡‘1147,–‹1149,“1151,“1155,“1157,“1160,“1162,“1164,“1166,“1168,“1171,“1173,“1176,“1177,“1178,“1179,“1180,“1181,“1182,“1183,Ž¡‘1184,–ÍÜ1185,“1187,“1188,“1193,“1195,“1197,“1199,“1201,“1204,“1206,“1209,“1211,“1214,“1216,“1219,“1221,“1223,“1225‘ª¨·i‘ -­UsedŽ¡‘in–ÕXsection“1232.Ž¦·h›ª¨«De ne‘UUÂF‘ÿ -«oQÇcusŽ‘#Ÿö«functions‘@­561,–ÕX563,“566,“568,“570,“572,“574,“582,“585˜·i‘ -­Used“in“section“589.Ž¦·h›ª¨«De ne‘UUÂIcosahedronŽ‘Cƒy«functions‘@­1471,–ÕX1474,“1476,“1478˜·i‘ -­Used“in“section“1493.Ž¦·h›ª¨«De ne‘UUÂLabQÇelŽ‘"ì «functions‘@­470,–ÕX471,“472˜·i‘ -­Used“in“section“589.Ž¦·h–ª¨«De ne‘UUÂLineŽ‘-«constructors‘@­596,›ÕX598“·i‘ -­Used˜in˜section˜613.Ž¦·h›ª¨«De ne‘UUÂLineŽ‘-«functions‘@­600,–ÕX605,“606,“607,“609,“934˜·i‘ -­Used“in“sections“613“and“936.Ž¦·h‘ª¨«De ne‘ycÂP®9athŽ‘„*«functions‘@­657,–û§661,“664,“666,“669,“671,“674,“676,“678,“681,“683,“685,“687,“689,“693,“696,“698,“701,“703,“705,Ž¡‘707,–ð709,“714,“720,“722,“724,“726,“729,“731,“734,“736,“739,“741,“743,“748,“750,“752,“755,“757,“759,“763,“764,“765,“766,“768,Ž¡‘770,–ð771,“776,“778,“785,“787,“794,“796,“802,“804,“807,“809,“813,“815,“821,“824,“826,“830,“832,“835,“837,“840,“842,“843,“844,Ž¡‘847,–ð849,“851,“853,“855,“857,“858,“859,“860,“861,“862,“863,“867,“869,“873,“875,“880,“882,“883,“884,“885,“886,“889,“891,“893,Ž¡‘897,–ÕX898,“899,“900,“903,“909,“912,“913,“914,“916,“918,“921,“933‘ª¨·i‘ -­Used“in“section“936.Ž¦·h‘ª¨«De ne‘1ÂPictureŽ‘,Öo«functions‘@­219,–!²226,“228,“232,“236,“239,“242,“245,“247,“249,“251,“373,“396,“543,“544,“545,“546,“548,“549,Ž¡‘550,–ÕX551,“552,“553,“554‘ª¨·i‘ -­Used“in“sections“260“and“589.Ž¦·h›ª¨«De ne‘UUÂPlaneŽ‘#Œ «functions‘@­620,–ÕX622,“624,“626,“629,“631,“634,“636,“641,“644,“646,“922˜·i‘ -­Used“in“sections“650“and“936.Ž¦·h›ª¨«De ne‘UUÂP•®9oin“tŽ‘"Dò«constructors‘@­280,–ÕX283,“287˜·i‘ -­Used“in“section“589.Ž¦·h‘ª¨«De ne‘dÂP•®9oin“tŽ‘"cF«functions‘@­285,–åt289,“292,“294,“296,“298,“300,“303,“305,“313,“315,“318,“320,“323,“325,“328,“330,“333,“335,“338,Ž¡‘340,–ð343,“346,“347,“350,“351,“353,“355,“361,“363,“365,“369,“371,“376,“378,“393,“399,“400,“401,“403,“405,“407,“411,“413,“415,Ž¡‘417,–ð432,“434,“439,“441,“443,“446,“448,“450,“452,“458,“462,“464,“467,“469,“475,“478,“480,“482,“484,“486,“489,“493,“495,“497,Ž¡‘499,–ð501,“503,“505,“508,“510,“512,“517,“518,“519,“520,“521,“522,“524,“526,“530,“531,“532,“533,“534,“535,“536,“537,“538,“539,Ž¡‘540,–è²541,“601,“603,“637,“717,“780,“781,“789,“790,“798,“799,“817,“818,“901,“904,“905,“906‘ª¨·i‘ -­Used–äÓin“sections“589,–è²613,“650,Ž¡‘and‘ÕX936.Ž¦·h‘ª¨«De ne‘¬fÂP®9olygonŽ‘0]º«functions‘@­979,–1Û981,“985,“986,“987,“988,“989,“990,“991,“992,“994,“996,“997,“998,“999,“1002,“1004,“1007,Ž¡‘1009,–ÕX1011,“1013,“1016,“1018,“1021,“1023‘ª¨·i‘ -­Used“in“section“1055.Ž¦·h–ª¨«De ne‘UUÂP®9olyhedronŽ‘@¸w«functions‘@­1433“·i‘ -­Used–ÕXin“section“1493.Ž¦·h‘ª¨«De ne‘¾ÂRectangleŽ‘9C«functions‘@­1062,–‡1065,“1067,“1070,“1072,“1075,“1077,“1080,“1083,“1086,“1088,“1091,“1093,“1228,“1229,Ž¡‘1230,–ÕX1231‘ª¨·i‘ -­Used“in“sections“1099“and“1232.ŽŽŽŒ‹˜) Šn ý‘ì«512‘­NAMES–ÕXOF“THE“SECTIONS’´*3DLDFPRÃŽGŽ €n ý•@P·h›ª¨«De ne‘^hÂRegu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘o´h«functions‘@­949,–Þü951,“954,“955,“956,“957,“958,“959,“960,“961,“962,“963,“965,“968˜·i‘ -­UsedŽ¤ ‘in–ÕXsection“971.Ž© &e·h›ª¨«De ne‘¢vÂRegu½‰™šs4Ž‘ÔwP®9olygonŽ‘Hà«functions‘@­1027,–'K1030,“1033,“1034,“1036,“1037,“1040,“1042,“1270,“1272,“1273,“1274,“1276,“1277˜·iŽ¡‘­Used–ÕXin“sections“1055“and“1278.Ž¦·h–ª¨«De ne‘UUÂShapQÇeŽ‘%–·«class‘@­199,›ÕX200“·i‘ -­Used˜in˜sections˜203˜and˜204.Ž¦·h–ª¨«De ne‘UUÂSolidu½‰™šs4Ž‘ÔwF‘ÿ -«acedŽ‘A {«functions‘@­1407“·i‘ -­Used–ÕXin“section“1409.Ž¦·h‘ª¨«De ne‘”9ÂSolidŽ‘ ¦I«functions‘@­1300,–*1302,“1304,“1306,“1308,“1310,“1314,“1317,“1319,“1321,“1323,“1325,“1327,“1330,“1332,“1334,Ž¡‘1336,–‹1338,“1340,“1342,“1344,“1347,“1349,“1351,“1353,“1356,“1358,“1360,“1362,“1365,“1367,“1370,“1372,“1374,“1376,“1378,Ž¡‘1380,–ÕX1384,“1387,“1390,“1393,“1396,“1399‘ª¨·i‘ -­Used“in“section“1401.Ž¦·h›ª¨«De ne‘UUÂT‘ÿ -«etrahedronŽ‘EF®«functions‘@­1440,–ÕX1443,“1444,“1445,“1447,“1449,“1451˜·i‘ -­Used“in“section“1493.Ž¦·h‘ª¨«De ne‘¶ÂT‘ÿ -«ransformŽ‘;߉«functions‘@­125,–<127,“129,“131,“133,“135,“137,“141,“143,“146,“148,“151,“153,“156,“159,“161,“162,“163,Ž¡‘164,–Å&172,“174,“177,“179,“182,“183,“184,“185,“186,“188,“372,“380,“381,“382,“383,“384,“385,“386,“387,“388,“395,“716‘ª¨·i‘ -­Used‘ÁinŽ¡‘sections–ÕX194,“589,“and“936.Ž¦·h›ª¨«De ne‘UUÂT‘ÿ -«runcu½‰™šs4Ž‘ÔwOctahedronŽ‘dyT«functions‘@­1485,–ÕX1488,“1490,“1491˜·i‘ -­Used“in“section“1493.Ž¦·h–ª¨«De ne‘UUÂb•QÇo“olu½‰™šs4Ž›Ôwp“oin®9tu½‰™šs4Ž˜quadrupleŽ‘s<«functions‘@­271“·i‘ -­Used–ÕXin“section“589.Ž¦·h–ª¨«De ne‘UUÂb•QÇo“olu½‰™šs4Ž‘Ôwp“oin®9tŽ‘;üð«functions‘@­269“·i‘ -­Cited–ÕXin“section“268.‘qÈUsed“in“section“589.Ž¦·h–ª¨«De ne‘UUÂb•QÇo“olu½‰™šs4Ž–Ôwrealu½‰™šs4Ž“pQÇoin®9tŽ‘Sœ «functions‘@­273“·i‘ -­Used–ÕXin“section“589.Ž¦·h–ª¨«De ne‘UUÂclassŽ‘5¦CircleŽ‘@ØÖ­1237“·i‘ -­Used–ÕXin“sections“1278“and“1279.Ž¦·h–ª¨«De ne‘UUÂclassŽ‘5¦ColorŽ‘>ÅH­56“·i‘ -­Used–ÕXin“sections“118“and“119.Ž¦·h–ª¨«De ne‘UUÂclassŽ‘5¦CubQÇoidŽ‘GÅD­1413“·i‘ -­Used–ÕXin“sections“1427“and“1428.Ž¦·h–ª¨«De ne‘UUÂclassŽ‘5¦DoQÇdecahedronŽ‘k58­1453“·i‘ -­Used–ÕXin“sections“1493“and“1494.Ž¦·h–ª¨«De ne‘UUÂclassŽ‘5¦EllipseŽ‘D^ƒ­1103“·i‘ -­Used–ÕXin“sections“1232“and“1233.Ž¦·h–ª¨«De ne‘UUÂclassŽ‘5¦F‘ÿ -«oQÇcusŽ‘?jö­556“·i‘ -­Used–ÕXin“sections“589“and“590.Ž¦·h–ª¨«De ne‘UUÂclassŽ‘5¦IcosahedronŽ‘_Ny­1467“·i‘ -­Used–ÕXin“sections“1493“and“1494.Ž¦·h–ª¨«De ne‘UUÂclassŽ‘5¦P®9athŽ‘;­654“·i‘ -­Used–ÕXin“sections“936“and“937.Ž¦·h–ª¨«De ne‘UUÂclassŽ‘5¦P•®9oin“tŽ‘>ò­264“·i‘ -­Used–ÕXin“sections“589“and“590.Ž¦·h–ª¨«De ne‘UUÂclassŽ‘5¦P®9olygonŽ‘Kz˜­975“·i‘ -­Used–ÕXin“sections“1055“and“1056.Ž¦·h–ª¨«De ne‘UUÂclassŽ‘5¦P®9olyhedronŽ‘\ƒw­1431“·i‘ -­Used–ÕXin“sections“1493“and“1494.Ž¦·h–ª¨«De ne‘UUÂclassŽ‘5¦RectangleŽ‘Tµ?­1059“·i‘ -­Used–ÕXin“sections“1099“and“1100.Ž¦·h–ª¨«De ne‘UUÂclassŽ‘5¦Regu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ’‹mB­941“·i‘ -­Used–ÕXin“sections“971“and“972.Ž¦·h–ª¨«De ne‘UUÂclassŽ‘5¦Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘cô^­1025“·i‘ -­Used–ÕXin“sections“1055“and“1056.Ž¦·h–ª¨«De ne‘UUÂclassŽ‘5¦Solidu½‰™šs4Ž‘ÔwF‘ÿ -«acedŽ‘]k{­1405“·i‘ -­Used–ÕXin“sections“1409“and“1410.Ž¦·h–ª¨«De ne‘UUÂclassŽ‘5¦SolidŽ‘;ó­1296“·i‘ -­Used–ÕXin“sections“1401“and“1402.Ž¦·h–ª¨«De ne‘UUÂclassŽ‘5¦T‘ÿ -«etrahedronŽ‘a®­1436“·i‘ -­Used–ÕXin“sections“1493“and“1494.Ž¦·h–ª¨«De ne‘UUÂclassŽ‘5¦T‘ÿ -«ransformŽ‘Vé'­122“·i‘ -­Used–ÕXin“sections“194“and“195.Ž¦·h–ª¨«De ne‘UUÂclassŽ‘5¦T‘ÿ -«runcu½‰™šs4Ž‘ÔwOctahedronŽ’€DT­1481“·i‘ -­Used–ÕXin“sections“1493“and“1494.Ž¦·h›ª¨«De ne‘UUÏdr‘ÿ}'aw‘‰ffŽ‘®axesŽ‘/[+«(‘ª®)‘@­925,–ÕX926,“927,“928,“930˜·i‘ -­Used“in“section“936.Ž¦·h–ª¨«De ne‘UUÂstaticŽ‘"ž.P•®9oin“tŽ‘AË«data‘UUmem¸ãbGers‘@­265“·i‘ -­Used–ÕXin“section“589.Ž¦·h–ª¨«De ne‘UUÂstaticŽ‘"ž.constŽ‘@ÈÐDoQÇdecahedronŽ’ŒÝ³«data‘UUmem¸ãbGers‘@­1454“·i‘ -­Used–ÕXin“section“1493.Ž¦·h–ª¨«De ne‘UUÂstaticŽ‘"ž.constŽ‘@ÈÐIcosahedronŽ’€öô«data‘UUmem¸ãbGers‘@­1468“·i‘ -­Used–ÕXin“section“1493.Ž¦·h–ª¨«De ne‘UUÂstaticŽ‘"ž.constŽ‘@ÈÐSolidŽ‘]›ü«data‘UUmem¸ãbGers‘@­1297“·i‘ -­Used–ÕXin“section“1401.Ž¦·h–ª¨«De ne‘UUÂstaticŽ‘"ž.constŽ‘@ÈÐT‘ÿ -«etrahedronŽ’‚º)«data‘UUmem¸ãbGers‘@­1437“·i‘ -­Used–ÕXin“section“1493.Ž¦·h–ª¨«De ne‘UUÂstaticŽ‘"ž.constŽ‘@ÈÐT‘ÿ -«runcu½‰™šs4Ž‘ÔwOctahedronŽ’¡ìÏ«data‘UUmem¸ãbGers‘@­1482“·i‘ -­Used–ÕXin“section“1493.Ž¦·h–ª¨«De ne‘UUÂstaticŽ‘"ž.EllipseŽ‘GÜ\«data‘UUmem¸ãbGers‘@­1104“·i‘ -­Used–ÕXin“section“1232.Ž¦·h–ª¨«De ne‘UUÂstaticŽ‘"ž.ShapQÇeŽ‘Dß«mem¸ãbGer‘UUv‘ÿqÇariables‘@­201“·i‘ -­Used–ÕXin“section“203.Ž¦·h–ª¨«De ne‘UUÂstaticŽ‘"ž.classŽ‘=~P®9athŽ‘Ye8«data‘UUmem¸ãbGers‘@­655“·i‘ -­Used–ÕXin“section“936.Ž¦·h–ª¨«De ne‘UUÂstructŽ‘$õLLineŽ‘?Ó­593“·i‘ -­Used–ÕXin“sections“613“and“614.Ž¦·h–ª¨«De ne‘UUÂstructŽ‘$õLPlaneŽ‘F³­617“·i‘ -­Used–ÕXin“sections“650“and“651.Ž¦·h–ª¨«Discard‘UUÏp‘ÿ}'ointsŽ‘!Ï?«and‘UUÏc–ÿ}'onne“ctorsŽ‘6ɇ­659“·i‘ -­Used–ÕXin“sections“657,“666,“671,“676,“and“687.Ž¦·h–ª¨«F‘ÿ*ªorw¸ãard‘UUdeclarations‘@­33“·i‘ -­Used–ÕXin“section“36.Ž¦·h‘ª¨«GCC–UU2.95“prinš¸ãt“v˜ersion,“cop˜yrigh˜t,“and“license“information‘@­1512‘ª¨·i‘ -­Used–ÕXin“section“1511.Ž¦·h‘ª¨«GCC–UU3.3“and“DEC“prinš¸ãt“v˜ersion,“cop˜yrigh˜t,“and“license“information‘@­1513‘ª¨·i‘ -­Used–ÕXin“section“1511.ŽŽŽŒ‹¯G Šn ý‘ì­3DLDFPRÃŽG’´*NAMES–ÕXOF“THE“SECTIONS‘«513Ž €n ý•@P·h›ª¨«GCC–UUcommand“line“option“proGcessing‘@­1508˜·i‘ -­Used–ÕXin“section“1507.Ž¤ $·h›ª¨«GNU–UUF‘ÿ*ªree“DoGcumen¸ãtation“License‘@­1523˜·i‘ -­Cited–ÕXin“section“1.Ž¡·h›ª¨«GNU–UUGeneral“Public“License‘@­1524˜·i‘ -­Cited–ÕXin“section“1.Ž¡·h–ª¨«Get‘UUinput‘@­1504“·iŽ¡h›ª¨«Global‘UUconstan¸ãts‘@­19,–ÕX25,“26,“115,“191,“274˜·i‘ -­Used“in“sections“35,“118,“194,“and“589.Ž¡·h›ª¨«Global‘UUv‘ÿqÇariables‘@­15,–ÕX16,“17,“39,“189,“257,“586˜·i‘ -­Cited“in“section“22.‘qÈUsed“in“sections“35,“52,“194,“260,“and“589.Ž¡·h‘ª¨«Handle–UUinš¸ãtersection“pGoin˜t‘@­1186‘ª¨·i‘ -­Used–ÕXin“section“1185.Ž¡·h‘ª¨«Include‘\ les‘@­11,–38,“55,“121,“197,“206,“263,“592,“616,“653,“939,“974,“1058,“1102,“1235,“1281,“1295,“1404,“1412,“1430,“1496,Ž¤ ‘1503‘ª¨·i‘ -­Used–%;in“sections“35,–9352,“118,“194,“203,“260,“589,“613,“650,“936,“971,“1055,“1099,“1232,“1278,“1292,“1401,“1409,Ž¡‘1427,–ÕX1493,“1500,“and“1520.Ž¤ $·h›ª¨«Initialize–UUcoGordinates“and“limits‘@­278˜·i‘ -­Used–ÕXin“sections“280,“283,“and“287.Ž¡·h–ª¨«Initialize‘UUÂstaticŽ‘"ž.LabQÇelŽ‘B4æ«data‘UUmem¸ãbGers‘@­209“·i‘ -­Used–ÕXin“section“260.Ž¡·h›ª¨«Main‘@­1514,–ÕX1515,“1516,“1517,“1518,“1519˜·i‘ -­Used“in“section“1520.Ž¡·h–ª¨«Ma‘Ž8jor‘UUÂColorsŽ‘(n3­112“·i‘ 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,‘=1267Ž‘=Ÿ™”‰feŽ“,‘=1268Ž‘=Ÿ™”‰feŽ“.Ž¡’ôऱx‘‰ffŽ‘®iŽ’ˬ:‘ +579Ž‘ +Ÿ™”‰feŽ‘,–BÐ580,“581,“583,“584,“585.Ž¡’ôऴX_YŽ’'¬:‘ +993Ž‘ +Ÿ™”‰feŽ‘,‘îG1221Ž‘îGŸ™”‰feŽ‘îK,‘îG1223.Ž¡’ôऴX_ZŽ’'¬:‘ +993Ž‘ +Ÿ™”‰feŽ‘,‘îG1221Ž‘îGŸ™”‰feŽ‘îK,‘îG1223.Ž¡’ôऱxxŽ’ÿÞܬ:‘ +1242Ž‘ +Ÿ™”‰feŽ‘,‘²œ1243Ž‘²œŸ™”‰feŽ–² ,‘²œ1390Ž‘²œŸ™”‰feŽ“,‘²œ1391Ž‘²œŸ™”‰feŽ“,‘²œ1395Ž‘²œŸ™”‰feŽ“,‘²œ1396Ž‘²œŸ™”‰feŽ“,‘²œ1399Ž‘²œŸ™”‰feŽ“,‘²œ1400Ž‘²œŸ™”‰feŽ“.Ž¡’ôऱxyŽ’ÿÄ‹¬:‘ +197Ž‘ +Ÿ™”‰feŽ‘,‘y198Ž‘yŸ™”‰feŽ–|,‘y245Ž‘yŸ™”‰feŽ“,‘y408Ž‘yŸ™”‰feŽ“,‘y409Ž‘yŸ™”‰feŽ“,‘y768Ž‘yŸ™”‰feŽ“,‘y769Ž‘yŸ™”‰feŽ“,‘y1056Ž‘yŸ™”‰feŽ–},‘y1057Ž‘yŸ™”‰feŽ“,Ž© ’à¦1239Ž’ট™”‰feŽ’àª,‘¢[1240Ž‘¢[Ÿ™”‰feŽ–¢_,‘¢[1392Ž‘¢[Ÿ™”‰feŽ“,‘¢[1393Ž‘¢[Ÿ™”‰feŽ“.Ž¡’ôऱxzŽ’ÿXv¬:‘ +197Ž‘ +Ÿ™”‰feŽ‘,‘”á198Ž‘”៙”‰feŽ–”ä,‘”á245Ž‘”៙”‰feŽ“,‘”á408Ž‘”៙”‰feŽ“,‘”á409Ž‘”៙”‰feŽ“,‘”á768Ž‘”៙”‰feŽ“,‘”á769Ž‘”៙”‰feŽ“,‘”á1056Ž‘”៙”‰feŽ–”å,‘”á1057Ž‘”៙”‰feŽ“,Ž¦’à¦1239Ž’ট™”‰feŽ’àª,‘¢[1240Ž‘¢[Ÿ™”‰feŽ–¢_,‘¢[1392Ž‘¢[Ÿ™”‰feŽ“,‘¢[1393Ž‘¢[Ÿ™”‰feŽ“.Ž¡’ôऱx0Ž’~¬:‘ +972Ž‘ +Ÿ™”‰feŽ‘.Ž¡’ôऱx1Ž’~¬:‘ +972Ž‘ +Ÿ™”‰feŽ‘.Ž¡’ôवyŽ’ú#œ¬:‘ +195Ž‘ +Ÿ™”‰feŽ‘,‘:—196Ž‘:—Ÿ™”‰feŽ–:š,‘:—200Ž‘:—Ÿ™”‰feŽ“,‘:—201Ž‘:—Ÿ™”‰feŽ“,‘:—203Ž‘:—Ÿ™”‰feŽ“,‘:—204Ž‘:—Ÿ™”‰feŽ“,‘:—205Ž‘:—Ÿ™”‰feŽ“,‘:—206Ž‘:—Ÿ™”‰feŽ“,‘:—280Ž‘:—Ÿ™”‰feŽ“,‘:—281Ž‘:—Ÿ™”‰feŽ“,Ž¦’à¦283Ž’ট™”‰feŽ’à©,‘Ò284Ž‘ÒŸ™”‰feŽ–Õ,‘Ò286Ž‘ÒŸ™”‰feŽ“,‘Ò287Ž‘ÒŸ™”‰feŽ“,‘Ò327Ž‘ÒŸ™”‰feŽ“,‘Ò328Ž‘ÒŸ™”‰feŽ“,‘Ò329Ž‘ÒŸ™”‰feŽ“,‘Ò330Ž‘ÒŸ™”‰feŽ“,‘Ò404Ž‘ÒŸ™”‰feŽ“,‘Ò405Ž‘ÒŸ™”‰feŽ“,Ž¦’à¦406Ž’ট™”‰feŽ’à©,‘>l407Ž‘>lŸ™”‰feŽ–>o,‘>l412Ž‘>lŸ™”‰feŽ“,‘>l413Ž‘>lŸ™”‰feŽ“,‘>l419Ž‘>lŸ™”‰feŽ“,‘>l420Ž‘>lŸ™”‰feŽ“,‘>l688Ž‘>lŸ™”‰feŽ“,‘>l756Ž‘>lŸ™”‰feŽ“,‘>l757Ž‘>lŸ™”‰feŽ“,Ž¦’à¦766Ž’ট™”‰feŽ’à©,‘~l767Ž‘~lŸ™”‰feŽ–~o,‘~l771Ž‘~lŸ™”‰feŽ“,‘~l772Ž‘~lŸ™”‰feŽ“,‘~l776Ž‘~lŸ™”‰feŽ“,‘~l777Ž‘~lŸ™”‰feŽ“,‘~l1047Ž‘~lŸ™”‰feŽ–~p,‘~l1048Ž‘~lŸ™”‰feŽ“,‘~l1054Ž‘~lŸ™”‰feŽ“,Ž¦’à¦1055Ž’ট™”‰feŽ’àª,‘<„1059Ž‘<„Ÿ™”‰feŽ–<ˆ,‘<„1060Ž‘<„Ÿ™”‰feŽ“,‘<„1064Ž‘<„Ÿ™”‰feŽ“,‘<„1065Ž‘<„Ÿ™”‰feŽ“,‘<„1222Ž‘<„Ÿ™”‰feŽ“,‘<„1235Ž‘<„Ÿ™”‰feŽ“,‘<„1236Ž‘<„Ÿ™”‰feŽ“,Ž¦’à¦1237Ž’ট™”‰feŽ’àª,‘ö¶1238Ž‘ö¶Ÿ™”‰feŽ–öº,‘ö¶1247Ž‘ö¶Ÿ™”‰feŽ“,‘ö¶1248Ž‘ö¶Ÿ™”‰feŽ“,‘ö¶1459Ž‘ö¶Ÿ™”‰feŽ“,‘ö¶1460Ž‘ö¶Ÿ™”‰feŽ“.Ž¡’ôऱy‘‰ffŽ‘®iŽ’~¬:‘ +579Ž‘ +Ÿ™”‰feŽ‘,–‡û580,“581,“583,“585.Ž¡’ôऱy‘‰ffŽ–®int‘‰ffŽ“pŽ’[‚¬:‘ +579Ž‘ +Ÿ™”‰feŽ‘,–àœ580,“581.Ž¡’ôऱy‘‰ffŽ–®int‘‰ffŽ“p‘‰ffŽ“zŽ’¹h¬:‘ +580Ž‘ +Ÿ™”‰feŽ‘.Ž¡’ôऱy‘‰ffŽ–®int‘‰ffŽ“qŽ’Ž¬:‘ +579Ž‘ +Ÿ™”‰feŽ‘,–ás580,“581.Ž¡’ôऱy‘‰ffŽ–®int‘‰ffŽ“q‘‰ffŽ“zŽ’6¬:‘ +580Ž‘ +Ÿ™”‰feŽ‘.Ž¡’ôऱy‘‰ffŽ‘®shiftŽ’‡7¬:‘ +1515Ž‘ +Ÿ™”‰feŽ‘.Ž¡’ôऱyel‘‚ØlowŽ’LU¬:‘ +152,‘Žw156Ž‘ŽwŸ™”‰feŽ–Žz,‘Žw157Ž‘ŽwŸ™”‰feŽ“,‘Žw1546.Ž¡’ôऱyel‘‚Ølow‘‰ffŽ‘®gr–ÿ}'e“enŽ’+I¬:‘ +152,‘;156Ž‘;Ÿ™”‰feŽ–;,‘;157Ž‘;Ÿ™”‰feŽ“,‘;1546.Ž¡’ôऱyxŽ’R¬:‘ +197Ž‘ +Ÿ™”‰feŽ‘,‘‹b198Ž‘‹bŸ™”‰feŽ–‹e,‘‹b245Ž‘‹bŸ™”‰feŽ“,‘‹b408Ž‘‹bŸ™”‰feŽ“,‘‹b409Ž‘‹bŸ™”‰feŽ“,‘‹b768Ž‘‹bŸ™”‰feŽ“,‘‹b769Ž‘‹bŸ™”‰feŽ“,‘‹b1056Ž‘‹bŸ™”‰feŽ–‹f,‘‹b1057Ž‘‹bŸ™”‰feŽ“,Ž¦’à¦1239Ž’ট™”‰feŽ’àª,‘¢[1240Ž‘¢[Ÿ™”‰feŽ–¢_,‘¢[1392Ž‘¢[Ÿ™”‰feŽ“,‘¢[1393Ž‘¢[Ÿ™”‰feŽ“.Ž¡’ôऱyyŽ’ÿü¬:‘ +1242Ž‘ +Ÿ™”‰feŽ‘,‘®r1243Ž‘®rŸ™”‰feŽ–®v,‘®r1390Ž‘®rŸ™”‰feŽ“,‘®r1391Ž‘®rŸ™”‰feŽ“,‘®r1395Ž‘®rŸ™”‰feŽ“,‘®r1396Ž‘®rŸ™”‰feŽ“,‘®r1399Ž‘®rŸ™”‰feŽ“,‘®r1400Ž‘®rŸ™”‰feŽ“.Ž¡’ôऱyzŽ’ÿì¬:‘ +197Ž‘ +Ÿ™”‰feŽ‘,‘’198Ž‘’Ÿ™”‰feŽ–’,‘’245Ž‘’Ÿ™”‰feŽ“,‘’408Ž‘’Ÿ™”‰feŽ“,‘’409Ž‘’Ÿ™”‰feŽ“,‘’768Ž‘’Ÿ™”‰feŽ“,‘’769Ž‘’Ÿ™”‰feŽ“,‘’1056Ž‘’Ÿ™”‰feŽ–’,‘’1057Ž‘’Ÿ™”‰feŽ“,Ž¦’à¦1239Ž’ট™”‰feŽ’àª,‘¢[1240Ž‘¢[Ÿ™”‰feŽ–¢_,‘¢[1392Ž‘¢[Ÿ™”‰feŽ“,‘¢[1393Ž‘¢[Ÿ™”‰feŽ“.ŽŽŽŽŽŒ‹!+À Šn ý‘ì¬514–¯INDEX’9?c3DLDF-1.1.5.1“°x¬1563Ž €n ý•@P±y0Ž‘ ÕS¬:‘ +972Ž‘ +Ÿ™”‰feŽ‘.Ž¤ ±y1Ž‘ ÕS¬:‘ +972Ž‘ +Ÿ™”‰feŽ‘.Ž¡µzŽ‘¬:‘ +195Ž‘ +Ÿ™”‰feŽ‘,‘?v196Ž‘?vŸ™”‰feŽ–?y,‘?v200Ž‘?vŸ™”‰feŽ“,‘?v201Ž‘?vŸ™”‰feŽ“,‘?v203Ž‘?vŸ™”‰feŽ“,‘?v204Ž‘?vŸ™”‰feŽ“,‘?v205Ž‘?vŸ™”‰feŽ“,‘?v206Ž‘?vŸ™”‰feŽ“,‘?v280Ž‘?vŸ™”‰feŽ“,‘?v281Ž‘?vŸ™”‰feŽ“,Ž¡‘283Ž‘Ÿ™”‰feŽ‘#,‘Ò284Ž‘ÒŸ™”‰feŽ–Õ,‘Ò286Ž‘ÒŸ™”‰feŽ“,‘Ò287Ž‘ÒŸ™”‰feŽ“,‘Ò327Ž‘ÒŸ™”‰feŽ“,‘Ò328Ž‘ÒŸ™”‰feŽ“,‘Ò329Ž‘ÒŸ™”‰feŽ“,‘Ò330Ž‘ÒŸ™”‰feŽ“,‘Ò404Ž‘ÒŸ™”‰feŽ“,‘Ò405Ž‘ÒŸ™”‰feŽ“,Ž¡‘406Ž‘Ÿ™”‰feŽ‘#,‘>l407Ž‘>lŸ™”‰feŽ–>o,‘>l412Ž‘>lŸ™”‰feŽ“,‘>l413Ž‘>lŸ™”‰feŽ“,‘>l419Ž‘>lŸ™”‰feŽ“,‘>l420Ž‘>lŸ™”‰feŽ“,‘>l688Ž‘>lŸ™”‰feŽ“,‘>l756Ž‘>lŸ™”‰feŽ“,‘>l757Ž‘>lŸ™”‰feŽ“,Ž¡‘766Ž‘Ÿ™”‰feŽ‘#,‘~l767Ž‘~lŸ™”‰feŽ–~o,‘~l771Ž‘~lŸ™”‰feŽ“,‘~l772Ž‘~lŸ™”‰feŽ“,‘~l776Ž‘~lŸ™”‰feŽ“,‘~l777Ž‘~lŸ™”‰feŽ“,‘~l1047Ž‘~lŸ™”‰feŽ–~p,‘~l1048Ž‘~lŸ™”‰feŽ“,‘~l1054Ž‘~lŸ™”‰feŽ“,Ž¡‘1055Ž‘Ÿ™”‰feŽ‘(,‘<„1059Ž‘<„Ÿ™”‰feŽ–<ˆ,‘<„1060Ž‘<„Ÿ™”‰feŽ“,‘<„1064Ž‘<„Ÿ™”‰feŽ“,‘<„1065Ž‘<„Ÿ™”‰feŽ“,‘<„1165Ž‘<„Ÿ™”‰feŽ“,‘<„1235Ž‘<„Ÿ™”‰feŽ“,‘<„1236Ž‘<„Ÿ™”‰feŽ“,Ž¡‘1237Ž‘Ÿ™”‰feŽ‘(,‘ö¶1238Ž‘ö¶Ÿ™”‰feŽ–öº,‘ö¶1247Ž‘ö¶Ÿ™”‰feŽ“,‘ö¶1248Ž‘ö¶Ÿ™”‰feŽ“,‘ö¶1459Ž‘ö¶Ÿ™”‰feŽ“,‘ö¶1460Ž‘ö¶Ÿ™”‰feŽ“.Ž¡±z‘‰ffŽ‘®axisŽ‘›¬:‘ +993Ž‘ +Ÿ™”‰feŽ‘.Ž¡±z‘‰ffŽ–®axis‘‰ffŽ“ptŽ‘&?P¬:‘ +1001Ž‘ +Ÿ™”‰feŽ‘.Ž¡±z‘‰ffŽ‘®iŽ‘ ]—¬:‘ +579Ž‘ +Ÿ™”‰feŽ‘,–Ši580,“582,“584,“585.Ž¡±z‘‰ffŽ–®int‘‰ffŽ“pŽ‘¶›¬:‘ +582Ž‘ +Ÿ™”‰feŽ‘,–ã583,“584.Ž¡±z‘‰ffŽ–®int‘‰ffŽ“qŽ‘t§¬:‘ +582Ž‘ +Ÿ™”‰feŽ‘,–ãñ583,“584.Ž¡´Z_YŽ‘F_¬:‘ +993Ž‘ +Ÿ™”‰feŽ‘,‘îG1221Ž‘îGŸ™”‰feŽ‘îK,‘îG1223.Ž¡±zxŽ‘ +qk¬:‘ +197Ž‘ +Ÿ™”‰feŽ‘,‘•2198Ž‘•2Ÿ™”‰feŽ–•5,‘•2245Ž‘•2Ÿ™”‰feŽ“,‘•2408Ž‘•2Ÿ™”‰feŽ“,‘•2409Ž‘•2Ÿ™”‰feŽ“,‘•2768Ž‘•2Ÿ™”‰feŽ“,‘•2769Ž‘•2Ÿ™”‰feŽ“,‘•21056Ž‘•2Ÿ™”‰feŽ–•6,‘•21057Ž‘•2Ÿ™”‰feŽ“,Ž¡‘1239Ž‘Ÿ™”‰feŽ‘(,‘¢[1240Ž‘¢[Ÿ™”‰feŽ–¢_,‘¢[1392Ž‘¢[Ÿ™”‰feŽ“,‘¢[1393Ž‘¢[Ÿ™”‰feŽ“.Ž¡±zyŽ‘ +W¬:‘ +197Ž‘ +Ÿ™”‰feŽ‘,‘–ƒ198Ž‘–ƒŸ™”‰feŽ––†,‘–ƒ245Ž‘–ƒŸ™”‰feŽ“,‘–ƒ408Ž‘–ƒŸ™”‰feŽ“,‘–ƒ409Ž‘–ƒŸ™”‰feŽ“,‘–ƒ768Ž‘–ƒŸ™”‰feŽ“,‘–ƒ769Ž‘–ƒŸ™”‰feŽ“,‘–ƒ1056Ž‘–ƒŸ™”‰feŽ––‡,‘–ƒ1057Ž‘–ƒŸ™”‰feŽ“,Ž¡‘1239Ž‘Ÿ™”‰feŽ‘(,‘¢[1240Ž‘¢[Ÿ™”‰feŽ–¢_,‘¢[1392Ž‘¢[Ÿ™”‰feŽ“,‘¢[1393Ž‘¢[Ÿ™”‰feŽ“.Ž¡±zzŽ‘ ë¬:‘ +1242Ž‘ +Ÿ™”‰feŽ‘,‘Ùí1243Ž‘Ùퟙ”‰feŽ–Ùñ,‘Ùí1390Ž‘Ùퟙ”‰feŽ“,‘Ùí1391Ž‘Ùퟙ”‰feŽ“,‘Ùí1395Ž‘Ùퟙ”‰feŽ“,‘Ùí1396Ž‘Ùퟙ”‰feŽ“,‘Ùí1399Ž‘Ùퟙ”‰feŽ“,‘Ùí1400Ž‘Ùퟙ”‰feŽ“.Ž¡±z0Ž‘ ¬:‘ +972Ž‘ +Ÿ™”‰feŽ‘.Ž¡±z1Ž‘ ¬:‘ +972Ž‘ +Ÿ™”‰feŽ‘.ŽŽŽŽŽŒ‹![¼ Šn ý‘ì¯3DLDF-1.1.5.1’ @”NAMES–ÕXOF“THE“SECTIONS‘¬515Ž €n ý•@P°h›ª¨¬Actions–UUin“main‘@¯1546,–ÕX1547˜°i‘ +¯Used“in“section“1557.Ž¤ .²°h–ª¨¬All‘UU­ColorsŽ‘(n3¯0“°i‘ +¯Cited–ÕXin“sections“153“and“158.Ž¡°h›ª¨¬Calculate–UUsecond-largest“±R–ÿ}'e“alŽ‘ª§¯69˜°i‘ +¯Used–ÕXin“section“68.Ž¡°h‘ª¨¬Chec•¸ãk›UUin“tersection˜pGoin“t˜loGcations‘@¯1228‘ª¨°i‘ +¯Used–ÕXin“section“1227.Ž¡°h›ª¨¬DEC–UUcommand“line“option“proGcessing‘@¯1551˜°i‘ +¯Used–ÕXin“section“1548.Ž¡°h›ª¨¬Declarations–Ü¡for“the“header“ le‘@¯21,–e23,“26,“29,“235,“237,“303,“320,“631,“655,“692˜°i‘ +¯Cited–HYin“section“24.‘­Used“inŽ© ‘sections–ÕX52,“240,“306,“634,“658,“and“695.Ž¡°h›ª¨¬Declare–UUI/O“functions‘@¯81,–ÕX84,“86,“88˜°i‘ +¯Used“in“section“92.Ž¡°h›ª¨¬Declare–UUP¸ãattern“functions‘@¯1320,–ÕX1323,“1326˜°i‘ +¯Used“in“sections“1329“and“1330.Ž¡°h›ª¨¬Declare–UUnamespace“­Pro‘£ŽjectionsŽ‘Aa¹¯256˜°i‘ +¯Used–ÕXin“section“305.Ž¡°h›ª¨¬Declare–UUnamespace“­SortingŽ‘,ÿŸ¯258˜°i‘ +¯Used–ÕXin“section“305.Ž¡°h›ª¨¬Declare–UUnon-mem¸ãbGer“non-template“functions“for“­ColorŽ‘#ä÷¯147˜°i‘ +¯Used–ÕXin“section“163.Ž¡°h›ª¨¬Declare–UUnon-mem¸ãbGer“non-template“functions“for“­P•®9oin“tŽ‘#/¡¯480,–ÕX534˜°i‘ +¯Used“in“section“634.Ž¡°h›ª¨¬Declare–UUnon-mem¸ãbGer“template“functions“for“­CircleŽ‘%ø…¯1286,–ÕX1287˜°i‘ +¯Used“in“sections“1315“and“1316.Ž¡°h›ª¨¬Declare–UUnon-mem¸ãbGer“template“functions“for“­ColorŽ‘#ä÷¯112,–ÕX113˜°i‘ +¯Used“in“sections“162“and“163.Ž¡°h›ª¨¬Declare–UUnon-mem¸ãbGer“template“functions“for“­CubQÇoidŽ‘,äó¯1462,–ÕX1463˜°i‘ +¯Used“in“sections“1468“and“1469.Ž¡°h›ª¨¬Declare–UUnon-mem¸ãbGer“template“functions“for“­EllipseŽ‘)~2¯1154,–ÕX1155˜°i‘ +¯Used“in“sections“1271“and“1272.Ž¡°h›ª¨¬Declare–UUnon-mem¸ãbGer“template“functions“for“­P®9athŽ‘ &½¯724,–ÕX725˜°i‘ +¯Used“in“sections“980“and“981.Ž¡°h›ª¨¬Declare–UUnon-mem¸ãbGer“template“functions“for“­P•®9oin“tŽ‘#/¡¯336,–ÕX337˜°i‘ +¯Used“in“sections“633“and“634.Ž¡°h›ª¨¬Declare–UUnon-mem¸ãbGer“template“functions“for“­RectangleŽ‘9Ôî¯1116,–ÕX1117˜°i‘ +¯Used“in“sections“1139“and“1140.Ž¡°h›ª¨¬Declare–UUnon-mem¸ãbGer“template“functions“for“­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘I ¯1083,–ÕX1084˜°i‘ +¯Used“in“sections“1097“and“1098.Ž¡°h›ª¨¬Declare–UUnon-mem¸ãbGer“template“functions“for“­SolidŽ‘!0¯1341,–ÕX1342˜°i‘ +¯Used“in“sections“1441“and“1442.Ž¡°h›ª¨¬Declare–UUparser“functions‘@¯1538˜°i‘ +¯Used–ÕXin“section“1542.Ž¡°h›ª¨¬Declare–UUutilit¸ãy“functions‘@¯24,–ÕX31˜°i‘ +¯Cited“in“section“24.‘qÈUsed“in“section“52.Ž¡°h›ª¨¬Declare‘UU­CircleŽ‘% Ö¬functions‘@¯1278,–ÕX1281,“1283,“1290,“1292,“1295,“1297,“1298,“1300,“1302,“1304˜°i‘ +¯Used“in“section“1276.Ž¡°h‘ª¨¬Declare‘w†­ColorŽ‘#>ª¬functions‘@¯97,–ù¬99,“102,“104,“107,“109,“114,“116,“118,“121,“123,“125,“127,“129,“131,“133,“135,“138,“141,“142,Ž¦‘143,–ÕX144,“146,“149,“151‘ª¨°i‘ +¯Used“in“section“95.Ž¡°h›ª¨¬Declare‘UU­CubQÇoidŽ‘+úD¬functions‘@¯1455,–ÕX1457,“1459,“1464,“1466˜°i‘ +¯Used“in“section“1453.Ž¡°h›ª¨¬Declare‘UU­DoQÇdecahedronŽ‘Oj8¬functions‘@¯1497,–ÕX1500,“1503,“1505˜°i‘ +¯Used“in“section“1494.Ž¡°h‘ª¨¬Declare‘Ü•­EllipseŽ‘)¢¬functions‘@¯1146,–e 1149,“1151,“1157,“1160,“1162,“1164,“1166,“1167,“1169,“1171,“1174,“1177,“1179,“1182,Ž¦‘1184,–‹1186,“1188,“1192,“1194,“1197,“1199,“1201,“1203,“1205,“1208,“1210,“1214,“1231,“1233,“1235,“1237,“1239,“1242,“1244,Ž¦‘1247,–ÕX1249,“1252,“1254,“1257,“1259,“1261,“1263‘ª¨°i‘ +¯Used“in“section“1143.Ž¡°h›ª¨¬Declare‘Z­F‘ÿ +«oQÇcusŽ‘%.¬functions‘@¯602,–¨Î604,“606,“609,“611,“613,“615,“617,“620,“621,“622,“623,“624,“625,“627,“628˜°i‘ +¯Used‘~ƒinŽ¦‘section‘ÕX600.Ž¡°h›ª¨¬Declare‘UU­IcosahedronŽ‘Cƒy¬functions‘@¯1511,–ÕX1514,“1516,“1518˜°i‘ +¯Used“in“section“1508.Ž¡°h–ª¨¬Declare‘UU­LabQÇelŽ‘"ì ¬functions‘@¯255“°i‘ +¯Used–ÕXin“section“253.Ž¡°h–ª¨¬Declare‘UU­LineŽ‘-¬constructors‘@¯639,›ÕX641“°i‘ +¯Used˜in˜section˜637.Ž¡°h›ª¨¬Declare‘UU­LineŽ‘-¬functions‘@¯643,–ÕX646,“648,“652˜°i‘ +¯Used“in“section“637.Ž¡°h‘ª¨¬Declare‘VÆ­P®9athŽ‘>ð¬functions‘@¯700,–Öà704,“707,“709,“712,“714,“717,“719,“721,“726,“728,“730,“732,“735,“738,“740,“743,“745,“747,“749,Ž¦‘751,–ð756,“762,“764,“766,“768,“771,“773,“776,“778,“781,“783,“785,“790,“792,“794,“797,“799,“801,“805,“810,“812,“818,“820,“827,Ž¦‘829,–ð836,“838,“844,“846,“849,“851,“855,“857,“863,“866,“868,“872,“874,“877,“879,“882,“884,“888,“889,“891,“893,“895,“897,“899,Ž¦‘909,–JÃ911,“914,“916,“918,“920,“921,“922,“923,“925,“932,“934,“936,“938,“940,“946,“952,“955,“959,“961,“964,“976‘ª¨°i‘ +¯Used‘3GinŽ¦‘section‘ÕX698.Ž¡°h‘ª¨¬Declare‘y­PictureŽ‘,-¬functions‘@¯263,–û×265,“267,“269,“270,“272,“274,“275,“276,“280,“283,“285,“286,“288,“289,“291,“293,“295,“298,Ž¦‘299,–ÕX300,“301‘ª¨°i‘ +¯Used“in“section“261.Ž¡°h›ª¨¬Declare‘UU­PlaneŽ‘#Œ ¬functions‘@¯663,–ÕX665,“667,“669,“672,“674,“677,“679,“684,“686,“687,“689˜°i‘ +¯Used“in“section“661.Ž¡°h›ª¨¬Declare‘UU­P•®9oin“tŽ‘"Dò¬constructors‘@¯324,–ÕX327,“331˜°i‘ +¯Used“in“section“309.Ž¡°h‘ª¨¬Declare‘$Û­P•®9oin“tŽ‘!ãþ¬functions‘@¯329,–´b333,“338,“340,“342,“344,“346,“349,“350,“352,“355,“357,“360,“362,“365,“367,“370,“372,“375,“377,Ž¦‘380,–ð382,“384,“385,“387,“389,“393,“396,“398,“400,“401,“404,“406,“408,“412,“414,“419,“421,“436,“438,“442,“446,“448,“450,“454,Ž¦‘456,–ð458,“460,“463,“464,“466,“467,“469,“470,“472,“473,“475,“477,“482,“484,“486,“488,“489,“491,“493,“495,“501,“505,“507,“510,Ž¦‘512,–Vw518,“521,“523,“525,“527,“529,“532,“536,“538,“540,“542,“544,“546,“548,“551,“553,“555,“557,“560,“567,“569,“572,“573‘ª¨°iŽ¦‘¯Used–ÕXin“section“309.ŽŽŽŒ‹!iÓ Šn ý‘ì¬516‘¯NAMES–ÕXOF“THE“SECTIONS’ @”3DLDF-1.1.5.1Ž €n ý•@P°h›ª¨¬Declare‘‰Ô­P®9olygonŽ‘0–¬functions‘@¯1022,– 1024,“1028,“1037,“1039,“1045,“1047,“1050,“1052,“1054,“1056,“1059,“1061,“1064,“1066˜°iŽ© ‘¯Used–ÕXin“section“1019.Ž¤ 1]°h–ª¨¬Declare‘UU­P®9olyhedronŽ‘@¸w¬functions‘@¯1473“°i‘ +¯Used–ÕXin“section“1472.Ž¡°h›ª¨¬Declare‘­RectangleŽ‘8r“¬functions‘@¯1103,–¬¨1106,“1108,“1111,“1113,“1119,“1122,“1125,“1127,“1130,“1132,“1135,“1136,“1137,“1138˜°iŽ¦‘¯Used–ÕXin“section“1101.Ž¡°h›ª¨¬Declare‘€ü­Regu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘où¬functions‘@¯987,–º988,“989,“990,“991,“992,“994,“997,“1008,“1011,“1013,“1014˜°i‘ +¯Used‘úsinŽ¦‘section‘ÕX985.Ž¡°h›ª¨¬Declare‘{X­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘Jud¬functions‘@¯1070,– ¼1073,“1076,“1079,“1087,“1089,“1091,“1092,“1093,“1095,“1096˜°i‘ +¯Used‘ÏBinŽ¦‘section‘ÕX1069.Ž¡°h–ª¨¬Declare‘UU­Solidu½‰™šs4Ž‘ÔwF‘ÿ +«acedŽ‘A {¬functions‘@¯1446“°i‘ +¯Used–ÕXin“section“1445.Ž¡°h‘ª¨¬Declare‘m%­SolidŽ‘ X!¬functions‘@¯1336,–î¥1338,“1343,“1345,“1348,“1350,“1353,“1356,“1358,“1360,“1362,“1364,“1366,“1369,“1371,“1373,Ž¦‘1375,–‹1377,“1379,“1381,“1383,“1386,“1388,“1390,“1392,“1395,“1397,“1399,“1401,“1404,“1406,“1408,“1409,“1411,“1413,“1415,Ž¦‘1417,–ÕX1419,“1423,“1426,“1429,“1432,“1435,“1438‘ª¨°i‘ +¯Used“in“section“1333.Ž¡°h›ª¨¬Declare‘UU­SystemŽ‘+ô¬functions‘@¯36,–ÕX38,“40,“43,“45,“47,“66,“71,“72˜°i‘ +¯Used“in“sections“34,“52,“65,“and“75.Ž¡°h›ª¨¬Declare‘UU­T‘ÿ +«etrahedronŽ‘EF®¬functions‘@¯1480,–ÕX1483,“1487,“1489,“1491˜°i‘ +¯Used“in“section“1477.Ž¡°h‘ª¨¬Declare‘‘Q­T‘ÿ +«ransformŽ‘;–¬functions‘@¯168,–170,“172,“174,“176,“178,“180,“182,“185,“187,“190,“192,“195,“197,“200,“202,“203,“205,Ž¦‘211,–ÕX212,“213,“216,“218,“221,“223,“226,“232‘ª¨°i‘ +¯Used“in“section“166.Ž¡°h›ª¨¬Declare‘UU­T‘ÿ +«runcu½‰™šs4Ž‘ÔwOctahedronŽ‘dyT¬functions‘@¯1525,–ÕX1528,“1530˜°i‘ +¯Used“in“section“1522.Ž¡°h–ª¨¬Declare‘UU±cr–ÿ}'e“ate‘‰ffŽ‘®newŽ‘2å¬(‘ª®)‘@¯56,‘ÕX58“°iŽ¡h–ª¨¬Declare‘UU±dr‘ÿ}'aw‘‰ffŽ‘®axesŽ‘/[+¬(‘ª®)‘@¯968,›ÕX973“°i‘ +¯Used˜in˜section˜981.Ž¡°h–ª¨¬Declare‘UU­namespaceŽ‘<øÏColorsŽ‘b­¯153“°i‘ +¯Cited–ÕXin“section“153.‘qÈUsed“in“section“162.Ž¡°h–ª¨¬Declare‘UU­namespaceŽ‘<øÏSystemŽ‘f¯34,›ÕX65“°i‘ +¯Used˜in˜sections˜51,˜52,˜74,˜and˜75.Ž¡°h›ª¨¬De ne–UUI/O“functions‘@¯82,–ÕX83,“85,“87,“89˜°i‘ +¯Used“in“section“91.Ž¡°h›ª¨¬De ne–UUP¸ãattern“functions‘@¯1321,–ÕX1324,“1327˜°i‘ +¯Used“in“section“1329.Ž¡°h–ª¨¬De ne‘UUclasses‘@¯253,›ÕX261“°i‘ +¯Used˜in˜sections˜305˜and˜306.Ž¡°h›ª¨¬De ne–UUcomparison“classes‘@¯498,–ÕX499,“500˜°i‘ +¯Cited“in“section“596.‘qÈUsed“in“sections“633“and“634.Ž¡°h›ª¨¬De ne–UUnon-mem¸ãbGer“non-template“functions“for“­ColorŽ‘#ä÷¯148˜°i‘ +¯Used–ÕXin“section“162.Ž¡°h›ª¨¬De ne–UUnon-mem¸ãbGer“non-template“functions“for“­P•®9oin“tŽ‘#/¡¯481,–ÕX535˜°i‘ +¯Used“in“section“633.Ž¡°h›ª¨¬De ne–UUparser“functions‘@¯1539˜°i‘ +¯Used–ÕXin“section“1541.Ž¡°h›ª¨¬De ne–UUutilit¸ãy“functions‘@¯25,–ÕX32˜°i‘ +¯Cited“in“section“25.‘qÈUsed“in“section“51.Ž¡°h›ª¨¬De ne‘UU­CircleŽ‘% Ö¬functions‘@¯1279,–ÕX1282,“1284,“1291,“1293,“1296,“1301,“1303,“1305˜°i‘ +¯Used“in“section“1315.Ž¡°h‘ª¨¬De ne‘|à­ColorŽ‘#I^¬functions‘@¯98,–ÿ\100,“103,“105,“108,“110,“115,“117,“119,“122,“124,“126,“128,“130,“132,“134,“136,“139,“145,“150,Ž¦‘152‘ª¨°i‘ +¯Used–ÕXin“section“162.Ž¡°h›ª¨¬De ne‘UU­CubQÇoidŽ‘+úD¬functions‘@¯1456,–ÕX1458,“1460,“1465,“1467˜°i‘ +¯Used“in“section“1468.Ž¡°h›ª¨¬De ne‘UU­DoQÇdecahedronŽ‘Oj8¬functions‘@¯1498,–ÕX1501,“1502,“1504,“1506˜°i‘ +¯Used“in“section“1534.Ž¡°h‘ª¨¬De ne‘ö­EllipseŽ‘)òŬfunctions‘@¯1147,–ô1150,“1152,“1158,“1161,“1165,“1168,“1170,“1172,“1173,“1175,“1178,“1180,“1183,“1185,Ž¦‘1187,–‹1189,“1193,“1195,“1198,“1200,“1202,“1204,“1206,“1209,“1211,“1215,“1216,“1217,“1218,“1219,“1220,“1221,“1222,“1223,Ž¦‘1224,–3š1226,“1227,“1232,“1234,“1236,“1238,“1240,“1243,“1245,“1248,“1250,“1253,“1255,“1258,“1260,“1262,“1264‘ª¨°i‘ +¯Used‘ ÀinŽ¦‘section‘ÕX1271.Ž¡°h›ª¨¬De ne‘UU­F‘ÿ +«oQÇcusŽ‘#Ÿö¬functions‘@¯605,–ÕX607,“610,“612,“614,“616,“618,“626,“629˜°i‘ +¯Used“in“section“633.Ž¡°h›ª¨¬De ne‘UU­IcosahedronŽ‘Cƒy¬functions‘@¯1512,–ÕX1515,“1517,“1519˜°i‘ +¯Used“in“section“1534.Ž¡°h›ª¨¬De ne‘UU­LabQÇelŽ‘"ì ¬functions‘@¯514,–ÕX515,“516˜°i‘ +¯Used“in“section“633.Ž¡°h–ª¨¬De ne‘UU­LineŽ‘-¬constructors‘@¯640,›ÕX642“°i‘ +¯Used˜in˜section˜657.Ž¡°h›ª¨¬De ne‘UU­LineŽ‘-¬functions‘@¯644,–ÕX649,“650,“651,“653,“978˜°i‘ +¯Used“in“sections“657“and“980.Ž¡°h‘ª¨¬De ne‘yc­P®9athŽ‘„*¬functions‘@¯701,–û§705,“708,“710,“713,“715,“718,“720,“722,“727,“729,“731,“733,“736,“739,“741,“744,“746,“748,“750,Ž¦‘752,–ð757,“763,“765,“767,“769,“772,“774,“777,“779,“782,“784,“786,“791,“793,“795,“798,“800,“802,“806,“807,“808,“809,“811,“813,Ž¦‘814,–ð819,“821,“828,“830,“837,“839,“845,“847,“850,“852,“856,“858,“864,“867,“869,“873,“875,“878,“880,“883,“885,“886,“887,“890,Ž¦‘892,–ð894,“896,“898,“900,“901,“902,“903,“904,“905,“906,“910,“912,“915,“917,“919,“924,“926,“927,“928,“929,“930,“933,“935,“937,Ž¦‘941,–ÕX942,“943,“944,“947,“953,“956,“957,“958,“960,“962,“965,“977‘ª¨°i‘ +¯Used“in“section“980.Ž¡°h‘ª¨¬De ne‘1­PictureŽ‘,Öo¬functions‘@¯264,–!²271,“273,“277,“281,“284,“287,“290,“292,“294,“296,“417,“440,“587,“588,“589,“590,“592,“593,Ž¦‘594,–ÕX595,“596,“597,“598‘ª¨°i‘ +¯Used“in“sections“305“and“633.Ž¡°h›ª¨¬De ne‘UU­PlaneŽ‘#Œ ¬functions‘@¯664,–ÕX666,“668,“670,“673,“675,“678,“680,“685,“688,“690,“966˜°i‘ +¯Used“in“sections“694“and“980.ŽŽŽŒ‹!€l Šn ý‘ì¯3DLDF-1.1.5.1’ @”NAMES–ÕXOF“THE“SECTIONS‘¬517Ž €n ý•@P°h›ª¨¬De ne‘UU­P•®9oin“tŽ‘"Dò¬constructors‘@¯325,–ÕX328,“332˜°i‘ +¯Used“in“section“633.Ž© -w°h‘ª¨¬De ne‘d­P•®9oin“tŽ‘"cF¬functions‘@¯330,–åt334,“339,“341,“343,“345,“347,“351,“356,“358,“361,“363,“366,“368,“371,“373,“376,“378,“381,“383,Ž¤ ‘386,–ð388,“390,“391,“394,“395,“397,“399,“405,“407,“409,“413,“415,“420,“422,“437,“443,“444,“445,“447,“449,“451,“455,“457,“459,Ž¡‘461,–ð476,“478,“483,“485,“487,“490,“492,“494,“496,“502,“506,“508,“511,“513,“519,“522,“524,“526,“528,“530,“533,“537,“539,“541,Ž¡‘543,–ð545,“547,“549,“552,“554,“556,“561,“562,“563,“564,“565,“566,“568,“570,“574,“575,“576,“577,“578,“579,“580,“581,“582,“583,Ž¡‘584,–è²585,“645,“647,“681,“760,“823,“824,“832,“833,“841,“842,“860,“861,“945,“948,“949,“950‘ª¨°i‘ +¯Used–äÓin“sections“633,–è²657,“694,Ž¡‘and‘ÕX980.Ž¦°h‘ª¨¬De ne‘ËÝ­P®9olygonŽ‘0œ¨¬functions‘@¯1023,–SI1025,“1029,“1030,“1031,“1032,“1033,“1034,“1035,“1036,“1038,“1040,“1041,“1042,“1043,Ž¡‘1046,–ÕX1048,“1051,“1053,“1055,“1057,“1060,“1062,“1065,“1067‘ª¨°i‘ +¯Used“in“section“1097.Ž¦°h–ª¨¬De ne‘UU­P®9olyhedronŽ‘@¸w¬functions‘@¯1474“°i‘ +¯Used–ÕXin“section“1534.Ž¦°h›ª¨¬De ne‘h­RectangleŽ‘9Á¬functions‘@¯1104,–éE1107,“1109,“1112,“1114,“1120,“1123,“1126,“1128,“1131,“1133,“1267,“1268,“1269,“1270˜°iŽ¡‘¯Used–ÕXin“sections“1139“and“1271.Ž¦°h‘ª¨¬De ne‘¾Q­Regu½‰™šs4Ž–ÔwClu½‰™šs4Ž“Planeu½‰™šs4Ž“Curv®9eŽ‘pt:¬functions‘@¯993,–Dä995,“998,“999,“1000,“1001,“1002,“1003,“1004,“1005,“1006,“1007,“1009,Ž¡‘1012‘ª¨°i‘ +¯Used–ÕXin“section“1015.Ž¦°h›ª¨¬De ne‘Ûü­Regu½‰™šs4Ž‘ÔwP®9olygonŽ‘I6¬¬functions‘@¯1071,–dj1074,“1077,“1078,“1080,“1081,“1307,“1309,“1310,“1311,“1313,“1314˜°i‘ +¯Used‘GÍinŽ¡‘sections–ÕX1097“and“1315.Ž¦°h–ª¨¬De ne‘UU­ShapQÇeŽ‘%–·¬class‘@¯244,›ÕX245“°i‘ +¯Used˜in˜sections˜248˜and˜249.Ž¦°h–ª¨¬De ne‘UU­Solidu½‰™šs4Ž‘ÔwF‘ÿ +«acedŽ‘A {¬functions‘@¯1447“°i‘ +¯Used–ÕXin“section“1449.Ž¦°h‘ª¨¬De ne‘”9­SolidŽ‘ ¦I¬functions‘@¯1337,–*1339,“1344,“1346,“1347,“1349,“1351,“1354,“1357,“1359,“1361,“1363,“1365,“1367,“1370,“1372,Ž¡‘1374,–‹1376,“1378,“1380,“1382,“1384,“1387,“1389,“1391,“1393,“1396,“1398,“1400,“1402,“1405,“1407,“1410,“1412,“1414,“1416,Ž¡‘1418,–ÕX1420,“1424,“1427,“1430,“1433,“1436,“1439‘ª¨°i‘ +¯Used“in“section“1441.Ž¦°h›ª¨¬De ne‘UU­SystemŽ‘+ô¬functions‘@¯37,–ÕX39,“41,“44,“46,“48,“67,“68˜°i‘ +¯Used“in“sections“51,“74,“and“75.Ž¦°h›ª¨¬De ne‘UU­T‘ÿ +«etrahedronŽ‘EF®¬functions‘@¯1481,–ÕX1484,“1485,“1486,“1488,“1490,“1492˜°i‘ +¯Used“in“section“1534.Ž¦°h‘ª¨¬De ne‘¶­T‘ÿ +«ransformŽ‘;߉¬functions‘@¯169,–<171,“173,“175,“177,“179,“181,“183,“186,“188,“191,“193,“196,“198,“201,“204,“206,“207,Ž¡‘208,–Vw209,“217,“219,“222,“224,“227,“228,“229,“230,“231,“233,“416,“424,“425,“426,“427,“428,“429,“430,“431,“432,“439,“759‘ª¨°iŽ¡‘¯Used–ÕXin“sections“239,“633,“and“980.Ž¦°h›ª¨¬De ne‘UU­T‘ÿ +«runcu½‰™šs4Ž‘ÔwOctahedronŽ‘dyT¬functions‘@¯1526,–ÕX1529,“1531,“1532˜°i‘ 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2003-12-10 15:47:05.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/3DLDFprg.mac 2004-01-12 22:26:01.000000000 +0100 @@ -1,7 +1,7 @@ %%%% 3DLDF.macs %%%% This file is part of 3DLDF, a package for three-dimensional drawing. -%%%% Copyright (C) 2003 Laurence D. Finston. +%%%% Copyright (C) 2003, 2004 Laurence D. 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All Rights Reserved. -11 dict begin -/FontInfo 7 dict dup begin -/version (1.0) readonly def -/Notice (Copyright (C) 1997 American Mathematical Society. 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w(,)g(1445,)e(1446)p 1678 2989 V -2 w(,)166 -3076 y(1447)p 166 3089 V -2 w(,)i(1459)p 382 3089 V -2 -w(,)g(1460)p 598 3089 V -2 w(,)g(1461,)e(1473)p 1030 -3089 V -2 w(,)i(1474)p 1246 3089 V -2 w(,)g(1487)p 1462 -3089 V -2 w(,)g(1488)p 1678 3089 V -2 w(.)0 3178 y Fi(ap)10 -b Fm(:)83 b(669)p 200 3191 125 4 v -1 w(,)40 b(671)p -388 3191 V -1 w(,)g(674)p 576 3191 V -2 w(,)h(676)p 764 -3191 V -2 w(.)0 3280 y Fi(app)l(end)14 b Fm(:)83 b(769)p -369 3293 V -1 w(,)43 b(770)p 560 3293 V -2 w(.)0 3382 -y Fi(apply)p 192 3382 26 4 v 32 w(tr)l(ansform)11 b Fm(:)83 -b(200)p 688 3395 125 4 v -1 w(,)24 b(305,)f(313,)g(318,)g(346,)g(350,)f -(374,)166 3481 y(379,)i(380,)f(381,)h(385,)f(389,)h(395,)g(397,)f(399,) -h(404)p 1547 3494 V -2 w(,)h(405)p 1719 3494 V -1 w(,)166 -3581 y(431,)f(436,)f(443,)h(451,)f(457,)h(463,)g(472,)f(476,)h(478,)f -(480,)166 3681 y(482,)34 b(484,)g(486,)g(489,)f(493,)h(495,)g(497,)g -(499,)g(501,)166 3780 y(503,)g(508,)g(529,)g(531,)f(549,)h(561,)g(572,) -g(596,)g(597,)166 3880 y(598,)g(624,)g(732,)g(740)p 715 -3893 V -2 w(,)h(741)p 897 3893 V -1 w(,)g(839,)f(888,)g(889,)g(891,)166 -3980 y(904,)f(979,)f(981,)h(1033,)f(1065,)g(1110,)g(1140,)g(1142,)166 -4079 y(1145,)f(1147,)g(1243,)g(1348)p 832 4092 167 4 -v -2 w(,)i(1349)p 1054 4092 V -2 w(,)g(1365.)0 4181 y -Fi(ar)l(c)p 116 4181 26 4 v 31 w(divisions)13 b Fm(:)83 -b(1286)p 573 4194 167 4 v -2 w(,)34 b(1287)p 796 4194 -V -2 w(,)f(1289)p 1018 4194 V -2 w(,)h(1290)p 1241 4194 -V -2 w(.)0 4283 y Fi(ar)l(g)12 b Fm(:)83 b(270)p 229 -4296 125 4 v -1 w(.)0 4385 y Fi(ar)l(g)p 116 4385 26 -4 v 31 w(ptr)13 b Fm(:)83 b(669)p 366 4398 125 4 v -1 -w(,)43 b(671)p 557 4398 V -2 w(.)0 4487 y Fi(ar)l(gc)10 -b Fm(:)83 b(1508,)41 b(1514)p 497 4500 167 4 v -2 w(.)0 -4589 y Fi(ar)l(gument)11 b Fm(:)83 b(556)p 454 4602 125 -4 v -1 w(.)0 4691 y Fi(ar)l(gv)14 b Fm(:)83 b(1508,)38 -b(1514)p 498 4704 167 4 v -2 w(,)i(1519.)0 4793 y Fi(arr)l(ow)14 -b Fm(:)83 b(654)p 325 4806 125 4 v -1 w(,)36 b(658,)f(661,)g(664,)g -(666,)g(669,)h(671,)f(674,)166 4893 y(676,)g(776,)f(856,)h(859,)f(861,) -h(863.)0 4994 y Fi(asctime)11 b Fm(:)83 b(43.)0 5096 -y Fi(asin)11 b Fm(:)83 b(1468.)0 5198 y Fi(assign)11 -b Fm(:)83 b(187)p 337 5211 V -1 w(,)36 b(188)p 521 5211 -V -2 w(,)g(506,)f(507)p 888 5211 V -2 w(,)h(508)p 1071 -5211 V -1 w(,)g(749)p 1255 5211 V -2 w(,)g(750)p 1438 -5211 V -2 w(,)g(769)p 1621 5211 V -1 w(,)166 5298 y(770)p -166 5311 V -1 w(,)k(771,)f(911)p 542 5311 V -1 w(,)h(912)p -730 5311 V -1 w(.)0 5400 y Fi(atan)11 b Fm(:)83 b(25,)40 -b(1268,)f(1454.)2033 263 y Fi(ax)14 b Fm(:)83 b(559,)28 -b(560)p 2411 276 V -2 w(,)i(561)p 2588 276 V -2 w(,)f(562)p -2764 276 V -1 w(,)g(563)p 2941 276 V -2 w(,)g(565)p 3117 -276 V -1 w(,)g(566)p 3294 276 V -1 w(,)g(567)p 3471 276 -V -2 w(,)g(568)p 3647 276 V -1 w(.)2033 365 y Fi(ax)p -2119 365 26 4 v 31 w(h)11 b Fm(:)83 b(1137)p 2304 378 -167 4 v -2 w(,)34 b(1168)p 2527 378 V -2 w(,)h(1177)p -2751 378 V -2 w(,)f(1179,)f(1183.)2033 466 y Fi(ax)p -2119 466 26 4 v 31 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w(,)h(1110)p 2983 1182 V -2 w(,)g(1193)p -3206 1182 V -2 w(.)2033 1270 y Fi(axis)p 2178 1270 26 -4 v 31 w(unknown)10 b Fm(:)83 b(1133)p 2641 1283 167 -4 v -2 w(,)39 b(1134)p 2869 1283 V -2 w(.)2033 1372 y -Fi(axis)p 2178 1372 26 4 v 31 w(v)13 b Fm(:)83 b(1059)p -2361 1385 167 4 v -2 w(,)31 b(1064,)d(1065,)h(1070,)f(1080,)h(1089,)f -(1093,)2199 1472 y(1103)p 2199 1485 V -2 w(,)f(1110,)e(1120,)g(1133,)g -(1136,)g(1152,)g(1157,)g(1163,)2199 1571 y(1167,)g(1177,)g(1178,)g -(1179,)g(1192,)g(1193,)g(1196,)g(1203,)2199 1671 y(1213,)37 -b(1243,)f(1255,)h(1256.)2033 1772 y Fi(axis)p 2178 1772 -26 4 v 31 w(v)p 2247 1772 V 31 w(half)23 b Fm(:)83 b(1064,)33 -b(1065)p 2756 1785 167 4 v -2 w(,)h(1110)p 2979 1785 -V -2 w(,)g(1193)p 3202 1785 V -2 w(.)2033 1874 y Ff(AXON)s -Fm(:)83 b(211)p 2318 1887 125 4 v -2 w(,)44 b(212)p 2509 -1887 V -1 w(.)2033 1975 y Fi(a0)16 b Fm(:)83 b(900)p -2239 1988 V -1 w(.)2033 2077 y Fi(a1)16 b Fm(:)83 b(900)p -2239 2090 V -1 w(.)2033 2178 y Fe(b)p Fm(:)g(13)p 2175 -2191 84 4 v -1 w(,)34 b(16)p 2315 2191 V -1 w(,)g(29)p -2455 2191 V -1 w(,)g(30)p 2595 2191 V -1 w(,)g(63)p 2735 -2191 V(,)g(64)p 2876 2191 V -1 w(,)g(65)p 3016 2191 V --1 w(,)g(66)p 3156 2191 V -1 w(,)g(68)p 3296 2191 V -1 -w(,)g(69)p 3436 2191 V -1 w(,)h(70)p 3577 2191 V -1 w(,)f(71)p -3717 2191 V -1 w(,)2199 2278 y(82)p 2199 2291 V -1 w(,)39 -b(83)p 2344 2291 V -1 w(,)f(84)p 2488 2291 V -1 w(,)g(85)p -2632 2291 V(,)g(90)p 2777 2291 V -1 w(,)g(91)p 2921 2291 -V -1 w(,)h(200)p 3066 2291 125 4 v -2 w(,)g(268)p 3252 -2291 V -2 w(,)g(270)p 3438 2291 V -2 w(,)g(272)p 3624 -2291 V -2 w(,)2199 2378 y(301)p 2199 2391 V -1 w(,)31 -b(350)p 2378 2391 V -2 w(,)g(393)p 2556 2391 V -1 w(,)g(690)p -2735 2391 V -1 w(,)g(879)p 2914 2391 V -2 w(,)g(880)p -3092 2391 V -1 w(,)g(906)p 3271 2391 V -1 w(,)g(1083)p -3450 2391 167 4 v -2 w(,)g(1127)p 3670 2391 V -2 w(,)2199 -2477 y(1183)p 2199 2490 V -2 w(,)42 b(1311)p 2430 2490 -V -2 w(,)f(1340)p 2660 2490 V -2 w(.)2033 2579 y Fi(b)p -2076 2579 26 4 v 31 w(x)14 b Fm(:)83 b(606)p 2261 2592 -125 4 v -2 w(.)2033 2680 y Fi(b)p 2076 2680 26 4 v 31 -w(y)12 b Fm(:)83 b(606)p 2260 2693 125 4 v -2 w(.)2033 -2782 y Fi(b)p 2076 2782 26 4 v 31 w(z)14 b Fm(:)83 b(606)p -2256 2795 125 4 v -1 w(.)2033 2883 y Fi(b)l(ack)14 b -Fm(:)83 b(545,)29 b(764,)f(765,)h(770,)f(886,)h(913,)f(933,)h(988,)f -(990,)2199 2983 y(1110,)j(1302,)g(1308,)g(1418,)g(1461,)g(1474.)2033 -3084 y Fi(b)l(ackgr)l(ound)14 b Fm(:)83 b(108,)39 b(1284.)2033 -3186 y Fi(b)l(ackgr)l(ound)p 2435 3186 26 4 v 31 w(c)l(olor)15 -b Fm(:)83 b(112)p 2756 3199 125 4 v -2 w(,)35 b(113)p -2938 3199 V -1 w(,)f(115,)g(415,)f(776,)g(802,)2199 3285 -y(806,)e(808,)h(823,)f(825,)g(862,)h(1283,)f(1284.)2033 -3387 y Fi(b)l(ackgr)l(ound)p 2435 3387 26 4 v 31 w(c)l(olor)p -2640 3387 V 32 w(ve)l(ctor)14 b Fm(:)83 b(115)p 3002 -3400 125 4 v -2 w(,)32 b(116)p 3181 3400 V -1 w(,)g(1389.)2033 -3488 y Fi(bb)10 b Fm(:)83 b(268)p 2225 3501 V -1 w(,)39 -b(272)p 2412 3501 V -2 w(,)h(1183)p 2599 3501 167 4 v --2 w(,)f(1268)p 2827 3501 V -2 w(.)2033 3590 y Fi(b)l(e)l(gin)11 -b Fm(:)83 b(249,)27 b(543,)h(545,)f(546,)g(549,)h(550,)f(552,)h(553,)f -(657,)2199 3690 y(659,)d(685,)f(734,)h(739,)f(741,)h(743,)g(765,)f -(766,)h(770,)f(771,)2199 3789 y(830,)h(840,)f(843,)h(859,)f(860,)h -(862,)g(867,)f(898,)h(900,)f(914,)2199 3889 y(988,)33 -b(990,)f(997,)h(1123,)f(1127,)g(1259,)g(1287,)g(1290,)2199 -3988 y(1302,)25 b(1308,)g(1342,)g(1344,)g(1347,)g(1349,)g(1365,)g -(1367,)2199 4088 y(1380,)g(1384,)g(1387,)g(1390,)g(1393,)g(1396,)g -(1399,)g(1418,)2199 4188 y(1424,)j(1433,)h(1461,)f(1465,)g(1474,)h -(1478,)f(1488.)2033 4289 y Fi(b)l(e)l(gin\014g)12 b Fm(:)83 -b(47)p 2414 4302 84 4 v -1 w(,)38 b(48)p 2558 4302 V --1 w(,)h(470,)e(1506.)2033 4391 y Fi(b)l(eta)11 b Fm(:)83 -b(1268)p 2292 4404 167 4 v -2 w(.)2033 4492 y Fk(bitset)t -Fm(:)g(16.)2033 4594 y Fi(black)14 b Fm(:)84 b(108,)29 -b(112)p 2509 4607 125 4 v -2 w(,)i(113)p 2687 4607 V --1 w(,)f(957,)f(1287,)g(1290,)g(1461.)2033 4695 y Fi(blue)11 -b Fm(:)83 b(108,)32 b(112)p 2473 4708 V -2 w(,)i(113)p -2654 4708 V -2 w(,)g(949,)e(957,)g(1287,)f(1443,)h(1461,)2199 -4795 y(1505.)2033 4896 y Fi(blue)p 2180 4896 26 4 v 31 -w(p)l(art)12 b Fm(:)83 b(56)p 2467 4909 84 4 v -1 w(,)41 -b(59,)e(61,)h(64,)g(66,)f(69,)h(71,)f(74,)h(75,)2199 -4996 y(76,)i(85,)g(91,)f(99.)2033 5097 y Fi(blue)p 2180 -5097 26 4 v 31 w(violet)13 b Fm(:)83 b(108,)35 b(112)p -2701 5110 125 4 v -2 w(,)h(113)p 2884 5110 V -1 w(,)g(1505.)2033 -5199 y Fk(b)s(o)s(ol)p 2219 5199 29 5 v 38 w(pair)6 b -Fm(:)83 b(12)p 2530 5212 84 4 v -1 w(.)2033 5300 y Fk(b)s(o)s(ol)p -2219 5300 29 5 v 38 w(p)s(oin)m(t)5 b Fm(:)83 b(33)p -2582 5313 84 4 v -1 w(,)25 b(267,)g(268)p 2887 5313 125 -4 v -2 w(,)h(269)p 3060 5313 V -2 w(,)g(270,)e(274,)g(275,)g(527,)2199 -5400 y(528,)g(529,)f(530,)h(603,)f(604,)h(640,)g(641,)f(642,)h(920,)f -(921,)p eop end -%%Page: 490 490 -TeXDict begin 490 489 bop 0 83 a Fm(490)140 b Fl(INDEX)2670 -b(3DLDFPR)n(G)142 b Fn(x)p Fm(1525)166 263 y(922,)32 -b(952,)g(963,)g(988,)f(990,)h(997,)g(1451.)0 367 y Fk(b)s(o)s(ol)p -186 367 29 5 v 38 w(p)s(oin)m(t)p 442 367 V 40 w(pair)5 -b Fm(:)83 b(267)p 754 380 125 4 v -1 w(,)33 b(274,)e(275,)h(952,)f -(953,)h(954,)166 467 y(964,)e(965,)f(984,)h(985,)g(993,)f(994,)h(999,)g -(1164,)f(1170,)166 567 y(1171,)38 b(1172,)f(1173,)h(1179,)f(1188,)h -(1221,)f(1228,)166 666 y(1263,)g(1264,)f(1265,)h(1266.)0 -771 y Fk(b)s(o)s(ol)p 186 771 29 5 v 38 w(p)s(oin)m(t)p -442 771 V 40 w(quadruple)5 b Fm(:)83 b(270)p 1007 784 -125 4 v -1 w(,)40 b(271)p 1195 784 V -1 w(,)g(274,)e(275,)166 -870 y(1174,)c(1175,)g(1176,)f(1267,)h(1268.)0 975 y Fk(b)s(o)s(ol)p -186 975 29 5 v 38 w(real)5 b Fm(:)83 b(12)p 487 988 84 -4 v -1 w(,)40 b(349,)f(350,)g(352,)f(353,)h(354,)f(355,)166 -1074 y(603,)k(961,)f(999.)0 1179 y Fk(b)s(o)s(ol)p 186 -1179 29 5 v 38 w(real)p 380 1179 V 41 w(p)s(oin)m(t)t -Fm(:)83 b(33)p 745 1192 84 4 v -1 w(,)36 b(272)p 887 -1192 125 4 v -2 w(,)g(273)p 1070 1192 V -1 w(,)g(274,)e(275,)h(603,)166 -1278 y(604,)42 b(605,)f(920.)0 1382 y Fk(b)s(o)s(ols)s -Fm(:)83 b(667,)39 b(952,)g(1299.)0 1487 y Fi(b)l(ot)p -109 1487 26 4 v 31 w(lft)12 b Fm(:)83 b(1065)p 327 1500 -167 4 v -2 w(.)0 1591 y Fi(b)l(ot)p 109 1591 26 4 v 31 -w(rt)11 b Fm(:)83 b(1065)p 315 1604 167 4 v -2 w(.)0 -1696 y Fi(bp)10 b Fm(:)83 b(268)p 196 1709 125 4 v -1 -w(,)34 b(530)p 378 1709 V -2 w(,)g(541,)e(603)p 740 1709 -V -1 w(,)h(641)p 921 1709 V -1 w(,)h(963)p 1103 1709 -V -2 w(,)g(988)p 1284 1709 V -1 w(,)f(990)p 1465 1709 -V -1 w(,)h(991,)166 1795 y(997)p 166 1808 V -1 w(,)45 -b(1451)p 359 1808 167 4 v -2 w(.)0 1899 y Fi(bpp)11 b -Fm(:)83 b(953,)30 b(954)p 418 1912 125 4 v -2 w(,)i(958,)e(959,)g(960,) -h(961,)f(963,)g(985)p 1493 1912 V -1 w(,)h(988,)166 1999 -y(990,)d(991,)g(992,)h(999)p 698 2012 V -2 w(,)h(1163,)d(1164)p -1093 2012 167 4 v -1 w(,)i(1188)p 1312 2012 V -2 w(,)h(1228)p -1531 2012 V -2 w(.)0 2103 y Fi(bpp)p 127 2103 26 4 v -32 w(e)10 b Fm(:)83 b(1179)p 308 2116 167 4 v -2 w(.)0 -2208 y Fi(bpp)p 127 2208 26 4 v 32 w(this)11 b Fm(:)83 -b(1179)p 400 2221 167 4 v -2 w(.)0 2312 y Fi(bpp0)17 -b Fm(:)83 b(1221)p 287 2325 V -2 w(.)0 2416 y Fi(bpp1)17 -b Fm(:)83 b(1221)p 287 2429 V -2 w(.)0 2521 y Fi(bp)l(q)12 -b Fm(:)83 b(1174)p 232 2534 V -2 w(,)32 b(1176)p 453 -2534 V -2 w(,)h(1184,)d(1186,)g(1188,)g(1268)p 1338 2534 -V -2 w(.)0 2625 y Fi(br)13 b Fm(:)83 b(355)p 192 2638 -125 4 v -1 w(,)45 b(999)p 385 2638 V -1 w(.)0 2730 y -Fi(br)p 78 2730 26 4 v 31 w(p)10 b Fm(:)83 b(603)p 262 -2743 125 4 v -2 w(.)0 2834 y Fi(br)p 78 2834 26 4 v 31 -w(q)12 b Fm(:)83 b(603)p 260 2847 125 4 v -2 w(.)0 2938 -y Fi(brp)10 b Fm(:)83 b(272)p 231 2951 V -1 w(,)37 b(603)p -416 2951 V -1 w(,)g(605)p 601 2951 V -1 w(,)g(606,)f(607.)0 -3043 y Fk(BUG)j(FIX)p Fm(:)84 b(119,)34 b(150,)g(265,)g(349,)g(386,)g -(397,)f(463,)166 3142 y(474,)h(545,)g(601,)g(623,)f(633,)h(672,)g(888,) -g(904,)g(953,)166 3242 y(967,)e(1064,)g(1152,)f(1163,)h(1192,)f(1309.)0 -3346 y Fk(BUGS)p Fm(:)84 b(395.)0 3450 y Fi(b0)16 b Fm(:)83 -b(900)p 202 3463 V -1 w(.)0 3555 y Fi(b1)16 b Fm(:)83 -b(900)p 202 3568 V -1 w(.)0 3659 y Fe(C)6 b Fm(:)83 b(31)p -171 3672 84 4 v -1 w(,)38 b(32)p 315 3672 V -1 w(,)g(1219)p -459 3672 167 4 v -2 w(,)g(1228)p 686 3672 V -2 w(,)f(1229)p -912 3672 V -2 w(.)0 3764 y Fe(c)p Fm(:)83 b(13)p 142 -3777 84 4 v -1 w(,)34 b(29)p 282 3777 V -1 w(,)g(30)p -422 3777 V -1 w(,)h(60)p 563 3777 V -1 w(,)f(61)p 703 -3777 V -1 w(,)g(72)p 843 3777 V -1 w(,)g(73)p 983 3777 -V -1 w(,)g(74)p 1123 3777 V -1 w(,)g(75)p 1263 3777 V --1 w(,)h(76)p 1404 3777 V -1 w(,)f(77)p 1544 3777 V -1 -w(,)g(78)p 1684 3777 V -1 w(,)166 3863 y(103)p 166 3876 -125 4 v -1 w(,)25 b(104)p 339 3876 V -2 w(,)g(270)p 511 -3876 V -1 w(,)g(317)p 684 3876 V -2 w(,)g(318)p 856 3876 -V -1 w(,)g(319)p 1029 3876 V -1 w(,)g(320)p 1202 3876 -V -2 w(,)g(695)p 1374 3876 V -1 w(,)g(696)p 1547 3876 -V -2 w(,)g(697)p 1719 3876 V -1 w(,)166 3963 y(698)p -166 3976 V -1 w(,)g(700)p 339 3976 V -2 w(,)g(701)p 511 -3976 V -1 w(,)g(702)p 684 3976 V -2 w(,)g(703)p 856 3976 -V -1 w(,)g(776)p 1029 3976 V -1 w(,)g(802)p 1202 3976 -V -2 w(,)g(807)p 1374 3976 V -1 w(,)g(824)p 1547 3976 -V -2 w(,)g(904)p 1719 3976 V -1 w(,)166 4062 y(908)p -166 4075 V -1 w(,)31 b(909)p 345 4075 V -1 w(,)h(1079)p -525 4075 167 4 v -2 w(,)g(1080)p 746 4075 V -2 w(,)f(1083)p -966 4075 V -2 w(,)h(1085)p 1187 4075 V -2 w(,)g(1086)p -1408 4075 V -2 w(,)g(1087)p 1629 4075 V -2 w(,)166 4162 -y(1088)p 166 4175 V -2 w(,)27 b(1123)p 382 4175 V -2 -w(,)g(1174)p 598 4175 V -2 w(,)g(1183)p 814 4175 V -2 -w(,)g(1193)p 1030 4175 V -2 w(,)g(1245)p 1246 4175 V --2 w(,)g(1248)p 1462 4175 V -2 w(,)g(1250)p 1678 4175 -V -2 w(,)166 4262 y(1253)p 166 4275 V -2 w(,)g(1254)p -382 4275 V -2 w(,)g(1258)p 598 4275 V -2 w(,)g(1259)p -814 4275 V -2 w(,)g(1267)p 1030 4275 V -2 w(,)g(1268)p -1246 4275 V -2 w(,)g(1270)p 1462 4275 V -2 w(,)g(1272)p -1678 4275 V -2 w(,)166 4361 y(1274)p 166 4374 V -2 w(,)g(1276)p -382 4374 V -2 w(,)g(1382)p 598 4374 V -2 w(,)g(1385)p -814 4374 V -2 w(,)g(1388)p 1030 4374 V -2 w(,)g(1417)p -1246 4374 V -2 w(,)g(1418)p 1462 4374 V -2 w(,)g(1419)p -1678 4374 V -2 w(,)166 4461 y(1420)p 166 4474 V -2 w(,)33 -b(1421)p 388 4474 V -2 w(,)g(1422)p 610 4474 V -2 w(,)g(1425)p -832 4474 V -2 w(,)g(1426)p 1054 4474 V -2 w(,)g(1506)p -1276 4474 V -2 w(.)0 4565 y Fi(c)p 43 4565 26 4 v 31 -w(iter)13 b Fm(:)83 b(657,)33 b(1382,)g(1384,)f(1385,)g(1387.)0 -4670 y Fi(c)p 43 4670 V 31 w(plane)11 b Fm(:)83 b(1268)p -376 4683 167 4 v -2 w(.)0 4774 y Fi(c)p 43 4774 26 4 -v 31 w(ptr)13 b Fm(:)83 b(1316)p 293 4787 167 4 v -2 -w(.)0 4878 y Fi(c)p 43 4878 26 4 v 31 w(r)l(adius)11 -b Fm(:)83 b(1267)p 405 4891 167 4 v -1 w(.)0 4983 y Fi(c)p -43 4983 26 4 v 31 w(str)12 b Fm(:)84 b(44.)0 5087 y Fi(c)p -43 5087 V 31 w(x)13 b Fm(:)84 b(904)p 228 5100 125 4 -v -2 w(,)45 b(906.)0 5191 y Fi(c)p 43 5191 26 4 v 31 -w(y)12 b Fm(:)83 b(904)p 227 5204 125 4 v -2 w(,)42 b(905,)f(906.)0 -5296 y Fi(c)p 43 5296 26 4 v 31 w(z)14 b Fm(:)83 b(904)p -223 5309 125 4 v -1 w(,)42 b(905,)f(906.)0 5400 y Fi(c)l(c)9 -b Fm(:)83 b(1183)p 187 5413 167 4 v -2 w(.)2033 263 y -Fi(c)l(c)l(enter)13 b Fm(:)83 b(1032)p 2406 276 V -2 -w(,)28 b(1033)p 2623 276 V -2 w(,)g(1035)p 2840 276 V --2 w(,)g(1036)p 3057 276 V -2 w(,)g(1037,)e(1064)p 3491 -276 V -2 w(,)i(1065)p 3708 276 V -2 w(,)2199 363 y(1066)p -2199 376 V -2 w(,)40 b(1067)p 2428 376 V -2 w(,)f(1109)p -2656 376 V -2 w(,)h(1110)p 2885 376 V -2 w(,)f(1111)p -3113 376 V -2 w(,)h(1112)p 3342 376 V -2 w(,)f(1242)p -3570 376 V -2 w(,)2199 462 y(1243)p 2199 475 V -2 w(,)j(1244)p -2430 475 V -2 w(,)f(1245)p 2660 475 V -2 w(.)2033 566 -y Fi(c)l(c)l(os)11 b Fm(:)83 b(161)p 2294 579 125 4 v --1 w(,)39 b(162,)f(163,)g(164.)2033 669 y Fi(Center)13 -b Fm(:)83 b(1164)p 2397 682 167 4 v -2 w(.)2033 772 y -Fi(c)l(enter)13 b Fm(:)83 b(941)p 2372 785 125 4 v -2 -w(,)36 b(948,)f(952,)f(953,)g(964,)h(966,)f(968,)g(969,)2199 -872 y(970,)e(975)p 2380 885 V -2 w(,)i(979,)d(981,)h(984,)g(985,)g -(990,)f(991,)h(1002,)2199 972 y(1021,)38 b(1024,)f(1027,)h(1033,)f -(1034,)h(1065,)f(1070,)2199 1071 y(1080,)h(1109,)f(1110,)h(1120,)f -(1127,)h(1140,)f(1142,)2199 1171 y(1163,)25 b(1171,)g(1179,)g(1192,)g -(1193,)g(1209,)g(1243,)g(1268,)2199 1270 y(1270,)g(1274,)g(1294,)g -(1296)p 2847 1283 167 4 v -2 w(,)i(1308,)e(1314,)g(1347,)g(1349,)2199 -1370 y(1420,)g(1429,)g(1440,)g(1444,)g(1445,)g(1457,)g(1459,)g(1461,) -2199 1470 y(1471,)37 b(1474,)f(1485,)h(1488.)2033 1573 -y Fi(c)l(enter)p 2258 1573 26 4 v 30 w(0)16 b Fm(:)83 -b(1448,)31 b(1461)p 2669 1586 167 4 v -2 w(,)i(1462)p -2891 1586 V -2 w(,)f(1475,)f(1489.)2033 1676 y Fi(c)l(enter)p -2258 1676 26 4 v 30 w(6)16 b Fm(:)83 b(1461)p 2447 1689 -167 4 v -2 w(.)2033 1780 y Fi(c)l(err)13 b Fm(:)83 b(69,)33 -b(71,)g(85,)g(87,)g(89,)g(91,)g(106,)f(108,)h(151,)f(153,)2199 -1879 y(161,)24 b(183,)f(188,)h(313,)f(318,)h(346,)g(347,)f(350,)h(351,) -f(380,)2199 1979 y(383,)h(393,)f(400,)h(401,)f(432,)h(443,)g(452,)f -(458,)h(462,)f(464,)2199 2079 y(472,)h(503,)f(505,)h(508,)f(536,)h -(540,)g(549,)f(550,)h(551,)f(561,)2199 2178 y(572,)h(606,)f(624,)h -(641,)f(644,)h(716,)g(717,)f(722,)h(743,)f(748,)2199 -2278 y(750,)h(763,)f(765,)h(776,)f(802,)h(807,)g(813,)f(821,)h(824,)f -(830,)2199 2378 y(842,)h(844,)f(858,)h(863,)f(867,)h(873,)g(880,)f -(883,)h(884,)f(885,)2199 2477 y(889,)34 b(891,)g(893,)g(897,)f(898,)h -(899,)g(901,)g(903,)g(904,)2199 2577 y(906,)g(912,)g(922,)g(927,)f -(933,)h(949,)g(951,)g(955,)g(962,)2199 2676 y(965,)e(968,)g(979,)f -(981,)h(986,)g(989,)g(994,)f(998,)h(1009,)2199 2776 y(1070,)25 -b(1086,)g(1088,)g(1110,)g(1127,)g(1134,)g(1145,)g(1147,)2199 -2876 y(1168,)g(1173,)g(1179,)g(1182,)g(1184,)g(1185,)g(1186,)g(1187,) -2199 2975 y(1193,)g(1216,)g(1221,)g(1228,)g(1229,)g(1256,)g(1259,)g -(1268,)2199 3075 y(1270,)g(1274,)g(1284,)g(1287,)g(1317,)g(1330,)g -(1365,)g(1367,)2199 3175 y(1463,)34 b(1476,)g(1508,)f(1515,)h(1516.) -2033 3278 y Fi(che)l(ck)14 b Fm(:)83 b(1192)p 2343 3291 -V -2 w(,)31 b(1193)p 2563 3291 V -1 w(,)g(1194,)e(1196,)g(1203,)g -(1213.)2033 3381 y Fi(che)l(ck)p 2228 3381 26 4 v 32 -w(pr)l(oje)l(ction)p 2614 3381 V 31 w(limits)12 b Fm(:)83 -b(252.)2033 3485 y Ff(CIRCLE)r Fm(:)g(1296)p 2405 3498 -167 4 v -2 w(,)28 b(1297)p 2622 3498 V -2 w(,)g(1316,)e(1317,)f(1329,)h -(1330,)g(1332.)2033 3588 y Fk(Circle)t Fm(:)83 b(33)p -2391 3601 84 4 v -1 w(,)38 b(686,)f(966,)f(1024,)h(1046,)f(1047,)g -(1049,)2199 3688 y(1050,)25 b(1051,)g(1053,)g(1054,)g(1174,)g(1175,)g -(1237)p 3495 3701 167 4 v -2 w(,)i(1239,)2199 3787 y(1240)p -2199 3800 V -2 w(,)g(1242,)e(1243)p 2631 3800 V -2 w(,)i(1245,)e(1247,) -g(1248,)g(1249,)g(1250,)2199 3887 y(1251,)g(1253,)g(1254,)g(1255,)g -(1256,)g(1258,)g(1259,)g(1262,)2199 3987 y(1264,)g(1266,)g(1267,)g -(1268,)g(1269,)g(1270,)g(1272,)g(1273,)2199 4086 y(1274,)g(1276,)g -(1277,)g(1286,)g(1287,)g(1288,)g(1289,)g(1290,)2199 4186 -y(1296,)g(1302,)g(1308,)g(1312,)g(1316,)g(1318,)g(1319,)g(1329,)2199 -4285 y(1342,)g(1344,)g(1347,)g(1349,)g(1365,)g(1367,)g(1379,)g(1380,) -2199 4385 y(1384,)j(1387,)h(1390,)f(1393,)g(1396,)h(1399,)f(1506.)2033 -4488 y Fi(cir)l(cles)12 b Fm(:)83 b(1296)p 2376 4501 -V -2 w(,)30 b(1302,)d(1308,)h(1316,)g(1317,)f(1319,)h(1329,)2199 -4588 y(1330,)d(1342,)g(1344,)g(1347,)g(1349,)g(1365,)g(1367,)g(1379,) -2199 4688 y(1380,)g(1382,)g(1384,)g(1385,)g(1387,)g(1388,)g(1390,)g -(1391,)2199 4787 y(1393,)34 b(1394,)g(1396,)f(1397,)h(1399.)2033 -4891 y Fk(Circles)t Fm(:)83 b(1178,)34 b(1258,)f(1286,)h(1289.)2033 -4994 y Fi(classes)12 b Fm(:)83 b(656.)2033 5097 y Fi(cle)l(an)11 -b Fm(:)83 b(136)p 2332 5110 125 4 v -1 w(,)28 b(137)p -2508 5110 V -1 w(,)h(141,)e(143,)g(151,)g(153,)g(156,)g(164,)h(172,) -2199 5197 y(174,)g(177,)g(179,)g(304)p 2730 5210 V -1 -w(,)h(305)p 2907 5210 V -1 w(,)g(395,)f(516,)g(517,)g(520.)2033 -5300 y Fi(cle)l(ar)14 b Fm(:)83 b(200)p 2323 5313 V -1 -w(,)38 b(221,)f(222,)g(232,)g(255)p 3067 5313 V -2 w(,)i(302)p -3253 5313 V -2 w(,)g(303)p 3439 5313 V -2 w(,)g(470,)2199 -5400 y(543,)32 b(546)p 2380 5413 V -2 w(,)i(659,)d(685,)h(686)p -2922 5413 V -1 w(,)h(687)p 3103 5413 V -2 w(,)h(709,)d(999,)h(1027,)p -eop end -%%Page: 491 491 -TeXDict begin 491 490 bop 0 83 a Fn(x)p Fm(1525)139 b -Fl(3DLDFPR)n(G)2671 b(INDEX)141 b Fm(491)166 263 y(1043,)38 -b(1078,)f(1080,)h(1118,)f(1251,)h(1287,)f(1290,)166 363 -y(1308,)g(1343)p 394 376 167 4 v -2 w(,)h(1344)p 621 -376 V -2 w(,)h(1424.)0 465 y Fi(close)11 b Fm(:)84 b(1519.)0 -567 y Fi(close)l(d)14 b Fm(:)83 b(967)p 331 580 125 4 -v -1 w(,)38 b(968)p 517 580 V -1 w(,)g(969)p 703 580 -V -1 w(,)g(970)p 889 580 V -1 w(.)0 669 y Fi(c)l(o)l(e\013s)11 -b Fm(:)83 b(960)p 312 682 V -1 w(.)0 770 y Fi(c)l(ol)13 -b Fm(:)84 b(134)p 217 783 V -2 w(,)40 b(135)p 404 783 -V -1 w(,)g(145)p 592 783 V -2 w(,)g(146)p 779 783 V -1 -w(.)0 872 y Fi(c)l(ol)p 102 872 26 4 v 31 w(ve)l(c)9 -b Fm(:)83 b(1461)p 353 885 167 4 v -1 w(.)0 974 y Fk(Color)t -Fm(:)g(56)p 341 987 84 4 v -1 w(,)32 b(58,)e(59)p 616 -987 V -1 w(,)i(60,)e(61)p 891 987 V -1 w(,)i(63,)e(64)p -1166 987 V -1 w(,)i(66,)e(68,)h(69)p 1579 987 V -1 w(,)g(71,)166 -1074 y(72,)h(73,)g(74,)g(75,)h(76,)f(77,)g(78,)g(81,)g(83,)g(85,)g(87,) -g(89,)166 1174 y(91,)e(93,)f(101,)g(103,)g(104,)g(106,)g(108,)h(111,)f -(112,)g(113,)166 1273 y(115,)24 b(116,)f(264,)h(409,)f(410,)h(411,)g -(412,)f(413,)h(419,)f(420,)166 1373 y(422,)h(423,)f(428,)h(429,)f(654,) -h(655,)g(657,)f(695,)h(696,)f(697,)166 1473 y(698,)h(700,)f(701,)h -(702,)f(703,)h(775,)g(776,)f(777,)h(778,)f(780,)166 1572 -y(781,)h(784,)f(785,)h(786,)f(787,)h(789,)g(790,)f(793,)h(794,)f(795,) -166 1672 y(796,)34 b(798,)g(799,)g(801,)f(802,)h(803,)g(804,)g(806,)g -(807,)166 1771 y(808,)g(809,)g(823,)g(824,)f(825,)h(826,)g(924,)g(925,) -g(929,)166 1871 y(930,)28 b(1049,)g(1050,)g(1053,)f(1054,)h(1097,)g -(1098,)f(1222,)166 1971 y(1223,)e(1224,)g(1225,)g(1230,)g(1231,)g -(1272,)g(1273,)g(1276,)166 2070 y(1277,)g(1283,)g(1284,)g(1286,)g -(1287,)g(1289,)g(1290,)g(1382,)166 2170 y(1383,)g(1384,)g(1385,)g -(1386,)g(1387,)g(1388,)g(1389,)g(1390,)166 2270 y(1391,)31 -b(1394,)g(1397,)g(1461,)g(1505,)g(1519.)0 2372 y Fi(c)l(olor)p -179 2372 26 4 v 32 w(iter)13 b Fm(:)83 b(1290.)0 2473 -y Fi(c)l(olor)p 179 2473 V 32 w(ptr)13 b Fm(:)83 b(1382,)33 -b(1384)p 654 2486 167 4 v -2 w(,)i(1385,)f(1387)p 1103 -2486 V -2 w(.)0 2575 y Fk(Colors)t Fm(:)83 b(67,)28 b(75,)f(107,)h(108) -p 825 2588 125 4 v -2 w(,)h(112)p 1001 2588 V -1 w(,)f(113)p -1177 2588 V -1 w(,)h(115)p 1354 2588 V -2 w(,)g(116)p -1530 2588 V -1 w(,)g(410,)166 2675 y(412,)24 b(415,)f(419,)h(420,)f -(422,)h(423,)g(427,)f(428,)h(429,)f(458,)166 2775 y(655,)h(775,)f(776,) -h(777,)f(784,)h(786,)g(801,)f(802,)h(803,)f(806,)166 -2874 y(808,)h(823,)f(825,)h(859,)f(861,)h(862,)g(863,)f(924,)h(949,)f -(957,)166 2974 y(1049,)i(1050,)g(1053,)g(1054,)g(1097,)g(1098,)g(1222,) -g(1224,)166 3074 y(1283,)g(1284,)g(1286,)g(1287)p 814 -3087 167 4 v -2 w(,)i(1289,)e(1290)p 1246 3087 V -2 w(,)i(1383,)e -(1384,)166 3173 y(1386,)j(1387,)h(1389,)f(1443)p 824 -3186 V -2 w(,)i(1451,)f(1461)p 1263 3186 V -2 w(,)h(1505)p -1482 3186 V -2 w(.)0 3275 y Fi(c)l(olors)12 b Fm(:)83 -b(1286)p 326 3288 V -2 w(,)37 b(1287)p 552 3288 V -2 -w(,)f(1289)p 777 3288 V -2 w(,)h(1290)p 1003 3288 V -2 -w(.)0 3377 y Fi(c)l(olumn)10 b Fm(:)83 b(581)p 373 3390 -125 4 v -1 w(,)38 b(582)p 559 3390 V -1 w(,)g(584)p 745 -3390 V -2 w(,)g(585)p 930 3390 V -1 w(.)0 3479 y Fk(Compare)p -383 3479 29 5 v 40 w(maxim)m(um)p 836 3479 V 39 w(z)6 -b Fm(:)83 b(453,)28 b(455)p 1202 3492 125 4 v -2 w(,)h(552,)f(1380.)0 -3581 y Fk(Compare)p 383 3581 29 5 v 40 w(mean)p 646 3581 -V 40 w(z)5 b Fm(:)83 b(453,)33 b(456)p 1017 3594 125 -4 v -1 w(,)h(552.)0 3683 y Fk(Compare)p 383 3683 29 5 -v 40 w(minim)m(um)p 820 3683 V 38 w(z)5 b Fm(:)83 b(453,)31 -b(454)p 1187 3696 125 4 v -1 w(,)h(552.)0 3785 y(Compiling:)83 -b(1280.)0 3887 y Fi(c)l(ongruent)p 359 3887 26 4 v 30 -w(\015ag)12 b Fm(:)83 b(1179)p 631 3900 167 4 v -2 w(.)0 -3989 y Fi(c)l(onne)l(ctor)13 b Fm(:)83 b(667,)38 b(668)p -653 4002 125 4 v -2 w(,)h(669)p 839 4002 V -1 w(,)g(670)p -1026 4002 V -2 w(,)g(671)p 1212 4002 V -1 w(,)g(769)p -1399 4002 V -2 w(,)g(770)p 1585 4002 V -1 w(,)166 4089 -y(881)p 166 4102 V -1 w(,)h(882)p 354 4102 V -1 w(,)g(885,)f(886.)0 -4190 y Fi(c)l(onne)l(ctor)p 352 4190 26 4 v 30 w(iter)14 -b Fm(:)83 b(859,)33 b(860,)h(862,)f(864.)0 4292 y Fi(c)l(onne)l(ctor)p -352 4292 V 30 w(ptr)14 b Fm(:)83 b(674)p 602 4305 125 -4 v -2 w(,)40 b(676)p 789 4305 V -1 w(.)0 4394 y Fi(c)l(onne)l(ctor)p -352 4394 26 4 v 30 w(string)12 b Fm(:)83 b(674)p 702 -4407 125 4 v -1 w(,)22 b(676)p 872 4407 V -2 w(,)g(859)p -1041 4407 V -1 w(,)g(860,)e(862,)h(864,)f(867)p 1719 -4407 V -1 w(.)0 4496 y Fi(c)l(onne)l(ctors)11 b Fm(:)83 -b(654)p 498 4509 V -1 w(,)37 b(657,)e(659,)h(664,)g(666,)f(669,)h(671,) -166 4596 y(674,)e(676,)g(685,)g(709,)f(759,)h(764,)g(765,)g(766,)g -(770,)166 4696 y(771,)g(859,)g(860,)g(862,)f(864,)h(866,)g(867,)g(885,) -g(886,)166 4795 y(898,)i(913,)g(914,)f(1070,)h(1110.)0 -4897 y Fi(c)l(onne)l(ctors)p 386 4897 26 4 v 30 w(iter)14 -b Fm(:)83 b(867.)0 4999 y Fi(c)l(onst)p 190 4999 V 30 -w(iter)l(ator)14 b Fm(:)83 b(543,)30 b(545,)f(657,)h(765,)g(766,)g -(770,)g(771,)166 5099 y(830,)g(867,)f(898,)h(900,)g(988,)f(990,)h(997,) -g(1123,)f(1127,)166 5198 y(1259,)c(1302,)g(1308,)g(1342,)g(1384,)g -(1387,)g(1390,)g(1393,)166 5298 y(1396,)37 b(1399,)f(1418,)h(1433.)0 -5400 y Fi(c)l(onsts)11 b Fm(:)83 b(24,)43 b(274.)2033 -263 y Fi(c)l(o)l(or)l(ds)12 b Fm(:)83 b(200)p 2372 276 -125 4 v -2 w(,)36 b(312)p 2555 276 V -1 w(,)g(313)p 2739 -276 V -2 w(,)g(314)p 2922 276 V -2 w(,)g(315)p 3105 276 -V -1 w(,)g(317)p 3289 276 V -2 w(,)g(318)p 3472 276 V --1 w(,)f(319)p 3655 276 V -1 w(,)2199 363 y(320)p 2199 -376 V -1 w(,)g(322)p 2382 376 V -2 w(,)h(323)p 2565 376 -V -2 w(,)g(324)p 2748 376 V -2 w(,)f(325)p 2930 376 V --1 w(,)g(327)p 3113 376 V -1 w(,)g(328)p 3296 376 V -1 -w(,)g(329)p 3479 376 V -2 w(,)h(330)p 3662 376 V -2 w(,)2199 -462 y(332)p 2199 475 V -1 w(,)f(333)p 2382 475 V -2 w(,)h(334)p -2565 475 V -2 w(,)g(335)p 2748 475 V -2 w(,)f(337)p 2930 -475 V -1 w(,)g(338)p 3113 475 V -1 w(,)g(339)p 3296 475 -V -1 w(,)g(340)p 3479 475 V -2 w(,)h(431)p 3662 475 V --2 w(,)2199 562 y(432)p 2199 575 V -1 w(,)h(866)p 2384 -575 V -2 w(,)h(867)p 2569 575 V -2 w(,)f(1341)p 2753 -575 167 4 v -2 w(,)h(1342)p 2980 575 V -2 w(.)2033 664 -y Fi(c)l(opy)13 b Fm(:)83 b(524)p 2310 677 125 4 v -2 -w(,)41 b(949)p 2498 677 V -2 w(,)f(957)p 2685 677 V -1 -w(,)g(1179)p 2873 677 167 4 v -2 w(,)g(1180,)f(1182,)f(1183,)2199 -764 y(1184,)k(1185.)2033 867 y Fi(c)l(opy)p 2196 867 -26 4 v 32 w(axis)p 2368 867 V 31 w(orientation)11 b Fm(:)83 -b(1183)p 2910 880 167 4 v -2 w(.)2033 969 y Fi(c)l(opy)p -2196 969 26 4 v 32 w(c)l(enter)12 b Fm(:)84 b(1179)p -2562 982 167 4 v -2 w(,)34 b(1180,)e(1182,)g(1183.)2033 -1072 y Fi(c)l(opy)p 2196 1072 26 4 v 32 w(normal)13 b -Fm(:)83 b(949)p 2597 1085 125 4 v -1 w(.)2033 1174 y -Ff(COPYRIGHT_3DLDF)n Fm(:)g(19)p 2797 1187 84 4 v -1 -w(,)31 b(20)p 2934 1187 V -1 w(,)f(1508,)e(1512,)h(1513.)2033 -1277 y Fi(c)l(orner)13 b Fm(:)84 b(1085)p 2384 1290 167 -4 v -2 w(,)42 b(1086)p 2615 1290 V -2 w(.)2033 1380 y -Fi(c)l(os)11 b Fm(:)83 b(162,)38 b(163,)g(164,)g(1110.)2033 -1482 y Fi(c)l(ounter)13 b Fm(:)83 b(864)p 2421 1495 125 -4 v -2 w(.)2033 1585 y Fi(c)l(out)12 b Fm(:)83 b(32,)30 -b(48,)h(50,)g(72,)g(93,)f(148,)g(174,)h(182,)f(183,)g(184,)2199 -1684 y(185,)24 b(186,)f(188,)h(249,)f(350,)h(380,)g(382,)f(385,)h(387,) -f(388,)2199 1784 y(395,)h(399,)f(400,)h(401,)f(405,)h(411,)g(432,)f -(434,)h(443,)f(446,)2199 1884 y(448,)h(452,)f(458,)h(462,)f(464,)h -(517,)g(519,)f(520,)h(521,)f(522,)2199 1983 y(530,)h(531,)f(532,)h -(533,)f(534,)h(535,)g(536,)f(537,)h(538,)f(540,)2199 -2083 y(541,)h(546,)f(548,)h(549,)f(550,)h(551,)g(552,)f(553,)h(561,)f -(574,)2199 2182 y(603,)h(605,)f(606,)h(607,)f(609,)h(644,)g(646,)f -(661,)h(664,)f(669,)2199 2282 y(674,)h(678,)f(681,)h(683,)f(685,)h -(687,)g(726,)f(776,)h(802,)f(807,)2199 2382 y(824,)h(830,)f(840,)h -(842,)f(843,)h(844,)g(847,)f(849,)h(857,)f(859,)2199 -2481 y(861,)h(862,)f(863,)h(864,)f(867,)h(869,)g(873,)f(875,)h(886,)f -(897,)2199 2581 y(900,)h(904,)f(906,)h(914,)f(921,)h(949,)g(954,)f -(955,)h(957,)f(958,)2199 2681 y(959,)h(960,)f(961,)h(963,)f(985,)h -(986,)g(988,)f(990,)h(991,)f(992,)2199 2780 y(996,)33 -b(997,)f(999,)h(1033,)f(1034,)g(1036,)g(1037,)g(1127,)2199 -2880 y(1168,)25 b(1176,)g(1177,)g(1179,)g(1180,)g(1182,)g(1183,)g -(1184,)2199 2979 y(1185,)g(1186,)g(1188,)g(1189,)g(1193,)g(1228,)g -(1229,)g(1259,)2199 3079 y(1268,)g(1284,)g(1290,)g(1308,)g(1317,)g -(1342,)g(1344,)g(1367,)2199 3179 y(1370,)g(1372,)g(1380,)g(1382,)g -(1384,)g(1385,)g(1387,)g(1388,)2199 3278 y(1390,)g(1393,)g(1396,)g -(1399,)g(1433,)g(1444,)g(1460,)g(1461,)2199 3378 y(1474,)j(1476,)h -(1488,)f(1508,)g(1512,)h(1513,)f(1519.)2033 3481 y Fi(cr)l(e)l(ate)11 -b Fm(:)83 b(200.)2033 3583 y Fi(cr)l(e)l(ate)p 2249 3583 -26 4 v 31 w(new)13 b Fm(:)83 b(31)p 2534 3596 84 4 v --1 w(,)40 b(32)p 2680 3596 V -1 w(,)g(200.)2033 3686 -y Fi(cr)l(e)l(ate)p 2249 3686 26 4 v 31 w(new)p 2420 -3686 V 30 w(cir)l(cle)12 b Fm(:)83 b(1247)p 2754 3699 -167 4 v -2 w(,)33 b(1248)p 2976 3699 V -2 w(,)h(1249)p -3199 3699 V -2 w(,)f(1250)p 3421 3699 V -2 w(,)g(1302,)2199 -3785 y(1308.)2033 3888 y Fi(cr)l(e)l(ate)p 2249 3888 -26 4 v 31 w(new)p 2420 3888 V 30 w(c)l(olor)14 b Fm(:)84 -b(72)p 2740 3901 84 4 v -1 w(,)35 b(776,)g(802,)f(807,)g(824,)h(1382,) -2199 3988 y(1385,)42 b(1388.)2033 4090 y Fi(cr)l(e)l(ate)p -2249 4090 26 4 v 31 w(new)p 2420 4090 V 30 w(cub)l(oid)14 -b Fm(:)83 b(1421)p 2791 4103 167 4 v -2 w(,)37 b(1422)p -3017 4103 V -2 w(.)2033 4193 y Fi(cr)l(e)l(ate)p 2249 -4193 26 4 v 31 w(new)p 2420 4193 V 30 w(el)t(lipse)13 -b Fm(:)83 b(1114)p 2787 4206 167 4 v -2 w(,)31 b(1115)p -3007 4206 V -2 w(,)g(1116)p 3227 4206 V -2 w(,)h(1117)p -3448 4206 V -2 w(,)f(1302,)2199 4292 y(1308.)2033 4395 -y Fi(cr)l(e)l(ate)p 2249 4395 26 4 v 31 w(new)p 2420 -4395 V 30 w(p)l(ath)12 b Fm(:)83 b(680)p 2713 4408 125 -4 v -2 w(,)26 b(681)p 2886 4408 V -2 w(,)g(682)p 3059 -4408 V -1 w(,)f(683)p 3232 4408 V -1 w(,)h(689,)e(776,)g(802,)2199 -4495 y(807,)34 b(813,)f(821,)h(824,)f(1302,)g(1308.)2033 -4597 y Fi(cr)l(e)l(ate)p 2249 4597 26 4 v 31 w(new)p -2420 4597 V 30 w(p)l(oint)13 b Fm(:)83 b(290,)34 b(291)p -2927 4610 125 4 v -2 w(,)i(292)p 3110 4610 V -2 w(,)g(293)p -3293 4610 V -2 w(,)g(294)p 3476 4610 V -1 w(,)f(295)p -3659 4610 V -1 w(,)2199 4697 y(296)p 2199 4710 V -1 w(,)g(343,)f(411,)g -(415,)f(462,)h(471,)g(657,)g(664,)g(666,)2199 4796 y(669,)g(671,)g -(674,)g(676,)f(755,)h(757,)g(765,)g(770,)g(885,)2199 -4896 y(886,)h(1034,)f(1065,)g(1070,)h(1110.)2033 4999 -y Fi(cr)l(e)l(ate)p 2249 4999 26 4 v 31 w(new)p 2420 -4999 V 30 w(r)l(e)l(ctangle)11 b Fm(:)83 b(1074)p 2879 -5012 167 4 v -2 w(,)40 b(1075)p 3108 5012 V -2 w(,)g(1076)p -3337 5012 V -2 w(,)g(1077)p 3566 5012 V -2 w(,)2199 5098 -y(1302,)d(1308,)f(1418,)h(1420.)2033 5201 y Fi(cr)l(e)l(ate)p -2249 5201 26 4 v 31 w(new)p 2420 5201 V 30 w(r)l(e)l(g)p -2553 5201 V 31 w(p)l(olygon)12 b Fm(:)83 b(1039)p 2965 -5214 167 4 v -2 w(,)34 b(1040)p 3188 5214 V -2 w(,)g(1041)p -3411 5214 V -2 w(,)g(1042)p 3634 5214 V -2 w(,)2199 5300 -y(1302,)k(1308,)f(1449,)h(1461,)f(1463,)h(1474,)f(1476,)2199 -5400 y(1488,)j(1490,)f(1491.)p eop end -%%Page: 492 492 -TeXDict begin 492 491 bop 0 83 a Fm(492)140 b Fl(INDEX)2670 -b(3DLDFPR)n(G)142 b Fn(x)p Fm(1525)0 263 y Fi(cr)l(e)l(ate)p -216 263 26 4 v 31 w(new)p 387 263 V 30 w(solid)15 b Fm(:)83 -b(1299,)33 b(1303)p 921 276 167 4 v -2 w(,)h(1304)p 1144 -276 V -1 w(,)g(1310,)f(1384,)166 363 y(1387,)h(1390,)g(1393,)f(1396,)h -(1399.)0 464 y Fi(cr)l(oss)11 b Fm(:)83 b(953,)36 b(954)p -481 477 125 4 v -2 w(,)h(956,)e(985)p 849 477 V -1 w(,)h(987.)0 -566 y Fi(cr)l(oss)p 184 566 26 4 v 31 w(pr)l(o)l(duct)12 -b Fm(:)83 b(500)p 592 579 125 4 v -1 w(,)32 b(501)p 772 -579 V -2 w(,)g(605,)f(644,)f(900,)h(954,)f(985,)166 666 -y(1070,)40 b(1082,)f(1083.)0 767 y Fi(ctr)13 b Fm(:)83 -b(318)p 220 780 V -1 w(,)44 b(346)p 412 780 V -1 w(.)0 -869 y Fk(Cub)s(oid)t Fm(:)83 b(442,)39 b(1309,)g(1411,)f(1413)p -1063 882 167 4 v -2 w(,)j(1415,)e(1416)p 1523 882 V -2 -w(,)166 968 y(1417,)f(1418)p 395 981 V -2 w(,)h(1419,)f(1420)p -852 981 V -2 w(,)h(1421,)f(1422,)f(1423,)166 1068 y(1424)p -166 1081 V -2 w(,)42 b(1425,)d(1426.)0 1170 y Fi(curr)p -158 1170 26 4 v 30 w(angle)11 b Fm(:)84 b(1110)p 487 -1183 167 4 v -2 w(.)0 1271 y Fi(curr)p 158 1271 26 4 -v 30 w(c)l(olor)15 b Fm(:)83 b(1286)p 478 1284 167 4 -v -2 w(.)0 1373 y Fi(curr)p 158 1373 26 4 v 30 w(lo)l(c)l(ation)12 -b Fm(:)83 b(1185)p 578 1386 167 4 v -2 w(.)0 1475 y Fi(curr)p -158 1475 26 4 v 30 w(p)l(oint)13 b Fm(:)83 b(1185)p 482 -1488 167 4 v -2 w(,)40 b(1186.)0 1576 y Fi(curr)p 158 -1576 26 4 v 30 w(x)14 b Fm(:)83 b(1110)p 342 1589 167 -4 v -2 w(.)0 1678 y Ff(CURR_Y)r Fm(:)g(264)p 372 1691 -125 4 v -2 w(,)39 b(265)p 558 1691 V -2 w(,)f(282,)f(284.)0 -1779 y Ff(CURR_Z)r Fm(:)83 b(264)p 372 1792 V -2 w(,)39 -b(265)p 558 1792 V -2 w(,)f(282,)f(284.)0 1881 y Fi(curr)p -158 1881 26 4 v 30 w(z)15 b Fm(:)83 b(1110)p 338 1894 -167 4 v -2 w(.)0 1983 y Fi(curr)l(ent)p 267 1983 26 4 -v 30 w(pictur)l(e)10 b Fm(:)83 b(257)p 655 1996 125 4 -v -1 w(,)28 b(258)p 831 1996 V -1 w(,)g(410,)f(414,)g(419,)g(422,)g -(425,)166 2082 y(428,)d(461,)f(463,)h(466,)f(468,)h(470,)g(775,)f(784,) -h(793,)f(801,)166 2182 y(806,)32 b(812,)g(820,)f(823,)h(829,)g(834,)g -(924,)f(929,)h(1049,)166 2282 y(1053,)25 b(1097,)g(1098,)g(1122,)g -(1124,)g(1222,)g(1224,)g(1283,)166 2381 y(1348,)g(1383,)g(1386,)g -(1389,)g(1392,)g(1395,)g(1398,)g(1506.)0 2483 y Fi(curve)p -199 2483 26 4 v 31 w(0)16 b Fm(:)83 b(957)p 389 2496 -125 4 v -2 w(.)0 2584 y Fi(curve)p 199 2584 26 4 v 31 -w(4)16 b Fm(:)83 b(957)p 389 2597 125 4 v -2 w(.)0 2686 -y Fi(cyan)11 b Fm(:)83 b(108,)35 b(112)p 468 2699 V -2 -w(,)h(113)p 651 2699 V -2 w(,)g(1461,)e(1505.)0 2788 -y Fi(cycle)12 b Fm(:)83 b(667)p 293 2801 V -2 w(,)28 -b(668,)f(669,)f(670,)h(671,)f(881)p 1170 2801 V -1 w(,)i(882)p -1346 2801 V -1 w(,)g(885,)e(886.)0 2889 y Fi(cycle)p -180 2889 26 4 v 32 w(switch)11 b Fm(:)83 b(654)p 546 -2902 125 4 v -1 w(,)34 b(657,)f(661,)g(664,)g(666,)g(669,)g(671,)166 -2989 y(674,)k(676,)g(867,)g(877,)g(909,)g(1030,)f(1033,)g(1040,)166 -3089 y(1042,)i(1062,)f(1065,)h(1070,)f(1075,)h(1077,)f(1107,)166 -3188 y(1110,)g(1240,)f(1243,)h(1248.)0 3290 y Fe(d)p -Fm(:)83 b(16)p 149 3303 84 4 v -1 w(,)36 b(21)p 291 3303 -V -1 w(,)h(22)p 434 3303 V -1 w(,)f(270)p 576 3303 125 -4 v -2 w(,)g(644)p 759 3303 V -1 w(,)g(904)p 943 3303 -V -1 w(,)g(1083)p 1127 3303 167 4 v -2 w(,)g(1183)p 1352 -3303 V -2 w(,)g(1312)p 1577 3303 V -2 w(,)166 3389 y(1419)p -166 3402 V -2 w(,)44 b(1420)p 399 3402 V -1 w(.)0 3491 -y Fi(d)p 47 3491 26 4 v 31 w(x)14 b Fm(:)83 b(904)p 232 -3504 125 4 v -2 w(,)45 b(906.)0 3593 y Fi(d)p 47 3593 -26 4 v 31 w(y)12 b Fm(:)83 b(904)p 231 3606 125 4 v -1 -w(,)42 b(905,)e(906.)0 3694 y Fi(d)p 47 3694 26 4 v 31 -w(z)14 b Fm(:)83 b(904)p 227 3707 125 4 v -1 w(,)42 b(905,)f(906.)0 -3796 y Fi(dashe)l(d)14 b Fm(:)84 b(654)p 357 3809 V -2 -w(,)35 b(657,)e(658,)h(661,)f(664,)h(666,)f(669,)h(671,)166 -3896 y(674,)g(676,)g(705,)g(776,)f(802,)h(807,)g(813,)g(821,)g(824,)166 -3995 y(859,)39 b(861,)g(862,)g(863.)0 4097 y Fi(datestamp)10 -b Fm(:)83 b(43)p 480 4110 84 4 v(,)42 b(44.)0 4198 y -Ff(DBL_MAX)q Fm(:)84 b(16.)0 4300 y Fi(dd)14 b Fm(:)83 -b(1183)p 204 4313 167 4 v -2 w(.)0 4402 y Fi(ddashe)l(d)15 -b Fm(:)83 b(419)p 399 4415 125 4 v -2 w(,)33 b(420)p -579 4415 V -1 w(,)f(422)p 759 4415 V -1 w(,)h(423)p 940 -4415 V -2 w(,)g(425)p 1120 4415 V -2 w(,)g(426)p 1300 -4415 V -2 w(,)g(428)p 1480 4415 V -1 w(,)f(429)p 1660 -4415 V -1 w(,)166 4501 y(775)p 166 4514 V -1 w(,)j(776)p -349 4514 V -2 w(,)h(777)p 532 4514 V -2 w(,)g(778)p 715 -4514 V -2 w(,)f(780)p 897 4514 V -1 w(,)g(781)p 1080 -4514 V -1 w(,)g(784)p 1263 4514 V -1 w(,)g(785)p 1446 -4514 V -2 w(,)h(786)p 1629 4514 V -2 w(,)166 4601 y(787)p -166 4614 V -1 w(,)f(789)p 349 4614 V -2 w(,)h(790)p 532 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1776 V -2 w(,)g(807)p 3407 1776 V -1 w(,)g(824)p -3580 1776 V -2 w(,)g(830)p 3752 1776 V -1 w(,)2199 1862 -y(840)p 2199 1875 V -1 w(,)g(842)p 2372 1875 V -2 w(,)g(843,)f(844,)f -(847)p 2889 1875 V -1 w(,)i(849)p 3062 1875 V -1 w(,)g(857)p -3235 1875 V -2 w(,)g(859,)f(861,)f(862,)2199 1962 y(863,)h(864,)f(873)p -2544 1975 V -1 w(,)i(875)p 2717 1975 V -2 w(,)g(882)p -2889 1975 V -1 w(,)g(886,)f(897)p 3235 1975 V -2 w(,)h(900,)f(904)p -3580 1975 V -2 w(,)h(906,)2199 2062 y(912)p 2199 2075 -V -1 w(,)g(914,)e(949)p 2544 2075 V -1 w(,)i(954)p 2717 -2075 V -2 w(,)g(955,)f(957,)g(958,)f(959,)h(960,)f(961,)2199 -2161 y(963,)h(985)p 2372 2174 V -2 w(,)h(986,)f(988,)f(990,)h(991,)g -(992,)f(996)p 3407 2174 V -1 w(,)i(997,)e(999,)2199 2261 -y(1033)p 2199 2274 167 4 v -2 w(,)k(1034,)e(1036)p 2631 -2274 V -2 w(,)i(1037,)e(1127)p 3063 2274 V -2 w(,)i(1168)p -3279 2274 V -2 w(,)g(1176)p 3495 2274 V -2 w(,)g(1177,)2199 -2361 y(1178,)e(1179,)g(1180,)g(1182,)g(1183,)g(1184,)g(1185,)g(1186,) -2199 2460 y(1188,)g(1193)p 2415 2473 V -2 w(,)i(1259)p -2631 2473 V -2 w(,)g(1268)p 2847 2473 V -2 w(,)g(1284)p -3063 2473 V -2 w(,)g(1287)p 3279 2473 V -2 w(,)g(1290)p -3495 2473 V -2 w(,)g(1308)p 3711 2473 V -2 w(,)2199 2560 -y(1317)p 2199 2573 V -2 w(,)g(1344)p 2415 2573 V -2 w(,)g(1367)p -2631 2573 V -2 w(,)g(1370)p 2847 2573 V -2 w(,)g(1372)p -3063 2573 V -2 w(,)g(1380)p 3279 2573 V -2 w(,)g(1382,)e(1384)p -3711 2573 V -2 w(,)2199 2659 y(1385,)g(1387)p 2415 2672 -V -2 w(,)i(1388,)e(1390)p 2847 2672 V -2 w(,)i(1393)p -3063 2672 V -2 w(,)g(1396)p 3279 2672 V -2 w(,)g(1399)p -3495 2672 V -2 w(,)g(1420)p 3711 2672 V -2 w(,)2199 2759 -y(1443)p 2199 2772 V -2 w(,)g(1460)p 2415 2772 V -2 w(,)g(1461,)e(1474) -p 2847 2772 V -2 w(,)i(1476)p 3063 2772 V -2 w(,)g(1488)p -3279 2772 V -2 w(,)g(1490)p 3495 2772 V -2 w(,)g(1508)p -3711 2772 V -2 w(.)2033 2861 y Fi(de)l(cimal)14 b Fm(:)84 -b(96,)38 b(97)p 2569 2874 84 4 v -1 w(,)i(98)p 2715 2874 -V -1 w(,)g(99)p 2861 2874 V -1 w(.)2033 2964 y Fi(default)p 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w(.)2033 3971 y Ff(DEFAULT_NUMBER_O)o(F_P)o(OI)o(NTS)m -Fm(:)84 b(1103)p 3190 3984 167 4 v -2 w(,)34 b(1104)p -3413 3984 V -2 w(,)g(1109,)2199 4070 y(1110,)j(1111,)f(1242,)h(1244.) -2033 4172 y Fi(de\014ne)p 2250 4172 26 4 v 31 w(c)l(olor)p -2455 4172 V 31 w(mp)10 b Fm(:)83 b(105)p 2707 4185 125 -4 v -1 w(,)36 b(106)p 2891 4185 V -1 w(,)g(108.)2033 -4275 y Fi(delta)p 2209 4275 26 4 v 31 w(x)14 b Fm(:)83 -b(522)p 2394 4288 125 4 v -1 w(.)2033 4377 y Fi(delta)p -2209 4377 26 4 v 31 w(x)p 2279 4377 V 30 w(p)10 b Fm(:)83 -b(532)p 2462 4390 125 4 v -1 w(,)42 b(533.)2033 4479 -y Fi(delta)p 2209 4479 26 4 v 31 w(x)p 2279 4479 V 30 -w(q)12 b Fm(:)83 b(532)p 2460 4492 125 4 v -1 w(,)42 -b(534.)2033 4582 y Fi(delta)p 2209 4582 26 4 v 31 w(y)12 -b Fm(:)83 b(522)p 2393 4595 125 4 v -1 w(.)2033 4684 -y Fi(delta)p 2209 4684 26 4 v 31 w(y)p 2280 4684 V 31 -w(p)10 b Fm(:)83 b(532)p 2464 4697 125 4 v -1 w(,)42 -b(533.)2033 4786 y Fi(delta)p 2209 4786 26 4 v 31 w(y)p -2280 4786 V 31 w(q)12 b Fm(:)83 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v 32 w(midd)t(le)12 b Fm(:)83 b(1283)p 706 377 167 -4 v -2 w(,)38 b(1284)p 933 377 V -2 w(.)0 466 y Fi(diameter)p -321 466 26 4 v 32 w(of)p 420 466 V 31 w(hexagon)12 b -Fm(:)83 b(1487)p 852 479 167 4 v -2 w(.)0 567 y Fi(diameter)p -321 567 26 4 v 32 w(of)p 420 567 V 31 w(triangle)11 b -Fm(:)84 b(1442)p 838 580 167 4 v -2 w(,)32 b(1446)p 1059 -580 V -2 w(,)h(1473)p 1281 580 V -2 w(.)0 669 y Fi(diameter)p -321 669 26 4 v 32 w(outer)13 b Fm(:)83 b(1283)p 655 682 -167 4 v -2 w(,)29 b(1284)p 873 682 V -1 w(,)g(1287)p -1092 682 V -2 w(,)h(1289)p 1311 682 V -2 w(,)g(1290)p -1530 682 V -2 w(.)0 770 y Fi(diameter)p 321 770 26 4 -v 32 w(outer)p 541 770 V 30 w(end)13 b Fm(:)83 b(1286)p -812 783 167 4 v -2 w(,)36 b(1287)p 1037 783 V -2 w(.)0 -871 y Fi(diameter)p 321 871 26 4 v 32 w(outer)p 541 871 -V 30 w(start)12 b Fm(:)83 b(1286)p 851 884 167 4 v -2 -w(,)35 b(1287)p 1075 884 V -2 w(.)0 973 y Fi(digit)p -163 973 26 4 v 32 w(optind)14 b Fm(:)83 b(1508)p 536 -986 167 4 v -2 w(.)0 1074 y Fi(dihe)l(dr)l(al)p 284 1074 -26 4 v 33 w(angle)11 b Fm(:)83 b(1413,)38 b(1436)p 844 -1087 167 4 v -2 w(,)i(1437)p 1073 1087 V -2 w(,)g(1443,)e(1453)p -1531 1087 V -2 w(,)166 1174 y(1454)p 166 1187 V -2 w(,)e(1460,)e(1467)p -616 1187 V -2 w(,)h(1468)p 840 1187 V -2 w(,)h(1474.)0 -1275 y Fi(dir)14 b Fm(:)83 b(565)p 222 1288 125 4 v -1 -w(,)35 b(566)p 405 1288 V -1 w(,)g(567)p 588 1288 V -2 -w(,)h(568)p 771 1288 V -2 w(,)g(595)p 954 1288 V -2 w(,)f(596)p -1136 1288 V -1 w(.)0 1376 y Fi(dir)p 107 1376 26 4 v -31 w(x)14 b Fm(:)83 b(560)p 292 1389 125 4 v -1 w(,)39 -b(561)p 479 1389 V -2 w(,)g(562)p 665 1389 V -1 w(,)g(563)p -852 1389 V -1 w(.)0 1478 y Fi(dir)p 107 1478 26 4 v 31 -w(y)12 b Fm(:)83 b(560)p 291 1491 125 4 v -1 w(,)39 b(561)p -478 1491 V -1 w(,)g(562)p 665 1491 V -2 w(,)g(563)p 851 -1491 V -1 w(.)0 1579 y Fi(dir)p 107 1579 26 4 v 31 w(z)15 -b Fm(:)83 b(560)p 288 1592 125 4 v -2 w(,)40 b(561)p -475 1592 V -2 w(,)f(562)p 661 1592 V -1 w(,)g(563)p 848 -1592 V -2 w(.)0 1681 y Fi(dir)l(e)l(ction)12 b Fm(:)83 -b(556)p 430 1694 V -2 w(,)31 b(557,)f(559,)f(561,)h(570,)g(572,)f(574,) -h(577,)166 1780 y(593)p 166 1793 V -1 w(,)35 b(594,)f(596,)g(597,)f -(598,)h(600,)g(601,)g(605,)g(606,)166 1880 y(609,)39 -b(934,)f(999,)h(1188.)0 1981 y Fi(dir)l(e)l(ction)p 317 -1981 26 4 v 31 w(line)12 b Fm(:)83 b(1164)p 592 1994 -167 4 v -2 w(.)0 2083 y Fi(dir)l(e)l(ction)p 317 2083 -26 4 v 31 w(pt)13 b Fm(:)83 b(1164)p 532 2096 167 4 v --2 w(.)0 2184 y Fi(dir)l(e)l(ction)p 317 2184 26 4 v -31 w(ve)l(ctor)14 b Fm(:)83 b(644)p 678 2197 125 4 v --1 w(.)0 2285 y Ff(DISCLAIMER_3DLDF)n Fm(:)g(19)p 808 -2298 84 4 v -1 w(,)32 b(20)p 946 2298 V -1 w(,)h(1512,)e(1513.)0 -2387 y Fi(dist)13 b Fm(:)83 b(559,)29 b(560)p 426 2400 -125 4 v -1 w(,)i(561)p 605 2400 V -1 w(,)g(562)p 784 -2400 V -2 w(,)h(563)p 963 2400 V -2 w(,)f(565)p 1141 -2400 V -1 w(,)g(566)p 1320 2400 V -1 w(,)g(567)p 1499 -2400 V -2 w(,)h(568)p 1678 2400 V -2 w(,)166 2486 y(923,)e(924)p -345 2499 V -2 w(,)h(925)p 523 2499 V -1 w(,)g(926,)f(928,)f(929)p -1059 2499 V -1 w(,)i(930)p 1238 2499 V -1 w(,)g(1268)p -1417 2499 167 4 v -2 w(.)0 2588 y Fi(distanc)l(e)11 b -Fm(:)83 b(556)p 407 2601 125 4 v -1 w(,)42 b(559,)f(561,)f(570,)h(572,) -g(574,)g(578,)166 2687 y(617)p 166 2700 V -1 w(,)35 b(619,)f(620,)g -(623,)f(624,)h(626,)g(629,)g(635,)g(636,)166 2787 y(641,)g(644,)g(646,) -g(954)p 715 2800 V -2 w(,)h(957,)f(985)p 1080 2800 V --1 w(,)h(988,)f(996)p 1446 2800 V -2 w(,)i(997,)166 2887 -y(1177,)k(1444)p 397 2900 167 4 v -2 w(,)h(1445.)0 2988 -y Fi(do)p 89 2988 26 4 v 31 w(apply)14 b Fm(:)83 b(200)p -422 3001 125 4 v -2 w(,)32 b(312)p 601 3001 V -2 w(,)g(313)p -780 3001 V -2 w(,)g(314)p 959 3001 V -2 w(,)g(315)p 1138 -3001 V -2 w(,)g(317)p 1317 3001 V -2 w(,)g(318)p 1496 -3001 V -2 w(,)g(319)p 1675 3001 V -2 w(,)166 3088 y(320)p -166 3101 V -1 w(,)j(322)p 349 3101 V -2 w(,)h(323)p 532 -3101 V -2 w(,)g(324)p 715 3101 V -2 w(,)f(325)p 897 3101 -V -1 w(,)g(327)p 1080 3101 V -1 w(,)g(328)p 1263 3101 -V -1 w(,)g(329)p 1446 3101 V -2 w(,)h(330)p 1629 3101 -V -2 w(,)166 3187 y(332)p 166 3200 V -1 w(,)f(333)p 349 -3200 V -2 w(,)h(334)p 532 3200 V -2 w(,)g(335)p 715 3200 -V -2 w(,)f(337)p 897 3200 V -1 w(,)g(338)p 1080 3200 -V -1 w(,)g(339)p 1263 3200 V -1 w(,)g(340)p 1446 3200 -V -2 w(,)h(431)p 1629 3200 V -2 w(,)166 3287 y(432)p -166 3300 V -1 w(,)h(866)p 351 3300 V -2 w(,)h(867)p 536 -3300 V -2 w(,)f(1341)p 720 3300 167 4 v -2 w(,)h(1342)p -947 3300 V -2 w(.)0 3388 y Fi(do)p 89 3388 26 4 v 31 -w(half)24 b Fm(:)83 b(1448)p 375 3401 167 4 v -2 w(,)28 -b(1462)p 592 3401 V -2 w(,)g(1463)p 809 3401 V -2 w(,)f(1475)p -1025 3401 V -2 w(,)h(1476)p 1242 3401 V -2 w(,)g(1489)p -1459 3401 V -2 w(,)g(1490)p 1676 3401 V -2 w(.)0 3490 -y Fi(do)p 89 3490 26 4 v 31 w(help)p 263 3490 V 32 w(lines)12 -b Fm(:)83 b(427,)34 b(654)p 756 3503 125 4 v -2 w(,)i(655)p -939 3503 V -1 w(,)f(794.)0 3591 y Fi(do)p 89 3591 26 -4 v 31 w(inner)14 b Fm(:)83 b(1284)p 427 3604 167 4 v --2 w(.)0 3692 y Fi(do)p 89 3692 26 4 v 31 w(lab)l(els)12 -b Fm(:)84 b(209,)27 b(216)p 600 3705 125 4 v -2 w(,)i(219,)e(229,)g -(230,)g(249,)g(544,)g(553.)0 3794 y Ff(DO_LABELS)q Fm(:)83 -b(208)p 503 3807 V -2 w(,)32 b(209)p 682 3807 V -2 w(,)g(216,)d(462,)h -(830,)g(1123.)0 3895 y Fi(do)p 89 3895 26 4 v 31 w(midd)t(le)13 -b Fm(:)83 b(1284)p 474 3908 167 4 v -2 w(.)0 3996 y Fi(do)p -89 3996 26 4 v 31 w(output)12 b Fm(:)83 b(264)p 463 4009 -125 4 v -2 w(,)30 b(280,)d(283,)h(285,)g(287,)g(289,)g(300,)g(439,)166 -4096 y(441,)c(458,)f(552,)h(654)p 684 4109 V -2 w(,)h(657,)f(661,)g -(664,)f(666,)h(669,)f(671,)166 4196 y(674,)h(676,)h(853,)f(855,)h(857,) -f(1296)p 1033 4209 167 4 v -2 w(,)i(1299,)e(1300,)g(1302,)166 -4295 y(1304,)h(1308,)g(1376,)g(1378,)g(1416,)g(1418,)g(1420,)g(1422,) -166 4395 y(1440,)g(1443,)g(1457,)g(1460,)g(1471,)g(1474,)g(1485,)g -(1488.)0 4496 y Fi(do)p 89 4496 26 4 v 31 w(p)l(ersp)11 -b Fm(:)83 b(200)p 419 4509 125 4 v -2 w(,)32 b(312)p -598 4509 V -2 w(,)g(313)p 777 4509 V -1 w(,)f(314)p 956 -4509 V -1 w(,)g(315)p 1135 4509 V -1 w(,)h(317)p 1315 -4509 V -2 w(,)g(318)p 1494 4509 V -2 w(,)g(319)p 1673 -4509 V -2 w(,)166 4596 y(320)p 166 4609 V -1 w(,)j(322)p -349 4609 V -2 w(,)h(323)p 532 4609 V -2 w(,)g(324)p 715 -4609 V -2 w(,)f(325)p 897 4609 V -1 w(,)g(327)p 1080 -4609 V -1 w(,)g(328)p 1263 4609 V -1 w(,)g(329)p 1446 -4609 V -2 w(,)h(330)p 1629 4609 V -2 w(,)166 4696 y(332)p -166 4709 V -1 w(,)f(333)p 349 4709 V -2 w(,)h(334)p 532 -4709 V -2 w(,)g(335)p 715 4709 V -2 w(,)f(337)p 897 4709 -V -1 w(,)g(338)p 1080 4709 V -1 w(,)g(339)p 1263 4709 -V -1 w(,)g(340)p 1446 4709 V -2 w(,)h(431)p 1629 4709 -V -2 w(,)166 4795 y(432)p 166 4808 V -1 w(,)h(866)p 351 -4808 V -2 w(,)h(867)p 536 4808 V -2 w(,)f(1341)p 720 -4808 167 4 v -2 w(,)h(1342)p 947 4808 V -2 w(.)0 4897 -y Fi(do)p 89 4897 26 4 v 31 w(sort)13 b Fm(:)83 b(547)p -373 4910 125 4 v -2 w(.)0 4998 y Fi(do)p 89 4998 26 4 -v 31 w(tr)l(ansform)11 b Fm(:)83 b(549)p 584 5011 125 -4 v -1 w(,)31 b(1127,)d(1192)p 982 5011 167 4 v -2 w(,)j(1193)p -1202 5011 V -2 w(,)g(1194,)e(1195,)166 5098 y(1196,)i(1197,)g(1203,)g -(1204,)g(1213,)g(1214.)0 5199 y Fi(do)p 89 5199 26 4 -v 31 w(warnings)12 b Fm(:)83 b(253)p 556 5212 125 4 v --1 w(,)31 b(254)p 735 5212 V -2 w(,)h(547,)d(548)p 1092 -5212 V -1 w(,)i(551,)f(554)p 1450 5212 V -1 w(.)0 5300 -y Fk(Do)s(decahedron)5 b Fm(:)83 b(196,)35 b(1312,)g(1429,)g(1453)p -1346 5313 167 4 v -2 w(,)h(1454,)166 5400 y(1456,)i(1457)p -395 5413 V -2 w(,)h(1459,)f(1460)p 852 5413 V -2 w(,)h(1463,)f(1464,)f -(1465,)2199 263 y(1473,)42 b(1477.)2033 364 y Fi(dot)13 -b Fm(:)83 b(208)p 2264 377 125 4 v -2 w(,)32 b(461)p -2443 377 V -1 w(,)g(462)p 2623 377 V -2 w(,)g(463)p 2802 -377 V -1 w(,)g(464)p 2982 377 V -1 w(,)g(471,)e(472,)h(828,)f(829)p -3700 377 V -1 w(,)2199 464 y(830)p 2199 477 V -1 w(,)k(831)p -2381 477 V -1 w(,)g(832)p 2563 477 V -1 w(,)g(1122)p -2745 477 167 4 v -2 w(,)h(1123)p 2969 477 V -2 w(,)f(1124.)2033 -565 y Fi(dot)p 2150 565 26 4 v 31 w(pr)l(o)l(duct)12 -b Fm(:)83 b(498)p 2558 578 125 4 v -1 w(,)23 b(499)p -2729 578 V -2 w(,)h(504,)d(505,)h(605,)f(624,)h(634,)f(641.)2033 -666 y Fi(dotlab)l(el)14 b Fm(:)83 b(207,)32 b(209,)g(461,)g(465,)f(466) -p 3144 679 V -1 w(,)i(467)p 3325 679 V -1 w(,)g(468)p -3506 679 V -2 w(,)h(469)p 3687 679 V -2 w(,)2199 766 -y(828,)c(834)p 2378 779 V -2 w(,)h(835)p 2556 779 V -1 -w(,)g(836)p 2735 779 V -1 w(,)g(837)p 2914 779 V -2 w(,)g(949,)f(957,)g -(1124)p 3450 779 167 4 v -2 w(,)h(1179,)2199 865 y(1182,)25 -b(1184,)g(1219,)g(1268,)g(1284,)g(1287,)g(1290,)g(1420,)2199 -965 y(1451,)j(1461,)h(1465,)f(1474,)g(1476,)h(1478,)f(1488.)2033 -1066 y Fi(double)p 2264 1066 26 4 v 32 w(r)l(ows)11 b -Fm(:)83 b(1283)p 2570 1079 167 4 v -2 w(,)40 b(1284)p -2799 1079 V -2 w(.)2033 1167 y Fi(doubles)12 b Fm(:)83 -b(12,)42 b(138.)2033 1269 y Fi(dp)10 b Fm(:)83 b(16)p -2233 1282 84 4 v -1 w(.)2033 1370 y Fi(dr)l(aw)14 b Fm(:)83 -b(418,)37 b(419)p 2509 1383 125 4 v -1 w(,)h(420)p 2695 -1383 V -2 w(,)h(427,)e(775)p 3067 1383 V -2 w(,)i(776)p -3253 1383 V -2 w(,)g(777)p 3439 1383 V -2 w(,)g(778)p -3625 1383 V -2 w(,)2199 1469 y(779,)34 b(780)p 2382 1482 -V -2 w(,)i(781)p 2565 1482 V -2 w(,)g(785,)d(787,)h(794,)g(805,)g(858,) -g(949,)2199 1569 y(957,)28 b(1223,)g(1225,)g(1230,)f(1231,)h(1272,)g -(1276,)f(1284,)2199 1669 y(1287,)38 b(1290,)f(1383)p -2656 1682 167 4 v -2 w(,)j(1384)p 2885 1682 V -2 w(,)f(1443,)f(1451,)f -(1461,)2199 1768 y(1465,)g(1478,)f(1506,)h(1525.)2033 -1869 y Ff(DRAW)s Fm(:)83 b(199)p 2318 1882 125 4 v -2 -w(,)37 b(201)p 2502 1882 V -2 w(,)f(776,)f(859,)g(1382.)2033 -1971 y Fi(dr)l(aw)p 2208 1971 26 4 v 31 w(axes)12 b Fm(:)83 -b(924)p 2505 1984 125 4 v -2 w(,)35 b(925)p 2687 1984 -V -2 w(,)g(929)p 2869 1984 V -2 w(,)g(930)p 3051 1984 -V -2 w(,)g(957.)2033 2072 y Fi(dr)l(aw)p 2208 2072 26 -4 v 31 w(c)l(olor)15 b Fm(:)83 b(654)p 2529 2085 125 -4 v -2 w(,)27 b(657,)f(661,)g(664,)g(666,)g(669,)g(671,)f(674,)2199 -2171 y(676,)34 b(681,)g(685,)g(686,)f(687,)h(696,)g(698,)g(775,)g(776,) -2199 2271 y(802,)g(806,)g(807,)g(813,)f(821,)h(824,)g(859,)g(861,)g -(862,)2199 2371 y(863,)i(864,)g(869,)f(1382,)h(1385.)2033 -2472 y Fi(dr)l(aw)p 2208 2472 26 4 v 31 w(c)l(olor)p -2413 2472 V 32 w(inner)13 b Fm(:)83 b(1283)p 2751 2485 -167 4 v -2 w(,)38 b(1284)p 2978 2485 V -2 w(.)2033 2573 -y Fi(dr)l(aw)p 2208 2573 26 4 v 31 w(c)l(olor)p 2413 -2573 V 32 w(iter)13 b Fm(:)83 b(1388,)37 b(1390.)2033 -2674 y Fi(dr)l(aw)p 2208 2674 V 31 w(c)l(olor)p 2413 -2674 V 32 w(midd)t(le)12 b Fm(:)83 b(1283)p 2798 2687 -167 4 v -2 w(,)37 b(1284)p 3024 2687 V -2 w(.)2033 2775 -y Fi(dr)l(aw)p 2208 2775 26 4 v 31 w(c)l(olor)p 2413 -2775 V 32 w(outer)13 b Fm(:)83 b(1283)p 2747 2788 167 -4 v -2 w(,)37 b(1284)p 2973 2788 V -2 w(.)2033 2877 y -Fi(dr)l(aw)p 2208 2877 26 4 v 31 w(c)l(olor)p 2413 2877 -V 32 w(ptr)13 b Fm(:)83 b(1388,)37 b(1390)p 2892 2890 -167 4 v -2 w(.)2033 2978 y Fi(dr)l(aw)p 2208 2978 26 -4 v 31 w(c)l(olors)12 b Fm(:)83 b(1388,)35 b(1389)p 2786 -2991 167 4 v -2 w(,)i(1390)p 3012 2991 V -2 w(.)2033 -3079 y Fi(dr)l(aw)p 2208 3079 26 4 v 31 w(help)11 b Fm(:)83 -b(427,)38 b(428)p 2681 3092 125 4 v -2 w(,)i(429)p 2868 -3092 V -2 w(,)f(791,)f(793)p 3241 3092 V -1 w(,)h(794)p -3428 3092 V -2 w(,)h(795)p 3615 3092 V -2 w(,)2199 3179 -y(796)p 2199 3192 V -1 w(,)g(798)p 2387 3192 V -2 w(,)g(799)p -2574 3192 V -1 w(,)g(1451.)2033 3280 y Fi(dr)l(aw)p 2208 -3280 26 4 v 31 w(in)p 2311 3280 V 31 w(cir)l(cle)12 b -Fm(:)83 b(1049)p 2646 3293 167 4 v -2 w(,)33 b(1050)p -2868 3293 V -2 w(,)g(1272)p 3090 3293 V -2 w(,)g(1273)p -3312 3293 V -2 w(.)2033 3381 y Fi(dr)l(aw)p 2208 3381 -26 4 v 31 w(in)p 2311 3381 V 31 w(el)t(lipse)12 b Fm(:)84 -b(1098)p 2679 3394 167 4 v -2 w(,)38 b(1231)p 2906 3394 -V -2 w(.)2033 3482 y Fi(dr)l(aw)p 2208 3482 26 4 v 31 -w(in)p 2311 3482 V 31 w(r)l(e)l(ctangle)11 b Fm(:)83 -b(1224)p 2771 3495 167 4 v -2 w(,)37 b(1225)p 2997 3495 -V -2 w(.)2033 3583 y Fi(dr)l(aw)p 2208 3583 26 4 v 31 -w(net)12 b Fm(:)83 b(1450)p 2465 3596 167 4 v -2 w(,)30 -b(1451)p 2684 3596 V -2 w(,)g(1464)p 2903 3596 V -2 w(,)f(1465)p -3121 3596 V -2 w(,)h(1477)p 3340 3596 V -2 w(,)g(1478)p -3559 3596 V -2 w(.)2033 3685 y Fi(dr)l(aw)p 2208 3685 -26 4 v 31 w(out)p 2354 3685 V 30 w(cir)l(cle)12 b Fm(:)83 -b(1053)p 2688 3698 167 4 v -2 w(,)33 b(1054)p 2910 3698 -V -2 w(,)f(1276)p 3131 3698 V -2 w(,)g(1277)p 3352 3698 -V -2 w(.)2033 3786 y Fi(dr)l(aw)p 2208 3786 26 4 v 31 -w(out)p 2354 3786 V 30 w(el)t(lipse)13 b Fm(:)83 b(1097)p -2721 3799 167 4 v -2 w(,)38 b(1230)p 2948 3799 V -2 w(.)2033 -3887 y Fi(dr)l(aw)p 2208 3887 26 4 v 31 w(out)p 2354 -3887 V 30 w(r)l(e)l(ctangle)11 b Fm(:)83 b(1222)p 2813 -3900 167 4 v -2 w(,)37 b(1223)p 3039 3900 V -2 w(.)2033 -3988 y Fi(dr)l(awarr)l(ow)15 b Fm(:)83 b(422)p 2529 4001 -125 4 v -2 w(,)38 b(423)p 2714 4001 V -2 w(,)g(654,)d(784)p -3083 4001 V -1 w(,)i(785)p 3268 4001 V -1 w(,)g(786)p -3453 4001 V -1 w(,)g(787)p 3638 4001 V -2 w(,)2199 4088 -y(789)p 2199 4101 V -1 w(,)j(790)p 2387 4101 V -1 w(,)g(856,)g(928.) -2033 4189 y Ff(DRAWDOT)q Fm(:)84 b(199)p 2449 4202 V --2 w(,)38 b(201)p 2634 4202 V -2 w(,)g(411,)e(458.)2033 -4290 y Fi(dr)l(awdot)13 b Fm(:)83 b(409,)29 b(410)p 2612 -4303 V -1 w(,)h(411)p 2790 4303 V -1 w(,)g(412)p 2968 -4303 V -1 w(,)g(413)p 3146 4303 V -1 w(,)g(465,)f(1451.)2033 -4391 y Fi(dr)l(awdot)p 2320 4391 26 4 v 32 w(c)l(olor)14 -b Fm(:)83 b(264)p 2641 4404 125 4 v -1 w(,)28 b(300,)f(302,)g(409,)g -(411,)g(415,)g(458.)2033 4492 y Fi(dr)l(awdot)p 2320 -4492 26 4 v 32 w(value)11 b Fm(:)83 b(264)p 2648 4505 -125 4 v -2 w(,)29 b(300,)e(302,)g(409,)g(411,)g(415,)f(458.)2033 -4594 y Fe(e)p Fm(:)83 b(644)p 2178 4607 V -2 w(,)33 b(904)p -2358 4607 V -1 w(,)g(1112)p 2539 4607 167 4 v -2 w(,)g(1114)p -2761 4607 V -2 w(,)g(1115)p 2983 4607 V -2 w(,)g(1116)p -3205 4607 V -2 w(,)g(1117)p 3427 4607 V -2 w(,)g(1119)p -3649 4607 V -2 w(,)2199 4693 y(1120)p 2199 4706 V -2 -w(,)27 b(1127)p 2415 4706 V -2 w(,)g(1165)p 2631 4706 -V -2 w(,)g(1166)p 2847 4706 V -2 w(,)g(1175)p 3063 4706 -V -2 w(,)g(1176)p 3279 4706 V -2 w(,)g(1189)p 3495 4706 -V -2 w(,)g(1228)p 3711 4706 V -2 w(,)2199 4793 y(1229)p -2199 4806 V -2 w(,)33 b(1230)p 2421 4806 V -2 w(,)g(1231)p -2643 4806 V -2 w(,)g(1243)p 2865 4806 V -2 w(,)g(1255)p -3087 4806 V -2 w(,)g(1256)p 3309 4806 V -2 w(.)2033 4894 -y Fi(e)p 2076 4894 26 4 v 31 w(axis)p 2247 4894 V 31 -w(h)11 b Fm(:)83 b(1256)p 2432 4907 167 4 v -2 w(.)2033 -4995 y Fi(e)p 2076 4995 26 4 v 31 w(axis)p 2247 4995 -V 31 w(orientation)11 b Fm(:)83 b(1178)p 2789 5008 167 -4 v -2 w(,)34 b(1179,)e(1183.)2033 5096 y Fi(e)p 2076 -5096 26 4 v 31 w(axis)p 2247 5096 V 31 w(orientation)p -2677 5096 V 31 w(r)l(otate)l(d)13 b Fm(:)83 b(1178)p -3069 5109 167 4 v -2 w(,)31 b(1179,)d(1183.)2033 5198 -y Fi(e)p 2076 5198 26 4 v 31 w(axis)p 2247 5198 V 31 -w(v)13 b Fm(:)83 b(1256)p 2430 5211 167 4 v -2 w(.)2033 -5299 y Fi(e)p 2076 5299 26 4 v 31 w(c)l(enter)13 b Fm(:)83 -b(1182)p 2441 5312 167 4 v -2 w(,)41 b(1183.)2033 5400 -y Fi(e)p 2076 5400 26 4 v 31 w(plane)11 b Fm(:)83 b(1176)p -2409 5413 167 4 v -2 w(,)39 b(1177,)e(1188.)p eop end -%%Page: 494 494 -TeXDict begin 494 493 bop 0 83 a Fm(494)140 b Fl(INDEX)2670 -b(3DLDFPR)n(G)142 b Fn(x)p Fm(1525)0 263 y Fi(e)p 43 -263 26 4 v 31 w(x)13 b Fm(:)84 b(904)p 228 276 125 4 -v -2 w(,)45 b(906.)0 366 y Fi(e)p 43 366 26 4 v 31 w(y)12 -b Fm(:)83 b(904)p 227 379 125 4 v -2 w(,)42 b(905,)f(906.)0 -470 y Fi(e)p 43 470 26 4 v 31 w(z)14 b Fm(:)83 b(904)p -223 483 125 4 v -1 w(,)42 b(905,)f(906.)0 573 y Fi(e)l(dge)p -157 573 26 4 v 31 w(r)l(adius)12 b Fm(:)83 b(1431)p 520 -586 167 4 v -2 w(,)32 b(1440,)e(1443,)g(1457,)h(1460,)f(1471,)166 -673 y(1474,)40 b(1485,)f(1488.)0 776 y Fi(e)l(dges)12 -b Fm(:)83 b(1405)p 304 789 V -2 w(,)32 b(1416,)e(1418,)f(1420,)h(1440,) -g(1443,)g(1457,)166 876 y(1460,)k(1471,)g(1474,)f(1485,)h(1488.)0 -979 y Fi(elements)11 b Fm(:)83 b(438,)30 b(440,)f(442,)h(453)p -965 992 125 4 v -2 w(,)h(549)p 1143 992 V -1 w(,)g(550,)f(551,)f(552,) -166 1079 y(839,)39 b(852,)g(854,)g(856)p 730 1092 V -1 -w(.)0 1182 y Ff(ELLIPSE)q Fm(:)84 b(1296)p 416 1195 167 -4 v -2 w(,)21 b(1297)p 626 1195 V -2 w(,)g(1316,)f(1317,)f(1329,)g -(1330,)h(1334.)0 1285 y Fk(Ellipse)s Fm(:)83 b(33)p 388 -1298 84 4 v -1 w(,)36 b(290,)f(644,)g(1094,)f(1095,)h(1096,)f(1097,)166 -1385 y(1098,)25 b(1103)p 382 1398 167 4 v -2 w(,)i(1104,)e(1106,)g -(1107)p 1030 1398 V -2 w(,)i(1109,)e(1110)p 1462 1398 -V -2 w(,)i(1112,)166 1485 y(1114,)e(1115,)g(1116,)g(1117,)g(1118,)g -(1119,)g(1120,)g(1123,)166 1584 y(1124,)g(1127,)g(1130,)g(1132,)g -(1133,)g(1134,)g(1137,)g(1140,)166 1684 y(1142,)g(1145,)g(1147,)g -(1149,)g(1151,)g(1152,)g(1155,)g(1157,)166 1784 y(1160,)g(1162,)g -(1164,)g(1165,)g(1166,)g(1167,)g(1168,)g(1171,)166 1883 -y(1173,)g(1174,)g(1175,)g(1176,)g(1178,)g(1179,)g(1182,)g(1189,)166 -1983 y(1192,)g(1193,)g(1195,)g(1196,)g(1197,)g(1199,)g(1201,)g(1203,) -166 2082 y(1204,)g(1206,)g(1209,)g(1211,)g(1213,)g(1214,)g(1216,)g -(1219,)166 2182 y(1221,)g(1223,)g(1225,)g(1226,)g(1228,)g(1229,)g -(1230,)g(1231,)166 2282 y(1237,)g(1243,)g(1251,)g(1253,)g(1254,)g -(1255,)g(1256,)g(1262,)166 2381 y(1264,)g(1266,)g(1268,)g(1296,)g -(1302,)g(1308,)g(1312,)g(1320,)166 2481 y(1321,)g(1329,)g(1342,)g -(1344,)g(1347,)g(1349,)g(1365,)g(1367,)166 2581 y(1379,)g(1380,)g -(1384,)g(1387,)g(1390,)g(1393,)g(1396,)g(1399.)0 2684 -y Fi(el)t(lipse)p 228 2684 26 4 v 32 w(pt0)16 b Fm(:)83 -b(1182)p 489 2697 167 4 v -1 w(.)0 2787 y Fi(el)t(lipse)p -228 2787 26 4 v 32 w(pt4)16 b Fm(:)83 b(1182)p 489 2800 -167 4 v -1 w(.)0 2891 y Fk(Ellipses)r Fm(:)g(1120,)34 -b(1175,)f(1178,)g(1179.)0 2994 y Fi(el)t(lipses)13 b -Fm(:)83 b(1296)p 376 3007 V -2 w(,)28 b(1302,)e(1308,)g(1316,)f(1317,)h -(1321,)g(1329,)166 3094 y(1330,)f(1342,)g(1344,)g(1347,)g(1349,)g -(1365,)g(1367,)g(1379,)166 3193 y(1380,)g(1382,)g(1384,)g(1385,)g -(1387,)g(1388,)g(1390,)g(1391,)166 3293 y(1393,)34 b(1394,)g(1396,)f -(1397,)h(1399.)0 3396 y Fi(El)t(lipsoid)16 b Fm(:)83 -b(1296.)0 3500 y Fi(end)13 b Fm(:)83 b(249,)30 b(543,)g(545,)g(546,)f -(549,)h(550,)g(552,)g(553,)g(657,)166 3599 y(659,)24 -b(685,)f(734,)h(739,)f(741,)h(743,)g(765,)f(766,)h(770,)f(771,)166 -3699 y(830,)34 b(840,)g(843,)g(864,)f(867,)h(881)p 1080 -3712 125 4 v -1 w(,)h(882)p 1263 3712 V -1 w(,)g(883,)f(884,)166 -3799 y(885,)e(886,)g(898,)f(900,)h(914,)g(988,)g(990,)f(997,)h(1123,) -166 3898 y(1127,)25 b(1259,)g(1287,)g(1290,)g(1302,)g(1308,)g(1342,)g -(1344,)166 3998 y(1347,)g(1349,)g(1365,)g(1367,)g(1380,)g(1382,)g -(1384,)g(1385,)166 4097 y(1387,)g(1388,)g(1390,)g(1393,)g(1396,)g -(1399,)g(1418,)g(1424,)166 4197 y(1433,)31 b(1461,)g(1465,)g(1474,)g -(1478,)g(1488.)0 4300 y Fi(end\014g)12 b Fm(:)83 b(49)p -330 4313 84 4 v -1 w(,)41 b(50)p 477 4313 V -1 w(,)h(1506.)0 -4404 y Fi(end)t(l)14 b Fm(:)83 b(44,)30 b(46,)f(48,)h(50,)g(85,)g(87,)g -(89,)g(91,)g(93,)g(148,)f(151,)166 4503 y(153,)24 b(182,)f(183,)h(185,) -f(186,)h(249,)g(318,)f(346,)h(380,)f(382,)166 4603 y(383,)h(385,)f -(387,)h(388,)f(400,)h(401,)g(405,)f(434,)h(446,)f(448,)166 -4703 y(452,)h(464,)f(519,)h(521,)f(522,)h(536,)g(537,)f(538,)h(541,)f -(548,)166 4802 y(551,)h(552,)f(561,)h(572,)f(574,)h(603,)g(605,)f(606,) -h(609,)f(641,)166 4902 y(646,)h(776,)f(802,)h(807,)f(824,)h(840,)g -(842,)f(843,)h(844,)f(847,)166 5001 y(849,)34 b(867,)g(886,)g(898,)f -(906,)h(914,)g(922,)g(927,)g(949,)166 5101 y(957,)g(958,)g(960,)g(961,) -f(962,)h(963,)g(968,)g(989,)g(990,)166 5201 y(996,)28 -b(1110,)g(1127,)g(1145,)f(1147,)h(1173,)g(1176,)f(1179,)166 -5300 y(1183,)e(1184,)g(1185,)g(1186,)g(1188,)g(1193,)g(1228,)g(1229,) -166 5400 y(1259,)g(1268,)g(1284,)g(1287,)g(1290,)g(1308,)g(1317,)g -(1330,)2199 263 y(1342,)g(1370,)g(1372,)g(1382,)g(1385,)g(1388,)g -(1433,)g(1444,)2199 363 y(1488,)31 b(1508,)g(1512,)g(1513,)g(1515,)g -(1516.)2033 466 y Fi(epicycloid)p 2389 466 26 4 v 34 -w(p)l(attern)p 2679 466 V 30 w(1)16 b Fm(:)83 b(1286)p -2868 479 167 4 v -2 w(,)33 b(1287)p 3090 479 V -2 w(,)g(1288.)2033 -569 y Fi(epicycloid)p 2389 569 26 4 v 34 w(p)l(attern)p -2679 569 V 30 w(3)16 b Fm(:)83 b(1286,)31 b(1289)p 3090 -582 167 4 v -2 w(,)i(1290)p 3312 582 V -2 w(.)2033 672 -y Fi(eps)12 b Fm(:)83 b(137)p 2265 685 125 4 v -2 w(,)32 -b(151)p 2444 685 V -1 w(,)g(153)p 2624 685 V -2 w(,)g(156)p -2803 685 V -1 w(,)g(161)p 2983 685 V -2 w(,)g(162,)f(163,)g(164,)f(305) -p 3701 685 V -1 w(,)2199 772 y(401)p 2199 785 V -1 w(,)j(405)p -2380 785 V -1 w(,)h(515,)e(516,)g(517)p 2924 785 V -1 -w(,)i(521,)e(522.)2033 875 y Fi(epsilon)12 b Fm(:)83 -b(15,)38 b(24,)g(135,)f(136,)g(137,)g(138)p 3248 888 -V -1 w(,)h(139,)g(150,)2199 974 y(151,)c(153,)g(156,)g(161,)f(305,)h -(308)p 3113 987 V -1 w(,)h(401,)f(405,)g(498,)2199 1074 -y(499,)g(515,)g(517,)g(606,)f(624,)h(633,)g(634,)g(948,)g(949,)2199 -1174 y(996,)28 b(1082,)g(1083,)g(1126,)f(1127,)h(1167,)g(1168,)f(1177,) -2199 1273 y(1193,)37 b(1256,)f(1258,)h(1259.)2033 1376 -y Fi(er)l(ase)11 b Fm(:)83 b(43.)2033 1480 y Fi(exchange)p -2360 1480 26 4 v 31 w(x)p 2430 1480 V 30 w(z)15 b Fm(:)83 -b(904)p 2610 1493 125 4 v -2 w(,)41 b(906.)2033 1583 -y Fi(exchange)p 2360 1583 26 4 v 31 w(y)p 2431 1583 V -31 w(z)15 b Fm(:)83 b(904)p 2612 1596 125 4 v -2 w(.)2033 -1686 y Fi(exit)12 b Fm(:)83 b(1508,)38 b(1515,)h(1516.)2033 -1789 y Fi(extr)l(act)11 b Fm(:)83 b(200)p 2394 1802 V --1 w(,)35 b(442)p 2577 1802 V -2 w(,)g(443)p 2759 1802 -V -2 w(,)g(457,)e(549,)g(839)p 3305 1802 V -1 w(,)h(840)p -3487 1802 V -1 w(,)h(841,)2199 1889 y(856,)j(1364)p 2386 -1902 167 4 v -2 w(,)h(1365)p 2614 1902 V -2 w(,)g(1379.)2033 -1992 y Fi(extr)l(emes)10 b Fm(:)83 b(549,)39 b(550)p -2651 2005 125 4 v -2 w(,)h(551.)2033 2095 y Fe(f)9 b -Fm(:)83 b(16)p 2189 2108 84 4 v -1 w(,)29 b(200)p 2324 -2108 125 4 v -2 w(,)g(210)p 2500 2108 V -1 w(,)g(253)p -2677 2108 V -2 w(,)h(312)p 2854 2108 V -2 w(,)f(313)p -3030 2108 V -1 w(,)g(314)p 3207 2108 V -2 w(,)g(315)p -3383 2108 V -1 w(,)g(317)p 3560 2108 V -2 w(,)h(318)p -3737 2108 V -2 w(,)2199 2194 y(319)p 2199 2207 V -1 w(,)35 -b(320)p 2382 2207 V -2 w(,)h(322)p 2565 2207 V -2 w(,)g(323)p -2748 2207 V -2 w(,)f(324)p 2930 2207 V -1 w(,)g(325)p -3113 2207 V -1 w(,)g(327)p 3296 2207 V -1 w(,)g(328)p -3479 2207 V -2 w(,)h(329)p 3662 2207 V -2 w(,)2199 2294 -y(330)p 2199 2307 V -1 w(,)f(332)p 2382 2307 V -2 w(,)h(333)p -2565 2307 V -2 w(,)g(334)p 2748 2307 V -2 w(,)f(335)p -2930 2307 V -1 w(,)g(337)p 3113 2307 V -1 w(,)g(338)p -3296 2307 V -1 w(,)g(339)p 3479 2307 V -2 w(,)h(340)p -3662 2307 V -2 w(,)2199 2394 y(398)p 2199 2407 V -1 w(,)f(399)p -2382 2407 V -2 w(,)h(402)p 2565 2407 V -2 w(,)g(431)p -2748 2407 V -2 w(,)f(432)p 2930 2407 V -1 w(,)g(442)p -3113 2407 V -1 w(,)g(443)p 3296 2407 V -1 w(,)g(472)p -3479 2407 V -2 w(,)h(548)p 3662 2407 V -2 w(,)2199 2493 -y(563)p 2199 2506 V -1 w(,)f(566)p 2382 2506 V -2 w(,)h(568)p -2565 2506 V -2 w(,)g(570)p 2748 2506 V -2 w(,)f(636)p -2930 2506 V -1 w(,)g(742)p 3113 2506 V -1 w(,)g(743)p -3296 2506 V -1 w(,)g(839)p 3479 2506 V -2 w(,)h(840)p -3662 2506 V -2 w(,)2199 2593 y(866)p 2199 2606 V -1 w(,)e(867)p -2381 2606 V -2 w(,)g(1341)p 2562 2606 167 4 v -2 w(,)g(1342)p -2785 2606 V -2 w(,)g(1364)p 3008 2606 V -2 w(,)g(1365)p -3231 2606 V -2 w(.)2033 2696 y Fi(fabs)12 b Fm(:)83 b(135,)29 -b(137,)h(151,)f(153,)g(156,)h(162,)f(163,)g(164,)g(183,)2199 -2796 y(305,)34 b(401,)g(405,)g(499,)f(516,)h(521,)g(522,)g(605,)g(624,) -2199 2895 y(634,)24 b(636,)h(949,)f(968,)h(996,)f(1083,)g(1127,)g -(1134,)g(1168,)2199 2995 y(1177,)31 b(1183,)g(1193,)g(1256,)g(1258,)g -(1259.)2033 3098 y Fi(fac)l(e)p 2177 3098 26 4 v 32 w(r)l(adius)11 -b Fm(:)83 b(1431)p 2540 3111 167 4 v -2 w(,)33 b(1440,)e(1443,)g(1457,) -g(1460,)g(1471,)2199 3198 y(1474,)40 b(1485,)f(1488.)2033 -3301 y Fi(fac)l(es)12 b Fm(:)83 b(1405)p 2324 3314 V --2 w(,)33 b(1416,)d(1418,)h(1420,)f(1440,)h(1443,)g(1457,)2199 -3400 y(1460,)j(1471,)g(1474,)f(1485,)h(1488.)2033 3504 -y Fi(factor)14 b Fm(:)83 b(200)p 2363 3517 125 4 v -1 -w(,)26 b(210)p 2537 3517 V -1 w(,)g(253)p 2711 3517 V --2 w(,)g(254)p 2884 3517 V -1 w(,)g(304)p 3058 3517 V --2 w(,)h(305)p 3232 3517 V -2 w(,)f(312)p 3405 3517 V --1 w(,)g(313)p 3579 3517 V -2 w(,)g(314)p 3752 3517 V --1 w(,)2199 3603 y(315)p 2199 3616 V -1 w(,)f(317)p 2372 -3616 V -2 w(,)g(318)p 2544 3616 V -1 w(,)g(319)p 2717 -3616 V -2 w(,)g(320)p 2889 3616 V -1 w(,)g(322)p 3062 -3616 V -1 w(,)g(323)p 3235 3616 V -2 w(,)g(324)p 3407 -3616 V -1 w(,)g(325)p 3580 3616 V -2 w(,)g(327)p 3752 -3616 V -1 w(,)2199 3703 y(328)p 2199 3716 V -1 w(,)g(329)p -2372 3716 V -2 w(,)g(330)p 2544 3716 V -1 w(,)g(332)p -2717 3716 V -2 w(,)g(333)p 2889 3716 V -1 w(,)g(334)p -3062 3716 V -1 w(,)g(335)p 3235 3716 V -2 w(,)g(337)p -3407 3716 V -1 w(,)g(338)p 3580 3716 V -2 w(,)g(339)p -3752 3716 V -1 w(,)2199 3802 y(340)p 2199 3815 V -1 w(,)g(398)p -2372 3815 V -2 w(,)g(399)p 2544 3815 V -1 w(,)g(400,)e(402)p -2889 3815 V -1 w(,)i(403)p 3062 3815 V -1 w(,)g(431)p -3235 3815 V -2 w(,)g(432)p 3407 3815 V -1 w(,)g(442)p -3580 3815 V -2 w(,)g(443)p 3752 3815 V -1 w(,)2199 3902 -y(472)p 2199 3915 V -1 w(,)g(516,)e(517)p 2544 3915 V --1 w(,)i(548)p 2717 3915 V -2 w(,)g(549,)f(553,)g(554)p -3235 3915 V -2 w(,)h(742)p 3407 3915 V -1 w(,)g(743)p -3580 3915 V -2 w(,)g(839)p 3752 3915 V -1 w(,)2199 4002 -y(840)p 2199 4015 V -1 w(,)g(866)p 2372 4015 V -1 w(,)h(867)p -2546 4015 V -2 w(,)g(967)p 2719 4015 V -1 w(,)g(968)p -2893 4015 V -2 w(,)g(1341)p 3066 4015 167 4 v -2 w(,)g(1342)p -3281 4015 V -2 w(,)g(1364)p 3496 4015 V -2 w(,)g(1365)p -3711 4015 V -2 w(.)2033 4105 y Fi(false)12 b Fm(:)83 -b(17,)27 b(47,)g(49,)h(59,)f(61,)g(64,)g(65,)h(66,)f(69,)g(71,)h(72,)f -(74,)2199 4204 y(97,)32 b(98,)f(99,)h(141,)f(143,)g(159,)g(161,)g(174,) -g(182,)g(187,)2199 4304 y(188,)24 b(209,)f(216,)h(229,)f(248,)h(269,)g -(273,)f(274,)h(280,)f(283,)2199 4404 y(287,)h(346,)f(350,)h(351,)f -(356,)h(357,)g(380,)f(395,)h(399,)f(401,)2199 4503 y(405,)h(409,)f -(411,)h(419,)f(420,)h(431,)g(432,)f(437,)h(439,)f(443,)2199 -4603 y(446,)h(448,)f(452,)h(458,)f(461,)h(462,)g(463,)f(464,)h(472,)f -(505,)2199 4703 y(507,)h(508,)f(517,)h(518,)f(521,)h(527,)g(529,)f -(530,)h(541,)f(546,)2199 4802 y(548,)h(549,)f(550,)h(552,)f(561,)h -(573,)g(603,)f(605,)h(607,)f(637,)2199 4902 y(641,)h(644,)f(658,)h -(661,)f(664,)h(666,)g(669,)f(671,)h(674,)f(676,)2199 -5001 y(678,)h(681,)f(683,)h(685,)f(687,)h(726,)g(743,)f(749,)h(750,)f -(775,)2199 5101 y(776,)h(777,)f(794,)h(802,)f(807,)h(824,)g(829,)f -(830,)h(831,)f(840,)2199 5201 y(842,)h(843,)f(844,)h(847,)f(849,)h -(853,)g(857,)f(868,)h(872,)f(873,)2199 5300 y(874,)34 -b(875,)g(881,)g(882,)f(897,)h(904,)g(906,)g(911,)g(912,)2199 -5400 y(920,)g(928,)g(943,)g(944,)f(945,)h(948,)g(949,)g(952,)g(954,)p -eop end -%%Page: 495 495 -TeXDict begin 495 494 bop 0 83 a Fn(x)p Fm(1525)139 b -Fl(3DLDFPR)n(G)2671 b(INDEX)141 b Fm(495)166 263 y(961,)28 -b(968,)f(985,)h(988,)f(996,)h(999,)g(1030,)f(1033,)g(1036,)166 -363 y(1040,)e(1042,)g(1062,)g(1065,)g(1070,)g(1075,)g(1077,)g(1083,)166 -462 y(1107,)g(1110,)g(1122,)g(1123,)g(1126,)g(1127,)g(1130,)g(1132,)166 -562 y(1163,)g(1168,)g(1175,)g(1176,)g(1179,)g(1188,)g(1192,)g(1193,)166 -662 y(1196,)g(1197,)g(1203,)g(1204,)g(1213,)g(1214,)g(1240,)g(1243,)166 -761 y(1248,)g(1258,)g(1259,)g(1267,)g(1268,)g(1284,)g(1287,)g(1290,)166 -861 y(1299,)g(1300,)g(1302,)g(1308,)g(1317,)g(1344,)g(1367,)g(1370,)166 -960 y(1372,)g(1376,)g(1380,)g(1382,)g(1384,)g(1385,)g(1387,)g(1388,)166 -1060 y(1390,)g(1393,)g(1396,)g(1399,)g(1416,)g(1418,)g(1420,)g(1440,) -166 1160 y(1443,)g(1457,)g(1460,)g(1462,)g(1464,)g(1471,)g(1474,)g -(1475,)166 1259 y(1476,)31 b(1485,)g(1488,)g(1489,)g(1490,)g(1508.)0 -1361 y Fi(\016l)t(l)p 124 1361 26 4 v 31 w(c)l(olor)15 -b Fm(:)83 b(801)p 445 1374 125 4 v -2 w(,)40 b(802)p -632 1374 V -1 w(,)g(803)p 820 1374 V -1 w(,)g(804)p 1008 -1374 V -2 w(,)g(805,)f(806)p 1383 1374 V -1 w(,)h(807)p -1571 1374 V -2 w(,)166 1461 y(808)p 166 1474 V -1 w(,)45 -b(809)p 359 1474 V -1 w(.)0 1563 y Fi(\014g)p 90 1563 -26 4 v 30 w(num)10 b Fm(:)83 b(39)p 391 1576 84 4 v -1 -w(,)40 b(40)p 537 1576 V -1 w(,)g(48,)f(50.)0 1665 y -Fi(\014l)t(l)13 b Fm(:)83 b(553,)30 b(801)p 391 1678 -125 4 v -2 w(,)h(802)p 569 1678 V -1 w(,)g(803)p 748 -1678 V -2 w(,)g(804)p 926 1678 V -1 w(,)f(805,)g(969,)f(970,)h(1284,) -166 1764 y(1385,)40 b(1386)p 397 1777 167 4 v -2 w(,)h(1387)p -627 1777 V -2 w(.)0 1866 y Ff(FILL)s Fm(:)83 b(199)p -285 1879 125 4 v -2 w(,)37 b(201)p 469 1879 V -2 w(,)f(802,)f(859,)g -(1385.)0 1968 y Fi(\014l)t(l)p 98 1968 26 4 v 31 w(c)l(olor)14 -b Fm(:)83 b(654)p 418 1981 125 4 v -1 w(,)31 b(657,)g(661,)f(664,)g -(666,)g(669,)g(671,)g(674,)166 2068 y(676,)k(681,)g(685,)g(686,)f(687,) -h(701,)g(703,)g(775,)g(776,)166 2168 y(801,)g(802,)g(806,)g(807,)f -(813,)h(821,)g(824,)g(859,)g(864,)166 2267 y(869,)41 -b(1284,)f(1385.)0 2369 y Fi(\014l)t(l)p 98 2369 26 4 -v 31 w(c)l(olor)p 303 2369 V 31 w(inner)14 b Fm(:)83 -b(1283)p 641 2382 167 4 v -2 w(,)38 b(1284)p 868 2382 -V -2 w(.)0 2471 y Fi(\014l)t(l)p 98 2471 26 4 v 31 w(c)l(olor)p -303 2471 V 31 w(iter)14 b Fm(:)83 b(1388,)37 b(1390.)0 -2573 y Fi(\014l)t(l)p 98 2573 V 31 w(c)l(olor)p 303 2573 -V 31 w(midd)t(le)13 b Fm(:)83 b(1283)p 688 2586 167 4 -v -2 w(,)38 b(1284)p 915 2586 V -2 w(.)0 2675 y Fi(\014l)t(l)p -98 2675 26 4 v 31 w(c)l(olor)p 303 2675 V 31 w(outer)13 -b Fm(:)84 b(1283)p 637 2688 167 4 v -2 w(,)38 b(1284)p -864 2688 V -2 w(.)0 2777 y Fi(\014l)t(l)p 98 2777 26 -4 v 31 w(c)l(olor)p 303 2777 V 31 w(ptr)14 b Fm(:)83 -b(1388,)37 b(1390)p 782 2790 167 4 v -2 w(.)0 2879 y -Fi(\014l)t(l)p 98 2879 26 4 v 31 w(c)l(olors)12 b Fm(:)83 -b(1388,)36 b(1389)p 677 2892 167 4 v -2 w(,)i(1390)p -904 2892 V -2 w(.)0 2981 y Fi(\014l)t(l)p 98 2981 26 -4 v 31 w(dr)l(aw)p 299 2981 V 31 w(value)11 b Fm(:)83 -b(654)p 626 2994 125 4 v -1 w(,)30 b(657,)f(661,)f(664,)h(666,)f(669,)h -(671,)166 3081 y(674,)34 b(676,)g(681,)g(693,)f(776,)h(802,)g(807,)g -(813,)g(821,)166 3180 y(824,)e(859,)h(861,)f(862,)g(863,)h(866,)f(867.) -0 3282 y Fi(\014l)t(l)p 98 3282 26 4 v 31 w(out)p 244 -3282 V 30 w(el)t(lipse)12 b Fm(:)83 b(1226.)0 3384 y -Fi(\014l)t(ldr)l(aw)14 b Fm(:)83 b(553,)32 b(805,)g(806)p -745 3397 125 4 v -1 w(,)h(807)p 926 3397 V -1 w(,)g(808)p -1107 3397 V -1 w(,)g(809)p 1288 3397 V -1 w(,)g(969,)f(970,)166 -3484 y(1284,)i(1389)p 391 3497 167 4 v -2 w(,)i(1390)p -616 3497 V -2 w(,)f(1398,)f(1506.)0 3586 y Ff(FILLDRAW)q -Fm(:)83 b(199)p 459 3599 125 4 v -1 w(,)34 b(201)p 641 -3599 V -2 w(,)g(807,)f(859,)g(1388.)0 3688 y Fi(\014rst)11 -b Fm(:)83 b(13)p 261 3701 84 4 v -1 w(,)35 b(30,)f(270)p -543 3701 125 4 v -2 w(,)h(271,)e(355,)g(541,)h(603,)f(633,)g(948,)166 -3787 y(949,)h(958,)g(959,)g(960,)f(961,)h(963,)g(988,)g(990,)g(991,)166 -3887 y(999,)28 b(1135,)g(1136,)g(1137,)f(1163,)h(1164,)g(1179,)f(1184,) -166 3987 y(1186,)34 b(1188,)g(1221,)f(1228,)h(1268.)0 -4089 y Fi(\014rst)p 149 4089 26 4 v 30 w(p)l(oint)p 359 -4089 V 31 w(ptr)13 b Fm(:)83 b(667)p 609 4102 125 4 v --2 w(,)31 b(672,)e(673)p 965 4102 V -1 w(,)h(674)p 1143 -4102 V -1 w(,)g(675)p 1321 4102 V -1 w(,)h(676)p 1500 -4102 V -2 w(.)0 4190 y Fi(\014rst)p 149 4190 26 4 v 30 -w(r)l(ow)13 b Fm(:)83 b(1283)p 421 4203 167 4 v -2 w(,)42 -b(1284)p 652 4203 V -2 w(.)0 4292 y Fi(\014xe)l(d)12 -b Fm(:)83 b(44,)41 b(864,)f(1512.)0 4394 y Fi(\015o)l(at\014eld)13 -b Fm(:)83 b(44,)42 b(1512.)0 4496 y Fi(\015o)l(ats)11 -b Fm(:)83 b(12,)39 b(24,)g(138,)f(502.)0 4598 y Fi(\015o)l(or)14 -b Fm(:)83 b(1185,)41 b(1256.)0 4700 y Ff(FLT_MAX)q Fm(:)84 -b(7,)43 b(16.)0 4802 y Fi(\015ush)10 b Fm(:)83 b(32,)25 -b(48,)g(50,)f(106,)g(108,)g(148,)g(151,)g(153,)g(161,)g(174,)166 -4902 y(182,)g(183,)f(184,)h(185,)f(186,)h(188,)g(249,)f(313,)h(318,)f -(346,)166 5001 y(350,)h(351,)f(380,)h(382,)f(383,)h(385,)g(387,)f(388,) -h(393,)f(399,)166 5101 y(400,)h(401,)f(405,)h(411,)f(432,)h(443,)g -(446,)f(448,)h(452,)f(458,)166 5201 y(462,)h(464,)f(472,)h(508,)f(517,) -h(519,)g(521,)f(522,)h(530,)f(531,)166 5300 y(532,)h(533,)f(534,)h -(535,)f(536,)h(537,)g(538,)f(540,)h(541,)f(546,)166 5400 -y(548,)h(549,)f(550,)h(551,)f(552,)h(553,)g(561,)f(572,)h(574,)f(603,) -2199 263 y(605,)h(606,)f(607,)h(624,)f(641,)h(644,)g(646,)f(661,)h -(664,)f(669,)2199 363 y(674,)h(678,)f(681,)h(683,)f(685,)h(743,)g(750,) -f(765,)h(776,)f(802,)2199 462 y(807,)h(813,)f(821,)h(824,)f(830,)h -(842,)g(843,)f(844,)h(847,)f(849,)2199 562 y(857,)h(858,)f(859,)h(861,) -f(862,)h(863,)g(864,)f(867,)h(873,)f(875,)2199 662 y(880,)h(883,)f -(884,)h(885,)f(886,)h(889,)g(891,)f(893,)h(897,)f(898,)2199 -761 y(899,)h(900,)f(901,)h(903,)f(904,)h(906,)g(912,)f(914,)h(921,)f -(922,)2199 861 y(927,)h(933,)f(949,)h(951,)f(954,)h(955,)g(957,)f(958,) -h(960,)f(961,)2199 960 y(962,)34 b(963,)g(965,)g(968,)f(979,)h(981,)g -(985,)g(986,)g(989,)2199 1060 y(990,)28 b(992,)f(994,)h(996,)f(998,)h -(999,)g(1033,)f(1034,)g(1036,)2199 1160 y(1037,)e(1070,)g(1086,)g -(1088,)g(1110,)g(1127,)g(1134,)g(1145,)2199 1259 y(1147,)g(1168,)g -(1173,)g(1177,)g(1179,)g(1180,)g(1182,)g(1183,)2199 1359 -y(1184,)g(1185,)g(1186,)g(1188,)g(1193,)g(1221,)g(1228,)g(1229,)2199 -1459 y(1259,)g(1268,)g(1270,)g(1274,)g(1284,)g(1287,)g(1290,)g(1308,) -2199 1558 y(1317,)g(1330,)g(1342,)g(1344,)g(1365,)g(1367,)g(1370,)g -(1372,)2199 1658 y(1382,)g(1384,)g(1385,)g(1387,)g(1388,)g(1390,)g -(1393,)g(1396,)2199 1757 y(1399,)g(1433,)g(1444,)g(1460,)g(1461,)g -(1463,)g(1474,)g(1476,)2199 1857 y(1488,)j(1508,)h(1512,)f(1513,)g -(1515,)h(1516,)f(1519.)2033 1960 y Fi(fmo)l(d)14 b Fm(:)83 -b(968,)42 b(1290.)2033 2063 y Fi(fmt\015ags)11 b Fm(:)83 -b(1512.)2033 2166 y Fi(fo)l(cus)11 b Fm(:)84 b(856.)2033 -2269 y Fk(F)-8 b(o)s(cus)t Fm(:)84 b(33)p 2380 2282 84 -4 v -1 w(,)28 b(122,)f(200,)g(210,)g(252,)f(253,)h(264,)g(311,)g(312,) -2199 2368 y(313,)d(314,)f(315,)h(317,)f(318,)h(319,)g(320,)f(322,)h -(323,)f(324,)2199 2468 y(325,)h(327,)f(328,)h(329,)f(330,)h(332,)g -(333,)f(334,)h(335,)f(337,)2199 2568 y(338,)34 b(339,)g(340,)g(397,)f -(398,)h(399,)g(402,)g(431,)g(432,)2199 2667 y(442,)g(443,)g(453,)g -(457,)f(472,)h(547,)g(548,)g(549,)g(552,)2199 2767 y(553,)g(556)p -2382 2780 125 4 v -2 w(,)i(557,)e(558)p 2748 2780 V -2 -w(,)h(559,)f(560,)g(561)p 3296 2780 V -1 w(,)h(563,)f(565,)2199 -2866 y(566)p 2199 2879 V -1 w(,)h(568,)f(569,)g(570,)f(572,)h(574,)g -(575,)g(581,)g(582,)2199 2966 y(584,)g(585,)g(586,)g(587,)f(742,)h -(743,)g(839,)g(840,)g(844,)2199 3066 y(866,)c(867,)h(923,)f(1341,)g -(1342,)g(1364,)g(1365.)2033 3169 y Fi(F)-6 b(o)l(cuses)11 -b Fm(:)83 b(122,)41 b(923.)2033 3272 y Fi(fo)l(cus0)16 -b Fm(:)83 b(1103)p 2377 3285 167 4 v -2 w(,)30 b(1109,)e(1110,)f(1120,) -h(1145,)f(1147,)h(1167,)2199 3371 y(1192,)37 b(1193,)f(1208,)h(1209.) -2033 3474 y Fi(fo)l(cus1)16 b Fm(:)83 b(1103)p 2377 3487 -V -2 w(,)30 b(1109,)e(1110,)f(1120,)h(1145,)f(1147,)h(1192,)2199 -3574 y(1193,)40 b(1208,)f(1209.)2033 3677 y Fi(found)13 -b Fm(:)83 b(988)p 2353 3690 125 4 v -1 w(.)2033 3780 -y Fi(fourth)11 b Fm(:)83 b(270)p 2367 3793 V -1 w(,)34 -b(271,)g(1184,)e(1186,)h(1188.)2033 3883 y Fi(fp)10 b -Fm(:)83 b(16)p 2216 3896 84 4 v(.)2033 3985 y Fi(fr)l(ont)12 -b Fm(:)83 b(933,)32 b(988,)g(990,)g(997,)g(1379,)g(1474.)2033 -4088 y Fe(g)s Fm(:)83 b(63)p 2182 4101 V -1 w(,)21 b(64)p -2309 4101 V -1 w(,)h(65)p 2437 4101 V -1 w(,)f(66)p 2564 -4101 V -1 w(,)g(68)p 2691 4101 V -1 w(,)h(69)p 2819 4101 -V -1 w(,)f(70)p 2946 4101 V -1 w(,)h(71)p 3074 4101 V --1 w(,)f(84)p 3201 4101 V -1 w(,)h(85)p 3329 4101 V -1 -w(,)f(88)p 3456 4101 V -1 w(,)g(89)p 3583 4101 V -1 w(,)h(1342)p -3711 4101 167 4 v -2 w(.)2033 4191 y Fi(get)p 2142 4191 -26 4 v 31 w(al)t(l)p 2261 4191 V 31 w(c)l(o)l(or)l(ds)12 -b Fm(:)83 b(312)p 2626 4204 125 4 v -1 w(,)30 b(313)p -2804 4204 V -1 w(,)h(314)p 2983 4204 V -2 w(,)g(315)p -3161 4204 V -1 w(,)f(432,)g(867.)2033 4294 y Fi(get)p -2142 4294 26 4 v 31 w(axis)p 2313 4294 V 30 w(h)11 b -Fm(:)84 b(1090)p 2498 4307 167 4 v -2 w(,)35 b(1091)p -2722 4307 V -2 w(,)g(1133,)f(1134,)f(1136,)h(1137,)2199 -4394 y(1152,)k(1159)p 2428 4407 V -2 w(,)h(1160)p 2656 -4407 V -2 w(,)h(1161)p 2885 4407 V -2 w(,)f(1162)p 3113 -4407 V -2 w(,)h(1163,)d(1164,)2199 4493 y(1168,)g(1177,)f(1183,)h -(1256.)2033 4596 y Fi(get)p 2142 4596 26 4 v 31 w(axis)p -2313 4596 V 30 w(v)14 b Fm(:)83 b(1092)p 2496 4609 167 -4 v -2 w(,)35 b(1093)p 2720 4609 V -2 w(,)h(1133,)d(1134,)h(1136,)f -(1137,)2199 4696 y(1152,)38 b(1154)p 2428 4709 V -2 w(,)h(1155)p -2656 4709 V -2 w(,)h(1156)p 2885 4709 V -2 w(,)f(1157)p -3113 4709 V -2 w(,)h(1163,)d(1164,)2199 4796 y(1168,)g(1177,)f(1183,)h -(1256.)2033 4899 y Fi(get)p 2142 4899 26 4 v 31 w(blue)p -2315 4899 V 30 w(p)l(art)13 b Fm(:)83 b(61,)34 b(93,)f(99)p -2883 4912 84 4 v -1 w(,)i(104,)f(106.)2033 5001 y Fi(get)p -2142 5001 26 4 v 31 w(c)l(enter)12 b Fm(:)83 b(957,)33 -b(978)p 2688 5014 125 4 v -2 w(,)h(979)p 2869 5014 V --1 w(,)g(980)p 3051 5014 V -2 w(,)g(981)p 3232 5014 V --1 w(,)g(1084,)e(1127,)2199 5101 y(1139)p 2199 5114 167 -4 v -2 w(,)27 b(1140)p 2415 5114 V -2 w(,)g(1141)p 2631 -5114 V -2 w(,)g(1142)p 2847 5114 V -2 w(,)g(1155,)e(1157,)g(1160,)g -(1162,)2199 5201 y(1163,)g(1164,)g(1178,)g(1179,)g(1182,)g(1193,)g -(1219,)g(1228,)2199 5300 y(1229,)g(1258,)g(1259,)g(1287,)g(1294,)g -(1313)p 3279 5313 V -2 w(,)i(1314)p 3495 5313 V -2 w(,)g(1330,)2199 -5400 y(1443,)h(1451,)h(1461,)f(1465,)g(1474,)h(1476,)f(1478.)p -eop end -%%Page: 496 496 -TeXDict begin 496 495 bop 0 83 a Fm(496)140 b Fl(INDEX)2670 -b(3DLDFPR)n(G)142 b Fn(x)p Fm(1525)0 263 y Fi(get)p 109 -263 26 4 v 31 w(cir)l(cle)11 b Fm(:)83 b(1312.)0 364 -y Fi(get)p 109 364 V 31 w(cir)l(cle)p 331 364 V 31 w(c)l(enter)13 -b Fm(:)83 b(1331)p 696 377 167 4 v -2 w(,)38 b(1332)p -923 377 V -2 w(.)0 466 y Fi(get)p 109 466 26 4 v 31 w(cir)l(cle)p -331 466 V 31 w(ptr)13 b Fm(:)83 b(1312,)29 b(1315,)g(1316,)f(1318)p -1240 479 167 4 v -2 w(,)j(1319)p 1460 479 V -2 w(.)0 -567 y Fi(get)p 109 567 26 4 v 31 w(c)l(o)l(e\016cients)11 -b Fm(:)83 b(946)p 645 580 125 4 v -1 w(,)33 b(960,)f(1136)p -1007 580 167 4 v -2 w(,)i(1137)p 1230 580 V -2 w(.)0 -668 y Fi(get)p 109 668 26 4 v 31 w(c)l(o)l(or)l(d)13 -b Fm(:)83 b(316,)29 b(317)p 619 681 125 4 v -1 w(,)h(318)p -797 681 V -1 w(,)g(319)p 975 681 V -1 w(,)g(320)p 1153 -681 V -1 w(,)g(323,)f(325,)g(328,)166 768 y(330,)37 b(333,)g(335,)g -(338,)f(340.)0 869 y Fi(get)p 109 869 26 4 v 31 w(c)l(opy)12 -b Fm(:)83 b(200)p 411 882 125 4 v -1 w(,)32 b(210)p 591 -882 V -2 w(,)g(222,)f(342)p 950 882 V -2 w(,)h(343)p -1129 882 V -1 w(,)g(471)p 1309 882 V -1 w(,)g(543,)e(545,)166 -969 y(688)p 166 982 V -1 w(,)h(689)p 345 982 V -2 w(,)h(1309)p -524 982 167 4 v -2 w(,)f(1310)p 744 982 V -2 w(,)g(1316,)f(1317,)f -(1380.)0 1070 y Fi(get)p 109 1070 26 4 v 31 w(diameter)14 -b Fm(:)83 b(1261)p 571 1083 167 4 v -2 w(.)0 1172 y Fi(get)p -109 1172 26 4 v 31 w(dir)l(e)l(ction)11 b Fm(:)83 b(577)p -564 1185 125 4 v -1 w(.)0 1273 y Fi(get)p 109 1273 26 -4 v 31 w(distanc)l(e)11 b Fm(:)83 b(12,)25 b(401,)h(578)p -849 1286 125 4 v -2 w(,)h(603,)e(604)p 1197 1286 V -2 -w(,)i(605)p 1371 1286 V -1 w(,)f(633)p 1545 1286 V -1 -w(,)g(634)p 1719 1286 V -1 w(,)166 1372 y(635)p 166 1385 -V -1 w(,)33 b(636)p 347 1385 V -1 w(,)h(637,)e(948,)g(949,)h(954,)f -(985.)0 1474 y Fi(get)p 109 1474 26 4 v 31 w(element)12 -b Fm(:)83 b(122,)28 b(145)p 708 1487 125 4 v -2 w(,)i(146)p -885 1487 V -2 w(,)f(581,)f(582,)g(584,)g(585.)0 1575 -y Fi(get)p 109 1575 26 4 v 31 w(el)t(lipse)12 b Fm(:)83 -b(1312.)0 1676 y Fi(get)p 109 1676 V 31 w(el)t(lipse)p -363 1676 V 32 w(c)l(enter)13 b Fm(:)83 b(1333)p 729 1689 -167 4 v -2 w(,)37 b(1334)p 955 1689 V -2 w(.)0 1778 y -Fi(get)p 109 1778 26 4 v 31 w(el)t(lipse)p 363 1778 V -32 w(ptr)13 b Fm(:)83 b(1312,)28 b(1315,)h(1316,)f(1320)p -1272 1791 167 4 v -2 w(,)i(1321)p 1491 1791 V -2 w(.)0 -1879 y Fi(get)p 109 1879 26 4 v 31 w(extr)l(emes)10 b -Fm(:)83 b(200)p 565 1892 125 4 v -2 w(,)31 b(444)p 743 -1892 V -2 w(,)f(551,)f(845)p 1098 1892 V -2 w(,)i(1367,)d(1368)p -1495 1892 167 4 v -2 w(.)0 1980 y Fi(get)p 109 1980 26 -4 v 31 w(fo)l(cus)11 b Fm(:)83 b(1144)p 432 1993 167 -4 v -2 w(,)32 b(1145)p 653 1993 V -1 w(,)g(1146)p 875 -1993 V -2 w(,)g(1147)p 1096 1993 V -2 w(,)h(1168.)0 2082 -y Fi(get)p 109 2082 26 4 v 31 w(gr)l(e)l(en)p 328 2082 -V 30 w(p)l(art)12 b Fm(:)83 b(61,)34 b(93,)f(98)p 895 -2095 84 4 v -1 w(,)h(104,)f(106.)0 2183 y Fi(get)p 109 -2183 26 4 v 31 w(last)p 265 2183 V 30 w(p)l(oint)13 b -Fm(:)83 b(716,)30 b(721,)h(722,)g(750,)f(892)p 1307 2196 -125 4 v -1 w(,)i(893)p 1487 2196 V -1 w(,)g(920,)166 -2283 y(921,)39 b(922,)g(965,)g(968,)g(984,)g(994,)h(1009,)e(1172,)166 -2382 y(1173,)k(1216.)0 2484 y Fi(get)p 109 2484 26 4 -v 31 w(line)11 b Fm(:)83 b(309)p 383 2497 125 4 v -2 -w(,)34 b(594,)d(601)p 744 2497 V -1 w(,)i(603,)f(932)p -1106 2497 V -1 w(,)h(933)p 1287 2497 V -1 w(.)0 2585 -y Fi(get)p 109 2585 26 4 v 31 w(line)p 271 2585 V 31 -w(switch)11 b Fm(:)83 b(418,)39 b(716,)f(717,)g(721,)h(748,)f(749,)166 -2685 y(876)p 166 2698 125 4 v -1 w(,)43 b(879,)e(920.)0 -2786 y Fi(get)p 109 2786 26 4 v 31 w(line)l(ar)p 344 -2786 V 31 w(e)l(c)l(c)l(entricity)12 b Fm(:)83 b(1148)p -894 2799 167 4 v -2 w(,)35 b(1149)p 1118 2799 V -2 w(.)0 -2887 y Fi(get)p 109 2887 26 4 v 31 w(maximum)p 495 2887 -V 30 w(z)14 b Fm(:)83 b(200)p 674 2900 125 4 v -1 w(,)37 -b(447)p 859 2900 V -1 w(,)h(448)p 1045 2900 V -2 w(,)g(455,)e(456,)g -(552,)166 2987 y(848)p 166 3000 V -1 w(,)j(849)p 353 -3000 V -1 w(,)g(1371)p 540 3000 167 4 v -2 w(,)h(1372)p -769 3000 V -2 w(.)0 3088 y Fi(get)p 109 3088 26 4 v 31 -w(me)l(an)p 331 3088 V 30 w(z)14 b Fm(:)83 b(199,)35 -b(200)p 694 3101 125 4 v -1 w(,)i(449)p 879 3101 V -2 -w(,)g(450)p 1063 3101 V -2 w(,)g(552,)e(850)p 1431 3101 -V -2 w(,)i(851)p 1615 3101 V -2 w(,)166 3188 y(1373)p -166 3201 167 4 v -2 w(,)44 b(1374)p 399 3201 V -1 w(.)0 -3289 y Fi(get)p 109 3289 26 4 v 31 w(mid)p 275 3289 V -31 w(p)l(oint)12 b Fm(:)83 b(1087)p 599 3302 167 4 v --2 w(,)34 b(1088)p 822 3302 V -2 w(,)f(1228,)e(1229.)0 -3390 y Fi(get)p 109 3390 26 4 v 31 w(minimum)p 486 3390 -V 30 w(z)14 b Fm(:)83 b(199,)27 b(200)p 841 3403 125 -4 v -2 w(,)h(445)p 1016 3403 V -1 w(,)g(446)p 1192 3403 -V -2 w(,)g(454,)e(456,)h(550,)166 3490 y(552,)36 b(846)p -351 3503 V -2 w(,)i(847)p 536 3503 V -2 w(,)f(1369)p -720 3503 167 4 v -2 w(,)h(1370)p 947 3503 V -2 w(.)0 -3591 y Fi(get)p 109 3591 26 4 v 31 w(name)10 b Fm(:)83 -b(93,)42 b(102)p 595 3604 125 4 v -2 w(,)h(104,)d(776,)h(802,)g(807,)g -(824,)166 3691 y(1382,)f(1385,)f(1388.)0 3792 y Fi(get)p -109 3792 26 4 v 31 w(net)11 b Fm(:)83 b(1431,)39 b(1443,)h(1448)p -826 3805 167 4 v -2 w(,)h(1449)p 1056 3805 V -2 w(,)g(1451,)e(1460,)166 -3892 y(1462)p 166 3905 V -2 w(,)h(1463)p 395 3905 V -2 -w(,)f(1465,)f(1475)p 852 3905 V -2 w(,)h(1476)p 1080 -3905 V -2 w(,)h(1478,)d(1483,)166 3992 y(1488,)j(1489)p -397 4005 V -2 w(,)h(1490)p 627 4005 V -2 w(.)0 4093 y -Fi(get)p 109 4093 26 4 v 31 w(normal)13 b Fm(:)83 b(513)p -509 4106 125 4 v -1 w(,)36 b(872,)f(873,)g(874,)g(875,)h(896)p -1430 4106 V -2 w(,)h(897)p 1614 4106 V -2 w(,)166 4193 -y(901)p 166 4206 V -1 w(,)29 b(902,)e(903,)h(948,)f(949,)h(968,)g -(1126,)f(1127,)g(1164,)166 4292 y(1228,)34 b(1229,)g(1268,)f(1270,)h -(1274.)0 4394 y Fi(get)p 109 4394 26 4 v 31 w(numeric)l(al)p -495 4394 V 30 w(e)l(c)l(c)l(entricity)12 b Fm(:)83 b(1150)p -1044 4407 167 4 v -2 w(,)34 b(1151)p 1267 4407 V -2 w(.)0 -4495 y Fi(get)p 109 4495 26 4 v 31 w(p)l(ath)11 b Fm(:)83 -b(602)p 402 4508 125 4 v -2 w(,)40 b(934)p 589 4508 V --2 w(,)g(1312.)0 4596 y Fi(get)p 109 4596 26 4 v 31 w(p)l(ath)p -290 4596 V 31 w(ptr)13 b Fm(:)83 b(1312,)32 b(1315,)g(1322)p -986 4609 167 4 v -2 w(,)i(1323)p 1209 4609 V -2 w(.)0 -4698 y Fi(get)p 109 4698 26 4 v 31 w(p)l(ersp)10 b Fm(:)83 -b(583)p 438 4711 125 4 v -2 w(.)0 4799 y Fi(get)p 109 -4799 26 4 v 31 w(p)l(ersp)p 327 4799 V 31 w(element)12 -b Fm(:)83 b(401,)34 b(584)p 932 4812 125 4 v -1 w(,)h(585)p -1115 4812 V -1 w(.)0 4900 y Fi(get)p 109 4900 26 4 v -31 w(plane)11 b Fm(:)83 b(619,)29 b(902)p 620 4913 125 -4 v -2 w(,)i(903)p 798 4913 V -2 w(,)g(904,)e(948,)g(949,)g(954,)g -(985,)166 5000 y(996,)38 b(1168,)f(1176,)g(1268.)0 5101 -y Fi(get)p 109 5101 26 4 v 31 w(p)l(oint)12 b Fm(:)83 -b(716,)29 b(717,)h(721,)f(722,)h(750,)f(765,)g(888)p -1503 5114 125 4 v -1 w(,)i(889)p 1682 5114 V -2 w(,)166 -5201 y(890)p 166 5214 V -1 w(,)k(891)p 349 5214 V -2 -w(,)h(903,)e(922,)f(949,)h(954,)g(957,)g(965,)g(968,)166 -5300 y(984,)f(985,)f(994,)h(1009,)f(1083,)g(1127,)g(1155,)g(1157,)166 -5400 y(1160,)25 b(1162,)g(1164,)g(1172,)g(1173,)g(1178,)g(1179,)g -(1182,)2199 263 y(1183,)g(1184,)g(1193,)g(1216,)g(1219,)g(1221,)g -(1228,)g(1229,)2199 363 y(1284,)g(1443,)g(1449,)g(1451,)g(1460,)g -(1461,)g(1463,)g(1465,)2199 462 y(1474,)31 b(1476,)g(1478,)g(1488,)g -(1490,)g(1491.)2033 564 y Fi(get)p 2142 564 26 4 v 31 -w(p)l(olygon)p 2441 564 V 32 w(c)l(enter)12 b Fm(:)83 -b(1329.)2033 665 y Fi(get)p 2142 665 V 31 w(p)l(osition)11 -b Fm(:)83 b(576)p 2566 678 125 4 v -1 w(.)2033 766 y -Fi(get)p 2142 766 26 4 v 31 w(r)l(adius)11 b Fm(:)83 -b(1045)p 2504 779 167 4 v -2 w(,)41 b(1260)p 2734 779 -V -2 w(.)2033 868 y Fi(get)p 2142 868 26 4 v 31 w(r)l(e)l(ctangle)10 -b Fm(:)83 b(1312.)2033 969 y Fi(get)p 2142 969 V 31 w(r)l(e)l(ctangle)p -2490 969 V 30 w(c)l(enter)13 b Fm(:)83 b(1335)p 2854 -982 167 4 v -2 w(,)36 b(1336)p 3079 982 V -2 w(.)2033 -1070 y Fi(get)p 2142 1070 26 4 v 31 w(r)l(e)l(ctangle)p -2490 1070 V 30 w(ptr)13 b Fm(:)84 b(1312,)29 b(1315,)h(1324)p -3181 1083 167 4 v -2 w(,)i(1325)p 3402 1083 V -2 w(.)2033 -1172 y Fi(get)p 2142 1172 26 4 v 31 w(r)l(e)l(d)p 2280 -1172 V 30 w(p)l(art)13 b Fm(:)83 b(61,)34 b(93,)g(97)p -2849 1185 84 4 v -1 w(,)i(104,)d(106.)2033 1273 y Fi(get)p -2142 1273 26 4 v 31 w(r)l(e)l(g)p 2276 1273 V 30 w(p)l(olygon)12 -b Fm(:)83 b(1312.)2033 1374 y Fi(get)p 2142 1374 V 31 -w(r)l(e)l(g)p 2276 1374 V 30 w(p)l(olygon)p 2574 1374 -V 32 w(c)l(enter)13 b Fm(:)83 b(1337)p 2940 1387 167 -4 v -2 w(,)35 b(1338)p 3164 1387 V -2 w(.)2033 1476 y -Fi(get)p 2142 1476 26 4 v 31 w(r)l(e)l(g)p 2276 1476 -V 30 w(p)l(olygon)p 2574 1476 V 32 w(ptr)13 b Fm(:)83 -b(1312,)29 b(1315,)g(1326)p 3265 1489 167 4 v -2 w(,)h(1327)p -3484 1489 V -1 w(.)2033 1577 y Fi(get)p 2142 1577 26 -4 v 31 w(shap)l(e)11 b Fm(:)83 b(1312.)2033 1678 y Fi(get)p -2142 1678 V 31 w(shap)l(e)p 2367 1678 V 31 w(c)l(enter)13 -b Fm(:)83 b(1296,)33 b(1329)p 2956 1691 167 4 v -2 w(,)i(1330)p -3180 1691 V -2 w(,)f(1332,)f(1334,)2199 1778 y(1336,)42 -b(1338.)2033 1879 y Fi(get)p 2142 1879 26 4 v 31 w(shap)l(e)p -2367 1879 V 31 w(ptr)13 b Fm(:)84 b(1296,)26 b(1312,)g(1315,)h(1316)p -3270 1892 167 4 v -2 w(,)h(1317)p 3487 1892 V -2 w(,)g(1318,)2199 -1979 y(1320,)37 b(1322,)f(1324,)h(1326.)2033 2080 y Fi(get)p -2142 2080 26 4 v 31 w(size)11 b Fm(:)83 b(894)p 2416 -2093 125 4 v -2 w(.)2033 2181 y Fi(get)p 2142 2181 26 -4 v 31 w(tr)l(ansform)10 b Fm(:)83 b(341)p 2636 2194 -125 4 v -1 w(,)40 b(580)p 2824 2194 V -2 w(.)2033 2283 -y Fi(get)p 2142 2283 26 4 v 31 w(tr)l(ansform)p 2525 -2283 V 30 w(element)12 b Fm(:)83 b(399,)32 b(581)p 3127 -2296 125 4 v -1 w(,)i(582)p 3309 2296 V -2 w(.)2033 2384 -y Fi(get)p 2142 2384 26 4 v 31 w(up)9 b Fm(:)83 b(579)p -2370 2397 125 4 v -1 w(.)2033 2485 y Fi(get)p 2142 2485 -26 4 v 31 w(use)p 2290 2485 V 30 w(name)10 b Fm(:)84 -b(93,)33 b(100)p 2767 2498 125 4 v -2 w(,)h(101)p 2948 -2498 V -1 w(,)g(104,)f(776,)g(802,)f(807,)2199 2585 y(824,)38 -b(1382,)f(1385,)g(1388.)2033 2686 y Fi(get)p 2142 2686 -26 4 v 31 w(w)13 b Fm(:)83 b(337)p 2342 2699 125 4 v --2 w(,)39 b(338)p 2528 2699 V -1 w(,)g(339)p 2715 2699 -V -2 w(,)g(340)p 2901 2699 V -1 w(.)2033 2788 y Fi(get)p -2142 2788 26 4 v 31 w(x)13 b Fm(:)83 b(264,)28 b(310,)f(316,)h(322)p -2856 2801 125 4 v -2 w(,)h(323)p 3032 2801 V -1 w(,)g(324)p -3209 2801 V -2 w(,)g(325)p 3385 2801 V -1 w(,)g(349,)e(371,)2199 -2887 y(372,)34 b(373,)g(378,)g(379,)f(395,)h(437,)g(463,)g(464,)g(472,) -2199 2987 y(476,)g(498,)g(500,)g(502,)f(516,)h(566,)g(568,)g(606,)g -(644,)2199 3087 y(731,)24 b(736,)h(843,)f(949,)h(957,)f(1018,)g(1023,)g -(1127,)g(1180,)2199 3186 y(1181,)34 b(1206,)g(1211,)f(1284,)h(1490.) -2033 3287 y Fi(get)p 2142 3287 26 4 v 31 w(y)11 b Fm(:)84 -b(327)p 2326 3300 125 4 v -2 w(,)38 b(328)p 2511 3300 -V -1 w(,)g(329)p 2697 3300 V -1 w(,)g(330)p 2883 3300 -V -2 w(,)h(349,)d(371,)h(372,)g(373,)2199 3387 y(378,)d(379,)g(395,)g -(437,)f(463,)h(464,)g(472,)g(476,)g(498,)2199 3487 y(500,)g(502,)g -(516,)g(566,)f(568,)h(606,)g(644,)g(731,)g(736,)2199 -3586 y(843,)f(949,)f(957,)h(1018,)f(1023,)g(1180,)g(1181,)g(1206,)2199 -3686 y(1211,)37 b(1463,)f(1474,)h(1476.)2033 3787 y Fi(get)p -2142 3787 26 4 v 31 w(z)14 b Fm(:)83 b(332)p 2322 3800 -125 4 v -1 w(,)29 b(333)p 2499 3800 V -2 w(,)g(334)p -2675 3800 V -1 w(,)g(335)p 2852 3800 V -1 w(,)g(349,)e(371,)h(372,)g -(373,)f(378,)2199 3887 y(379,)d(383,)f(463,)h(464,)f(476,)h(498,)g -(500,)f(502,)h(516,)f(566,)2199 3987 y(568,)32 b(606,)g(644,)f(731,)h -(736,)g(843,)g(949,)f(957,)h(1018,)2199 4086 y(1023,)f(1127,)g(1180,)g -(1181,)g(1206,)g(1211.)2033 4188 y Fi(getchar)14 b Fm(:)83 -b(182,)42 b(249,)h(458,)f(644,)g(685,)g(858,)g(863,)2199 -4287 y(869,)g(914,)f(949.)2033 4388 y Fi(getopt)p 2254 -4388 26 4 v 31 w(long)p 2433 4388 V 31 w(only)12 b Fm(:)83 -b(1508.)2033 4490 y Fi(gr)l(ay)12 b Fm(:)83 b(108,)41 -b(112)p 2492 4503 125 4 v -2 w(,)h(113)p 2681 4503 V --2 w(.)2033 4591 y Fi(gr)l(e)l(en)10 b Fm(:)83 b(108,)29 -b(112)p 2515 4604 V -1 w(,)h(113)p 2693 4604 V -2 w(,)g(1287,)f(1443,)f -(1461,)g(1505.)2033 4692 y Fi(gr)l(e)l(en)p 2226 4692 -26 4 v 30 w(p)l(art)13 b Fm(:)83 b(56)p 2513 4705 84 -4 v -1 w(,)38 b(59,)f(61,)h(64,)f(66,)g(69,)h(71,)f(74,)g(75,)2199 -4792 y(76,)42 b(85,)g(89,)f(98.)2033 4893 y Fi(gr)l(e)l(en)p -2226 4893 26 4 v 30 w(yel)t(low)15 b Fm(:)83 b(108,)34 -b(112)p 2776 4906 125 4 v -1 w(,)h(113)p 2959 4906 V --2 w(,)g(1505.)2033 4995 y Fe(h)p Fm(:)83 b(1419)p 2187 -5008 167 4 v -2 w(,)45 b(1420)p 2421 5008 V -2 w(.)2033 -5096 y Fi(h)p 2080 5096 26 4 v 31 w(length)11 b Fm(:)83 -b(1228)p 2437 5109 167 4 v -2 w(,)41 b(1229)p 2667 5109 -V -2 w(.)2033 5197 y Fi(half)23 b Fm(:)83 b(33,)42 b(966,)f(969)p -2631 5210 125 4 v -2 w(.)2033 5299 y Ff(HAVE_FLOAT_H)o -Fm(:)83 b(7.)2033 5400 y Ff(HAVE_LIMITS_H)o Fm(:)g(7.)p -eop end -%%Page: 497 497 -TeXDict begin 497 496 bop 0 83 a Fn(x)p Fm(1525)139 b -Fl(3DLDFPR)n(G)2671 b(INDEX)141 b Fm(497)0 263 y Ff(HAVE_STDLIB_H)o -Fm(:)83 b(7.)0 367 y Fi(height)13 b Fm(:)83 b(1413)p -332 380 167 4 v -1 w(,)39 b(1420,)e(1426.)0 471 y Fi(help)p -148 471 26 4 v 32 w(c)l(olor)14 b Fm(:)83 b(112)p 469 -484 125 4 v -1 w(,)38 b(113)p 655 484 V -1 w(,)h(115,)e(427,)g(428,)h -(429,)f(654)p 1587 484 V -2 w(,)166 571 y(655)p 166 584 -V -1 w(,)j(793,)e(795,)h(1451.)0 675 y Fi(help)p 148 -675 26 4 v 32 w(c)l(olor)p 354 675 V 31 w(ve)l(ctor)14 -b Fm(:)83 b(115)p 715 688 125 4 v -1 w(,)38 b(116)p 901 -688 V -2 w(.)0 778 y Fi(help)p 148 778 26 4 v 32 w(dash)p -340 778 V 32 w(p)l(attern)10 b Fm(:)83 b(654)p 739 791 -125 4 v -1 w(,)33 b(655)p 920 791 V -2 w(,)h(793,)e(795.)0 -882 y Ff(HELP_INDEX)p Fm(:)83 b(1508)p 546 895 167 4 -v -2 w(.)0 986 y Fi(hex)p 124 986 26 4 v 31 w(p)l(attern)p -411 986 V 30 w(1)16 b Fm(:)83 b(1280,)34 b(1283)p 825 -999 167 4 v -2 w(,)i(1284)p 1050 999 V -2 w(.)0 1090 -y Fi(hex)p 124 1090 26 4 v 31 w(p)l(attern1)15 b Fm(:)83 -b(397.)0 1194 y Fi(hexagon)p 293 1194 V 31 w(ctr)13 b -Fm(:)83 b(1284)p 539 1207 167 4 v -1 w(.)0 1298 y Fi(hexagon)p -293 1298 26 4 v 31 w(diameter)15 b Fm(:)83 b(1488)p 756 -1311 167 4 v -2 w(,)34 b(1489)p 979 1311 V -2 w(,)g(1490)p -1202 1311 V -2 w(.)0 1402 y Fi(hexagon)p 293 1402 26 -4 v 31 w(r)l(adius)12 b Fm(:)83 b(1481)p 656 1415 167 -4 v -2 w(,)35 b(1485,)f(1488.)0 1506 y Fi(hi)14 b Fm(:)83 -b(181,)41 b(182)p 377 1519 125 4 v -2 w(,)i(184.)0 1610 -y Fi(horizontal)14 b Fm(:)84 b(400)p 479 1623 V -2 w(.)0 -1714 y Fi(hr)14 b Fm(:)83 b(182)p 197 1727 V -2 w(,)43 -b(184,)e(185.)0 1818 y Fi(hv)14 b Fm(:)83 b(182)p 200 -1831 V -2 w(,)45 b(186.)0 1922 y Fe(i)p Fm(:)83 b(16)p -135 1935 84 4 v -1 w(,)31 b(22)p 272 1935 V -1 w(,)h(47)p -410 1935 V -1 w(,)f(48)p 547 1935 V -1 w(,)g(49)p 684 -1935 V -1 w(,)h(50)p 822 1935 V -1 w(,)f(127)p 959 1935 -125 4 v -1 w(,)g(131)p 1138 1935 V -1 w(,)g(133)p 1317 -1935 V -1 w(,)g(137)p 1496 1935 V -1 w(,)g(141)p 1675 -1935 V -1 w(,)166 2022 y(143)p 166 2035 V -1 w(,)25 b(148)p -339 2035 V -2 w(,)g(161)p 511 2035 V -1 w(,)g(164)p 684 -2035 V -2 w(,)g(172)p 856 2035 V -1 w(,)g(174)p 1029 -2035 V -1 w(,)g(182)p 1202 2035 V -2 w(,)g(303)p 1374 -2035 V -1 w(,)g(305)p 1547 2035 V -2 w(,)g(395)p 1719 -2035 V -1 w(,)166 2121 y(399)p 166 2134 V -1 w(,)35 b(405)p -349 2134 V -2 w(,)h(452)p 532 2134 V -2 w(,)g(486)p 715 -2134 V -2 w(,)f(495)p 897 2134 V -1 w(,)g(508)p 1080 -2134 V -1 w(,)g(551)p 1263 2134 V -1 w(,)g(828)p 1446 -2134 V -2 w(,)h(840)p 1629 2134 V -2 w(,)166 2221 y(843)p -166 2234 V -1 w(,)31 b(844)p 345 2234 V -2 w(,)g(881)p -523 2234 V -1 w(,)g(885)p 702 2234 V -1 w(,)g(886)p 881 -2234 V -2 w(,)g(957)p 1059 2234 V -1 w(,)g(968)p 1238 -2234 V -1 w(,)g(1034)p 1417 2234 167 4 v -2 w(,)g(1065)p -1637 2234 V -2 w(,)166 2320 y(1110)p 166 2333 V -2 w(,)c(1127)p -382 2333 V -2 w(,)g(1179)p 598 2333 V -2 w(,)g(1185)p -814 2333 V -2 w(,)g(1259)p 1030 2333 V -2 w(,)g(1284)p -1246 2333 V -2 w(,)g(1287)p 1462 2333 V -2 w(,)g(1342)p -1678 2333 V -2 w(,)166 2420 y(1367)p 166 2433 V -2 w(,)g(1420)p -382 2433 V -2 w(,)g(1443)p 598 2433 V -2 w(,)g(1449)p -814 2433 V -2 w(,)g(1451)p 1030 2433 V -2 w(,)g(1460)p -1246 2433 V -2 w(,)g(1463)p 1462 2433 V -2 w(,)g(1465)p -1678 2433 V -2 w(,)166 2520 y(1474)p 166 2533 V -2 w(,)33 -b(1475)p 388 2533 V -2 w(,)g(1476)p 610 2533 V -2 w(,)g(1478)p -832 2533 V -2 w(,)g(1488)p 1054 2533 V -2 w(,)g(1490)p -1276 2533 V -2 w(.)0 2624 y Fi(i)p 30 2624 26 4 v 31 -w(max)14 b Fm(:)83 b(1284)p 325 2637 167 4 v -2 w(.)0 -2728 y Fi(i)p 30 2728 26 4 v 31 w(min)11 b Fm(:)83 b(1284)p -313 2741 167 4 v -2 w(.)0 2832 y Fk(Icosahedron)5 b Fm(:)83 -b(658,)28 b(1429,)f(1467)p 1006 2845 V -2 w(,)i(1468,)f(1470,)f(1471)p -1661 2845 V -2 w(,)166 2931 y(1473,)37 b(1474)p 394 2944 -V -2 w(,)h(1476,)f(1478.)0 3035 y Ff(IDENTITY_TRANSFO)o(RM)n -Fm(:)83 b(191)p 895 3048 125 4 v -1 w(,)36 b(192)p 1079 -3048 V -2 w(.)0 3139 y Fk(ifstream)t Fm(:)83 b(39,)42 -b(40.)0 3243 y Fi(in)p 77 3243 26 4 v 31 w(angle)11 b -Fm(:)83 b(1185)p 406 3256 167 4 v -2 w(.)0 3347 y Fi(in)p -77 3347 26 4 v 31 w(cir)l(cle)11 b Fm(:)83 b(1024,)34 -b(1047)p 636 3360 167 4 v -2 w(,)h(1270)p 860 3360 V --2 w(,)h(1272.)0 3451 y Fi(in)p 77 3451 26 4 v 31 w(distanc)l(e)11 -b Fm(:)83 b(1228)p 510 3464 167 4 v -2 w(.)0 3555 y Fi(in)p -77 3555 26 4 v 31 w(el)t(lipse)12 b Fm(:)83 b(1096)p -444 3568 167 4 v -2 w(,)38 b(1229)p 671 3568 V -2 w(,)g(1231.)0 -3659 y Fi(in)p 77 3659 26 4 v 31 w(r)l(e)l(ctangle)10 -b Fm(:)83 b(1220)p 536 3672 167 4 v -2 w(,)37 b(1221)p -762 3672 V -2 w(,)g(1225.)0 3763 y Fi(in)p 77 3763 26 -4 v 31 w(str)l(e)l(am)10 b Fm(:)83 b(39)p 456 3776 84 -4 v -1 w(,)33 b(40)p 595 3776 V -1 w(,)h(42,)e(44,)h(1518,)f(1519.)0 -3867 y Fi(in)p 77 3867 26 4 v 31 w(str)l(e)l(am)p 345 -3867 V 30 w(name)10 b Fm(:)84 b(42)p 682 3880 84 4 v --1 w(,)38 b(43)p 826 3880 V -1 w(,)g(44.)0 3971 y Fi(initialize)p -315 3971 26 4 v 32 w(c)l(olors)12 b Fm(:)84 b(107)p 669 -3984 125 4 v -2 w(,)34 b(108)p 850 3984 V -2 w(,)g(112,)f(1519.)0 -4075 y Fi(initialize)p 315 4075 26 4 v 32 w(io)11 b Fm(:)83 -b(42)p 526 4088 84 4 v -1 w(,)36 b(43)p 668 4088 V -1 -w(,)g(1518,)e(1519.)0 4179 y Fi(inner)p 197 4179 26 4 -v 31 w(cir)l(cle)11 b Fm(:)83 b(1287)p 531 4192 167 4 -v -2 w(,)40 b(1290)p 760 4192 V -2 w(.)0 4282 y Fi(internal)p -288 4282 26 4 v 31 w(angle)11 b Fm(:)83 b(1025)p 617 -4295 167 4 v -2 w(,)33 b(1027,)e(1033,)g(1034.)0 4386 -y Fi(interse)l(ction)p 426 4386 26 4 v 31 w(ctr)13 b -Fm(:)83 b(1185)p 672 4399 167 4 v -2 w(,)38 b(1186.)0 -4490 y Fi(interse)l(ction)p 426 4490 26 4 v 31 w(line)11 -b Fm(:)83 b(594,)30 b(643)p 879 4503 125 4 v -2 w(,)h(644)p -1057 4503 V -1 w(,)g(999,)f(1188.)0 4594 y Fi(interse)l(ction)p -426 4594 26 4 v 31 w(p)l(oint)12 b Fm(:)83 b(33,)35 b(272,)f(527,)g -(528)p 1258 4607 125 4 v -1 w(,)h(529)p 1441 4607 V -1 -w(,)h(530)p 1625 4607 V -2 w(,)166 4694 y(603)p 166 4707 -V -1 w(,)f(604,)f(640)p 532 4707 V -2 w(,)i(641)p 715 -4707 V -2 w(,)f(642)p 897 4707 V -1 w(,)g(920)p 1080 -4707 V -1 w(,)g(921)p 1263 4707 V -1 w(,)g(922)p 1446 -4707 V -2 w(,)h(953,)166 4794 y(963,)31 b(988,)g(990,)g(997,)f(1444,)h -(1450,)f(1451.)0 4898 y Fi(interse)l(ction)p 426 4898 -26 4 v 31 w(p)l(oints)11 b Fm(:)83 b(268,)30 b(528,)g(644,)g(952,)f -(953)p 1498 4911 125 4 v -1 w(,)i(954)p 1677 4911 V -1 -w(,)166 4997 y(964)p 166 5010 V -1 w(,)25 b(965)p 339 -5010 V -2 w(,)g(984)p 511 5010 V -1 w(,)g(985)p 684 5010 -V -2 w(,)g(991,)f(993)p 1029 5010 V -1 w(,)h(994)p 1202 -5010 V -2 w(,)g(995)p 1374 5010 V -1 w(,)g(996)p 1547 -5010 V -2 w(,)g(999,)166 5097 y(1164,)g(1170)p 382 5110 -167 4 v -2 w(,)i(1171)p 598 5110 V -2 w(,)g(1172)p 814 -5110 V -2 w(,)g(1173)p 1030 5110 V -2 w(,)g(1174,)e(1175)p -1462 5110 V -2 w(,)i(1176)p 1678 5110 V -2 w(,)166 5196 -y(1179,)e(1188,)g(1189,)g(1221,)g(1228,)g(1262,)g(1263)p -1462 5209 V -2 w(,)i(1264)p 1678 5209 V -2 w(,)166 5296 -y(1265)p 166 5309 V -2 w(,)33 b(1266)p 388 5309 V -2 -w(,)g(1267)p 610 5309 V -2 w(,)g(1268)p 832 5309 V -2 -w(,)g(1432)p 1054 5309 V -2 w(,)g(1433)p 1276 5309 V --2 w(.)0 5400 y Fi(ints)11 b Fm(:)83 b(667.)2033 263 -y Ff(INVALID_BOOL_POI)o(NT)n Fm(:)g(271,)34 b(273,)g(274)p -3294 276 125 4 v -1 w(,)h(275)p 3477 276 V -2 w(,)h(536,)2199 -363 y(540,)f(541,)f(603,)h(641,)f(921,)h(922.)2033 464 -y Ff(INVALID_BOOL_POI)o(NT_)o(PA)o(IR)n Fm(:)83 b(274)p -3146 477 V -2 w(,)34 b(275)p 3327 477 V -2 w(,)f(954,)f(955,)2199 -564 y(962,)e(963,)f(965,)h(985,)g(986,)f(989,)h(994,)g(1173.)2033 -666 y Ff(INVALID_BOOL_POI)o(NT_)o(QU)o(ADR)o(UP)o(LE)n -Fm(:)83 b(274)p 3364 679 V -2 w(,)26 b(275)p 3537 679 -V -1 w(,)g(1176,)2199 765 y(1179,)i(1182,)h(1184,)f(1185,)g(1186,)h -(1187,)f(1268.)2033 867 y Ff(INVALID_BOOL_REA)o(L_P)o(OI)o(NT)n -Fm(:)83 b(274)p 3146 880 V -2 w(,)31 b(275)p 3324 880 -V -1 w(,)g(606.)2033 969 y Ff(INVALID_LINE)o Fm(:)83 -b(610)p 2666 982 V -1 w(,)33 b(611)p 2847 982 V -2 w(,)g(644,)e(932,)g -(933.)2033 1070 y Ff(INVALID_PATH)o Fm(:)83 b(883.)2033 -1172 y Ff(INVALID_PLANE)o Fm(:)g(619,)36 b(623,)g(646,)g(647)p -3265 1185 V -1 w(,)h(648)p 3450 1185 V -1 w(,)g(903,)2199 -1272 y(904,)44 b(949.)2033 1373 y Ff(INVALID_POINT)o -Fm(:)83 b(24,)29 b(269,)f(273,)g(274)p 3200 1386 V -2 -w(,)i(275)p 3377 1386 V -2 w(,)g(350,)e(432,)2199 1473 -y(462,)34 b(507,)g(508,)g(518,)f(527,)h(536,)g(541,)g(603,)g(605,)2199 -1573 y(607,)g(610,)g(623,)g(624,)f(641,)h(647,)g(873,)g(889,)g(891,) -2199 1672 y(893,)g(896,)g(897,)g(898,)f(900,)h(901,)g(903,)g(951,)g -(952,)2199 1772 y(955,)g(958,)g(959,)g(960,)f(961,)h(979,)g(981,)g -(986,)g(988,)2199 1872 y(999,)28 b(1086,)g(1088,)g(1126,)f(1127,)h -(1145,)g(1147,)f(1163,)2199 1971 y(1164,)e(1179,)g(1184,)g(1188,)g -(1192,)g(1221,)g(1329,)g(1330,)2199 2071 y(1440,)34 b(1456,)g(1457,)f -(1471,)h(1485.)2033 2173 y Ff(INVALID_REAL)o Fm(:)83 -b(12,)24 b(15,)g(16)p 2928 2186 84 4 v -1 w(,)g(24,)g(25,)f(27)p -3319 2186 V -1 w(,)i(30,)e(191,)g(273,)2199 2272 y(274,)h(318,)f(346,)h -(347,)f(349,)h(350,)g(351,)f(355,)h(382,)f(385,)2199 -2372 y(387,)h(401,)f(452,)h(503,)f(505,)h(518,)g(533,)f(534,)h(535,)f -(536,)2199 2471 y(538,)h(539,)f(540,)h(541,)f(623,)h(624,)g(842,)f -(844,)h(879,)f(880,)2199 2571 y(946,)30 b(947,)f(949,)h(958,)g(959,)f -(960,)h(961,)g(1152,)f(1155,)2199 2671 y(1157,)c(1160,)g(1162,)g(1168,) -g(1183,)g(1184,)g(1192,)g(1193,)2199 2770 y(1440,)g(1456,)g(1457,)g -(1471,)g(1485,)g(1514,)g(1515,)g(1516.)2033 2872 y Ff(INVALID_REAL_PAI) -o(R)n Fm(:)83 b(25)p 2884 2885 V -1 w(,)35 b(27)p 3025 -2885 V -1 w(,)g(1134.)2033 2974 y Ff(INVALID_REAL_SHO)o(RT)n -Fm(:)83 b(24,)34 b(25)p 3069 2987 V -1 w(,)i(27)p 3211 -2987 V -1 w(.)2033 3075 y Ff(INVALID_TRANSFOR)o(M)n Fm(:)83 -b(24,)29 b(183,)f(191)p 3197 3088 125 4 v -1 w(,)i(192)p -3375 3088 V -2 w(,)g(716,)e(717,)2199 3175 y(722,)36 -b(748,)g(750,)f(1009,)h(1216.)2033 3277 y Fi(inverse)11 -b Fm(:)83 b(181)p 2405 3290 V -1 w(,)34 b(182)p 2587 -3290 V -2 w(,)g(187)p 2768 3290 V -1 w(,)g(188)p 2950 -3290 V -1 w(,)g(395,)e(561,)h(572,)f(961,)2199 3376 y(1182,)i(1228,)g -(1229,)f(1270,)h(1274.)2033 3478 y Fi(invert)12 b Fm(:)83 -b(187.)2033 3580 y Fi(ios)12 b Fm(:)83 b(44,)44 b(1512.)2033 -3681 y Fi(ios)p 2139 3681 26 4 v 31 w(b)l(ase)11 b Fm(:)83 -b(44.)2033 3783 y Fi(ip)10 b Fm(:)83 b(16)p 2216 3796 -84 4 v(.)2033 3885 y Fi(is)p 2097 3885 26 4 v 31 w(cir)l(cular)14 -b Fm(:)83 b(1258)p 2518 3898 167 4 v -2 w(,)40 b(1259)p -2747 3898 V -2 w(.)2033 3987 y Fi(is)p 2097 3987 26 4 -v 31 w(cubic)10 b Fm(:)83 b(944)p 2423 4000 125 4 v -2 -w(,)39 b(1129)p 2609 4000 167 4 v -2 w(,)g(1130)p 2837 -4000 V -2 w(.)2033 4088 y Fi(is)p 2097 4088 26 4 v 31 -w(cycle)12 b Fm(:)83 b(763,)36 b(864,)h(877)p 2787 4101 -125 4 v -2 w(,)h(912.)2033 4190 y Fi(is)p 2097 4190 26 -4 v 31 w(el)t(lipse)12 b Fm(:)83 b(1152.)2033 4292 y -Fi(is)p 2097 4292 V 31 w(el)t(liptic)l(al)15 b Fm(:)83 -b(1126)p 2545 4305 167 4 v -2 w(,)33 b(1127)p 2767 4305 -V -2 w(,)f(1155,)f(1157,)g(1160,)f(1162,)2199 4391 y(1192,)40 -b(1193,)f(1194.)2033 4493 y Fi(is)p 2097 4493 26 4 v -31 w(identity)12 b Fm(:)83 b(140)p 2514 4506 125 4 v --1 w(,)38 b(141)p 2700 4506 V -1 w(,)g(142)p 2886 4506 -V -2 w(,)g(143)p 3071 4506 V -1 w(,)g(174,)e(283,)h(307)p -3628 4506 V -1 w(,)2199 4593 y(399,)g(405,)g(472,)g(549,)f(553.)2033 -4694 y Fi(is)p 2097 4694 26 4 v 31 w(in)p 2200 4694 V -31 w(triangle)11 b Fm(:)83 b(357)p 2617 4707 125 4 v --1 w(,)37 b(904)p 2802 4707 V -1 w(,)g(991.)2033 4796 -y Fi(is)p 2097 4796 26 4 v 31 w(line)11 b Fm(:)83 b(876,)42 -b(879.)2033 4898 y Fi(is)p 2097 4898 V 31 w(line)l(ar)14 -b Fm(:)83 b(716,)30 b(721,)h(722,)f(749,)h(750,)f(874)p -3344 4911 125 4 v -1 w(,)h(875)p 3523 4911 V -1 w(,)h(876,)2199 -4997 y(879,)g(880,)g(920,)f(921,)h(922,)g(933,)g(965,)f(994,)h(1009,) -2199 5097 y(1172,)40 b(1173,)f(1216.)2033 5199 y Fi(is)p -2097 5199 26 4 v 31 w(on)p 2217 5199 V 31 w(fr)l(e)l(e)p -2376 5199 V 31 w(stor)l(e)10 b Fm(:)83 b(95)p 2691 5212 -84 4 v -1 w(,)31 b(200)p 2828 5212 125 4 v -2 w(,)g(344)p -3006 5212 V -2 w(,)g(685,)e(687,)g(698,)g(703,)2199 5298 -y(871)p 2199 5311 V -1 w(,)42 b(1339)p 2389 5311 167 -4 v -2 w(,)g(1340)p 2620 5311 V -2 w(.)2033 5400 y Fi(is)p -2097 5400 26 4 v 31 w(on)p 2217 5400 V 31 w(line)11 b -Fm(:)83 b(349,)38 b(354)p 2678 5413 125 4 v -2 w(,)h(355)p -2864 5413 V -1 w(.)p eop end -%%Page: 498 498 -TeXDict begin 498 497 bop 0 83 a Fm(498)140 b Fl(INDEX)2670 -b(3DLDFPR)n(G)142 b Fn(x)p Fm(1525)0 263 y Fi(is)p 64 -263 26 4 v 31 w(on)p 184 263 V 31 w(plane)11 b Fm(:)83 -b(356)p 517 276 125 4 v -1 w(,)35 b(637)p 700 276 V -1 -w(,)h(904,)e(1168.)0 364 y Fi(is)p 64 364 26 4 v 31 w(on)p -184 364 V 31 w(se)l(gment)11 b Fm(:)83 b(349)p 614 377 -125 4 v -1 w(,)30 b(350)p 792 377 V -1 w(,)h(352)p 971 -377 V -2 w(,)g(353)p 1149 377 V -1 w(,)f(355,)f(541,)h(603,)166 -464 y(961,)35 b(963,)f(988,)h(990,)f(991,)h(999.)0 565 -y Fi(is)p 64 565 26 4 v 31 w(op)l(en)11 b Fm(:)83 b(106,)41 -b(108.)0 667 y Fi(is)p 64 667 V 31 w(p)l(ar)l(al)t(lel)15 -b Fm(:)83 b(1082.)0 768 y Fi(is)p 64 768 V 31 w(planar)14 -b Fm(:)83 b(872)p 439 781 125 4 v -1 w(,)33 b(873)p 620 -781 V -1 w(,)g(901,)g(942,)f(1044,)f(1083,)h(1258,)166 -868 y(1259,)40 b(1270,)f(1274.)0 969 y Fi(is)p 64 969 -26 4 v 31 w(quadr)l(atic)10 b Fm(:)83 b(943)p 537 982 -125 4 v -1 w(,)37 b(960,)g(1128)p 908 982 167 4 v -2 -w(.)0 1070 y Fi(is)p 64 1070 26 4 v 31 w(quartic)9 b -Fm(:)83 b(945)p 456 1083 125 4 v -1 w(,)38 b(1131)p 642 -1083 167 4 v -2 w(,)h(1132)p 870 1083 V -2 w(.)0 1172 -y Fi(is)p 64 1172 26 4 v 31 w(r)l(e)l(ctangular)13 b -Fm(:)83 b(1082)p 610 1185 167 4 v -2 w(,)39 b(1083)p -838 1185 V -2 w(.)0 1273 y Fi(ise)l(ct)p 164 1273 26 -4 v 31 w(line)11 b Fm(:)83 b(1188)p 438 1286 167 4 v --2 w(.)0 1374 y Ff(ISO)s Fm(:)g(211)p 241 1387 125 4 -v -1 w(,)44 b(212)p 433 1387 V -1 w(.)0 1476 y Fi(iter)13 -b Fm(:)84 b(249,)29 b(543,)h(545,)g(546,)g(549,)g(550,)g(551,)f(552,)h -(659,)166 1575 y(685,)24 b(734,)f(739,)h(741,)f(743,)h(765,)g(766,)f -(770,)h(771,)f(830,)166 1675 y(840,)32 b(843,)g(898,)f(900,)h(914,)g -(988,)g(990,)f(997,)h(1123,)166 1774 y(1127,)25 b(1259,)g(1287,)g -(1302,)g(1308,)g(1342,)g(1344,)g(1347,)166 1874 y(1349,)g(1365,)g -(1367,)g(1380,)g(1382,)g(1384,)g(1385,)g(1387,)166 1974 -y(1388,)g(1390,)g(1391,)g(1393,)g(1394,)g(1396,)g(1397,)g(1399,)166 -2073 y(1418,)j(1424,)h(1461,)f(1465,)g(1474,)h(1478,)f(1488.)0 -2175 y Fi(iter)p 131 2175 26 4 v 31 w(ctr)13 b Fm(:)83 -b(1290)p 377 2188 167 4 v -2 w(.)0 2276 y Fi(iter)l(ator)14 -b Fm(:)83 b(249,)31 b(546,)h(549,)g(553,)g(659,)f(685,)h(734,)g(739,) -166 2376 y(741,)c(743,)f(840,)h(843,)f(859,)h(914,)g(1287,)f(1290,)g -(1308,)166 2475 y(1344,)e(1347,)g(1349,)g(1365,)g(1367,)g(1380,)g -(1424,)g(1433,)166 2575 y(1461,)34 b(1465,)g(1474,)f(1478,)h(1488.)0 -2676 y Fi(iter0)16 b Fm(:)83 b(1433.)0 2777 y Fi(iter1)16 -b Fm(:)83 b(1433.)0 2879 y Fe(j)5 b Fm(:)83 b(127)p 145 -2892 125 4 v -1 w(,)27 b(131)p 320 2892 V -2 w(,)h(133)p -495 2892 V -2 w(,)g(137)p 670 2892 V -2 w(,)g(141)p 845 -2892 V -2 w(,)g(143)p 1020 2892 V -2 w(,)g(148)p 1195 -2892 V -2 w(,)g(172)p 1370 2892 V -2 w(,)f(174)p 1544 -2892 V -1 w(,)g(182)p 1719 2892 V -1 w(,)166 2978 y(399)p -166 2991 V -1 w(,)k(405)p 345 2991 V -1 w(,)h(452)p 525 -2991 V -2 w(,)g(1284)p 704 2991 167 4 v -2 w(,)g(1287)p -925 2991 V -2 w(,)g(1463)p 1146 2991 V -2 w(,)g(1476)p -1367 2991 V -2 w(.)0 3080 y Fe(k)s Fm(:)83 b(174)p 152 -3093 125 4 v -2 w(,)43 b(182)p 342 3093 V -1 w(,)f(1284)p -532 3093 167 4 v -2 w(.)0 3181 y Fi(kil)t(l)p 114 3181 -26 4 v 32 w(lab)l(els)12 b Fm(:)83 b(231)p 449 3194 125 -4 v -1 w(,)41 b(232)p 638 3194 V -1 w(.)0 3282 y Fi(known)11 -b Fm(:)83 b(1133)p 346 3295 167 4 v -2 w(,)39 b(1134)p -574 3295 V -2 w(,)g(1135.)0 3384 y Fe(l)q Fm(:)83 b(597)p -132 3397 125 4 v -1 w(,)32 b(598)p 312 3397 V -1 w(,)g(599)p -492 3397 V -2 w(,)g(600)p 671 3397 V -1 w(,)g(601)p 851 -3397 V -2 w(,)g(604)p 1030 3397 V -1 w(,)g(605)p 1210 -3397 V -2 w(,)g(999)p 1389 3397 V -1 w(.)0 3485 y Fi(l)p -26 3485 26 4 v 31 w(p)10 b Fm(:)83 b(603)p 210 3498 125 -4 v -2 w(.)0 3586 y Fi(l)p 26 3586 26 4 v 31 w(q)12 b -Fm(:)83 b(603)p 208 3599 125 4 v -2 w(.)0 3688 y Fi(lab)l(el)14 -b Fm(:)83 b(207,)28 b(209,)h(227)p 631 3701 V -2 w(,)h(228)p -808 3701 V -2 w(,)g(264,)f(265,)f(461)p 1340 3701 V -2 -w(,)i(462)p 1517 3701 V -1 w(,)g(463)p 1695 3701 V -2 -w(,)166 3787 y(464)p 166 3800 V -1 w(,)35 b(465,)f(467,)g(469,)f(828,)h -(829)p 1080 3800 V -1 w(,)h(830)p 1263 3800 V -1 w(,)g(831)p -1446 3800 V -2 w(,)h(832)p 1629 3800 V -2 w(,)166 3887 -y(835,)d(923,)f(928,)h(1122)p 711 3900 167 4 v -2 w(,)h(1123)p -934 3900 V -2 w(,)g(1124,)e(1443,)g(1451,)166 3987 y(1465,)37 -b(1474,)f(1476,)h(1478.)0 4088 y Fk(Lab)s(el)5 b Fm(:)83 -b(208)p 341 4101 125 4 v -2 w(,)36 b(209,)e(210,)g(216,)h(222,)f(227,)g -(228,)g(264,)166 4188 y(461,)g(462,)g(470)p 532 4201 -V -2 w(,)i(471,)d(472,)h(543,)g(545,)g(546,)g(553,)166 -4287 y(830,)41 b(923,)g(1123.)0 4388 y Fk(Lab)s(els)t -Fm(:)83 b(196,)32 b(207,)g(208,)g(209,)g(216,)g(552.)0 -4490 y Fi(lab)l(els)12 b Fm(:)83 b(216)p 308 4503 V -1 -w(,)37 b(221,)f(228,)g(232,)g(249,)g(462)p 1233 4503 -V -2 w(,)i(543,)e(545,)166 4589 y(546,)42 b(548,)f(553.)0 -4691 y Fi(lamb)l(da)12 b Fm(:)83 b(906)p 367 4704 V -1 -w(.)0 4792 y Fi(lamb)l(da)p 254 4792 26 4 v 32 w(denominator)14 -b Fm(:)83 b(904)p 857 4805 125 4 v -1 w(,)36 b(906.)0 -4893 y Fi(last)p 130 4893 26 4 v 31 w(c)l(onne)l(ctor)13 -b Fm(:)83 b(763)p 622 4906 125 4 v -2 w(,)35 b(764,)f(770)p -987 4906 V -2 w(,)h(913)p 1169 4906 V -1 w(.)0 4995 y -Fi(lbl)13 b Fm(:)84 b(462)p 200 5008 V -2 w(,)43 b(471)p -390 5008 V -2 w(,)g(543)p 580 5008 V -2 w(.)0 5096 y -Ff(LDF_GCC_2_95)o Fm(:)83 b(5,)33 b(6,)f(7,)g(8,)g(21,)g(22,)g(1511.)0 -5197 y Ff(LDF_GCC_3_3)p Fm(:)83 b(5,)40 b(6,)g(7)p 800 -5210 42 4 v(.)0 5299 y Ff(LDF_PUBLIC)p Fm(:)83 b(5,)43 -b(7)p 654 5312 V -1 w(.)0 5400 y Ff(LDF_REAL_DOUBLE)n -Fm(:)83 b(12)p 764 5413 84 4 v -1 w(,)33 b(16,)g(1515,)e(1516.)2033 -263 y Ff(LDF_REAL_FLOAT)o Fm(:)83 b(12)p 2754 276 V -1 -w(,)36 b(16,)g(1515.)2033 364 y Fi(left)13 b Fm(:)83 -b(148.)2033 465 y Fi(left)p 2150 465 26 4 v 31 w(shift)13 -b Fm(:)83 b(1284)p 2449 478 167 4 v -2 w(.)2033 567 y -Fi(light)p 2192 567 26 4 v 31 w(gr)l(ay)13 b Fm(:)83 -b(108,)38 b(112)p 2675 580 125 4 v -2 w(,)i(113)p 2862 -580 V -2 w(.)2033 668 y Fi(limit)13 b Fm(:)83 b(1289)p -2319 681 167 4 v -2 w(,)43 b(1290)p 2551 681 V -2 w(.)2033 -769 y Fk(Line)5 b Fm(:)83 b(33)p 2325 782 84 4 v -1 w(,)40 -b(272,)f(309,)g(528,)g(591,)g(593)p 3223 782 125 4 v --1 w(,)h(594,)f(595,)2199 869 y(596)p 2199 882 V -1 w(,)c(597,)f(598)p -2565 882 V -2 w(,)i(599,)d(600,)h(601,)g(602,)g(603,)g(604,)2199 -968 y(605,)g(609,)g(610,)g(611,)f(643,)h(644,)g(662,)g(920,)g(932,)2199 -1068 y(933,)39 b(934,)f(999,)h(1188.)2033 1169 y Fi(line)p -2169 1169 26 4 v 31 w(switch)12 b Fm(:)83 b(654)p 2535 -1182 125 4 v -2 w(,)37 b(657,)f(661,)f(664,)h(666,)f(669,)h(671,)2199 -1269 y(674,)h(676,)g(874,)g(875,)g(876,)g(1030,)f(1040,)g(1042,)2199 -1369 y(1062,)i(1065,)f(1070,)h(1075,)f(1077,)h(1107,)f(1110,)2199 -1468 y(1240,)j(1243,)f(1248.)2033 1569 y Fi(line)l(ar)p -2242 1569 26 4 v 31 w(e)l(c)l(c)l(entricity)12 b Fm(:)83 -b(1103)p 2792 1582 167 4 v -2 w(,)46 b(1109,)e(1110,)f(1149,)2199 -1669 y(1192,)f(1193.)2033 1770 y Fk(Lines)t Fm(:)83 b(528,)32 -b(591,)g(594,)g(603,)g(952,)h(1175.)2033 1871 y Fi(lo)l(c)l(altime)12 -b Fm(:)83 b(43.)2033 1973 y Fi(lo)l(c)l(ation)12 b Fm(:)83 -b(948)p 2428 1986 125 4 v -2 w(,)36 b(949)p 2611 1986 -V -1 w(,)g(953,)e(963,)h(1167)p 3162 1986 167 4 v -2 -w(,)h(1168)p 3387 1986 V -2 w(,)g(1184,)2199 2072 y(1185,)42 -b(1188.)2033 2174 y Fi(lo)l(c)l(ation)p 2315 2174 26 -4 v 32 w(switch)11 b Fm(:)83 b(1185)p 2681 2187 167 4 -v -2 w(.)2033 2275 y Fi(long)p 2186 2275 26 4 v 31 w(options)12 -b Fm(:)83 b(1508)p 2590 2288 167 4 v -2 w(.)2033 2376 -y Fi(lo)l(op)p 2181 2376 26 4 v 32 w(ctr)13 b Fm(:)83 -b(867)p 2428 2389 125 4 v -2 w(.)2033 2477 y Fi(lt)12 -b Fm(:)83 b(43)p 2200 2490 84 4 v -1 w(.)2033 2578 y -Fe(M)9 b Fm(:)83 b(1228)p 2229 2591 167 4 v -2 w(,)44 -b(1229)p 2462 2591 V -2 w(.)2033 2680 y Fe(m)p Fm(:)83 -b(345)p 2212 2693 125 4 v -1 w(,)42 b(346)p 2402 2693 -V -1 w(,)h(508)p 2593 2693 V -2 w(.)2033 2781 y Fi(mag)12 -b Fm(:)83 b(505)p 2299 2794 V -1 w(,)38 b(1168)p 2485 -2794 167 4 v -2 w(,)f(1258)p 2711 2794 V -2 w(,)h(1259)p -2938 2794 V -2 w(.)2033 2882 y Fi(magenta)11 b Fm(:)83 -b(108,)33 b(112)p 2635 2895 125 4 v -2 w(,)h(113)p 2816 -2895 V -1 w(,)g(1461,)e(1505.)2033 2983 y Fi(magnitude)11 -b Fm(:)83 b(388,)36 b(502)p 2708 2996 V -1 w(,)h(503)p -2893 2996 V -1 w(,)g(505,)g(507,)f(508,)g(557,)2199 3083 -y(605,)30 b(949,)h(1070,)f(1127,)f(1155,)h(1157,)g(1160,)g(1162,)2199 -3183 y(1167,)38 b(1168,)f(1193,)h(1228,)f(1229,)h(1258,)f(1259,)2199 -3282 y(1268,)j(1270,)f(1444.)2033 3383 y Fi(mag0)16 b -Fm(:)84 b(1258)p 2346 3396 167 4 v 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4402 167 4 -v -2 w(.)2033 4491 y Fi(max)p 2187 4491 26 4 v 30 w(hexagons)12 -b Fm(:)83 b(1283)p 2652 4504 167 4 v -2 w(,)39 b(1284)p -2880 4504 V -2 w(.)2033 4592 y Ff(MAX_REAL)q Fm(:)83 -b(12,)32 b(15,)g(16)p 2770 4605 84 4 v -1 w(,)i(24,)e(25,)g(27)p -3188 4605 V -1 w(,)h(503,)e(843,)h(844,)2199 4691 y(1514,)40 -b(1515,)f(1516.)2033 4793 y Ff(MAX_REAL_SQRT)o Fm(:)83 -b(24,)33 b(25)p 2850 4806 V -1 w(,)h(26)p 2990 4806 V --1 w(,)g(27)p 3130 4806 V -1 w(,)g(503.)2033 4894 y Fi(max)p -2187 4894 26 4 v 30 w(x)p 2256 4894 V 30 w(pr)l(oj)18 -b Fm(:)83 b(252,)28 b(253)p 2722 4907 125 4 v -1 w(,)h(254)p -2899 4907 V -1 w(,)g(547,)g(548)p 3254 4907 V -2 w(,)h(551,)e(554)p -3608 4907 V -2 w(.)2033 4995 y Fi(max)p 2187 4995 26 -4 v 30 w(y)p 2257 4995 V 31 w(pr)l(oj)18 b Fm(:)83 b(253)p -2547 5008 125 4 v -2 w(,)34 b(254)p 2728 5008 V -1 w(,)g(548)p -2910 5008 V -2 w(,)g(551,)f(554)p 3273 5008 V -2 w(.)2033 -5096 y Ff(MAX_Z)r Fm(:)83 b(213)p 2361 5109 V -1 w(,)32 -b(214)p 2541 5109 V -2 w(,)g(253,)f(254,)f(453,)g(547,)h(552.)2033 -5198 y Fi(max)p 2187 5198 26 4 v 30 w(z)p 2251 5198 V -31 w(pr)l(oj)17 b Fm(:)83 b(253)p 2540 5211 125 4 v -1 -w(,)34 b(254)p 2722 5211 V -2 w(,)h(548)p 2904 5211 V --2 w(,)f(551,)f(554)p 3267 5211 V -2 w(.)2033 5299 y -Ff(MEAN_Z)r Fm(:)83 b(213)p 2405 5312 V -1 w(,)38 b(214)p -2591 5312 V -2 w(,)g(453,)f(552.)2033 5400 y Fi(me)l(asur)l(ement)p -2511 5400 26 4 v 30 w(units)10 b Fm(:)83 b(264)p 2831 -5413 125 4 v -1 w(,)30 b(265)p 3009 5413 V -1 w(,)g(437,)f(458,)g(472.) -p eop end -%%Page: 499 499 -TeXDict begin 499 498 bop 0 83 a Fn(x)p Fm(1525)139 b -Fl(3DLDFPR)n(G)2671 b(INDEX)141 b Fm(499)0 263 y Fi(me)l(diate)11 -b Fm(:)84 b(511)p 395 276 125 4 v -2 w(,)31 b(512)p 573 -276 V -1 w(,)g(1070,)f(1087,)f(1088,)h(1270,)f(1443,)166 -363 y(1445,)34 b(1451,)g(1461,)f(1474,)h(1478.)0 464 -y Fi(mid)p 140 464 26 4 v 31 w(p)l(oint)13 b Fm(:)83 -b(1087.)0 565 y Fi(mid)p 140 565 V 31 w(pt)12 b Fm(:)84 -b(1270)p 355 578 167 4 v -2 w(.)0 666 y Fi(min)11 b Fm(:)83 -b(15,)38 b(843,)f(1268,)g(1367.)0 767 y Ff(MIN_REAL)q -Fm(:)83 b(843,)40 b(844.)0 868 y Fi(min)p 145 868 26 -4 v 31 w(x)p 215 868 V 30 w(pr)l(oj)17 b Fm(:)83 b(252,)28 -b(253)p 680 881 125 4 v -1 w(,)i(254)p 858 881 V -2 w(,)g(547,)e(548)p -1212 881 V -1 w(,)h(551,)g(554)p 1567 881 V -2 w(.)0 -969 y Fi(min)p 145 969 26 4 v 31 w(y)p 216 969 V 30 w(pr)l(oj)18 -b Fm(:)83 b(253)p 505 982 125 4 v -2 w(,)34 b(254)p 686 -982 V -1 w(,)g(548)p 868 982 V -1 w(,)g(551,)e(554)p -1231 982 V -1 w(.)0 1070 y Ff(MIN_Z)r Fm(:)83 b(213)p -328 1083 V -1 w(,)36 b(214)p 512 1083 V -1 w(,)g(453,)f(547,)g(552.)0 -1171 y Fi(min)p 145 1171 26 4 v 31 w(z)p 210 1171 V 30 -w(pr)l(oj)17 b Fm(:)84 b(253)p 499 1184 125 4 v -2 w(,)34 -b(254)p 680 1184 V -1 w(,)g(548)p 862 1184 V -2 w(,)h(551,)d(554)p -1225 1184 V -1 w(.)0 1272 y Fi(mo)l(dify)13 b Fm(:)83 -b(84)p 357 1285 84 4 v -1 w(,)45 b(85)p 508 1285 V -1 -w(.)0 1373 y Fi(move)p 191 1373 26 4 v 31 w(b)l(ack)14 -b Fm(:)83 b(1284)p 489 1386 167 4 v -2 w(.)0 1474 y Fi(mu)10 -b Fm(:)83 b(906)p 229 1487 125 4 v -1 w(.)0 1575 y Fi(mu)p -118 1575 26 4 v 30 w(denominator)14 b Fm(:)83 b(904)p -719 1588 125 4 v -1 w(,)38 b(906.)0 1676 y Fi(mx)14 b -Fm(:)83 b(644)p 227 1689 V -2 w(.)0 1777 y Fi(my)12 b -Fm(:)83 b(644)p 226 1790 V -2 w(.)0 1878 y Fi(mz)14 b -Fm(:)83 b(644)p 222 1891 V -1 w(.)0 1979 y Fe(n)p Fm(:)g(60)p -156 1992 84 4 v -1 w(,)28 b(61)p 290 1992 V -1 w(,)h(63)p -425 1992 V -1 w(,)f(64)p 559 1992 V -1 w(,)h(65)p 694 -1992 V -1 w(,)f(66)p 828 1992 V -1 w(,)h(182)p 963 1992 -125 4 v -2 w(,)g(345)p 1139 1992 V -2 w(,)g(346)p 1315 -1992 V -2 w(,)f(623)p 1490 1992 V -1 w(,)g(624)p 1666 -1992 V -1 w(.)0 2080 y Fi(name)11 b Fm(:)83 b(56)p 312 -2093 84 4 v -1 w(,)39 b(59,)g(61,)f(64,)h(66,)f(67,)g(69,)h(71,)f(74,)h -(75,)166 2180 y(81,)h(102,)f(106,)g(1508.)0 2281 y Fi(new)p -145 2281 26 4 v 31 w(c)l(o)l(or)l(dinates)12 b Fm(:)83 -b(405)p 690 2294 125 4 v -2 w(.)0 2382 y Fi(new)p 145 -2382 26 4 v 31 w(shap)l(e)p 370 2382 V 31 w(ptr)14 b -Fm(:)83 b(32.)0 2483 y Fi(nnumb)l(er)p 319 2483 V 29 -w(of)p 415 2483 V 32 w(p)l(oints)11 b Fm(:)83 b(1109)p -773 2496 167 4 v -2 w(,)30 b(1110)p 992 2496 V -1 w(,)g(1111)p -1212 2496 V -2 w(,)g(1112)p 1431 2496 V -2 w(,)g(1242)p -1650 2496 V -2 w(,)166 2582 y(1243)p 166 2595 V -2 w(,)42 -b(1244)p 397 2595 V -2 w(,)f(1245)p 627 2595 V -2 w(.)0 -2683 y Ff(NO_SORT)q Fm(:)84 b(213)p 416 2696 125 4 v --2 w(,)38 b(214)p 601 2696 V -2 w(,)g(453,)e(547.)0 2784 -y Fi(non)p 141 2784 26 4 v 30 w(stop)10 b Fm(:)83 b(458,)41 -b(863.)0 2886 y Fi(normal)13 b Fm(:)84 b(605)p 375 2899 -125 4 v -2 w(,)34 b(606,)f(617)p 738 2899 V -2 w(,)h(619,)e(620,)h -(623,)f(624,)h(626,)166 2985 y(629,)h(634,)g(641,)g(644,)f(646,)h(903)p -1080 2998 V -1 w(,)h(954,)f(955,)g(956,)166 3085 y(963,)c(968)p -345 3098 V -2 w(,)h(985,)f(986,)g(987,)f(990,)h(996,)g(1126,)f(1127)p -1637 3098 167 4 v -2 w(,)166 3184 y(1164)p 166 3197 V --2 w(,)e(1176,)e(1178,)g(1179,)g(1181,)g(1228)p 1246 -3197 V -2 w(,)i(1229)p 1462 3197 V -2 w(,)g(1268)p 1678 -3197 V -2 w(,)166 3284 y(1270)p 166 3297 V -2 w(,)39 -b(1274)p 394 3297 V -2 w(,)f(1287)p 621 3297 V -2 w(,)h(1290)p -849 3297 V -2 w(.)0 3385 y Fi(normal)p 260 3385 26 4 -v 31 w(p)l(oint)13 b Fm(:)83 b(1178)p 585 3398 167 4 -v -2 w(,)39 b(1179.)0 3486 y Fi(normal)p 260 3486 26 -4 v 31 w(unit)12 b Fm(:)83 b(605)p 549 3499 125 4 v -2 -w(.)0 3587 y Fi(normal)p 260 3587 26 4 v 31 w(x)14 b -Fm(:)83 b(1181)p 445 3600 167 4 v -2 w(,)41 b(1182.)0 -3688 y Fi(normal)p 260 3688 26 4 v 31 w(y)12 b Fm(:)83 -b(1181)p 444 3701 167 4 v -2 w(,)41 b(1182.)0 3789 y -Fi(normal)p 260 3789 26 4 v 31 w(z)15 b Fm(:)83 b(1181)p -441 3802 167 4 v -2 w(,)41 b(1182.)0 3890 y Fi(nul)t(l)p -143 3890 26 4 v 30 w(c)l(o)l(or)l(dinates)13 b Fm(:)83 -b(15)p 688 3903 84 4 v -1 w(,)33 b(23)p 827 3903 V -1 -w(,)f(277,)g(278,)f(399.)0 3991 y Fi(numb)l(er)p 272 -3991 26 4 v 30 w(of)p 369 3991 V 31 w(p)l(oints)12 b -Fm(:)83 b(941)p 727 4004 125 4 v -2 w(,)35 b(948,)e(949,)g(957,)g(967,) -g(968,)166 4091 y(1110,)38 b(1120,)f(1127,)h(1155,)f(1157,)h(1179,)f -(1182,)166 4190 y(1193,)j(1219,)f(1243.)0 4292 y Fi(numb)l(er)p -272 4292 26 4 v 30 w(of)p 369 4292 V 31 w(p)l(olygon)p -668 4292 V 32 w(typ)l(es)12 b Fm(:)83 b(1431)p 991 4305 -167 4 v -2 w(,)30 b(1440,)e(1443,)g(1457,)166 4391 y(1460,)34 -b(1471,)g(1474,)f(1485,)h(1488.)0 4492 y Fi(numer)l(ator)13 -b Fm(:)83 b(641)p 495 4505 125 4 v -2 w(,)41 b(1183)p -683 4505 167 4 v -2 w(.)0 4593 y Fk(n)m(umeric)p 339 -4593 29 5 v 40 w(limits)s Fm(:)83 b(15,)32 b(16,)g(23,)g(265,)f(843.)0 -4694 y Fi(numeric)l(al)p 360 4694 26 4 v 31 w(e)l(c)l(c)l(entricity)12 -b Fm(:)83 b(1103)p 910 4707 167 4 v -2 w(,)36 b(1109,)d(1110,)h(1151,) -166 4794 y(1192,)42 b(1193.)0 4895 y Fi(nx)13 b Fm(:)84 -b(644)p 206 4908 125 4 v -2 w(.)0 4996 y Fi(ny)12 b Fm(:)83 -b(644)p 205 5009 V -2 w(.)0 5097 y Fi(nz)14 b Fm(:)83 -b(644)p 201 5110 V -1 w(.)0 5198 y Fi(o\013set)12 b Fm(:)83 -b(1284)p 311 5211 167 4 v -2 w(.)0 5299 y Fi(o\013sets)11 -b Fm(:)83 b(1286)p 344 5312 V -2 w(,)42 b(1287)p 575 -5312 V -2 w(.)0 5400 y Fk(ofstream)5 b Fm(:)83 b(39,)41 -b(40.)2033 263 y Fi(old)p 2143 263 26 4 v 32 w(axis)p -2315 263 V 31 w(h)11 b Fm(:)83 b(1193)p 2500 276 167 -4 v -2 w(.)2033 365 y Fi(old)p 2143 365 26 4 v 32 w(axis)p -2315 365 V 31 w(v)13 b Fm(:)83 b(1193)p 2498 378 167 -4 v -2 w(.)2033 466 y Fi(on)p 2127 466 26 4 v 31 w(fr)l(e)l(e)p -2286 466 V 31 w(stor)l(e)10 b Fm(:)83 b(56)p 2601 479 -84 4 v -1 w(,)32 b(59,)f(61,)g(64,)f(69,)h(71,)g(72,)g(95,)g(264)p -3704 479 125 4 v -2 w(,)2199 566 y(280,)j(283,)g(287,)g(290,)f(292,)h -(294,)g(296,)g(301,)g(344,)2199 666 y(432,)g(654)p 2382 -679 V -2 w(,)i(656,)e(661,)f(664,)h(669,)g(671,)g(674,)g(676,)2199 -765 y(678,)j(681,)g(683,)g(690,)g(871,)g(1025)p 3129 -778 167 4 v -2 w(,)h(1030,)e(1033,)2199 865 y(1040,)i(1042,)f(1059)p -2656 878 V -2 w(,)j(1062,)d(1065,)h(1070,)f(1075,)2199 -965 y(1077,)25 b(1107,)g(1110,)g(1115,)g(1117,)g(1240,)g(1243,)g(1248,) -2199 1064 y(1250,)g(1296)p 2415 1077 V -2 w(,)i(1299,)e(1300,)g(1302,)g -(1304,)g(1311,)g(1342,)2199 1164 y(1416,)g(1418,)g(1420,)g(1422,)g -(1440,)g(1443,)g(1457,)g(1460,)2199 1263 y(1471,)37 b(1474,)f(1485,)h -(1488.)2033 1365 y Fi(on)p 2127 1365 26 4 v 31 w(se)l(gment)11 -b Fm(:)83 b(953,)40 b(961)p 2746 1378 125 4 v -2 w(.)2033 -1467 y Fi(op)l(en)11 b Fm(:)83 b(44.)2033 1569 y Fi(optar)l(g)12 -b Fm(:)84 b(1508.)2033 1670 y Fi(optind)14 b Fm(:)83 -b(1508.)2033 1772 y Fi(option)12 b Fm(:)83 b(1508.)2033 -1874 y Fi(option)p 2264 1874 26 4 v 32 w(ctr)13 b Fm(:)83 -b(1508)p 2511 1887 167 4 v -2 w(.)2033 1975 y Fi(option)p -2264 1975 26 4 v 32 w(index)14 b Fm(:)83 b(1508)p 2602 -1988 167 4 v -2 w(.)2033 2077 y Fi(or)l(ange)11 b Fm(:)83 -b(108,)31 b(112)p 2568 2090 125 4 v -1 w(,)h(113)p 2748 -2090 V -2 w(,)g(1443,)f(1461,)f(1505.)2033 2179 y Fi(or)l(ange)p -2276 2179 26 4 v 31 w(r)l(e)l(d)13 b Fm(:)83 b(112)p -2528 2192 125 4 v -1 w(,)41 b(113)p 2717 2192 V -1 w(.)2033 -2280 y Fi(orientation)12 b Fm(:)83 b(949)p 2550 2293 -V -2 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30 w(distanc)l(e)11 b Fm(:)83 b(1228)p 2585 -3402 167 4 v -2 w(.)2033 3490 y Fi(out)p 2153 3490 26 -4 v 30 w(el)t(lipse)13 b Fm(:)83 b(1095)p 2520 3503 167 -4 v -2 w(,)37 b(1228)p 2746 3503 V -2 w(,)g(1230.)2033 -3592 y Fi(out)p 2153 3592 26 4 v 30 w(r)l(e)l(ctangle)11 -b Fm(:)83 b(1218)p 2612 3605 167 4 v -2 w(,)33 b(1219)p -2834 3605 V -2 w(,)h(1221,)d(1223.)2033 3694 y Fi(out)p -2153 3694 26 4 v 30 w(str)l(e)l(am)10 b Fm(:)83 b(39)p -2531 3707 84 4 v -1 w(,)34 b(40)p 2671 3707 V -1 w(,)f(44,)f(46,)g(48,) -h(50,)f(67,)g(106,)g(108,)2199 3794 y(264,)i(414,)g(436,)g(457,)f(458,) -h(461,)g(472,)g(856,)g(859,)2199 3893 y(861,)g(862,)f(863,)h(864,)f -(1398,)g(1519.)2033 3995 y Fi(out)p 2153 3995 26 4 v -30 w(str)l(e)l(am)p 2420 3995 V 30 w(name)11 b Fm(:)83 -b(42)p 2757 4008 84 4 v -1 w(,)38 b(43)p 2901 4008 V --1 w(,)f(44.)2033 4097 y Fi(outer)p 2226 4097 26 4 v -30 w(cir)l(cle)12 b Fm(:)83 b(1287)p 2560 4110 167 4 -v -2 w(,)40 b(1290)p 2789 4110 V -2 w(.)2033 4198 y Fi(outer)p -2226 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26 4 v 31 w(inner)p 270 1662 V -31 w(c)l(opy)12 b Fm(:)83 b(1284)p 572 1675 167 4 v -2 -w(.)0 1764 y Fi(p)p 47 1764 26 4 v 31 w(iter)13 b Fm(:)83 -b(657.)0 1866 y Fi(p)p 47 1866 V 31 w(m)p 146 1866 V -30 w(c)l(o)l(or)l(d)14 b Fm(:)83 b(346)p 478 1879 125 -4 v -1 w(,)41 b(347.)0 1968 y Fi(p)p 47 1968 26 4 v 31 -w(mag)12 b Fm(:)83 b(505)p 339 1981 125 4 v -1 w(.)0 -2070 y Fi(p)p 47 2070 26 4 v 31 w(midd)t(le)12 b Fm(:)83 -b(1284)p 431 2083 167 4 v -2 w(.)0 2172 y Fi(p)p 47 2172 -26 4 v 31 w(midd)t(le)p 318 2172 V 32 w(c)l(opy)13 b -Fm(:)83 b(1284)p 622 2185 167 4 v -2 w(.)0 2274 y Fi(p)p -47 2274 26 4 v 31 w(n)p 125 2274 V 30 w(c)l(o)l(or)l(d)14 -b Fm(:)83 b(346)p 457 2287 125 4 v -2 w(,)42 b(347.)0 -2376 y Fi(p)p 47 2376 26 4 v 31 w(outer)13 b Fm(:)83 -b(1284)p 380 2389 167 4 v -2 w(.)0 2478 y Fi(p)p 47 2478 -26 4 v 31 w(outer)p 266 2478 V 30 w(c)l(opy)13 b Fm(:)83 -b(1284)p 568 2491 167 4 v -2 w(.)0 2580 y Fi(p)p 47 2580 -26 4 v 31 w(x)14 b Fm(:)83 b(517)p 232 2593 125 4 v -2 -w(,)36 b(518,)d(519,)h(520,)g(521,)g(522.)0 2682 y Fi(p)p -47 2682 26 4 v 31 w(x)p 117 2682 V 30 w(sign)11 b Fm(:)83 -b(521)p 403 2695 125 4 v -1 w(.)0 2784 y Fi(p)p 47 2784 -26 4 v 31 w(y)12 b Fm(:)83 b(517)p 231 2797 125 4 v -1 -w(,)35 b(518,)e(519,)h(520,)g(521,)g(522.)0 2886 y Fi(p)p -47 2886 26 4 v 31 w(y)p 118 2886 V 31 w(sign)11 b Fm(:)83 -b(521)p 405 2899 125 4 v -2 w(.)0 2988 y Fi(p)p 47 2988 -26 4 v 31 w(z)14 b Fm(:)83 b(517)p 227 3001 125 4 v -1 -w(,)35 b(518,)f(519,)g(520,)g(521,)f(522.)0 3090 y Fi(p)p -47 3090 26 4 v 31 w(z)p 112 3090 V 30 w(sign)11 b Fm(:)83 -b(521)p 398 3103 125 4 v -1 w(.)0 3192 y Fi(p)l(a)11 -b Fm(:)83 b(425)p 197 3205 V -1 w(,)34 b(426)p 379 3205 -V -2 w(,)g(757)p 560 3205 V -2 w(,)g(762)p 741 3205 V --1 w(,)f(763)p 922 3205 V -1 w(,)h(764,)e(765,)g(766,)g(767)p -1647 3205 V -1 w(,)166 3292 y(768)p 166 3305 V -1 w(,)25 -b(769)p 339 3305 V -2 w(,)g(770)p 511 3305 V -1 w(,)g(771,)e(780)p -856 3305 V -1 w(,)i(789)p 1029 3305 V -1 w(,)g(798)p -1202 3305 V -2 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y(671,)h(673,)f(674,)h(676,)f(677,)h(678)p -1029 4417 V -1 w(,)h(680,)e(681,)h(682,)f(683,)166 4503 -y(684)p 166 4516 V -1 w(,)i(685)p 339 4516 V -2 w(,)g(686,)f(687,)f -(689,)h(693,)g(696,)f(698,)h(701,)f(703,)166 4603 y(705,)h(707,)f(709,) -h(714,)f(716,)h(717,)g(720,)f(721,)h(722,)f(724,)166 -4703 y(726,)h(729,)f(731,)h(732,)f(734,)h(736,)g(739,)f(741,)h(743,)f -(747,)166 4802 y(748,)h(750,)f(752,)h(754,)f(755,)h(756,)g(757,)f(759,) -h(762,)f(763,)166 4902 y(766,)h(767,)f(768,)h(769,)f(770,)h(771,)g -(776,)f(777,)h(778,)f(779,)166 5001 y(780,)h(781,)f(785,)h(787,)f(789,) -h(790,)g(791,)f(794,)h(796,)f(798,)166 5101 y(799,)h(802,)f(804,)h -(805,)f(807,)h(809,)g(813,)f(815,)h(817,)f(818,)166 5201 -y(821,)h(824,)f(826,)h(830,)f(832,)h(835,)g(837,)f(839,)h(840,)f(841,) -166 5300 y(842,)h(847,)f(849,)h(851,)f(853,)h(855,)g(856,)f(857,)h -(858,)f(860,)166 5400 y(862,)h(864,)f(867,)h(869,)f(873,)h(874,)g(875,) -f(879,)h(880,)f(881,)2199 263 y(882,)h(883,)f(886,)h(889,)f(891,)h -(893,)g(896,)f(897,)h(898,)f(901,)2199 363 y(903,)h(904,)f(909,)h(911,) -f(912,)h(915,)g(916,)f(917,)h(918,)f(920,)2199 462 y(921,)h(922,)f -(933,)h(934,)f(941,)h(942,)g(948,)f(964,)h(965,)f(967,)2199 -562 y(968,)28 b(969,)f(970,)h(975,)f(993,)h(994,)g(1001,)f(1002,)g -(1008,)2199 662 y(1009,)e(1021,)g(1025,)g(1026,)g(1027,)g(1037,)g -(1043,)g(1044,)2199 761 y(1078,)g(1080,)g(1081,)g(1082,)g(1084,)g -(1118,)g(1120,)g(1165,)2199 861 y(1172,)g(1173,)g(1193,)g(1209,)g -(1215,)g(1216,)g(1219,)g(1251,)2199 960 y(1262,)g(1265,)g(1266,)g -(1284,)g(1287,)g(1290,)g(1296,)g(1302,)2199 1060 y(1308,)g(1322,)g -(1323,)g(1342,)g(1344,)g(1347,)g(1348,)g(1349,)2199 1160 -y(1365,)g(1367,)g(1379,)g(1380,)g(1384,)g(1387,)g(1390,)g(1393,)2199 -1259 y(1396,)g(1398,)g(1399,)g(1451,)g(1464,)g(1478,)g(1483,)g(1525.) -2033 1362 y Ff(PATH)s Fm(:)83 b(1296)p 2318 1375 167 -4 v -2 w(,)37 b(1297)p 2544 1375 V -2 w(,)g(1316,)e(1317.)2033 -1465 y Fk(P)m(aths)6 b Fm(:)83 b(207,)34 b(549,)g(656,)f(662,)h(763,)g -(765,)g(828,)g(839,)2199 1564 y(872,)i(876,)h(879,)f(920,)g(1379.)2033 -1667 y Fi(p)l(aths)12 b Fm(:)83 b(1296)p 2335 1680 V --2 w(,)32 b(1302,)e(1308,)g(1316,)g(1317,)g(1323,)g(1342,)2199 -1767 y(1344,)38 b(1347,)f(1349,)h(1365,)f(1367,)h(1379,)f(1380,)2199 -1866 y(1382,)25 b(1384,)g(1385,)g(1387,)g(1388,)g(1390,)g(1391,)g -(1393,)2199 1966 y(1394,)37 b(1396,)f(1397,)h(1399.)2033 -2069 y Fi(p)l(a0)17 b Fm(:)83 b(1219)p 2278 2082 V -2 -w(.)2033 2171 y Fi(p)l(en)11 b Fm(:)83 b(264)p 2273 2184 -125 4 v -2 w(,)32 b(278,)e(300,)g(302,)g(409,)g(411,)h(415,)f(458,)g -(461,)2199 2271 y(465,)k(654)p 2382 2284 V -2 w(,)i(657,)e(658,)f(661,) -h(664,)g(666,)g(669,)g(671,)2199 2371 y(674,)g(676,)g(707,)g(776,)f -(802,)h(807,)g(813,)g(821,)g(824,)2199 2470 y(859,)39 -b(861,)g(862,)h(863.)2033 2573 y Fi(p)l(en)p 2161 2573 -26 4 v 31 w(inner)13 b Fm(:)83 b(1283)p 2498 2586 167 -4 v -2 w(,)40 b(1284)p 2727 2586 V -1 w(.)2033 2676 y -Fi(p)l(en)p 2161 2676 26 4 v 31 w(midd)t(le)12 b Fm(:)83 -b(1283)p 2545 2689 167 4 v -2 w(,)40 b(1284)p 2774 2689 -V -2 w(.)2033 2779 y Fi(p)l(en)p 2161 2779 26 4 v 31 -w(outer)13 b Fm(:)83 b(1283)p 2494 2792 167 4 v -2 w(,)40 -b(1284)p 2723 2792 V -2 w(.)2033 2881 y Fi(p)l(entagon)p -2358 2881 26 4 v 31 w(diameter)14 b Fm(:)83 b(1459)p -2820 2894 167 4 v -2 w(,)44 b(1460)p 3053 2894 V -2 w(,)g(1462)p -3286 2894 V -2 w(,)g(1463)p 3519 2894 V -2 w(,)2199 2981 -y(1464)p 2199 2994 V -2 w(,)g(1465)p 2432 2994 V -1 w(.)2033 -3084 y Fi(p)l(entagon)p 2358 3084 26 4 v 31 w(r)l(adius)12 -b Fm(:)83 b(1453)p 2721 3097 167 4 v -2 w(,)35 b(1457,)d(1460.)2033 -3186 y Fi(p)l(ents)11 b Fm(:)83 b(1463)p 2335 3199 V --2 w(.)2033 3289 y Fi(p)l(ersp)10 b Fm(:)83 b(556)p 2336 -3302 125 4 v -1 w(,)30 b(559,)e(561,)h(570,)f(572,)h(574,)g(583,)f -(585.)2033 3392 y Ff(PERSP)r Fm(:)83 b(211)p 2361 3405 -V -1 w(,)36 b(212)p 2545 3405 V -1 w(,)g(253,)f(254,)g(312,)g(314,)g -(317,)g(319,)2199 3492 y(322,)f(324,)g(327,)g(329,)f(332,)h(334,)g -(337,)g(339,)g(398,)2199 3591 y(402,)39 b(431,)f(866,)h(1341.)2033 -3694 y Fi(p)l(ersp)p 2225 3694 26 4 v 31 w(tr)l(ansform)11 -b Fm(:)83 b(397.)2033 3797 y Fi(phi)14 b Fm(:)83 b(1287)p -2262 3810 167 4 v -2 w(,)44 b(1290)p 2495 3810 V -2 w(.)2033 -3899 y Ff(PI)t Fm(:)83 b(24,)28 b(25)p 2366 3912 84 4 -v -1 w(,)h(27)p 2501 3912 V -1 w(,)g(36)p 2636 3912 V --1 w(,)g(162,)e(163,)h(164,)g(505,)f(1110,)g(1268,)2199 -3999 y(1437,)e(1443,)g(1454,)g(1460,)g(1468,)g(1474,)g(1482,)g(1488.) -2033 4102 y Fi(pictur)l(e)11 b Fm(:)83 b(409,)33 b(410)p -2579 4115 125 4 v -2 w(,)i(411)p 2761 4115 V -2 w(,)g(412)p -2943 4115 V -2 w(,)g(413)p 3125 4115 V -2 w(,)g(414)p -3307 4115 V -1 w(,)f(415)p 3489 4115 V -1 w(,)g(416)p -3671 4115 V -1 w(,)2199 4201 y(417)p 2199 4214 V -1 w(,)25 -b(419)p 2372 4214 V -2 w(,)g(420)p 2544 4214 V -1 w(,)g(422)p -2717 4214 V -2 w(,)g(423)p 2889 4214 V -1 w(,)g(425)p -3062 4214 V -1 w(,)g(426)p 3235 4214 V -2 w(,)g(428)p -3407 4214 V -1 w(,)g(429)p 3580 4214 V -2 w(,)g(461)p -3752 4214 V -1 w(,)2199 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w(,)g(814)p -3062 4613 V -1 w(,)g(815)p 3235 4613 V -2 w(,)g(817)p -3407 4613 V -1 w(,)g(818)p 3580 4613 V -2 w(,)g(820)p -3752 4613 V -1 w(,)2199 4700 y(821)p 2199 4713 V -1 w(,)g(823)p -2372 4713 V -2 w(,)g(824)p 2544 4713 V -1 w(,)g(825)p -2717 4713 V -2 w(,)g(826)p 2889 4713 V -1 w(,)g(829)p -3062 4713 V -1 w(,)g(830)p 3235 4713 V -2 w(,)g(831)p -3407 4713 V -1 w(,)g(832)p 3580 4713 V -2 w(,)g(834)p -3752 4713 V -1 w(,)2199 4799 y(835)p 2199 4812 V -1 w(,)33 -b(836)p 2380 4812 V -2 w(,)h(837)p 2561 4812 V -2 w(,)f(924)p -2741 4812 V -1 w(,)g(925)p 2922 4812 V -1 w(,)g(928,)f(929)p -3284 4812 V -2 w(,)h(930)p 3464 4812 V -1 w(,)g(1049)p -3645 4812 167 4 v -2 w(,)2199 4899 y(1050)p 2199 4912 -V -2 w(,)27 b(1053)p 2415 4912 V -2 w(,)g(1054)p 2631 -4912 V -2 w(,)g(1097)p 2847 4912 V -2 w(,)g(1098)p 3063 -4912 V -2 w(,)g(1122)p 3279 4912 V -2 w(,)g(1123)p 3495 -4912 V -2 w(,)g(1124)p 3711 4912 V -2 w(,)2199 4998 y(1222)p -2199 5011 V -2 w(,)g(1223)p 2415 5011 V -2 w(,)g(1224)p -2631 5011 V -2 w(,)g(1225)p 2847 5011 V -2 w(,)g(1230)p -3063 5011 V -2 w(,)g(1231)p 3279 5011 V -2 w(,)g(1272)p -3495 5011 V -2 w(,)g(1273)p 3711 5011 V -2 w(,)2199 5098 -y(1276)p 2199 5111 V -2 w(,)g(1277)p 2415 5111 V -2 w(,)g(1283)p -2631 5111 V -2 w(,)g(1284)p 2847 5111 V -2 w(,)g(1383)p -3063 5111 V -2 w(,)g(1384)p 3279 5111 V -2 w(,)g(1386)p -3495 5111 V -2 w(,)g(1387)p 3711 5111 V -2 w(,)2199 5198 -y(1389)p 2199 5211 V -2 w(,)g(1390)p 2415 5211 V -2 w(,)g(1392)p -2631 5211 V -2 w(,)g(1393)p 2847 5211 V -2 w(,)g(1395)p -3063 5211 V -2 w(,)g(1396)p 3279 5211 V -2 w(,)g(1398)p -3495 5211 V -2 w(,)g(1399)p 3711 5211 V -2 w(.)2033 5300 -y Fk(Picture)5 b Fm(:)83 b(33)p 2451 5313 84 4 v -1 w(,)34 -b(196,)f(200,)f(208)p 2954 5313 125 4 v -2 w(,)i(209,)f(213,)f(216)p -3498 5313 V -1 w(,)h(218,)2199 5400 y(219)p 2199 5413 -V -1 w(,)25 b(220,)e(221,)h(222,)f(224,)h(226,)g(228,)f(229,)h(232,)f -(233,)p eop end -%%Page: 501 501 -TeXDict begin 501 500 bop 0 83 a Fn(x)p Fm(1525)139 b -Fl(3DLDFPR)n(G)2671 b(INDEX)141 b Fm(501)166 263 y(236,)24 -b(239,)f(242,)h(245,)f(247,)h(249,)g(251,)f(252,)h(257,)f(258,)166 -363 y(264,)h(373,)f(396,)h(397,)f(400,)h(409,)g(410,)f(411,)h(412,)f -(413,)166 462 y(414,)h(415,)f(416,)h(417,)f(419,)h(420,)g(422,)f(423,)h -(425,)f(426,)166 562 y(428,)h(429,)f(438,)h(440,)f(442,)h(453,)g(457,)f -(461,)h(462,)f(463,)166 662 y(464,)h(466,)f(467,)h(468,)f(469,)h(543,)g -(544)p 1202 675 125 4 v -2 w(,)h(545,)f(546,)f(548,)166 -761 y(551,)h(552,)f(553,)h(554,)f(654,)h(686,)g(775,)f(776,)h(777,)f -(778,)166 861 y(780,)34 b(781,)g(784,)g(785,)f(786,)h(787,)g(789,)g -(790,)g(793,)166 960 y(794,)g(795,)g(796,)g(798,)f(799,)h(801,)g(802,)g -(803,)g(804,)166 1060 y(806,)g(807,)g(808,)g(809,)f(812,)h(813,)g(814,) -g(815,)g(817,)166 1160 y(818,)g(820,)g(821,)g(823,)f(824,)h(825,)g -(826,)g(829,)g(830,)166 1259 y(831,)g(832,)g(834,)g(835,)f(836,)h(837,) -g(839,)g(841,)g(844,)166 1359 y(852,)e(854,)g(856,)f(858,)h(924,)g -(925,)g(929,)f(930,)h(1049,)166 1459 y(1050,)25 b(1053,)g(1054,)g -(1097,)g(1098,)g(1122,)g(1123,)g(1124,)166 1558 y(1222,)g(1223,)g -(1224,)g(1225,)g(1226,)g(1230,)g(1231,)g(1272,)166 1658 -y(1273,)g(1276,)g(1277,)g(1283,)g(1284,)g(1309,)g(1348,)g(1379,)166 -1757 y(1383,)g(1384,)g(1386,)g(1387,)g(1389,)g(1390,)g(1392,)g(1393,) -166 1857 y(1395,)34 b(1396,)g(1398,)f(1399,)h(1450.)0 -1965 y Fk(Pictures)5 b Fm(:)83 b(122,)26 b(207,)f(209,)h(216,)f(233,)h -(264,)f(686,)h(1299.)0 2072 y Fi(pink)14 b Fm(:)83 b(112)p -272 2085 V -1 w(,)44 b(113)p 464 2085 V -2 w(.)0 2180 -y Fi(pl)13 b Fm(:)84 b(643)p 183 2193 V -2 w(,)35 b(644)p -365 2193 V -2 w(,)g(949)p 547 2193 V -2 w(,)g(954)p 729 -2193 V -2 w(,)g(955,)e(956,)g(963,)g(985)p 1457 2193 -V -2 w(,)i(986,)166 2280 y(987,)k(990,)g(996)p 542 2293 -V -1 w(,)h(999.)0 2387 y Fi(pl)p 68 2387 26 4 v 31 w(normal)14 -b Fm(:)83 b(644)p 469 2400 125 4 v -2 w(.)0 2495 y Fk(Plane)5 -b Fm(:)83 b(12,)29 b(33)p 482 2508 84 4 v -1 w(,)i(356,)e(594,)g(615,)g -(617)p 1153 2508 125 4 v -2 w(,)i(619,)e(620)p 1509 2508 -V -2 w(,)i(621,)166 2594 y(622)p 166 2607 V -1 w(,)k(623,)f(624)p -532 2607 V -2 w(,)i(625,)d(626,)h(628,)g(629,)g(630,)g(631,)166 -2694 y(633,)g(634,)g(635,)g(636,)f(637,)h(641,)g(643,)g(644,)g(646,)166 -2794 y(647,)g(648,)g(902,)g(903,)f(904,)h(922,)g(948,)g(949,)g(953,)166 -2893 y(954,)i(985,)g(996,)f(1176,)h(1268.)0 3001 y Fk(Planes)t -Fm(:)84 b(615,)38 b(644,)g(1175.)0 3109 y Fk(P)m(oin)m(t)5 -b Fm(:)83 b(2,)33 b(33)p 433 3122 84 4 v -1 w(,)g(122)p -572 3122 125 4 v -2 w(,)g(149,)f(157,)g(166,)f(168,)h(196,)f(199,)166 -3208 y(200,)24 b(208)p 339 3221 V -2 w(,)h(210,)f(224,)f(240,)h(243,)g -(262,)f(264)p 1374 3221 V -1 w(,)i(265,)e(267,)166 3308 -y(268,)h(272,)f(274,)h(275,)f(278,)h(279,)g(280)p 1202 -3321 V -2 w(,)h(282,)f(283)p 1547 3321 V -2 w(,)h(284,)166 -3407 y(285,)f(286,)f(287)p 511 3420 V -1 w(,)i(288,)e(289,)h(290,)g -(291,)f(292,)h(293,)f(294,)166 3507 y(295,)h(296,)f(297)p -511 3520 V -1 w(,)i(298)p 684 3520 V -2 w(,)g(299,)f(300,)g(303,)f -(305,)h(309,)f(313,)166 3607 y(315,)h(318,)f(320,)h(323,)f(325,)h(328,) -g(330,)f(333,)h(335,)f(338,)166 3706 y(340,)h(343,)f(345,)h(346,)f -(349,)h(350,)g(351,)f(352,)h(353,)f(354,)166 3806 y(355,)h(357,)f(361,) -h(363,)f(365,)h(369,)g(370,)f(371,)h(372,)f(373,)166 -3906 y(376,)h(377,)f(378,)h(379,)f(380,)h(381)p 1029 -3919 V -1 w(,)h(382,)e(383,)h(386,)f(392,)166 4005 y(393,)h(395,)f -(396,)h(399,)f(402,)h(403,)g(404,)f(405,)h(407,)f(411,)166 -4105 y(413,)h(415,)f(417,)h(419,)f(420,)h(422,)g(423,)f(425,)h(426,)f -(428,)166 4204 y(429,)h(432,)f(434,)h(436,)f(437,)h(439,)g(441,)f(442,) -h(443,)f(446,)166 4304 y(448,)h(450,)f(452,)h(458,)f(461,)h(462,)g -(463,)f(464,)h(465,)f(467,)166 4404 y(469,)h(471,)f(472,)h(475,)f(477,) -h(478,)g(479,)f(480,)h(481,)f(482,)166 4503 y(483,)h(484,)f(485,)h -(486,)f(488,)h(489,)g(490,)f(491,)h(492,)f(493,)166 4603 -y(495,)h(496,)f(497,)h(498,)f(499,)h(500,)g(501,)f(502,)h(503,)f(504,) -166 4703 y(505,)h(507,)f(508,)h(509,)f(510,)h(511,)g(512,)f(513,)h -(516,)f(517,)166 4802 y(523,)h(524,)f(525,)h(526,)f(527,)h(528,)g(529,) -f(530,)h(541,)f(549,)166 4902 y(553,)h(556,)f(557,)h(565,)f(566,)h -(567,)g(568,)f(576,)h(577,)f(579,)166 5001 y(591,)h(593,)f(594,)h(595,) -f(596,)h(601,)g(603,)f(604,)h(605,)f(606,)166 5101 y(615,)h(617,)f -(623,)h(624,)f(633,)h(634,)g(635,)f(637,)h(640,)f(641,)166 -5201 y(644,)h(654,)f(657,)h(659,)f(663,)h(664,)g(665,)f(666,)h(667,)f -(669,)166 5300 y(671,)h(672,)f(673,)h(674,)f(675,)h(676,)g(685,)f(717,) -h(719,)f(720,)166 5400 y(730,)h(731,)f(732,)h(734,)f(735,)h(736,)g -(739,)f(741,)h(743,)f(748,)2199 263 y(751,)h(752,)f(754,)h(755,)f(756,) -h(757,)g(765,)f(770,)h(780,)f(781,)2199 363 y(789,)h(790,)f(791,)h -(798,)f(799,)h(817,)g(818,)f(828,)h(830,)f(839,)2199 -462 y(840,)h(843,)f(844,)h(856,)f(859,)h(867,)g(873,)f(875,)h(885,)f -(886,)2199 562 y(888,)h(889,)f(890,)h(891,)f(892,)h(893,)g(896,)f(897,) -h(900,)f(901,)2199 662 y(903,)h(904,)f(914,)h(920,)f(921,)h(923,)g -(924,)f(925,)h(928,)f(929,)2199 761 y(930,)h(934,)f(941,)h(948,)f(949,) -h(950,)g(951,)f(952,)h(953,)f(954,)2199 861 y(957,)h(964,)f(965,)h -(967,)f(968,)h(975,)g(978,)f(979,)h(980,)f(981,)2199 -960 y(984,)32 b(985,)g(988,)f(990,)h(995,)g(996,)g(997,)f(999,)h(1006,) -2199 1060 y(1007,)25 b(1017,)g(1018,)g(1022,)g(1023,)g(1032,)g(1033,)g -(1034,)2199 1160 y(1035,)g(1036,)g(1064,)g(1065,)g(1066,)g(1067,)g -(1068,)g(1069,)2199 1259 y(1070,)g(1071,)g(1072,)g(1082,)g(1083,)g -(1085,)g(1086,)g(1087,)2199 1359 y(1088,)g(1103,)g(1109,)g(1110,)g -(1111,)g(1112,)g(1123,)g(1126,)2199 1459 y(1127,)g(1139,)g(1140,)g -(1141,)g(1142,)g(1144,)g(1145,)g(1146,)2199 1558 y(1147,)g(1163,)g -(1164,)g(1167,)g(1168,)g(1170,)g(1171,)g(1172,)2199 1658 -y(1177,)g(1178,)g(1179,)g(1182,)g(1183,)g(1185,)g(1188,)g(1193,)2199 -1757 y(1205,)g(1206,)g(1210,)g(1211,)g(1213,)g(1214,)g(1219,)g(1228,) -2199 1857 y(1229,)g(1242,)g(1243,)g(1244,)g(1245,)g(1256,)g(1258,)g -(1259,)2199 1957 y(1262,)g(1263,)g(1264,)g(1268,)g(1270,)g(1274,)g -(1284,)g(1287,)2199 2056 y(1288,)g(1290,)g(1296,)g(1313,)g(1314,)g -(1329,)g(1330,)g(1331,)2199 2156 y(1332,)g(1333,)g(1334,)g(1335,)g -(1336,)g(1337,)g(1338,)g(1357,)2199 2256 y(1358,)g(1361,)g(1362,)g -(1419,)g(1420,)g(1432,)g(1433,)g(1442,)2199 2355 y(1443,)g(1444,)g -(1446,)g(1447,)g(1449,)g(1450,)g(1451,)g(1459,)2199 2455 -y(1460,)g(1461,)g(1462,)g(1463,)g(1464,)g(1465,)g(1473,)g(1474,)2199 -2554 y(1476,)31 b(1478,)g(1487,)g(1488,)g(1490,)g(1506.)2033 -2660 y Fi(p)l(oint)12 b Fm(:)84 b(617)p 2332 2673 V -2 -w(,)38 b(619,)f(620,)f(623,)g(624,)h(626,)f(629,)h(634,)2199 -2759 y(646,)i(903)p 2387 2772 V -2 w(,)h(985,)f(1163.)2033 -2865 y Fi(p)l(oint)p 2218 2865 26 4 v 31 w(iter)13 b -Fm(:)83 b(859,)34 b(861,)f(862,)g(863,)g(864.)2033 2970 -y Fi(p)l(oint)p 2218 2970 V 31 w(on)p 2338 2970 V 31 -w(line)11 b Fm(:)83 b(644)p 2612 2983 125 4 v -2 w(.)2033 -3075 y Fk(p)s(oin)m(t)p 2255 3075 29 5 v 40 w(pair)5 -b Fm(:)83 b(267)p 2567 3088 125 4 v -2 w(.)2033 3180 -y Fi(p)l(oint)p 2218 3180 26 4 v 31 w(ptr)13 b Fm(:)83 -b(674)p 2468 3193 125 4 v -1 w(,)42 b(676)p 2658 3193 -V -2 w(.)2033 3285 y Fk(P)m(oin)m(ts)5 b Fm(:)83 b(2,)29 -b(122,)e(138,)h(168,)f(207,)h(262,)g(264,)f(265,)h(290,)2199 -3385 y(349,)34 b(379,)g(397,)g(402,)f(418,)h(442,)g(451,)g(518,)g(520,) -2199 3485 y(527,)g(531,)g(549,)g(594,)f(602,)h(654,)g(662,)g(667,)g -(721,)2199 3584 y(732,)g(764,)g(765,)g(769,)f(770,)h(828,)g(839,)g -(841,)g(842,)2199 3684 y(856,)g(858,)g(864,)g(867,)f(876,)h(885,)g -(886,)g(896,)g(898,)2199 3784 y(904,)28 b(913,)f(920,)h(948,)f(967,)h -(999,)g(1024,)f(1082,)g(1126,)2199 3883 y(1172,)34 b(1175,)g(1258,)f -(1348,)h(1450.)2033 3988 y Fi(p)l(oints)11 b Fm(:)83 -b(654)p 2364 4001 V -1 w(,)26 b(657,)e(659,)h(664,)f(666,)h(669,)f -(671,)h(672,)f(674,)2199 4088 y(676,)g(685,)f(732,)h(734,)f(739,)h -(741,)g(743,)f(748,)h(755,)f(757,)2199 4188 y(764,)h(765,)f(770,)h -(776,)f(802,)h(807,)g(813,)f(821,)h(824,)f(830,)2199 -4287 y(839)p 2199 4300 V -1 w(,)i(840,)e(842,)h(843,)f(856,)h(858,)g -(859,)f(862,)h(864,)f(866,)2199 4387 y(867,)h(878,)f(880,)h(881,)f -(884,)h(885,)g(886,)f(889,)h(891,)f(893,)2199 4487 y(894,)34 -b(897,)g(899,)g(900,)f(913,)h(914,)g(920,)g(921,)g(933,)2199 -4586 y(969,)c(970,)f(979,)h(981,)g(988,)f(990,)h(997,)g(1001,)f(1024,) -2199 4686 y(1034,)c(1065,)g(1070,)g(1086,)g(1088,)g(1110,)g(1123,)g -(1126,)2199 4785 y(1127,)31 b(1178,)g(1258)p 2643 4798 -167 4 v -2 w(,)i(1259,)e(1270,)g(1274.)2033 4891 y Fi(p)l(oints)p -2252 4891 26 4 v 31 w(iter)13 b Fm(:)83 b(867.)2033 4996 -y Fk(P)m(olygon)5 b Fm(:)83 b(973,)28 b(975)p 2657 5009 -125 4 v -1 w(,)i(977,)f(979,)f(981,)h(983,)g(985,)f(988,)2199 -5096 y(994,)33 b(995,)f(996,)h(1000,)f(1002,)g(1004,)g(1007,)g(1009,) -2199 5195 y(1011,)38 b(1013,)f(1016,)h(1018,)f(1021,)h(1023,)f(1025,) -2199 5295 y(1057,)g(1059,)f(1084,)h(1296.)2033 5400 y -Fi(Polygons)13 b Fm(:)83 b(999.)p eop end -%%Page: 502 502 -TeXDict begin 502 501 bop 0 83 a Fm(502)140 b Fl(INDEX)2670 -b(3DLDFPR)n(G)142 b Fn(x)p Fm(1525)0 263 y Fi(p)l(olygons)12 -b Fm(:)84 b(1296.)0 365 y Fi(p)l(olyhe)l(d)15 b Fm(:)83 -b(1477.)0 466 y Fk(P)m(olyhedra)6 b Fm(:)83 b(528,)30 -b(1294,)g(1429,)f(1446,)h(1448.)0 568 y Fk(P)m(olyhedron)5 -b Fm(:)83 b(1296,)26 b(1329,)g(1429,)g(1431)p 1239 581 -167 4 v -2 w(,)j(1433,)d(1436,)166 668 y(1440,)f(1446,)g(1453,)g(1457,) -g(1467,)g(1471,)g(1481,)g(1485.)0 769 y Fi(p)l(op)p 127 -769 26 4 v 32 w(b)l(ack)14 b Fm(:)83 b(685.)0 871 y(p)r(orting:)g(656.) -0 972 y(P)n(orting:)e(864.)0 1074 y Fi(p)l(ortr)l(ait)13 -b Fm(:)83 b(1464)p 388 1087 167 4 v -2 w(,)35 b(1465)p -612 1087 V -2 w(,)h(1477)p 837 1087 V -2 w(,)g(1478)p -1062 1087 V -2 w(.)0 1176 y Fi(p)l(os)12 b Fm(:)83 b(565)p -232 1189 125 4 v -2 w(,)23 b(566)p 402 1189 V -1 w(,)f(567)p -572 1189 V -1 w(,)h(568)p 743 1189 V -2 w(,)g(595)p 913 -1189 V -1 w(,)g(596)p 1084 1189 V -2 w(,)g(1122)p 1254 -1189 167 4 v -2 w(,)g(1123)p 1466 1189 V -2 w(,)g(1124)p -1678 1189 V -2 w(.)0 1277 y Fi(p)l(os)p 119 1277 26 4 -v 31 w(x)14 b Fm(:)83 b(560)p 304 1290 125 4 v -2 w(,)38 -b(561)p 489 1290 V -1 w(,)f(562)p 674 1290 V -1 w(,)h(563)p -860 1290 V -2 w(,)g(923,)e(924)p 1230 1290 V -2 w(,)i(925)p -1415 1290 V -1 w(,)f(926,)166 1377 y(927,)i(928,)g(929)p -542 1390 V -1 w(,)h(930)p 730 1390 V -1 w(.)0 1479 y -Fi(p)l(os)p 119 1479 26 4 v 31 w(y)12 b Fm(:)83 b(560)p -303 1492 125 4 v -1 w(,)37 b(561)p 488 1492 V -1 w(,)h(562)p -674 1492 V -2 w(,)g(563)p 859 1492 V -2 w(,)g(923,)e(924)p -1229 1492 V -1 w(,)i(925)p 1415 1492 V -2 w(,)g(926,)166 -1578 y(927,)h(928,)g(929)p 542 1591 V -1 w(,)h(930)p -730 1591 V -1 w(.)0 1680 y Fi(p)l(os)p 119 1680 26 4 -v 31 w(z)15 b Fm(:)83 b(560)p 300 1693 125 4 v -2 w(,)38 -b(561)p 485 1693 V -1 w(,)f(562)p 670 1693 V -1 w(,)h(563)p -856 1693 V -2 w(,)g(923,)f(924)p 1227 1693 V -2 w(,)h(925)p -1412 1693 V -1 w(,)g(926,)166 1779 y(927,)h(928,)g(929)p -542 1792 V -1 w(,)h(930)p 730 1792 V -1 w(.)0 1881 y -Fi(p)l(osition)12 b Fm(:)83 b(208)p 399 1894 V -2 w(,)33 -b(462,)e(471,)g(472,)h(556)p 1120 1894 V -2 w(,)h(557,)e(559,)g(561,) -166 1981 y(570,)24 b(572,)f(574,)h(576,)f(593)p 856 1994 -V -1 w(,)i(594,)f(596,)f(597,)h(598,)f(600,)166 2080 -y(601,)32 b(605,)g(606,)g(609,)f(934,)h(999,)g(1188.)0 -2182 y Fi(p)l(osition)p 286 2182 26 4 v 32 w(str)12 b -Fm(:)84 b(461)p 529 2195 125 4 v -2 w(,)23 b(462)p 699 -2195 V -2 w(,)g(463)p 869 2195 V -2 w(,)g(464)p 1039 -2195 V -2 w(,)g(466)p 1209 2195 V -1 w(,)f(467)p 1379 -2195 V -1 w(,)g(468)p 1549 2195 V -1 w(,)g(469)p 1719 -2195 V -1 w(.)0 2284 y Fi(p)l(osition)p 286 2284 26 4 -v 32 w(string)11 b Fm(:)83 b(829)p 637 2297 125 4 v -1 -w(,)40 b(830)p 825 2297 V -2 w(,)g(831)p 1012 2297 V --1 w(,)f(832)p 1199 2297 V -1 w(,)h(834)p 1387 2297 V --2 w(,)g(835)p 1574 2297 V -1 w(,)166 2383 y(836)p 166 -2396 V -1 w(,)45 b(837)p 359 2396 V -1 w(.)0 2485 y Fi(pp)l(en)11 -b Fm(:)83 b(410)p 282 2498 V -1 w(,)29 b(411)p 459 2498 -V -1 w(,)g(412)p 636 2498 V -1 w(,)g(413)p 813 2498 V --1 w(,)g(414)p 990 2498 V -1 w(,)g(415)p 1167 2498 V --1 w(,)g(416)p 1344 2498 V -1 w(,)g(417)p 1521 2498 V --1 w(,)g(419)p 1698 2498 V -1 w(,)166 2584 y(420)p 166 -2597 V -1 w(,)c(422)p 339 2597 V -2 w(,)g(423)p 511 2597 -V -1 w(,)g(425)p 684 2597 V -2 w(,)g(426)p 856 2597 V --1 w(,)g(428)p 1029 2597 V -1 w(,)g(429)p 1202 2597 V --2 w(,)g(775)p 1374 2597 V -1 w(,)g(776)p 1547 2597 V --2 w(,)g(777)p 1719 2597 V -1 w(,)166 2684 y(778)p 166 -2697 V -1 w(,)g(780)p 339 2697 V -2 w(,)g(781)p 511 2697 -V -1 w(,)g(784)p 684 2697 V -2 w(,)g(785)p 856 2697 V --1 w(,)g(786)p 1029 2697 V -1 w(,)g(787)p 1202 2697 V --2 w(,)g(789)p 1374 2697 V -1 w(,)g(790)p 1547 2697 V --2 w(,)g(793)p 1719 2697 V -1 w(,)166 2784 y(794)p 166 -2797 V -1 w(,)g(795)p 339 2797 V -2 w(,)g(796)p 511 2797 -V -1 w(,)g(798)p 684 2797 V -2 w(,)g(799)p 856 2797 V --1 w(,)g(806)p 1029 2797 V -1 w(,)g(807)p 1202 2797 V --2 w(,)g(808)p 1374 2797 V -1 w(,)g(809)p 1547 2797 V --2 w(,)g(812)p 1719 2797 V -1 w(,)166 2883 y(813)p 166 -2896 V -1 w(,)g(814)p 339 2896 V -2 w(,)g(815)p 511 2896 -V -1 w(,)g(817)p 684 2896 V -2 w(,)g(818)p 856 2896 V --1 w(,)g(823)p 1029 2896 V -1 w(,)g(824)p 1202 2896 V --2 w(,)g(825)p 1374 2896 V -1 w(,)g(826)p 1547 2896 V --2 w(,)g(923)p 1719 2896 V -1 w(,)166 2983 y(924)p 166 -2996 V -1 w(,)g(925)p 339 2996 V -1 w(,)h(928,)e(929)p -686 2996 V -1 w(,)i(930)p 860 2996 V -2 w(,)g(1049)p -1033 2996 167 4 v -2 w(,)g(1050)p 1248 2996 V -2 w(,)g(1053)p -1463 2996 V -2 w(,)g(1054)p 1678 2996 V -2 w(,)166 3083 -y(1097)p 166 3096 V -2 w(,)h(1098)p 382 3096 V -2 w(,)g(1222)p -598 3096 V -2 w(,)g(1223)p 814 3096 V -2 w(,)g(1224)p -1030 3096 V -2 w(,)g(1225)p 1246 3096 V -2 w(,)g(1230)p -1462 3096 V -2 w(,)g(1231)p 1678 3096 V -2 w(,)166 3182 -y(1272)p 166 3195 V -2 w(,)g(1273)p 382 3195 V -2 w(,)g(1276)p -598 3195 V -2 w(,)g(1277)p 814 3195 V -2 w(,)g(1382,)e(1383)p -1246 3195 V -2 w(,)i(1384)p 1462 3195 V -2 w(,)g(1388,)166 -3282 y(1389)p 166 3295 V -2 w(,)g(1390)p 382 3295 V -2 -w(,)g(1391,)e(1392)p 814 3295 V -2 w(,)i(1393)p 1030 -3295 V -2 w(,)g(1397,)e(1398)p 1462 3295 V -2 w(,)i(1399)p -1678 3295 V -2 w(.)0 3383 y Fi(ppt)13 b Fm(:)83 b(268)p -231 3396 125 4 v -2 w(,)45 b(272)p 423 3396 V -2 w(.)0 -3485 y Fi(pp0)17 b Fm(:)83 b(528)p 249 3498 V -2 w(,)45 -b(603)p 441 3498 V -2 w(.)0 3587 y Fi(pp1)17 b Fm(:)83 -b(528)p 249 3600 V -2 w(,)45 b(603)p 441 3600 V -2 w(.)0 -3688 y Fi(pr)l(e)l(cision)12 b Fm(:)83 b(1444,)36 b(1512,)g(1513.)0 -3790 y Fi(pr)l(o)l(gr)l(am)p 295 3790 26 4 v 31 w(name)11 -b Fm(:)83 b(42)p 633 3803 84 4 v -1 w(,)39 b(43)p 778 -3803 V -1 w(,)f(44.)0 3892 y Fi(pr)l(oj)17 b Fm(:)83 -b(200)p 263 3905 125 4 v -1 w(,)30 b(210)p 441 3905 V --1 w(,)g(254)p 619 3905 V -1 w(,)g(312)p 797 3905 V -1 -w(,)g(313)p 975 3905 V -1 w(,)g(314)p 1153 3905 V -1 -w(,)g(315)p 1331 3905 V -1 w(,)g(317)p 1509 3905 V -1 -w(,)g(318)p 1687 3905 V -1 w(,)166 3991 y(319)p 166 4004 -V -1 w(,)35 b(320)p 349 4004 V -2 w(,)h(322)p 532 4004 -V -2 w(,)g(323)p 715 4004 V -2 w(,)f(324)p 897 4004 V --1 w(,)g(325)p 1080 4004 V -1 w(,)g(327)p 1263 4004 V --1 w(,)g(328)p 1446 4004 V -2 w(,)h(329)p 1629 4004 V --2 w(,)166 4091 y(330)p 166 4104 V -1 w(,)f(332)p 349 -4104 V -2 w(,)h(333)p 532 4104 V -2 w(,)g(334)p 715 4104 -V -2 w(,)f(335)p 897 4104 V -1 w(,)g(337)p 1080 4104 -V -1 w(,)g(338)p 1263 4104 V -1 w(,)g(339)p 1446 4104 -V -2 w(,)h(340)p 1629 4104 V -2 w(,)166 4190 y(398)p -166 4203 V -1 w(,)f(399)p 349 4203 V -2 w(,)h(400,)e(402)p -715 4203 V -2 w(,)h(403)p 897 4203 V -1 w(,)g(431)p 1080 -4203 V -1 w(,)g(432)p 1263 4203 V -1 w(,)g(442)p 1446 -4203 V -2 w(,)h(443)p 1629 4203 V -2 w(,)166 4290 y(472)p -166 4303 V -1 w(,)f(548)p 349 4303 V -2 w(,)h(549,)e(553,)f(554)p -897 4303 V -1 w(,)i(742)p 1080 4303 V -1 w(,)g(743)p -1263 4303 V -1 w(,)g(839)p 1446 4303 V -2 w(,)h(840)p -1629 4303 V -2 w(,)166 4390 y(866)p 166 4403 V -1 w(,)e(867)p -348 4403 V -2 w(,)g(1341)p 529 4403 167 4 v -2 w(,)g(1342)p -752 4403 V -2 w(,)g(1364)p 975 4403 V -2 w(,)g(1365)p -1198 4403 V -2 w(.)0 4491 y Fi(pr)l(oj)p 145 4491 26 -4 v 32 w(on)p 266 4491 V 30 w(x)p 335 4491 V 30 w(z)p -399 4491 V 31 w(plane)11 b Fm(:)83 b(381)p 732 4504 125 -4 v -1 w(,)31 b(382,)f(383,)g(384,)g(386.)0 4593 y Ff(PROJ_VALUE)p -Fm(:)83 b(264.)0 4695 y Ff(PROJ_VALUES)p Fm(:)g(264)p -590 4708 V -2 w(,)33 b(265)p 770 4708 V -1 w(,)g(463,)f(464,)f(829.)0 -4796 y Ff(PROJ_VALUES_X_Y)n Fm(:)83 b(264)p 764 4809 -V -1 w(,)35 b(265)p 947 4809 V -1 w(,)g(463.)0 4898 y -Fi(pr)l(oje)l(ct)13 b Fm(:)83 b(313,)33 b(316,)h(318,)f(397,)g(398)p -1088 4911 V -1 w(,)h(399)p 1270 4911 V -1 w(,)h(402)p -1453 4911 V -2 w(,)g(403)p 1635 4911 V -1 w(,)166 4997 -y(431,)f(436,)g(442,)g(443,)f(444,)h(451,)g(457,)g(463,)g(472,)166 -5097 y(742)p 166 5110 V -1 w(,)e(743)p 346 5110 V -1 -w(,)h(839,)e(841,)g(845,)h(1283,)f(1365.)0 5199 y Fi(pr)l(oje)l(ction) -12 b Fm(:)83 b(253)p 472 5212 V -1 w(.)0 5300 y Fk(Pro)5 -b(jections)g Fm(:)83 b(211)p 586 5313 V -2 w(,)33 b(212)p -766 5313 V -2 w(,)g(253,)d(254,)h(312,)g(314,)g(317,)166 -5400 y(319,)j(322,)g(324,)g(327,)f(329,)h(332,)g(334,)g(337,)g(339,) -2199 263 y(398,)d(400)p 2379 276 V -1 w(,)i(402,)e(431,)g(866,)h(1341,) -f(1505)p 3323 276 167 4 v -2 w(.)2033 365 y Fi(pr)l(oje)l(ctive)p -2379 365 26 4 v 32 w(c)l(o)l(or)l(dinates)12 b Fm(:)83 -b(264)p 2925 378 125 4 v -1 w(,)36 b(265,)e(278,)g(300,)g(303,)2199 -464 y(313,)g(318,)g(397,)g(399,)f(400,)h(401,)g(431,)g(436,)g(443,)2199 -564 y(452,)j(457,)g(458,)g(463,)f(841.)2033 665 y Fi(pr)l(oje)l(ctive)p -2379 665 26 4 v 32 w(extr)l(emes)11 b Fm(:)83 b(252,)28 -b(264)p 3014 678 125 4 v -1 w(,)i(278,)e(300,)h(444,)g(446,)2199 -765 y(448,)24 b(450,)f(452,)h(453,)f(551)p 2889 778 V --1 w(,)i(654)p 3062 778 V -1 w(,)g(656,)e(657,)h(661,)f(664,)2199 -865 y(666,)34 b(669,)g(671,)g(674,)f(676,)h(842,)g(843,)g(844,)g(845,) -2199 964 y(847,)f(849,)f(851,)h(1030,)f(1033,)g(1040,)g(1042,)g(1296)p -3636 977 167 4 v -2 w(,)2199 1064 y(1299,)25 b(1300,)g(1302,)g(1308,)g -(1367,)g(1368,)g(1370,)g(1372,)2199 1163 y(1374,)31 b(1379,)g(1416,)g -(1418,)g(1420,)g(1422.)2033 1265 y Fi(pt)12 b Fm(:)83 -b(208)p 2221 1278 125 4 v -1 w(,)34 b(210,)f(268)p 2585 -1278 V -2 w(,)h(269,)f(270,)g(272)p 3130 1278 V -2 w(,)i(273,)d(309)p -3493 1278 V -1 w(,)i(411)p 3675 1278 V -1 w(,)2199 1365 -y(415)p 2199 1378 V -1 w(,)h(425)p 2382 1378 V -2 w(,)h(426)p -2565 1378 V -2 w(,)g(428)p 2748 1378 V -2 w(,)f(429)p -2930 1378 V -1 w(,)g(462,)f(470,)g(471,)g(472,)2199 1464 -y(541,)g(545,)g(546,)g(553,)f(601)p 2930 1477 V -1 w(,)i(603,)f(605,)g -(606,)g(607,)2199 1564 y(641,)g(754)p 2382 1577 V -2 -w(,)i(755)p 2565 1577 V -2 w(,)g(756)p 2748 1577 V -2 -w(,)f(757)p 2930 1577 V -1 w(,)g(798)p 3113 1577 V -1 -w(,)g(799)p 3296 1577 V -1 w(,)g(817)p 3479 1577 V -2 -w(,)h(818)p 3662 1577 V -2 w(,)2199 1663 y(958,)e(959,)g(960,)g(961,)f -(963,)h(988,)g(990,)g(991,)g(997,)2199 1763 y(999,)28 -b(1163,)g(1164,)g(1179,)f(1184,)h(1186,)g(1188,)f(1221,)2199 -1863 y(1228,)k(1268,)g(1357)p 2643 1876 167 4 v -2 w(,)i(1358)p -2865 1876 V -2 w(,)g(1444,)e(1451.)2033 1964 y Fi(pt)p -2108 1964 26 4 v 31 w(c4)16 b Fm(:)83 b(949)p 2336 1977 -125 4 v -2 w(.)2033 2066 y Fi(pt)p 2108 2066 26 4 v 31 -w(iter)13 b Fm(:)83 b(1433.)2033 2167 y Fi(pt)p 2108 -2167 V 31 w(on)p 2228 2167 V 30 w(x)p 2297 2167 V 30 -w(axis)12 b Fm(:)83 b(382)p 2580 2180 125 4 v -2 w(.)2033 -2269 y Fi(pt)p 2108 2269 26 4 v 31 w(on)p 2228 2269 V -30 w(z)p 2292 2269 V 31 w(axis)11 b Fm(:)83 b(383)p 2575 -2282 125 4 v -1 w(,)38 b(384,)f(386.)2033 2370 y Fi(pt)p -2108 2370 26 4 v 31 w(ve)l(ctor)13 b Fm(:)83 b(953,)39 -b(954)p 2656 2383 125 4 v -1 w(,)i(955,)e(956,)g(963,)g(985)p -3409 2383 V -1 w(,)h(986,)2199 2470 y(987,)k(990.)2033 -2571 y Fi(ptr)13 b Fm(:)83 b(997)p 2257 2584 V -1 w(,)44 -b(1312)p 2449 2584 167 4 v -2 w(.)2033 2673 y Fi(pts)11 -b Fm(:)83 b(1420)p 2254 2686 V -2 w(,)37 b(1443)p 2480 -2686 V -2 w(,)f(1444,)e(1445,)h(1449)p 3156 2686 V -2 -w(,)h(1451)p 3381 2686 V -2 w(,)h(1460)p 3607 2686 V --2 w(,)2199 2772 y(1461,)h(1463)p 2428 2785 V -2 w(,)h(1464)p -2656 2785 V -2 w(,)h(1474)p 2885 2785 V -2 w(,)f(1476)p -3113 2785 V -2 w(,)h(1478)p 3342 2785 V -2 w(,)f(1488)p -3570 2785 V -2 w(,)2199 2872 y(1490)p 2199 2885 V -2 -w(,)44 b(1491.)2033 2973 y Fi(pt0)16 b Fm(:)83 b(149)p -2267 2986 125 4 v -1 w(,)31 b(717)p 2446 2986 V -1 w(,)h(948)p -2626 2986 V -2 w(,)g(949)p 2805 2986 V -1 w(,)g(954)p -2985 2986 V -2 w(,)g(957,)f(961,)f(963,)g(984)p 3702 -2986 V -1 w(,)2199 3073 y(985)p 2199 3086 V -1 w(,)20 -b(988,)g(990,)f(991,)g(1069)p 2872 3086 167 4 v -2 w(,)i(1070)p -3082 3086 V -2 w(,)f(1071)p 3291 3086 V -2 w(,)h(1072)p -3501 3086 V -2 w(,)g(1163,)2199 3173 y(1164)p 2199 3186 -V -2 w(,)27 b(1171)p 2415 3186 V -2 w(,)g(1179)p 2631 -3186 V -2 w(,)g(1188)p 2847 3186 V -2 w(,)g(1219)p 3063 -3186 V -2 w(,)g(1263)p 3279 3186 V -2 w(,)g(1264)p 3495 -3186 V -2 w(,)g(1284)p 3711 3186 V -2 w(.)2033 3274 y -Fi(pt0)p 2150 3274 26 4 v 31 w(h)11 b Fm(:)83 b(949)p -2335 3287 125 4 v -1 w(,)39 b(957)p 2522 3287 V -2 w(,)g(959,)e(960.) -2033 3376 y Fi(pt0)p 2150 3376 26 4 v 31 w(v)13 b Fm(:)83 -b(949)p 2333 3389 125 4 v -1 w(,)39 b(957)p 2520 3389 -V -2 w(,)g(958,)f(960.)2033 3477 y Fi(pt1)16 b Fm(:)83 -b(149)p 2267 3490 V -1 w(,)31 b(717)p 2446 3490 V -1 -w(,)h(949)p 2626 3490 V -2 w(,)g(954)p 2805 3490 V -1 -w(,)g(957,)e(961,)h(963,)f(984)p 3523 3490 V -1 w(,)h(985)p -3702 3490 V -1 w(,)2199 3577 y(988,)i(990,)f(991,)h(1069)p -2744 3590 167 4 v -2 w(,)h(1070)p 2967 3590 V -2 w(,)g(1071)p -3190 3590 V -2 w(,)g(1072)p 3413 3590 V -2 w(,)g(1171)p -3636 3590 V -2 w(,)2199 3676 y(1179)p 2199 3689 V -2 -w(,)39 b(1219)p 2427 3689 V -2 w(,)f(1263)p 2654 3689 -V -2 w(,)h(1264)p 2882 3689 V -2 w(.)2033 3778 y Fi(pt1)p -2150 3778 26 4 v 31 w(h)11 b Fm(:)83 b(957)p 2335 3791 -125 4 v -1 w(,)43 b(959.)2033 3879 y Fi(pt1)p 2150 3879 -26 4 v 31 w(v)13 b Fm(:)83 b(957)p 2333 3892 125 4 v --1 w(.)2033 3981 y Fi(pt2)16 b Fm(:)83 b(149)p 2267 3994 -V -1 w(,)30 b(1069)p 2445 3994 167 4 v -2 w(,)g(1070)p -2664 3994 V -2 w(,)g(1071)p 2883 3994 V -2 w(,)g(1072)p -3102 3994 V -2 w(,)g(1179)p 3321 3994 V -2 w(,)g(1219)p -3540 3994 V -2 w(.)2033 4082 y Fi(pt20)16 b Fm(:)83 b(1183)p -2309 4095 V -1 w(,)42 b(1184.)2033 4184 y Fi(pt21)16 -b Fm(:)83 b(1183)p 2309 4197 V -1 w(,)42 b(1184.)2033 -4285 y Fi(pt22)16 b Fm(:)83 b(1183)p 2309 4298 V -1 w(,)42 -b(1184.)2033 4387 y Fi(pt23)16 b Fm(:)83 b(1183)p 2309 -4400 V -1 w(,)42 b(1184.)2033 4488 y Fi(pt3)16 b Fm(:)83 -b(1069)p 2267 4501 V -2 w(,)32 b(1070)p 2488 4501 V -2 -w(,)g(1071)p 2709 4501 V -2 w(,)h(1072)p 2931 4501 V --2 w(,)f(1179)p 3152 4501 V -2 w(,)g(1219)p 3373 4501 -V -2 w(.)2033 4590 y Fi(pt4)16 b Fm(:)83 b(1070)p 2267 -4603 V -2 w(,)44 b(1219)p 2500 4603 V -2 w(.)2033 4691 -y Fi(pt5)16 b Fm(:)83 b(1070)p 2267 4704 V -2 w(,)44 -b(1219)p 2500 4704 V -2 w(.)2033 4793 y Fi(pt6)16 b Fm(:)83 -b(1070)p 2267 4806 V -2 w(,)44 b(1219)p 2500 4806 V -2 -w(.)2033 4894 y Fi(pt7)16 b Fm(:)83 b(1070)p 2267 4907 -V -2 w(,)44 b(1219)p 2500 4907 V -2 w(.)2033 4996 y Fi(pt8)16 -b Fm(:)83 b(1070)p 2267 5009 V -2 w(,)44 b(1219)p 2500 -5009 V -2 w(.)2033 5097 y Fi(pt9)16 b Fm(:)83 b(1219)p -2267 5110 V -2 w(.)2033 5199 y Fi(purple)11 b Fm(:)83 -b(108,)40 b(112)p 2562 5212 125 4 v -2 w(,)h(113)p 2750 -5212 V -1 w(.)2033 5300 y Fi(push)p 2201 5300 26 4 v -31 w(b)l(ack)14 b Fm(:)83 b(226,)28 b(228,)f(443,)h(543,)g(545,)f(549,) -h(657,)g(664,)2199 5400 y(666,)c(669,)f(671,)h(674,)f(676,)h(709,)g -(755,)f(757,)h(759,)f(764,)p eop end -%%Page: 503 503 -TeXDict begin 503 502 bop 0 83 a Fn(x)p Fm(1525)139 b -Fl(3DLDFPR)n(G)2671 b(INDEX)141 b Fm(503)166 263 y(765,)24 -b(766,)f(770,)h(771,)f(840,)h(885,)g(886,)f(913,)h(997,)f(999,)166 -363 y(1034,)i(1065,)g(1070,)g(1110,)g(1287,)g(1302,)g(1308,)g(1365,)166 -462 y(1379,)g(1380,)g(1418,)g(1420,)g(1433,)g(1449,)g(1461,)g(1463,)166 -562 y(1474,)31 b(1476,)g(1488,)g(1490,)g(1491,)g(1505.)0 -667 y Fi(p0)16 b Fm(:)83 b(166)p 206 680 125 4 v -1 w(,)33 -b(168)p 387 680 V -1 w(,)g(243)p 568 680 V -1 w(,)g(349)p -749 680 V -2 w(,)h(350)p 930 680 V -2 w(,)f(351,)f(352)p -1291 680 V -1 w(,)h(353)p 1472 680 V -1 w(,)g(354)p 1653 -680 V -2 w(,)166 766 y(355)p 166 779 V -1 w(,)25 b(357)p -339 779 V -2 w(,)g(379,)f(380)p 684 779 V -2 w(,)h(381,)f(389,)g(392)p -1202 779 V -2 w(,)h(393)p 1374 779 V -1 w(,)g(395)p 1547 -779 V -2 w(,)g(396)p 1719 779 V -1 w(,)166 866 y(476,)34 -b(529)p 349 879 V -2 w(,)i(530)p 532 879 V -2 w(,)g(531,)d(541,)h(640)p -1080 879 V -1 w(,)h(641)p 1263 879 V -1 w(,)g(663)p 1446 -879 V -2 w(,)h(664)p 1629 879 V -2 w(,)166 965 y(665)p -166 978 V -1 w(,)f(666)p 349 978 V -2 w(,)h(719)p 532 -978 V -2 w(,)g(720)p 715 978 V -2 w(,)f(721)p 897 978 -V -1 w(,)g(748)p 1080 978 V -1 w(,)g(751)p 1263 978 V --1 w(,)g(752)p 1446 978 V -2 w(,)h(900)p 1629 978 V -2 -w(,)166 1065 y(904)p 166 1078 V -1 w(,)31 b(953)p 345 -1078 V -1 w(,)h(1006)p 525 1078 167 4 v -2 w(,)g(1007)p -746 1078 V -2 w(,)f(1088)p 966 1078 V -2 w(,)h(1127)p -1187 1078 V -2 w(,)g(1170)p 1408 1078 V -2 w(,)g(1213)p -1629 1078 V -2 w(,)166 1165 y(1214)p 166 1178 V -2 w(,)h(1228)p -388 1178 V -2 w(,)g(1287)p 610 1178 V -2 w(,)g(1290)p -832 1178 V -2 w(,)g(1361)p 1054 1178 V -2 w(,)g(1362)p -1276 1178 V -2 w(.)0 1269 y Ff(P0)t Fm(:)83 b(1444)p -198 1282 V -2 w(.)0 1374 y Fi(p0)p 89 1374 26 4 v 31 -w(x)14 b Fm(:)83 b(531)p 274 1387 125 4 v -1 w(,)34 b(532,)g(535,)f -(536,)g(538,)g(540.)0 1479 y Fi(p0)p 89 1479 26 4 v 31 -w(y)12 b Fm(:)83 b(531)p 273 1492 125 4 v -1 w(,)37 b(532,)e(535,)h -(536,)f(539.)0 1583 y Fi(p0)p 89 1583 26 4 v 31 w(z)15 -b Fm(:)83 b(531)p 270 1596 125 4 v -2 w(,)37 b(532,)f(536,)g(538,)f -(540.)0 1688 y Fi(p1)16 b Fm(:)83 b(166)p 206 1701 V --1 w(,)33 b(168)p 387 1701 V -1 w(,)g(243)p 568 1701 -V -1 w(,)g(349)p 749 1701 V -2 w(,)h(350)p 930 1701 V --2 w(,)f(351,)f(352)p 1291 1701 V -1 w(,)h(353)p 1472 -1701 V -1 w(,)g(354)p 1653 1701 V -2 w(,)166 1788 y(355)p -166 1801 V -1 w(,)25 b(357)p 339 1801 V -2 w(,)g(379,)f(380)p -684 1801 V -2 w(,)h(381,)f(382,)g(383,)f(385,)h(386,)f(387,)166 -1887 y(388,)34 b(389,)g(392)p 532 1900 V -2 w(,)i(393)p -715 1900 V -2 w(,)f(395)p 897 1900 V -1 w(,)g(396)p 1080 -1900 V -1 w(,)g(529)p 1263 1900 V -1 w(,)g(530)p 1446 -1900 V -2 w(,)h(531,)166 1987 y(541,)e(640)p 349 2000 -V -2 w(,)i(641)p 532 2000 V -2 w(,)g(663)p 715 2000 V --2 w(,)f(664)p 897 2000 V -1 w(,)g(665)p 1080 2000 V --1 w(,)g(666)p 1263 2000 V -1 w(,)g(719)p 1446 2000 V --2 w(,)h(720)p 1629 2000 V -2 w(,)166 2086 y(721,)30 -b(748)p 345 2099 V -2 w(,)h(751)p 523 2099 V -1 w(,)g(752)p -702 2099 V -1 w(,)g(900)p 881 2099 V -2 w(,)g(904)p 1059 -2099 V -1 w(,)g(953)p 1238 2099 V -1 w(,)g(1006)p 1417 -2099 167 4 v -2 w(,)g(1007)p 1637 2099 V -2 w(,)166 2186 -y(1088)p 166 2199 V -2 w(,)i(1170)p 388 2199 V -2 w(,)g(1213)p -610 2199 V -2 w(,)g(1214)p 832 2199 V -2 w(,)g(1361)p -1054 2199 V -2 w(,)g(1362)p 1276 2199 V -2 w(.)0 2291 -y Ff(P1)t Fm(:)83 b(1444)p 198 2304 V -2 w(.)0 2395 y -Fi(p1)p 89 2395 26 4 v 31 w(x)14 b Fm(:)83 b(531)p 274 -2408 125 4 v -1 w(,)39 b(532,)f(536,)g(540.)0 2500 y -Fi(p1)p 89 2500 26 4 v 31 w(y)12 b Fm(:)83 b(531)p 273 -2513 125 4 v -1 w(,)42 b(532,)e(536.)0 2605 y Fi(p1)p -89 2605 26 4 v 31 w(z)15 b Fm(:)83 b(531)p 270 2618 125 -4 v -2 w(,)40 b(532,)e(536,)f(540.)0 2709 y Fi(p2)16 -b Fm(:)83 b(357)p 206 2722 V -1 w(,)37 b(900)p 391 2722 -V -2 w(,)g(904)p 575 2722 V -1 w(,)f(1088)p 759 2722 -167 4 v -2 w(,)h(1287)p 985 2722 V -2 w(.)0 2814 y Ff(P2)t -Fm(:)83 b(1444)p 198 2827 V -2 w(.)0 2919 y Fe(q)s Fm(:)g(513)p -146 2932 125 4 v -1 w(,)30 b(516)p 324 2932 V -1 w(,)g(886)p -502 2932 V -2 w(,)h(901)p 680 2932 V -2 w(,)g(904)p 858 -2932 V -2 w(,)g(1168)p 1036 2932 167 4 v -2 w(,)f(1422)p -1255 2932 V -2 w(,)h(1506)p 1475 2932 V -2 w(.)0 3023 -y Fi(q)p 43 3023 26 4 v 31 w(pl)13 b Fm(:)83 b(904)p -251 3036 125 4 v -1 w(.)0 3128 y Fi(qq0)16 b Fm(:)83 -b(528)p 240 3141 V -1 w(,)44 b(603)p 432 3141 V -1 w(.)0 -3233 y Fi(qq1)16 b Fm(:)83 b(528)p 240 3246 V -1 w(,)44 -b(603)p 432 3246 V -1 w(.)0 3337 y Fi(Quader)13 b Fm(:)84 -b(1411.)0 3442 y Fi(quarter)13 b Fm(:)83 b(33,)40 b(966,)f(970)p -715 3455 V -1 w(.)0 3546 y Fi(q0)16 b Fm(:)83 b(529)p -202 3559 V -1 w(,)38 b(530)p 388 3559 V -2 w(,)g(531,)e(541,)h(988)p -944 3559 V -2 w(.)0 3651 y Fi(q0)p 85 3651 26 4 v 31 -w(x)14 b Fm(:)83 b(531)p 270 3664 125 4 v -1 w(,)34 b(532,)g(535,)f -(536,)g(538,)g(540.)0 3756 y Fi(q0)p 85 3756 26 4 v 31 -w(y)12 b Fm(:)83 b(531)p 269 3769 125 4 v -1 w(,)39 b(532,)f(535,)g -(536.)0 3860 y Fi(q0)p 85 3860 26 4 v 31 w(z)15 b Fm(:)83 -b(531)p 266 3873 125 4 v -2 w(,)37 b(532,)f(536,)f(538,)h(540.)0 -3965 y Fi(q1)16 b Fm(:)83 b(529)p 202 3978 V -1 w(,)38 -b(530)p 388 3978 V -2 w(,)g(531,)e(541,)h(988)p 944 3978 -V -2 w(.)0 4070 y Fi(q1)p 85 4070 26 4 v 31 w(x)14 b -Fm(:)83 b(531)p 270 4083 125 4 v -1 w(,)39 b(532,)f(536,)g(540.)0 -4174 y Fi(q1)p 85 4174 26 4 v 31 w(y)12 b Fm(:)83 b(531)p -269 4187 125 4 v -1 w(,)41 b(532,)g(536.)0 4279 y Fi(q1)p -85 4279 26 4 v 31 w(z)15 b Fm(:)83 b(531)p 266 4292 125 -4 v -2 w(,)40 b(532,)d(536,)h(540.)0 4384 y Fe(r)s Fm(:)83 -b(63)p 146 4397 84 4 v -1 w(,)25 b(64)p 277 4397 V -1 -w(,)g(65)p 408 4397 V -1 w(,)g(66)p 539 4397 V -1 w(,)g(68)p -670 4397 V -1 w(,)g(69)p 801 4397 V(,)g(70)p 933 4397 -V -1 w(,)g(71)p 1064 4397 V -1 w(,)g(84)p 1195 4397 V --1 w(,)g(85)p 1326 4397 V -1 w(,)g(86)p 1457 4397 V -1 -w(,)g(87)p 1588 4397 V -1 w(,)g(126)p 1719 4397 125 4 -v -1 w(,)166 4483 y(127)p 166 4496 V -1 w(,)g(134)p 339 -4496 V -2 w(,)g(135)p 511 4496 V -1 w(,)g(171)p 684 4496 -V -2 w(,)g(172)p 856 4496 V -1 w(,)g(176)p 1029 4496 -V -1 w(,)g(177)p 1202 4496 V -2 w(,)g(272)p 1374 4496 -V -1 w(,)g(350)p 1547 4496 V -2 w(,)g(485)p 1719 4496 -V -1 w(,)166 4583 y(486)p 166 4596 V -1 w(,)g(488)p 339 -4596 V -2 w(,)g(489)p 511 4596 V -1 w(,)g(491)p 684 4596 -V -2 w(,)g(494)p 856 4596 V -1 w(,)g(495)p 1029 4596 -V -1 w(,)g(496)p 1202 4596 V -2 w(,)g(497)p 1374 4596 -V -1 w(,)g(499)p 1547 4596 V -2 w(,)g(501)p 1719 4596 -V -1 w(,)166 4683 y(503)p 166 4696 V -1 w(,)g(511)p 339 -4696 V -2 w(,)g(512)p 511 4696 V -1 w(,)g(522)p 684 4696 -V -2 w(,)g(633)p 856 4696 V -1 w(,)g(634)p 1029 4696 -V -1 w(,)g(768)p 1202 4696 V -2 w(,)g(770)p 1374 4696 -V -1 w(,)g(840)p 1547 4696 V -2 w(,)g(901)p 1719 4696 -V -1 w(,)166 4782 y(995)p 166 4795 V -1 w(,)31 b(996)p -345 4795 V -1 w(,)h(1039)p 525 4795 167 4 v -2 w(,)g(1040)p -746 4795 V -2 w(,)f(1041)p 966 4795 V -2 w(,)h(1042)p -1187 4795 V -2 w(,)g(1067)p 1408 4795 V -2 w(,)g(1072)p -1629 4795 V -2 w(,)166 4882 y(1075)p 166 4895 V -2 w(,)27 -b(1077)p 382 4895 V -2 w(,)g(1115)p 598 4895 V -2 w(,)g(1117)p -814 4895 V -2 w(,)g(1127)p 1030 4895 V -2 w(,)g(1134)p -1246 4895 V -2 w(,)g(1137)p 1462 4895 V -2 w(,)g(1219)p -1678 4895 V -2 w(,)166 4981 y(1223)p 166 4994 V -2 w(,)j(1225)p -385 4994 V -2 w(,)h(1228)p 605 4994 V -2 w(,)f(1270)p -824 4994 V -2 w(,)g(1432)p 1043 4994 V -2 w(,)h(1433)p -1263 4994 V -2 w(,)f(1490)p 1482 4994 V -2 w(.)0 5086 -y Fi(r)p 40 5086 26 4 v 31 w(fabs)12 b Fm(:)83 b(633,)42 -b(634)p 514 5099 125 4 v -2 w(.)0 5191 y Fi(r)p 40 5191 -26 4 v 31 w(iter)13 b Fm(:)83 b(997.)0 5295 y Fi(r)p -40 5295 V 31 w(pl)13 b Fm(:)83 b(996)p 248 5308 125 4 -v -1 w(,)44 b(999.)0 5400 y Fi(r)p 40 5400 26 4 v 31 -w(ptr)13 b Fm(:)83 b(997)p 290 5413 125 4 v -2 w(.)2033 -263 y Fi(r)l(adius)12 b Fm(:)83 b(1025)p 2370 276 167 -4 v -2 w(,)30 b(1027,)e(1033)p 2808 276 V -2 w(,)i(1034,)e(1045,)g -(1237)p 3465 276 V -2 w(,)i(1243,)2199 363 y(1254,)e(1256,)h(1260,)f -(1261,)g(1267,)h(1268,)f(1274.)2033 470 y Fi(r)l(adius)p -2257 470 26 4 v 31 w(inner)13 b Fm(:)83 b(1287)p 2594 -483 167 4 v -2 w(,)37 b(1289,)d(1290)p 3045 483 V -2 -w(.)2033 578 y Fi(r)l(adius)p 2257 578 26 4 v 31 w(known)11 -b Fm(:)83 b(1134)p 2629 591 167 4 v -2 w(,)39 b(1135.)2033 -686 y Fi(r)l(adius)p 2257 686 26 4 v 31 w(outer)13 b -Fm(:)83 b(1287)p 2590 699 167 4 v -2 w(,)37 b(1289,)d(1290)p -3041 699 V -2 w(.)2033 793 y Fi(r)l(adius)p 2257 793 -26 4 v 31 w(r)l(atio)10 b Fm(:)83 b(1289)p 2567 806 167 -4 v -2 w(.)2033 901 y Fi(r)l(adius)p 2257 901 26 4 v -31 w(unknown)10 b Fm(:)83 b(1134)p 2720 914 167 4 v -2 -w(,)38 b(1135.)2033 1008 y Fi(r)l(cs)p 2141 1008 26 4 -v 30 w(id)14 b Fm(:)83 b(10)p 2353 1021 84 4 v -1 w(,)34 -b(37)p 2493 1021 V -1 w(,)g(54)p 2633 1021 V -1 w(,)g(120)p -2773 1021 125 4 v -2 w(,)g(196)p 2954 1021 V -1 w(,)f(205)p -3135 1021 V -1 w(,)h(262)p 3317 1021 V -2 w(,)g(591)p -3498 1021 V -1 w(,)f(615)p 3679 1021 V -1 w(,)2199 1108 -y(652)p 2199 1121 V -1 w(,)h(938)p 2381 1121 V -2 w(,)g(973)p -2562 1121 V -1 w(,)g(1057)p 2744 1121 167 4 v -2 w(,)g(1101)p -2967 1121 V -2 w(,)g(1234)p 3190 1121 V -2 w(,)g(1280)p -3413 1121 V -2 w(,)g(1294)p 3636 1121 V -2 w(,)2199 1208 -y(1403)p 2199 1221 V -2 w(,)i(1411)p 2424 1221 V -2 w(,)g(1429)p -2649 1221 V -2 w(,)f(1495)p 2873 1221 V -2 w(,)h(1502)p -3098 1221 V -2 w(.)2033 1315 y Fk(real)5 b Fm(:)83 b(12)p -2300 1328 84 4 v -1 w(,)29 b(13,)e(15,)h(16,)g(20,)g(23,)f(24,)h(25,)g -(26,)g(27,)f(29,)h(30,)2199 1415 y(36,)k(56,)g(67,)g(68,)h(69,)f(70,)g -(71,)g(84,)g(85,)g(86,)g(87,)g(88,)2199 1515 y(89,)f(90,)g(91,)g(96,)g -(97,)g(98,)f(99,)h(126,)g(127,)f(128,)h(129,)2199 1614 -y(134,)24 b(135,)f(137,)h(138,)f(145,)h(146,)g(150,)f(151,)h(152,)f -(153,)2199 1714 y(155,)h(156,)f(158,)h(159,)f(160,)h(161,)g(166,)f -(167,)h(171,)f(172,)2199 1813 y(176,)h(177,)f(181,)h(182,)f(200,)h -(210,)g(235,)f(236,)h(238,)f(239,)2199 1913 y(241,)h(242,)f(243,)h -(252,)f(253,)h(254,)g(264,)f(265,)h(272,)f(282,)2199 -2013 y(283,)h(284,)f(285,)h(295,)f(296,)h(305,)g(308,)f(312,)h(313,)f -(314,)2199 2112 y(315,)h(317,)f(318,)h(319,)f(320,)h(322,)g(323,)f -(324,)h(325,)f(327,)2199 2212 y(328,)h(329,)f(330,)h(332,)f(333,)h -(334,)g(335,)f(337,)h(338,)f(339,)2199 2312 y(340,)h(345,)f(346,)h -(349,)f(350,)h(351,)g(360,)f(361,)h(362,)f(363,)2199 -2411 y(364,)h(365,)f(368,)h(369,)f(375,)h(376,)g(379,)f(380,)h(389,)f -(392,)2199 2511 y(393,)h(394,)f(395,)h(396,)f(398,)h(399,)g(401,)f -(402,)h(403,)f(405,)2199 2610 y(431,)h(432,)f(442,)h(443,)f(444,)h -(445,)g(446,)f(447,)h(448,)f(449,)2199 2710 y(450,)h(465,)f(472,)h -(485,)f(486,)h(488,)g(489,)f(490,)h(491,)f(494,)2199 -2810 y(495,)h(496,)f(497,)h(498,)f(499,)h(502,)g(503,)f(504,)h(505,)f -(508,)2199 2909 y(511,)h(512,)f(517,)h(522,)f(531,)h(532,)g(533,)f -(534,)h(535,)f(536,)2199 3009 y(538,)h(548,)f(550,)h(551,)f(554,)h -(556,)g(559,)f(560,)h(561,)f(562,)2199 3109 y(563,)h(565,)f(566,)h -(567,)f(568,)h(571,)g(572,)f(578,)h(581,)f(582,)2199 -3208 y(584,)h(585,)f(606,)h(617,)f(633,)h(634,)g(636,)f(641,)h(644,)f -(654,)2199 3308 y(713,)h(714,)f(716,)h(717,)f(719,)h(720,)g(721,)f -(722,)h(723,)f(724,)2199 3407 y(725,)h(726,)f(728,)h(729,)f(733,)h -(734,)g(742,)f(743,)h(839,)f(840,)2199 3507 y(843,)h(845,)f(846,)h -(847,)f(848,)h(849,)g(850,)f(851,)h(866,)f(867,)2199 -3607 y(879,)h(880,)f(896,)h(904,)f(906,)h(924,)g(925,)f(929,)h(930,)f -(946,)2199 3706 y(947,)h(948,)f(949,)h(950,)f(951,)h(957,)g(960,)f -(967,)h(968,)f(969,)2199 3806 y(970,)30 b(996,)h(1003,)f(1004,)f(1006,) -h(1007,)g(1008,)g(1009,)2199 3906 y(1010,)25 b(1011,)g(1012,)g(1013,)g -(1015,)g(1016,)g(1020,)g(1021,)2199 4005 y(1025,)g(1032,)g(1033,)g -(1035,)g(1036,)g(1045,)g(1059,)g(1064,)2199 4105 y(1065,)g(1066,)g -(1067,)g(1090,)g(1091,)g(1092,)g(1093,)g(1103,)2199 4204 -y(1109,)g(1110,)g(1111,)g(1112,)g(1127,)g(1133,)g(1134,)g(1136,)2199 -4304 y(1137,)g(1148,)g(1149,)g(1150,)g(1151,)g(1154,)g(1155,)g(1156,) -2199 4404 y(1157,)g(1159,)g(1160,)g(1161,)g(1162,)g(1163,)g(1164,)g -(1168,)2199 4503 y(1177,)g(1181,)g(1183,)g(1185,)g(1193,)g(1196,)g -(1197,)g(1198,)2199 4603 y(1199,)g(1200,)g(1201,)g(1203,)g(1204,)g -(1208,)g(1209,)g(1213,)2199 4703 y(1214,)g(1215,)g(1216,)g(1228,)g -(1229,)g(1237,)g(1242,)g(1243,)2199 4802 y(1244,)g(1245,)g(1256,)g -(1258,)g(1259,)g(1260,)g(1261,)g(1267,)2199 4902 y(1268,)g(1270,)g -(1283,)g(1284,)g(1286,)g(1287,)g(1289,)g(1290,)2199 5001 -y(1296,)g(1341,)g(1342,)g(1350,)g(1351,)g(1352,)g(1353,)g(1355,)2199 -5101 y(1356,)g(1359,)g(1360,)g(1361,)g(1362,)g(1364,)g(1365,)g(1367,) -2199 5201 y(1368,)g(1369,)g(1370,)g(1371,)g(1372,)g(1373,)g(1374,)g -(1413,)2199 5300 y(1419,)g(1420,)g(1431,)g(1436,)g(1437,)g(1442,)g -(1443,)g(1444,)2199 5400 y(1446,)g(1447,)g(1448,)g(1449,)g(1450,)g -(1451,)g(1453,)g(1454,)p eop end -%%Page: 504 504 -TeXDict begin 504 503 bop 0 83 a Fm(504)140 b Fl(INDEX)2670 -b(3DLDFPR)n(G)142 b Fn(x)p Fm(1525)166 263 y(1459,)25 -b(1460,)g(1462,)g(1463,)g(1464,)g(1465,)g(1467,)g(1468,)166 -363 y(1473,)g(1474,)g(1475,)g(1476,)g(1477,)g(1478,)g(1481,)g(1482,)166 -462 y(1487,)31 b(1488,)g(1489,)g(1490,)g(1516,)g(1518.)0 -565 y Fi(r)l(e)l(al)p 133 565 26 4 v 31 w(limits)12 b -Fm(:)83 b(15,)39 b(16)p 624 578 84 4 v -1 w(,)i(23)p -771 578 V -1 w(.)0 667 y Fk(real)p 160 667 29 5 v 40 -w(pair)5 b Fm(:)83 b(12)p 472 680 84 4 v -1 w(,)24 b(25,)f(27,)g(29,)g -(30,)g(949,)f(957,)h(1133,)f(1134.)0 770 y Fk(real)p -160 770 29 5 v 40 w(short)5 b Fm(:)83 b(12)p 522 783 -84 4 v -1 w(,)29 b(25,)f(27,)g(633,)f(634,)g(635,)h(636,)f(948.)0 -873 y Fk(real)p 160 873 29 5 v 40 w(triple)t Fm(:)83 -b(13)p 533 886 84 4 v -1 w(,)34 b(946,)d(960,)h(1136,)f(1137.)0 -975 y Fk(reals)t Fm(:)84 b(12,)43 b(277.)0 1078 y Ff(RECTANGLE)q -Fm(:)83 b(1296)p 503 1091 167 4 v -2 w(,)33 b(1297)p -725 1091 V -2 w(,)g(1316,)e(1317,)g(1329,)g(1330,)166 -1177 y(1336.)0 1280 y Fk(Rectangle)t Fm(:)83 b(290,)28 -b(973,)f(975,)g(977,)h(1000,)f(1025,)g(1057,)166 1380 -y(1059)p 166 1393 V -2 w(,)g(1061,)e(1062)p 598 1393 -V -2 w(,)i(1063,)e(1064,)g(1065)p 1246 1393 V -2 w(,)i(1067,)e(1068,) -166 1479 y(1069,)g(1070)p 382 1492 V -2 w(,)i(1072,)e(1074,)g(1075,)g -(1076,)g(1077,)g(1078,)166 1579 y(1079,)g(1080,)g(1081,)g(1082,)g -(1083,)g(1084,)g(1086,)g(1088,)166 1678 y(1089,)g(1091,)g(1093,)g -(1218,)g(1219,)g(1220,)g(1221,)g(1222,)166 1778 y(1223,)g(1224,)g -(1225,)g(1228,)g(1229,)g(1230,)g(1231,)g(1296,)166 1878 -y(1302,)g(1308,)g(1324,)g(1325,)g(1329,)g(1342,)g(1344,)g(1347,)166 -1977 y(1349,)g(1365,)g(1367,)g(1379,)g(1380,)g(1384,)g(1387,)g(1390,) -166 2077 y(1393,)g(1396,)g(1399,)g(1418,)g(1420,)g(1424,)g(1483,)g -(1490.)0 2180 y Fi(r)l(e)l(ctangles)11 b Fm(:)83 b(1296)p -468 2193 V -2 w(,)35 b(1302,)f(1308,)f(1316,)g(1317,)g(1325,)166 -2279 y(1329,)38 b(1330,)f(1342,)h(1344,)f(1347,)h(1349,)f(1365,)166 -2379 y(1367,)h(1379,)f(1380,)h(1382,)f(1384,)h(1385,)f(1387,)166 -2478 y(1388,)h(1390,)f(1391,)h(1393,)f(1394,)h(1396,)f(1397,)166 -2578 y(1399,)g(1418,)f(1420,)h(1424.)0 2681 y Fk(Rectangles)t -Fm(:)83 b(1080.)0 2783 y Fi(r)l(e)l(d)13 b Fm(:)83 b(108,)30 -b(112)p 405 2796 125 4 v -1 w(,)h(113)p 584 2796 V -1 -w(,)g(655,)f(1443,)g(1461,)g(1505.)0 2886 y Fi(r)l(e)l(d)p -112 2886 26 4 v 31 w(or)l(ange)11 b Fm(:)83 b(112.)0 -2988 y Fi(r)l(e)l(d)p 112 2988 V 31 w(p)l(art)12 b Fm(:)83 -b(56)p 399 3001 84 4 v -1 w(,)42 b(59,)g(61,)f(64,)g(66,)h(69,)f(71,)h -(74,)f(75,)166 3088 y(76,)h(85,)f(87,)h(97.)0 3191 y -Fi(r)l(ef)p 99 3191 26 4 v 31 w(pt)12 b Fm(:)83 b(948)p -313 3204 125 4 v -1 w(,)28 b(949)p 489 3204 V -2 w(,)g(952,)e(953)p -839 3204 V -1 w(,)h(954)p 1014 3204 V -1 w(,)h(957,)e(963,)g(964)p -1540 3204 V -1 w(,)i(965)p 1716 3204 V -2 w(.)0 3293 -y Fk(Reg)p 168 3293 29 5 v 39 w(Cl)p 303 3293 V 40 w(Plane)p -578 3293 V 40 w(Curv)m(e)5 b Fm(:)84 b(290,)28 b(940,)h(941)p -1333 3306 125 4 v -1 w(,)h(942,)f(947,)166 3393 y(948,)24 -b(949,)f(951,)h(952,)f(953,)h(954,)g(957,)f(964,)h(965,)f(966,)166 -3492 y(967,)c(968,)g(969,)h(970,)f(1025,)g(1103,)f(1120,)h(1167,)g -(1171.)0 3595 y Fk(Reg)p 168 3595 29 5 v 39 w(Cl)p 303 -3595 V 40 w(Plane)p 578 3595 V 40 w(Curv)m(es)5 b Fm(:)83 -b(941,)33 b(952.)0 3698 y Ff(REG_POLYGON)p Fm(:)83 b(1296)p -590 3711 167 4 v -2 w(,)41 b(1297)p 820 3711 V -1 w(,)g(1316,)f(1317,)f -(1329,)166 3797 y(1330,)j(1338.)0 3900 y Fk(Reg)p 168 -3900 29 5 v 39 w(P)m(olygon)5 b Fm(:)83 b(290,)35 b(386,)g(973,)g(975,) -h(977,)f(1000,)166 3999 y(1024,)j(1025)p 395 4012 167 -4 v -2 w(,)h(1026,)f(1027,)f(1029,)h(1030)p 1309 4012 -V -2 w(,)h(1032,)166 4099 y(1033)p 166 4112 V -2 w(,)h(1036,)d(1037,)h -(1039,)f(1040,)h(1041,)f(1042,)166 4199 y(1043,)25 b(1044,)g(1057,)g -(1078,)g(1081,)g(1084,)g(1270,)g(1272,)166 4298 y(1273,)g(1274,)g -(1276,)g(1277,)g(1284,)g(1296,)g(1302,)g(1308,)166 4398 -y(1312,)g(1326,)g(1327,)g(1329,)g(1342,)g(1344,)g(1347,)g(1349,)166 -4497 y(1365,)g(1367,)g(1379,)g(1380,)g(1384,)g(1387,)g(1390,)g(1393,) -166 4597 y(1396,)g(1399,)g(1432,)g(1433,)g(1448,)g(1449,)g(1451,)g -(1461,)166 4697 y(1462,)g(1463,)g(1465,)g(1474,)g(1475,)g(1476,)g -(1478,)g(1483,)166 4796 y(1488,)37 b(1489,)f(1490,)h(1491.)0 -4899 y Fk(Reg)p 168 4899 29 5 v 39 w(P)m(olygons)t Fm(:)83 -b(658,)37 b(1284.)0 5001 y Fi(r)l(e)l(g)p 108 5001 26 -4 v 30 w(p)l(olygons)13 b Fm(:)83 b(1296)p 554 5014 167 -4 v -2 w(,)30 b(1302,)e(1308,)g(1316,)h(1317,)f(1327,)166 -5101 y(1329,)d(1330,)g(1342,)g(1344,)g(1347,)g(1349,)g(1365,)g(1367,) -166 5201 y(1379,)g(1380,)g(1382,)g(1384,)g(1385,)g(1387,)g(1388,)g -(1390,)166 5300 y(1391,)g(1393,)g(1394,)g(1396,)g(1397,)g(1399,)g -(1433,)g(1443,)166 5400 y(1444,)g(1445,)g(1460,)g(1461,)g(1474,)g -(1488,)g(1490)p 1462 5413 V -2 w(,)i(1491.)2033 263 y -Fi(R)l(e)l(gular)p 2310 263 26 4 v 30 w(Close)l(d)p 2572 -263 V 32 w(Plane)p 2808 263 V 32 w(Curve)10 b Fm(:)83 -b(940.)2033 364 y Fi(r)l(eset)12 b Fm(:)83 b(125,)28 -b(132)p 2497 377 125 4 v -2 w(,)h(133)p 2673 377 V -1 -w(,)g(256,)f(278,)g(303,)g(405,)f(407,)h(545,)2199 464 -y(546,)j(553,)g(561,)g(572,)f(1127,)h(1451,)f(1488.)2033 -565 y Fi(r)l(eset)p 2207 565 26 4 v 30 w(angle)11 b Fm(:)84 -b(571)p 2536 578 125 4 v -2 w(,)41 b(572)p 2724 578 V --1 w(.)2033 667 y Fi(r)l(eset)p 2207 667 26 4 v 30 w(tr)l(ansform)11 -b Fm(:)83 b(224,)33 b(256)p 2883 680 125 4 v -1 w(,)h(406)p -3065 680 V -2 w(,)h(407)p 3247 680 V -2 w(.)2033 768 -y Fi(r)l(esize)11 b Fm(:)83 b(278,)36 b(399,)f(405,)h(657,)f(661,)h -(664,)f(669,)h(674,)2199 868 y(867,)28 b(1030,)g(1033,)g(1040,)f(1042,) -h(1300,)g(1302,)f(1367,)2199 967 y(1416,)37 b(1418,)f(1420,)h(1422.) -2033 1069 y Fi(r)l(everse)11 b Fm(:)83 b(911)p 2402 1082 -V -1 w(,)35 b(912)p 2585 1082 V -1 w(,)h(914,)e(915)p -2952 1082 V -1 w(,)h(916)p 3135 1082 V -1 w(.)2033 1170 -y Fi(right)p 2206 1170 26 4 v 31 w(shift)13 b Fm(:)83 -b(1284)p 2505 1183 167 4 v -2 w(.)2033 1272 y Fi(r)l(otate)10 -b Fm(:)84 b(149,)25 b(160)p 2533 1285 125 4 v -2 w(,)i(161)p -2707 1285 V -1 w(,)f(164,)f(166)p 3055 1285 V -1 w(,)i(167)p -3230 1285 V -2 w(,)g(181,)e(200)p 3578 1285 V -1 w(,)h(241)p -3752 1285 V -1 w(,)2199 1371 y(242)p 2199 1384 V -1 w(,)f(243)p -2372 1384 V -2 w(,)g(360)p 2544 1384 V -1 w(,)g(361)p -2717 1384 V -2 w(,)g(379,)f(382,)g(385,)f(387,)h(388,)f(389,)2199 -1471 y(392)p 2199 1484 V -1 w(,)i(393)p 2372 1484 V -2 -w(,)g(394)p 2544 1484 V -1 w(,)g(395)p 2717 1484 V -2 -w(,)g(396)p 2889 1484 V -1 w(,)g(561,)f(572,)f(713)p -3407 1484 V -1 w(,)i(714)p 3580 1484 V -2 w(,)g(716)p -3752 1484 V -1 w(,)2199 1570 y(717)p 2199 1583 V -1 w(,)31 -b(719)p 2378 1583 V -2 w(,)g(720)p 2556 1583 V -1 w(,)g(721)p -2735 1583 V -1 w(,)g(722)p 2914 1583 V -2 w(,)g(957,)f(968,)g(1003)p -3450 1583 167 4 v -2 w(,)h(1004)p 3670 1583 V -2 w(,)2199 -1670 y(1006)p 2199 1683 V -2 w(,)c(1007)p 2415 1683 V --2 w(,)g(1008)p 2631 1683 V -2 w(,)g(1009)p 2847 1683 -V -2 w(,)g(1034,)e(1065,)g(1110,)g(1127,)2199 1770 y(1164,)g(1174,)g -(1179,)g(1196)p 2847 1783 V -2 w(,)i(1197)p 3063 1783 -V -2 w(,)g(1213)p 3279 1783 V -2 w(,)g(1214)p 3495 1783 -V -2 w(,)g(1215)p 3711 1783 V -2 w(,)2199 1869 y(1216)p -2199 1882 V -2 w(,)g(1228,)e(1229,)g(1268,)g(1287,)g(1290,)g(1359)p -3495 1882 V -2 w(,)i(1360)p 3711 1882 V -2 w(,)2199 1969 -y(1361)p 2199 1982 V -2 w(,)g(1362)p 2415 1982 V -2 w(,)g(1420,)e -(1443,)g(1445,)g(1451,)g(1461,)g(1462,)2199 2069 y(1463,)j(1465,)h -(1474,)f(1476,)g(1478,)h(1488,)f(1490.)2033 2170 y Fi(r)l(otate)p -2247 2170 26 4 v 31 w(ar)l(ound)13 b Fm(:)83 b(166,)40 -b(167,)g(243,)g(379,)g(392,)g(394,)2199 2270 y(395,)f(396,)g(716,)g 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b(129)p 2497 3090 V -2 w(.)2033 -3178 y Fi(r0)p 2115 3178 26 4 v 31 w(1)16 b Fm(:)83 b(128)p -2305 3191 125 4 v -1 w(,)44 b(129)p 2497 3191 V -2 w(.)2033 -3280 y Fi(r0)p 2115 3280 26 4 v 31 w(2)16 b Fm(:)83 b(128)p -2305 3293 125 4 v -1 w(,)44 b(129)p 2497 3293 V -2 w(.)2033 -3381 y Fi(r0)p 2115 3381 26 4 v 31 w(3)16 b Fm(:)83 b(128)p -2305 3394 125 4 v -1 w(,)44 b(129)p 2497 3394 V -2 w(.)2033 -3483 y Fi(r1)16 b Fm(:)83 b(990)p 2232 3496 V -1 w(,)42 -b(991,)e(1221)p 2611 3496 167 4 v -2 w(.)2033 3584 y -Fi(r1)p 2115 3584 26 4 v 31 w(0)16 b Fm(:)83 b(128)p -2305 3597 125 4 v -1 w(,)44 b(129)p 2497 3597 V -2 w(.)2033 -3685 y Fi(r1)p 2115 3685 26 4 v 31 w(1)16 b Fm(:)83 b(128)p -2305 3698 125 4 v -1 w(,)44 b(129)p 2497 3698 V -2 w(.)2033 -3787 y Fi(r1)p 2115 3787 26 4 v 31 w(2)16 b Fm(:)83 b(128)p -2305 3800 125 4 v -1 w(,)44 b(129)p 2497 3800 V -2 w(.)2033 -3888 y Fi(r1)p 2115 3888 26 4 v 31 w(3)16 b Fm(:)83 b(128)p -2305 3901 125 4 v -1 w(,)44 b(129)p 2497 3901 V -2 w(.)2033 -3989 y 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w(,)44 b(129)p 2497 4813 V -2 w(.)2033 -4902 y Fe(s)p Fm(:)83 b(80)p 2178 4915 84 4 v -1 w(,)32 -b(81)p 2316 4915 V -1 w(,)f(225)p 2453 4915 125 4 v -1 -w(,)g(226)p 2632 4915 V -1 w(,)g(464)p 2811 4915 V -1 -w(,)g(634)p 2990 4915 V -1 w(,)g(636)p 3169 4915 V -1 -w(,)h(692)p 3349 4915 V -2 w(,)g(693)p 3528 4915 V -2 -w(,)g(704)p 3707 4915 V -2 w(,)2199 5001 y(705)p 2199 -5014 V -1 w(,)j(706)p 2382 5014 V -2 w(,)h(707)p 2565 -5014 V -2 w(,)g(708)p 2748 5014 V -2 w(,)f(709)p 2930 -5014 V -1 w(,)g(758)p 3113 5014 V -1 w(,)g(759)p 3296 -5014 V -1 w(,)g(886)p 3479 5014 V -2 w(,)h(963)p 3662 -5014 V -2 w(,)2199 5101 y(1123)p 2199 5114 167 4 v -2 -w(,)k(1144)p 2428 5114 V -2 w(,)f(1145)p 2656 5114 V --2 w(,)h(1146)p 2885 5114 V -2 w(,)f(1147)p 3113 5114 -V -2 w(,)h(1301)p 3342 5114 V -2 w(,)f(1302)p 3570 5114 -V -2 w(,)2199 5201 y(1304)p 2199 5214 V -2 w(,)h(1307)p -2428 5214 V -2 w(,)f(1308)p 2656 5214 V -2 w(,)h(1310)p -2885 5214 V -2 w(,)f(1316)p 3113 5214 V -2 w(,)h(1317)p -3342 5214 V -2 w(,)f(1318)p 3570 5214 V -2 w(,)2199 5300 -y(1319)p 2199 5313 V -2 w(,)h(1320)p 2428 5313 V -2 w(,)f(1321)p -2656 5313 V -2 w(,)h(1322)p 2885 5313 V -2 w(,)f(1323)p -3113 5313 V -2 w(,)h(1324)p 3342 5313 V -2 w(,)f(1325)p -3570 5313 V -2 w(,)2199 5400 y(1326)p 2199 5413 V -2 -w(,)27 b(1327)p 2415 5413 V -2 w(,)g(1329)p 2631 5413 -V -2 w(,)g(1330)p 2847 5413 V -2 w(,)g(1331)p 3063 5413 -V -2 w(,)g(1332)p 3279 5413 V -2 w(,)g(1333)p 3495 5413 -V -2 w(,)g(1334)p 3711 5413 V -2 w(,)p eop end -%%Page: 505 505 -TeXDict begin 505 504 bop 0 83 a Fn(x)p Fm(1525)139 b -Fl(3DLDFPR)n(G)2671 b(INDEX)141 b Fm(505)166 263 y(1335)p -166 276 167 4 v -2 w(,)27 b(1336)p 382 276 V -2 w(,)g(1337)p -598 276 V -2 w(,)g(1338)p 814 276 V -2 w(,)g(1379)p 1030 -276 V -2 w(,)g(1380)p 1246 276 V -2 w(,)g(1384)p 1462 -276 V -2 w(,)g(1387)p 1678 276 V -2 w(,)166 363 y(1390)p -166 376 V -2 w(,)39 b(1393)p 394 376 V -2 w(,)f(1396)p -621 376 V -2 w(,)h(1399)p 849 376 V -2 w(.)0 464 y Fi(s)p -39 464 26 4 v 30 w(e)11 b Fm(:)83 b(1188)p 219 477 167 -4 v -2 w(,)44 b(1189.)0 566 y Fi(s)p 39 566 26 4 v 30 -w(t)12 b Fm(:)83 b(1188)p 210 579 167 4 v -2 w(,)44 b(1189.)0 -667 y Fi(save)p 157 667 26 4 v 31 w(angle)11 b Fm(:)84 -b(1185)p 487 680 167 4 v -2 w(.)0 769 y Fi(save)p 157 -769 26 4 v 31 w(z)15 b Fm(:)83 b(401)p 338 782 125 4 -v -2 w(.)0 870 y Fi(sc)l(ale)11 b Fm(:)83 b(150)p 286 -883 V -1 w(,)29 b(151)p 463 883 V -1 w(,)g(200)p 640 -883 V -2 w(,)h(235)p 817 883 V -2 w(,)g(236)p 994 883 -V -2 w(,)f(362)p 1170 883 V -1 w(,)g(363)p 1347 883 V --1 w(,)g(723)p 1524 883 V -1 w(,)g(724)p 1701 883 V -2 -w(,)166 970 y(1010)p 166 983 167 4 v -2 w(,)e(1011)p -382 983 V -2 w(,)g(1198)p 598 983 V -2 w(,)g(1199)p 814 -983 V -2 w(,)g(1228,)e(1258,)g(1350)p 1462 983 V -2 w(,)i(1351)p -1678 983 V -2 w(.)0 1071 y Fi(sc)l(ale)p 174 1071 26 -4 v 31 w(value)11 b Fm(:)83 b(1228)p 501 1084 167 4 v --2 w(.)0 1173 y Fi(se)l(c)l(ond)13 b Fm(:)83 b(13)p 352 -1186 84 4 v -1 w(,)30 b(30,)g(270)p 625 1186 125 4 v --2 w(,)g(271,)f(355,)g(603,)f(633,)h(637,)g(949,)166 -1272 y(954,)j(958,)g(959,)f(960,)h(961,)g(985,)g(988,)f(999,)h(1135,) -166 1372 y(1136,)38 b(1137,)f(1163,)h(1164,)f(1179,)h(1184,)f(1186,)166 -1472 y(1188,)g(1221,)f(1228,)h(1268.)0 1573 y Fi(se)l(gment)12 -b Fm(:)83 b(33,)32 b(966,)g(967)p 725 1586 V -1 w(,)i(968)p -907 1586 V -2 w(,)g(969,)e(970.)0 1675 y Fi(set)12 b -Fm(:)83 b(65)p 218 1688 84 4 v -1 w(,)32 b(66)p 356 1688 -V -1 w(,)g(70)p 494 1688 V -1 w(,)g(71)p 632 1688 V -1 -w(,)g(284)p 770 1688 125 4 v -1 w(,)g(285)p 950 1688 -V -2 w(,)g(288)p 1129 1688 V -1 w(,)g(289)p 1309 1688 -V -2 w(,)g(296,)f(382,)166 1774 y(383,)j(541,)g(561,)g(562)p -715 1787 V -2 w(,)h(563)p 897 1787 V -1 w(,)g(567)p 1080 -1787 V -1 w(,)g(568)p 1263 1787 V -1 w(,)g(572,)f(665)p -1629 1787 V -2 w(,)166 1874 y(666)p 166 1887 V -1 w(,)f(670)p -347 1887 V -2 w(,)h(671)p 528 1887 V -2 w(,)f(675,)f(676,)g(958,)g -(959,)f(960,)h(1035)p 1612 1887 167 4 v -2 w(,)166 1973 -y(1036)p 166 1986 V -2 w(,)40 b(1037,)d(1066)p 623 1986 -V -2 w(,)j(1067)p 852 1986 V -2 w(,)f(1071)p 1080 1986 -V -2 w(,)h(1072)p 1309 1986 V -2 w(,)f(1111)p 1537 1986 -V -2 w(,)166 2073 y(1112)p 166 2086 V -2 w(,)h(1184,)d(1244)p -623 2086 V -2 w(,)j(1245)p 852 2086 V -2 w(,)f(1268,)f(1270,)f(1274,) -166 2173 y(1284,)25 b(1287,)g(1420,)g(1446)p 814 2186 -V -2 w(,)i(1447)p 1030 2186 V -2 w(,)g(1449,)e(1451,)g(1463,)166 -2272 y(1474,)37 b(1476,)f(1478,)h(1490.)0 2374 y Fi(set)p -105 2374 26 4 v 30 w(blue)p 277 2374 V 31 w(p)l(art)12 -b Fm(:)83 b(90)p 564 2387 84 4 v -1 w(,)42 b(91)p 712 -2387 V -1 w(.)0 2475 y Fi(set)p 105 2475 26 4 v 30 w(c)l(onne)l(ctors) -11 b Fm(:)83 b(708)p 628 2488 125 4 v -1 w(,)37 b(709)p -813 2488 V -2 w(,)h(901.)0 2577 y Fi(set)p 105 2577 26 -4 v 30 w(cycle)12 b Fm(:)83 b(885,)34 b(886,)f(908)p -788 2590 125 4 v -1 w(,)i(909)p 971 2590 V -2 w(,)g(968.)0 -2678 y Fi(set)p 105 2678 26 4 v 30 w(dash)p 295 2678 -V 32 w(p)l(attern)10 b Fm(:)83 b(704)p 694 2691 125 4 -v -1 w(,)40 b(705)p 882 2691 V -1 w(,)g(1382,)e(1385,)g(1388,)166 -2778 y(1391,)i(1394,)f(1397.)0 2879 y Fi(set)p 105 2879 -26 4 v 30 w(dr)l(aw)p 305 2879 V 32 w(c)l(olor)14 b Fm(:)83 -b(695)p 626 2892 125 4 v -2 w(,)36 b(696)p 809 2892 V --1 w(,)f(697)p 992 2892 V -1 w(,)g(698)p 1175 2892 V --1 w(,)h(1382,)d(1385,)166 2979 y(1388,)k(1391,)f(1394,)h(1397.)0 -3081 y Fi(set)p 105 3081 26 4 v 30 w(element)12 b Fm(:)83 -b(122,)31 b(134)p 706 3094 125 4 v -2 w(,)h(135)p 885 -3094 V -2 w(,)g(559,)e(561,)g(572.)0 3182 y Fi(set)p -105 3182 26 4 v 30 w(extr)l(emes)11 b Fm(:)83 b(200)p -561 3195 125 4 v -2 w(,)34 b(451)p 742 3195 V -2 w(,)g(452)p -923 3195 V -1 w(,)f(550,)g(552,)f(841)p 1467 3195 V -2 -w(,)i(842)p 1648 3195 V -1 w(,)166 3282 y(858,)41 b(1366)p -356 3295 167 4 v -2 w(,)h(1367)p 587 3295 V -2 w(.)0 -3383 y Fi(set)p 105 3383 26 4 v 30 w(\014l)t(l)p 228 -3383 V 31 w(c)l(olor)14 b Fm(:)83 b(700)p 548 3396 125 -4 v -1 w(,)40 b(701)p 736 3396 V -1 w(,)g(702)p 924 3396 -V -2 w(,)h(703)p 1112 3396 V -2 w(,)f(1382,)f(1385,)166 -3483 y(1388,)e(1391,)f(1394,)h(1397.)0 3584 y Fi(set)p -105 3584 26 4 v 30 w(\014l)t(l)p 228 3584 V 31 w(dr)l(aw)p -429 3584 V 32 w(value)11 b Fm(:)83 b(692)p 757 3597 125 -4 v -2 w(,)37 b(693)p 941 3597 V -2 w(,)f(1382,)f(1385,)f(1388,)166 -3684 y(1391,)40 b(1394,)f(1397.)0 3785 y Fi(set)p 105 -3785 26 4 v 30 w(gr)l(e)l(en)p 323 3785 V 31 w(p)l(art)12 -b Fm(:)83 b(88)p 610 3798 84 4 v -1 w(,)41 b(89)p 757 -3798 V -1 w(.)0 3887 y Fi(set)p 105 3887 26 4 v 30 w(minimum)p -481 3887 V 31 w(z)14 b Fm(:)83 b(451.)0 3988 y Fi(set)p -105 3988 V 30 w(name)11 b Fm(:)83 b(80)p 442 4001 84 -4 v -1 w(,)43 b(81)p 591 4001 V -1 w(.)0 4090 y Fi(set)p -105 4090 26 4 v 30 w(on)p 224 4090 V 31 w(fr)l(e)l(e)p -383 4090 V 31 w(stor)l(e)10 b Fm(:)83 b(32,)31 b(200)p -836 4103 125 4 v -1 w(,)g(301)p 1015 4103 V -1 w(,)h(690)p -1195 4103 V -2 w(,)g(1311)p 1374 4103 167 4 v -2 w(.)0 -4191 y Fi(set)p 105 4191 26 4 v 30 w(p)l(en)11 b Fm(:)83 -b(706)p 370 4204 125 4 v -1 w(,)32 b(707)p 550 4204 V --1 w(,)h(1382,)d(1385,)h(1388,)g(1391,)g(1394,)166 4291 -y(1397.)0 4393 y Fi(set)p 105 4393 26 4 v 30 w(r)l(e)l(d)p -242 4393 V 31 w(p)l(art)12 b Fm(:)83 b(86)p 529 4406 -84 4 v -1 w(,)42 b(87)p 677 4406 V -1 w(.)0 4494 y Fi(set)p -105 4494 26 4 v 30 w(tr)l(ansform)11 b Fm(:)83 b(244)p -599 4507 125 4 v -1 w(,)40 b(245)p 787 4507 V -2 w(.)0 -4596 y Fi(set)p 105 4596 26 4 v 30 w(use)p 252 4596 V -31 w(name)10 b Fm(:)83 b(82)p 589 4609 84 4 v -1 w(,)41 -b(83)p 736 4609 V -1 w(.)0 4697 y Fi(setf)22 b Fm(:)83 -b(44,)43 b(1512.)0 4799 y Fi(setpr)l(e)l(cision)12 b -Fm(:)83 b(148.)0 4900 y Fi(setw)13 b Fm(:)83 b(148.)0 -5001 y Fk(Shap)s(e)5 b Fm(:)83 b(196,)33 b(199)p 545 -5014 125 4 v -2 w(,)i(200,)e(201,)g(216,)g(225,)g(226,)g(249,)166 -5101 y(264,)24 b(302,)f(342,)h(343,)f(411,)h(415,)g(438,)f(440,)h(442,) -f(443,)166 5201 y(453,)h(454,)f(455,)h(456,)f(457,)h(543,)g(545,)f -(546,)h(547,)f(549,)166 5300 y(550,)h(551,)f(552,)h(654,)f(686,)h(688,) -g(689,)f(776,)h(802,)f(807,)166 5400 y(813,)32 b(821,)g(824,)f(839,)h -(840,)g(852,)g(854,)f(856,)h(1296,)2199 263 y(1309,)25 -b(1310,)g(1312,)g(1316,)g(1317,)g(1329,)g(1348,)g(1364,)2199 -363 y(1365,)g(1379,)g(1380,)g(1382,)g(1384,)g(1385,)g(1387,)g(1388,) -2199 462 y(1390,)g(1391,)g(1393,)g(1394,)g(1396,)g(1397,)g(1399,)g -(1411.)2033 564 y Fi(shap)l(e)p 2232 564 26 4 v 32 w(typ)l(e)11 -b Fm(:)83 b(1316)p 2520 577 167 4 v -2 w(,)34 b(1317)p -2743 577 V -2 w(,)h(1329)p 2967 577 V -2 w(,)f(1330)p -3190 577 V -2 w(.)2033 667 y Fk(Shap)s(es)t Fm(:)83 b(196,)32 -b(207,)f(213,)g(252,)g(262,)g(453,)g(457,)g(545,)2199 -766 y(547,)k(549,)f(551,)h(591,)f(615,)h(686.)2033 868 -y Fi(shap)l(es)12 b Fm(:)83 b(216)p 2379 881 125 4 v --1 w(,)35 b(221,)f(226,)g(249,)g(409)p 3111 881 V -1 -w(,)h(442)p 3294 881 V -1 w(,)g(457)p 3477 881 V -1 w(,)g(543,)2199 -968 y(545,)f(546,)f(548,)h(549,)f(1309,)g(1379.)2033 -1070 y Fi(she)l(ar)14 b Fm(:)83 b(152)p 2340 1083 V -1 -w(,)35 b(153)p 2523 1083 V -2 w(,)h(200)p 2706 1083 V --2 w(,)g(364)p 2889 1083 V -2 w(,)f(365)p 3071 1083 V --1 w(,)g(725)p 3254 1083 V -1 w(,)g(726)p 3437 1083 V --1 w(,)g(1012)p 3620 1083 167 4 v -2 w(,)2199 1170 y(1013)p -2199 1183 V -2 w(,)e(1200)p 2421 1183 V -2 w(,)g(1201)p -2643 1183 V -2 w(,)g(1258,)e(1352)p 3087 1183 V -2 w(,)i(1353)p -3309 1183 V -2 w(.)2033 1272 y Fi(shift)13 b Fm(:)83 -b(155)p 2306 1285 125 4 v -1 w(,)30 b(156)p 2484 1285 -V -2 w(,)g(157)p 2661 1285 V -1 w(,)g(181,)e(200)p 3016 -1285 V -1 w(,)h(238)p 3193 1285 V -1 w(,)h(239)p 3371 -1285 V -2 w(,)g(240)p 3548 1285 V -1 w(,)g(368)p 3726 -1285 V -2 w(,)2199 1372 y(369)p 2199 1385 V -1 w(,)25 -b(370)p 2372 1385 V -2 w(,)g(371)p 2544 1385 V -1 w(,)g(372)p -2717 1385 V -2 w(,)g(373)p 2889 1385 V -1 w(,)g(374,)f(381,)f(389,)h -(478,)f(480,)2199 1471 y(482,)h(484,)f(561,)h(572,)f(728)p -2889 1484 V -1 w(,)i(729)p 3062 1484 V -1 w(,)g(730)p -3235 1484 V -2 w(,)g(731)p 3407 1484 V -1 w(,)g(732,)e(949,)2199 -1571 y(957,)30 b(968,)h(1015)p 2558 1584 167 4 v -2 w(,)h(1016)p -2779 1584 V -2 w(,)f(1017)p 2999 1584 V -1 w(,)g(1018)p -3220 1584 V -2 w(,)h(1034,)e(1065,)2199 1671 y(1110,)25 -b(1127,)g(1164,)g(1174,)g(1179,)g(1180,)g(1188,)g(1190,)2199 -1770 y(1193,)g(1203)p 2415 1783 V -2 w(,)i(1204)p 2631 -1783 V -2 w(,)g(1205)p 2847 1783 V -2 w(,)g(1206)p 3063 -1783 V -2 w(,)g(1219,)e(1228,)g(1229,)2199 1870 y(1268,)g(1270,)g -(1274,)g(1284,)g(1287,)g(1290,)g(1355)p 3495 1883 V -2 -w(,)i(1356)p 3711 1883 V -2 w(,)2199 1969 y(1357)p 2199 -1982 V -2 w(,)g(1358)p 2415 1982 V -2 w(,)g(1420,)e(1445,)g(1449,)g -(1451,)g(1461,)g(1463,)2199 2069 y(1474,)31 b(1476,)g(1478,)g(1488,)g -(1490,)g(1491.)2033 2171 y Fi(shift)p 2192 2171 26 4 -v 31 w(times)12 b Fm(:)83 b(158)p 2529 2184 125 4 v -2 -w(,)27 b(159)p 2703 2184 V -1 w(,)g(374,)f(375)p 3053 -2184 V -1 w(,)h(376)p 3228 2184 V -2 w(,)h(377)p 3403 -2184 V -2 w(,)g(378)p 3578 2184 V -2 w(,)f(732,)2199 -2271 y(733)p 2199 2284 V -1 w(,)36 b(734)p 2383 2284 -V -2 w(,)g(735)p 2566 2284 V -1 w(,)g(736)p 2750 2284 -V -1 w(,)g(1020)p 2934 2284 167 4 v -2 w(,)g(1021)p 3159 -2284 V -2 w(,)g(1022)p 3384 2284 V -2 w(,)h(1023)p 3610 -2284 V -2 w(,)2199 2370 y(1208)p 2199 2383 V -2 w(,)i(1209)p -2427 2383 V -2 w(,)f(1210)p 2654 2383 V -2 w(,)h(1211)p -2882 2383 V -2 w(.)2033 2473 y Fi(shift)p 2192 2473 26 -4 v 31 w(x)14 b Fm(:)83 b(923,)33 b(924)p 2559 2486 125 -4 v -2 w(,)h(925)p 2740 2486 V -1 w(,)f(928,)g(929)p -3103 2486 V -2 w(,)h(930)p 3284 2486 V -1 w(.)2033 2575 -y Fi(shift)p 2192 2575 26 4 v 31 w(y)12 b Fm(:)83 b(923,)33 -b(924)p 2558 2588 125 4 v -2 w(,)h(925)p 2739 2588 V --1 w(,)g(928,)e(929)p 3102 2588 V -2 w(,)i(930)p 3283 -2588 V -1 w(.)2033 2677 y Fi(shift)p 2192 2677 26 4 v -31 w(z)15 b Fm(:)83 b(923,)32 b(924)p 2554 2690 125 4 -v -1 w(,)i(925)p 2736 2690 V -2 w(,)g(928,)f(929)p 3099 -2690 V -2 w(,)h(930)p 3280 2690 V -1 w(.)2033 2779 y -Fi(show)14 b Fm(:)83 b(92)p 2326 2792 84 4 v -1 w(,)33 -b(93)p 2465 2792 V -1 w(,)g(147)p 2604 2792 125 4 v -1 -w(,)g(148)p 2785 2792 V -1 w(,)g(159,)e(182,)h(200)p -3327 2792 V -2 w(,)i(248)p 3508 2792 V -2 w(,)f(249)p -3688 2792 V -1 w(,)2199 2879 y(251,)24 b(346,)f(350,)h(381,)f(382,)h -(385,)g(387,)f(388,)h(389,)f(431)p 3752 2892 V -1 w(,)2199 -2978 y(432)p 2199 2991 V -1 w(,)i(434,)e(503,)h(530,)f(541,)h(549,)g -(561,)f(573)p 3407 2991 V -1 w(,)i(574)p 3580 2991 V --2 w(,)g(603,)2199 3078 y(605,)34 b(606,)g(608)p 2565 -3091 V -2 w(,)i(609)p 2748 3091 V -2 w(,)f(644,)f(645)p -3113 3091 V -1 w(,)h(646)p 3296 3091 V -1 w(,)g(685,)f(866)p -3662 3091 V -2 w(,)2199 3178 y(867)p 2199 3191 V -1 w(,)h(869,)f(900,)g -(904,)f(914,)h(949,)g(954,)g(955,)g(957,)2199 3277 y(958,)e(961,)g -(963,)f(985,)h(986,)g(988,)g(990,)f(996,)h(1127,)2199 -3377 y(1176,)25 b(1178,)g(1179,)g(1182,)g(1184,)g(1185,)g(1188,)g -(1228,)2199 3477 y(1229,)34 b(1268,)g(1341)p 2649 3490 -167 4 v -2 w(,)h(1342)p 2873 3490 V -2 w(,)h(1444.)2033 -3579 y Fi(show)p 2211 3579 26 4 v 32 w(c)l(olors)12 b -Fm(:)83 b(868)p 2564 3592 125 4 v -2 w(,)41 b(869)p 2752 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Ff(SILENT_INDEX)o Fm(:)83 -b(1508)p 2666 4509 167 4 v -1 w(.)2033 4598 y Fi(sin)11 -b Fm(:)83 b(162,)38 b(163,)g(164,)g(1110.)2033 4700 y -Fi(size)11 b Fm(:)83 b(43,)32 b(249,)g(546,)g(548,)g(549,)g(552,)f -(656,)h(657,)g(659,)2199 4800 y(764,)i(765,)g(770,)g(776,)f(802,)h -(807,)g(813,)g(821,)g(824,)2199 4899 y(830,)g(840,)g(842,)g(858,)f -(859,)h(860,)g(862,)g(866,)g(867,)2199 4999 y(878)p 2199 -5012 125 4 v -1 w(,)h(884,)f(885,)g(886,)f(889,)h(891,)g(893,)g(894,)g -(897,)2199 5099 y(899,)j(913,)g(979,)g(981,)g(990,)g(1270,)f(1274,)g -(1287,)2199 5198 y(1308,)25 b(1317,)g(1319,)g(1321,)g(1323,)g(1325,)g -(1327,)g(1329,)2199 5298 y(1330,)37 b(1342,)f(1433,)h(1476.)2033 -5400 y Fi(Slop)l(e)11 b Fm(:)83 b(957)p 2336 5413 V -1 -w(,)33 b(958,)f(959,)g(960,)g(1136)p 3060 5413 167 4 -v -2 w(,)h(1137)p 3282 5413 V -2 w(.)p eop end -%%Page: 506 506 -TeXDict begin 506 505 bop 0 83 a Fm(506)140 b Fl(INDEX)2670 -b(3DLDFPR)n(G)142 b Fn(x)p Fm(1525)0 263 y Fi(slop)l(e)11 -b Fm(:)84 b(345)p 291 276 125 4 v -2 w(,)35 b(346)p 473 -276 V -2 w(,)g(347,)e(879)p 837 276 V -2 w(,)i(880)p -1019 276 V -2 w(,)g(957.)0 364 y Fi(slop)l(e)p 178 364 -26 4 v 32 w(p)p 252 364 V 31 w(x)p 322 364 V 30 w(y)11 -b Fm(:)84 b(533)p 505 377 125 4 v -2 w(,)36 b(535,)f(536,)g(537.)0 -466 y Fi(slop)l(e)p 178 466 26 4 v 32 w(p)p 252 466 V -31 w(x)p 322 466 V 30 w(z)14 b Fm(:)83 b(533)p 501 479 -125 4 v -1 w(,)36 b(538,)f(539,)g(540.)0 567 y Fi(slop)l(e)p -178 567 26 4 v 32 w(p)p 252 567 V 31 w(z)p 317 567 V -30 w(y)12 b Fm(:)83 b(533)p 500 580 125 4 v -1 w(,)41 -b(536.)0 669 y Fi(slop)l(e)p 178 669 26 4 v 32 w(q)p -248 669 V 30 w(x)p 317 669 V 30 w(y)12 b Fm(:)83 b(534)p -500 682 125 4 v -1 w(,)36 b(535,)f(536,)g(537.)0 770 -y Fi(slop)l(e)p 178 770 26 4 v 32 w(q)p 248 770 V 30 -w(x)p 317 770 V 30 w(z)15 b Fm(:)83 b(534)p 497 783 125 -4 v -2 w(,)39 b(538,)e(539.)0 871 y Fi(slop)l(e)p 178 -871 26 4 v 32 w(q)p 248 871 V 30 w(z)p 312 871 V 31 w(y)12 -b Fm(:)83 b(534)p 496 884 125 4 v -2 w(,)42 b(536.)0 -973 y Fk(Solid)t Fm(:)83 b(409,)36 b(549,)h(656,)f(1296)p -874 986 167 4 v -2 w(,)i(1297,)e(1299,)g(1300)p 1555 -986 V -2 w(,)166 1072 y(1301,)25 b(1302)p 382 1085 V --2 w(,)i(1303,)e(1304,)g(1305)p 1030 1085 V -2 w(,)i(1306)p -1246 1085 V -2 w(,)g(1307,)e(1308,)166 1172 y(1309,)g(1310,)g(1314,)g -(1316,)g(1317,)g(1319,)g(1321,)g(1323,)166 1272 y(1325,)g(1327,)g -(1329,)g(1330,)g(1332,)g(1334,)g(1336,)g(1338,)166 1371 -y(1340,)g(1342,)g(1343,)g(1344,)g(1347,)g(1349,)g(1351,)g(1353,)166 -1471 y(1356,)g(1358,)g(1360,)g(1362,)g(1365,)g(1367,)g(1370,)g(1372,) -166 1570 y(1374,)g(1376,)g(1378,)g(1379,)g(1380,)g(1384,)g(1387,)g -(1390,)166 1670 y(1393,)g(1396,)g(1398,)g(1399,)g(1405,)g(1426,)g -(1440,)g(1443,)166 1770 y(1457,)31 b(1460,)g(1471,)g(1474,)g(1485,)g -(1488.)0 1871 y Fk(Solid)p 212 1871 29 5 v 39 w(F)-8 -b(aced)5 b Fm(:)84 b(1405)p 596 1884 167 4 v -2 w(,)27 -b(1413,)e(1431,)h(1440,)f(1443,)h(1457,)166 1971 y(1460,)34 -b(1471,)g(1474,)f(1485,)h(1488.)0 2072 y Fk(Solids)s -Fm(:)83 b(549,)36 b(999,)g(1296,)f(1299.)0 2173 y Fi(solve)11 -b Fm(:)84 b(947)p 291 2186 125 4 v -2 w(,)31 b(949,)e(958,)h(959,)f -(1133)p 1004 2186 167 4 v -2 w(,)i(1134)p 1224 2186 V --2 w(,)f(1167.)0 2275 y Fi(solve)p 178 2275 26 4 v 32 -w(quadr)l(atic)10 b Fm(:)83 b(29)p 652 2288 84 4 v -1 -w(,)38 b(30)p 796 2288 V -1 w(,)f(960.)0 2376 y Fi(sort)12 -b Fm(:)83 b(552,)42 b(1380.)0 2478 y Fi(sort)p 144 2478 -26 4 v 31 w(value)11 b Fm(:)83 b(253)p 471 2491 125 4 -v -2 w(,)30 b(254)p 648 2491 V -1 w(,)g(453,)f(547)p -1004 2491 V -2 w(,)h(548)p 1181 2491 V -1 w(,)g(552,)f(554)p -1537 2491 V -2 w(.)0 2579 y Fk(Sorting)6 b Fm(:)83 b(213)p -417 2592 V -2 w(,)31 b(214)p 595 2592 V -1 w(,)f(253,)g(254,)f(453,)g -(547,)h(548)p 1487 2592 V -2 w(.)0 2680 y Fi(Spher)l(e)11 -b Fm(:)83 b(1296.)0 2782 y Fi(spir)l(al)14 b Fm(:)83 -b(1287)p 315 2795 167 4 v -2 w(,)43 b(1290)p 547 2795 -V -2 w(.)0 2883 y Fi(spir)l(al)p 200 2883 26 4 v 32 w(c)l(ounter)12 -b Fm(:)83 b(1287)p 614 2896 167 4 v -1 w(,)38 b(1290)p -842 2896 V -2 w(.)0 2984 y Fi(sqrt)12 b Fm(:)83 b(25,)24 -b(26,)h(30,)f(503,)g(1110,)g(1135,)f(1183,)g(1193,)h(1268.)0 -3086 y Fi(ss)p 73 3086 26 4 v 30 w(c)l(opy)13 b Fm(:)83 -b(1184)p 375 3099 167 4 v -2 w(.)0 3187 y Fi(ss)p 73 -3187 26 4 v 30 w(e)11 b Fm(:)83 b(1184)p 253 3200 167 -4 v -2 w(.)0 3289 y Fi(ssides)12 b Fm(:)83 b(1032)p 325 -3302 V -2 w(,)34 b(1033)p 548 3302 V -2 w(,)g(1035)p -771 3302 V -2 w(,)f(1036)p 993 3302 V -2 w(,)h(1037.)0 -3390 y Fi(ssin)11 b Fm(:)83 b(161)p 257 3403 125 4 v --2 w(,)40 b(162,)e(163,)g(164.)0 3491 y Fi(start)12 b -Fm(:)83 b(881)p 285 3504 V -2 w(,)35 b(882)p 467 3504 -V -2 w(,)g(883,)e(884,)g(885,)g(886.)0 3593 y Fi(start)p -172 3593 26 4 v 30 w(pt)12 b Fm(:)83 b(1290)p 385 3606 -167 4 v -2 w(.)0 3694 y Fk(std)5 b Fm(:)83 b(9)p 239 -3707 42 4 v -1 w(,)46 b(914.)0 3795 y Fi(stderr)13 b -Fm(:)83 b(503,)34 b(923,)f(1192,)g(1228,)f(1229.)0 3897 -y Fi(stdout)12 b Fm(:)83 b(47,)38 b(49,)h(503,)f(866.)0 -3998 y Fi(step)10 b Fm(:)83 b(1286)p 258 4011 167 4 v --2 w(,)43 b(1287)p 490 4011 V -2 w(.)0 4100 y Fi(stop)10 -b Fm(:)83 b(248)p 262 4113 125 4 v -2 w(,)40 b(249)p -449 4113 V -2 w(,)g(868)p 636 4113 V -2 w(,)g(869)p 823 -4113 V -2 w(.)0 4201 y Fi(str)13 b Fm(:)83 b(463,)40 -b(464,)h(1342.)0 4302 y Fi(str)l(e)l(am)10 b Fm(:)83 -b(45.)0 4404 y Fk(string)6 b Fm(:)83 b(10,)30 b(19,)f(20,)h(37,)g(42,)g -(43,)g(54,)g(56,)g(60,)g(61,)g(63,)166 4503 y(64,)h(65,)g(66,)g(80,)g -(81,)g(92,)f(93,)h(102,)g(120,)f(147,)h(148,)166 4603 -y(196,)24 b(200,)f(205,)h(208,)f(248,)h(249,)g(250,)f(251,)h(262,)f -(264,)166 4703 y(265,)h(410,)f(411,)h(412,)f(413,)h(414,)g(415,)f(416,) -h(417,)f(419,)166 4802 y(420,)h(422,)f(423,)h(425,)f(426,)h(428,)g -(429,)f(431,)h(432,)f(433,)166 4902 y(434,)h(461,)f(462,)h(463,)f(464,) -h(466,)g(467,)f(468,)h(469,)f(573,)166 5001 y(574,)h(591,)f(608,)h -(609,)f(615,)h(645,)g(646,)f(652,)h(654,)f(655,)166 5101 -y(657,)h(667,)f(668,)h(669,)f(670,)h(671,)g(674,)f(676,)h(704,)f(705,) -166 5201 y(706,)h(707,)f(708,)h(709,)f(758,)h(759,)g(763,)f(766,)h -(769,)f(770,)166 5300 y(771,)h(775,)f(776,)h(777,)f(778,)h(780,)g(781,) -f(784,)h(785,)f(786,)166 5400 y(787,)h(789,)f(790,)h(793,)f(794,)h -(795,)g(796,)f(798,)h(799,)f(806,)2199 263 y(807,)h(808,)f(809,)h(812,) -f(813,)h(814,)g(815,)f(817,)h(818,)f(823,)2199 363 y(824,)34 -b(825,)g(826,)g(829,)f(830,)h(831,)g(832,)g(834,)g(835,)2199 -462 y(836,)g(837,)g(859,)g(866,)f(867,)h(872,)g(873,)g(874,)g(875,)2199 -562 y(881,)g(882,)g(886,)g(898,)f(913,)h(914,)g(924,)g(925,)g(929,)2199 -662 y(930,)f(938,)f(973,)h(1049,)f(1050,)g(1053,)g(1054,)g(1057,)2199 -761 y(1097,)25 b(1098,)g(1101,)g(1122,)g(1123,)g(1124,)g(1188,)g(1222,) -2199 861 y(1223,)g(1224,)g(1225,)g(1230,)g(1231,)g(1234,)g(1272,)g -(1273,)2199 960 y(1276,)g(1277,)g(1280,)g(1283,)g(1284,)g(1294,)g -(1341,)g(1342,)2199 1060 y(1383,)g(1384,)g(1389,)g(1390,)g(1392,)g -(1393,)g(1398,)g(1399,)2199 1160 y(1403,)31 b(1411,)g(1429,)g(1495,)g -(1502,)g(1518.)2033 1261 y Fk(strings)t Fm(:)83 b(461,)36 -b(766,)g(771,)f(1284.)2033 1363 y Fk(stringstream)t Fm(:)83 -b(464,)38 b(1342.)2033 1464 y Fi(subp)l(ath)11 b Fm(:)83 -b(881)p 2417 1477 V -1 w(,)40 b(882)p 2605 1477 V -2 -w(,)h(968.)2033 1566 y Fi(subp)l(ath)p 2305 1566 26 4 -v 31 w(size)11 b Fm(:)83 b(967)p 2579 1579 125 4 v -1 -w(,)40 b(968)p 2767 1579 V -1 w(.)2033 1667 y Fi(suppr)l(ess)p -2338 1667 26 4 v 31 w(lab)l(els)12 b Fm(:)83 b(216,)38 -b(229)p 2859 1680 125 4 v -2 w(.)2033 1769 y Fi(suppr)l(ess)p -2338 1769 26 4 v 31 w(output)11 b Fm(:)83 b(200)p 2711 -1782 125 4 v -1 w(,)37 b(438)p 2896 1782 V -1 w(,)g(439)p -3081 1782 V -1 w(,)g(550,)f(551,)g(552,)2199 1869 y(852)p -2199 1882 V -1 w(,)j(853)p 2386 1882 V -1 w(,)g(1375)p -2573 1882 167 4 v -2 w(,)h(1376)p 2802 1882 V -2 w(.)2033 -1970 y Fi(suppr)l(ess)p 2338 1970 26 4 v 31 w(warnings)11 -b Fm(:)83 b(948)p 2804 1983 125 4 v -1 w(,)38 b(949)p -2990 1983 V -2 w(.)2033 2072 y Fi(suppr)l(ess)p 2338 -2072 26 4 v 31 w(x)14 b Fm(:)83 b(923.)2033 2173 y Fi(suppr)l(ess)p -2338 2173 V 31 w(y)12 b Fm(:)83 b(923.)2033 2275 y Fi(suppr)l(ess)p -2338 2275 V 31 w(z)14 b Fm(:)83 b(923.)2033 2376 y(surface)38 -b(hiding:)83 b(999.)2033 2478 y Fi(surfac)l(e)p 2291 -2478 V 31 w(ve)l(ctor)14 b Fm(:)83 b(953,)29 b(954)p -2830 2491 125 4 v -2 w(,)i(956,)e(984,)g(985)p 3364 2491 -V -2 w(,)i(987.)2033 2580 y(system)36 b(dep)r(endencies:)83 -b(1516.)2033 2681 y Fi(s1)16 b Fm(:)83 b(454)p 2231 2694 -V -1 w(,)42 b(455)p 2421 2694 V -1 w(,)g(456)p 2611 2694 -V -1 w(.)2033 2783 y Fi(s2)16 b Fm(:)83 b(454)p 2231 -2796 V -1 w(,)42 b(455)p 2421 2796 V -1 w(,)g(456)p 2611 -2796 V -1 w(.)2033 2884 y Fe(t)p Fm(:)83 b(130)p 2169 -2897 V -1 w(,)28 b(131)p 2345 2897 V -2 w(,)g(143)p 2520 -2897 V -1 w(,)g(149)p 2696 2897 V -2 w(,)g(151)p 2871 -2897 V -1 w(,)g(153)p 3047 2897 V -2 w(,)g(156)p 3222 -2897 V -1 w(,)g(173)p 3398 2897 V -2 w(,)g(174)p 3573 -2897 V -1 w(,)g(177)p 3749 2897 V -1 w(,)2199 2984 y(178)p -2199 2997 V -1 w(,)35 b(179)p 2382 2997 V -2 w(,)h(182)p -2565 2997 V -2 w(,)g(210)p 2748 2997 V -2 w(,)f(244)p -2930 2997 V -1 w(,)g(245)p 3113 2997 V -1 w(,)g(246)p -3296 2997 V -1 w(,)g(247)p 3479 2997 V -2 w(,)h(360)p -3662 2997 V -2 w(,)2199 3083 y(362)p 2199 3096 V -1 w(,)f(364)p -2382 3096 V -2 w(,)h(369)p 2565 3096 V -2 w(,)g(375)p -2748 3096 V -2 w(,)f(380)p 2930 3096 V -1 w(,)g(393)p -3113 3096 V -1 w(,)g(395)p 3296 3096 V -1 w(,)g(396)p -3479 3096 V -2 w(,)h(472)p 3662 3096 V -2 w(,)2199 3183 -y(474)p 2199 3196 V -1 w(,)f(475)p 2382 3196 V -2 w(,)h(512)p -2565 3196 V -2 w(,)g(606)p 2748 3196 V -2 w(,)f(714)p -2930 3196 V -1 w(,)g(716)p 3113 3196 V -1 w(,)g(720)p -3296 3196 V -1 w(,)g(724)p 3479 3196 V -2 w(,)h(726)p -3662 3196 V -2 w(,)2199 3283 y(729)p 2199 3296 V -1 w(,)d(738)p -2380 3296 V -2 w(,)h(739)p 2561 3296 V -2 w(,)f(748)p -2741 3296 V -1 w(,)g(749)p 2922 3296 V -1 w(,)g(750)p -3103 3296 V -2 w(,)h(752)p 3284 3296 V -2 w(,)f(904)p -3464 3296 V -1 w(,)g(1001)p 3645 3296 167 4 v -2 w(,)2199 -3382 y(1002)p 2199 3395 V -2 w(,)27 b(1004)p 2415 3395 -V -2 w(,)g(1007)p 2631 3395 V -2 w(,)g(1011)p 2847 3395 -V -2 w(,)g(1013)p 3063 3395 V -2 w(,)g(1016)p 3279 3395 -V -2 w(,)g(1110)p 3495 3395 V -2 w(,)g(1127)p 3711 3395 -V -2 w(,)2199 3482 y(1174)p 2199 3495 V -2 w(,)g(1179)p -2415 3495 V -2 w(,)g(1192)p 2631 3495 V -2 w(,)g(1193)p -2847 3495 V -2 w(,)g(1194)p 3063 3495 V -2 w(,)g(1195)p -3279 3495 V -2 w(,)g(1197)p 3495 3495 V -2 w(,)g(1199)p -3711 3495 V -2 w(,)2199 3582 y(1201)p 2199 3595 V -2 -w(,)g(1204)p 2415 3595 V -2 w(,)g(1214)p 2631 3595 V --2 w(,)g(1228)p 2847 3595 V -2 w(,)g(1229)p 3063 3595 -V -2 w(,)g(1270)p 3279 3595 V -2 w(,)g(1274)p 3495 3595 -V -2 w(,)g(1284)p 3711 3595 V -2 w(,)2199 3681 y(1346)p -2199 3694 V -2 w(,)g(1347)p 2415 3694 V -2 w(,)g(1348)p -2631 3694 V -2 w(,)g(1351)p 2847 3694 V -2 w(,)g(1353)p -3063 3694 V -2 w(,)g(1356)p 3279 3694 V -2 w(,)g(1358)p -3495 3694 V -2 w(,)g(1360)p 3711 3694 V -2 w(,)2199 3781 -y(1362)p 2199 3794 V -2 w(,)36 b(1447)p 2424 3794 V -2 -w(,)g(1451)p 2649 3794 V -2 w(,)f(1461)p 2873 3794 V --2 w(,)h(1488)p 3098 3794 V -2 w(.)2033 3882 y Fi(t)p -2066 3882 26 4 v 30 w(al)t(l)14 b Fm(:)83 b(161)p 2299 -3895 125 4 v -1 w(,)44 b(164.)2033 3984 y Fi(t)p 2066 -3984 26 4 v 30 w(inverse)11 b Fm(:)83 b(961)p 2463 3997 -125 4 v -1 w(,)33 b(1179)p 2644 3997 167 4 v -2 w(,)g(1182,)e(1184,)g -(1186.)2033 4086 y Fi(t)p 2066 4086 26 4 v 30 w(x)14 -b Fm(:)83 b(161)p 2250 4099 125 4 v -1 w(,)42 b(162,)f(164,)f(517)p -2819 4099 V -1 w(,)i(518,)f(519,)g(520,)f(521,)2199 4185 -y(522,)i(904)p 2390 4198 V -2 w(,)h(906.)2033 4287 y -Fi(t)p 2066 4287 26 4 v 30 w(x)p 2135 4287 V 30 w(sign)11 -b Fm(:)83 b(521)p 2421 4300 125 4 v -1 w(.)2033 4388 -y Fi(t)p 2066 4388 26 4 v 30 w(y)12 b Fm(:)83 b(161)p -2249 4401 125 4 v -1 w(,)32 b(163,)g(164,)f(517)p 2790 -4401 V -1 w(,)h(518,)g(519,)f(520,)g(521,)h(522,)2199 -4488 y(904)p 2199 4501 V -1 w(,)43 b(905,)e(906.)2033 -4589 y Fi(t)p 2066 4589 26 4 v 30 w(y)p 2136 4589 V 31 -w(sign)11 b Fm(:)83 b(521)p 2423 4602 125 4 v -1 w(.)2033 -4691 y Fi(t)p 2066 4691 26 4 v 30 w(z)15 b Fm(:)83 b(161)p -2246 4704 125 4 v -2 w(,)43 b(164,)e(517)p 2626 4704 -V -2 w(,)i(518,)e(519,)g(520,)g(521,)g(522,)2199 4791 -y(904)p 2199 4804 V -1 w(,)i(905,)e(906.)2033 4892 y -Fi(t)p 2066 4892 26 4 v 30 w(z)p 2130 4892 V 31 w(sign)11 -b Fm(:)83 b(521)p 2417 4905 125 4 v -2 w(.)2033 4994 -y Fi(temp)10 b Fm(:)83 b(503)p 2325 5007 V -2 w(,)39 -b(904)p 2511 5007 V -1 w(,)g(905,)e(906.)2033 5095 y -Fi(temp)p 2214 5095 26 4 v 31 w(b)l(o)l(ol)13 b Fm(:)83 -b(1188)p 2494 5108 167 4 v -2 w(,)41 b(1189.)2033 5197 -y Fi(temp)p 2214 5197 26 4 v 31 w(cir)l(cle)11 b Fm(:)83 -b(1287)p 2548 5210 167 4 v -2 w(.)2033 5298 y Fi(temp)p -2214 5298 26 4 v 31 w(cir)l(cle)p 2436 5298 V 31 w(c)l(enter)13 -b Fm(:)83 b(1287)p 2801 5311 167 4 v -2 w(.)2033 5400 -y Fi(temp)p 2214 5400 26 4 v 31 w(cir)l(cle)p 2436 5400 -V 31 w(normal)14 b Fm(:)83 b(1287)p 2837 5413 167 4 v --2 w(.)p eop end -%%Page: 507 507 -TeXDict begin 507 506 bop 0 83 a Fn(x)p Fm(1525)139 b -Fl(3DLDFPR)n(G)2671 b(INDEX)141 b Fm(507)0 263 y Fi(temp)p -181 263 26 4 v 31 w(c)l(o)l(or)l(dinates)12 b Fm(:)83 -b(397,)34 b(399)p 909 276 125 4 v -1 w(,)i(401.)0 365 -y Fi(temp)p 181 365 26 4 v 31 w(matrix)14 b Fm(:)83 b(174)p -564 378 125 4 v -2 w(.)0 466 y Fi(temp)p 181 466 26 4 -v 31 w(pt)12 b Fm(:)83 b(605)p 395 479 125 4 v -2 w(.)0 -568 y Fi(temp)p 181 568 26 4 v 31 w(string)11 b Fm(:)83 -b(1188)p 531 581 167 4 v -2 w(,)40 b(1189.)0 670 y Fi(temp1)16 -b Fm(:)83 b(161)p 340 683 125 4 v -1 w(,)38 b(162,)f(163,)g(164.)0 -772 y Fi(temp2)16 b Fm(:)83 b(161)p 340 785 V -1 w(,)38 -b(162,)f(163,)g(164.)0 873 y Fi(test)p 133 873 26 4 v -30 w(angle)11 b Fm(:)83 b(1185)p 461 886 167 4 v -2 w(.)0 -975 y Fi(test)p 133 975 26 4 v 30 w(p)l(oints)11 b Fm(:)83 -b(357,)40 b(904.)0 1077 y Fi(T)-6 b(etr)l(ahe)l(dr)l(a)12 -b Fm(:)83 b(1444.)0 1178 y Fk(T)-8 b(etrahedron)6 b Fm(:)83 -b(1429,)37 b(1436)p 854 1191 167 4 v -2 w(,)j(1437,)d(1439,)g(1440)p -1539 1191 V -2 w(,)166 1278 y(1442,)25 b(1443)p 382 1291 -V -2 w(,)i(1444,)e(1446,)g(1447,)g(1448,)g(1449,)g(1451.)0 -1380 y Fi(tex)p 110 1380 26 4 v 30 w(str)l(e)l(am)10 -b Fm(:)83 b(39)p 488 1393 84 4 v -1 w(,)34 b(40)p 628 -1393 V -1 w(,)g(44,)f(45,)h(46,)f(1519.)0 1481 y Fi(tex)p -110 1481 26 4 v 30 w(str)l(e)l(am)p 377 1481 V 30 w(name)11 -b Fm(:)83 b(42)p 714 1494 84 4 v -1 w(,)37 b(43)p 857 -1494 V -1 w(,)h(44.)0 1583 y Fi(text)11 b Fm(:)83 b(92)p -250 1596 V -1 w(,)25 b(93)p 381 1596 V -1 w(,)g(147)p -512 1596 125 4 v -1 w(,)f(148)p 684 1596 V -1 w(,)h(200)p -857 1596 V -1 w(,)f(208)p 1029 1596 V -1 w(,)h(248)p -1202 1596 V -2 w(,)g(249)p 1374 1596 V -1 w(,)g(250)p -1547 1596 V -2 w(,)g(251)p 1719 1596 V -1 w(,)166 1683 -y(431)p 166 1696 V -1 w(,)g(432)p 339 1696 V -2 w(,)g(433)p -511 1696 V -1 w(,)g(434)p 684 1696 V -2 w(,)g(462,)f(471,)g(472,)f(608) -p 1374 1696 V -1 w(,)i(609)p 1547 1696 V -2 w(,)g(645)p -1719 1696 V -1 w(,)166 1782 y(646)p 166 1795 V -1 w(,)j(866)p -342 1795 V -1 w(,)g(867)p 518 1795 V -1 w(,)g(872)p 694 -1795 V -1 w(,)g(873)p 870 1795 V -1 w(,)g(874)p 1046 -1795 V -1 w(,)g(875)p 1222 1795 V -1 w(,)h(1341)p 1399 -1795 167 4 v -2 w(,)f(1342)p 1616 1795 V -2 w(.)0 1884 -y Fi(text)p 138 1884 26 4 v 29 w(short)13 b Fm(:)83 b(463)p -462 1897 125 4 v -1 w(,)29 b(464)p 639 1897 V -2 w(,)h(468)p -816 1897 V -2 w(,)g(469)p 993 1897 V -2 w(,)g(828)p 1170 -1897 V -2 w(,)f(829)p 1346 1897 V -1 w(,)g(830)p 1523 -1897 V -1 w(,)g(831)p 1700 1897 V -1 w(,)166 1984 y(832)p -166 1997 V -1 w(,)38 b(834)p 352 1997 V -2 w(,)h(835)p -538 1997 V -2 w(,)g(836)p 724 1997 V -2 w(,)f(837)p 909 -1997 V -1 w(.)0 2085 y Fi(text)p 138 2085 26 4 v 29 w(str)13 -b Fm(:)83 b(461)p 378 2098 125 4 v -1 w(,)33 b(462)p -559 2098 V -1 w(,)g(466)p 740 2098 V -1 w(,)g(467)p 921 -2098 V -1 w(,)g(573)p 1102 2098 V -1 w(,)g(574)p 1283 -2098 V -1 w(.)0 2187 y Fi(theta)11 b Fm(:)83 b(1287)p -295 2200 167 4 v -2 w(,)43 b(1290)p 527 2200 V -2 w(.)0 -2289 y Fi(theta)p 183 2289 26 4 v 31 w(total)13 b Fm(:)83 -b(1290)p 489 2302 167 4 v -2 w(.)0 2390 y Fi(thir)l(d)13 -b Fm(:)84 b(13)p 288 2403 84 4 v -1 w(,)44 b(270)p 438 -2403 125 4 v -2 w(,)h(271,)d(960,)h(1136,)f(1137,)h(1184,)166 -2490 y(1186,)f(1188.)0 2592 y Fi(this)11 b Fm(:)84 b(78,)32 -b(143,)g(149,)g(151,)g(153,)f(156,)h(159,)g(164,)g(171,)166 -2691 y(173,)24 b(174,)f(177,)h(179,)f(188,)h(224,)g(239,)f(284,)h(285,) -f(287,)166 2791 y(289,)h(315,)f(320,)h(343,)f(345,)h(346,)g(349,)f -(350,)h(351,)f(353,)166 2891 y(356,)h(357,)f(388,)h(392,)f(393,)h(395,) -g(409,)f(411,)h(415,)f(418,)166 2990 y(431,)h(432,)f(442,)h(443,)f -(462,)h(463,)g(478,)f(482,)h(489,)f(493,)166 3090 y(497,)h(499,)f(501,) -h(503,)f(504,)h(507,)g(508,)f(510,)h(512,)f(523,)166 -3190 y(524,)h(526,)f(544,)h(545,)f(557,)h(563,)g(566,)f(568,)h(570,)f -(601,)166 3289 y(622,)h(626,)f(637,)h(646,)f(657,)h(677,)g(678,)f(689,) -h(714,)f(716,)166 3389 y(720,)h(724,)f(726,)h(729,)f(750,)h(751,)g -(752,)f(754,)h(757,)f(762,)166 3488 y(764,)h(768,)f(770,)h(771,)f(776,) -h(780,)g(789,)f(798,)h(802,)f(807,)166 3588 y(813,)h(817,)f(821,)h -(824,)f(840,)h(872,)g(874,)f(881,)h(886,)f(896)p 1719 -3601 V -1 w(,)166 3688 y(901,)34 b(904,)g(912,)g(914,)f(915,)h(916,)g -(920,)g(932,)g(948,)166 3787 y(949,)24 b(953,)h(957,)f(967,)h(999,)f -(1004,)g(1007,)g(1011,)g(1013,)166 3887 y(1016,)h(1027,)g(1037,)g -(1067,)g(1072,)g(1080,)g(1112,)g(1120,)166 3987 y(1126,)g(1127,)g -(1152,)g(1167,)g(1176,)g(1178,)g(1179,)g(1192,)166 4086 -y(1196,)g(1198,)g(1199,)g(1200,)g(1201,)g(1203,)g(1213,)g(1243,)166 -4186 y(1245,)g(1253,)g(1254,)g(1255,)g(1256,)g(1258,)g(1308,)g(1310,) -166 4285 y(1351,)g(1353,)g(1356,)g(1358,)g(1360,)g(1362,)g(1365,)g -(1384,)166 4385 y(1387,)j(1390,)h(1393,)f(1396,)g(1399,)h(1426,)f -(1447.)0 4487 y Fi(this)p 134 4487 26 4 v 31 w(axis)p -305 4487 V 31 w(orientation)11 b Fm(:)84 b(1178)p 848 -4500 167 4 v -2 w(,)35 b(1179.)0 4588 y Fi(this)p 134 -4588 26 4 v 31 w(option)p 391 4588 V 32 w(optind)13 b -Fm(:)83 b(1508)p 763 4601 167 4 v -1 w(.)0 4690 y Fi(this)p -134 4690 26 4 v 31 w(plane)11 b Fm(:)83 b(1176)p 467 -4703 167 4 v -1 w(,)35 b(1177,)e(1178,)g(1179,)g(1181,)h(1188,)166 -4790 y(1268)p 166 4803 V -2 w(.)0 4891 y Fi(thr)l(eshold)14 -b Fm(:)83 b(1516)p 440 4904 V -2 w(.)0 4993 y Fi(time)11 -b Fm(:)83 b(43.)0 5095 y Fk(tm)t Fm(:)h(43.)0 5197 y -Fi(tolower)14 b Fm(:)83 b(313,)27 b(318,)g(346,)h(380,)f(432,)g(561,)g -(867,)g(1134.)0 5298 y Fi(top)p 117 5298 26 4 v 31 w(lft)12 -b Fm(:)83 b(1065)p 335 5311 167 4 v -1 w(.)0 5400 y Fi(top)p -117 5400 26 4 v 31 w(rt)12 b Fm(:)83 b(1065)p 324 5413 -167 4 v -2 w(.)2033 263 y Fi(tr)l(ac)l(e)10 b Fm(:)84 -b(529)p 2323 276 125 4 v -2 w(,)39 b(530)p 2509 276 V --1 w(,)g(920)p 2696 276 V -2 w(,)g(921)p 2882 276 V -1 -w(.)2033 368 y Fi(tr)l(ac)l(e)p 2211 368 26 4 v 30 w(x)p -2280 368 V 31 w(z)p 2345 368 V 30 w(0)16 b Fm(:)83 b(957)p -2534 381 125 4 v -1 w(.)2033 473 y Fk(T)-8 b(ransform)5 -b Fm(:)84 b(122)p 2575 486 V -2 w(,)35 b(124,)e(125)p -2939 486 V -1 w(,)h(126,)g(127)p 3304 486 V -2 w(,)h(128,)e(129)p -3668 486 V -1 w(,)2199 573 y(130,)24 b(131,)f(133,)h(135,)f(137,)h -(138,)g(141,)f(143,)h(146,)f(148,)2199 673 y(149,)h(150,)f(151,)h(152,) -f(153,)h(155,)g(156,)f(157,)h(158,)f(159,)2199 772 y(160,)h(161,)f -(166,)h(167,)f(168,)h(172,)g(173,)f(174,)h(176,)f(177,)2199 -872 y(178,)h(179,)f(181,)h(182,)f(187,)h(188,)g(189,)f(190,)h(191,)f -(192,)2199 972 y(200,)h(210,)f(216,)h(235,)f(236,)h(238,)g(239,)f(240,) -h(241,)f(242,)2199 1071 y(243,)h(244,)f(245,)h(246,)f(247,)h(264,)g -(341,)f(360,)h(361,)f(362,)2199 1171 y(363,)h(364,)f(365,)h(368,)f -(369,)h(370,)g(371,)f(372,)h(373,)f(375,)2199 1270 y(376,)h(377,)f -(378,)h(379,)f(380,)h(392,)g(393,)f(394,)h(395,)f(396,)2199 -1370 y(397,)h(404,)f(472,)h(474,)f(475,)h(553,)g(556,)f(559,)h(561,)f -(572,)2199 1470 y(580,)h(581,)f(583,)h(584,)f(710,)h(713,)g(714,)f -(716,)h(717,)f(719,)2199 1569 y(720,)34 b(721,)g(722,)g(723,)f(724,)h -(725,)g(726,)g(728,)g(729,)2199 1669 y(730,)g(731,)g(732,)g(738,)f -(739,)h(747,)g(748,)g(749,)g(750,)2199 1769 y(751,)28 -b(752,)f(949,)h(953,)f(957,)h(961,)g(1000,)f(1001,)g(1002,)2199 -1868 y(1003,)e(1004,)g(1006,)g(1007,)g(1008,)g(1009,)g(1010,)g(1011,) -2199 1968 y(1012,)g(1013,)g(1015,)g(1016,)g(1017,)g(1018,)g(1024,)g -(1057,)2199 2068 y(1110,)g(1127,)g(1179,)g(1182,)g(1192,)g(1193,)g -(1194,)g(1195,)2199 2167 y(1196,)g(1197,)g(1198,)g(1199,)g(1200,)g -(1201,)g(1203,)g(1204,)2199 2267 y(1205,)g(1206,)g(1213,)g(1214,)g -(1215,)g(1216,)g(1228,)g(1229,)2199 2366 y(1270,)g(1274,)g(1284,)g -(1346,)g(1347,)g(1348,)g(1350,)g(1351,)2199 2466 y(1352,)g(1353,)g -(1355,)g(1356,)g(1357,)g(1358,)g(1359,)g(1360,)2199 2566 -y(1361,)31 b(1362,)g(1451,)g(1459,)g(1461,)g(1488.)2033 -2671 y Fi(tr)l(ansform)11 b Fm(:)83 b(216)p 2502 2684 -V -2 w(,)29 b(224,)f(236,)f(239,)h(242,)f(245,)h(247,)f(249,)2199 -2770 y(251,)d(256,)f(264)p 2544 2783 V -1 w(,)i(278,)e(300,)h(302,)g -(303,)f(307,)h(341,)f(361,)2199 2870 y(363,)h(365,)f(369,)h(375,)f -(376,)h(378,)g(393,)f(396,)h(397,)f(399,)2199 2970 y(404,)h(405,)f -(407,)h(431,)f(432,)h(434,)g(474,)f(475,)h(486,)f(494,)2199 -3069 y(543,)34 b(545,)g(546,)g(549,)f(553,)h(556)p 3113 -3082 V -1 w(,)h(557,)f(561,)g(570,)2199 3169 y(572,)e(574,)h(580,)f -(581,)g(582,)h(584,)f(597.)2033 3274 y Fi(tr)l(ansforms)11 -b Fm(:)83 b(732.)2033 3379 y Fk(T)-8 b(ransforms)5 b -Fm(:)83 b(122,)39 b(138.)2033 3485 y Fi(triangle)p 2312 -3485 26 4 v 31 w(diameter)15 b Fm(:)83 b(1443)p 2775 -3498 167 4 v -2 w(,)32 b(1447)p 2996 3498 V -2 w(,)g(1448)p -3217 3498 V -2 w(,)g(1449)p 3438 3498 V -2 w(,)g(1450)p -3659 3498 V -2 w(,)2199 3584 y(1451)p 2199 3597 V -2 -w(,)h(1474)p 2421 3597 V -2 w(,)g(1475)p 2643 3597 V --2 w(,)g(1476)p 2865 3597 V -2 w(,)g(1477)p 3087 3597 -V -2 w(,)g(1478)p 3309 3597 V -2 w(.)2033 3690 y Fi(triangle)p -2312 3690 26 4 v 31 w(r)l(adius)12 b Fm(:)83 b(1436)p -2675 3703 167 4 v -2 w(,)38 b(1440,)f(1443,)f(1467)p -3357 3703 V -2 w(,)i(1471,)2199 3789 y(1474.)2033 3894 -y Fi(triangles)12 b Fm(:)83 b(1449)p 2459 3907 V -2 w(,)41 -b(1476)p 2689 3907 V -2 w(.)2033 4000 y Fi(triangles)p -2346 4000 26 4 v 31 w(size)11 b Fm(:)83 b(1475)p 2620 -4013 167 4 v -2 w(,)39 b(1476)p 2848 4013 V -2 w(.)2033 -4105 y Fi(true)10 b Fm(:)83 b(17,)34 b(32,)g(47,)g(48,)g(49,)g(50,)g -(60,)h(61,)f(63,)g(64,)g(66,)2199 4204 y(72,)28 b(104,)f(112,)g(141,)g -(143,)g(159,)g(161,)g(174,)g(182,)g(188,)2199 4304 y(200,)d(209,)f -(216,)h(219,)f(230,)h(253,)g(254,)f(280,)h(283,)f(285,)2199 -4404 y(287,)h(289,)f(290,)h(292,)f(294,)h(296,)g(300,)f(301,)h(312,)f -(314,)2199 4503 y(317,)h(319,)f(322,)h(324,)f(327,)h(329,)g(332,)f -(334,)h(337,)f(339,)2199 4603 y(346,)h(349,)f(350,)h(351,)f(355,)h -(356,)g(357,)f(380,)h(393,)f(395,)2199 4703 y(399,)h(400,)f(401,)h -(405,)f(411,)h(418,)g(427,)f(431,)h(432,)f(441,)2199 -4802 y(443,)h(446,)f(448,)h(452,)f(458,)h(461,)g(462,)f(464,)h(467,)f -(469,)2199 4902 y(472,)h(506,)f(507,)h(510,)f(517,)h(520,)g(527,)f -(529,)h(530,)f(541,)2199 5001 y(544,)h(546,)f(548,)h(549,)f(551,)h -(552,)g(553,)f(561,)h(574,)f(603,)2199 5101 y(605,)h(606,)f(624,)h -(637,)f(641,)h(644,)g(655,)f(661,)h(664,)f(666,)2199 -5201 y(669,)h(671,)f(674,)h(676,)f(678,)h(681,)g(683,)f(685,)h(687,)f -(690,)2199 5300 y(698,)h(703,)f(726,)h(743,)f(769,)h(771,)g(776,)f -(785,)h(787,)f(802,)2199 5400 y(807,)h(824,)f(830,)h(835,)f(840,)h -(842,)g(844,)f(847,)h(849,)f(855,)p eop end -%%Page: 508 508 -TeXDict begin 508 507 bop 0 83 a Fm(508)140 b Fl(INDEX)2670 -b(3DLDFPR)n(G)142 b Fn(x)p Fm(1525)166 263 y(856,)24 -b(857,)f(859,)h(861,)f(863,)h(866,)g(872,)f(873,)h(874,)f(875,)166 -363 y(876,)h(882,)f(897,)h(900,)f(904,)h(906,)g(908,)f(912,)h(915,)f -(916,)166 462 y(949,)h(953,)f(954,)h(961,)f(967,)h(969,)g(970,)f(985,)h -(988,)f(991,)166 562 y(995,)30 b(996,)h(1030,)f(1033,)f(1036,)h(1037,)g -(1040,)g(1042,)166 662 y(1062,)25 b(1065,)g(1070,)g(1075,)g(1077,)g -(1107,)g(1110,)g(1115,)166 761 y(1117,)g(1124,)g(1126,)g(1127,)g(1128,) -g(1164,)g(1175,)g(1176,)166 861 y(1178,)g(1179,)g(1183,)g(1184,)g -(1185,)g(1186,)g(1188,)g(1192,)166 960 y(1193,)g(1194,)g(1195,)g(1240,) -g(1243,)g(1248,)g(1250,)g(1258,)166 1060 y(1259,)g(1267,)g(1268,)g -(1284,)g(1290,)g(1300,)g(1302,)g(1304,)166 1160 y(1308,)g(1311,)g -(1317,)g(1340,)g(1341,)g(1344,)g(1367,)g(1370,)166 1259 -y(1372,)g(1378,)g(1380,)g(1384,)g(1387,)g(1390,)g(1393,)g(1396,)166 -1359 y(1399,)g(1416,)g(1418,)g(1420,)g(1422,)g(1440,)g(1443,)g(1450,) -166 1459 y(1451,)g(1457,)g(1460,)g(1463,)g(1464,)g(1471,)g(1474,)g -(1476,)166 1558 y(1477,)31 b(1478,)g(1485,)g(1488,)g(1490,)g(1508.)0 -1660 y Fi(trunc)8 b Fm(:)83 b(21)p 307 1673 84 4 v -1 -w(,)39 b(22)p 452 1673 V -1 w(,)g(97,)f(98,)h(99.)0 1761 -y Fk(T)-8 b(runc)p 249 1761 29 5 v 41 w(Octahedron)6 -b Fm(:)83 b(401,)38 b(1429,)g(1481)p 1301 1774 167 4 -v -1 w(,)i(1482,)166 1861 y(1484,)34 b(1485)p 391 1874 -V -2 w(,)i(1487,)d(1488)p 840 1874 V -2 w(,)j(1490.)0 -1962 y Fi(tt)11 b Fm(:)83 b(43)p 173 1975 84 4 v -1 w(.)0 -2064 y Fi(t0)16 b Fm(:)83 b(957)p 192 2077 125 4 v -2 -w(,)42 b(961,)f(1182)p 571 2077 167 4 v -2 w(.)0 2165 -y Fi(t1)16 b Fm(:)83 b(949)p 192 2178 125 4 v -2 w(,)45 -b(1182)p 384 2178 167 4 v -2 w(.)0 2266 y Fi(t2)16 b -Fm(:)83 b(949)p 192 2279 125 4 v -2 w(.)0 2368 y Fi(t3)16 -b Fm(:)83 b(949)p 192 2381 V -2 w(.)0 2469 y Fe(u)p Fm(:)g(60)p -154 2482 84 4 v -1 w(,)39 b(61)p 299 2482 V -1 w(,)g(63)p -444 2482 V -1 w(,)g(64)p 589 2482 V -1 w(,)h(65)p 735 -2482 V -1 w(,)f(66)p 880 2482 V -1 w(.)0 2571 y Fi(u)p -50 2571 26 4 v 30 w(x)14 b Fm(:)83 b(606)p 234 2584 125 -4 v -2 w(.)0 2672 y Fi(u)p 50 2672 26 4 v 30 w(y)12 b -Fm(:)83 b(606)p 233 2685 125 4 v -1 w(.)0 2774 y Fi(u)p -50 2774 26 4 v 30 w(z)15 b Fm(:)83 b(606)p 230 2787 125 -4 v -2 w(.)0 2875 y Fi(unalign)p 270 2875 26 4 v 31 w(up)9 -b Fm(:)83 b(561)p 498 2888 125 4 v -1 w(,)41 b(572)p -687 2888 V -1 w(.)0 2976 y Ff(UNDRAW)r Fm(:)83 b(199)p -372 2989 V -2 w(,)36 b(201)p 555 2989 V -2 w(,)f(813,)f(861,)g(1391.)0 -3078 y Fi(undr)l(aw)13 b Fm(:)83 b(414,)32 b(425)p 562 -3091 V -1 w(,)i(426)p 744 3091 V -2 w(,)g(812)p 925 3091 -V -2 w(,)g(813)p 1106 3091 V -2 w(,)g(814)p 1287 3091 -V -2 w(,)g(815)p 1468 3091 V -1 w(,)f(817)p 1649 3091 -V -1 w(,)166 3177 y(818)p 166 3190 V -1 w(,)42 b(1392)p -356 3190 167 4 v -2 w(,)g(1393)p 587 3190 V -2 w(.)0 -3279 y Fi(undr)l(aw)p 267 3279 26 4 v 31 w(in)p 370 3279 -V 30 w(el)t(lipse)13 b Fm(:)83 b(1226.)0 3380 y Ff(UNDRAWDOT)q -Fm(:)g(199)p 503 3393 125 4 v -2 w(,)37 b(201)p 687 3393 -V -2 w(,)g(415,)e(458.)0 3482 y Fi(undr)l(awdot)13 b -Fm(:)83 b(414)p 493 3495 V -2 w(,)37 b(415)p 677 3495 -V -2 w(,)g(416)p 861 3495 V -2 w(,)g(417)p 1045 3495 -V -2 w(.)0 3583 y Ff(UNFILL)r Fm(:)83 b(199)p 372 3596 -V -2 w(,)36 b(201)p 555 3596 V -2 w(,)f(821,)f(861,)g(1394.)0 -3685 y Fi(un\014l)t(l)12 b Fm(:)83 b(820)p 303 3698 V --1 w(,)35 b(821)p 486 3698 V -1 w(,)g(1394,)e(1395)p -893 3698 167 4 v -2 w(,)i(1396)p 1117 3698 V -2 w(.)0 -3786 y Fi(un\014l)t(l)p 190 3786 26 4 v 30 w(dr)l(aw)14 -b Fm(:)83 b(1398.)0 3888 y Ff(UNFILLDRAW)p Fm(:)g(199)p -546 3901 125 4 v -1 w(,)33 b(201)p 727 3901 V -2 w(,)h(824,)d(862,)h -(1397.)0 3989 y Fi(un\014l)t(ldr)l(aw)14 b Fm(:)83 b(823)p -475 4002 V -2 w(,)31 b(824)p 653 4002 V -1 w(,)g(825)p -832 4002 V -1 w(,)g(826)p 1011 4002 V -2 w(,)h(1398)p -1190 4002 167 4 v -2 w(,)f(1399)p 1410 4002 V -2 w(.)0 -4090 y Fi(unit)p 150 4090 26 4 v 30 w(ve)l(ctor)13 b -Fm(:)83 b(350,)24 b(393,)g(395,)g(506,)g(507)p 1201 4103 -125 4 v -2 w(,)i(508)p 1374 4103 V -2 w(,)g(509)p 1547 -4103 V -2 w(,)f(510)p 1719 4103 V -1 w(,)166 4190 y(605,)32 -b(624,)g(900,)f(949,)h(953,)g(954,)g(985,)f(995,)h(1070,)166 -4290 y(1127,)25 b(1164,)g(1178,)g(1183,)g(1193,)g(1228,)g(1229,)g -(1268.)0 4391 y Fi(unsuppr)l(ess)p 397 4391 26 4 v 30 -w(lab)l(els)12 b Fm(:)83 b(230)p 730 4404 125 4 v -1 -w(.)0 4493 y Fi(unsuppr)l(ess)p 397 4493 26 4 v 30 w(output)11 -b Fm(:)83 b(200)p 769 4506 125 4 v -1 w(,)32 b(440)p -949 4506 V -2 w(,)h(441)p 1129 4506 V -2 w(,)f(552,)f(854)p -1488 4506 V -2 w(,)h(855)p 1667 4506 V -1 w(,)166 4592 -y(1377)p 166 4605 167 4 v -2 w(,)44 b(1378)p 399 4605 -V -1 w(.)0 4694 y Fi(up)9 b Fm(:)84 b(556)p 203 4707 -125 4 v -2 w(,)29 b(557,)f(559,)f(561,)h(570,)g(572,)f(574,)h(579,)g -(923.)0 4795 y Fi(use)p 122 4795 26 4 v 30 w(name)11 -b Fm(:)83 b(56)p 459 4808 84 4 v -1 w(,)39 b(59,)g(61,)f(64,)g(66,)h -(69,)f(71,)g(74,)h(75,)166 4895 y(83,)k(101,)f(409.)0 -4996 y Fi(user)p 157 4996 26 4 v 30 w(c)l(o)l(or)l(dinates)12 -b Fm(:)83 b(264)p 701 5009 125 4 v -1 w(,)36 b(278,)f(300,)f(303,)h -(313,)f(318,)166 5096 y(431,)44 b(635.)0 5197 y Fi(user)p -157 5197 26 4 v 30 w(tr)l(ansform)11 b Fm(:)83 b(189)p -651 5210 125 4 v -1 w(,)37 b(190)p 836 5210 V -2 w(,)g(283.)0 -5299 y Ff(USER_VALUE)p Fm(:)83 b(264.)0 5400 y Ff(USER_VALUES)p -Fm(:)g(264)p 590 5413 V -2 w(,)36 b(265)p 773 5413 V --2 w(,)g(463,)d(464.)2033 263 y Ff(USER_VALUES_X_Y)n -Fm(:)83 b(264)p 2797 276 V -1 w(,)35 b(265)p 2980 276 -V -1 w(,)g(463.)2033 364 y Fe(v)s Fm(:)83 b(315)p 2182 -377 V -1 w(,)32 b(432)p 2362 377 V -2 w(,)g(443)p 2541 -377 V -1 w(,)g(549)p 2721 377 V -2 w(,)g(840)p 2900 377 -V -1 w(,)g(867)p 3080 377 V -2 w(,)g(996)p 3259 377 V --1 w(,)g(1365)p 3439 377 167 4 v -2 w(,)g(1367)p 3660 -377 V -2 w(,)2199 464 y(1383)p 2199 477 V -2 w(,)40 b(1384)p -2428 477 V -2 w(,)f(1386)p 2656 477 V -2 w(,)h(1387)p -2885 477 V -2 w(,)f(1433)p 3113 477 V -2 w(,)h(1451)p -3342 477 V -2 w(,)f(1465)p 3570 477 V -2 w(,)2199 564 -y(1478)p 2199 577 V -2 w(,)44 b(1505)p 2432 577 V -1 -w(.)2033 665 y Fi(v)p 2076 665 26 4 v 31 w(c)l(o)l(or)l(d)13 -b Fm(:)83 b(960)p 2408 678 125 4 v -1 w(.)2033 767 y -Fi(v)p 2076 767 26 4 v 31 w(inter)l(c)l(ept)12 b Fm(:)83 -b(960)p 2531 780 125 4 v -2 w(,)38 b(1136)p 2716 780 -167 4 v -2 w(,)g(1137)p 2943 780 V -2 w(.)2033 868 y -Fi(v)p 2076 868 26 4 v 31 w(length)11 b Fm(:)83 b(1228)p -2433 881 167 4 v -2 w(,)41 b(1229)p 2663 881 V -2 w(.)2033 -969 y Fi(v)p 2076 969 26 4 v 31 w(x)14 b Fm(:)83 b(606)p -2261 982 125 4 v -2 w(.)2033 1071 y Fi(v)p 2076 1071 -26 4 v 31 w(y)12 b Fm(:)83 b(606)p 2260 1084 125 4 v --2 w(.)2033 1172 y Fi(v)p 2076 1172 26 4 v 31 w(z)14 -b Fm(:)83 b(606)p 2256 1185 125 4 v -1 w(.)2033 1274 -y Fi(va)p 2118 1274 26 4 v 31 w(ar)l(g)12 b Fm(:)83 b(669,)37 -b(671,)g(674,)g(676.)2033 1375 y Fi(va)p 2118 1375 V -31 w(end)13 b Fm(:)83 b(669,)37 b(671,)g(674,)g(676.)2033 -1477 y Fi(va)p 2118 1477 V 31 w(start)12 b Fm(:)83 b(669,)36 -b(671,)g(674,)h(676.)2033 1578 y Fk(v)-5 b(alarra)m(y)8 -b Fm(:)83 b(15,)34 b(23,)f(200,)g(264,)g(277,)g(312,)g(313,)g(314,)2199 -1678 y(315,)h(399,)g(405,)g(432,)f(444,)h(550,)g(551,)g(654,)g(845,) -2199 1777 y(867,)k(1296,)f(1367,)g(1368.)2033 1879 y -Fk(v)-5 b(alarra)m(ys)7 b Fm(:)83 b(277.)2033 1980 y -Fk(v)m(ector)6 b Fm(:)83 b(115,)33 b(116,)g(200,)f(216,)h(249,)g(409,)g -(442,)f(443,)2199 2080 y(453,)24 b(457,)f(462,)h(543,)f(545,)h(546,)g -(548,)f(549,)h(553,)f(654,)2199 2179 y(657,)h(659,)f(685,)h(708,)f -(734,)h(739,)g(741,)f(743,)h(765,)f(766,)2199 2279 y(770,)h(771,)f -(791,)h(830,)f(839,)h(840,)g(843,)f(856,)h(859,)f(867,)2199 -2379 y(898,)34 b(900,)g(914,)g(988,)f(990,)h(995,)g(996,)g(997,)g(999,) -2199 2478 y(1123,)25 b(1127,)g(1259,)g(1286,)g(1287,)g(1289,)g(1290,)g -(1296,)2199 2578 y(1302,)g(1308,)g(1342,)g(1344,)g(1347,)g(1349,)g -(1364,)g(1365,)2199 2678 y(1367,)g(1379,)g(1380,)g(1383,)g(1384,)g -(1386,)g(1387,)g(1389,)2199 2777 y(1390,)g(1393,)g(1396,)g(1399,)g -(1418,)g(1424,)g(1432,)g(1433,)2199 2877 y(1448,)g(1449,)g(1451,)g -(1461,)g(1462,)g(1463,)g(1465,)g(1474,)2199 2976 y(1475,)j(1476,)h -(1478,)f(1488,)g(1489,)h(1490,)f(1505.)2033 3078 y Fk(v)m(ectors)6 -b Fm(:)83 b(1379.)2033 3179 y Fi(verb)l(ose)11 b Fm(:)83 -b(17,)25 b(357)p 2541 3192 125 4 v -1 w(,)g(872)p 2714 -3192 V -1 w(,)g(873)p 2887 3192 V -1 w(,)g(874)p 3060 -3192 V -1 w(,)g(875)p 3233 3192 V -1 w(,)g(904)p 3406 -3192 V -1 w(,)g(906,)f(991,)2199 3279 y(1175)p 2199 3292 -167 4 v -2 w(,)30 b(1176)p 2418 3292 V -2 w(,)h(1186,)d(1188,)g(1189)p -3076 3292 V -2 w(,)j(1267)p 3296 3292 V -2 w(,)f(1268)p -3515 3292 V -2 w(.)2033 3380 y Ff(VERBOSE_GLOBAL)o Fm(:)83 -b(17)p 2754 3393 84 4 v -1 w(,)29 b(18)p 2889 3393 V --1 w(,)h(872,)d(873,)h(874,)g(875,)g(904,)2199 3480 y(1175,)34 -b(1176,)g(1267,)f(1268,)h(1508.)2033 3581 y Ff(VERBOSE_INDEX)o -Fm(:)83 b(1508)p 2710 3594 167 4 v -2 w(.)2033 3683 y -Ff(VERSION_INDEX)o Fm(:)g(1508)p 2710 3696 V -2 w(.)2033 -3784 y Ff(VERSION_3DLDF)o Fm(:)g(19)p 2710 3797 84 4 -v -1 w(,)33 b(20)p 2849 3797 V -1 w(,)f(1508,)f(1512,)g(1513,)f(1518,) -2199 3884 y(1519.)2033 3985 y Fi(vertex)14 b Fm(:)83 -b(1034)p 2369 3998 167 4 v -2 w(.)2033 4087 y Fi(vertex)p -2254 4087 26 4 v 30 w(r)l(adius)12 b Fm(:)83 b(1431)p -2616 4100 167 4 v -2 w(,)28 b(1440,)f(1443,)f(1457,)h(1460,)f(1471,) -2199 4186 y(1474,)40 b(1485,)f(1488.)2033 4288 y Fi(vertic)l(al)14 -b Fm(:)83 b(400)p 2414 4301 125 4 v -2 w(.)2033 4389 -y Fi(vertic)l(es)12 b Fm(:)83 b(1405)p 2421 4402 167 -4 v -2 w(,)26 b(1416,)e(1418,)g(1420,)g(1440,)g(1443,)g(1457,)2199 -4489 y(1460,)34 b(1471,)g(1474,)f(1485,)h(1488.)2033 -4590 y Fi(view)p 2194 4590 26 4 v 32 w(c)l(o)l(or)l(dinates)12 -b Fm(:)83 b(264)p 2740 4603 125 4 v -2 w(,)36 b(278,)e(300,)h(303,)f -(313,)g(318,)2199 4690 y(431,)44 b(635.)2033 4791 y Ff(VIEW_VALUE)p -Fm(:)83 b(264.)2033 4893 y Ff(VIEW_VALUES)p Fm(:)g(264)p -2623 4906 V -2 w(,)33 b(265)p 2803 4906 V -1 w(,)g(463,)f(464,)f(830.) -2033 4994 y Ff(VIEW_VALUES_X_Y)n Fm(:)83 b(264)p 2797 -5007 V -1 w(,)33 b(265)p 2978 5007 V -2 w(,)h(463,)d(829.)2033 -5096 y Fi(violet)13 b Fm(:)83 b(108,)37 b(112)p 2530 -5109 V -1 w(,)h(113)p 2716 5109 V -2 w(,)h(1505.)2033 -5197 y Fi(violet)p 2230 5197 26 4 v 32 w(r)l(e)l(d)13 -b Fm(:)83 b(108,)35 b(112)p 2667 5210 125 4 v -2 w(,)i(113)p -2851 5210 V -2 w(,)g(1505.)2033 5299 y Fi(vx)14 b Fm(:)83 -b(644)p 2230 5312 V -1 w(.)2033 5400 y Fi(vy)12 b Fm(:)83 -b(644)p 2229 5413 V -1 w(.)p eop end -%%Page: 509 509 -TeXDict begin 509 508 bop 0 83 a Fn(x)p Fm(1525)139 b -Fl(3DLDFPR)n(G)2671 b(INDEX)141 b Fm(509)0 263 y Fi(vz)15 -b Fm(:)83 b(644)p 193 276 125 4 v -2 w(.)0 364 y Fi(v0)16 -b Fm(:)83 b(350)p 202 377 V -1 w(.)0 465 y Fi(v1)16 b -Fm(:)83 b(350)p 202 478 V -1 w(.)0 567 y Fi(v2)16 b Fm(:)83 -b(350)p 202 580 V -1 w(.)0 668 y Fe(w)s Fm(:)g(1419)p -168 681 167 4 v -2 w(,)41 b(1420)p 398 681 V -2 w(,)h(1433)p -629 681 V -2 w(.)0 769 y Fi(w)p 60 769 26 4 v 31 w(x)13 -b Fm(:)84 b(606)p 245 782 125 4 v -2 w(.)0 870 y Fi(w)p -60 870 26 4 v 31 w(y)12 b Fm(:)83 b(606)p 244 883 125 -4 v -2 w(.)0 972 y Fi(w)p 60 972 26 4 v 31 w(z)14 b Fm(:)83 -b(606)p 240 985 125 4 v -1 w(.)0 1073 y Fi(web)10 b Fm(:)83 -b(1477.)0 1174 y Fi(white)11 b Fm(:)83 b(108,)40 b(112)p -494 1187 V -1 w(,)h(113)p 683 1187 V -2 w(.)0 1275 y -Fi(width)12 b Fm(:)83 b(1413)p 310 1288 167 4 v -2 w(,)39 -b(1420,)f(1426.)0 1377 y Ff(WORDS_BIGENDIAN)n Fm(:)83 -b(1516.)0 1478 y Fi(world)p 200 1478 26 4 v 32 w(c)l(o)l(or)l(dinates) -12 b Fm(:)83 b(264)p 746 1491 125 4 v -1 w(,)33 b(265,)f(277,)g(278,)g -(283,)g(300,)166 1577 y(303,)24 b(305,)f(313,)h(318,)f(345,)h(346,)g -(349,)f(351,)h(379,)f(381,)166 1677 y(384,)h(386,)f(389,)h(399,)f(400,) -h(405,)g(431,)f(443,)h(463,)f(476,)166 1777 y(478,)h(480,)f(482,)h -(484,)f(486,)h(495,)g(498,)f(499,)h(500,)f(501,)166 1876 -y(502,)30 b(503,)g(508,)h(516,)f(517,)g(531,)g(556,)g(904.)0 -1977 y Ff(WORLD_VALUE)p Fm(:)83 b(264.)0 2079 y Ff(WORLD_VALUES)o -Fm(:)g(264)p 633 2092 V -1 w(,)30 b(265)p 811 2092 V --1 w(,)g(463,)f(464,)g(829,)g(830.)0 2180 y Ff(WORLD_VALUES_X_Y)n -Fm(:)83 b(264)p 808 2193 V -2 w(,)31 b(265)p 986 2193 -V -2 w(,)g(463,)d(464,)h(829.)0 2281 y Ff(WORLD_VALUES_Z)o -Fm(:)83 b(264)p 721 2294 V -2 w(,)34 b(265)p 902 2294 -V -2 w(,)g(463,)e(464.)0 2382 y Fi(write)p 186 2382 26 -4 v 31 w(fo)l(oters)12 b Fm(:)83 b(45)p 570 2395 84 4 -v -1 w(,)38 b(46)p 714 2395 V -1 w(,)h(1519.)0 2484 y -Fe(x)p Fm(:)84 b(150)p 154 2497 125 4 v -2 w(,)27 b(151)p -328 2497 V -2 w(,)f(155)p 501 2497 V -1 w(,)g(156)p 675 -2497 V -1 w(,)g(158)p 849 2497 V -1 w(,)g(159)p 1023 -2497 V -1 w(,)g(160)p 1197 2497 V -1 w(,)g(161)p 1371 -2497 V -1 w(,)g(235)p 1545 2497 V -1 w(,)g(236)p 1719 -2497 V -1 w(,)166 2583 y(238)p 166 2596 V -1 w(,)f(239)p -339 2596 V -2 w(,)g(241)p 511 2596 V -1 w(,)g(242)p 684 -2596 V -2 w(,)g(282)p 856 2596 V -1 w(,)g(283)p 1029 -2596 V -1 w(,)g(284)p 1202 2596 V -2 w(,)g(285)p 1374 -2596 V -1 w(,)g(295)p 1547 2596 V -2 w(,)g(296)p 1719 -2596 V -1 w(,)166 2683 y(360)p 166 2696 V -1 w(,)g(361)p -339 2696 V -2 w(,)g(362)p 511 2696 V -1 w(,)g(363)p 684 -2696 V -2 w(,)g(368)p 856 2696 V -1 w(,)g(369)p 1029 -2696 V -1 w(,)g(375)p 1202 2696 V -2 w(,)g(376)p 1374 -2696 V -1 w(,)g(644)p 1547 2696 V -2 w(,)g(713)p 1719 -2696 V -1 w(,)166 2782 y(714)p 166 2795 V -1 w(,)31 b(723)p -345 2795 V -2 w(,)g(724)p 523 2795 V -1 w(,)g(728)p 702 -2795 V -1 w(,)g(729)p 881 2795 V -2 w(,)g(733)p 1059 -2795 V -1 w(,)g(734)p 1238 2795 V -1 w(,)g(1003)p 1417 -2795 167 4 v -2 w(,)g(1004)p 1637 2795 V -2 w(,)166 2882 -y(1010)p 166 2895 V -2 w(,)c(1011)p 382 2895 V -2 w(,)g(1015)p -598 2895 V -2 w(,)g(1016)p 814 2895 V -2 w(,)g(1020)p -1030 2895 V -2 w(,)g(1021)p 1246 2895 V -2 w(,)g(1127)p -1462 2895 V -2 w(,)g(1183)p 1678 2895 V -2 w(,)166 2982 -y(1196)p 166 2995 V -2 w(,)g(1197)p 382 2995 V -2 w(,)g(1198)p -598 2995 V -2 w(,)g(1199)p 814 2995 V -2 w(,)g(1208)p -1030 2995 V -2 w(,)g(1209)p 1246 2995 V -2 w(,)g(1419)p -1462 2995 V -2 w(,)g(1420)p 1678 2995 V -2 w(.)0 3083 -y Fi(x)p 44 3083 26 4 v 30 w(axis)11 b Fm(:)84 b(949)p -327 3096 125 4 v -2 w(.)0 3184 y Fi(x)p 44 3184 26 4 -v 30 w(axis)p 214 3184 V 31 w(pt)12 b Fm(:)83 b(957)p -428 3197 125 4 v -1 w(,)35 b(1127)p 611 3197 167 4 v --1 w(,)g(1228)p 836 3197 V -2 w(,)h(1229)p 1061 3197 -V -2 w(.)0 3285 y Fi(x)p 44 3285 26 4 v 30 w(i)13 b Fm(:)83 -b(535)p 213 3298 125 4 v -1 w(,)35 b(536,)f(537,)g(539,)g(540,)g(541.)0 -3387 y Ff(X_Y)s Fm(:)83 b(949)p 241 3400 V -1 w(,)41 -b(1182)p 430 3400 167 4 v -2 w(,)g(1184.)0 3488 y Ff(X_Z)s -Fm(:)83 b(949)p 241 3501 125 4 v -1 w(,)41 b(1182)p 430 -3501 167 4 v -2 w(,)g(1184.)0 3589 y Fi(xx)13 b Fm(:)83 -b(1203)p 197 3602 V -2 w(,)23 b(1204)p 409 3602 V -2 -w(,)f(1350)p 620 3602 V -2 w(,)h(1351)p 832 3602 V -2 -w(,)f(1355)p 1043 3602 V -2 w(,)h(1356)p 1255 3602 V --2 w(,)f(1359)p 1466 3602 V -2 w(,)h(1360)p 1678 3602 -V -2 w(.)0 3690 y Fi(xy)11 b Fm(:)83 b(152)p 196 3703 -125 4 v -1 w(,)30 b(153)p 374 3703 V -2 w(,)g(200)p 551 -3703 V -2 w(,)g(364)p 728 3703 V -2 w(,)g(365)p 905 3703 -V -1 w(,)f(725)p 1082 3703 V -1 w(,)g(726)p 1259 3703 -V -1 w(,)h(1012)p 1437 3703 167 4 v -2 w(,)f(1013)p 1655 -3703 V -2 w(,)166 3790 y(1200)p 166 3803 V -2 w(,)39 -b(1201)p 394 3803 V -2 w(,)f(1352)p 621 3803 V -2 w(,)h(1353)p -849 3803 V -2 w(.)0 3891 y Fi(xz)14 b Fm(:)83 b(152)p -193 3904 125 4 v -1 w(,)29 b(153)p 370 3904 V -1 w(,)h(200)p -548 3904 V -2 w(,)g(364)p 725 3904 V -1 w(,)f(365)p 902 -3904 V -1 w(,)h(725)p 1080 3904 V -2 w(,)g(726)p 1257 -3904 V -1 w(,)f(1012)p 1434 3904 167 4 v -2 w(,)h(1013)p -1653 3904 V -2 w(,)166 3991 y(1200)p 166 4004 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Fi(z)p 2072 2156 26 4 v 31 w(int)p 2203 2156 V -30 w(q)12 b Fm(:)83 b(538)p 2384 2169 125 4 v -2 w(,)41 -b(539,)e(540.)2033 2256 y Ff(Z_Y)s Fm(:)83 b(949)p 2274 -2269 V -1 w(,)41 b(1182)p 2463 2269 167 4 v -2 w(,)g(1184.)2033 -2355 y Fi(zx)14 b Fm(:)83 b(152)p 2226 2368 125 4 v -2 -w(,)30 b(153)p 2403 2368 V -1 w(,)f(200)p 2580 2368 V --1 w(,)h(364)p 2758 2368 V -2 w(,)g(365)p 2935 2368 V --1 w(,)g(725)p 3113 2368 V -2 w(,)g(726)p 3290 2368 V --2 w(,)g(1012)p 3467 2368 167 4 v -2 w(,)g(1013)p 3686 -2368 V -2 w(,)2199 2455 y(1200)p 2199 2468 V -2 w(,)39 -b(1201)p 2427 2468 V -2 w(,)f(1352)p 2654 2468 V -2 w(,)h(1353)p -2882 2468 V -2 w(.)2033 2554 y Fi(zy)12 b Fm(:)83 b(152)p -2225 2567 125 4 v -2 w(,)30 b(153)p 2402 2567 V -1 w(,)g(200)p -2580 2567 V -2 w(,)g(364)p 2757 2567 V -1 w(,)f(365)p -2934 2567 V -1 w(,)h(725)p 3112 2567 V -2 w(,)g(726)p -3289 2567 V -1 w(,)g(1012)p 3467 2567 167 4 v -2 w(,)g(1013)p -3686 2567 V -2 w(,)2199 2654 y(1200)p 2199 2667 V -2 -w(,)39 b(1201)p 2427 2667 V -2 w(,)f(1352)p 2654 2667 -V -2 w(,)h(1353)p 2882 2667 V -2 w(.)2033 2754 y Fi(zz)14 -b Fm(:)83 b(1203)p 2221 2767 V -2 w(,)24 b(1204)p 2434 -2767 V -2 w(,)g(1350)p 2647 2767 V -2 w(,)g(1351)p 2860 -2767 V -2 w(,)g(1355)p 3073 2767 V -2 w(,)f(1356)p 3285 -2767 V -2 w(,)h(1359)p 3498 2767 V -2 w(,)g(1360)p 3711 -2767 V -2 w(.)2033 2853 y Fi(z0)16 b Fm(:)83 b(928)p -2231 2866 125 4 v -1 w(.)2033 2953 y Fi(z1)16 b Fm(:)83 -b(928)p 2231 2966 V -1 w(.)p eop end -%%Page: 510 510 -TeXDict begin 510 509 bop 0 83 a Fm(510)140 b Fl(NAMES)23 -b(OF)g(THE)h(SECTIONS)2306 b(3DLDFPR)n(G)0 263 y Fn(h)14 -b Fm(Actions)28 b(in)g(main)35 b Fl(1505,)24 b(1506)15 -b Fn(i)83 b Fl(Used)24 b(in)f(section)i(1519.)0 364 y -Fn(h)14 b Fm(All)28 b Fk(Colors)39 b Fl(0)14 b Fn(i)84 -b Fl(Cited)24 b(in)f(sections)i(109)f(and)g(114.)0 466 -y Fn(h)14 b Fm(Chec)n(k)27 b(in)n(tersection)g(p)r(oin)n(t)h(lo)r -(cations)34 b Fl(1189)15 b Fn(i)83 b Fl(Used)24 b(in)f(section)i(1188.) -0 567 y Fn(h)14 b Fm(DEC)28 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Fl(Used)24 -b(in)f(section)i(56.)0 2083 y Fn(h)14 b Fm(Declare)27 -b Fk(Cub)s(oid)k Fm(functions)36 b Fl(1415,)24 b(1417,)g(1419,)h(1421,) -f(1423,)g(1425)15 b Fn(i)84 b Fl(Used)23 b(in)h(section)g(1413.)0 -2184 y Fn(h)14 b Fm(Declare)27 b Fk(Do)s(decahedron)33 -b Fm(functions)i Fl(1456,)24 b(1459,)h(1462,)f(1464)15 -b Fn(i)83 b Fl(Used)24 b(in)f(section)i(1453.)0 2285 -y Fn(h)14 b Fm(Declare)31 b Fk(Ellipse)k Fm(functions)h -Fl(1106,)28 b(1109,)h(1111,)g(1114,)g(1116,)g(1119,)g(1122,)g(1124,)g -(1126,)g(1128,)g(1129,)g(1131,)g(1133,)g(1136,)f(1139,)166 -2385 y(1141,)e(1144,)h(1146,)f(1148,)h(1150,)f(1154,)h(1156,)f(1159,)h -(1161,)f(1163,)g(1165,)h(1167,)f(1170,)h(1172,)f(1175,)h(1192,)f(1194,) -h(1196,)f(1198,)g(1200,)166 2485 y(1203,)e(1205,)h(1208,)f(1210,)g -(1213,)g(1215,)h(1218,)f(1220,)g(1222,)g(1224)15 b Fn(i)84 -b Fl(Used)24 b(in)f(section)h(1103.)0 2586 y Fn(h)14 -b Fm(Declare)33 b Fk(F)-8 b(o)s(cus)39 b Fm(functions)d -Fl(558,)30 b(560,)h(562,)g(565,)g(567,)g(569,)g(571,)f(573,)h(576,)g -(577,)g(578,)g(579,)g(580,)f(581,)h(583,)g(584)15 b Fn(i)83 -b Fl(Used)29 b(in)166 2686 y(section)c(556.)0 2787 y -Fn(h)14 b Fm(Declare)27 b Fk(Icosahedron)33 b Fm(functions)i -Fl(1470,)25 b(1473,)f(1475,)g(1477)15 b Fn(i)83 b Fl(Used)24 -b(in)g(section)g(1467.)0 2888 y Fn(h)14 b Fm(Declare)27 -b Fk(Lab)s(el)32 b Fm(functions)k Fl(210)14 b Fn(i)84 -b Fl(Used)24 b(in)f(section)i(208.)0 2990 y Fn(h)14 b -Fm(Declare)27 b Fk(Line)32 b Fm(constructors)i Fl(595,)24 -b(597)14 b Fn(i)84 b Fl(Used)23 b(in)h(section)g(593.)0 -3091 y Fn(h)14 b Fm(Declare)27 b Fk(Line)32 b Fm(functions)k -Fl(599,)24 b(602,)g(604,)g(608)14 b Fn(i)84 b Fl(Used)23 -b(in)h(section)g(593.)0 3192 y Fn(h)14 b Fm(Declare)27 -b Fk(P)m(ath)34 b Fm(functions)h Fl(656,)24 b(660,)g(663,)g(665,)g -(668,)g(670,)g(673,)g(675,)h(677,)f(680,)g(682,)g(684,)g(686,)g(688,)g -(690,)g(692,)g(695,)g(697,)g(700,)g(702,)166 3292 y(704,)h(706,)g(708,) -g(713,)f(719,)h(721,)g(723,)g(725,)g(728,)g(730,)f(733,)h(735,)g(738,)g -(740,)g(742,)g(747,)g(749,)f(751,)h(754,)g(756,)g(758,)g(762,)g(767,)f -(769,)h(775,)166 3392 y(777,)g(784,)g(786,)g(793,)f(795,)h(801,)g(803,) -g(806,)g(808,)g(812,)f(814,)h(820,)g(823,)g(825,)g(829,)g(831,)g(834,)f -(836,)h(839,)g(841,)g(845,)g(846,)g(848,)f(850,)h(852,)166 -3491 y(854,)j(856,)g(866,)h(868,)f(871,)g(872,)g(874,)g(876,)g(877,)h -(878,)f(879,)g(881,)g(888,)g(890,)g(892,)h(894,)f(896,)g(902,)g(908,)g -(911,)g(915,)h(917,)f(920,)g(932)15 b Fn(i)166 3591 y -Fl(Used)24 b(in)f(section)i(654.)0 3692 y Fn(h)14 b Fm(Declare)28 -b Fk(Picture)34 b Fm(functions)i Fl(218,)25 b(220,)g(222,)g(224,)h -(225,)f(227,)g(229,)g(230,)h(231,)f(235,)g(238,)g(240,)h(241,)f(243,)g -(244,)g(246,)g(248,)h(250,)f(253,)166 3792 y(254,)f(255,)g(256)15 -b Fn(i)83 b Fl(Used)24 b(in)f(section)i(216.)0 3893 y -Fn(h)14 b Fm(Declare)27 b Fk(Plane)32 b Fm(functions)k -Fl(619,)24 b(621,)g(623,)g(625,)g(628,)g(630,)g(633,)g(635,)g(640,)g -(642,)g(643,)g(645)14 b Fn(i)84 b Fl(Used)24 b(in)f(section)i(617.)0 -3995 y Fn(h)14 b Fm(Declare)27 b Fk(P)m(oin)m(t)33 b -Fm(constructors)g Fl(279,)24 b(282,)g(286)15 b Fn(i)83 -b Fl(Used)24 b(in)f(section)i(264.)0 4096 y Fn(h)14 b -Fm(Declare)25 b Fk(P)m(oin)m(t)32 b Fm(functions)j Fl(284,)23 -b(288,)g(291,)g(293,)g(295,)g(297,)g(299,)g(301,)g(302,)f(304,)h(307,)g -(308,)g(309,)g(312,)g(314,)g(317,)g(319,)g(322,)g(324,)g(327,)166 -4196 y(329,)i(332,)g(334,)g(337,)f(339,)h(341,)g(342,)g(344,)g(345,)g -(349,)f(352,)h(354,)g(356,)g(357,)g(360,)g(362,)g(364,)f(368,)h(370,)g -(375,)g(377,)g(392,)g(394,)f(398,)h(402,)166 4295 y(404,)g(406,)g(410,) -g(412,)f(414,)h(416,)g(419,)g(420,)g(422,)g(423,)f(425,)h(426,)g(428,)g -(429,)g(431,)g(433,)g(438,)f(440,)h(442,)g(444,)g(445,)g(447,)g(449,)f -(451,)h(457,)166 4395 y(461,)g(463,)g(466,)g(468,)f(474,)h(477,)g(479,) -g(481,)g(483,)g(485,)f(488,)h(492,)g(494,)g(496,)g(498,)g(500,)g(502,)f -(504,)h(507,)g(509,)g(511,)g(513,)g(516,)f(523,)h(525,)166 -4495 y(528,)f(529)15 b Fn(i)83 b Fl(Used)24 b(in)f(section)i(264.)0 -4596 y Fn(h)14 b Fm(Declare)27 b Fk(P)m(olygon)32 b Fm(functions)j -Fl(978,)24 b(980,)g(984,)f(993,)h(995,)g(1001,)g(1003,)g(1006,)g(1008,) -g(1010,)g(1012,)g(1015,)g(1017,)g(1020,)g(1022)15 b Fn(i)84 -b Fl(Used)166 4696 y(in)23 b(section)i(975.)0 4797 y -Fn(h)14 b Fm(Declare)27 b Fk(P)m(olyhedron)33 b Fm(functions)i -Fl(1432)15 b Fn(i)83 b Fl(Used)24 b(in)g(section)g(1431.)0 -4898 y Fn(h)14 b Fm(Declare)27 b Fk(Rectangle)32 b Fm(functions)k -Fl(1061,)24 b(1064,)g(1066,)h(1069,)f(1071,)h(1074,)f(1076,)g(1079,)h -(1082,)f(1085,)h(1087,)f(1090,)g(1092,)h(1095,)f(1096,)166 -4998 y(1097,)g(1098)15 b Fn(i)84 b Fl(Used)23 b(in)h(section)g(1059.)0 -5099 y Fn(h)14 b Fm(Declare)33 b Fk(Reg)p 519 5099 29 -5 v 39 w(Cl)p 654 5099 V 40 w(Plane)p 929 5099 V 40 w(Curv)m(e)40 -b Fm(functions)35 b Fl(943,)c(944,)f(945,)h(946,)f(947,)h(948,)f(950,)h -(953,)g(964,)f(967,)h(969,)f(970)15 b Fn(i)83 b Fl(Used)29 -b(in)166 5199 y(section)c(941.)0 5300 y Fn(h)14 b Fm(Declare)26 -b Fk(Reg)p 512 5300 V 39 w(P)m(olygon)31 b Fm(functions)k -Fl(1026,)23 b(1029,)h(1032,)f(1035,)g(1039,)g(1041,)h(1045,)f(1047,)g -(1049,)h(1050,)f(1051,)g(1053,)g(1054)15 b Fn(i)84 b -Fl(Used)166 5400 y(in)23 b(section)i(1025.)p eop end -%%Page: 511 511 -TeXDict begin 511 510 bop 0 83 a Fl(3DLDFPR)n(G)2306 -b(NAMES)23 b(OF)g(THE)h(SECTIONS)141 b Fm(511)0 263 y -Fn(h)14 b Fm(Declare)27 b Fk(Solid)p 557 263 29 5 v 39 -w(F)-8 b(aced)33 b Fm(functions)j Fl(1406)15 b Fn(i)83 -b Fl(Used)24 b(in)f(section)i(1405.)0 368 y Fn(h)14 b -Fm(Declare)28 b Fk(Solid)k Fm(functions)j Fl(1299,)25 -b(1301,)h(1303,)f(1305,)g(1307,)g(1309,)g(1311,)g(1313,)g(1316,)g -(1318,)g(1320,)g(1322,)g(1324,)h(1326,)f(1329,)g(1331,)166 -467 y(1333,)h(1335,)h(1337,)f(1339,)h(1341,)f(1343,)h(1346,)f(1348,)h -(1350,)f(1352,)g(1355,)h(1357,)f(1359,)h(1361,)f(1364,)h(1366,)f(1368,) -h(1369,)f(1371,)g(1373,)166 567 y(1375,)e(1377,)h(1379,)f(1383,)g -(1386,)g(1389,)h(1392,)f(1395,)g(1398)15 b Fn(i)83 b -Fl(Used)24 b(in)g(section)g(1296.)0 671 y Fn(h)14 b Fm(Declare)27 -b Fk(T)-8 b(etrahedron)33 b Fm(functions)j Fl(1439,)24 -b(1442,)h(1446,)f(1448,)g(1450)15 b Fn(i)83 b Fl(Used)24 -b(in)f(section)i(1436.)0 776 y Fn(h)14 b Fm(Declare)29 -b Fk(T)-8 b(ransform)35 b Fm(functions)h Fl(124,)26 b(126,)g(128,)g -(130,)g(132,)g(134,)g(136,)g(138,)g(140,)g(142,)g(145,)g(147,)g(150,)g -(152,)g(155,)g(157,)g(158,)g(160,)166 875 y(166,)e(167,)g(168,)g(171,)g -(173,)g(176,)g(178,)g(181,)g(187)15 b Fn(i)83 b Fl(Used)24 -b(in)f(section)i(122.)0 980 y Fn(h)14 b Fm(Declare)27 -b Fk(T)-8 b(runc)p 594 980 V 41 w(Octahedron)33 b Fm(functions)j -Fl(1484,)24 b(1487,)h(1489)15 b Fn(i)83 b Fl(Used)24 -b(in)f(section)i(1481.)0 1084 y Fn(h)14 b Fm(Declare)27 -b Fi(dr)l(aw)p 520 1084 26 4 v 31 w(axes)11 b Fm(\()k(\))35 -b Fl(924,)24 b(929)15 b Fn(i)83 b Fl(Used)24 b(in)f(section)i(937.)0 -1189 y Fn(h)14 b Fm(Declare)27 b Fk(namespace)33 b(Colors)39 -b Fl(109)14 b Fn(i)84 b Fl(Cited)24 b(in)f(section)i(109.)120 -b(Used)24 b(in)f(section)i(118.)0 1293 y Fn(h)14 b Fm(De\014ne)28 -b(I/O)f(functions)36 b Fl(43,)23 b(44,)h(46,)g(48,)f(50)15 -b Fn(i)83 b Fl(Used)24 b(in)f(section)i(52.)0 1398 y -Fn(h)14 b Fm(De\014ne)28 b(P)n(attern)f(functions)35 -b Fl(1284,)25 b(1287,)f(1290)15 b Fn(i)83 b Fl(Used)24 -b(in)f(section)i(1292.)0 1502 y Fn(h)14 b Fm(De\014ne)28 -b(classes)34 b Fl(208,)24 b(216)15 b Fn(i)83 b Fl(Used)24 -b(in)f(sections)i(260)f(and)g(261.)0 1607 y Fn(h)14 b -Fm(De\014ne)28 b(comparison)e(classes)34 b Fl(454,)24 -b(455,)g(456)15 b Fn(i)83 b Fl(Cited)24 b(in)f(section)i(552.)120 -b(Used)24 b(in)g(sections)g(589)g(and)h(590.)0 1711 y -Fn(h)14 b Fm(De\014ne)28 b(non-mem)n(b)r(er)f(functions)h(for)f -Fk(Color)39 b Fl(104)15 b Fn(i)83 b Fl(Used)24 b(in)g(section)g(118.)0 -1816 y Fn(h)14 b Fm(De\014ne)28 b(non-mem)n(b)r(er)f(functions)h(for)f -Fk(P)m(oin)m(ts)40 b Fl(437,)24 b(491)15 b Fn(i)83 b -Fl(Used)24 b(in)f(section)i(589.)0 1920 y Fn(h)14 b Fm(De\014ne)28 -b(parser)e(functions)36 b Fl(1498)15 b Fn(i)83 b Fl(Used)24 -b(in)f(section)i(1500.)0 2025 y Fn(h)14 b Fm(De\014ne)28 -b(utilit)n(y)g(functions)36 b Fl(22,)24 b(30,)f(32)15 -b Fn(i)83 b Fl(Cited)24 b(in)f(section)i(22.)120 b(Used)24 -b(in)f(section)i(35.)0 2129 y Fn(h)14 b Fm(De\014ne)28 -b Fk(Circle)k Fm(functions)k Fl(1240,)24 b(1243,)g(1245,)h(1248,)f -(1250,)g(1254,)g(1256,)h(1259,)f(1264,)g(1266,)g(1268)15 -b Fn(i)84 b Fl(Used)23 b(in)h(section)g(1278.)0 2234 -y Fn(h)14 b Fm(De\014ne)28 b Fk(Color)k Fm(functions)j -Fl(59,)24 b(61,)g(64,)f(66,)h(69,)f(71,)h(74,)g(76,)f(78,)h(81,)g(83,)f -(85,)h(87,)f(89,)h(91,)g(93,)f(101,)h(106,)g(108)15 b -Fn(i)83 b Fl(Used)24 b(in)f(section)i(118.)0 2338 y Fn(h)14 -b Fm(De\014ne)28 b Fk(Cub)s(oid)k Fm(functions)j Fl(1416,)24 -b(1418,)h(1420,)f(1422,)g(1424,)h(1426)15 b Fn(i)83 b -Fl(Used)24 b(in)f(section)i(1427.)0 2443 y Fn(h)14 b -Fm(De\014ne)28 b Fk(Do)s(decahedron)33 b Fm(functions)i -Fl(1457,)25 b(1460,)f(1461,)g(1463,)g(1465)15 b Fn(i)84 -b Fl(Used)24 b(in)f(section)i(1493.)0 2547 y Fn(h)14 -b Fm(De\014ne)28 b Fk(Ellipse)i Fm(functions)36 b Fl(1107,)24 -b(1110,)g(1112,)g(1115,)g(1117,)g(1120,)g(1123,)g(1127,)g(1130,)h -(1132,)f(1134,)g(1135,)g(1137,)g(1140,)g(1142,)g(1145,)166 -2647 y(1147,)i(1149,)h(1151,)f(1155,)h(1157,)f(1160,)h(1162,)f(1164,)h -(1166,)f(1168,)g(1171,)h(1173,)f(1176,)h(1177,)f(1178,)h(1179,)f(1180,) -h(1181,)f(1182,)g(1183,)166 2746 y(1184,)e(1185,)g(1187,)g(1188,)g -(1193,)g(1195,)g(1197,)g(1199,)g(1201,)g(1204,)g(1206,)g(1209,)g(1211,) -g(1214,)g(1216,)g(1219,)g(1221,)g(1223,)g(1225)15 b Fn(i)84 -b Fl(Used)166 2846 y(in)23 b(section)i(1232.)0 2951 y -Fn(h)14 b Fm(De\014ne)28 b Fk(F)-8 b(o)s(cus)32 b Fm(functions)k -Fl(561,)24 b(563,)g(566,)g(568,)g(570,)g(572,)g(574,)g(582,)g(585)14 -b Fn(i)84 b Fl(Used)24 b(in)f(section)h(589.)0 3055 y -Fn(h)14 b Fm(De\014ne)28 b Fk(Icosahedron)33 b Fm(functions)j -Fl(1471,)24 b(1474,)g(1476,)g(1478)15 b Fn(i)84 b Fl(Used)23 -b(in)h(section)g(1493.)0 3160 y Fn(h)14 b Fm(De\014ne)28 -b Fk(Lab)s(el)33 b Fm(functions)i Fl(470,)24 b(471,)g(472)15 -b Fn(i)83 b Fl(Used)24 b(in)f(section)i(589.)0 3264 y -Fn(h)14 b Fm(De\014ne)28 b Fk(Line)k Fm(constructors)i -Fl(596,)24 b(598)15 b Fn(i)83 b Fl(Used)24 b(in)f(section)i(613.)0 -3369 y Fn(h)14 b Fm(De\014ne)28 b Fk(Line)k Fm(functions)k -Fl(600,)24 b(605,)g(606,)g(607,)g(609,)g(934)15 b Fn(i)83 -b Fl(Used)24 b(in)f(sections)h(613)h(and)f(936.)0 3473 -y Fn(h)14 b Fm(De\014ne)29 b Fk(P)m(ath)35 b Fm(functions)h -Fl(657,)25 b(661,)g(664,)g(666,)h(669,)f(671,)g(674,)g(676,)h(678,)f -(681,)g(683,)g(685,)g(687,)h(689,)f(693,)g(696,)g(698,)h(701,)f(703,)g -(705,)166 3573 y(707,)g(709,)g(714,)g(720,)f(722,)h(724,)g(726,)g(729,) -g(731,)g(734,)f(736,)h(739,)g(741,)g(743,)g(748,)g(750,)g(752,)f(755,)h -(757,)g(759,)g(763,)g(764,)g(765,)f(766,)h(768,)166 3672 -y(770,)g(771,)g(776,)g(778,)f(785,)h(787,)g(794,)g(796,)g(802,)g(804,)f -(807,)h(809,)g(813,)g(815,)g(821,)g(824,)g(826,)f(830,)h(832,)g(835,)g -(837,)g(840,)g(842,)f(843,)h(844,)166 3772 y(847,)g(849,)g(851,)g(853,) -f(855,)h(857,)g(858,)g(859,)g(860,)g(861,)f(862,)h(863,)g(867,)g(869,)g -(873,)g(875,)g(880,)f(882,)h(883,)g(884,)g(885,)g(886,)g(889,)f(891,)h -(893,)166 3872 y(897,)f(898,)g(899,)g(900,)g(903,)g(909,)g(912,)g(913,) -g(914,)g(916,)g(918,)g(921,)g(933)15 b Fn(i)83 b Fl(Used)24 -b(in)f(section)i(936.)0 3976 y Fn(h)14 b Fm(De\014ne)31 -b Fk(Picture)k Fm(functions)g Fl(219,)27 b(226,)f(228,)h(232,)f(236,)h -(239,)f(242,)h(245,)f(247,)g(249,)h(251,)f(373,)h(396,)f(543,)h(544,)f -(545,)h(546,)f(548,)h(549,)166 4076 y(550,)d(551,)g(552,)g(553,)g(554) -15 b Fn(i)83 b Fl(Used)24 b(in)f(sections)i(260)f(and)g(589.)0 -4180 y Fn(h)14 b Fm(De\014ne)28 b Fk(Plane)33 b Fm(functions)i -Fl(620,)24 b(622,)g(624,)g(626,)g(629,)g(631,)g(634,)g(636,)g(641,)g -(644,)g(646,)g(922)15 b Fn(i)83 b Fl(Used)24 b(in)f(sections)i(650)f -(and)g(936.)0 4285 y Fn(h)14 b Fm(De\014ne)28 b Fk(P)m(oin)m(t)33 -b Fm(constructors)h Fl(280,)24 b(283,)g(287)14 b Fn(i)84 -b Fl(Used)23 b(in)h(section)g(589.)0 4389 y Fn(h)14 b -Fm(De\014ne)29 b Fk(P)m(oin)m(t)k Fm(functions)j Fl(285,)24 -b(289,)h(292,)f(294,)h(296,)f(298,)h(300,)f(303,)h(305,)f(313,)h(315,)f -(318,)h(320,)f(323,)h(325,)f(328,)h(330,)f(333,)h(335,)f(338,)166 -4489 y(340,)h(343,)g(346,)g(347,)f(350,)h(351,)g(353,)g(355,)g(361,)g -(363,)f(365,)h(369,)g(371,)g(376,)g(378,)g(393,)g(399,)f(400,)h(401,)g -(403,)g(405,)g(407,)g(411,)f(413,)h(415,)166 4588 y(417,)g(432,)g(434,) -g(439,)f(441,)h(443,)g(446,)g(448,)g(450,)g(452,)f(458,)h(462,)g(464,)g -(467,)g(469,)g(475,)g(478,)f(480,)h(482,)g(484,)g(486,)g(489,)g(493,)f -(495,)h(497,)166 4688 y(499,)g(501,)g(503,)g(505,)f(508,)h(510,)g(512,) -g(517,)g(518,)g(519,)f(520,)h(521,)g(522,)g(524,)g(526,)g(530,)g(531,)f -(532,)h(533,)g(534,)g(535,)g(536,)g(537,)f(538,)h(539,)166 -4788 y(540,)g(541,)f(601,)h(603,)f(637,)h(717,)g(780,)f(781,)h(789,)g -(790,)f(798,)h(799,)f(817,)h(818,)g(901,)f(904,)h(905,)f(906)15 -b Fn(i)83 b Fl(Used)25 b(in)f(sections)g(589,)h(613,)g(650,)166 -4887 y(and)f(936.)0 4992 y Fn(h)14 b Fm(De\014ne)31 b -Fk(P)m(olygon)k Fm(functions)h Fl(979,)27 b(981,)g(985,)g(986,)g(987,)g -(988,)g(989,)g(990,)g(991,)f(992,)h(994,)g(996,)g(997,)g(998,)g(999,)g -(1002,)h(1004,)f(1007,)166 5091 y(1009,)d(1011,)h(1013,)f(1016,)g -(1018,)g(1021,)h(1023)15 b Fn(i)83 b Fl(Used)24 b(in)f(section)i(1055.) -0 5196 y Fn(h)14 b Fm(De\014ne)28 b Fk(P)m(olyhedron)33 -b Fm(functions)i Fl(1433)15 b Fn(i)84 b Fl(Used)24 b(in)f(section)h -(1493.)0 5300 y Fn(h)14 b Fm(De\014ne)30 b Fk(Rectangle)j -Fm(functions)j Fl(1062,)25 b(1065,)h(1067,)g(1070,)g(1072,)f(1075,)h -(1077,)g(1080,)g(1083,)g(1086,)f(1088,)h(1091,)g(1093,)g(1228,)g(1229,) -166 5400 y(1230,)e(1231)15 b Fn(i)84 b Fl(Used)23 b(in)h(sections)g -(1099)h(and)f(1232.)p eop end -%%Page: 512 512 -TeXDict begin 512 511 bop 0 83 a Fm(512)140 b Fl(NAMES)23 -b(OF)g(THE)h(SECTIONS)2306 b(3DLDFPR)n(G)0 263 y Fn(h)14 -b Fm(De\014ne)29 b Fk(Reg)p 472 263 29 5 v 39 w(Cl)p -607 263 V 39 w(Plane)p 881 263 V 40 w(Curv)m(e)34 b Fm(functions)i -Fl(949,)24 b(951,)g(954,)g(955,)h(956,)f(957,)g(958,)h(959,)f(960,)g -(961,)g(962,)h(963,)f(965,)g(968)15 b Fn(i)83 b Fl(Used)166 -363 y(in)23 b(section)i(971.)0 464 y Fn(h)14 b Fm(De\014ne)31 -b Fk(Reg)p 474 464 V 39 w(P)m(olygon)k Fm(functions)g -Fl(1027,)27 b(1030,)g(1033,)g(1034,)g(1036,)g(1037,)g(1040,)g(1042,)g -(1270,)g(1272,)f(1273,)h(1274,)g(1276,)g(1277)15 b Fn(i)166 -563 y Fl(Used)24 b(in)f(sections)i(1055)f(and)h(1278.)0 -664 y Fn(h)14 b Fm(De\014ne)28 b Fk(Shap)s(e)33 b Fm(class)h -Fl(199,)24 b(200)15 b Fn(i)83 b Fl(Used)24 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-(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) -f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h -(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)58 b(54)165 -b(20)0 363 y(Include)28 b(\014les)66 b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h -(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) -h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h -(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) -h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)58 -b(55)165 b(20)0 462 y Fk(Color)27 b Fm(class)g(de\014nition)36 -b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) -h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h +b(90)165 b(28)0 2013 y Fl(Color)95 b(\()p Fk(colors.web)p +Fl(\))32 b Fm(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) +h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h 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Fm(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f (.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f -(.)h(.)f(.)h(.)f(.)58 b(120)165 b(36)0 4603 y(Include)28 +(.)h(.)f(.)h(.)f(.)58 b(164)165 b(46)0 1415 y(Include)28 b(\014les)66 b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) -h(.)f(.)h(.)f(.)h(.)f(.)58 b(121)165 b(36)0 4703 y Fk(T)-8 -b(ransform)28 b Fm(class)f(de\014nition)44 b(.)18 b(.)h(.)f(.)h(.)f(.)h +h(.)f(.)h(.)f(.)h(.)f(.)58 b(165)165 b(46)0 1515 y Fl(T)-8 +b(ransform)27 b Fm(class)g(de\014nition)44 b(.)18 b(.)h(.)f(.)h(.)f(.)h (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.) f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) -58 b(122)165 b(36)0 4802 y(Constructors)29 b(.)19 b(.)f(.)h(.)f(.)h(.)f +58 b(166)165 b(46)0 1614 y(Constructors)29 b(.)19 b(.)f(.)h(.)f(.)h(.)f (.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f (.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 -b(123)165 b(36)166 4902 y(Default)28 b(constructor)38 +b(167)165 b(46)166 1714 y(Default)28 b(constructor)38 b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) -h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 b(124)165 -b(36)166 5001 y(Constructor)26 b(with)i(one)g Fk(real)f +h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 b(168)165 +b(46)166 1813 y(Constructor)26 b(with)i(one)g Fl(real)f Fm(argumen)n(t)38 b(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f (.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 -b(126)165 b(37)166 5101 y(Constructor)26 b(with)i(16)f -Fk(real)h Fm(argumen)n(ts)46 b(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g +b(170)165 b(47)166 1913 y(Constructor)26 b(with)i(16)f +Fl(real)h Fm(argumen)n(ts)46 b(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f -(.)h(.)f(.)58 b(128)165 b(37)0 5201 y(Assignmen)n(t)36 +(.)h(.)f(.)58 b(172)165 b(47)0 2013 y(Assignmen)n(t)36 b(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h (.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h -(.)f(.)h(.)f(.)58 b(130)165 b(38)0 5300 y(Reset)28 b(to)f(iden)n(tit)n +(.)f(.)h(.)f(.)58 b(174)165 b(48)0 2112 y(Reset)28 b(to)f(iden)n(tit)n (y)h(matrix)34 b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.) f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 -b(132)165 b(38)0 5400 y(Setting)28 b(v)-5 b(alues)34 +b(176)165 b(48)0 2212 y(Setting)28 b(v)-5 b(alues)34 b(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f (.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h -(.)f(.)58 b(134)165 b(39)p eop end -%%Page: 517 517 -TeXDict begin 517 516 bop 0 83 a Fl(3DLDFPR)n(G)2515 -b(T)-6 b(ABLE)24 b(OF)f(CONTENTS)141 b Fm(iii)0 263 y(Clean)41 -b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) -h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f -(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) -h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f -(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 b(136)165 b(39)0 -363 y(Epsilon)62 b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f +(.)f(.)58 b(178)165 b(49)0 2312 y(Clean)41 b(.)19 b(.)f(.)h(.)f(.)h(.)f (.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) -f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f +f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f (.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) -f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 b(138)165 -b(40)0 462 y(T)-7 b(est)28 b(for)f(iden)n(tit)n(y)g(matrix)54 -b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) -h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h +f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h +(.)f(.)58 b(180)165 b(49)0 2411 y(Epsilon)62 b(.)19 b(.)f(.)h(.)f(.)h +(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) +h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) -h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 b(139)165 -b(40)166 562 y(Non-const)27 b(v)n(ersion)55 b(.)18 b(.)h(.)f(.)h(.)f(.) h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f -(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) +(.)58 b(182)165 b(50)0 2511 y(T)-7 b(est)28 b(for)f(iden)n(tit)n(y)g +(matrix)54 b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f +(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f -(.)h(.)f(.)h(.)f(.)58 b(140)165 b(40)166 662 y Fk(const)28 -b Fm(v)n(ersion)38 b(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h -(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.) -f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h -(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) -h(.)f(.)58 b(142)165 b(40)0 761 y(Querying)38 b(.)18 +(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 +b(184)165 b(50)166 2610 y(Non-const)27 b(v)n(ersion)55 +b(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) +f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f +(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) +f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 b(185)165 +b(50)166 2710 y Fl(const)28 b Fm(v)n(ersion)38 b(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h -(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) -h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h -(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) -h(.)f(.)h(.)f(.)58 b(144)165 b(41)166 861 y(Get)28 b(elemen)n(t)57 -b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) -h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h -(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) -h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 -b(145)165 b(41)0 960 y(Sho)n(w)57 b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f +(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.) +f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h +(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 +b(187)165 b(51)0 2810 y(Querying)38 b(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f(.) +h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f 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b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h +b(302)165 b(77)0 4970 y(Putting)28 b Fl(Picture)g Fm(and)f +Fl(Lab)s(el)h Fm(together)50 b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h (.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h -(.)f(.)h(.)f(.)h(.)f(.)58 b(259)165 b(67)0 3109 y Fk(P)m(oin)m(t)96 -b(\()p Fj(points.web)p Fk(\))38 b Fm(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f(.)h +(.)f(.)h(.)f(.)h(.)f(.)58 b(304)165 b(77)0 5101 y Fl(P)m(oin)m(t)96 +b(\()p Fk(points.web)p Fl(\))38 b Fm(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f(.)h (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.) f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) -h(.)f(.)58 b(262)165 b(69)0 3208 y(Include)28 b(\014les)66 +h(.)f(.)58 b(307)165 b(79)0 5201 y(Include)28 b(\014les)66 b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f -(.)h(.)f(.)58 b(263)165 b(69)0 3308 y Fk(P)m(oin)m(t)28 +(.)h(.)f(.)58 b(308)165 b(79)0 5300 y Fl(P)m(oin)m(t)28 b Fm(class)f(de\014nition)42 b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.) f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) -h(.)f(.)58 b(264)165 b(69)0 3407 y(T)n(yp)r(e)27 b(de\014nitions)h(and) +h(.)f(.)58 b(309)165 b(79)0 5400 y(T)n(yp)r(e)27 b(de\014nitions)h(and) g(utilit)n(y)g(structures)64 b(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f (.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f -(.)h(.)f(.)h(.)f(.)58 b(266)165 b(71)166 3507 y Fk(p)s(oin)m(t)p -390 3507 29 4 v 34 w(pair)28 b Fm(and)f Fk(b)s(o)s(ol)p -960 3507 V 33 w(p)s(oin)m(t)p 1211 3507 V 34 w(pair)49 +(.)h(.)f(.)h(.)f(.)58 b(311)165 b(81)p eop +%%Page: 525 5 +525 4 bop 0 83 a Fj(3DLDF-1.1.5.1)2469 b(T)-6 b(ABLE)24 +b(OF)f(CONTENTS)141 b Fm(v)166 263 y Fl(p)s(oin)m(t)p +390 263 29 4 v 34 w(pair)28 b Fm(and)f Fl(b)s(o)s(ol)p +960 263 V 33 w(p)s(oin)m(t)p 1211 263 V 34 w(pair)49 b Fm(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f (.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 -b(267)165 b(71)166 3607 y Fk(b)s(o)s(ol)p 354 3607 V -33 w(p)s(oin)m(t)65 b Fm(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h -(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) 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y(Default)28 -b(Constructor)f(for)g Fk(b)s(o)s(ol)p 1406 3806 V 32 -w(p)s(oin)m(t)p 1656 3806 V 34 w(quadruple)57 b Fm(.)18 -b(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h -(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 -b(271)165 b(74)166 3906 y Fk(b)s(o)s(ol)p 354 3906 V -33 w(real)p 543 3906 V 34 w(p)s(oin)m(t)41 b Fm(.)19 -b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f -(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) -h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f -(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 b(272)165 -b(74)332 4005 y(Default)28 b(Constructor)f(for)g Fk(b)s(o)s(ol)p -1406 4005 V 32 w(real)p 1594 4005 V 35 w(p)s(oin)m(t)g +(.)f(.)h(.)f(.)h(.)f(.)58 b(315)165 b(83)332 562 y(Default)28 +b(Constructor)f(for)g Fl(b)s(o)s(ol)p 1406 562 V 32 w(p)s(oin)m(t)p +1656 562 V 34 w(quadruple)57 b Fm(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) 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4902 y(Setting)28 b(function)40 b(.)18 b(.)h(.)f(.)h(.)f(.)h +h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 b(331)165 +b(88)332 1658 y(Setting)28 b(function)40 b(.)18 b(.)h(.)f(.)h(.)f(.)h (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.) f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) -h(.)f(.)58 b(288)165 b(78)0 5001 y(Pseudo-constructor)25 +h(.)f(.)58 b(333)165 b(88)0 1757 y(Pseudo-constructor)25 b(for)i(dynamic)g(allo)r(cation)35 b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)g (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f -(.)h(.)f(.)58 b(290)165 b(79)166 5101 y(Optional)27 b(p)r(oin)n(ter)g -(argumen)n(t)61 b(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) -f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f +(.)h(.)f(.)58 b(335)165 b(89)166 1857 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f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f (.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) -f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 b(317)165 b(84)498 1658 -y Fk(const)28 b Fm(v)n(ersion)38 b(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f(.)h +f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 b(360)165 b(94)498 3551 +y Fl(const)28 b Fm(v)n(ersion)38 b(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f(.)h (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.) f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 -b(319)165 b(84)332 1757 y(Get)28 b(x)43 b(.)19 b(.)f(.)h(.)f(.)h(.)f(.) +b(362)165 b(94)332 3650 y(Get)28 b(x)43 b(.)19 b(.)f(.)h(.)f(.)h(.)f(.) h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f (.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f 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y(Three)27 -b Fk(real)h Fm(argumen)n(ts)g(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) +h(.)f(.)h(.)f(.)h(.)f(.)58 b(411)123 b(104)664 1359 y(Three)27 +b Fl(real)h Fm(argumen)n(ts)g(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f (.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) -f(.)h(.)f(.)58 b(368)165 b(95)664 4746 y Fk(P)m(oin)m(t)28 +f(.)h(.)f(.)58 b(412)123 b(105)664 1459 y Fl(P)m(oin)m(t)28 b Fm(argumen)n(t)67 b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f (.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) -f(.)h(.)f(.)h(.)f(.)58 b(370)165 b(95)498 4846 y Fk(T)-8 -b(ransform)28 b Fm(v)n(ersion)33 b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f +f(.)h(.)f(.)h(.)f(.)58 b(414)123 b(105)498 1558 y Fl(T)-8 +b(ransform)27 b Fm(v)n(ersion)33 b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f 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y(Three)27 b Fk(real)h Fm(argumen)n(ts)g(.)19 +b(418)123 b(105)498 1857 y(Three)27 b Fl(real)h Fm(argumen)n(ts)g(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 -b(375)165 b(96)498 5244 y Fk(P)m(oin)m(t)28 b Fm(argumen)n(t)67 +b(419)123 b(106)498 1957 y Fl(P)m(oin)m(t)28 b Fm(argumen)n(t)67 b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) -h(.)f(.)h(.)f(.)58 b(377)165 b(96)332 5344 y(Alignmen)n(t)28 +h(.)f(.)h(.)f(.)58 b(421)123 b(106)332 2056 y(Alignmen)n(t)28 b(with)g(an)f(axis)61 b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h (.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h -(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 b(379)165 b(96)p eop -end -%%Page: 520 520 -TeXDict begin 520 519 bop 0 83 a Fm(vi)141 b Fl(T)-6 -b(ABLE)24 b(OF)f(CONTENTS)2517 b(3DLDFPR)n(G)498 263 -y Fm(Normalize)27 b(p)r(oin)n(t)39 b(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f(.)h -(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.) -f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h -(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 -b(389)123 b(100)332 363 y(Rotation)27 b(around)g(an)g(arbitrary)f(axis) -47 b(.)18 b(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f +(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 b(423)123 b(106)498 +2156 y(Normalize)27 b(p)r(oin)n(t)39 b(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f +(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.) +h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f 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b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.) f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) -h(.)f(.)58 b(395)123 b(102)498 861 y Fk(Picture)28 b +h(.)f(.)58 b(439)123 b(112)498 2754 y Fl(Picture)28 b Fm(v)n(ersion)k(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f (.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f -(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 b(396)123 b(103)166 -960 y(Pro)5 b(jection)36 b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f +(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 b(440)123 b(113)166 +2853 y(Pro)5 b(jection)36 b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f (.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f 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f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 -b(476)123 b(129)166 1259 y(V)-7 b(ector)27 b(addition)60 +b(520)123 b(139)166 3152 y(V)-7 b(ector)27 b(addition)60 b(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f (.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 -b(477)123 b(129)166 1359 y(V)-7 b(ector)27 b(addition)h(with)g +b(521)123 b(139)166 3252 y(V)-7 b(ector)27 b(addition)h(with)g (assignmen)n(t)64 b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f -(.)h(.)f(.)58 b(479)123 b(129)166 1459 y(V)-7 b(ector)27 +(.)h(.)f(.)58 b(523)123 b(139)166 3351 y(V)-7 b(ector)27 b(subtraction)k(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f 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y Fl(P)m(oin)m(t)28 +b Fm(argumen)n(ts)34 b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h +(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.) +f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h +(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) +58 b(667)123 b(184)0 1088 y(Assignmen)n(t)36 b(.)18 b(.)h(.)f(.)h(.)f +(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) +f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f +(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) +f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 +b(669)123 b(185)0 1188 y(Comparing)26 b Fl(Planes)45 +b Fm(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f +(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.) h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f -(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 -b(627)123 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y(Coplanar)26 b(case)31 +58 b(1039)122 b(295)332 2981 y(Coplanar)26 b(case)31 b(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f (.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) -f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)58 b(997)123 -b(288)332 960 y(P)n(arallel)26 b(case)45 b(.)19 b(.)f(.)h(.)f(.)h(.)f +f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)58 b(1041)122 +b(296)332 3081 y(P)n(arallel)26 b(case)45 b(.)19 b(.)f(.)h(.)f(.)h(.)f (.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f (.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) -f(.)h(.)f(.)h(.)f(.)58 b(998)123 b(288)332 1060 y(Non-parallel,)26 +f(.)h(.)f(.)h(.)58 b(1042)122 b(296)332 3180 y(Non-parallel,)26 b(non-coplanar)g(case)60 b(.)18 b(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f 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b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h -(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.) -h(.)f(.)h(.)f(.)h(.)58 b(1482)122 b(458)0 4783 y(Constructors)26 +(.)h(.)f(.)h(.)58 b(1509)122 b(456)0 1085 y(Constructors)26 b(and)h(setting)h(functions)69 b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h (.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.) f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h -(.)f(.)h(.)f(.)h(.)f(.)h(.)58 b(1483)122 b(458)166 4882 +(.)f(.)h(.)f(.)h(.)f(.)h(.)58 b(1510)122 b(456)166 1185 y(Default)28 b(constructor)38 b(.)19 b(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.) f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)58 -b(1484)122 b(458)166 4982 y(Cen)n(ter,)27 b(diameter)g(of)h(hexagon,)e -(and)i(angles)f(.)19 b(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)f 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Fd(:b)22 b Fm(=)h +Fh(true)10 b Fm(;)332 4846 y Fl(if)42 b Fm(\()p Fe(DEBUG)s +Fm(\))f Fh(c)l(out)36 b Fi(\034)25 b Fe("\\nExiting)p +Fk( )p Fe(Circ)o(le:)o(:i)-7 b(ntersection_point)o(s\()o(c)h(onst)p +Fk( )p Fe(Circle&\).")22 b Fi(\034)j Fh(end)t(l)38 b +Fi(\034)581 4945 y Fh(end)t(l)f Fi(\034)23 b Fh(\015ush)10 +b Fm(;)332 5045 y Fl(return)33 b Fh(bp)l(q)12 b Fm(;)249 +5145 y Fi(g)249 5244 y Fl(else)31 b(if)41 b Fm(\()p Fh(dist)36 +b Fd(<)23 b Fm(\()p Fh(r)l(adius)30 b Fm(+)18 b Fd(c:)p +Fh(r)l(adius)12 b Fm(\)\))42 b Fi(f)332 5344 y Fl(if)f +Fm(\()p Fh(dist)36 b Fd(>)23 b Fh(max)14 b Fm(\()p Fh(r)l(adius)e +Fd(;)i(c:)p Fh(r)l(adius)d Fm(\))19 b Fi(\000)f Fh(min)11 +b Fm(\()p Fh(r)l(adius)h Fd(;)i(c:)p Fh(r)l(adius)d Fm(\)\))42 +b Fi(f)p eop +%%Page: 380 400 +380 399 bop 0 83 a Fm(380)140 b Fl(CIR)m(CLE)23 b Fj(AR)n(GUMENT)2019 +b(3DLDF-1.1.5.1)141 b Fi(x)p Fm(1305)415 263 y Fl(if)41 +b Fm(\()p Fh(verb)l(ose)30 b Fi(_)19 b Fe(DEBUG)s Fm(\))41 +b Fh(c)l(out)35 b Fi(\034)23 b Fe("t)p Fk( )p Fe(and)p +Fk( )p Fe(c)p Fk( )p Fe(have)p Fk( )p Fe(2)p Fk( )o Fe(int)o(e)-6 +b(rsections.\\n")o Fm(;)415 388 y Fl(real)33 b Fd(a)23 +b Fm(=)f Fh(r)l(adius)12 b Fm(;)415 487 y Fl(real)33 +b Fh(bb)f Fm(=)23 b Fd(c:)p Fh(r)l(adius)30 b Fi(\003)18 +b Fd(c:)p Fh(r)l(adius)12 b Fm(;)415 587 y Fl(real)33 +b Fh(b)l(eta)g Fm(=)23 b(2)18 b Fi(\003)g Fh(atan)11 +b Fm(\()p Fh(sqrt)h Fm(\(\()p Fh(bb)29 b Fi(\000)18 b +Fm(\(\()p Fh(dist)31 b Fi(\000)18 b Fd(a)p Fm(\))h Fi(\003)f +Fm(\()p Fh(dist)31 b Fi(\000)18 b Fd(a)p Fm(\)\)\))p +Fd(=)p Fm(\(\(\()p Fh(dist)32 b Fm(+)18 b Fd(a)p Fm(\))h +Fi(\003)f Fm(\()p Fh(dist)31 b Fm(+)18 b Fd(a)p Fm(\)\))h +Fi(\000)f Fh(bb)10 b Fm(\)\)\);)415 711 y Fh(b)l(eta)34 +b Fi(\003)p Fm(=)22 b(180)o Fd(=)p Fe(PI)s Fm(;)415 811 +y Fl(if)41 b Fm(\()p Fh(verb)l(ose)30 b Fi(_)19 b Fe(DEBUG)s +Fm(\))41 b Fh(c)l(out)35 b Fi(\034)23 b Fe("beta)p Fk( )p +Fe(==)p Fk( )p Fe(")g Fi(\034)g Fh(b)l(eta)34 b Fi(\034)23 +b Fh(end)t(l)37 b Fi(\034)23 b Fh(\015ush)10 b Fm(;)415 +936 y Fl(P)m(oin)m(t)33 b Fd(P)12 b Fm(\()p Fd(c:)p Fh(c)l(enter)31 +b Fi(\000)18 b Fh(c)l(enter)13 b Fm(\);)415 1060 y Fd(P)f(:)p +Fh(unit)p 653 1060 26 4 v 30 w(ve)l(ctor)h Fm(\()p Fh(true)d +Fm(\);)415 1160 y Fd(P)35 b Fi(\003)p Fm(=)22 b Fh(r)l(adius)12 +b Fm(;)415 1259 y Fd(P)g(:)p Fh(shift)h Fm(\()p Fh(c)l(enter)g +Fm(\);)415 1384 y Fl(P)m(oin)m(t)33 b Fh(normal)j Fm(=)23 +b Fh(get)p 1160 1384 V 31 w(normal)13 b Fm(\()h(\);)415 +1508 y Fh(normal)g Fd(:)p Fh(shift)f Fm(\()p Fh(c)l(enter)g +Fm(\);)415 1608 y Fl(if)41 b Fm(\()p Fe(DEBUG)s Fm(\))h +Fi(f)498 1708 y Fd(P)12 b(:)p Fh(dotlab)l(el)i Fm(\()p +Fe("P")t Fm(\);)498 1807 y Fd(P)e(:)p Fh(show)i Fm(\()p +Fe("P")t Fm(\);)498 1907 y Fh(normal)g Fd(:)p Fh(show)g +Fm(\()p Fe("normal")q Fm(\);)415 2006 y Fi(g)415 2106 +y Fh(bp)l(q)e Fd(:)p Fh(\014rst)g Fd(:b)22 b Fm(=)h Fh(true)10 +b Fm(;)415 2206 y Fh(bp)l(q)i Fd(:)p Fh(\014rst)g Fd(:)p +Fh(pt)35 b Fm(=)23 b Fd(P)11 b Fm(;)415 2305 y Fh(bp)l(q)h +Fd(:)p Fh(\014rst)g Fd(:)p Fh(pt)g 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Fj(INDEX)2600 b(3DLDF-1.1.5.1)141 +b Fi(x)p Fm(1563)166 263 y(1342)p 166 276 167 4 v -2 +w(,)27 b(1347,)e(1349,)g(1422,)g(1424,)g(1425,)g(1427,)g(1428,)166 +363 y(1430,)g(1433,)g(1436,)g(1439,)g(1458,)g(1460,)g(1462)p +1462 376 V -2 w(,)i(1463)p 1678 376 V -2 w(,)166 462 +y(1490,)e(1502,)g(1504,)g(1515,)g(1517,)g(1529,)g(1531,)g(1532.)0 +566 y Fh(cr)l(e)l(ate)p 216 566 26 4 v 31 w(new)p 387 +566 V 30 w(cir)l(cle)12 b Fm(:)83 b(1286,)35 b(1287.)0 +670 y Fh(cr)l(e)l(ate)p 216 670 V 31 w(new)p 387 670 +V 30 w(c)l(olor)14 b Fm(:)84 b(111.)0 774 y Fh(cr)l(e)l(ate)p +216 774 V 31 w(new)p 387 774 V 30 w(cub)l(oid)14 b Fm(:)83 +b(1462.)0 878 y Fh(cr)l(e)l(ate)p 216 878 V 31 w(new)p +387 878 V 30 w(el)t(lipse)13 b Fm(:)83 b(1154,)35 b(1155.)0 +982 y Fh(cr)l(e)l(ate)p 216 982 V 31 w(new)p 387 982 +V 30 w(p)l(ath)11 b Fm(:)84 b(724,)37 b(725.)0 1086 y +Fh(cr)l(e)l(ate)p 216 1086 V 31 w(new)p 387 1086 V 30 +w(p)l(oint)13 b Fm(:)83 b(335.)0 1190 y Fh(cr)l(e)l(ate)p +216 1190 V 31 w(new)p 387 1190 V 30 w(r)l(e)l(ctangle)11 +b Fm(:)83 b(1116,)34 b(1117.)0 1294 y Fh(cr)l(e)l(ate)p +216 1294 V 31 w(new)p 387 1294 V 30 w(r)l(e)l(g)p 520 +1294 V 31 w(p)l(olygon)12 b Fm(:)83 b(1083,)32 b(1084.)0 +1398 y Fh(cr)l(e)l(ate)p 216 1398 V 31 w(new)p 387 1398 +V 30 w(solid)15 b Fm(:)83 b(1341.)0 1502 y Fh(cr)l(oss)11 +b Fm(:)83 b(997,)34 b(998)p 479 1515 125 4 v -1 w(,)h(1000,)e(1029)p +886 1515 167 4 v -2 w(,)i(1031.)0 1606 y Fh(cr)l(oss)p +184 1606 26 4 v 31 w(pr)l(o)l(duct)12 b Fm(:)83 b(544)p +592 1619 125 4 v -1 w(,)29 b(545)p 769 1619 V -1 w(,)h(649,)e(688,)g +(944,)g(998,)g(1029,)166 1705 y(1112,)40 b(1122,)f(1123.)0 +1809 y Fh(ctr)13 b Fm(:)83 b(361)p 220 1822 V -1 w(,)44 +b(390)p 412 1822 V -1 w(.)0 1913 y Fl(Cub)s(oid)t Fm(:)83 +b(486,)39 b(1348,)g(1451,)f(1453)p 1063 1926 167 4 v +-2 w(,)j(1455,)e(1456)p 1523 1926 V -2 w(,)166 2013 y(1457,)f(1458)p +395 2026 V -2 w(,)h(1459,)f(1460)p 852 2026 V -2 w(,)h(1462,)f(1463,)f +(1464,)166 2113 y(1465)p 166 2126 V -2 w(,)42 b(1466,)d(1467.)0 +2216 y Fh(curr)p 158 2216 26 4 v 30 w(angle)11 b Fm(:)84 +b(1150)p 487 2229 167 4 v -2 w(.)0 2320 y Fh(curr)p 158 +2320 26 4 v 30 w(c)l(olor)15 b Fm(:)83 b(1323)p 478 2333 +167 4 v -2 w(.)0 2424 y Fh(curr)p 158 2424 26 4 v 30 +w(lo)l(c)l(ation)12 b Fm(:)83 b(1224)p 578 2437 167 4 +v -2 w(.)0 2528 y Fh(curr)p 158 2528 26 4 v 30 w(p)l(oint)13 +b Fm(:)83 b(1224)p 482 2541 167 4 v -2 w(,)40 b(1225.)0 +2632 y Fh(curr)p 158 2632 26 4 v 30 w(x)14 b Fm(:)83 +b(1150)p 342 2645 167 4 v -2 w(.)0 2736 y Fe(CURR_Y)r +Fm(:)g(309)p 372 2749 125 4 v -2 w(,)39 b(310)p 558 2749 +V -2 w(,)f(327,)f(329.)0 2840 y Fe(CURR_Z)r Fm(:)83 b(309)p +372 2853 V -2 w(,)39 b(310)p 558 2853 V -2 w(,)f(327,)f(329.)0 +2944 y Fh(curr)p 158 2944 26 4 v 30 w(z)15 b Fm(:)83 +b(1150)p 338 2957 167 4 v -2 w(.)0 3048 y Fh(curr)l(ent)p +267 3048 26 4 v 30 w(pictur)l(e)10 b Fm(:)83 b(302)p +655 3061 125 4 v -1 w(,)28 b(303)p 831 3061 V -1 w(,)g(454,)f(458,)g +(463,)g(466,)g(469,)166 3148 y(472,)d(505,)f(507,)h(510,)f(512,)h(514,) +g(818,)f(827,)h(836,)f(844,)166 3247 y(849,)32 b(855,)g(863,)f(866,)h +(872,)g(877,)g(968,)f(973,)h(1091,)166 3347 y(1095,)25 +b(1137,)g(1138,)g(1160,)g(1162,)g(1261,)g(1263,)g(1320,)166 +3447 y(1388,)g(1423,)g(1426,)g(1429,)g(1432,)g(1435,)g(1438,)g(1547.)0 +3551 y Fh(curve)p 199 3551 26 4 v 31 w(0)16 b Fm(:)83 +b(1001)p 389 3564 167 4 v -2 w(.)0 3654 y Fh(curve)p +199 3654 26 4 v 31 w(4)16 b Fm(:)83 b(1001)p 389 3667 +167 4 v -2 w(.)0 3758 y Fh(cyan)11 b Fm(:)83 b(152,)35 +b(156)p 468 3771 125 4 v -2 w(,)h(157)p 651 3771 V -2 +w(,)g(1502,)e(1546.)0 3862 y Fh(cycle)12 b Fm(:)83 b(711)p +293 3875 V -2 w(,)28 b(712,)f(713,)f(714,)h(715,)f(925)p +1170 3875 V -1 w(,)i(926)p 1346 3875 V -1 w(,)g(929,)e(930.)0 +3966 y Fh(cycle)p 180 3966 26 4 v 32 w(switch)11 b Fm(:)83 +b(698)p 546 3979 125 4 v -1 w(,)34 b(701,)f(705,)g(708,)g(710,)g(713,)g +(715,)166 4066 y(718,)24 b(720,)h(910,)f(921,)h(953,)f(1074,)g(1077,)g +(1104,)g(1107,)166 4166 y(1112,)34 b(1147,)g(1150,)f(1279,)h(1282.)0 +4270 y Fd(d)p Fm(:)83 b(24)p 149 4283 84 4 v -1 w(,)44 +b(25)p 299 4283 V -1 w(,)g(315)p 449 4283 125 4 v -2 +w(,)g(688)p 640 4283 V -2 w(,)g(948)p 831 4283 V -2 w(,)g(1123)p +1022 4283 167 4 v -2 w(,)g(1222)p 1255 4283 V -2 w(,)f(1352)p +1487 4283 V -2 w(,)166 4369 y(1459)p 166 4382 V -2 w(,)h(1460)p +399 4382 V -1 w(.)0 4473 y Fh(d)p 47 4473 26 4 v 31 w(x)14 +b Fm(:)83 b(948)p 232 4486 125 4 v -2 w(,)45 b(950.)0 +4577 y Fh(d)p 47 4577 26 4 v 31 w(y)12 b Fm(:)83 b(948)p +231 4590 125 4 v -1 w(,)42 b(949,)e(950.)0 4681 y Fh(d)p +47 4681 26 4 v 31 w(z)14 b Fm(:)83 b(948)p 227 4694 125 +4 v -1 w(,)42 b(949,)f(950.)0 4785 y Fh(dashe)l(d)14 +b Fm(:)84 b(698)p 357 4798 V -2 w(,)35 b(701,)e(702,)h(705,)f(708,)h +(710,)f(713,)h(715,)166 4885 y(718,)g(720,)g(748,)g(819,)f(845,)h(850,) +g(856,)g(864,)g(867,)166 4984 y(902,)39 b(904,)g(905,)g(906.)0 +5088 y Fh(datestamp)10 b Fm(:)83 b(82)p 480 5101 84 4 +v(,)42 b(83.)0 5192 y Fe(DBL_MAX)q Fm(:)84 b(19,)39 b(66,)g(1546.)0 +5296 y Fe(DBL_SIZE)q Fm(:)83 b(68)p 459 5309 V -1 w(.)0 +5400 y Fh(dd)14 b Fm(:)83 b(1222)p 204 5413 167 4 v -2 +w(.)2033 263 y Fh(ddashe)l(d)15 b Fm(:)83 b(463)p 2432 +276 125 4 v -1 w(,)32 b(464)p 2612 276 V -1 w(,)g(466)p +2792 276 V -1 w(,)h(467)p 2973 276 V -2 w(,)g(469)p 3153 +276 V -2 w(,)g(470)p 3333 276 V -2 w(,)g(472)p 3513 276 +V -1 w(,)f(473)p 3693 276 V -1 w(,)2199 363 y(818)p 2199 +376 V -1 w(,)j(819)p 2382 376 V -2 w(,)h(820)p 2565 376 +V -2 w(,)g(821)p 2748 376 V -2 w(,)f(823)p 2930 376 V +-1 w(,)g(824)p 3113 376 V -1 w(,)g(827)p 3296 376 V -1 +w(,)g(828)p 3479 376 V -2 w(,)h(829)p 3662 376 V -2 w(,)2199 +462 y(830)p 2199 475 V -1 w(,)f(832)p 2382 475 V -2 w(,)h(833)p +2565 475 V -2 w(,)g(836)p 2748 475 V -2 w(,)f(837)p 2930 +475 V -1 w(,)g(838)p 3113 475 V -1 w(,)g(839)p 3296 475 +V -1 w(,)g(841)p 3479 475 V -2 w(,)h(842)p 3662 475 V +-2 w(,)2199 562 y(849)p 2199 575 V -1 w(,)f(850)p 2382 +575 V -2 w(,)h(851)p 2565 575 V -2 w(,)g(852)p 2748 575 +V -2 w(,)f(855)p 2930 575 V -1 w(,)g(856)p 3113 575 V +-1 w(,)g(857)p 3296 575 V -1 w(,)g(858)p 3479 575 V -2 +w(,)h(860)p 3662 575 V -2 w(,)2199 662 y(861)p 2199 675 +V -1 w(,)f(866)p 2382 675 V -2 w(,)h(867)p 2565 675 V +-2 w(,)g(868)p 2748 675 V -2 w(,)f(869)p 2930 675 V -1 +w(,)g(967,)f(968)p 3296 675 V -1 w(,)h(969)p 3479 675 +V -2 w(,)h(972,)2199 761 y(973)p 2199 774 V -1 w(,)31 +b(974)p 2378 774 V -1 w(,)h(1091)p 2558 774 167 4 v -2 +w(,)g(1092)p 2779 774 V -2 w(,)f(1095)p 2999 774 V -1 +w(,)g(1096)p 3220 774 V -2 w(,)h(1137)p 3441 774 V -2 +w(,)g(1138)p 3662 774 V -2 w(,)2199 861 y(1261)p 2199 +874 V -2 w(,)27 b(1262)p 2415 874 V -2 w(,)g(1263)p 2631 +874 V -2 w(,)g(1264)p 2847 874 V -2 w(,)g(1269)p 3063 +874 V -2 w(,)g(1270)p 3279 874 V -2 w(,)g(1309)p 3495 +874 V -2 w(,)g(1310)p 3711 874 V -2 w(,)2199 960 y(1313)p +2199 973 V -2 w(,)g(1314)p 2415 973 V -2 w(,)g(1422,)e(1423)p +2847 973 V -2 w(,)i(1424)p 3063 973 V -2 w(,)g(1428,)e(1429)p +3495 973 V -2 w(,)i(1430)p 3711 973 V -2 w(,)2199 1060 +y(1431,)k(1432)p 2421 1073 V -2 w(,)i(1433)p 2643 1073 +V -2 w(,)g(1437,)e(1438)p 3087 1073 V -2 w(,)i(1439)p +3309 1073 V -2 w(.)2033 1165 y Fh(ddiameter)15 b Fm(:)83 +b(1076)p 2512 1178 V -2 w(,)34 b(1077)p 2735 1178 V -1 +w(,)g(1079)p 2959 1178 V -2 w(,)h(1080)p 3183 1178 V +-2 w(,)f(1081,)f(1281)p 3630 1178 V -2 w(,)2199 1264 +y(1282)p 2199 1277 V -2 w(,)42 b(1283)p 2430 1277 V -2 +w(,)f(1284)p 2660 1277 V -2 w(.)2033 1369 y Fh(ddr)l(aw)p +2250 1369 26 4 v 32 w(c)l(olor)14 b Fm(:)83 b(463)p 2571 +1382 125 4 v -1 w(,)35 b(464)p 2754 1382 V -2 w(,)g(466)p +2936 1382 V -1 w(,)g(467)p 3119 1382 V -2 w(,)g(472)p +3301 1382 V -1 w(,)f(473)p 3483 1382 V -1 w(,)h(818)p +3666 1382 V -2 w(,)2199 1469 y(819)p 2199 1482 V -1 w(,)g(820)p +2382 1482 V -2 w(,)h(821)p 2565 1482 V -2 w(,)g(823)p +2748 1482 V -2 w(,)f(824)p 2930 1482 V -1 w(,)g(827)p +3113 1482 V -1 w(,)g(828)p 3296 1482 V -1 w(,)g(829)p +3479 1482 V -2 w(,)h(830)p 3662 1482 V -2 w(,)2199 1568 +y(832)p 2199 1581 V -1 w(,)f(833)p 2382 1581 V -2 w(,)h(836)p +2565 1581 V -2 w(,)g(837)p 2748 1581 V -2 w(,)f(838)p +2930 1581 V -1 w(,)g(839)p 3113 1581 V -1 w(,)g(841)p +3296 1581 V -1 w(,)g(842)p 3479 1581 V -2 w(,)h(848,)2199 +1668 y(849)p 2199 1681 V -1 w(,)f(850)p 2382 1681 V -2 +w(,)h(851)p 2565 1681 V -2 w(,)g(852)p 2748 1681 V -2 +w(,)f(866)p 2930 1681 V -1 w(,)g(867)p 3113 1681 V -1 +w(,)g(868)p 3296 1681 V -1 w(,)g(869)p 3479 1681 V -2 +w(,)h(968)p 3662 1681 V -2 w(,)2199 1768 y(969)p 2199 +1781 V -1 w(,)g(972,)e(973)p 2566 1781 V -1 w(,)i(974)p +2750 1781 V -1 w(,)g(1091)p 2934 1781 167 4 v -2 w(,)g(1092)p +3159 1781 V -2 w(,)g(1095)p 3384 1781 V -2 w(,)h(1096)p +3610 1781 V -2 w(,)2199 1867 y(1137)p 2199 1880 V -2 +w(,)27 b(1138)p 2415 1880 V -2 w(,)g(1261)p 2631 1880 +V -2 w(,)g(1262)p 2847 1880 V -2 w(,)g(1263)p 3063 1880 +V -2 w(,)g(1264)p 3279 1880 V -2 w(,)g(1269)p 3495 1880 +V -2 w(,)g(1270)p 3711 1880 V -2 w(,)2199 1967 y(1309)p +2199 1980 V -2 w(,)39 b(1310)p 2427 1980 V -2 w(,)f(1313)p +2654 1980 V -2 w(,)h(1314)p 2882 1980 V -2 w(.)2033 2072 +y Fh(ddr)l(awdot)p 2362 2072 26 4 v 32 w(c)l(olor)14 +b Fm(:)84 b(453,)30 b(454)p 2863 2085 125 4 v -1 w(,)i(455)p +3043 2085 V -1 w(,)g(456)p 3223 2085 V -1 w(,)g(457)p +3403 2085 V -2 w(.)2033 2176 y Fe(DEBUG)r Fm(:)83 b(204)p +2361 2189 V -1 w(,)26 b(206)p 2535 2189 V -1 w(,)g(219)p +2709 2189 V -1 w(,)g(227)p 2883 2189 V -1 w(,)g(228,)f(229,)g(230,)g +(231,)f(233)p 3752 2189 V -1 w(,)2199 2276 y(390)p 2199 +2289 V -1 w(,)h(394)p 2372 2289 V -2 w(,)g(424)p 2544 +2289 V -1 w(,)g(425,)e(426,)h(429,)g(431,)f(432,)h(433,)f(439)p +3752 2289 V -1 w(,)2199 2376 y(443)p 2199 2389 V -1 w(,)i(444,)e(445,)h +(449)p 2717 2389 V -2 w(,)h(455)p 2889 2389 V -1 w(,)g(476)p +3062 2389 V -1 w(,)g(487)p 3235 2389 V -2 w(,)g(490)p +3407 2389 V -1 w(,)g(492)p 3580 2389 V -2 w(,)g(496)p +3752 2389 V -1 w(,)2199 2475 y(502)p 2199 2488 V -1 w(,)g(506)p +2372 2488 V -2 w(,)g(508)p 2544 2488 V -1 w(,)g(547)p +2717 2488 V -2 w(,)g(549)p 2889 2488 V -1 w(,)g(561)p +3062 2488 V -1 w(,)g(562,)e(563,)h(564,)f(565,)2199 2575 +y(566,)h(574)p 2372 2588 V -2 w(,)h(575,)f(576,)f(577,)h(578,)g(579,)f +(580,)h(581,)f(582,)2199 2674 y(584,)h(585,)f(590)p 2544 +2687 V -1 w(,)i(592)p 2717 2687 V -2 w(,)g(593,)f(594,)g(595,)f(596,)h +(597,)f(605)p 3752 2687 V -1 w(,)2199 2774 y(647)p 2199 +2787 V -1 w(,)35 b(649)p 2382 2787 V -2 w(,)h(650,)e(651,)f(688)p +2930 2787 V -1 w(,)i(705)p 3113 2787 V -1 w(,)g(708)p +3296 2787 V -1 w(,)g(713)p 3479 2787 V -2 w(,)h(718)p +3662 2787 V -2 w(,)2199 2874 y(722)p 2199 2887 V -1 w(,)f(727)p +2382 2887 V -2 w(,)h(729)p 2565 2887 V -2 w(,)g(769)p +2748 2887 V -2 w(,)f(819)p 2930 2887 V -1 w(,)g(845)p +3113 2887 V -1 w(,)g(850)p 3296 2887 V -1 w(,)g(867)p +3479 2887 V -2 w(,)h(873)p 3662 2887 V -2 w(,)2199 2973 +y(883)p 2199 2986 V -1 w(,)f(885)p 2382 2986 V -2 w(,)h(886,)e(887,)f +(890)p 2930 2986 V -1 w(,)i(892)p 3113 2986 V -1 w(,)g(900)p +3296 2986 V -1 w(,)g(902,)f(904,)2199 3073 y(905,)g(906,)g(907,)g(917)p +2748 3086 V -2 w(,)h(919)p 2930 3086 V -1 w(,)g(926)p +3113 3086 V -1 w(,)g(930,)f(941)p 3479 3086 V -2 w(,)i(944,)2199 +3173 y(948)p 2199 3186 V -1 w(,)31 b(950,)e(956)p 2556 +3186 V -1 w(,)i(958,)f(993)p 2914 3186 V -2 w(,)h(998)p +3092 3186 V -1 w(,)g(999,)f(1001,)f(1002,)2199 3272 y(1003,)c(1004,)g +(1005,)g(1007,)g(1029)p 3063 3285 167 4 v -2 w(,)i(1030,)e(1032,)g +(1034,)2199 3372 y(1035,)g(1036,)g(1040)p 2631 3385 V +-2 w(,)i(1041,)e(1043,)g(1077)p 3279 3385 V -2 w(,)i(1078,)e(1080)p +3711 3385 V -2 w(,)2199 3471 y(1081,)g(1165)p 2415 3484 +V -2 w(,)i(1206)p 2631 3484 V -2 w(,)g(1215)p 2847 3484 +V -2 w(,)g(1216,)e(1217,)g(1218,)g(1219,)2199 3571 y(1221,)g(1222,)g +(1223,)g(1224,)g(1225,)g(1227,)g(1232)p 3495 3584 V -2 +w(,)i(1296)p 3711 3584 V -2 w(,)2199 3671 y(1305)p 2199 +3684 V -2 w(,)g(1321)p 2415 3684 V -2 w(,)g(1324)p 2631 +3684 V -2 w(,)g(1327)p 2847 3684 V -2 w(,)g(1346)p 3063 +3684 V -2 w(,)g(1347,)e(1357)p 3495 3684 V -2 w(,)i(1384)p +3711 3684 V -2 w(,)2199 3770 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w(,)g(159,)d(454,)h(456,)g(463,)g +(464,)2199 4383 y(466,)i(467,)g(502,)g(818,)f(820,)h(827,)g(829,)g +(844,)g(846,)2199 4483 y(849,)c(851,)f(902,)h(904,)g(905,)f(906,)h +(968,)g(1091,)f(1092,)2199 4583 y(1095,)c(1096,)g(1137,)g(1138,)g +(1261,)g(1263,)g(1320,)g(1321,)2199 4682 y(1324,)37 b(1424,)f(1427,)h +(1492.)2033 4787 y Fh(default)p 2279 4787 26 4 v 31 w(c)l(olor)p +2484 4787 V 32 w(ve)l(ctor)14 b Fm(:)83 b(159)p 2846 +4800 125 4 v -2 w(,)33 b(160)p 3026 4800 V -1 w(,)f(1323,)f(1326,)g +(1423,)2199 4887 y(1426,)42 b(1429.)2033 4991 y Fh(default)p +2279 4991 26 4 v 31 w(fo)l(cus)12 b Fm(:)83 b(356,)32 +b(361,)f(441,)h(446,)g(447,)f(475,)h(487,)2199 5091 y(501,)39 +b(598,)g(630)p 2575 5104 125 4 v -1 w(,)i(631)p 2764 +5104 V -2 w(.)2033 5196 y Fe(DEFAULT_NUMBER_O)o(F_P)o(OI)o(NTS)m +Fm(:)84 b(1143)p 3190 5209 167 4 v -2 w(,)34 b(1144)p +3413 5209 V -2 w(,)g(1149,)2199 5295 y(1150,)j(1151,)f(1281,)h(1283.) +2033 5400 y Fh(de\014ne)p 2250 5400 26 4 v 31 w(c)l(olor)p +2455 5400 V 31 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+b(49)p 482 5214 84 4 v -1 w(,)i(400,)e(638,)g(659,)g(661)p +1153 5214 125 4 v -2 w(,)i(663,)e(664)p 1509 5214 V -2 +w(,)i(665,)166 5300 y(666)p 166 5313 V -1 w(,)k(667,)f(668)p +532 5313 V -2 w(,)i(669,)d(670,)h(672,)g(673,)g(674,)g(675,)166 +5400 y(677,)g(678,)g(679,)g(680,)f(681,)h(685,)g(687,)g(688,)g(690,) +2199 263 y(691,)g(692,)g(946,)g(947,)f(948,)h(966,)g(992,)g(993,)g +(997,)2199 363 y(998,)h(1029,)f(1040,)g(1215,)h(1305.)2033 +490 y Fl(Planes)t Fm(:)84 b(659,)38 b(688,)g(1214.)2033 +618 y Fl(P)m(oin)m(t)5 b Fm(:)83 b(2,)35 b(19,)f(49)p +2609 631 84 4 v -1 w(,)h(166)p 2750 631 125 4 v -1 w(,)g(194,)f(202,)f +(211,)h(213,)g(241,)2199 718 y(244,)24 b(245,)f(253)p +2544 731 V -1 w(,)i(255,)e(269,)h(285,)g(288,)f(307,)h(309)p +3580 731 V -2 w(,)h(310,)2199 817 y(312,)f(313,)f(317,)h(319,)f(320,)h +(323,)g(324,)f(325)p 3407 830 V -1 w(,)i(327,)e(328)p +3752 830 V -1 w(,)2199 917 y(329,)h(330,)f(331,)h(332)p +2717 930 V -2 w(,)h(333,)f(334,)g(335,)f(336,)h(337,)f(338)p +3752 930 V 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y(404,)h(405,)f(406,)h(407,)f(408,)h +(409,)g(412,)f(413,)h(419,)f(420,)2199 5400 y(423,)h(424,)f(433,)h +(436,)f(437,)h(438,)g(439,)f(440,)h(442,)f(443,)p eop +%%Page: 508 528 +508 527 bop 0 83 a Fm(508)140 b Fj(INDEX)2600 b(3DLDF-1.1.5.1)141 +b Fi(x)p Fm(1563)166 263 y(445,)24 b(446,)f(447,)h(449,)f(475,)h(476,)g +(486,)f(487,)h(488,)f(489,)166 363 y(490,)h(491,)f(492,)h(493,)f(494,)h +(509,)g(516,)f(529,)h(530,)f(532,)166 462 y(533,)h(534,)f(535,)h(538,)f +(539,)h(540,)g(541,)f(542,)h(543,)f(546,)166 562 y(547,)h(548,)f(549,)h +(552,)f(555,)h(556,)g(561,)f(566,)h(575,)f(576,)166 662 +y(577,)h(578,)f(579,)h(580,)f(582,)h(592,)g(594,)f(595,)h(598,)f(600,) +166 761 y(603,)h(604,)f(605,)h(606,)f(607,)h(609,)g(610,)f(611,)h(612,) +f(615,)166 861 y(616,)h(622,)f(625,)h(626,)f(628,)h(629,)g(650,)f(661,) +h(677,)f(678,)166 960 y(680,)h(685,)f(688,)h(698,)f(756,)h(757,)g(759,) +f(760,)h(762,)f(763,)166 1060 y(764,)h(765,)f(766,)h(767,)f(768,)h +(769,)g(771,)f(772,)h(776,)f(777,)166 1160 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1072 26 4 v 29 +w(str)13 b Fm(:)83 b(505)p 2411 1085 125 4 v -1 w(,)33 +b(506)p 2592 1085 V -1 w(,)g(510)p 2773 1085 V -1 w(,)g(511)p +2954 1085 V -1 w(,)g(617)p 3135 1085 V -1 w(,)g(618)p +3316 1085 V -1 w(.)2033 1174 y Fh(theta)11 b Fm(:)83 +b(1324)p 2328 1187 167 4 v -2 w(,)43 b(1327)p 2560 1187 +V -2 w(.)2033 1277 y Fh(theta)p 2216 1277 26 4 v 31 w(total)13 +b Fm(:)83 b(1327)p 2522 1290 167 4 v -2 w(.)2033 1380 +y Fh(thir)l(d)14 b Fm(:)83 b(16)p 2321 1393 84 4 v -1 +w(,)42 b(315)p 2469 1393 125 4 v -2 w(,)g(316,)f(1004,)e(1174,)h(1175,) +g(1223,)2199 1479 y(1225,)i(1227.)2033 1582 y Fh(this)12 +b Fm(:)83 b(119,)29 b(188,)h(194,)g(196,)g(198,)g(201,)f(204,)h(209,)g +(216,)2199 1681 y(218,)24 b(219,)f(222,)h(224,)f(233,)h(269,)g(284,)f +(329,)h(330,)f(332,)2199 1781 y(334,)h(358,)f(363,)h(386,)f(389,)h +(390,)g(393,)f(394,)h(395,)f(397,)2199 1881 y(400,)h(401,)f(432,)h +(436,)f(437,)h(439,)g(453,)f(455,)h(459,)f(462,)2199 +1980 y(475,)h(476,)f(486,)h(487,)f(506,)h(507,)g(522,)f(526,)h(533,)f +(537,)2199 2080 y(541,)h(543,)f(545,)h(547,)f(548,)h(551,)g(552,)f +(554,)h(556,)f(567,)2199 2180 y(568,)h(570,)f(588,)h(589,)f(601,)h +(607,)g(610,)f(612,)h(614,)f(645,)2199 2279 y(666,)h(670,)f(681,)h +(690,)f(701,)h(721,)g(722,)f(731,)h(757,)f(759,)2199 +2379 y(763,)h(767,)f(769,)h(772,)f(793,)h(794,)g(795,)f(797,)h(800,)f +(805,)2199 2478 y(807,)h(811,)f(813,)h(814,)f(819,)h(823,)g(832,)f +(841,)h(845,)f(850,)2199 2578 y(856,)h(860,)f(864,)h(867,)f(883,)h +(916,)g(918,)f(925,)h(930,)f(940)p 3752 2591 V -1 w(,)2199 +2678 y(945,)h(948,)f(956,)h(958,)f(959,)h(960,)g(964,)f(976,)h(992,)f +(993,)2199 2777 y(997,)28 b(1001,)g(1011,)g(1043,)f(1048,)h(1051,)g +(1055,)f(1057,)2199 2877 y(1060,)e(1071,)g(1081,)g(1109,)g(1114,)g +(1120,)g(1152,)g(1158,)2199 2977 y(1164,)g(1165,)g(1190,)g(1205,)g +(1215,)g(1217,)g(1218,)g(1231,)2199 3076 y(1235,)g(1237,)g(1238,)g +(1239,)g(1240,)g(1242,)g(1252,)g(1282,)2199 3176 y(1284,)g(1290,)g +(1291,)g(1292,)g(1293,)g(1295,)g(1346,)g(1347,)2199 3275 +y(1349,)g(1391,)g(1393,)g(1396,)g(1398,)g(1400,)g(1402,)g(1405,)2199 +3375 y(1424,)g(1427,)g(1430,)g(1433,)g(1436,)g(1439,)g(1467,)g(1488.) +2033 3478 y Fh(this)p 2167 3478 26 4 v 31 w(axis)p 2338 +3478 V 31 w(orientation)11 b Fm(:)84 b(1217)p 2881 3491 +167 4 v -2 w(,)35 b(1218.)2033 3580 y Fh(this)p 2167 +3580 26 4 v 31 w(option)p 2424 3580 V 32 w(optind)13 +b Fm(:)83 b(1549)p 2796 3593 167 4 v -1 w(.)2033 3683 +y Fh(this)p 2167 3683 26 4 v 31 w(plane)11 b Fm(:)84 +b(1215)p 2501 3696 167 4 v -2 w(,)35 b(1216,)e(1217,)g(1218,)g(1220,)h +(1227,)2199 3782 y(1305)p 2199 3795 V -2 w(.)2033 3885 +y Fh(time)11 b Fm(:)83 b(82.)2033 3988 y Fl(tm)s Fm(:)h(82.)2033 +4090 y Fh(tolower)14 b Fm(:)83 b(356,)27 b(361,)h(390,)f(424,)g(476,)g +(605,)g(910,)g(1172.)2033 4193 y Fh(top)p 2150 4193 26 +4 v 31 w(lft)12 b Fm(:)83 b(1107)p 2368 4206 167 4 v +-1 w(.)2033 4295 y Fh(top)p 2150 4295 26 4 v 31 w(rt)12 +b Fm(:)83 b(1107)p 2357 4308 167 4 v -2 w(.)2033 4398 +y Fh(tr)l(ac)l(e)10 b Fm(:)84 b(573)p 2323 4411 125 4 +v -2 w(,)39 b(574)p 2509 4411 V -1 w(,)g(964)p 2696 4411 +V -2 w(,)g(965)p 2882 4411 V -1 w(.)2033 4500 y Fh(tr)l(ac)l(e)p +2211 4500 26 4 v 30 w(x)p 2280 4500 V 31 w(z)p 2345 4500 +V 30 w(0)16 b Fm(:)83 b(1001)p 2534 4513 167 4 v -2 w(.)2033 +4603 y Fl(T)-8 b(ransform)t Fm(:)84 b(166)p 2575 4616 +125 4 v -2 w(,)35 b(168,)e(169)p 2939 4616 V -1 w(,)h(170,)g(171)p +3304 4616 V -2 w(,)h(172,)e(173)p 3668 4616 V -1 w(,)2199 +4703 y(174,)24 b(175,)f(177,)h(179,)f(181,)h(182,)g(183,)f(186,)h(188,) +f(191,)2199 4802 y(193,)h(194,)f(195,)h(196,)f(197,)h(198,)g(200,)f +(201,)h(202,)f(203,)2199 4902 y(204,)h(205,)f(206,)h(211,)f(212,)h +(213,)g(217,)f(218,)h(219,)f(221,)2199 5001 y(222,)h(223,)f(224,)h +(226,)f(227,)h(232,)g(233,)f(234,)h(235,)f(236,)2199 +5101 y(237,)h(245,)f(255,)h(261,)f(280,)h(281,)g(283,)f(284,)h(285,)f +(286,)2199 5201 y(287,)h(288,)f(289,)h(290,)f(291,)h(292,)g(309,)f +(384,)h(404,)f(405,)2199 5300 y(406,)h(407,)f(408,)h(409,)f(412,)h +(413,)g(414,)f(415,)h(416,)f(417,)2199 5400 y(419,)h(420,)f(421,)h +(422,)f(423,)h(424,)g(436,)f(437,)h(438,)f(439,)p eop +%%Page: 512 532 +512 531 bop 0 83 a Fm(512)140 b Fj(INDEX)2600 b(3DLDF-1.1.5.1)141 +b Fi(x)p Fm(1563)166 263 y(440,)24 b(441,)f(448,)h(516,)f(518,)h(519,)g +(597,)f(600,)h(603,)f(605,)166 363 y(616,)h(624,)f(625,)h(627,)f(628,)h +(753,)g(756,)f(757,)h(759,)f(760,)166 462 y(762,)h(763,)f(764,)h(765,)f +(766,)h(767,)g(768,)f(769,)h(771,)f(772,)166 562 y(773,)h(774,)f(775,)h +(781,)f(782,)h(790,)g(791,)f(792,)h(793,)f(794,)166 662 +y(795,)33 b(993,)f(997,)h(1001,)f(1005,)g(1044,)g(1045,)g(1046,)166 +761 y(1047,)25 b(1048,)g(1050,)g(1051,)g(1052,)g(1053,)g(1054,)g(1055,) +166 861 y(1056,)g(1057,)g(1059,)g(1060,)g(1061,)g(1062,)g(1068,)g +(1099,)166 960 y(1150,)g(1165,)g(1218,)g(1221,)g(1231,)g(1232,)g(1233,) +g(1234,)166 1060 y(1235,)g(1236,)g(1237,)g(1238,)g(1239,)g(1240,)g +(1242,)g(1243,)166 1160 y(1244,)g(1245,)g(1252,)g(1253,)g(1254,)g +(1255,)g(1267,)g(1268,)166 1259 y(1307,)g(1311,)g(1321,)g(1386,)g +(1387,)g(1388,)g(1390,)g(1391,)166 1359 y(1392,)g(1393,)g(1395,)g +(1396,)g(1397,)g(1398,)g(1399,)g(1400,)166 1459 y(1401,)31 +b(1402,)g(1492,)g(1500,)g(1502,)g(1529.)0 1565 y Fh(tr)l(ansform)11 +b Fm(:)83 b(261)p 469 1578 125 4 v -2 w(,)29 b(269,)f(281,)f(284,)h +(287,)f(290,)h(292,)f(294,)166 1665 y(296,)d(301,)f(309)p +511 1678 V -1 w(,)i(323,)e(341,)h(344,)g(345,)f(349,)h(384,)f(405,)166 +1764 y(407,)h(409,)f(413,)h(419,)f(420,)h(422,)g(437,)f(440,)h(441,)f +(443,)166 1864 y(448,)h(449,)f(451,)h(475,)f(476,)h(478,)g(518,)f(519,) +h(530,)f(538,)166 1964 y(587,)34 b(589,)g(590,)g(593,)f(597,)h(600)p +1080 1977 V -1 w(,)h(601,)f(605,)g(614,)166 2063 y(616,)e(618,)h(624,)f +(625,)g(626,)h(628,)f(641.)0 2170 y Fh(tr)l(ansforms)11 +b Fm(:)83 b(775.)0 2277 y Fl(T)-8 b(ransforms)t Fm(:)83 +b(166,)39 b(182.)0 2383 y Fh(triangle)p 279 2383 26 4 +v 31 w(diameter)15 b Fm(:)83 b(1484)p 742 2396 167 4 +v -2 w(,)32 b(1488)p 963 2396 V -2 w(,)g(1489)p 1184 +2396 V -2 w(,)g(1490)p 1405 2396 V -2 w(,)g(1491)p 1626 +2396 V -2 w(,)166 2483 y(1492)p 166 2496 V -2 w(,)h(1515)p +388 2496 V -2 w(,)g(1516)p 610 2496 V -2 w(,)g(1517)p +832 2496 V -2 w(,)g(1518)p 1054 2496 V -2 w(,)g(1519)p +1276 2496 V -2 w(.)0 2589 y Fh(triangle)p 279 2589 26 +4 v 31 w(r)l(adius)12 b Fm(:)83 b(1477)p 642 2602 167 +4 v -2 w(,)38 b(1481,)f(1484,)f(1508)p 1324 2602 V -2 +w(,)i(1512,)166 2689 y(1515.)0 2796 y Fh(triangles)12 +b Fm(:)83 b(1490)p 426 2809 V -2 w(,)41 b(1517)p 656 +2809 V -2 w(.)0 2902 y Fh(triangles)p 313 2902 26 4 v +31 w(size)11 b Fm(:)83 b(1516)p 587 2915 167 4 v -2 w(,)39 +b(1517)p 815 2915 V -2 w(.)0 3009 y Fh(true)10 b Fm(:)83 +b(20,)33 b(86,)g(87,)g(88,)g(89,)f(99,)h(100,)g(102,)f(103,)h(105,)166 +3109 y(121,)24 b(148,)f(156,)h(186,)f(188,)h(204,)g(206,)f(219,)h(227,) +f(233,)166 3208 y(245,)h(254,)f(261,)h(264,)f(275,)h(298,)g(299,)f +(325,)h(328,)f(330,)166 3308 y(332,)h(334,)f(335,)h(341,)f(342,)h(355,) +g(357,)f(360,)h(362,)f(365,)166 3407 y(367,)h(370,)f(372,)h(375,)f +(377,)h(380,)g(382,)f(390,)h(393,)f(394,)166 3507 y(395,)h(399,)f(400,) +h(401,)f(424,)h(437,)g(439,)f(443,)h(444,)f(445,)166 +3607 y(449,)h(455,)f(462,)h(471,)f(475,)h(476,)g(485,)f(487,)h(490,)f +(492,)166 3706 y(496,)h(502,)f(505,)h(506,)f(508,)h(511,)g(513,)f(516,) +h(547,)f(550,)166 3806 y(551,)h(554,)f(561,)h(564,)f(571,)h(573,)g +(574,)f(585,)h(588,)f(590,)166 3906 y(592,)h(593,)f(595,)h(596,)f(597,) +h(605,)g(618,)f(647,)h(649,)f(650,)166 4005 y(668,)h(681,)f(685,)h +(688,)f(699,)h(705,)g(708,)f(710,)h(713,)f(715,)166 4105 +y(718,)h(720,)f(722,)h(727,)f(729,)h(732,)g(741,)f(746,)h(769,)f(786,) +166 4204 y(812,)h(814,)f(819,)h(828,)f(830,)h(845,)g(850,)f(867,)h +(873,)f(878,)166 4304 y(883,)h(885,)f(887,)h(890,)f(892,)h(898,)g(899,) +f(900,)h(902,)f(904,)166 4404 y(906,)34 b(909,)g(916,)g(917,)f(918,)h +(919,)g(920,)g(926,)g(941,)166 4503 y(944,)g(948,)g(950,)g(952,)f(956,) +h(959,)g(960,)g(993,)g(997,)166 4603 y(998,)28 b(1005,)g(1011,)g(1013,) +f(1014,)h(1029,)g(1032,)f(1035,)166 4703 y(1039,)e(1040,)g(1074,)g +(1077,)g(1080,)g(1081,)g(1104,)g(1107,)166 4802 y(1112,)g(1147,)g +(1150,)g(1162,)g(1164,)g(1165,)g(1166,)g(1202,)166 4902 +y(1212,)g(1214,)g(1215,)g(1217,)g(1218,)g(1222,)g(1223,)g(1224,)166 +5001 y(1225,)g(1227,)g(1231,)g(1232,)g(1233,)g(1234,)g(1279,)g(1282,) +166 5101 y(1295,)g(1296,)g(1304,)g(1305,)g(1321,)g(1327,)g(1337,)g +(1339,)166 5201 y(1346,)g(1347,)g(1350,)g(1357,)g(1380,)g(1381,)g +(1384,)g(1407,)166 5300 y(1410,)g(1412,)g(1418,)g(1420,)g(1424,)g +(1427,)g(1430,)g(1433,)166 5400 y(1436,)g(1439,)g(1456,)g(1458,)g +(1460,)g(1481,)g(1484,)g(1491,)2199 263 y(1492,)g(1498,)g(1501,)g +(1504,)g(1505,)g(1512,)g(1515,)g(1517,)2199 363 y(1518,)31 +b(1519,)g(1526,)g(1529,)g(1531,)g(1549.)2033 464 y Fh(trunc)8 +b Fm(:)83 b(24)p 2340 477 84 4 v -1 w(,)38 b(25)p 2484 +477 V -1 w(,)f(141,)f(142,)g(143.)2033 565 y Fl(T)-8 +b(runc)p 2282 565 29 5 v 41 w(Octahedron)6 b Fm(:)83 +b(445,)38 b(1470,)h(1522)p 3335 578 167 4 v -2 w(,)h(1523,)2199 +664 y(1525,)34 b(1526)p 2424 677 V -2 w(,)i(1528,)d(1529)p +2873 677 V -2 w(,)j(1531.)2033 765 y Fh(tt)11 b Fm(:)83 +b(82)p 2206 778 84 4 v -1 w(.)2033 866 y Fh(t0)16 b Fm(:)83 +b(1001)p 2225 879 167 4 v -2 w(,)41 b(1005,)e(1221)p +2685 879 V -2 w(.)2033 967 y Fh(t1)16 b Fm(:)83 b(993)p +2225 980 125 4 v -2 w(,)45 b(1221)p 2417 980 167 4 v +-2 w(.)2033 1068 y Fh(t2)16 b Fm(:)83 b(993)p 2225 1081 +125 4 v -2 w(.)2033 1169 y Fh(t3)16 b Fm(:)83 b(993)p +2225 1182 V -2 w(.)2033 1270 y Fd(u)p Fm(:)g(37)p 2187 +1283 84 4 v -1 w(,)35 b(99)p 2328 1283 V -1 w(,)g(100)p +2469 1283 125 4 v -2 w(,)g(102)p 2651 1283 V -1 w(,)g(103)p +2834 1283 V -2 w(,)g(104)p 3016 1283 V -1 w(,)g(105)p +3199 1283 V -2 w(.)2033 1371 y Fh(u)p 2083 1371 26 4 +v 30 w(x)14 b Fm(:)83 b(650)p 2267 1384 125 4 v -2 w(.)2033 +1472 y Fh(u)p 2083 1472 26 4 v 30 w(y)12 b Fm(:)83 b(650)p +2266 1485 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Fj(1455,)24 +b(1457,)g(1459,)h(1464,)f(1466)15 b Fi(i)83 b Fj(Used)24 +b(in)f(section)i(1453.)0 3092 y Fi(h)14 b Fm(Declare)27 +b Fl(Do)s(decahedron)33 b Fm(functions)i Fj(1497,)24 +b(1500,)h(1503,)f(1505)15 b Fi(i)83 b Fj(Used)24 b(in)f(section)i +(1494.)0 3193 y Fi(h)14 b Fm(Declare)31 b Fl(Ellipse)k +Fm(functions)h Fj(1146,)28 b(1149,)h(1151,)g(1157,)g(1160,)g(1162,)g +(1164,)g(1166,)g(1167,)g(1169,)g(1171,)g(1174,)g(1177,)g(1179,)f(1182,) +166 3293 y(1184,)e(1186,)h(1188,)f(1192,)h(1194,)f(1197,)h(1199,)f +(1201,)h(1203,)f(1205,)g(1208,)h(1210,)f(1214,)h(1231,)f(1233,)h(1235,) +f(1237,)h(1239,)f(1242,)g(1244,)166 3392 y(1247,)e(1249,)h(1252,)f +(1254,)g(1257,)g(1259,)h(1261,)f(1263)15 b Fi(i)83 b +Fj(Used)24 b(in)f(section)i(1143.)0 3493 y Fi(h)14 b +Fm(Declare)33 b Fl(F)-8 b(o)s(cus)39 b Fm(functions)d +Fj(602,)30 b(604,)h(606,)g(609,)g(611,)g(613,)g(615,)f(617,)h(620,)g +(621,)g(622,)g(623,)g(624,)f(625,)h(627,)g(628)15 b Fi(i)83 +b Fj(Used)29 b(in)166 3593 y(section)c(600.)0 3694 y +Fi(h)14 b Fm(Declare)27 b Fl(Icosahedron)33 b Fm(functions)i +Fj(1511,)25 b(1514,)f(1516,)g(1518)15 b Fi(i)83 b Fj(Used)24 +b(in)g(section)g(1508.)0 3795 y Fi(h)14 b Fm(Declare)27 +b Fl(Lab)s(el)32 b Fm(functions)k Fj(255)14 b Fi(i)84 +b Fj(Used)24 b(in)f(section)i(253.)0 3897 y Fi(h)14 b +Fm(Declare)27 b Fl(Line)32 b Fm(constructors)i Fj(639,)24 +b(641)14 b Fi(i)84 b Fj(Used)23 b(in)h(section)g(637.)0 +3998 y Fi(h)14 b Fm(Declare)27 b Fl(Line)32 b Fm(functions)k +Fj(643,)24 b(646,)g(648,)g(652)14 b Fi(i)84 b Fj(Used)23 +b(in)h(section)g(637.)0 4099 y Fi(h)14 b Fm(Declare)27 +b Fl(P)m(ath)34 b Fm(functions)h Fj(700,)24 b(704,)g(707,)g(709,)g +(712,)g(714,)g(717,)g(719,)h(721,)f(726,)g(728,)g(730,)g(732,)g(735,)g +(738,)g(740,)g(743,)g(745,)g(747,)g(749,)166 4198 y(751,)h(756,)g(762,) +g(764,)f(766,)h(768,)g(771,)g(773,)g(776,)g(778,)f(781,)h(783,)g(785,)g +(790,)g(792,)g(794,)g(797,)f(799,)h(801,)g(805,)g(810,)g(812,)g(818,)f +(820,)h(827,)166 4298 y(829,)g(836,)g(838,)g(844,)f(846,)h(849,)g(851,) +g(855,)g(857,)g(863,)f(866,)h(868,)g(872,)g(874,)g(877,)g(879,)g(882,)f +(884,)h(888,)g(889,)g(891,)g(893,)g(895,)f(897,)h(899,)166 +4398 y(909,)j(911,)g(914,)f(916,)h(918,)g(920,)g(921,)g(922,)f(923,)h +(925,)g(932,)g(934,)g(936,)f(938,)h(940,)g(946,)g(952,)f(955,)h(959,)g +(961,)g(964,)g(976)14 b Fi(i)84 b Fj(Used)26 b(in)166 +4497 y(section)f(698.)0 4598 y Fi(h)14 b Fm(Declare)28 +b Fl(Picture)34 b Fm(functions)i Fj(263,)25 b(265,)g(267,)g(269,)h +(270,)f(272,)g(274,)g(275,)h(276,)f(280,)g(283,)g(285,)h(286,)f(288,)g +(289,)g(291,)g(293,)h(295,)f(298,)166 4698 y(299,)f(300,)g(301)15 +b Fi(i)83 b Fj(Used)24 b(in)f(section)i(261.)0 4799 y +Fi(h)14 b Fm(Declare)27 b Fl(Plane)32 b Fm(functions)k +Fj(663,)24 b(665,)g(667,)g(669,)g(672,)g(674,)g(677,)g(679,)g(684,)g +(686,)g(687,)g(689)14 b Fi(i)84 b Fj(Used)24 b(in)f(section)i(661.)0 +4900 y Fi(h)14 b Fm(Declare)27 b Fl(P)m(oin)m(t)33 b +Fm(constructors)g Fj(324,)24 b(327,)g(331)15 b Fi(i)83 +b Fj(Used)24 b(in)f(section)i(309.)0 5001 y Fi(h)14 b +Fm(Declare)25 b Fl(P)m(oin)m(t)32 b Fm(functions)j Fj(329,)23 +b(333,)g(338,)g(340,)g(342,)g(344,)g(346,)g(349,)g(350,)f(352,)h(355,)g +(357,)g(360,)g(362,)g(365,)g(367,)g(370,)g(372,)g(375,)g(377,)166 +5101 y(380,)i(382,)g(384,)g(385,)f(387,)h(389,)g(393,)g(396,)g(398,)g +(400,)f(401,)h(404,)g(406,)g(408,)g(412,)g(414,)g(419,)f(421,)h(436,)g +(438,)g(442,)g(446,)g(448,)f(450,)h(454,)166 5201 y(456,)g(458,)g(460,) +g(463,)f(464,)h(466,)g(467,)g(469,)g(470,)g(472,)f(473,)h(475,)g(477,)g +(482,)g(484,)g(486,)g(488,)f(489,)h(491,)g(493,)g(495,)g(501,)g(505,)f +(507,)h(510,)166 5300 y(512,)j(518,)g(521,)h(523,)f(525,)g(527,)g(529,) +g(532,)g(536,)h(538,)f(540,)g(542,)g(544,)g(546,)g(548,)h(551,)f(553,)g +(555,)g(557,)g(560,)g(567,)h(569,)f(572,)g(573)15 b Fi(i)166 +5400 y Fj(Used)24 b(in)f(section)i(309.)p eop +%%Page: 516 536 +516 535 bop 0 83 a Fm(516)140 b Fj(NAMES)23 b(OF)g(THE)h(SECTIONS)2235 +b(3DLDF-1.1.5.1)0 263 y Fi(h)14 b Fm(Declare)29 b Fl(P)m(olygon)34 +b Fm(functions)h Fj(1022,)26 b(1024,)g(1028,)g(1037,)g(1039,)h(1045,)f +(1047,)g(1050,)g(1052,)g(1054,)g(1056,)g(1059,)g(1061,)g(1064,)g(1066) +15 b Fi(i)166 363 y Fj(Used)24 b(in)f(section)i(1019.)0 +464 y Fi(h)14 b Fm(Declare)27 b Fl(P)m(olyhedron)33 b +Fm(functions)i Fj(1473)15 b Fi(i)83 b Fj(Used)24 b(in)g(section)g +(1472.)0 565 y Fi(h)14 b Fm(Declare)25 b Fl(Rectangle)30 +b Fm(functions)35 b Fj(1103,)23 b(1106,)g(1108,)g(1111,)g(1113,)g +(1119,)g(1122,)g(1125,)g(1127,)g(1130,)g(1132,)g(1135,)g(1136,)g(1137,) +g(1138)15 b Fi(i)166 665 y Fj(Used)24 b(in)f(section)i(1101.)0 +766 y Fi(h)14 b Fm(Declare)28 b Fl(Reg)p 514 766 29 5 +v 40 w(Cl)p 650 766 V 39 w(Plane)p 924 766 V 40 w(Curv)m(e)35 +b Fm(functions)g Fj(987,)26 b(988,)f(989,)h(990,)f(991,)h(992,)f(994,)h +(997,)f(1008,)h(1011,)g(1013,)g(1014)15 b Fi(i)83 b Fj(Used)25 +b(in)166 866 y(section)g(985.)0 967 y Fi(h)14 b Fm(Declare)37 +b Fl(Reg)p 523 967 V 39 w(P)m(olygon)k Fm(functions)36 +b Fj(1070,)e(1073,)h(1076,)f(1079,)h(1087,)f(1089,)g(1091,)h(1092,)f +(1093,)h(1095,)f(1096)15 b Fi(i)83 b Fj(Used)32 b(in)166 +1066 y(section)25 b(1069.)0 1168 y Fi(h)14 b Fm(Declare)27 +b Fl(Solid)p 557 1168 V 39 w(F)-8 b(aced)33 b Fm(functions)j +Fj(1446)15 b Fi(i)83 b Fj(Used)24 b(in)f(section)i(1445.)0 +1269 y Fi(h)14 b Fm(Declare)28 b Fl(Solid)k Fm(functions)j +Fj(1336,)25 b(1338,)h(1343,)f(1345,)g(1348,)g(1350,)g(1353,)g(1356,)g +(1358,)g(1360,)g(1362,)g(1364,)g(1366,)h(1369,)f(1371,)g(1373,)166 +1369 y(1375,)h(1377,)h(1379,)f(1381,)h(1383,)f(1386,)h(1388,)f(1390,)h +(1392,)f(1395,)g(1397,)h(1399,)f(1401,)h(1404,)f(1406,)h(1408,)f(1409,) +h(1411,)f(1413,)g(1415,)166 1468 y(1417,)e(1419,)h(1423,)f(1426,)g +(1429,)g(1432,)h(1435,)f(1438)15 b Fi(i)83 b Fj(Used)24 +b(in)f(section)i(1333.)0 1569 y Fi(h)14 b Fm(Declare)27 +b Fl(System)k Fm(functions)36 b Fj(36,)23 b(38,)h(40,)g(43,)f(45,)h +(47,)g(66,)f(71,)h(72)14 b Fi(i)84 b Fj(Used)24 b(in)f(sections)h(34,)g +(52,)g(65,)f(and)i(75.)0 1671 y Fi(h)14 b Fm(Declare)27 +b Fl(T)-8 b(etrahedron)33 b Fm(functions)j Fj(1480,)24 +b(1483,)h(1487,)f(1489,)g(1491)15 b Fi(i)83 b Fj(Used)24 +b(in)f(section)i(1477.)0 1772 y Fi(h)14 b Fm(Declare)29 +b Fl(T)-8 b(ransform)34 b Fm(functions)i Fj(168,)26 b(170,)g(172,)g +(174,)g(176,)g(178,)g(180,)g(182,)g(185,)g(187,)g(190,)g(192,)g(195,)g +(197,)g(200,)g(202,)g(203,)g(205,)166 1871 y(211,)e(212,)g(213,)g(216,) +g(218,)g(221,)g(223,)g(226,)g(232)15 b Fi(i)83 b Fj(Used)24 +b(in)f(section)i(166.)0 1973 y Fi(h)14 b Fm(Declare)27 +b Fl(T)-8 b(runc)p 594 1973 V 41 w(Octahedron)33 b Fm(functions)j +Fj(1525,)24 b(1528,)h(1530)15 b Fi(i)83 b Fj(Used)24 +b(in)f(section)i(1522.)0 2074 y Fi(h)14 b Fm(Declare)27 +b Fh(cr)l(e)l(ate)p 561 2074 26 4 v 31 w(new)13 b Fm(\()h(\))36 +b Fj(56,)23 b(58)15 b Fi(i)0 2175 y(h)f Fm(Declare)27 +b Fh(dr)l(aw)p 520 2175 V 31 w(axes)11 b Fm(\()k(\))35 +b Fj(968,)24 b(973)15 b Fi(i)83 b Fj(Used)24 b(in)f(section)i(981.)0 +2276 y Fi(h)14 b Fm(Declare)27 b Fl(namespace)32 b(Colors)39 +b Fj(153)14 b Fi(i)84 b Fj(Cited)24 b(in)f(section)i(153.)120 +b(Used)24 b(in)f(section)i(162.)0 2378 y Fi(h)14 b Fm(Declare)27 +b Fl(namespace)32 b(System)38 b Fj(34,)24 b(65)14 b Fi(i)84 +b Fj(Used)23 b(in)h(sections)g(51,)g(52,)g(74,)f(and)h(75.)0 +2479 y Fi(h)14 b Fm(De\014ne)28 b(I/O)f(functions)36 +b Fj(82,)23 b(83,)h(85,)g(87,)f(89)15 b Fi(i)83 b Fj(Used)24 +b(in)f(section)i(91.)0 2580 y Fi(h)14 b Fm(De\014ne)28 +b(P)n(attern)f(functions)35 b Fj(1321,)25 b(1324,)f(1327)15 +b Fi(i)83 b Fj(Used)24 b(in)f(section)i(1329.)0 2681 +y Fi(h)14 b Fm(De\014ne)28 b(classes)34 b Fj(253,)24 +b(261)15 b Fi(i)83 b Fj(Used)24 b(in)f(sections)i(305)f(and)g(306.)0 +2782 y Fi(h)14 b Fm(De\014ne)28 b(comparison)e(classes)34 +b Fj(498,)24 b(499,)g(500)15 b Fi(i)83 b Fj(Cited)24 +b(in)f(section)i(596.)120 b(Used)24 b(in)g(sections)g(633)g(and)h(634.) +0 2884 y Fi(h)14 b Fm(De\014ne)28 b(non-mem)n(b)r(er)f(non-template)h +(functions)f(for)h Fl(Color)39 b Fj(148)15 b Fi(i)83 +b Fj(Used)24 b(in)f(section)i(162.)0 2985 y Fi(h)14 b +Fm(De\014ne)28 b(non-mem)n(b)r(er)f(non-template)h(functions)f(for)h +Fl(P)m(oin)m(t)40 b Fj(481,)24 b(535)15 b Fi(i)83 b Fj(Used)24 +b(in)f(section)i(633.)0 3086 y Fi(h)14 b Fm(De\014ne)28 +b(parser)e(functions)36 b Fj(1539)15 b Fi(i)83 b Fj(Used)24 +b(in)f(section)i(1541.)0 3187 y Fi(h)14 b Fm(De\014ne)28 +b(utilit)n(y)g(functions)36 b Fj(25,)24 b(32)14 b Fi(i)83 +b Fj(Cited)24 b(in)g(section)g(25.)120 b(Used)24 b(in)g(section)g(51.)0 +3289 y Fi(h)14 b Fm(De\014ne)28 b Fl(Circle)k Fm(functions)k +Fj(1279,)24 b(1282,)g(1284,)h(1291,)f(1293,)g(1296,)g(1301,)h(1303,)f +(1305)15 b Fi(i)83 b Fj(Used)24 b(in)f(section)i(1315.)0 +3390 y Fi(h)14 b Fm(De\014ne)30 b Fl(Color)j Fm(functions)i +Fj(98,)25 b(100,)g(103,)h(105,)f(108,)h(110,)f(115,)g(117,)h(119,)f +(122,)g(124,)h(126,)f(128,)g(130,)h(132,)f(134,)g(136,)h(139,)f(145,)g +(150,)166 3489 y(152)15 b Fi(i)83 b Fj(Used)24 b(in)f(section)i(162.)0 +3591 y Fi(h)14 b Fm(De\014ne)28 b Fl(Cub)s(oid)k Fm(functions)j +Fj(1456,)24 b(1458,)h(1460,)f(1465,)g(1467)15 b Fi(i)84 +b Fj(Used)23 b(in)h(section)g(1468.)0 3692 y Fi(h)14 +b Fm(De\014ne)28 b Fl(Do)s(decahedron)33 b Fm(functions)i +Fj(1498,)25 b(1501,)f(1502,)g(1504,)g(1506)15 b Fi(i)84 +b Fj(Used)24 b(in)f(section)i(1534.)0 3793 y Fi(h)14 +b Fm(De\014ne)34 b Fl(Ellipse)i Fm(functions)f Fj(1147,)c(1150,)f +(1152,)g(1158,)h(1161,)f(1165,)g(1168,)h(1170,)f(1172,)g(1173,)h(1175,) +f(1178,)g(1180,)h(1183,)f(1185,)166 3893 y(1187,)c(1189,)h(1193,)f +(1195,)h(1198,)f(1200,)h(1202,)f(1204,)h(1206,)f(1209,)g(1211,)h(1215,) +f(1216,)h(1217,)f(1218,)h(1219,)f(1220,)h(1221,)f(1222,)g(1223,)166 +3992 y(1224,)h(1226,)h(1227,)f(1232,)g(1234,)h(1236,)f(1238,)g(1240,)h +(1243,)f(1245,)g(1248,)h(1250,)f(1253,)g(1255,)h(1258,)f(1260,)g(1262,) +h(1264)14 b Fi(i)84 b Fj(Used)26 b(in)166 4092 y(section)f(1271.)0 +4193 y Fi(h)14 b Fm(De\014ne)28 b Fl(F)-8 b(o)s(cus)32 +b Fm(functions)k Fj(605,)24 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+(1318,)g(1332,)h(1444,)166 2480 y(1452,)h(1471,)g(1537,)h(1544)15 +b Fi(i)83 b Fj(Used)26 b(in)g(sections)g(12,)h(51,)g(61,)f(74,)h(91,)g +(162,)f(239,)h(248,)g(305,)g(633,)g(657,)g(694,)g(980,)g(1015,)g(1097,) +g(1139,)166 2579 y(1271,)d(1315,)h(1329,)f(1441,)g(1449,)g(1468,)h +(1534,)f(1541,)g(and)g(1558.)0 2680 y Fi(h)14 b Fm(Initialize)28 +b(co)r(ordinates)e(and)h(limits)36 b Fj(323)15 b Fi(i)83 +b Fj(Used)24 b(in)f(sections)i(325,)f(328,)g(and)g(332.)0 +2781 y Fi(h)14 b Fm(Initialize)28 b Fl(static)k(Lab)s(el)h +Fm(data)27 b(mem)n(b)r(ers)35 b Fj(254)14 b Fi(i)84 b +Fj(Used)23 b(in)h(section)g(305.)0 2882 y Fi(h)14 b Fm(Lo)r(op)27 +b(for)g(testing)h(bits)35 b Fj(70)15 b Fi(i)83 b Fj(Cited)24 +b(in)f(section)i(66.)0 2983 y Fi(h)14 b Fm(Main)35 b +Fj(1555,)24 b(1556,)h(1557)15 b Fi(i)83 b Fj(Used)24 +b(in)f(section)i(1558.)0 3084 y Fi(h)14 b Fm(Ma)5 b(jor)26 +b Fl(Colors)39 b Fj(156)15 b Fi(i)83 b Fj(Cited)25 b(in)e(sections)h +(153)h(and)f(158.)120 b(Used)24 b(in)f(section)i(153.)0 +3184 y Fi(h)14 b Fm(Normalize)27 b(p)r(oin)n(t)35 b Fj(433)15 +b Fi(i)83 b Fj(Used)24 b(in)f(section)i(425.)0 3285 y +Fi(h)14 b Fm(Output)28 b Fl(P)m(ath)42 b Fj(907)14 b +Fi(i)84 b Fj(Used)23 b(in)h(sections)g(902,)g(904,)g(905,)g(and)g(906.) +0 3386 y Fi(h)14 b Fm(Prin)n(t)27 b(v)n(ersion,)f(cop)n(yrigh)n(t,)g +(and)h(license)h(information)34 b Fj(1552)15 b Fi(i)84 +b Fj(Used)23 b(in)h(section)g(1556.)0 3487 y Fi(h)14 +b Fm(Pro)r(cess)26 b(command)h(line)h(options)35 b Fj(1548)15 +b Fi(i)83 b Fj(Used)24 b(in)f(section)i(1555.)0 3588 +y Fi(h)14 b Fm(Pro)r(cess)26 b(v)n(ectors)g(for)h Fh(dr)l(aw)14 +b Fm(\()g(\))36 b Fj(1422)15 b Fi(i)83 b Fj(Used)24 b(in)f(section)i +(1424.)0 3688 y Fi(h)14 b Fm(Pro)r(cess)26 b(v)n(ectors)g(for)h +Fh(\014l)t(l)13 b Fm(\()h(\))36 b Fj(1425)15 b Fi(i)83 +b Fj(Used)24 b(in)f(section)i(1427.)0 3789 y Fi(h)14 +b Fm(Pro)r(cess)26 b(v)n(ectors)g(for)h Fh(\014l)t(ldr)l(aw)14 +b Fm(\()g(\))36 b Fj(1428)15 b Fi(i)83 b Fj(Used)24 b(in)f(section)i +(1430.)0 3890 y Fi(h)14 b Fm(Pro)r(cess)26 b(v)n(ectors)g(for)h +Fh(undr)l(aw)13 b Fm(\()h(\))36 b Fj(1431)15 b Fi(i)83 +b Fj(Used)24 b(in)f(section)i(1433.)0 3991 y Fi(h)14 +b Fm(Pro)r(cess)26 b(v)n(ectors)g(for)h Fh(un\014l)t(l)12 +b Fm(\()j(\))35 b Fj(1434)15 b Fi(i)83 b Fj(Used)24 b(in)g(section)g +(1436.)0 4092 y Fi(h)14 b Fm(Pro)r(cess)26 b(v)n(ectors)g(for)h +Fh(un\014l)t(ldr)l(aw)14 b Fm(\()g(\))35 b Fj(1437)15 +b Fi(i)84 b Fj(Used)23 b(in)h(section)g(1439.)0 4193 +y Fi(h)14 b Fm(T)n(yp)r(e)28 b(de\014nitions)35 b Fj(15,)24 +b(312,)g(313,)g(315,)g(317)14 b Fi(i)84 b Fj(Cited)24 +b(in)f(section)i(15.)120 b(Used)24 b(in)f(sections)h(51,)g(52,)g(633,)g +(and)g(634.)0 4293 y Fi(h)14 b Fm(Utilit)n(y)28 b(classes)34 +b Fj(16)15 b Fi(i)83 b Fj(Used)24 b(in)f(sections)i(51)f(and)g(52.)0 +4394 y Fi(h)14 b Fm(V)-7 b(ersion)27 b(con)n(trol)f(iden)n(ti\014er)35 +b Fj(5,)24 b(13,)g(53,)f(63,)h(76,)g(93,)g(164,)g(241,)g(250,)g(307,)g +(635,)g(659,)g(696,)g(982,)g(1017,)g(1099,)h(1141,)f(1273,)g(1317,)h +(1331,)166 4494 y(1443,)i(1451,)g(1470,)h(1536,)f(1543)15 +b Fi(i)83 b Fj(Used)26 b(in)g(sections)h(11,)f(51,)h(61,)f(74,)h(91,)g +(162,)g(239,)g(248,)f(305,)h(633,)g(657,)g(694,)g(980,)g(1015,)g(1097,) +166 4593 y(1139,)d(1271,)h(1315,)f(1329,)g(1441,)g(1449,)h(1468,)f +(1534,)g(1541,)g(and)h(1558.)0 4694 y Fi(h)14 b Fe(circles.h)80 +b Fj(1316)15 b Fi(i)0 4795 y(h)f Fe(colors.h)80 b Fj(163)15 +b Fi(i)0 4896 y(h)f Fe(creatnew.h)79 b Fj(62)15 b Fi(i)0 +4997 y(h)f Fe(cuboid.h)80 b Fj(1469)15 b Fi(i)0 5098 +y(h)f Fe(curves.h)80 b Fj(1016)15 b Fi(i)0 5198 y(h)f +Fe(ellipses.h)79 b Fj(1272)15 b Fi(i)0 5299 y(h)f Fe(gsltmplt.h)79 +b Fj(75)15 b Fi(i)0 5400 y(h)f Fe(io.h)82 b Fj(92)14 +b Fi(i)p eop +%%Page: 519 539 +519 538 bop 0 83 a Fj(3DLDF-1.1.5.1)2235 b(NAMES)23 b(OF)g(THE)h +(SECTIONS)141 b Fm(519)0 263 y Fi(h)14 b Fe(lines.h)80 +b Fj(658)15 b Fi(i)0 363 y(h)f Fe(loader.h)80 b Fj(12)14 +b Fi(i)0 462 y(h)g Fe(parser.h)80 b Fj(1542)15 b Fi(i)0 +562 y(h)f Fe(paths.h)80 b Fj(981)15 b Fi(i)0 662 y(h)f +Fe(patterns.h)79 b Fj(1330)15 b Fi(i)0 761 y(h)f Fe(pictures.h)79 +b Fj(306)15 b Fi(i)0 861 y(h)f Fe(planes.h)80 b Fj(695)15 +b Fi(i)0 960 y(h)f Fe(points.h)80 b Fj(634)15 b Fi(i)0 +1060 y(h)f Fe(polygons.h)79 b Fj(1098)15 b Fi(i)0 1160 +y(h)f Fe(polyhed.h)80 b Fj(1535)15 b Fi(i)0 1259 y(h)f +Fe(pspglb.h)80 b Fj(52)14 b Fi(i)0 1359 y(h)g Fe(rectangs.h)79 +b Fj(1140)15 b Fi(i)0 1459 y(h)f Fe(shapes.h)80 b Fj(249)15 +b Fi(i)0 1558 y(h)f Fe(solfaced.h)79 b Fj(1450)15 b Fi(i)0 +1658 y(h)f Fe(solids.h)80 b Fj(1442)15 b Fi(i)0 1757 +y(h)f Fe(transfor.h)79 b Fj(240)15 b Fi(i)0 1857 y(h)f +Fl(Line)32 b Fm(global)27 b(constan)n(ts)34 b Fj(654)15 +b Fi(i)83 b Fj(Used)24 b(in)f(section)i(657.)0 1957 y +Fi(h)14 b Fl(Plane)33 b Fm(global)26 b(constan)n(ts)34 +b Fj(691)15 b Fi(i)83 b Fj(Used)24 b(in)f(section)i(694.)0 +2056 y Fi(h)14 b Fl(extern)33 b Fm(All)28 b Fl(Colors)39 +b Fj(0)14 b Fi(i)83 b Fj(Cited)25 b(in)e(section)i(154.)0 +2156 y Fi(h)14 b Fl(extern)33 b Fm(Ma)5 b(jor)26 b Fl(Colors)39 +b Fj(157)15 b Fi(i)83 b Fj(Cited)24 b(in)g(section)g(154.)121 +b(Used)23 b(in)h(section)g(154.)0 2256 y Fi(h)14 b Fl(extern)33 +b Fm(declaration)26 b(of)i(namespace)e Fl(Pro)5 b(jections)40 +b Fj(257)15 b Fi(i)83 b Fj(Used)24 b(in)g(section)g(306.)0 +2355 y Fi(h)14 b Fl(extern)33 b Fm(declaration)26 b(of)i(namespace)e +Fl(Sorting)41 b Fj(259)15 b Fi(i)83 b Fj(Used)24 b(in)f(section)i(306.) +0 2455 y Fi(h)14 b Fl(extern)33 b Fm(global)26 b(constan)n(t)h +(declarations)34 b Fj(160)15 b Fi(i)83 b Fj(Used)24 b(in)f(section)i +(163.)0 2554 y Fi(h)14 b Fl(extern)33 b Fm(v)-5 b(ariable)27 +b(declarations)33 b Fj(79)14 b Fi(i)84 b Fj(Used)24 b(in)f(section)i +(92.)0 2654 y Fi(h)14 b Fl(extern)33 b(namespace)e(Colors)h +Fm(declaration)i Fj(154)14 b Fi(i)84 b Fj(Cited)24 b(in)f(sections)i +(154)f(and)g(158.)121 b(Used)23 b(in)h(section)g(163.)p +eop %%Trailer - +end userdict /end-hook known{end-hook}if %%EOF diff -Naur 3DLDF-1.1.4/CWEB/3DLDFprg.web 3DLDF-1.1.5.1/CWEB/3DLDFprg.web --- 3DLDF-1.1.4/CWEB/3DLDFprg.web 2003-12-10 15:50:41.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/3DLDFprg.web 2004-01-16 17:28:24.000000000 +0100 @@ -3,7 +3,7 @@ @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -30,7 +30,7 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: 3DLDFprg.web,v 1.5 2003/12/10 14:50:41 lfinsto1 Exp $ @> +@q $Id: 3DLDFprg.web,v 1.10 2004/01/16 16:28:24 lfinsto1 Exp $ @> @q 3DLDF.web @> @q LDF 2003.04.15. This file is used for cweaving the @> @@ -50,7 +50,7 @@ @q * Copyright and License.@> -@* Copyright and License.\newline +@* Copyright and License.\hfil\break \begingroup \parskip=10pt Copyright \copyright{} 2003 Laurence D. Finston. @@ -143,7 +143,7 @@ To write my \.{.web} files, I wrote a \.{cweb-mode} for Emacs and a number of Emacs-Lisp functions to go with it. It is not currently -included in the 3DLDF distribution (Version 1.1.4), but I may include it in a +included in the 3DLDF distribution (Version 1.1.5.1), but I may include it in a later version. However, GNU is at work at an official cweb-mode of its own, so you might want to use it instead, if it's available. @@ -168,7 +168,7 @@ See {\tt http://www-cs-faculty.stanford.edu/knuth/cweb.html} for more information about CWEB. The WEB (for Pascal) and CWEB packages are available from the CTAN archive, {\tt ftp.dante.de} -and\newline +and\hfil\break {\tt http:://www.dante.de}. Donald Knuth's books @@ -359,6 +359,10 @@ @i pspglb.web @q@> + +@i creatnew.web @q@> + +@i gsltmplt.web @q@> @i io.web @q@> @@ -402,7 +406,6 @@ @i main.web @q@> -#endif @q ******* test_routines.web @> @@ -460,10 +463,18 @@ %Gill, Robert W.\ %{\it Creative Perspective}. %London 1975. -%Thames and Hudson Ltd.\newline +%Thames and Hudson Ltd.\hfil\break %\hbox{ISBN~0-500-27056-2.} \entry +Harbison, Samuel~P., and Guy~L. Steele Jr. +{\it C, A Reference Manual}. +Prentice Hall. +Englewood Cliffs, New Jersey 1995. +\hbox{ISBN~0-13-326232-4 $\{$Case$\}$.}\hfil\break +\hbox{ISBN~0-13-326224-3 $\{$Paperback$\}$.} + +\entry Hobby, John D.\ {\it A User's Manual for MetaPost}. AT\&T Bell Laboratories. @@ -472,14 +483,14 @@ \entry Jones, Huw. {\it Computer Graphics through Key Mathematics}. -Springer-Verlag London Limited 2001.\newline +Springer-Verlag London Limited 2001.\hfil\break \hbox{ISBN~1-85233-422-3.} \entry Knuth, Donald Ervin. {\it Metafont: The Program}. Computers and Typesetting; D.\ Addison Wesley Publishing Company, Inc. -Reading, Massachusetts 1986.\newline +Reading, Massachusetts 1986.\hfil\break \hbox{ISBN~0-201-13438-1.} \entry @@ -493,7 +504,7 @@ Knuth, Donald Ervin. {\it {TeX}: The Program}. Computers and Typesetting; B.\ Addison Wesley Publishing Company, Inc. -Reading, Massachusetts 1986.\newline +Reading, Massachusetts 1986.\hfil\break \hbox{ISBN~0-201-13437-3.} \entry @@ -504,14 +515,14 @@ \entry Knuth, Donald E. and Silvio Levy. -{\it The {\bf CWEB} System of Structured Documentation}.\newline +{\it The {\bf CWEB} System of Structured Documentation}.\hfil\break \hbox{Version 3.64---February 2002.} \entry Salomon, David. {\it Computer Graphics and Geometric Modeling}. Berlin 1999. -Springer-Verlag.\newline +Springer-Verlag.\hfil\break \hbox{ISBN: 0-387-98682-0.} @@ -520,7 +531,7 @@ %{\it GNU Make. A Program for Directing Recompilation. %{\tt make} Version 3.79}. %Boston 2000. -%Free Software Foundation, Inc.\newline +%Free Software Foundation, Inc.\hfil\break %\hbox{ISBN: 1-882114-80-9.} \entry @@ -535,21 +546,21 @@ {\it The \CPLUSPLUS/ Programming Language}. Special Edition. Reading, Massachusetts 2000. -Addison-Wesley.\newline +Addison-Wesley.\hfil\break \hbox{ISBN~0-201-70073-5.} \entry Stroustrup, Bjarne. {\it The Design and Evolution of \CPLUSPLUS/}. Reading, Massachusetts 1994. -Addison-Wesley Publishing Company.\newline +Addison-Wesley Publishing Company.\hfil\break \hbox{ISBN~0-201-54330-3.} %\entry %Vredeman de Vries, Jan. %{\it Perspective}. %New York 1968. -%Dover Publications, Inc.\newline +%Dover Publications, Inc.\hfil\break %\hbox{Standard Book Number: 486-21086-4.} %\smallskip % @@ -563,7 +574,7 @@ %White, Gwen. %{\it Perspective. A Guide for Artists, Architects and Designers}. %London 1968 and 1982. -%B T Batsford Ltd.\newline +%B T Batsford Ltd.\hfil\break %\hbox{ISBN~0-7134-3412-0.} \endgroup @@ -621,6 +632,6 @@ \initials{LDF 2002.10.11.} Another problem is that ``\\{operator\AM}'' and ``\\{operator\AM=}'' use the italic ampersand. It would be possible to fix this, but slightly tricky.@:!! TO DO@> TO DO: Fix this! - + diff -Naur 3DLDF-1.1.4/CWEB/3DLDFtex.bas 3DLDF-1.1.5.1/CWEB/3DLDFtex.bas --- 3DLDF-1.1.4/CWEB/3DLDFtex.bas 2003-11-28 14:37:59.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/3DLDFtex.bas 2004-01-12 22:26:37.000000000 +0100 @@ -3,7 +3,7 @@ %% * Copyright and License.@> %%% This file is part of 3DLDF, a package for three-dimensional drawing. -%%% Copyright (C) 2003 Laurence D. Finston. +%%% Copyright (C) 2003, 2004 Laurence D. Finston. %%% 3DLDF is free software; you can redistribute it and/or modify %%% it under the terms of the GNU General Public License as published by @@ -30,7 +30,7 @@ %%% s246794@stud.uni-goettingen.de -%%%% $Id: 3DLDFtex.bas,v 1.1 2003/11/28 13:37:59 lfinsto1 Exp $ +%%%% $Id: 3DLDFtex.bas,v 1.3 2004/01/12 21:26:37 lfinsto1 Exp $ \newif\ifxlrg \newif\ifavier diff -Naur 3DLDF-1.1.4/CWEB/3DLDFtex.tex 3DLDF-1.1.5.1/CWEB/3DLDFtex.tex --- 3DLDF-1.1.4/CWEB/3DLDFtex.tex 2003-12-10 15:54:46.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/3DLDFtex.tex 2004-01-12 22:26:58.000000000 +0100 @@ -1,12 +1,11 @@ %%%% 3DLDFtex.tex -%%%% $Id: 3DLDFtex.tex,v 1.2 2003/12/10 14:54:46 lfinsto1 Exp $ +%%%% $Id: 3DLDFtex.tex,v 1.5 2004/01/12 21:26:58 lfinsto1 Exp $ - %%%% * Copyright and License.@> %%%% This file is part of 3DLDF, a package for three-dimensional drawing. -%%%% Copyright (C) 2003 Laurence D. Finston. +%%%% Copyright (C) 2003, 2004 Laurence D. Finston. %%%% 3DLDF is free software; you can redistribute it and/or modify %%%% it under the terms of the GNU General Public License as published by @@ -33,7 +32,7 @@ %%%% s246794@stud.uni-goettingen.de -%%%% $Id: 3DLDFtex.tex,v 1.2 2003/12/10 14:54:46 lfinsto1 Exp $ +%%%% $Id: 3DLDFtex.tex,v 1.5 2004/01/12 21:26:58 lfinsto1 Exp $ \input epsf @@ -41,16 +40,16 @@ \input 3DLDFtex.bas -\landscapetrue -%\landscapefalse +%\landscapetrue +\landscapefalse %\xlrgtrue %\xlrgfalse -%\aviertrue +\aviertrue %\avierfalse -\adreitrue +%\adreitrue %\adreifalse diff -Naur 3DLDF-1.1.4/CWEB/ChangeLog 3DLDF-1.1.5.1/CWEB/ChangeLog --- 3DLDF-1.1.4/CWEB/ChangeLog 2003-12-10 18:34:24.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/ChangeLog 2004-01-16 19:18:23.000000000 +0100 @@ -1,3 +1,505 @@ +2004-01-16 Laurence Finston + + * Makefile.am: LDF 2004.01.16. + Changed `3DLDF.pdf' to `3DLDFprg.pdf' in `EXTRA_DIST'. + + * Makefile.am: LDF 2004.01.16. + Added `3DLDFprg.pdf' to `EXTRA_DIST'. + + * Makefile.am, pspglb.web, cwebmac.tex, 3DLDFprg.web: LDF 2004.01.16. + Changed release number to 1.1.5.1. + +2004-01-14 Laurence Finston + + * cwebmac.tex: LDF 2004.01.14. + Changed `\title' to "3DLDF 1.1.5". + + * ellipses.web: LDF 2004.01.14. + In |intersection_points()| with |Ellipse| argument: + Changed |step| argument from |real| to |const real|. + +2004-01-12 Laurence Finston + + * Makefile.am: LDF 2004.01.12. + Changed version number from `1.1.4' to `1.1.5'. + + * utility.web, tsthdweb, transfor.web, subex2.web, subex1.web, solids.web, solfaced.web, shapes.web, rectangs.web, polyhed.web, polygons.web, points.web, planes.web, pictures.web, patterns.web, paths.web, parser.web, main.web, loader.web, lines.web, ldfr, io.web, gsltmplt.web: + LDF 2004.01.12. + Changed copyright date from ``2003'' to ``2003, 2004''. + + * pspglb.web, exampman.web, examples.web, examples.mp, ellipses.web, curves.web, cuboid.web, creatnew.web, colors.web, cnepspng.el, circles.web, Makefile.am, 3DLDFtex.tex, 3DLDFtex.bas, 3DLDFprg.web, 3DLDFprg.mac, 3DLDFmp.mp: + LDF 2004.01.12. + Changed copyright date from ``2004'' to ``2003, 2004''. + + * exampman.web, examples.web, examples.mp: LDF 2004.01.12. + Changed copyright date to 2004. + + * ellipses.web: LDF 2004.01.12. + Changed copyright date to 2004. + + Added |real step| argument to the version of |Ellipse::intersection_points()| that takes + an |Ellipse| argument. 3 is the default value. + + * curves.web, cuboid.web, creatnew.web, colors.web, cnepspng.el, circles.web, Makefile.am, 3DLDFtex.tex, 3DLDFtex.bas: + LDF 2004.01.12. + Changed copyright date to 2004. + + * 3DLDFprg.web: LDF 2004.01.12. + Removed erroneous `#endif'. + + * 3DLDFprg.web: LDF 2004.01.12. + Changed version number from `1.1.4' to `1.1.5'. + Changed copyright date to 2004. + + * 3DLDFmp.mp, 3DLDFprg.mac: LDF 2004.01.12. + Changed copyright date to 2004. + + * pspglb.web: LDF 2004.01.12. + Changed version number from `1.1.4' to `1.1.5'. + Changed copyright date to 2004. + + * cwebmac.tex: LDF 2004.01.12. + Changed version number from `1.1.4' to `1.1.5'. + Changed date to ``January 2004''. + + * Makefile.am: LDF 2004.01.12. + BUG FIX: Added `touch 3DLDFmp.mp' to the `3DLDFmp.mp' target. This ensures that + TeX and dvips will be run, if MetaPost is run on `3DLDFmp.mp'. This happens if + `3DLDFput.mp' is newer than `3DLDFmp.mp', but the latter isn't changed, so TeX and dvips + weren't being run. I'm surprized nobody's complained about this. + + Added `PHONY' targets as synonyms for certain targets: + `cpl' for `3dldf'. For compiling and linking `3dldf'. + + `mp' for `3DLDFmp.mp'. For running MetaPost on `3DLDFmp.mp'. + + `ldf' for `3DLDFput.mp'. For running `3dldf'. + + * Makefile.am: LDF 2004.01.12. + Added `examples.mp' and `exampman.web' to `EXTRA_DIST'. + + Added `PHONY' target `pdf' for generating `3DLDFprg.pdf'. + +2004-01-09 Laurence Finston + + * exampman.web, examples.mp: New file. + + * Makefile.am: LDF 2004.01.09. + Added `cnepspng.el' to `EXTRA_DIST'. The former contains + the Emacs-Lisp definitions of the functions `convert-eps' and `convert-eps-loop'. + These functions are used for converting the EPS files generated by MetaPost to + the structured PostScript and PNG formats. + + * cnepspng.el: LDF 2004.01.09. + Put in the copyright, license, and contact information. Commented-out + the calls to `local-set-key'. + + * cnepspng.el: LDF 2004.01.09. + Edited the documentation strings of `convert-eps and `convert-eps-loop'. + + * cnepspng.el: LDF 2004.01.09. + Completed definitions of `convert-eps and `convert-eps-loop'. + + * cnepspng.el: New file. + +2004-01-06 Laurence Finston + + * main.web: LDF 2004.01.06. + Changed calls to |get_second_largest()|, so that the |verbose| argument + is |false|. + + * solids.web: LDF 2004.01.06. + Made |set_on_free_store()| non-inline. + + * points.web: LDF 2004.01.06. + Made |is_on_free_store()| non-inline. + + * paths.web: LDF 2004.01.06. + Made |set_on_free_store()| and |is_on_free_store()| non-inline. + + * colors.web: LDF 2004.01.06. + Made |is_on_free_store()| non-inline. + + * lines.web, io.web, gsltmplt.web, examples.web, ellipses.web, curves.web, cuboid.web, colors.web, circles.web: + LDF 2004.01.06. + Removed CWEB comment with RCS ID. It's not needed, because + it's in |static string rcs_id|. + + * utility.web: LDF 2004.01.06. + Removed CWEB comment with RCS ID. It's not needed, because + it's in |static string rcs_id|. + + Now including `creatnew.h'. + + Replaced calls of |create_new_point()| with calls to + |create_new()|. + + * transfor.web: LDF 2004.01.06. + Removed CWEB comment with RCS ID. It's not needed, because + it's in |static string rcs_id|. + + Made |epsilon()| non-inline. It now returns different values, depending + on the value of |LDF_REAL_DOUBLE|. This is because it's now possible + to |typedef real| to |float| or |double|. + + * solids.web: LDF 2004.01.06. + Removed CWEB comment with RCS ID. It's not needed, because + it's in |static string rcs_id|. + + Now including `creatnew.h'. + + Replaced |create_new_solid()| with specializations of + the template function |create_new()|. + Added the section + |@|, which + contains the declarations of the specializations. + + Replaced calls of |create_new_()| with calls to + the appropriate specialization of the template function + |create_new()|. + + * solfaced.web, shapes.web: LDF 2004.01.06. + Removed CWEB comment with RCS ID. It's not needed, because + it's in |static string rcs_id|. + + * rectangs.web: LDF 2004.01.06. + Removed CWEB comment with RCS ID. It's not needed, because + it's in |static string rcs_id|. + + Now including `creatnew.h'. + + Replaced |create_new_rectangle()| with specializations of + the template function |create_new()|. + Added the section + |@|, which + contains the declarations of the specializations. + + Replaced calls of |create_new_point()| with calls to + |create_new()|. + + * pspglb.web: LDF 2004.01.06. + Merged in changes from my development version. + + Removed CWEB comment with RCS ID. It's not needed, because + it's in |static string rcs_id|. + + Moved code for including the library header file `limits' or `limits.h' from + `loader.web' to this file. It's only used here. + + Now using |#define| instead of |@@d| for + the definitions of |LDF_REAL_FLOAT| and |LDF_REAL_DOUBLE|. If |@@d| + is used, the definitions are only written to \filename{pspglb.c}. + Using |#define|, and writing |@| to + \filename{pspglb.h} makes the definitions available to the files that + include \filename{pspglb.h}. + + Changed the way |MAX_REAL| and |MAX_REAL_SQRT| are declared. They are no + longer |const|, because setting their values requires function calls. + |MAX_REAL| is set by using |get_second_largest()| in |main()|. Following this, + |MAX_REAL_SQRT| is set to |sqrt(MAX_REAL)|. + + Added |extern const bool ldf_real_float| and |extern const bool ldf_real_double| + for use in non-conditionally compiled code. They are set according to the values + of |LDF_REAL_FLOAT| and |LDF_REAL_DOUBLE|. + + Added |namespace System| and declarations and definitions for functions belonging + to it: |get_endianness()|, |is_big_endian()|, |is_little_endian()|, + |get_register_width()|, |is_32_bit()|, and |is_64_bit()|. + The template function |get_second_largest()| also belongs to |namespace System|, but + it is declared and defined in `gsltmplt.web'. This is because of the way templates + are instantiated by the GNU C++ compiler GCC 3.3. + + Added the sections |@| and + |@|. + + * polygons.web: LDF 2004.01.06. + Removed CWEB comment with RCS ID. It's not needed, because + it's in |static string rcs_id|. + + Now including `creatnew.h'. + + Replaced |create_new_reg_polygon()| with specializations of + the template function |create_new()|. + Added the section + |@|, which + contains the declarations of the specializations. + + Replaced calls of |create_new_point()| with calls to + |create_new()|. + + * polyhed.web: LDF 2004.01.06. + Removed CWEB comment with RCS ID. It's not needed, because + it's in |static string rcs_id|. + + Now including `creatnew.h'. + + Replaced calls of |create_new_reg_polygon()| with calls to + |create_new()|. + + * points.web: LDF 2004.01.06. + Removed CWEB comment with RCS ID. It's not needed, because + it's in |static string rcs_id|. + + Now including `creatnew.h'. + + Replaced |create_new_point()| with specializations of + the template function |create_new()|. + Added the section + |@|, which + contains the declarations of the specializations. + + Replaced calls of |create_new_point()| with calls to + |create_new()|. + + Changed the name of the sections + |@| and + |@| to + |@| and + |@|, + respectively. + + Made |set_on_free_store()| non-inline. + + Made |epsilon()| non-inline. It now also contains conditionally compiled + code. It returns different values depending on the value of + |LDF_REAL_DOUBLE|. This is because it now works to |typedef real| to + |double|. However, I haven't tested the value that |epsilon()| returns + when |real == double|. For that matter, I haven't performed proper tests + on the value it returns when |real == float|. + + Added |bool DEBUG| in |magnitude()|. + + * planes.web: LDF 2004.01.06. + Removed CWEB comment with RCS ID. It's not needed, because + it's in |static string rcs_id|. + + * pictures.web: LDF 2004.01.06. + Removed CWEB comment with RCS ID. It's not needed, because + it's in |static string rcs_id|. + + Minor formatting change. + + * patterns.web, paths.web: LDF 2004.01.06. + Removed CWEB comment with RCS ID. It's not needed, because + it's in |static string rcs_id|. + + * paths.web: LDF 2004.01.06. + Now including `creatnew.h'. + + Replaced |create_new_path()| with specializations of + the template function |create_new()|. + Added the section + |@|, which + contains the declarations of the specializations. + + Replaced calls of |create_new_()| with calls to the + appropriate specialization of |create_new()|. + + * parser.web: LDF 2004.01.06. + Removed CWEB comment with RCS ID. It's not needed, because + it's in |static string rcs_id|. + + Added a comment about including the library header file `map'. + + * main.web: LDF 2004.01.06. + Removed CWEB comment with RCS ID. It's not needed, because + it's in |static string rcs_id|. + + Moved a C++ comment to TeX text. + + Now including `creatnew.h' and `gsltmplt.h'. + + Now setting |MAX_REAL| and |MAX_REAL_SQRT| at the beginning of + |main()| using |get_second_largest()|. Removed error handling code, since + |get_second_largest()| takes care of it. + + * gsltmplt.web: LDF 2004.01.06. + Initial revision. + Copied this file from my development directory. + + This file contains the definition of the template function + |template Real get_second_largest(Real, bool)|, + and declarations of specializations + for |Real == float| and |Real == double|. + + |get_second_largest()| is used in |main()| for setting the value + of |real MAX_REAL|. + + Because of the way the GNU C++ compiler GCC 3.3 instantiates + templates, the definition must be included in all of the CWEB files + that declare or use specializations of |get_second_largest()|. + So the definition is written to `gsltmplt.h', + and not just the declaration, as with non-template functions. + Currently, only `main.web' includes `gsltmplt.h'. + + It's not really necessary to compile the definition here. + However, I do so, in order to catch errors earlier, if there are any. + + In addition, it simplifies the rules for building the executable `3dldf', if + all of the CWEB files are handled similarly. + However, I don't believe it would cause + a problem to compile an empty `.cxx' file. + + * loader.web: LDF 2004.01.06. + Merged in changes from my development version. + + Now including `stdlib.h' and `string' + and invoking `using namespace std' + in the code that's compiled. + It's not necessary to include `stdlib.h' when using GCC 3.3, + but I think it's safer. + + Added the section |@| and put the `#include' commands + into it. This section is now written to `loader.h', instead of writing + the individual blocks of code to it. + + Removed some outdated TeX text. + + I have now decided not to try to get rid of this file. I've put a couple of |#include| + commands into other files. The remaining ones are needed in enough CWEB files that + I think it's best to keep them here. + + Removed the code that includes `limits' or `limits.h' to `pspglb.web'. + + Removed `#include ' to `parser.web'. + + `Makefile.am' now handles + `loader.web' like all the other CWEB files. Removed the rules + that handled the `loader.' files in special ways from `Makefile.am'. + + `loader.c' is now compiled. The C++ code consists merely of the |static string rcs_id|, + which is written to `loader.o'. + Added a section for this. + + Now defining |_GNU_SOURCE| only if it's not already defined. + + * gsltmplt.web: New file. + + * ellipses.web: LDF 2004.01.06. + Now including `creatnew.h'. + + Replaced |create_new_ellipse()| with specializations of + the template function |create_new()|. + + Added the section + |@|. + + Replaced calls to |Rectangle::create_new_point()| with + calls to |create_new()|. + + * cuboid.web: LDF 2004.01.06. + Now including `creatnew.h'. + + Replaced |create_new_cuboid()| with specializations of + the template function |create_new()|. + + Added the section + |@|. + + Replaced calls to |Rectangle::create_new_rectangle()| with + calls to |create_new()|. + + * creatnew.web: LDF 2004.01.06. + Initial version. + Copied this file from my development directory. + + It contains the definition of the template functions + |template C* create_new(const C*)| and + |template C* create_new(const C&)|. + + Because of the way the GNU C++ compiler GCC 3.3 instantiates + templates, the definition must be included in all of the CWEB files + that declare or use specializations of |create_new()|. + So, the definition is written to `creatnew.h', and not just the declaration, as will + non-template functions. + + Therefore, it's not really necessary to compile the definition here. However, I do so, + in order to catch errors earlier, if there are any. + + In addition, it simplifies the rules for building the executable `3dldf', if + all of the CWEB files are handled similarly. However, I don't believe it would cause + a problem to compile an empty `.cxx' file. + + * creatnew.web: New file. + + * colors.web: LDF 2004.01.06. + Now including `creatnew.h'. + + Replaced |create_new_color()| with specializations of + the template function |create_new()|. + Added a version taking a |const Color&| argument. + + Added the section + |@|. + + Changed the section |@| to + |@| + + Added |set_on_free_store()|, which is required by the template definition of + |create_new()|. + + Moved a C++ comment to a TeX section. + + * circles.web: LDF 2004.01.06. + Now including `creatnew.h'. + + Replaced |create_new_circle()| with specializations of + the template function |create_new()|. + + Added the section + |@|. + + * Makefile.am: LDF 2004.01.06. + `loader.web' is now handled like all the other CWEB files. Removed the rules + that handled the `loader.' files in special ways. + + `loader.c' is now compiled. The C++ code consists merely of the |static string rcs_id|, + which is written to `loader.o'. + + Added code for handling `creatnew.web' and `gsltmplt.web', and the files generated + from them. + + Added `PHONY' target `show' for echoing the values of variables to standard output. + + * 3DLDFtex.tex: LDF 2004.01.06. + Now setting `\aviertrue' and `\landscapefalse'. + + * 3DLDFprg.web: LDF 2004.01.06. + Changed `\newline' to `\hfil\break'. + + Now including `creatnew.web' and 'gsltmplt.web'. + + Added bibliography entry for Harbison, _C, A Reference Manual_. + + * 3DLDFmp.mp: LDF 2004.01.06. + Removed Emacs Local Variables list. + +2003-12-21 Laurence Finston + + * 3DLDFmp.mp: LDF 2003.12.21. + Added local variables list for Emacs. + +2003-12-16 Laurence Finston + + * tsthdweb: LDF 2003.12.16. + Changed the |diff| command used for comparing .h to .hbk. + It now ignores lines begining with ``#line'' rather than + ``#''. + + This is the same change as I made for the C++ files before the last check-in + on 2003/12/14. I didn't think to do it for the header file. + +2003-12-14 Laurence Finston + + * tsthdweb: LDF 2003.12.14. + BUG FIX: + Changed the |diff| command used for comparing .c to .cxx. + It now ignores lines begining with ``#line'' rather than + ``#''. + + This ensures that changes involving preprocessor variables cause + recompilation and relinking. + 2003-12-10 Laurence Finston * utility.web: LDF 2003.12.10. diff -Naur 3DLDF-1.1.4/CWEB/Makefile.am 3DLDF-1.1.5.1/CWEB/Makefile.am --- 3DLDF-1.1.4/CWEB/Makefile.am 2003-12-10 16:05:16.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/Makefile.am 2004-01-16 19:18:00.000000000 +0100 @@ -1,8 +1,8 @@ -#### 3DLDF-1.1.4/CWEB/Makefile.am +#### 3DLDF-1.1.5.1/CWEB/Makefile.am #### Created by Laurence D. Finston (LDF). # This file is part of 3DLDF, a package for three-dimensional drawing. -# Copyright (C) 2003 Laurence D. Finston. +# Copyright (C) 2003, 2004 Laurence D. Finston. # 3DLDF is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by @@ -29,11 +29,12 @@ # s246794@stud.uni-goettingen.de -# $Id: Makefile.am,v 1.16 2003/12/10 15:05:15 lfinsto1 Exp $ +# $Id: Makefile.am,v 1.26 2004/01/16 18:18:00 lfinsto1 Exp $ bin_PROGRAMS = 3dldf -3dldf_SOME_CWEBS = pspglb.web io.web colors.web transfor.web shapes.web \ +3dldf_SOME_CWEBS = loader.web pspglb.web creatnew.web gsltmplt.web io.web colors.web \ + transfor.web shapes.web \ pictures.web points.web lines.web planes.web paths.web \ curves.web polygons.web rectangs.web ellipses.web \ circles.web patterns.web solids.web solfaced.web \ @@ -48,19 +49,25 @@ 3dldf_c_files = $(nodist_3dldf_SOURCES:.cxx=.c) -3dldf_CWEBS := $(3dldf_SOME_CWEBS) main.web loader.web - +3dldf_CWEBS := $(3dldf_SOME_CWEBS) main.web + EXTRA_DIST = .rcsfreeze.log .rcsfreeze.log.dev $(3dldf_CWEBS) \ - 3DLDFprg.dvi 3DLDFprg.mac \ + 3DLDFprg.dvi 3DLDFprg.mac 3DLDFprg.pdf \ 3DLDFprg.ps 3DLDFprg.web 3DLDFmp.mp \ - 3DLDFtex.bas 3DLDFtex.tex ChangeLog.dev cwebmac.tex \ - fdl.tex gpl.tex stamp-h.in \ + 3DLDFtex.bas 3DLDFtex.tex ChangeLog.dev cnepspng.el \ + cwebmac.tex examples.mp exampman.web fdl.tex gpl.tex stamp-h.in \ tsthdweb + + # stamp-h1 stamp-h. Removed from EXTRA_DIST. I don't think they're needed # LDF 2003.11.25. + +# -frepo is needed because I'm now using template functions. +# LDF 2003.12.31. +AM_CXXFLAGS = -frepo # This is needed, because 3dldf fails with a "Segmentation fault", if # the executable is linked using $(3dldf_OBJECTS). This may cause @@ -70,7 +77,7 @@ cuboid.o solfaced.o solids.o patterns.o circles.o \ ellipses.o rectangs.o polygons.o curves.o paths.o \ planes.o lines.o points.o pictures.o shapes.o transfor.o \ - colors.o io.o pspglb.o + colors.o io.o pspglb.o loader.o # 3dldf_mpgens contains the Encapsulated PostScript (EPS) files generated by Metapost, # and a couple of other files, also generated by MetaPost. LDF 2003.11.16. @@ -82,11 +89,11 @@ CLEANFILES := $(3dldf_c_files) $(3dldf_mpgens) 3DLDFprg.idx 3DLDFprg.log 3DLDFprg.scn \ 3DLDFprg.toc 3DLDFput.mp 3DLDFput.tex \ 3DLDFtex.dvi 3DLDFtex.log 3DLDFtex.ps \ - Makefile loader.c \ + Makefile \ $(3dldf_headers) $(3dldf_header_timers) \ $(3dldf_cweb_timers) \ $(nodist_3dldf_SOURCES) $(3dldf_OBJECTS) \ - config.h loader.h loader.tim stamp-h stamp-h1 + config.h stamp-h stamp-h1 # mostlyclean leaves the .cxx, .h, and .tim files, but deletes the object files. @@ -99,11 +106,11 @@ MAINTAINERCLEANFILES := $(3dldf_c_files) $(3dldf_mpgens) 3DLDFprg.idx 3DLDFprg.log 3DLDFprg.scn \ 3DLDFprg.toc 3DLDFput.mp 3DLDFput.tex \ 3DLDFtex.dvi 3DLDFtex.log 3DLDFtex.ps \ - Makefile loader.c \ + Makefile \ $(3dldf_headers) $(3dldf_header_timers) \ $(3dldf_cweb_timers) \ $(nodist_3dldf_SOURCES) $(3dldf_OBJECTS) \ - config.h loader.h loader.tim stamp-h stamp-h1 \ + config.h stamp-h stamp-h1 \ 3DLDFprg.dvi 3DLDFprg.ps @@ -112,111 +119,113 @@ dummy: @echo "dummy in CWEB/Makefile.am." -3dldf: loader.tim $(3dldf_OBJECTS) +.PHONY : cpl +cpl: 3dldf + +3dldf: $(3dldf_OBJECTS) -rm -f -r 3dldf @echo "Linking 3dldf" $(CXXLINK) $(3dldf_OBS_REVERSED) -loader.tim: loader.h - -loader.h: loader.web - @echo "ctangling loader.web." - $(CTANGLE) loader.web - $(SHELL) $(srcdir)/tsthdweb loader 2 $(CTANGLE) - pspglb.o: loader.tim pspglb.tmw +loader.o: loader.tmw - io.o: loader.tim pspglb.tim io.tmw +pspglb.o: loader.tim pspglb.tmw - colors.o: loader.tim pspglb.tim io.tim colors.tmw +creatnew.o: loader.tim pspglb.tim creatnew.tmw - transfor.o: loader.tim pspglb.tim io.tim colors.tim transfor.tmw +gsltmplt.o: loader.tim pspglb.tim gsltmplt.tmw - shapes.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim shapes.tmw +io.o: loader.tim pspglb.tim io.tmw - pictures.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tmw +colors.o: loader.tim pspglb.tim creatnew.tim io.tim colors.tmw - points.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tmw +transfor.o: loader.tim pspglb.tim io.tim colors.tim transfor.tmw - lines.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tmw +shapes.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim shapes.tmw - planes.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tmw +pictures.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tmw - paths.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tmw +points.o: loader.tim pspglb.tim creatnew.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tmw - curves.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tmw +lines.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tmw - polygons.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tmw +planes.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tmw - rectangs.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.tmw +paths.o: loader.tim pspglb.tim creatnew.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tmw - ellipses.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ +curves.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.tim ellipses.tmw + paths.tim curves.tmw - circles.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ - circles.tmw +polygons.o: loader.tim pspglb.tim creatnew.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tmw - patterns.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ - circles.tim patterns.tmw +rectangs.o: loader.tim pspglb.tim creatnew.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.tmw - solids.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ - circles.tim patterns.tim solids.tmw +ellipses.o: loader.tim pspglb.tim creatnew.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.tim ellipses.tmw - solfaced.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ - circles.tim patterns.tim solids.tim solfaced.tmw +circles.o: loader.tim pspglb.tim creatnew.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ + circles.tmw - cuboid.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ - circles.tim patterns.tim solids.tim solfaced.tim cuboid.tmw +patterns.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ + circles.tim patterns.tmw - polyhed.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ - circles.tim patterns.tim solids.tim solfaced.tim cuboid.tim \ - polyhed.tmw +solids.o: loader.tim pspglb.tim creatnew.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ + circles.tim patterns.tim solids.tmw - utility.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ - circles.tim patterns.tim solids.tim solfaced.tim cuboid.tim \ - polyhed.tim utility.tmw +solfaced.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ + circles.tim patterns.tim solids.tim solfaced.tmw - parser.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ - circles.tim patterns.tim solids.tim solfaced.tim cuboid.tim \ - polyhed.tim utility.tim parser.tmw +cuboid.o: loader.tim pspglb.tim creatnew.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ + circles.tim patterns.tim solids.tim solfaced.tim cuboid.tmw - examples.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ - circles.tim patterns.tim solids.tim solfaced.tim cuboid.tim \ - polyhed.tim utility.tim parser.tim examples.tmw +polyhed.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ + circles.tim patterns.tim solids.tim solfaced.tim cuboid.tim \ + polyhed.tmw - main.o: $(3dldf_header_timers) main.tmw +utility.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ + circles.tim patterns.tim solids.tim solfaced.tim cuboid.tim \ + polyhed.tim utility.tmw +parser.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ + circles.tim patterns.tim solids.tim solfaced.tim cuboid.tim \ + polyhed.tim utility.tim parser.tmw + +examples.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ + circles.tim patterns.tim solids.tim solfaced.tim cuboid.tim \ + polyhed.tim utility.tim parser.tim examples.tmw + +main.o: $(3dldf_header_timers) main.tmw # ### Commented-out. Currently, main.web is the only CWEB file that # ### doesn't create a header. If I add any others, I can comment this @@ -268,6 +277,10 @@ @echo "$@ doesn't exist. Calling tsthdweb $*" $(SHELL) $(srcdir)/tsthdweb $* 0 $(CTANGLE) + + + + ## The "run" target and its prerequisites are for generating the ## PostScript file containing the drawings. LDF 2003.11.11. @@ -282,9 +295,16 @@ @echo "Running TeX on 3DLDFtex.tex to create 3DLDFtex.dvi." tex 3DLDFtex +.PHONY : mp +mp : 3DLDFmp.mp + 3DLDFmp.mp: 3DLDFput.mp @echo "Running Metapost on 3DLDFmp to create EPS files." mpost 3DLDFmp + touch 3DLDFmp.mp + +.PHONY : ldf +ldf : 3DLDFput.mp 3DLDFput.mp : 3dldf @echo "Running 3dldf to create 3DLDFput.mp." @@ -295,7 +315,13 @@ ## _3DLDF: The Program_ in PostScript format. There's an implicit target ## for the .dvi files. LDF 2003.11.11. + +.PHONY : pdf +pdf: 3DLDFprg.pdf +3DLDFprg.pdf: 3DLDFprg.ps + @echo Running \"ps2pdf 3DLDFprg.ps\" + ps2pdf 3DLDFprg.ps .PHONY : ps ps: 3DLDFprg.ps @@ -338,6 +364,12 @@ @echo "Regenerating the tags table for the CWEB files." etags 3DLDFprg.web $(3dldf_CWEBS) +.PHONY: show +show: + echo "3dldf_OBJECTS == $(3dldf_OBJECTS)" + echo "CXXFLAGS == $(CXXFLAGS)" + echo "AM_CXXFLAGS == $(AM_CXXFLAGS)" + ## Local Variables: ## mode:Makefile ## End: diff -Naur 3DLDF-1.1.4/CWEB/Makefile.in 3DLDF-1.1.5.1/CWEB/Makefile.in --- 3DLDF-1.1.4/CWEB/Makefile.in 2003-12-10 18:41:52.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/Makefile.in 2004-01-16 19:18:51.000000000 +0100 @@ -14,11 +14,11 @@ @SET_MAKE@ -#### 3DLDF-1.1.4/CWEB/Makefile.am +#### 3DLDF-1.1.5.1/CWEB/Makefile.am #### Created by Laurence D. Finston (LDF). # This file is part of 3DLDF, a package for three-dimensional drawing. -# Copyright (C) 2003 Laurence D. Finston. +# Copyright (C) 2003, 2004 Laurence D. Finston. # 3DLDF is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by @@ -44,7 +44,7 @@ # lfinsto1@gwdg.de # s246794@stud.uni-goettingen.de -# $Id: Makefile.am,v 1.16 2003/12/10 15:05:15 lfinsto1 Exp $ +# $Id: Makefile.am,v 1.26 2004/01/16 18:18:00 lfinsto1 Exp $ srcdir = @srcdir@ top_srcdir = @top_srcdir@ @@ -143,7 +143,8 @@ bin_PROGRAMS = 3dldf -3dldf_SOME_CWEBS = pspglb.web io.web colors.web transfor.web shapes.web \ +3dldf_SOME_CWEBS = loader.web pspglb.web creatnew.web gsltmplt.web io.web colors.web \ + transfor.web shapes.web \ pictures.web points.web lines.web planes.web paths.web \ curves.web polygons.web rectangs.web ellipses.web \ circles.web patterns.web solids.web solfaced.web \ @@ -157,19 +158,24 @@ nodist_3dldf_SOURCES = $(3dldf_SOME_CWEBS:.web=.cxx) main.cxx 3dldf_c_files = $(nodist_3dldf_SOURCES:.cxx=.c) -3dldf_CWEBS := $(3dldf_SOME_CWEBS) main.web loader.web +3dldf_CWEBS := $(3dldf_SOME_CWEBS) main.web EXTRA_DIST = .rcsfreeze.log .rcsfreeze.log.dev $(3dldf_CWEBS) \ - 3DLDFprg.dvi 3DLDFprg.mac \ + 3DLDFprg.dvi 3DLDFprg.mac 3DLDFprg.pdf \ 3DLDFprg.ps 3DLDFprg.web 3DLDFmp.mp \ - 3DLDFtex.bas 3DLDFtex.tex ChangeLog.dev cwebmac.tex \ - fdl.tex gpl.tex stamp-h.in \ + 3DLDFtex.bas 3DLDFtex.tex ChangeLog.dev cnepspng.el \ + cwebmac.tex examples.mp exampman.web fdl.tex gpl.tex stamp-h.in \ tsthdweb # stamp-h1 stamp-h. Removed from EXTRA_DIST. I don't think they're needed # LDF 2003.11.25. +# -frepo is needed because I'm now using template functions. +# LDF 2003.12.31. +AM_CXXFLAGS = -frepo + + # This is needed, because 3dldf fails with a "Segmentation fault", if # the executable is linked using $(3dldf_OBJECTS). This may cause # problems, if 3dldf isn't built using the GNU C++ compiler (GCC). @@ -177,7 +183,7 @@ cuboid.o solfaced.o solids.o patterns.o circles.o \ ellipses.o rectangs.o polygons.o curves.o paths.o \ planes.o lines.o points.o pictures.o shapes.o transfor.o \ - colors.o io.o pspglb.o + colors.o io.o pspglb.o loader.o @@ -191,11 +197,11 @@ CLEANFILES := $(3dldf_c_files) $(3dldf_mpgens) 3DLDFprg.idx 3DLDFprg.log 3DLDFprg.scn \ 3DLDFprg.toc 3DLDFput.mp 3DLDFput.tex \ 3DLDFtex.dvi 3DLDFtex.log 3DLDFtex.ps \ - Makefile loader.c \ + Makefile \ $(3dldf_headers) $(3dldf_header_timers) \ $(3dldf_cweb_timers) \ $(nodist_3dldf_SOURCES) $(3dldf_OBJECTS) \ - config.h loader.h loader.tim stamp-h stamp-h1 + config.h stamp-h stamp-h1 @@ -209,11 +215,11 @@ MAINTAINERCLEANFILES := $(3dldf_c_files) $(3dldf_mpgens) 3DLDFprg.idx 3DLDFprg.log 3DLDFprg.scn \ 3DLDFprg.toc 3DLDFput.mp 3DLDFput.tex \ 3DLDFtex.dvi 3DLDFtex.log 3DLDFtex.ps \ - Makefile loader.c \ + Makefile \ $(3dldf_headers) $(3dldf_header_timers) \ $(3dldf_cweb_timers) \ $(nodist_3dldf_SOURCES) $(3dldf_OBJECTS) \ - config.h loader.h loader.tim stamp-h stamp-h1 \ + config.h stamp-h stamp-h1 \ 3DLDFprg.dvi 3DLDFprg.ps subdir = CWEB @@ -223,7 +229,8 @@ bin_PROGRAMS = 3dldf$(EXEEXT) PROGRAMS = $(bin_PROGRAMS) -am__objects_1 = pspglb.$(OBJEXT) io.$(OBJEXT) colors.$(OBJEXT) \ +am__objects_1 = loader.$(OBJEXT) pspglb.$(OBJEXT) creatnew.$(OBJEXT) \ + gsltmplt.$(OBJEXT) io.$(OBJEXT) colors.$(OBJEXT) \ transfor.$(OBJEXT) shapes.$(OBJEXT) pictures.$(OBJEXT) \ points.$(OBJEXT) lines.$(OBJEXT) planes.$(OBJEXT) \ paths.$(OBJEXT) curves.$(OBJEXT) polygons.$(OBJEXT) \ @@ -241,17 +248,19 @@ depcomp = $(SHELL) $(top_srcdir)/depcomp am__depfiles_maybe = depfiles @AMDEP_TRUE@DEP_FILES = ./$(DEPDIR)/circles.Po ./$(DEPDIR)/colors.Po \ -@AMDEP_TRUE@ ./$(DEPDIR)/cuboid.Po ./$(DEPDIR)/curves.Po \ -@AMDEP_TRUE@ ./$(DEPDIR)/ellipses.Po ./$(DEPDIR)/examples.Po \ +@AMDEP_TRUE@ ./$(DEPDIR)/creatnew.Po ./$(DEPDIR)/cuboid.Po \ +@AMDEP_TRUE@ ./$(DEPDIR)/curves.Po ./$(DEPDIR)/ellipses.Po \ +@AMDEP_TRUE@ ./$(DEPDIR)/examples.Po ./$(DEPDIR)/gsltmplt.Po \ @AMDEP_TRUE@ ./$(DEPDIR)/io.Po ./$(DEPDIR)/lines.Po \ -@AMDEP_TRUE@ ./$(DEPDIR)/main.Po ./$(DEPDIR)/parser.Po \ -@AMDEP_TRUE@ ./$(DEPDIR)/paths.Po ./$(DEPDIR)/patterns.Po \ -@AMDEP_TRUE@ ./$(DEPDIR)/pictures.Po ./$(DEPDIR)/planes.Po \ -@AMDEP_TRUE@ ./$(DEPDIR)/points.Po ./$(DEPDIR)/polygons.Po \ -@AMDEP_TRUE@ ./$(DEPDIR)/polyhed.Po ./$(DEPDIR)/pspglb.Po \ -@AMDEP_TRUE@ ./$(DEPDIR)/rectangs.Po ./$(DEPDIR)/shapes.Po \ -@AMDEP_TRUE@ ./$(DEPDIR)/solfaced.Po ./$(DEPDIR)/solids.Po \ -@AMDEP_TRUE@ ./$(DEPDIR)/transfor.Po ./$(DEPDIR)/utility.Po +@AMDEP_TRUE@ ./$(DEPDIR)/loader.Po ./$(DEPDIR)/main.Po \ +@AMDEP_TRUE@ ./$(DEPDIR)/parser.Po ./$(DEPDIR)/paths.Po \ +@AMDEP_TRUE@ ./$(DEPDIR)/patterns.Po ./$(DEPDIR)/pictures.Po \ +@AMDEP_TRUE@ ./$(DEPDIR)/planes.Po ./$(DEPDIR)/points.Po \ +@AMDEP_TRUE@ ./$(DEPDIR)/polygons.Po ./$(DEPDIR)/polyhed.Po \ +@AMDEP_TRUE@ ./$(DEPDIR)/pspglb.Po ./$(DEPDIR)/rectangs.Po \ +@AMDEP_TRUE@ ./$(DEPDIR)/shapes.Po ./$(DEPDIR)/solfaced.Po \ +@AMDEP_TRUE@ ./$(DEPDIR)/solids.Po ./$(DEPDIR)/transfor.Po \ +@AMDEP_TRUE@ ./$(DEPDIR)/utility.Po CXXCOMPILE = $(CXX) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) \ $(AM_CPPFLAGS) $(CPPFLAGS) $(AM_CXXFLAGS) $(CXXFLAGS) CXXLD = $(CXX) @@ -324,12 +333,15 @@ @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/circles.Po@am__quote@ @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/colors.Po@am__quote@ +@AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/creatnew.Po@am__quote@ @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/cuboid.Po@am__quote@ @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/curves.Po@am__quote@ @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/ellipses.Po@am__quote@ @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/examples.Po@am__quote@ +@AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/gsltmplt.Po@am__quote@ @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/io.Po@am__quote@ @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/lines.Po@am__quote@ +@AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/loader.Po@am__quote@ @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/main.Po@am__quote@ @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/parser.Po@am__quote@ @AMDEP_TRUE@@am__include@ @am__quote@./$(DEPDIR)/paths.Po@am__quote@ @@ -540,110 +552,112 @@ dummy: @echo "dummy in CWEB/Makefile.am." -3dldf: loader.tim $(3dldf_OBJECTS) +.PHONY : cpl +cpl: 3dldf + +3dldf: $(3dldf_OBJECTS) -rm -f -r 3dldf @echo "Linking 3dldf" $(CXXLINK) $(3dldf_OBS_REVERSED) -loader.tim: loader.h +loader.o: loader.tmw -loader.h: loader.web - @echo "ctangling loader.web." - $(CTANGLE) loader.web - $(SHELL) $(srcdir)/tsthdweb loader 2 $(CTANGLE) +pspglb.o: loader.tim pspglb.tmw - pspglb.o: loader.tim pspglb.tmw +creatnew.o: loader.tim pspglb.tim creatnew.tmw - io.o: loader.tim pspglb.tim io.tmw +gsltmplt.o: loader.tim pspglb.tim gsltmplt.tmw - colors.o: loader.tim pspglb.tim io.tim colors.tmw +io.o: loader.tim pspglb.tim io.tmw - transfor.o: loader.tim pspglb.tim io.tim colors.tim transfor.tmw +colors.o: loader.tim pspglb.tim creatnew.tim io.tim colors.tmw - shapes.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim shapes.tmw +transfor.o: loader.tim pspglb.tim io.tim colors.tim transfor.tmw - pictures.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tmw +shapes.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim shapes.tmw - points.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tmw +pictures.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tmw - lines.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tmw +points.o: loader.tim pspglb.tim creatnew.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tmw - planes.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tmw +lines.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tmw - paths.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tmw +planes.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tmw - curves.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tmw +paths.o: loader.tim pspglb.tim creatnew.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tmw - polygons.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ +curves.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tmw + paths.tim curves.tmw - rectangs.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.tmw +polygons.o: loader.tim pspglb.tim creatnew.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tmw - ellipses.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.tim ellipses.tmw +rectangs.o: loader.tim pspglb.tim creatnew.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.tmw - circles.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ - circles.tmw +ellipses.o: loader.tim pspglb.tim creatnew.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.tim ellipses.tmw - patterns.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ - circles.tim patterns.tmw +circles.o: loader.tim pspglb.tim creatnew.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ + circles.tmw - solids.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ - circles.tim patterns.tim solids.tmw +patterns.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ + circles.tim patterns.tmw - solfaced.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ - circles.tim patterns.tim solids.tim solfaced.tmw +solids.o: loader.tim pspglb.tim creatnew.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ + circles.tim patterns.tim solids.tmw - cuboid.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ - circles.tim patterns.tim solids.tim solfaced.tim cuboid.tmw +solfaced.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ + circles.tim patterns.tim solids.tim solfaced.tmw - polyhed.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ - circles.tim patterns.tim solids.tim solfaced.tim cuboid.tim \ - polyhed.tmw +cuboid.o: loader.tim pspglb.tim creatnew.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ + circles.tim patterns.tim solids.tim solfaced.tim cuboid.tmw - utility.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ - circles.tim patterns.tim solids.tim solfaced.tim cuboid.tim \ - polyhed.tim utility.tmw +polyhed.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ + circles.tim patterns.tim solids.tim solfaced.tim cuboid.tim \ + polyhed.tmw - parser.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ - circles.tim patterns.tim solids.tim solfaced.tim cuboid.tim \ - polyhed.tim utility.tim parser.tmw +utility.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ + circles.tim patterns.tim solids.tim solfaced.tim cuboid.tim \ + polyhed.tim utility.tmw - examples.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ - circles.tim patterns.tim solids.tim solfaced.tim cuboid.tim \ - polyhed.tim utility.tim parser.tim examples.tmw +parser.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ + circles.tim patterns.tim solids.tim solfaced.tim cuboid.tim \ + polyhed.tim utility.tim parser.tmw + +examples.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.tim ellipses.tim \ + circles.tim patterns.tim solids.tim solfaced.tim cuboid.tim \ + polyhed.tim utility.tim parser.tim examples.tmw - main.o: $(3dldf_header_timers) main.tmw +main.o: $(3dldf_header_timers) main.tmw # ### Commented-out. Currently, main.web is the only CWEB file that # ### doesn't create a header. If I add any others, I can comment this @@ -700,14 +714,28 @@ @echo "Running TeX on 3DLDFtex.tex to create 3DLDFtex.dvi." tex 3DLDFtex +.PHONY : mp +mp : 3DLDFmp.mp + 3DLDFmp.mp: 3DLDFput.mp @echo "Running Metapost on 3DLDFmp to create EPS files." mpost 3DLDFmp + touch 3DLDFmp.mp + +.PHONY : ldf +ldf : 3DLDFput.mp 3DLDFput.mp : 3dldf @echo "Running 3dldf to create 3DLDFput.mp." 3dldf +.PHONY : pdf +pdf: 3DLDFprg.pdf + +3DLDFprg.pdf: 3DLDFprg.ps + @echo Running \"ps2pdf 3DLDFprg.ps\" + ps2pdf 3DLDFprg.ps + .PHONY : ps ps: 3DLDFprg.ps @@ -746,6 +774,12 @@ TAGS : 3DLDFprg.web $(3dldf_CWEBS) @echo "Regenerating the tags table for the CWEB files." etags 3DLDFprg.web $(3dldf_CWEBS) + +.PHONY: show +show: + echo "3dldf_OBJECTS == $(3dldf_OBJECTS)" + echo "CXXFLAGS == $(CXXFLAGS)" + echo "AM_CXXFLAGS == $(AM_CXXFLAGS)" # Tell versions [3.59,3.63) of GNU make to not export all variables. # Otherwise a system limit (for SysV at least) may be exceeded. .NOEXPORT: diff -Naur 3DLDF-1.1.4/CWEB/circles.web 3DLDF-1.1.5.1/CWEB/circles.web --- 3DLDF-1.1.4/CWEB/circles.web 2003-12-10 16:09:04.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/circles.web 2004-01-12 22:27:22.000000000 +0100 @@ -3,7 +3,7 @@ @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -52,8 +52,6 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: circles.web,v 1.4 2003/12/10 15:09:04 lfinsto1 Exp $ @> - @q * Circle.@> @** Circle\quad ({\tt circles\PERIOD web}).\hfil It won't be possible to make circles recede to the @@ -71,13 +69,14 @@ @f Circle Shape @= static string rcs_id - = "$Id: circles.web,v 1.4 2003/12/10 15:09:04 lfinsto1 Exp $"; + = "$Id: circles.web,v 1.8 2004/01/12 21:27:22 lfinsto1 Exp $"; @q * Include files.@> @* Include files. @= #include "loader.h" #include "pspglb.h" +#include "creatnew.h" #include "io.h" #include "colors.h" #include "transfor.h" @@ -188,56 +187,48 @@ @q * Pseudo-constructor for dynamic allocation.@> @* Pseudo-constructor for dynamic allocation. -@q ** Optional pointer argument.@> -@*1 Optional pointer argument. +@q ** Pointer argument.@> +@*1 Pointer argument. @^\cfunc{Circle}{create\_new\_circle}@> \LOG -\initials{LDF 2003.07.27.} Made non-inline. Made argument |p| |const Circle*|. +\initials{LDF 2003.07.27.} Made non-inline. +Made argument |p| |const Circle*|. \initials{LDF 2003.08.10.} Removed redefinition of the default argument |const Circle* p = 0| from the definition. The DEC compiler complained, but GCC didn't. -\ENDLOG -@= -static -Circle* -create_new_circle(const Circle* p = 0); -@ -@= -Circle* -Circle::create_new_circle(const Circle* p) -{ - Circle* c = new(Circle); - if (p != 0) - *c = *p; - c->on_free_store = true; - c->cycle_switch = true; - c->line_switch = false; - return c; -} +\initials{LDF 2003.12.30.} Replaced |Circle::create_new_circle()| +with a specialization of |template C* create_new()| for +|Circle|. + +\initials{LDF 2003.12.30.} Changed the argument. It's now a +|const Circle*|. + +\initials{LDF 2003.12.30.} Removed default argument ``0'', because +this caused a compiler error when using the DEC \CPLUSPLUS/ compiler. +Apparently, it suffices to declare a default argument in the template +declaration. +\ENDLOG +@= +Circle* +create_new(const Circle* c); -@q ** Required Circle argument.@> -@*1 Required {\bf Circle} argument. -@^\cfunc{Circle}{create\_new\_circle}@> +@q ** Reference argument.@> +@*1 Reference argument. \LOG \initials{LDF 2003.07.27.} Made non-inline. -\ENDLOG -@= -static -Circle* -create_new_circle(const Circle& p); -@ -@= -Circle* -Circle::create_new_circle(const Circle& p) -{ - Circle* c = new(Circle); - *c = p; - c->on_free_store = true; - return c; -} +\initials{LDF 2003.12.30.} Replaced |Circle::create_new_circle()| +with a specialization of |template C* create_new()| for +|Circle|. + +\initials{LDF 2003.12.30.} Changed argument from |Circle| to |const Circle&|. +\ENDLOG +@= +Circle* +create_new(const Circle& c); + @q * Destructor. @> @* Destructor. @@ -960,11 +951,14 @@ @@; @@; @@; +@@; @ This is what's written to \filename{circles.h}. @(circles.h@>= @@; +@@; + + - - \ No newline at end of file + diff -Naur 3DLDF-1.1.4/CWEB/cnepspng.el 3DLDF-1.1.5.1/CWEB/cnepspng.el --- 3DLDF-1.1.4/CWEB/cnepspng.el 1970-01-01 01:00:00.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/cnepspng.el 2004-01-12 22:27:29.000000000 +0100 @@ -0,0 +1,180 @@ +;;;; cnepspng.el +;;;; Created LDF 2003.12.16. + +;;;; This file is part of 3DLDF, a package for three-dimensional drawing. +;;;; Copyright (C) 2003, 2004 Laurence D. Finston. + +;;;; 3DLDF is free software; you can redistribute it and/or modify +;;;; it under the terms of the GNU General Public License as published by +;;;; the Free Software Foundation; either version 2 of the License, or +;;;; (at your option) any later version. + +;;;; 3DLDF is distributed in the hope that it will be useful, +;;;; but WITHOUT ANY WARRANTY; without even the implied warranty of +;;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +;;;; GNU General Public License for more details. + +;;;; You should have received a copy of the GNU General Public License +;;;; along with 3DLDF; if not, write to the Free Software +;;;; Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + +;;;; 3DLDF is a GNU package. +;;;; It is part of the GNU Project of the +;;;; Free Software Foundation +;;;; and is published under the GNU General Public License. +;;;; See the website http://www.gnu.org +;;;; for more information. +;;;; 3DLDF is available for downloading from +;;;; http://www.gnu.org/3DLDF. +;;;; It is also available from +;;;; http://www.dante.de/software/ctan/, the Dante www-server +;;;; and from http://wwwuser.gwdg.de/~lfinsto1, +;;;; the author's website. + +;;;; Please send bug reports to bug-3DLDF@gnu.org +;;;; The mailing list help-3DLDF@gnu.org is available for people to +;;;; ask other users for help. +;;;; The mailing list info-3DLDF@gnu.org is for sending +;;;; announcements to users. To subscribe to these mailing lists, send an +;;;; email with ``subscribe '' as the subject. + +;;;; The author can be contacted at: + +;;;; Laurence D. Finston +;;;; Kreuzbergring 41 +;;;; D-37075 Goettingen +;;;; Germany + +;;;; lfinsto1@gwdg.de +;;;; s246794@stud.uni-goettingen.de + + +;; (local-set-key [C-kp-begin] 'convert-eps) +;; (local-set-key [C-kp-right] 'convert-eps-loop) + +(defun convert-eps (filename do-not-delete-files) + "convert-eps converts an Encapsulated PostScript (EPS) file to a +structured PostScript (PS) file and a Portable Network Graphics (PNG) file. +It is used for converting the EPS files generated by MetaPost to PS and PNG files +of the same size and shape and using the same fonts. This function is needed +because the Computer Modern fonts are not used when `prologues' is set to 1 +in the MetaPost file. + +If called interactively, convert-eps prompts for a filename with +its extension. + +If do-not-delete-files is nil, the .tex, .dvi, and .log files +will be deleted. This is the case when convert-eps is called +interactively with no prefix argument. +If convert-eps is called interactively with a prefix +argument, or non-interactively with a non-nil +do-not-delete-files argument, these files will not be deleted." + + (interactive "fEnter a filename or type to convert this file: +P") + + (let (tex-filename dvi-filename log-filename ps-filename png-filename) + + (setq filename (file-name-nondirectory filename)) + + (setq tex-filename (concat filename "_.tex")) + (setq dvi-filename (concat filename "_.dvi")) + (setq log-filename (concat filename "_.log")) + (setq ps-filename (concat filename ".ps")) + (setq png-filename (concat filename ".png")) + + (find-file-other-window tex-filename) + (erase-buffer) + (insert (concat "\\advance\\voffset by -1in +\\advance\\hoffset by -1in +\\nopagenumbers +\\input epsf +\\epsfverbosetrue +\\def\\epsfsize#1#2{#1}\n\n +\\setbox0=\\vbox{\\epsffile{" filename "}} +\\vsize=\\ht0 +\\hsize=\\wd0 +\\special{papersize=\\the\\wd0,\\the\\ht0} +\\box0\n\\bye\n")) + + (save-buffer) + (kill-buffer nil) + (shell-command (concat "clear && tex " tex-filename + " && dvips -o " ps-filename " " dvi-filename + " && convert " ps-filename " " png-filename)) + + (if do-not-delete-files + (progn + (message "Not deleting generated files") + ) + ;; else + (progn + (message "Deleting generated files") + (delete-file tex-filename) + (delete-file dvi-filename) + (delete-file log-filename) + ) + ) ;; if + (sit-for 2) + (message nil) + ) ;; let + ) ;; defun convert-eps + +(defun convert-eps-loop (arg start end do-not-delete-files) + "convert-eps-loop converts a set of EPS image files to the PS and PNG formats. +The files must all have the same filename, and the extensions must form a range of +positive integers. + +If called interactively, convert-eps-loop prompts for `filename' +with no extension, and the starting and ending numbers of the range. + +For all integers i such that start <= i <= end, convert-eps-loop checks +whether a file named `filename.i' exists. If it does, it calls +convert-eps, passing `filename.i' as the latter's filename argument. + +do-not-delete-files is also passed to convert-eps. +If it's nil, the .tex, .dvi, and .log files will be deleted. +This is the case when convert-eps-loop is called interactively +with no prefix argument. +If convert-eps-loop is called interactively with a prefix +argument, or non-interactively with a non-nil +do-not-delete-files argument, these files will not be deleted." + + (interactive "MEnter a filename: +nStart: +nEnd: +P") + +(if (or (not (eq start (truncate start))) + (not (eq end (truncate end)))) + (progn + (message "ERROR! start or end isn't an integer!") + (sit-for 2) + ) ;; then progn + ;; else + (progn + (message (concat "Start: " (number-to-string start))) + (sit-for 1) + (message (concat "End: " (number-to-string end))) + (while (<= start end) + (setq filename (concat arg "." (number-to-string start))) + (if (file-exists-p filename) + (convert-eps filename do-not-delete-files) + ;; else + (progn + (message (concat filename " doesn't exist")) + (sit-for 1) + (message nil) + ) ;; else progn + ) + (setq start (1+ start)) + );; while + ) ;; else progn + ) ;; if +) ;; defun convert-eps-loop + + + + + + diff -Naur 3DLDF-1.1.4/CWEB/colors.web 3DLDF-1.1.5.1/CWEB/colors.web --- 3DLDF-1.1.4/CWEB/colors.web 2003-12-10 16:22:33.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/colors.web 2004-01-12 22:27:38.000000000 +0100 @@ -1,9 +1,9 @@ @q colors.web @> - + @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -52,8 +52,6 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: colors.web,v 1.2 2003/12/10 15:22:33 lfinsto1 Exp $ @> - @q * Color.@> @** Color\quad ({\tt colors\PERIOD web}).\hfil \LOG @@ -68,13 +66,14 @@ \ENDLOG @= static string rcs_id - = "$Id: colors.web,v 1.2 2003/12/10 15:22:33 lfinsto1 Exp $"; + = "$Id: colors.web,v 1.7 2004/01/12 21:27:38 lfinsto1 Exp $"; @q * Include files.@> @* Include files. @= #include "loader.h" #include "pspglb.h" +#include "creatnew.h" #include "io.h" @q * Color class definition.@> @@ -82,12 +81,16 @@ \initials{LDF 2002.09.25.} @:!!@> !! Remember to change the constructors, setting functions, and assignment operator if I add or change anything here!! + +\LOG +\initials{LDF 2002.10.06.} Added. |on_free_store|. +\ENDLOG @= class Color { string name; bool use_name; - bool on_free_store; /* LDF 2002.10.06. Added. */ + bool on_free_store; real red_part; real green_part; real blue_part; @@ -350,24 +353,27 @@ @q * Pseudo-constructor for dynamic allocation. @> @* Pseudo-constructor for dynamic allocation. -@^\cfunc{Color}{create\_new\_color}@> -@= -inline -static +\LOG +\initials{LDF 2003.12.30.} Replaced |Color::create_new_color()| with +specializations of |template C* create_new()|. +\ENDLOG + +@q ** Pointer argument. @> +@*1 Pointer argument. +@= Color* -create_new_color() -{ - bool DEBUG = false; /* |true| */ - if (DEBUG) - cout << "Entering Color::create_new_color().\n"; - Color* c = new(Color); - c->on_free_store = true; - if (DEBUG) - cout << "Exiting Color::create_new_color().\n"; - return c; -} +create_new(const Color* c); +@q ** Reference argument. @> +@*1 Reference argument. +\LOG +\initials{LDF 2004.1.2.} Added this declaration. +\ENDLOG +@= +Color* +create_new(const Color& c); + @q * Assignment.@> @* Assignment. @@ -432,6 +438,27 @@ @q * Modifying.@> @* Modifying. +@q ** Set on free store.@> +@*1 Set on free store. +@^\cfunc{Color}{set\_on\_free\_store}@> + +\LOG +\initials{LDF 2003.12.30.} Added this function. +\ENDLOG +@= +bool +set_on_free_store(bool b = true); + +@ +@= +bool +Color::set_on_free_store(bool b) +{ + on_free_store = b; + return b; +} + + @q ** Set name.@> @*1 Set name. @^\cfunc{Color}{set\_name}@> @@ -671,10 +698,17 @@ @q ** Is on free store.@> @*1 Is on free store. @^\cfunc{Color}{is\_on\_free\_store}@> +\LOG +\initials{LDF 2004.01.06.} Made non-inline. +\ENDLOG @= -inline bool -is_on_free_store() const +is_on_free_store() const; + +@ +@= +bool +Color::is_on_free_store() const { return on_free_store; } @@ -762,11 +796,11 @@ @q * Output operator@> @* Output operator. @^\ofunc{$\ll$}@> -@= +@= ostream& operator<<(ostream& o, const Color& c); @ -@= +@= ostream& operator<<(ostream& o, const Color& c) { if (c.get_use_name() == true) @@ -1134,18 +1168,18 @@ @@; @@; @@; -@@; +@@; +@@; @@; @ This is written to \filename{colors.h}. -@:BUG FIX@> BUG FIX: The preprocessor ``|define|'' command must be -here, otherwise it's not written to the header file. Using ``|@@d|'' -above doesn't do it. @(colors.h@>= @@; @<|extern| |namespace Colors| declaration@>@; -@@; +@@; +@@; @<|extern| global constant declarations@>@; - + + diff -Naur 3DLDF-1.1.4/CWEB/creatnew.web 3DLDF-1.1.5.1/CWEB/creatnew.web --- 3DLDF-1.1.4/CWEB/creatnew.web 1970-01-01 01:00:00.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/creatnew.web 2004-01-12 22:27:44.000000000 +0100 @@ -0,0 +1,153 @@ +@q creatnew.web @> + +@q * Copyright and License.@> + +@q This file is part of 3DLDF, a package for three-dimensional drawing. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> + +@q 3DLDF is free software; you can redistribute it and/or modify @> +@q it under the terms of the GNU General Public License as published by @> +@q the Free Software Foundation; either version 2 of the License, or @> +@q (at your option) any later version. @> + +@q 3DLDF is distributed in the hope that it will be useful, @> +@q but WITHOUT ANY WARRANTY; without even the implied warranty of @> +@q MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the @> +@q GNU General Public License for more details. @> + +@q You should have received a copy of the GNU General Public License @> +@q along with 3DLDF; if not, write to the Free Software @> +@q Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA @> + +@q 3DLDF is a GNU package. @> +@q It is part of the GNU Project of the @> +@q Free Software Foundation @> +@q and is published under the GNU General Public License. @> +@q See the website http://www.gnu.org @> +@q for more information. @> +@q 3DLDF is available for downloading from @> +@q http://www.gnu.org/3DLDF. @> +@q It is also available from @> +@q http://www.dante.de/software/ctan/, the Dante www-server @> +@q and from http://wwwuser.gwdg.de/~lfinsto1, @> +@q the author's website. @> + +@q (``@@'' stands for a single at-sign in the following paragraph.) @> + +@q Please send bug reports to bug-3DLDF@@gnu.org @> +@q The mailing list help-3DLDF@@gnu.org is available for people to @> +@q ask other users for help. @> +@q The mailing list info-3DLDF@@gnu.org is for sending @> +@q announcements to users. To subscribe to these mailing lists, send an @> +@q email with ``subscribe '' as the subject. @> + +@q The author can be contacted at: @> + +@q Laurence D. Finston @> +@q Kreuzbergring 41 @> +@q D-37075 Goettingen @> +@q Germany @> + +@q lfinsto1@@gwdg.de (@@ stands for a single ``at'' sign.)@> +@q s246794@@stud.uni-goettingen.de @> + + +@q * Dynamic allocation for |Shapes|.@> +@** Dynamic allocation for {\bf Shapes}. +\LOG +\initials{LDF 2003.12.29.} Added this template function. + +\initials{LDF 2004.1.2.} Moved the code in this file from +\filename{pspglb.web} to \filename{creatnew.web}. +\ENDLOG + +@= +static string rcs_id + = "$Id: creatnew.web,v 1.4 2004/01/12 21:27:44 lfinsto1 Exp $"; + +@q * Include files.@> +@* Include files. +@= +#include "loader.h" +#include "pspglb.h" + +@q * Dynamic allocation for |Shapes|.@> +@* Dynamic allocation for {\bf Shapes}. + + +@q ** Pointer argument.@> +@*1 Pointer argument.@> +@= +template +C* +create_new(const C* arg); + +@ +@= +template +C* +create_new(const C* arg) +{ + + C* obj = new(C); + obj->set_on_free_store(); + if (arg != 0) + *obj = *arg; + return obj; +} + + +@q ** Reference argument.@> +@*1 Reference argument.@> +@= +template +C* +create_new(const C& arg); + +@ +@= +template +C* +create_new(const C& arg) +{ + C* obj = new(C); + obj->set_on_free_store(); + *obj = arg; + return obj; +} + +@q * Putting creatnew together.@> +@* Putting {\tt creatnew} together. + +@q ** This is what's compiled.@> +@ This is what's compiled. +I don't really need to compile the definition of |create_new()| here, +because it must be included in all of the files that instantiate it, +anyway. However, that may become unnecessary later, in which case it +will have to be compiled here. In addition, if there's something +wrong with the definition, it may be helpful to catch the error here. +\initials{LDF 2004.1.2.} +@c +@@; +@@; +@@; + +@q ** This is what's written to \filename{creatnew.h}.@> +@ This is what's written to the \filename{creatnew.h}. +The file \filename{creatnew.h} must be included by all files that +define specializations of |create_new()|. +\initials{LDF 2003.12.29.} +@(creatnew.h@>= +@@; + + + +@q Local Variables: @> +@q mode:CWEB @> +@q eval:(display-time) @> +@q run-cweb-on-file:"3DLDF.web" @> +@q eval:(read-abbrev-file) @> +@q indent-tabs-mode:nil @> +@q eval:(outline-minor-mode) @> +@q End: @> + diff -Naur 3DLDF-1.1.4/CWEB/cuboid.web 3DLDF-1.1.5.1/CWEB/cuboid.web --- 3DLDF-1.1.4/CWEB/cuboid.web 2003-12-10 16:26:05.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/cuboid.web 2004-01-12 22:27:52.000000000 +0100 @@ -3,7 +3,7 @@ @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -52,8 +52,6 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: cuboid.web,v 1.2 2003/12/10 15:26:04 lfinsto1 Exp $ @> - @q * Cuboid.@> @** Cuboid\quad ({\tt cuboid\PERIOD web}).\hfil @@ -91,7 +89,7 @@ @f Cuboid Solid @= static string rcs_id - = "$Id: cuboid.web,v 1.2 2003/12/10 15:26:04 lfinsto1 Exp $"; + = "$Id: cuboid.web,v 1.6 2004/01/12 21:27:51 lfinsto1 Exp $"; @q * Include files.@> @@ -99,6 +97,7 @@ @= #include "loader.h" #include "pspglb.h" +#include "creatnew.h" #include "io.h" #include "colors.h" #include "transfor.h" @@ -182,7 +181,7 @@ iter != c.rectangles.end(); iter++) { - rectangles.push_back(Rectangle::create_new_rectangle()); + rectangles.push_back(create_new(0)); *(rectangles.back()) = **iter; } } @@ -225,8 +224,8 @@ for (int i = 0; i < 6; i++) { - rectangles.push_back(Rectangle::create_new_rectangle()); - } + rectangles.push_back(create_new(0)); + } rectangles[0]->set(pts[1], pts[2], pts[3], pts[4]); /* front */ rectangles[1]->set(pts[5], pts[6], pts[7], pts[8]); /* back */ @@ -243,30 +242,34 @@ pts[i].dotlabel(i); } - - @q * Pseudo-constructor for dynamic allocation.@> @* Pseudo-constructor for dynamic allocation. -@^\cfunc{Cuboid}{create\_new\_cuboid}@> +@q ** Pointer argument.@> +@*1 Pointer argument. + +\LOG \initials{LDF 2002.04.22.} Added this function. -@= -static -Cuboid* -create_new_cuboid(const Cuboid* c = 0); -@ -@= -Cuboid* -Cuboid::create_new_cuboid(const Cuboid* c) -{ - Cuboid* q = new(Cuboid); - if (c != 0) - *q = *c; - q->on_free_store = true; - q->do_output = true; - q->projective_extremes.resize(6, 0); - return q; -} +\initials{LDF 2003.12.30.} Replaced |Cuboid::create_new_cuboid()| +with a specialization of |template C* create_new()| for +|Cuboid|. The argument is now |const|. +\ENDLOG + + +@= +Cuboid* +create_new(const Cuboid* c); + +@q ** Reference argument.@> +@*1 Reference argument. +\LOG +LDF 2003.12.30. Added this function. +\ENDLOG + + +@= +Cuboid* +create_new(const Cuboid& c); @q * Destructor. @> @* Destructor. @@ -317,10 +320,12 @@ @@; @@; @@; +@@; @ This is what's written to \filename{cuboid.h}. @(cuboid.h@>= @@; +@@; diff -Naur 3DLDF-1.1.4/CWEB/curves.web 3DLDF-1.1.5.1/CWEB/curves.web --- 3DLDF-1.1.4/CWEB/curves.web 2003-12-10 16:27:57.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/curves.web 2004-01-12 22:27:59.000000000 +0100 @@ -3,7 +3,7 @@ @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -52,8 +52,6 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: curves.web,v 1.2 2003/12/10 15:27:57 lfinsto1 Exp $ @> - @q * Curves.@> @** Curves\quad ({\tt curves\PERIOD web}).\hfil @@ -71,7 +69,7 @@ @f Curve Path @= static string rcs_id - = "$Id: curves.web,v 1.2 2003/12/10 15:27:57 lfinsto1 Exp $"; + = "$Id: curves.web,v 1.5 2004/01/12 21:27:59 lfinsto1 Exp $"; @q * Include files.@> @* Include files. diff -Naur 3DLDF-1.1.4/CWEB/cwebmac.tex 3DLDF-1.1.5.1/CWEB/cwebmac.tex --- 3DLDF-1.1.4/CWEB/cwebmac.tex 2003-12-10 16:30:20.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/cwebmac.tex 2004-01-16 17:30:09.000000000 +0100 @@ -9,7 +9,7 @@ %%%% If your CWEB package contains a newer version, you can copy it, %%%% and add my changes to your copy (carefully). LDF 2003.08.25. -%% $Id: cwebmac.tex,v 1.4 2003/12/10 15:30:20 lfinsto1 Exp $ +%% $Id: cwebmac.tex,v 1.7 2004/01/16 16:30:09 lfinsto1 Exp $ % standard macros for CWEB listings (in addition to plain.tex) % Version 3.64 --- February 2002 @@ -450,16 +450,16 @@ \gtitle={\.{CWEB} output} % this running head is reset by starred sections \mark{\noexpand\nullsec0{\the\gtitle}} -\def\title{\expandafter\uppercase\expandafter{\jobname}} +\def\title{3DLDF-1.1.5.1} \def\topofcontents{\centerline{\titlefont\docname}% %% %% Beginning of new material. LDF 2003.08.25. \medskip -\centerline{\titlefont Version 1.1.4}% +\centerline{\titlefont Version 1.1.5.1}% \medskip \centerline{\titlefont by Laurence D. Finston}% \medskip -\centerline{{\rm November 2003}}% +\centerline{{\rm January 2004}}% %% End of new material. LDF 2003.08.25. %% \vskip.7in diff -Naur 3DLDF-1.1.4/CWEB/ellipses.web 3DLDF-1.1.5.1/CWEB/ellipses.web --- 3DLDF-1.1.4/CWEB/ellipses.web 2003-12-10 16:32:20.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/ellipses.web 2004-01-14 18:56:19.000000000 +0100 @@ -3,7 +3,7 @@ @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -52,8 +52,6 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: ellipses.web,v 1.2 2003/12/10 15:32:20 lfinsto1 Exp $ @> - @q * Ellipse.@> @** Ellipse\quad ({\tt ellipses\PERIOD web}).\hfil @@ -71,13 +69,14 @@ @f Ellipse Path @= static string rcs_id - = "$Id: ellipses.web,v 1.2 2003/12/10 15:32:20 lfinsto1 Exp $"; + = "$Id: ellipses.web,v 1.7 2004/01/14 17:56:19 lfinsto1 Exp $"; @q * Include files.@> @* Include files. @= #include "loader.h" #include "pspglb.h" +#include "creatnew.h" #include "io.h" #include "colors.h" #include "transfor.h" @@ -234,7 +233,8 @@ curr_angle = 2*i*PI/number_of_points; curr_x = axis_h/2 * cos(curr_angle); curr_z = axis_v/2 * sin(curr_angle); - points.push_back(Point::create_new_point(curr_x, 0, curr_z)); + points.push_back(create_new(0)); + points.back()->set(curr_x, 0, curr_z); *(points.back()) *= t; /* Rotate |*(points.back())| around the x, y, and z-axes and shift it to |center|. */ @@ -270,56 +270,34 @@ @q ** Pseudo-constructor for dynamic allocation.@> @*1 Pseudo-constructor for dynamic allocation. -@q *** Optional pointer argument.@> -@*2 Optional pointer argument. -@^\cfunc{Ellipse}{create\_new\_ellipse}@> +@q *** Pointer argument.@> +@*2 Pointer argument. \LOG \initials{LDF 2002.11.06.} Added optional |const Ellipse*| argument. -\ENDLOG -@= -static -Ellipse* -create_new_ellipse(const Ellipse* e = 0); -@ -@= -Ellipse* -Ellipse::create_new_ellipse(const Ellipse* e) -{ - Ellipse* r = new(Ellipse); - - if (e != 0) - *r = *e; +\initials{LDF 2003.12.30.} Replaced |Ellipse::create_new_ellipse()| +with a specialization of |template C* create_new()| for +|Ellipse|. +\ENDLOG +@= +Ellipse* +create_new(const Ellipse* c); - r->on_free_store = true; - return r; -} +@q *** Reference argument.@> +@*2 Reference argument. -@q *** Required Ellipse argument.@> -@*2 Required {\bf Ellipse} argument. -@^\cfunc{Ellipse}{create\_new\_ellipse}@> \LOG \initials{LDF 2002.11.06.} Added this function. -\ENDLOG -@= -static -Ellipse* -create_new_ellipse(const Ellipse& e); - -@ -@= -Ellipse* -Ellipse::create_new_ellipse(const Ellipse& e) -{ - Ellipse* r = new(Ellipse); - - *r = e; +\initials{LDF 2003.12.30.} Replaced |Ellipse::create_new_ellipse()| +with a specialization of |template C* create_new()| for +|Ellipse|. +\ENDLOG - r->on_free_store = true; - return r; -} +@= +Ellipse* +create_new(const Ellipse& c); @q * Destructor. @> @* Destructor. @@ -1295,6 +1273,21 @@ @^\cfunc{Ellipse}{intersection\_points}@> @:!! TO DO@> TO DO: Read through and explain. \initials{LDF 2002.11.06.} +The |step| argument is used in the case that the |Ellipses| +have different centers and/or axis orientation. It is the number of +degrees of rotation performed while the algorithm is searching for an +intersection. The default is 3, which should work as long as the +|Ellipses| don't differ too much in size. \initials{LDF 2004.01.12.} + +If the |verbose| argument is |true|, information about the +intersection points is printed to standard output. \initials{LDF 2003.07.01.} + +If the |Ellipses| are coplanar, the intersection points of the +perimeters of the |Ellipses| are returned. If the planes of the +|Ellipses| are perpendicular or skew, the intersection line of the +planes is found. Then, the intersection points of the this line with +the |Ellipses|, if they exist. + @:!! TO DO@> TO DO: \initials{LDF 2003.07.20.} The following code found only one intersection: @c @@ -1306,20 +1299,13 @@ bool_point_quadruple bpq = t.intersection_points(c); #endif -@ \initials{LDF 2003.07.20.} +@ When |c| was rotated by $15^\circ$ or $45^\circ$, |intersection_points()| found both intersections. Try to find out why! I want to write a |Circle| version with an |Ellipse| argument, and vice versa. If I do, I may not have to worry about this problem. +@ \initials{LDF 2003.07.20.} -If the |verbose| argument is |true|, information about the -intersection points is printed to standard output. \initials{LDF 2003.07.01.} - -If the |Ellipses| are coplanar, the intersection points of the -perimeters of the |Ellipses| are returned. If the planes of the -|Ellipses| are perpendicular or skew, the intersection line of the -planes is found. Then, the intersection points of the this line with -the |Ellipses|, if they exist. \LOG \initials{LDF 2002.04.12.} Actually, it looks as if the equations @@ -1372,19 +1358,22 @@ \initials{LDF 2003.08.14.} Setting |verbose| to |true| if |VERBOSE_GLOBAL| is |true|. Added |VERBOSE_GLOBAL| to\newline \filename{pspglb.web} today. + +\initials{LDF 2004.01.12.} Added |real step| argument, with 3 as its +default value. \ENDLOG @q *** Declaration.@> @= virtual bool_point_quadruple -intersection_points(Ellipse e, bool verbose = false) const; +intersection_points(Ellipse e, const real step = 3, bool verbose = false) const; @q *** Definition.@> @ @= bool_point_quadruple -Ellipse::intersection_points(Ellipse e, bool verbose) const +Ellipse::intersection_points(Ellipse e, const real step, bool verbose) const { bool DEBUG = false; /* |true| */ @@ -2124,7 +2113,7 @@ } /* End of ``Ellipses have the same center and axis orientation''. */ @q ***** (5) Ellipses have different centers and/or axis orientation.@> -@ Ellipses have different centers and/or axis orientation. +@ |Ellipses| have different centers and/or axis orientation. There is no simple algebraic solution for this case, so I have to implement a numerical one here. @= @@ -2152,7 +2141,7 @@ << "Searching for Ellipse intersections. " << "This can take some time...\n\n" << flush; - for (real i = 0; i < 360; i += .5) + for (real i = 0; i < 360; i += step) { if (DEBUG) cout << "i == " << i << endl << flush; @@ -3207,9 +3196,11 @@ @@; @@; @@; +@@; @ This is what's written to \filename{ellipses.h}. @(ellipses.h@>= @@; +@@; diff -Naur 3DLDF-1.1.4/CWEB/examples.mp 3DLDF-1.1.5.1/CWEB/examples.mp --- 3DLDF-1.1.4/CWEB/examples.mp 1970-01-01 01:00:00.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/examples.mp 2004-01-12 22:28:13.000000000 +0100 @@ -0,0 +1,10605 @@ +%%%% examples.mp + +%% * Copyright and License.@> + +%%% This file is part of 3DLDF, a package for three-dimensional drawing. +%%% Copyright (C) 2003, 2004 Laurence D. Finston. + +%%% 3DLDF is free software; you can redistribute it and/or modify +%%% it under the terms of the GNU General Public License as published by +%%% the Free Software Foundation; either version 2 of the License, or +%%% (at your option) any later version. + +%%% 3DLDF is distributed in the hope that it will be useful, +%%% but WITHOUT ANY WARRANTY; without even the implied warranty of +%%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +%%% GNU General Public License for more details. + +%%% You should have received a copy of the GNU General Public License +%%% along with 3DLDF; if not, write to the Free Software +%%% Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + +%%% The author can be contacted at: + +%%% Laurence D. Finston +%%% Kreuzbergring 41 +%%% D-37075 Goettingen +%%% Germany + +%%% lfinsto1@gwdg.de +%%% s246794@stud.uni-goettingen.de + + +%%%%% $Id: examples.mp,v 1.3 2004/01/12 21:28:13 lfinsto1 Exp $ + +cm := magstep3 * cm; + +verbatimtex \magnification=\magstep3 etex; + +input boxes; + +pickup pencircle scaled .25mm; + +%% LDF 2003.01.15. Added the following two lines. This sets the +%% margins of the boxes around the examples. The original default is +%% 3. +defaultdx:=.75cm; +defaultdy:=.75cm; + +%%% Color definitions. + +color yellow; yellow = (1.000000, 1.000000, 0.000000); +color cyan; cyan = (0.000000, 1.000000, 1.000000); +color magenta; magenta = (1.000000, 0.000000, 1.000000); +color orange; orange = (1.000000, 0.647059, 0.000000); +color violet; violet = (0.933333, 0.509804, 0.933333); +color purple; purple = (0.627451, 0.125490, 0.941176); +color yellow_green; yellow_green = (0.603922, 0.803922, 0.196078); +color green_yellow; green_yellow = (0.678431, 1.000000, 0.184314); +color blue_violet; blue_violet = (0.541176, 0.168627, 0.886275); +color gray; gray = (0.752941, 0.752941, 0.752941); +color light_gray; light_gray = (0.827451, 0.827451, 0.827451); +color violet_red; violet_red = (0.815686, 0.125490, 0.564706); +color default_background; default_background = (1.000000, 1.000000, 1.000000); + +%%% End of Color definitions. + +beginfig(1); +draw (0.000000cm, 0.000000cm) -- (3.000000cm, 0.000000cm) + -- (3.000000cm, 3.000000cm) -- (0.000000cm, 3.000000cm) -- cycle; +draw (0.000000cm, 0.000000cm) -- (3.000000cm, 0.000000cm) + -- (7.500000cm, 3.000000cm) -- (4.500000cm, 3.000000cm) -- cycle dashed evenly; +dotlabel.llft(btex $P_0$ = $Q_0$ = (0, 0) etex, (0.000000cm, 0.000000cm)); +dotlabel.lrt(btex $P_1$ = $Q_1$ = (3, 0) etex, (3.000000cm, 0.000000cm)); +dotlabel.ulft(btex $P_2$ = (3, 3) etex, (3.000000cm, 3.000000cm)); +dotlabel.ulft(btex $P_3$ = (0, 3) etex, (0.000000cm, 3.000000cm)); +label(btex $r$ etex, (1.500000cm, 1.500000cm)); +label(btex $q$ etex, (3.750000cm, 1.500000cm)); +dotlabel.top(btex $Q_2$ = (7.5, 3) etex, (7.500000cm, 3.000000cm)); +dotlabel.top(btex $Q_3$ = (4.5, 3) etex, (4.500000cm, 3.000000cm)); +boxit.b(currentpicture); +draw bpath b withpen pencircle scaled .25mm; +endfig; + +beginfig(2); + +drawarrow (-5.333333cm, -6.666667cm) -- (-3.200000cm, -4.000000cm) withcolor gray; +draw (-2.657473cm, -4.520526cm) .. (-3.128652cm, -3.697729cm) + .. (-3.863067cm, -3.421290cm) .. (-4.535907cm, -3.932255cm) + .. 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(-1.731345cm, -4.650055cm) .. (-2.016862cm, -4.651997cm) + .. (-2.301416cm, -4.652649cm) .. (-2.580087cm, -4.651997cm) + .. (-2.848101cm, -4.650055cm) .. (-3.101010cm, -4.646873cm) + .. (-3.334841cm, -4.642525cm) .. (-3.546226cm, -4.637115cm) + .. (-3.732480cm, -4.630762cm) .. (-3.891641cm, -4.623602cm) + .. (-4.022471cm, -4.615778cm) .. (-4.124418cm, -4.607435cm) + .. (-4.197549cm, -4.598717cm) .. (-4.242470cm, -4.589760cm) + .. (-4.260231cm, -4.580694cm) .. (-4.252227cm, -4.571633cm) + .. (-4.220110cm, -4.562682cm) .. (-4.165699cm, -4.553930cm) + .. (-4.090909cm, -4.545455cm) .. (-3.997689cm, -4.537321cm) + .. (-3.887974cm, -4.529583cm) .. (-3.763645cm, -4.522284cm) + .. (-3.626507cm, -4.515457cm) .. (-3.478268cm, -4.509129cm) + .. (-3.320530cm, -4.503321cm) .. (-3.154789cm, -4.498045cm) + .. (-2.982431cm, -4.493314cm) .. (-2.804744cm, -4.489132cm) + .. (-2.622917cm, -4.485507cm) .. (-2.438059cm, -4.482437cm) + .. (-2.251206cm, -4.479926cm) .. (-2.063332cm, -4.477973cm) + .. (-1.875361cm, -4.476580cm) .. (-1.688182cm, -4.475743cm) + .. (-1.502663cm, -4.475464cm) .. (-1.319657cm, -4.475743cm) + .. (-1.140021cm, -4.476580cm) .. (-0.964621cm, -4.477973cm) + .. (-0.794351cm, -4.479926cm) .. (-0.630137cm, -4.482437cm) + .. (-0.472951cm, -4.485507cm) .. (-0.323819cm, -4.489132cm) + .. (-0.183827cm, -4.493314cm) .. (-0.054129cm, -4.498045cm) + .. (0.064050cm, -4.503320cm) .. (0.169416cm, -4.509129cm) + .. (0.260604cm, -4.515457cm) .. (0.336191cm, -4.522284cm) + .. (0.394707cm, -4.529583cm) .. (0.434656cm, -4.537321cm) .. cycle; +draw (0.454545cm, -4.545455cm) .. (0.434656cm, -4.537321cm) + .. (0.394707cm, -4.529583cm) .. (0.336191cm, -4.522284cm) + .. (0.260604cm, -4.515457cm) .. (0.169416cm, -4.509129cm) + .. (0.064050cm, -4.503321cm) .. (-0.054130cm, -4.498045cm) + .. (-0.183828cm, -4.493314cm) .. (-0.323819cm, -4.489133cm) + .. (-0.472952cm, -4.485507cm) .. (-0.630137cm, -4.482437cm) + .. (-0.794351cm, -4.479927cm) .. (-0.964621cm, -4.477974cm) + .. (-1.140021cm, -4.476580cm) .. (-1.319658cm, -4.475743cm) + .. (-1.502663cm, -4.475464cm) .. (-1.688183cm, -4.475743cm) + .. (-1.875361cm, -4.476580cm) .. (-2.063332cm, -4.477974cm) + .. (-2.251207cm, -4.479927cm) .. (-2.438060cm, -4.482438cm) + .. (-2.622918cm, -4.485507cm) .. (-2.804744cm, -4.489133cm) + .. (-2.982432cm, -4.493314cm) .. (-3.154789cm, -4.498045cm) + .. (-3.320531cm, -4.503321cm) .. (-3.478268cm, -4.509130cm) + .. (-3.626507cm, -4.515457cm) .. (-3.763645cm, -4.522284cm) + .. (-3.887974cm, -4.529583cm) .. (-3.997689cm, -4.537322cm) + .. (-4.090909cm, -4.545455cm) .. (-4.165699cm, -4.553930cm) + .. (-4.220110cm, -4.562682cm) .. (-4.252227cm, -4.571633cm) + .. (-4.260231cm, -4.580694cm) .. (-4.242470cm, -4.589761cm) + .. (-4.197548cm, -4.598717cm) .. (-4.124418cm, -4.607435cm) + .. (-4.022471cm, -4.615778cm) .. (-3.891641cm, -4.623601cm) + .. (-3.732479cm, -4.630762cm) .. (-3.546226cm, -4.637115cm) + .. (-3.334840cm, -4.642525cm) .. (-3.101009cm, -4.646872cm) + .. (-2.848101cm, -4.650054cm) .. (-2.580086cm, -4.651996cm) + .. (-2.301416cm, -4.652648cm) .. (-2.016861cm, -4.651996cm) + .. (-1.731344cm, -4.650054cm) .. (-1.449741cm, -4.646872cm) + .. (-1.176717cm, -4.642525cm) .. (-0.916552cm, -4.637115cm) + .. (-0.673022cm, -4.630762cm) .. (-0.449306cm, -4.623601cm) + .. (-0.247932cm, -4.615777cm) .. (-0.070766cm, -4.607435cm) + .. (0.080967cm, -4.598717cm) .. (0.206638cm, -4.589760cm) + .. (0.306144cm, -4.580694cm) .. (0.379834cm, -4.571633cm) + .. (0.428425cm, -4.562682cm) .. (0.452923cm, -4.553930cm) .. cycle; +draw (0.454545cm, -4.545455cm) .. (0.452923cm, -4.728010cm) + .. (0.428425cm, -4.916531cm) .. (0.379834cm, -5.109349cm) + .. (0.306144cm, -5.304522cm) .. (0.206638cm, -5.499819cm) + .. (0.080967cm, -5.692737cm) .. (-0.070766cm, -5.880526cm) + .. (-0.247932cm, -6.060231cm) .. (-0.449306cm, -6.228766cm) + .. (-0.673022cm, -6.382993cm) .. (-0.916552cm, -6.519830cm) + .. (-1.176718cm, -6.636371cm) .. (-1.449743cm, -6.730008cm) + .. (-1.731345cm, -6.798560cm) .. (-2.016862cm, -6.840377cm) + .. (-2.301416cm, -6.854433cm) .. (-2.580087cm, -6.840377cm) + .. (-2.848101cm, -6.798560cm) .. (-3.101010cm, -6.730008cm) + .. (-3.334841cm, -6.636371cm) .. (-3.546226cm, -6.519830cm) + .. (-3.732480cm, -6.382993cm) .. (-3.891641cm, -6.228766cm) + .. (-4.022471cm, -6.060231cm) .. (-4.124418cm, -5.880525cm) + .. (-4.197549cm, -5.692737cm) .. (-4.242470cm, -5.499819cm) + .. (-4.260231cm, -5.304522cm) .. (-4.252227cm, -5.109350cm) + .. (-4.220110cm, -4.916531cm) .. (-4.165699cm, -4.728010cm) + .. (-4.090909cm, -4.545455cm) .. (-3.997689cm, -4.370261cm) + .. (-3.887974cm, -4.203583cm) .. (-3.763645cm, -4.046351cm) + .. (-3.626507cm, -3.899301cm) .. (-3.478268cm, -3.763001cm) + .. (-3.320530cm, -3.637880cm) .. (-3.154789cm, -3.524251cm) + .. (-2.982431cm, -3.422334cm) .. (-2.804744cm, -3.332275cm) + .. (-2.622917cm, -3.254165cm) .. (-2.438060cm, -3.188055cm) + .. (-2.251206cm, -3.133968cm) .. (-2.063332cm, -3.091909cm) + .. (-1.875361cm, -3.061874cm) .. (-1.688182cm, -3.043858cm) + .. (-1.502663cm, -3.037853cm) .. (-1.319657cm, -3.043858cm) + .. (-1.140021cm, -3.061874cm) .. (-0.964621cm, -3.091909cm) + .. (-0.794351cm, -3.133968cm) .. (-0.630137cm, -3.188055cm) + .. (-0.472951cm, -3.254165cm) .. (-0.323819cm, -3.332275cm) + .. (-0.183827cm, -3.422335cm) .. (-0.054129cm, -3.524252cm) + .. (0.064050cm, -3.637880cm) .. (0.169416cm, -3.763001cm) + .. (0.260604cm, -3.899301cm) .. (0.336191cm, -4.046352cm) + .. (0.394707cm, -4.203584cm) .. (0.434656cm, -4.370262cm) .. cycle; +draw (0.454545cm, -4.545455cm) .. (0.434656cm, -4.370261cm) + .. (0.394707cm, -4.203584cm) .. (0.336191cm, -4.046351cm) + .. (0.260604cm, -3.899301cm) .. (0.169416cm, -3.763001cm) + .. (0.064050cm, -3.637880cm) .. (-0.054130cm, -3.524251cm) + .. (-0.183828cm, -3.422335cm) .. (-0.323819cm, -3.332275cm) + .. (-0.472952cm, -3.254165cm) .. (-0.630137cm, -3.188055cm) + .. (-0.794351cm, -3.133968cm) .. (-0.964621cm, -3.091909cm) + .. (-1.140021cm, -3.061874cm) .. (-1.319658cm, -3.043858cm) + .. (-1.502663cm, -3.037853cm) .. (-1.688183cm, -3.043858cm) + .. (-1.875361cm, -3.061874cm) .. (-2.063332cm, -3.091909cm) + .. (-2.251207cm, -3.133968cm) .. (-2.438060cm, -3.188055cm) + .. (-2.622918cm, -3.254165cm) .. (-2.804744cm, -3.332275cm) + .. (-2.982432cm, -3.422335cm) .. (-3.154789cm, -3.524251cm) + .. (-3.320531cm, -3.637880cm) .. (-3.478268cm, -3.763001cm) + .. (-3.626507cm, -3.899301cm) .. (-3.763645cm, -4.046351cm) + .. (-3.887974cm, -4.203584cm) .. (-3.997689cm, -4.370262cm) + .. (-4.090909cm, -4.545455cm) .. (-4.165699cm, -4.728010cm) + .. (-4.220110cm, -4.916531cm) .. (-4.252227cm, -5.109350cm) + .. (-4.260231cm, -5.304522cm) .. (-4.242470cm, -5.499819cm) + .. (-4.197548cm, -5.692737cm) .. (-4.124418cm, -5.880526cm) + .. (-4.022471cm, -6.060232cm) .. (-3.891641cm, -6.228766cm) + .. (-3.732479cm, -6.382993cm) .. (-3.546225cm, -6.519830cm) + .. (-3.334840cm, -6.636371cm) .. (-3.101009cm, -6.730008cm) + .. (-2.848101cm, -6.798560cm) .. (-2.580086cm, -6.840377cm) + .. (-2.301416cm, -6.854433cm) .. (-2.016861cm, -6.840377cm) + .. (-1.731344cm, -6.798560cm) .. (-1.449741cm, -6.730008cm) + .. (-1.176717cm, -6.636370cm) .. (-0.916552cm, -6.519830cm) + .. (-0.673022cm, -6.382993cm) .. (-0.449306cm, -6.228766cm) + .. (-0.247932cm, -6.060231cm) .. (-0.070766cm, -5.880525cm) + .. (0.080967cm, -5.692737cm) .. (0.206638cm, -5.499819cm) + .. (0.306144cm, -5.304522cm) .. (0.379834cm, -5.109349cm) + .. (0.428425cm, -4.916531cm) .. (0.452923cm, -4.728009cm) .. cycle; +draw (0.454545cm, -4.545455cm) .. (0.436722cm, -4.630041cm) + .. (0.398385cm, -4.711268cm) .. (0.340785cm, -4.788570cm) + .. (0.265233cm, -4.861472cm) .. (0.173073cm, -4.929571cm) + .. (0.065660cm, -4.992537cm) .. (-0.055665cm, -5.050100cm) + .. (-0.189578cm, -5.102040cm) .. (-0.334789cm, -5.148183cm) + .. (-0.490042cm, -5.188392cm) .. (-0.654118cm, -5.222560cm) + .. (-0.825833cm, -5.250610cm) .. (-1.004037cm, -5.272481cm) + .. (-1.187606cm, -5.288130cm) .. (-1.375439cm, -5.297530cm) + .. (-1.566445cm, -5.300665cm) .. (-1.759541cm, -5.297530cm) + .. (-1.953640cm, -5.288130cm) .. (-2.147642cm, -5.272481cm) + .. (-2.340427cm, -5.250610cm) .. (-2.530842cm, -5.222561cm) + .. (-2.717697cm, -5.188392cm) .. (-2.899755cm, -5.148183cm) + .. (-3.075728cm, -5.102040cm) .. (-3.244267cm, -5.050100cm) + .. (-3.403967cm, -4.992537cm) .. (-3.553359cm, -4.929571cm) + .. (-3.690918cm, -4.861471cm) .. (-3.815071cm, -4.788570cm) + .. (-3.924207cm, -4.711268cm) .. (-4.016695cm, -4.630042cm) + .. (-4.090909cm, -4.545455cm) .. (-4.145261cm, -4.458159cm) + .. (-4.178236cm, -4.368907cm) .. (-4.188439cm, -4.278546cm) + .. (-4.174647cm, -4.188021cm) .. (-4.135867cm, -4.098369cm) + .. (-4.071393cm, -4.010710cm) .. (-3.980878cm, -3.926229cm) + .. (-3.864376cm, -3.846154cm) .. (-3.722411cm, -3.771733cm) + .. (-3.556002cm, -3.704195cm) .. (-3.366701cm, -3.644721cm) + .. (-3.156584cm, -3.594395cm) .. (-2.928243cm, -3.554177cm) + .. (-2.684732cm, -3.524855cm) .. (-2.429504cm, -3.507018cm) + .. (-2.166323cm, -3.501031cm) .. (-1.899150cm, -3.507018cm) + .. (-1.632033cm, -3.524855cm) .. (-1.368972cm, -3.554177cm) + .. (-1.113819cm, -3.594396cm) .. (-0.870152cm, -3.644721cm) + .. (-0.641200cm, -3.704196cm) .. (-0.429768cm, -3.771733cm) + .. (-0.238187cm, -3.846155cm) .. (-0.068303cm, -3.926229cm) + .. (0.078533cm, -4.010710cm) .. (0.201446cm, -4.098369cm) + .. (0.299994cm, -4.188021cm) .. (0.374137cm, -4.278546cm) + .. (0.424174cm, -4.368908cm) .. (0.450701cm, -4.458160cm) .. cycle; +draw (0.454545cm, -4.545455cm) .. (0.450701cm, -4.458159cm) + .. (0.424174cm, -4.368907cm) .. (0.374136cm, -4.278546cm) + .. (0.299994cm, -4.188020cm) .. (0.201446cm, -4.098368cm) + .. (0.078534cm, -4.010710cm) .. (-0.068303cm, -3.926228cm) + .. (-0.238188cm, -3.846154cm) .. (-0.429768cm, -3.771733cm) + .. (-0.641201cm, -3.704195cm) .. (-0.870153cm, -3.644720cm) + .. (-1.113819cm, -3.594395cm) .. (-1.368973cm, -3.554176cm) + .. (-1.632033cm, -3.524854cm) .. (-1.899151cm, -3.507018cm) + .. (-2.166323cm, -3.501030cm) .. (-2.429504cm, -3.507018cm) + .. (-2.684731cm, -3.524854cm) .. (-2.928243cm, -3.554176cm) + .. (-3.156585cm, -3.594395cm) .. (-3.366701cm, -3.644720cm) + .. (-3.556003cm, -3.704195cm) .. (-3.722410cm, -3.771733cm) + .. (-3.864376cm, -3.846154cm) .. (-3.980878cm, -3.926228cm) + .. (-4.071394cm, -4.010710cm) .. (-4.135867cm, -4.098369cm) + .. (-4.174647cm, -4.188021cm) .. (-4.188439cm, -4.278545cm) + .. (-4.178236cm, -4.368907cm) .. (-4.145261cm, -4.458160cm) + .. (-4.090909cm, -4.545455cm) .. (-4.016694cm, -4.630042cm) + .. (-3.924207cm, -4.711268cm) .. (-3.815071cm, -4.788570cm) + .. (-3.690918cm, -4.861472cm) .. (-3.553359cm, -4.929572cm) + .. (-3.403967cm, -4.992538cm) .. (-3.244268cm, -5.050101cm) + .. (-3.075728cm, -5.102041cm) .. (-2.899755cm, -5.148183cm) + .. (-2.717696cm, -5.188393cm) .. (-2.530841cm, -5.222562cm) + .. (-2.340426cm, -5.250611cm) .. (-2.147642cm, -5.272481cm) + .. (-1.953640cm, -5.288131cm) .. (-1.759540cm, -5.297531cm) + .. (-1.566445cm, -5.300666cm) .. (-1.375438cm, -5.297531cm) + .. (-1.187606cm, -5.288131cm) .. (-1.004036cm, -5.272481cm) + .. (-0.825833cm, -5.250611cm) .. (-0.654117cm, -5.222562cm) + .. (-0.490041cm, -5.188392cm) .. (-0.334789cm, -5.148183cm) + .. (-0.189578cm, -5.102041cm) .. (-0.055665cm, -5.050101cm) + .. (0.065659cm, -4.992538cm) .. (0.173074cm, -4.929571cm) + .. (0.265233cm, -4.861472cm) .. (0.340785cm, -4.788570cm) + .. (0.398385cm, -4.711268cm) .. (0.436723cm, -4.630042cm) .. cycle; +draw (0.454545cm, -4.545455cm) .. (0.436722cm, -4.319889cm) + .. (0.398385cm, -4.103285cm) .. (0.340785cm, -3.897146cm) + .. (0.265233cm, -3.702742cm) .. (0.173073cm, -3.521142cm) + .. (0.065660cm, -3.353231cm) .. (-0.055665cm, -3.199731cm) + .. (-0.189578cm, -3.061224cm) .. (-0.334789cm, -2.938177cm) + .. (-0.490042cm, -2.830954cm) .. (-0.654118cm, -2.739836cm) + .. (-0.825833cm, -2.665038cm) .. (-1.004037cm, -2.606716cm) + .. (-1.187606cm, -2.564985cm) .. (-1.375439cm, -2.539918cm) + .. (-1.566445cm, -2.531557cm) .. (-1.759541cm, -2.539918cm) + .. (-1.953640cm, -2.564985cm) .. (-2.147642cm, -2.606716cm) + .. (-2.340427cm, -2.665038cm) .. (-2.530842cm, -2.739836cm) + .. (-2.717697cm, -2.830954cm) .. (-2.899755cm, -2.938177cm) + .. (-3.075728cm, -3.061224cm) .. (-3.244268cm, -3.199731cm) + .. (-3.403967cm, -3.353231cm) .. (-3.553359cm, -3.521143cm) + .. (-3.690918cm, -3.702742cm) .. (-3.815071cm, -3.897145cm) + .. (-3.924207cm, -4.103285cm) .. (-4.016695cm, -4.319889cm) + .. (-4.090909cm, -4.545455cm) .. (-4.145261cm, -4.778241cm) + .. (-4.178236cm, -5.016247cm) .. (-4.188439cm, -5.257212cm) + .. (-4.174647cm, -5.498612cm) .. (-4.135866cm, -5.737683cm) + .. (-4.071393cm, -5.971441cm) .. (-3.980878cm, -6.196725cm) + .. (-3.864376cm, -6.410257cm) .. (-3.722410cm, -6.608713cm) + .. (-3.556002cm, -6.788814cm) .. (-3.366701cm, -6.947414cm) + .. (-3.156584cm, -7.081614cm) .. (-2.928242cm, -7.188863cm) + .. (-2.684731cm, -7.267056cm) .. (-2.429503cm, -7.314620cm) + .. (-2.166323cm, -7.330585cm) .. (-1.899150cm, -7.314620cm) + .. (-1.632033cm, -7.267056cm) .. (-1.368972cm, -7.188863cm) + .. (-1.113818cm, -7.081614cm) .. (-0.870152cm, -6.947414cm) + .. (-0.641200cm, -6.788813cm) .. (-0.429768cm, -6.608713cm) + .. (-0.238187cm, -6.410256cm) .. (-0.068303cm, -6.196724cm) + .. (0.078533cm, -5.971441cm) .. (0.201446cm, -5.737683cm) + .. (0.299994cm, -5.498612cm) .. (0.374137cm, -5.257210cm) + .. (0.424174cm, -5.016246cm) .. (0.450701cm, -4.778240cm) .. cycle; +draw (0.454545cm, -4.545455cm) .. (0.450701cm, -4.778241cm) + .. (0.424174cm, -5.016247cm) .. (0.374136cm, -5.257211cm) + .. (0.299994cm, -5.498612cm) .. (0.201446cm, -5.737683cm) + .. (0.078534cm, -5.971441cm) .. (-0.068303cm, -6.196725cm) + .. (-0.238188cm, -6.410256cm) .. (-0.429768cm, -6.608713cm) + .. (-0.641201cm, -6.788814cm) .. (-0.870152cm, -6.947413cm) + .. (-1.113819cm, -7.081614cm) .. (-1.368973cm, -7.188863cm) + .. (-1.632033cm, -7.267056cm) .. (-1.899151cm, -7.314620cm) + .. (-2.166323cm, -7.330585cm) .. (-2.429504cm, -7.314620cm) + .. (-2.684731cm, -7.267056cm) .. (-2.928243cm, -7.188863cm) + .. (-3.156585cm, -7.081614cm) .. (-3.366701cm, -6.947413cm) + .. (-3.556003cm, -6.788814cm) .. (-3.722410cm, -6.608714cm) + .. (-3.864376cm, -6.410256cm) .. (-3.980878cm, -6.196724cm) + .. (-4.071394cm, -5.971441cm) .. (-4.135867cm, -5.737683cm) + .. (-4.174647cm, -5.498612cm) .. (-4.188439cm, -5.257211cm) + .. (-4.178236cm, -5.016247cm) .. (-4.145261cm, -4.778241cm) + .. (-4.090909cm, -4.545455cm) .. (-4.016694cm, -4.319888cm) + .. (-3.924207cm, -4.103285cm) .. (-3.815071cm, -3.897145cm) + .. (-3.690918cm, -3.702742cm) .. (-3.553359cm, -3.521142cm) + .. (-3.403967cm, -3.353231cm) .. (-3.244268cm, -3.199730cm) + .. (-3.075728cm, -3.061224cm) .. (-2.899755cm, -2.938177cm) + .. (-2.717696cm, -2.830954cm) .. (-2.530841cm, -2.739836cm) + .. (-2.340426cm, -2.665037cm) .. (-2.147642cm, -2.606716cm) + .. (-1.953640cm, -2.564985cm) .. (-1.759540cm, -2.539917cm) + .. (-1.566445cm, -2.531557cm) .. (-1.375438cm, -2.539917cm) + .. (-1.187606cm, -2.564985cm) .. (-1.004036cm, -2.606716cm) + .. (-0.825833cm, -2.665038cm) .. (-0.654117cm, -2.739836cm) + .. (-0.490041cm, -2.830954cm) .. (-0.334789cm, -2.938177cm) + .. (-0.189578cm, -3.061225cm) .. (-0.055665cm, -3.199731cm) + .. (0.065659cm, -3.353231cm) .. (0.173074cm, -3.521143cm) + .. (0.265233cm, -3.702742cm) .. (0.340785cm, -3.897146cm) + .. (0.398385cm, -4.103286cm) .. (0.436723cm, -4.319889cm) .. cycle; +draw (0.454545cm, -4.545455cm) .. (0.439852cm, -4.711102cm) + .. (0.404020cm, -4.872417cm) .. (0.347899cm, -5.028029cm) + .. (0.272475cm, -5.176687cm) .. (0.178852cm, -5.317256cm) + .. (0.068225cm, -5.448719cm) .. (-0.058132cm, -5.570170cm) + .. (-0.198889cm, -5.680817cm) .. (-0.352669cm, -5.779969cm) + .. (-0.518058cm, -5.867033cm) .. (-0.693622cm, -5.941511cm) + .. (-0.877904cm, -6.002990cm) .. (-1.069436cm, -6.051140cm) + .. (-1.266739cm, -6.085709cm) .. (-1.468325cm, -6.106522cm) + .. (-1.672701cm, -6.113471cm) .. (-1.878367cm, -6.106522cm) + .. (-2.083814cm, -6.085709cm) .. (-2.287532cm, -6.051140cm) + .. (-2.487999cm, -6.002990cm) .. (-2.683689cm, -5.941511cm) + .. (-2.873073cm, -5.867033cm) .. (-3.054618cm, -5.779969cm) + .. (-3.226796cm, -5.680817cm) .. (-3.388085cm, -5.570170cm) + .. (-3.536979cm, -5.448719cm) .. (-3.672000cm, -5.317256cm) + .. (-3.791708cm, -5.176687cm) .. (-3.894716cm, -5.028029cm) + .. (-3.979713cm, -4.872417cm) .. (-4.045478cm, -4.711102cm) + .. (-4.090909cm, -4.545455cm) .. (-4.115046cm, -4.376958cm) + .. (-4.117097cm, -4.207204cm) .. (-4.096470cm, -4.037880cm) + .. (-4.052799cm, -3.870756cm) .. (-3.985969cm, -3.707661cm) + .. (-3.896147cm, -3.550467cm) .. (-3.783796cm, -3.401057cm) + .. (-3.649697cm, -3.261292cm) .. (-3.494956cm, -3.132979cm) + .. (-3.321002cm, -3.017833cm) .. (-3.129589cm, -2.917440cm) + .. (-2.922770cm, -2.833218cm) .. (-2.702876cm, -2.766384cm) + .. (-2.472477cm, -2.717919cm) .. (-2.234340cm, -2.688545cm) + .. (-1.991379cm, -2.678705cm) .. (-1.746591cm, -2.688545cm) + .. (-1.503004cm, -2.717919cm) .. (-1.263612cm, -2.766384cm) + .. (-1.031316cm, -2.833219cm) .. (-0.808869cm, -2.917440cm) + .. (-0.598826cm, -3.017834cm) .. (-0.403507cm, -3.132979cm) + .. (-0.224955cm, -3.261292cm) .. (-0.064922cm, -3.401057cm) + .. (0.075153cm, -3.550468cm) .. (0.194145cm, -3.707661cm) + .. (0.291238cm, -3.870756cm) .. (0.365921cm, -4.037882cm) + .. (0.417968cm, -4.207205cm) .. (0.447416cm, -4.376959cm) .. cycle; +draw (0.454545cm, -4.545455cm) .. (0.447416cm, -4.376958cm) + .. (0.417968cm, -4.207205cm) .. (0.365921cm, -4.037881cm) + .. (0.291238cm, -3.870756cm) .. (0.194144cm, -3.707661cm) + .. (0.075153cm, -3.550468cm) .. (-0.064922cm, -3.401057cm) + .. (-0.224956cm, -3.261292cm) .. (-0.403507cm, -3.132979cm) + .. (-0.598827cm, -3.017833cm) .. (-0.808869cm, -2.917440cm) + .. (-1.031316cm, -2.833218cm) .. (-1.263613cm, -2.766384cm) + .. (-1.503005cm, -2.717919cm) .. (-1.746591cm, -2.688545cm) + .. (-1.991379cm, -2.678705cm) .. (-2.234341cm, -2.688545cm) + .. (-2.472477cm, -2.717919cm) .. (-2.702876cm, -2.766384cm) + .. (-2.922771cm, -2.833218cm) .. (-3.129590cm, -2.917440cm) + .. (-3.321003cm, -3.017833cm) .. (-3.494956cm, -3.132979cm) + .. (-3.649698cm, -3.261292cm) .. (-3.783797cm, -3.401057cm) + .. (-3.896147cm, -3.550468cm) .. (-3.985969cm, -3.707661cm) + .. (-4.052799cm, -3.870756cm) .. (-4.096470cm, -4.037881cm) + .. (-4.117097cm, -4.207205cm) .. (-4.115046cm, -4.376958cm) + .. (-4.090909cm, -4.545455cm) .. (-4.045478cm, -4.711102cm) + .. (-3.979713cm, -4.872417cm) .. (-3.894716cm, -5.028030cm) + .. (-3.791708cm, -5.176687cm) .. (-3.672000cm, -5.317256cm) + .. (-3.536979cm, -5.448719cm) .. (-3.388085cm, -5.570170cm) + .. (-3.226796cm, -5.680818cm) .. (-3.054618cm, -5.779969cm) + .. (-2.873072cm, -5.867033cm) .. (-2.683689cm, -5.941511cm) + .. (-2.487998cm, -6.002990cm) .. (-2.287532cm, -6.051140cm) + .. (-2.083815cm, -6.085710cm) .. (-1.878366cm, -6.106522cm) + .. (-1.672701cm, -6.113471cm) .. (-1.468325cm, -6.106522cm) + .. (-1.266739cm, -6.085710cm) .. (-1.069436cm, -6.051140cm) + .. (-0.877904cm, -6.002990cm) .. (-0.693622cm, -5.941511cm) + .. (-0.518058cm, -5.867033cm) .. (-0.352668cm, -5.779969cm) + .. (-0.198889cm, -5.680817cm) .. (-0.058132cm, -5.570170cm) + .. (0.068225cm, -5.448719cm) .. (0.178852cm, -5.317256cm) + .. (0.272475cm, -5.176687cm) .. (0.347899cm, -5.028029cm) + .. (0.404020cm, -4.872417cm) .. (0.439852cm, -4.711102cm) .. cycle; +draw (0.454545cm, -4.545455cm) .. (0.439852cm, -4.302963cm) + .. (0.404020cm, -4.066814cm) .. (0.347899cm, -3.839012cm) + .. (0.272475cm, -3.621392cm) .. (0.178852cm, -3.415614cm) + .. (0.068225cm, -3.223166cm) .. (-0.058132cm, -3.045373cm) + .. (-0.198889cm, -2.883396cm) .. (-0.352669cm, -2.738248cm) + .. (-0.518058cm, -2.610794cm) .. (-0.693622cm, -2.501766cm) + .. (-0.877904cm, -2.411768cm) .. (-1.069436cm, -2.341281cm) + .. (-1.266739cm, -2.290674cm) .. (-1.468325cm, -2.260208cm) + .. (-1.672701cm, -2.250035cm) .. (-1.878367cm, -2.260208cm) + .. (-2.083815cm, -2.290674cm) .. (-2.287532cm, -2.341281cm) + .. (-2.487999cm, -2.411768cm) .. (-2.683689cm, -2.501767cm) + .. (-2.873073cm, -2.610795cm) .. (-3.054618cm, -2.738248cm) + .. (-3.226796cm, -2.883396cm) .. (-3.388085cm, -3.045373cm) + .. (-3.536979cm, -3.223166cm) .. (-3.672000cm, -3.415614cm) + .. (-3.791708cm, -3.621392cm) .. (-3.894717cm, -3.839012cm) + .. (-3.979713cm, -4.066814cm) .. (-4.045478cm, -4.302963cm) + .. (-4.090909cm, -4.545455cm) .. (-4.115046cm, -4.792116cm) + .. (-4.117097cm, -5.040619cm) .. (-4.096470cm, -5.288493cm) + .. (-4.052799cm, -5.533146cm) .. (-3.985969cm, -5.771901cm) + .. (-3.896147cm, -6.002017cm) .. (-3.783796cm, -6.220739cm) + .. (-3.649697cm, -6.425342cm) .. (-3.494956cm, -6.613178cm) + .. (-3.321002cm, -6.781740cm) .. (-3.129589cm, -6.928706cm) + .. (-2.922770cm, -7.051998cm) .. (-2.702876cm, -7.149837cm) + .. (-2.472477cm, -7.220785cm) .. (-2.234340cm, -7.263784cm) + .. (-1.991379cm, -7.278190cm) .. (-1.746591cm, -7.263784cm) + .. (-1.503004cm, -7.220785cm) .. (-1.263612cm, -7.149837cm) + .. (-1.031316cm, -7.051998cm) .. (-0.808869cm, -6.928706cm) + .. (-0.598826cm, -6.781740cm) .. (-0.403507cm, -6.613178cm) + .. (-0.224955cm, -6.425340cm) .. (-0.064922cm, -6.220738cm) + .. (0.075153cm, -6.002017cm) .. (0.194145cm, -5.771900cm) + .. (0.291238cm, -5.533146cm) .. (0.365921cm, -5.288491cm) + .. (0.417968cm, -5.040618cm) .. (0.447416cm, -4.792115cm) .. cycle; +draw (0.454545cm, -4.545455cm) .. (0.447416cm, -4.792116cm) + .. (0.417968cm, -5.040619cm) .. (0.365921cm, -5.288492cm) + .. (0.291238cm, -5.533146cm) .. (0.194144cm, -5.771901cm) + .. (0.075153cm, -6.002017cm) .. (-0.064922cm, -6.220738cm) + .. (-0.224956cm, -6.425341cm) .. (-0.403507cm, -6.613178cm) + .. (-0.598827cm, -6.781740cm) .. (-0.808869cm, -6.928705cm) + .. (-1.031316cm, -7.051998cm) .. (-1.263613cm, -7.149837cm) + .. (-1.503005cm, -7.220785cm) .. (-1.746591cm, -7.263784cm) + .. (-1.991379cm, -7.278190cm) .. (-2.234341cm, -7.263784cm) + .. (-2.472477cm, -7.220785cm) .. (-2.702876cm, -7.149837cm) + .. (-2.922771cm, -7.051998cm) .. (-3.129589cm, -6.928705cm) + .. (-3.321003cm, -6.781740cm) .. (-3.494956cm, -6.613179cm) + .. (-3.649697cm, -6.425341cm) .. (-3.783796cm, -6.220738cm) + .. (-3.896147cm, -6.002017cm) .. (-3.985969cm, -5.771900cm) + .. (-4.052799cm, -5.533146cm) .. (-4.096470cm, -5.288492cm) + .. (-4.117097cm, -5.040619cm) .. (-4.115046cm, -4.792116cm) + .. (-4.090909cm, -4.545455cm) .. (-4.045478cm, -4.302963cm) + .. (-3.979713cm, -4.066813cm) .. (-3.894716cm, -3.839012cm) + .. (-3.791708cm, -3.621392cm) .. (-3.672000cm, -3.415613cm) + .. (-3.536979cm, -3.223166cm) .. (-3.388085cm, -3.045372cm) + .. (-3.226796cm, -2.883396cm) .. (-3.054619cm, -2.738248cm) + .. (-2.873073cm, -2.610794cm) .. (-2.683689cm, -2.501766cm) + .. (-2.487998cm, -2.411767cm) .. (-2.287532cm, -2.341280cm) + .. (-2.083815cm, -2.290674cm) .. (-1.878366cm, -2.260207cm) + .. (-1.672701cm, -2.250035cm) .. (-1.468325cm, -2.260207cm) + .. (-1.266739cm, -2.290674cm) .. (-1.069436cm, -2.341281cm) + .. (-0.877904cm, -2.411768cm) .. (-0.693622cm, -2.501766cm) + .. (-0.518058cm, -2.610795cm) .. (-0.352668cm, -2.738248cm) + .. (-0.198889cm, -2.883397cm) .. (-0.058132cm, -3.045373cm) + .. (0.068225cm, -3.223166cm) .. (0.178852cm, -3.415614cm) + .. (0.272476cm, -3.621392cm) .. (0.347899cm, -3.839013cm) + .. (0.404020cm, -4.066814cm) .. (0.439852cm, -4.302964cm) .. cycle; +draw (0.454545cm, -4.545455cm) .. (0.443602cm, -4.768220cm) + .. (0.410876cm, -4.988842cm) .. (0.356683cm, -5.205193cm) + .. (0.281544cm, -5.415189cm) .. (0.186185cm, -5.616810cm) + .. (0.071522cm, -5.808114cm) .. (-0.061340cm, -5.987257cm) + .. (-0.211121cm, -6.152515cm) .. (-0.376379cm, -6.302296cm) + .. (-0.555522cm, -6.435158cm) .. (-0.746826cm, -6.549821cm) + .. (-0.948447cm, -6.645181cm) .. (-1.158444cm, -6.720319cm) + .. 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(-5.824873cm, -3.920111cm) .. (-5.911437cm, -3.841655cm) + .. (-6.005274cm, -3.772060cm) .. (-6.105481cm, -3.711998cm) + .. (-6.211091cm, -3.662048cm) .. (-6.321090cm, -3.622690cm) + .. (-6.434417cm, -3.594303cm) .. (-6.549980cm, -3.577161cm) + .. (-6.666667cm, -3.571429cm) .. (-6.783354cm, -3.577161cm) + .. (-6.898918cm, -3.594303cm) .. (-7.012244cm, -3.622690cm) + .. (-7.122242cm, -3.662048cm) .. (-7.227853cm, -3.711999cm) + .. (-7.328060cm, -3.772060cm) .. (-7.421897cm, -3.841654cm) + .. (-7.508461cm, -3.920111cm) .. (-7.586918cm, -4.006675cm) + .. (-7.656512cm, -4.100512cm) .. (-7.716573cm, -4.200718cm) + .. (-7.766524cm, -4.306330cm) .. (-7.805882cm, -4.416328cm) + .. (-7.834269cm, -4.529655cm) .. (-7.851410cm, -4.645218cm) + .. (-7.857143cm, -4.761905cm) .. (-7.851410cm, -4.878592cm) + .. (-7.834269cm, -4.994155cm) .. (-7.805882cm, -5.107482cm) + .. (-7.766523cm, -5.217481cm) .. (-7.716573cm, -5.323092cm) + .. (-7.656512cm, -5.423298cm) .. (-7.586917cm, -5.517135cm) + .. (-7.508461cm, -5.603699cm) .. (-7.421897cm, -5.682155cm) + .. (-7.328060cm, -5.751750cm) .. (-7.227853cm, -5.811811cm) + .. (-7.122242cm, -5.861762cm) .. (-7.012244cm, -5.901120cm) + .. (-6.898918cm, -5.929507cm) .. (-6.783354cm, -5.946649cm) + .. (-6.666667cm, -5.952381cm) .. (-6.549980cm, -5.946649cm) + .. (-6.434416cm, -5.929507cm) .. (-6.321089cm, -5.901120cm) + .. (-6.211091cm, -5.861761cm) .. (-6.105481cm, -5.811811cm) + .. (-6.005273cm, -5.751750cm) .. (-5.911437cm, -5.682155cm) + .. (-5.824872cm, -5.603698cm) .. (-5.746416cm, -5.517135cm) + .. (-5.676822cm, -5.423298cm) .. (-5.616761cm, -5.323092cm) + .. (-5.566810cm, -5.217481cm) .. (-5.527452cm, -5.107481cm) + .. (-5.499065cm, -4.994155cm) .. (-5.481923cm, -4.878592cm) .. cycle; +draw (-7.508461cm, -3.920111cm) -- (-8.298825cm, -4.332754cm); +draw (-6.666667cm, -3.571429cm) -- (-7.368421cm, -3.947368cm); +draw (-5.824873cm, -3.920111cm) -- (-6.438017cm, -4.332754cm); +draw (-5.476191cm, -4.761905cm) -- (-6.052632cm, -5.263158cm); +draw (-6.052632cm, -5.263158cm) .. (-6.058968cm, -5.134188cm) + .. (-6.077914cm, -5.006460cm) .. (-6.109289cm, -4.881204cm) + .. (-6.152790cm, -4.759627cm) .. (-6.207998cm, -4.642899cm) + .. (-6.274382cm, -4.532145cm) .. (-6.351302cm, -4.428430cm) + .. (-6.438017cm, -4.332754cm) .. (-6.533693cm, -4.246039cm) + .. (-6.637408cm, -4.169119cm) .. (-6.748162cm, -4.102735cm) + .. (-6.864890cm, -4.047527cm) .. (-6.986467cm, -4.004026cm) + .. (-7.111723cm, -3.972651cm) .. (-7.239451cm, -3.953704cm) + .. (-7.368421cm, -3.947368cm) .. (-7.497391cm, -3.953704cm) + .. (-7.625119cm, -3.972651cm) .. (-7.750375cm, -4.004026cm) + .. (-7.871952cm, -4.047527cm) .. (-7.988680cm, -4.102736cm) + .. (-8.099435cm, -4.169119cm) .. (-8.203149cm, -4.246039cm) + .. (-8.298825cm, -4.332754cm) .. (-8.385540cm, -4.428430cm) + .. (-8.462461cm, -4.532145cm) .. (-8.528844cm, -4.642899cm) + .. (-8.584053cm, -4.759627cm) .. (-8.627553cm, -4.881204cm) + .. (-8.658928cm, -5.006460cm) .. (-8.677875cm, -5.134188cm) + .. (-8.684211cm, -5.263158cm) .. (-8.677875cm, -5.392128cm) + .. (-8.658928cm, -5.519856cm) .. (-8.627553cm, -5.645112cm) + .. (-8.584052cm, -5.766689cm) .. (-8.528844cm, -5.883417cm) + .. (-8.462461cm, -5.994172cm) .. (-8.385540cm, -6.097886cm) + .. (-8.298825cm, -6.193562cm) .. (-8.203149cm, -6.280277cm) + .. (-8.099435cm, -6.357197cm) .. (-7.988680cm, -6.423581cm) + .. (-7.871952cm, -6.478789cm) .. (-7.750375cm, -6.522290cm) + .. (-7.625119cm, -6.553665cm) .. (-7.497391cm, -6.572611cm) + .. (-7.368421cm, -6.578948cm) .. (-7.239451cm, -6.572611cm) + .. (-7.111723cm, -6.553665cm) .. (-6.986467cm, -6.522290cm) + .. (-6.864890cm, -6.478788cm) .. (-6.748162cm, -6.423581cm) + .. (-6.637407cm, -6.357197cm) .. (-6.533693cm, -6.280277cm) + .. (-6.438017cm, -6.193561cm) .. (-6.351302cm, -6.097886cm) + .. (-6.274382cm, -5.994172cm) .. (-6.207998cm, -5.883417cm) + .. (-6.152790cm, -5.766689cm) .. (-6.109289cm, -5.645111cm) + .. (-6.077914cm, -5.519855cm) .. (-6.058968cm, -5.392128cm) .. cycle; +draw (-1.817046cm, -1.889861cm) -- (0.409088cm, -1.533842cm) + -- (2.008737cm, 0.403776cm) -- (-0.210306cm, 0.515899cm) -- cycle; +draw (2.008737cm, -3.942897cm) -- (0.409088cm, -1.533842cm) + -- (2.008737cm, 0.403776cm) -- (4.189326cm, -2.090883cm) -- cycle; +draw (-0.210306cm, -5.037776cm) -- (2.008737cm, -3.942897cm) + -- (0.409088cm, -1.533842cm) -- (-1.817046cm, -1.889861cm) -- cycle; +draw (-0.210306cm, -5.037776cm) -- (2.008737cm, -3.942897cm) + -- (4.189326cm, -2.090883cm) -- (2.181570cm, -2.813345cm) -- cycle; +draw (4.189326cm, -2.090883cm) -- (2.008737cm, 0.403776cm) + -- (-0.210306cm, 0.515899cm) -- (2.181570cm, -2.813345cm) -- cycle; +draw (-0.210306cm, -5.037776cm) -- (2.181570cm, -2.813345cm) + -- (-0.210306cm, 0.515899cm) -- (-1.817046cm, -1.889861cm) -- cycle; +draw (3.572904cm, 0.933339cm) -- (4.454080cm, 0.805375cm); +draw (4.650180cm, 1.279513cm) .. (4.699692cm, 1.327155cm) + .. (4.753742cm, 1.370601cm) .. (4.811902cm, 1.409419cm) + .. (4.873697cm, 1.443204cm) .. (4.938611cm, 1.471586cm) + .. (5.006083cm, 1.494233cm) .. (5.075518cm, 1.510853cm) + .. (5.146282cm, 1.521207cm) .. (5.217714cm, 1.525104cm) + .. (5.289126cm, 1.522417cm) .. (5.359808cm, 1.513078cm) + .. (5.429044cm, 1.497090cm) .. (5.496107cm, 1.474524cm) + .. (5.560280cm, 1.445527cm) .. (5.620858cm, 1.410322cm) + .. (5.677159cm, 1.369206cm) .. (5.728541cm, 1.322555cm) + .. (5.774400cm, 1.270813cm) .. (5.814194cm, 1.214498cm) + .. (5.847441cm, 1.154188cm) .. (5.873738cm, 1.090519cm) + .. (5.892757cm, 1.024176cm) .. (5.904265cm, 0.955884cm) + .. (5.908117cm, 0.886393cm) .. (5.904265cm, 0.816473cm) + .. (5.892757cm, 0.746898cm) .. (5.873737cm, 0.678436cm) + .. (5.847441cm, 0.611837cm) .. (5.814194cm, 0.547821cm) + .. (5.774400cm, 0.487071cm) .. (5.728541cm, 0.430219cm) + .. (5.677159cm, 0.377842cm) .. (5.620858cm, 0.330452cm) + .. (5.560280cm, 0.288496cm) .. (5.496107cm, 0.252348cm) + .. (5.429044cm, 0.222309cm) .. (5.359808cm, 0.198604cm) + .. (5.289126cm, 0.181389cm) .. (5.217714cm, 0.170744cm) + .. (5.146282cm, 0.166681cm) .. (5.075518cm, 0.169148cm) + .. (5.006083cm, 0.178031cm) .. (4.938611cm, 0.193158cm) + .. (4.873697cm, 0.214307cm) .. (4.811903cm, 0.241206cm) + .. (4.753742cm, 0.273542cm) .. (4.699692cm, 0.310965cm) + .. (4.650180cm, 0.353090cm) .. (4.605593cm, 0.399503cm) + .. (4.566270cm, 0.449768cm) .. (4.532502cm, 0.503422cm) + .. (4.504538cm, 0.559990cm) .. (4.482580cm, 0.618978cm) + .. (4.466784cm, 0.679883cm) .. (4.457262cm, 0.742188cm) + .. (4.454080cm, 0.805375cm) .. (4.457262cm, 0.868915cm) + .. (4.466784cm, 0.932282cm) .. (4.482580cm, 0.994947cm) + .. (4.504539cm, 1.056382cm) .. (4.532502cm, 1.116066cm) + .. (4.566270cm, 1.173484cm) .. (4.605594cm, 1.228131cm) .. cycle; +draw (3.786769cm, 0.410075cm) -- (4.650180cm, 0.353090cm); +draw (3.786769cm, 1.486014cm) -- (4.650180cm, 1.279513cm); +draw (0.725956cm, -0.038837cm) -- (2.032222cm, -0.033367cm) + -- (4.427044cm, 2.774759cm) -- (3.294595cm, 3.338603cm) -- cycle; +draw (3.363155cm, -1.601377cm) -- (2.032222cm, -0.033367cm) + -- (4.427044cm, 2.774759cm) -- (6.383579cm, 1.233164cm) -- cycle; +draw (2.132413cm, -1.898338cm) -- (3.363155cm, -1.601377cm) + -- (2.032222cm, -0.033367cm) -- (0.725956cm, -0.038837cm) -- cycle; +draw (2.132413cm, -1.898338cm) -- (3.363155cm, -1.601377cm) + -- (6.383579cm, 1.233164cm) -- (5.525396cm, 1.525796cm) -- cycle; +draw (2.132413cm, -1.898338cm) -- (5.525396cm, 1.525796cm) + -- (3.294595cm, 3.338603cm) -- (0.725956cm, -0.038837cm) -- cycle; +draw (6.383579cm, 1.233164cm) -- (4.427044cm, 2.774759cm) + -- (3.294595cm, 3.338603cm) -- (5.525396cm, 1.525796cm) -- cycle; +draw (4.331959cm, 0.194645cm) -- (5.146282cm, 0.166681cm); +draw (4.331959cm, 1.776424cm) -- (5.146282cm, 1.521207cm); +draw (2.571044cm, -3.287452cm) .. (2.623537cm, -3.241180cm) + .. (2.671554cm, -3.196870cm) .. (2.714636cm, -3.154912cm) + .. (2.752341cm, -3.115692cm) .. (2.784251cm, -3.079592cm) + .. (2.809972cm, -3.046988cm) .. (2.829147cm, -3.018239cm) + .. (2.841454cm, -2.993694cm) .. (2.846620cm, -2.973675cm) + .. (2.844427cm, -2.958482cm) .. (2.834716cm, -2.948376cm) + .. (2.817402cm, -2.943584cm) .. (2.792477cm, -2.944282cm) + .. (2.760016cm, -2.950593cm) .. (2.720191cm, -2.962583cm) + .. (2.673267cm, -2.980248cm) .. (2.619613cm, -3.003514cm) + .. (2.559698cm, -3.032231cm) .. (2.494092cm, -3.066172cm) + .. (2.423461cm, -3.105029cm) .. (2.348565cm, -3.148418cm) + .. (2.270241cm, -3.195880cm) .. (2.189391cm, -3.246887cm) + .. (2.106977cm, -3.300852cm) .. (2.023988cm, -3.357134cm) + .. (1.941436cm, -3.415056cm) .. (1.860326cm, -3.473912cm) + .. (1.781643cm, -3.532984cm) .. (1.706330cm, -3.591556cm) + .. (1.635270cm, -3.648926cm) .. (1.569271cm, -3.704419cm) + .. (1.509056cm, -3.757402cm) .. (1.455248cm, -3.807289cm) + .. (1.408368cm, -3.853556cm) .. (1.368824cm, -3.895741cm) + .. (1.336920cm, -3.933450cm) .. (1.312845cm, -3.966364cm) + .. (1.296693cm, -3.994233cm) .. (1.288453cm, -4.016878cm) + .. (1.288027cm, -4.034185cm) .. (1.295237cm, -4.046109cm) + .. (1.309830cm, -4.052660cm) .. (1.331491cm, -4.053903cm) + .. (1.359851cm, -4.049949cm) .. (1.394499cm, -4.040957cm) + .. (1.434983cm, -4.027117cm) .. (1.480828cm, -4.008656cm) + .. (1.531531cm, -3.985823cm) .. (1.586578cm, -3.958895cm) + .. (1.645441cm, -3.928164cm) .. (1.707584cm, -3.893939cm) + .. (1.772470cm, -3.856540cm) .. (1.839559cm, -3.816300cm) + .. (1.908312cm, -3.773558cm) .. (1.978191cm, -3.728662cm) + .. (2.048663cm, -3.681964cm) .. (2.119197cm, -3.633823cm) + .. (2.189267cm, -3.584601cm) .. (2.258351cm, -3.534667cm) + .. (2.325931cm, -3.484392cm) .. (2.391494cm, -3.434151cm) + .. (2.454533cm, -3.384325cm) .. (2.514548cm, -3.335296cm) .. cycle; +draw (2.048663cm, -3.681964cm) -- (2.484673cm, -4.326973cm); +draw (4.922043cm, 0.443843cm) -- (5.677159cm, 0.377842cm); +draw (4.922043cm, 1.608380cm) -- (5.677159cm, 1.369206cm); +draw (2.571044cm, -3.287452cm) -- (3.032066cm, -3.926653cm); +draw (5.180943cm, 1.043915cm) -- (5.908117cm, 0.886393cm); +draw (1.531531cm, -3.985823cm) -- (1.962617cm, -4.663504cm); +draw (3.032066cm, -3.926653cm) .. (3.088719cm, -3.881763cm) + .. (3.141046cm, -3.839295cm) .. (3.188554cm, -3.799631cm) + .. (3.230766cm, -3.763147cm) .. (3.267226cm, -3.730210cm) + .. (3.297500cm, -3.701179cm) .. (3.321185cm, -3.676393cm) + .. (3.337913cm, -3.656176cm) .. (3.347362cm, -3.640824cm) + .. (3.349263cm, -3.630603cm) .. (3.343406cm, -3.625740cm) + .. (3.329655cm, -3.626421cm) .. (3.307949cm, -3.632778cm) + .. (3.278318cm, -3.644886cm) .. (3.240885cm, -3.662756cm) + .. (3.195876cm, -3.686326cm) .. (3.143624cm, -3.715462cm) + .. (3.084568cm, -3.749949cm) .. 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+draw (1.732051cm, 2.000000cm) -- (0.866026cm, 0.500000cm) + -- (2.598076cm, 0.500000cm) -- cycle; +draw (1.732051cm, -1.000000cm) -- (2.598076cm, 0.500000cm) + -- (0.866025cm, 0.500000cm) -- cycle; +draw (0.866025cm, 3.500000cm) -- (0.000000cm, 2.000000cm) + -- (1.732051cm, 2.000000cm) -- cycle; +draw (0.866025cm, 0.500000cm) -- (1.732051cm, 2.000000cm) + -- (0.000000cm, 2.000000cm) -- cycle; +draw (0.000000cm, 2.000000cm) -- (-0.866025cm, 0.500000cm) + -- (0.866025cm, 0.500000cm) -- cycle; +draw (0.000000cm, -1.000000cm) -- (0.866025cm, 0.500000cm) + -- (-0.866025cm, 0.500000cm) -- cycle; +label(btex 0 etex, (0.000000cm, 0.000000cm)); +label(btex 1 etex, (0.000000cm, 1.000000cm)); +label(btex 2 etex, (0.866025cm, 1.500000cm)); +label(btex 3 etex, (0.866025cm, 2.500000cm)); +label(btex 4 etex, (1.732051cm, 0.000000cm)); +label(btex 5 etex, (1.732051cm, 1.000000cm)); +label(btex 6 etex, (2.598076cm, 1.500000cm)); +label(btex 7 etex, (2.598076cm, 2.500000cm)); +label(btex 8 etex, (3.464102cm, 0.000000cm)); +label(btex 9 etex, (3.464102cm, 1.000000cm)); +label(btex 10 etex, (4.330127cm, 1.500000cm)); +label(btex 11 etex, (4.330127cm, 2.500000cm)); +label(btex 12 etex, (5.196153cm, 0.000000cm)); +label(btex 13 etex, (5.196153cm, 1.000000cm)); +label(btex 14 etex, (6.062178cm, 1.500000cm)); +label(btex 15 etex, (6.062178cm, 2.500000cm)); +label(btex 16 etex, (6.928204cm, 0.000000cm)); +label(btex 17 etex, (6.928204cm, 1.000000cm)); +label(btex 18 etex, (7.794229cm, 1.500000cm)); +label(btex 19 etex, (7.794229cm, 2.500000cm)); +boxit.b(currentpicture); +draw bpath b withpen pencircle scaled .25mm; +endfig; +beginfig(199); +draw (2.722151cm, 7.000000cm) -- (-7.777758cm, 2.000000cm) dashed evenly; +draw (2.722151cm, 7.000000cm) -- (2.222242cm, 2.000000cm) dashed evenly; +draw (-3.080074cm, 7.000000cm) -- (8.880021cm, 2.000000cm) dashed evenly; +draw (-3.080074cm, 7.000000cm) -- (3.880021cm, 2.000000cm) dashed evenly; +draw (-1.942727cm, 4.778610cm) -- (-7.639159cm, 7.000000cm) dashed evenly; +draw (-1.942727cm, 4.778610cm) -- (6.414319cm, 7.000000cm) dashed evenly; +draw (3.519178cm, 4.241138cm) -- (-7.639159cm, 7.000000cm) dashed evenly; +drawarrow (7.000000cm, 8.000000cm) -- (7.000000cm, 7.000000cm); +draw (3.519178cm, 4.241138cm) -- (6.414319cm, 7.000000cm) dashed evenly; +drawarrow (1.000000cm, 1.000000cm) -- (1.000000cm, 2.000000cm); +draw (1.000000cm, 2.000000cm) -- (7.000000cm, 7.000000cm) dashed withdots; +draw (3.000000cm, 2.000000cm) -- (0.000000cm, 7.000000cm) dashed withdots; +drawarrow (3.000000cm, 1.000000cm) -- (3.000000cm, 2.000000cm); +draw (-8.500000cm, 2.000000cm) -- (9.500000cm, 2.000000cm); +draw (-8.500000cm, 7.000000cm) -- (9.500000cm, 7.000000cm); +draw (0.000000cm, 0.000000cm) -- (0.000000cm, 7.000000cm); +fill (2.333333cm, 3.111111cm) -- (3.519178cm, 4.241138cm) + -- (-0.358176cm, 5.199800cm) -- (-1.942727cm, 4.778610cm) -- cycle withcolor gray; +draw (2.333333cm, 3.111111cm) -- (3.519178cm, 4.241138cm) + -- (-0.358176cm, 5.199800cm) -- (-1.942727cm, 4.778610cm) -- cycle; +dotlabel.bot(btex focus etex, (0.000000cm, 0.000000cm)); +dotlabel.top(btex CV etex, (0.000000cm, 7.000000cm)); +dotlabel.llft(btex horizon etex, (9.500000cm, 7.000000cm)); +dotlabel.ulft(btex ground line etex, (9.500000cm, 2.000000cm)); +dotlabel.top(btex VP $47.5^\circ$r etex, (6.414319cm, 7.000000cm)); +dotlabel.top(btex MP $47.5^\circ$r etex, (-3.080074cm, 7.000000cm)); +dotlabel.top(btex VP $42.5^\circ$l etex, (-7.639159cm, 7.000000cm)); +dotlabel.top(btex MP $42.5^\circ$l etex, (2.722151cm, 7.000000cm)); +dotlabel.top(btex MP-CV etex, (7.000000cm, 8.000000cm)); +dotlabel.bot(btex $x_{r_0}=3$ etex, (3.000000cm, 1.000000cm)); +dotlabel.bot(btex $z_{r_0}=2$ etex, (1.000000cm, 1.000000cm)); +dotlabel.bot(btex $r_0$ etex, (2.333333cm, 3.111111cm)); +dotlabel.bot(btex 0 etex, (3.880021cm, 2.000000cm)); +dotlabel.bot(btex 5 etex, (8.880021cm, 2.000000cm)); +dotlabel.rt(btex $r_1$ etex, (3.519178cm, 4.241138cm)); +dotlabel.bot(btex 0 etex, (2.222242cm, 2.000000cm)); +dotlabel.bot(btex 10 etex, (-7.777758cm, 2.000000cm)); +dotlabel.lft(btex $r_3$ etex, (-1.942727cm, 4.778610cm)); +dotlabel.top(btex $r_2$ etex, (-0.358176cm, 5.199800cm)); +label(btex $R$ etex, (0.493499cm, 4.538876cm)); +label.lft(btex CV:\space\space\space etex, (7.000000cm, 1.600000cm)); +label.rt(btex center of vision etex, (7.000000cm, 1.600000cm)); +label.lft(btex VP:\space\space\space etex, (7.000000cm, 1.200000cm)); +label.rt(btex vanishing point etex, (7.000000cm, 1.200000cm)); +label.lft(btex MP:\space\space\space etex, (7.000000cm, 0.800000cm)); +label.rt(btex measuring point etex, (7.000000cm, 0.800000cm)); +label.lft(btex l:\space\space\space etex, (7.000000cm, 0.400000cm)); +label.rt(btex left etex, (7.000000cm, 0.400000cm)); +label.lft(btex r:\space\space\space etex, (7.000000cm, 0.000000cm)); +label.rt(btex right etex, (7.000000cm, 0.000000cm)); +boxit.b(currentpicture); +draw bpath b withpen pencircle scaled .25mm; +endfig; + + +bye; + + + + +%% Local Variables: +%% mode:Metafont +%% eval:(if metapost-keymap nil (load "metapost-keymap")) +%% eval:(use-local-map metapost-mode-map) +%% eval:(local-set-key [f9] 'mp-file) +%% eval:(read-abbrev-file "~/.abbrev_defs") +%% run-mp-on-file:"examples.mp" +%% run-tex-on-file:"3DLDFtex.tex" +%% run-dvips-on-file:"3DLDFtex.dvi" +%% End: diff -Naur 3DLDF-1.1.4/CWEB/examples.web 3DLDF-1.1.5.1/CWEB/examples.web --- 3DLDF-1.1.4/CWEB/examples.web 2003-12-10 16:38:11.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/examples.web 2004-01-12 22:28:20.000000000 +0100 @@ -3,7 +3,7 @@ @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -52,8 +52,6 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: examples.web,v 1.2 2003/12/10 15:38:11 lfinsto1 Exp $ @> - @q * Include files.@> @ Include files. @= @@ -87,7 +85,7 @@ \ENDLOG @= static string rcs_id - = "$Id: examples.web,v 1.2 2003/12/10 15:38:11 lfinsto1 Exp $"; + = "$Id: examples.web,v 1.5 2004/01/12 21:28:20 lfinsto1 Exp $"; @q * The examples function.@> @* The examples function. diff -Naur 3DLDF-1.1.4/CWEB/exampman.web 3DLDF-1.1.5.1/CWEB/exampman.web --- 3DLDF-1.1.4/CWEB/exampman.web 1970-01-01 01:00:00.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/exampman.web 2004-01-12 22:28:27.000000000 +0100 @@ -0,0 +1,3953 @@ +@q exampman.web@> +@q Originally generated by running texi2dvi 3DLDF.texi.@> + +@q * Copyright and License.@> + + +@q This file is part of 3DLDF, a package for three-dimensional drawing. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> + +@q 3DLDF is free software; you can redistribute it and/or modify @> +@q it under the terms of the GNU General Public License as published by @> +@q the Free Software Foundation; either version 2 of the License, or @> +@q (at your option) any later version. @> + +@q 3DLDF is distributed in the hope that it will be useful, @> +@q but WITHOUT ANY WARRANTY; without even the implied warranty of @> +@q MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the @> +@q GNU General Public License for more details. @> + +@q You should have received a copy of the GNU General Public License @> +@q along with 3DLDF; if not, write to the Free Software @> +@q Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA @> + +@q 3DLDF is a GNU package. @> +@q It is part of the GNU Project of the @> +@q Free Software Foundation @> +@q and is published under the GNU General Public License. @> +@q See the website http://www.gnu.org @> +@q for more information. @> +@q 3DLDF is available for downloading from @> +@q http://www.gnu.org/3DLDF. @> +@q It is also available from @> +@q http://www.dante.de/software/ctan/, the Dante www-server @> +@q and from http://wwwuser.gwdg.de/~lfinsto1, @> +@q the author's website. @> + +@q (``@@'' stands for a single at-sign in the following paragraph.) @> + +@q Please send bug reports to bug-3DLDF@@gnu.org @> +@q The mailing list help-3DLDF@@gnu.org is available for people to @> +@q ask other users for help. @> +@q The mailing list info-3DLDF@@gnu.org is for sending @> +@q announcements to users. To subscribe to these mailing lists, send an @> +@q email with ``subscribe '' as the subject. @> + +@q The author can be contacted at: @> + +@q Laurence D. Finston @> +@q Kreuzbergring 41 @> +@q D-37075 Goettingen @> +@q Germany @> + +@q lfinsto1@@gwdg.de (@@ stands for a single ``at'' sign.)@> +@q s246794@@stud.uni-goettingen.de @> + + +@q $Id: exampman.web,v 1.3 2004/01/12 21:28:27 lfinsto1 Exp $@> + + +@i subex1.web + +beginfig(1); +{ +Point P0; +Point P1(3); +Point P2(3, 3); +Point P3(0, 3); +Rectangle r(P0, P1, P2, P3); +r.draw(); +r.get_point(0).dotlabel("$P_0$ = $Q_0$ = (0, 0)", "llft"); +r.get_point(1).dotlabel("$P_1$ = $Q_1$ = (3, 0)", "lrt"); +r.get_point(2).dotlabel("$P_2$ = (3, 3)", "ulft"); +r.get_point(3).dotlabel("$P_3$ = (0, 3)", "ulft"); +r.get_center().label("$r$", ""); +Rectangle q(r); +q.shear(1.5); +Point q_center(q.get_center()); +q_center.label("$q$", ""); +q.get_point(2).dotlabel("$Q_2$ = (7.5, 3)"); +q.get_point(3).dotlabel("$Q_3$ = (4.5, 3)"); +q.draw(black, "evenly"); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(1); +current_picture.clear(); + + + +beginfig(2); +{ +default_focus.set(4, 5, -10, 4, 5, 10, 10); +draw_axes(gray); +Point p0 (-1.06066, 0, 1.06066); +Point p1 (1.06066, 0, -1.06066); +p1 *= p0.rotate(0, 30, 30); +p0.dotlabel("p0", "lft"); +p1.dotlabel("p1"); +p0.draw(p1); +Point p2(1.06066, 0, 1.06066); +p2.dotlabel("p2", "rt"); +Point p3(p2); +p3.rotate(p1, p0, 45); +p3.dotlabel("p3", "rt"); +Point p4(p2); +p4.rotate(p1, p0, 90); +p4.dotlabel("p4"); +Point p5(p2); +p5.rotate(p1, p0, 135); +p5.dotlabel("p5"); +Point p6(p2); +p6.rotate(p1, p0); +p6.dotlabel("p6", "lft"); +Path pa("..", false, &p2, &p3, &p4, &p5, &p6, 0); +pa.draw(); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(2); +current_picture.clear(); + +beginfig(3); +{ +Point P(0, 1); +P.drawdot(Colors::black, "pencircle scaled 3mm"); +Point p0(P);p0.shift(0, .5);p0.label("$P$",""); +Point mid; +mid = P.mediate(p0); +Point pt[4]; +for (int i = 0; i < 4; ++i) + pt[i] = mid; +pt[0].shift(-.5, -.5); +pt[1].shift(.5, -.5); +pt[2].shift(.5, .5); +pt[3].shift(-.5, .5); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(3); +current_picture.clear(); + +beginfig(4); +{ +Point P(0, 1); +P.drawdot(black, "pencircle scaled 3mm"); +P.undrawdot("pencircle scaled 2mm"); +Point p0(P);p0.shift(0, .5);p0.label("$P$", ""); +Point mid; +mid = P.mediate(p0); +Point pt[4]; +for (int i = 0; i < 4; ++i) + pt[i] = mid; +pt[0].shift(-.5, -.5); +pt[1].shift(.5, -.5); +pt[2].shift(.5, .5); +pt[3].shift(-.5, .5); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(4); +current_picture.clear(); + +beginfig(5); +{ +Point p0; +Point p1(2, 2); +p0.draw(p1); +p0.dotlabel("$p_0$", "lft"); +p1.dotlabel("$p_1$", "rt"); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(5); +current_picture.clear(); + +beginfig(6); +{ +Point p0; +Point p1(2, 2); +p0.draw(p1, Colors::gray, "", +"pensquare scaled .5cm rotated 45"); +p0.dotlabel("$p_0$", "lft"); +p1.dotlabel("$p_1$", "rt"); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(6); +current_picture.clear(); + +beginfig(7); +{ +Point p0; +Point p1(2, 2); +p0.draw(p1, Colors::gray, "evenly", +"pensquare scaled .5cm rotated 45"); +p0.undraw(p1, "evenly scaled 6", "pencircle scaled .2cm"); +p0.dotlabel("$p_0$", "lft"); +p1.dotlabel("$p_1$", "rt"); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(7); +current_picture.clear(); + +beginfig(8); +{ +Point p0; +Point p1(1); +Point p2(2); +Point p3(p0); +Point p4(p1); +Point p5(p2); +p3 *= p4 *= p5.shift(0, 1); +p0.draw(p1); +p1.draw(p2); +p2.draw(p5); +p5.draw(p4); +p4.draw(p3); +p3.draw(p0); +p0.label("$p_0$", ""); +p1.dotlabel(1); +p2.dotlabel("p2", "bot"); +p3.dotlabel("This is $p_3$", "lft"); +p4.label(4); +p5.label("$\\leftarrow p_5$", "rt"); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(8); +current_picture.clear(); + +beginfig(9); +{ +Point A; +Point B(2, 2); +A.dotlabel("A", "lft"); +B.dotlabel("B", "rt"); +Path p(A, B); +p.draw(); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(9); +current_picture.clear(); + +beginfig(10); +{ +default_focus.set(7, 5, -10, 7, 5, 10, 10); +draw_axes(gray, 1.5, "rt"); +Point p[3]; +p[0].shift(1); +p[1].set(1, 2, 2); +p[2].set(1, 0, 2); +p[0].dotlabel("(1, 0, 0)", "bot"); +p[1].dotlabel("(1, 2, 2)", "rt"); +p[2].dotlabel("(1, 0, 2)", "rt"); +Path pa("--", true, &p[0], &p[1], &p[2], 0); +pa.draw(); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(10); +current_picture.clear(); + +beginfig(11); +{ +default_focus.set(7, 5, -10, 7, 5, 10, 10); +draw_axes(gray); +Point p[8]; +p[0].set(-2); +p[1].set(2); +p[2].set(0, 0, -2); +p[3].set(0, 0, 2); +p[4] = p[0].mediate(p[2]); +p[5] = p[2].mediate(p[1]); +p[6] = p[1].mediate(p[3]); +p[7] = p[3].mediate(p[0]); +p[4] *= p[5] *= p[6] *= p[7].shift(0, 1); +p[0].dotlabel("$p_0$", "bot"); +p[1].dotlabel("$p_1$"); +p[2].dotlabel("$p_2$"); +p[3].dotlabel("$p_3$"); +p[4].dotlabel("$p_4$"); +p[5].dotlabel("$p_5$"); +p[6].dotlabel("$p_6$"); +p[7].dotlabel("$p_7$"); +Path pa(&p[0], "..", &p[4], "...", &p[2], + "..", &p[5], "...", &p[1], "..", &p[6], "...", &p[3], "..", &p[7], "...", 0); +pa.draw(); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(11); +current_picture.clear(); + +beginfig(12); +{ +Point pt[5]; +pt[0].set(-1, -2); +pt[1].set(0, -3); +pt[2].set(1, 0); +pt[3].set(2, 1); +pt[4].set(-1, 2); +pt[0].dotlabel(Point::WORLD_VALUES_X_Y, "lft"); +pt[1].dotlabel(Point::WORLD_VALUES_X_Y, "bot"); +pt[2].dotlabel(Point::WORLD_VALUES_X_Y, "rt"); +pt[3].dotlabel(Point::WORLD_VALUES_X_Y, "rt"); +pt[4].dotlabel(Point::WORLD_VALUES_X_Y, "lft"); +Path pa("..", true, &pt[0], &pt[1], &pt[2], &pt[3], &pt[4], 0); +pa.draw(); +current_picture.output(Projections::PARALLEL_X_Y); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(12); +current_picture.clear(); + +beginfig(13); +pa.fill(Colors::gray); +current_picture.output(Projections::PARALLEL_X_Y); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(13); +current_picture.clear(); + +beginfig(14); +Point p0(-3, 0, 1); +Point p1(3, 1, 1); +p0.dotlabel(Point::WORLD_VALUES, "bot"); +p1.dotlabel(Point::WORLD_VALUES, "bot"); +p0.draw(p1); +pa.filldraw(); +current_picture.output(Projections::PARALLEL_X_Y); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(14); +current_picture.clear(); + +beginfig(15); +pa.filldraw(black, gray, "", "pensquare xscaled 3mm yscaled 1mm rotated 60"); +current_picture.output(Projections::PARALLEL_X_Y); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(15); +current_picture.clear(); + +beginfig(16); +p0.dotlabel(Point::WORLD_VALUES, "bot"); +p1.dotlabel(Point::WORLD_VALUES, "bot"); +pa.fill(gray); +p0.undraw(p1, "", "pencircle scaled 3mm"); +current_picture.output(Projections::PARALLEL_X_Y); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(16); +current_picture.clear(); + +beginfig(17); +pa.fill(gray); +Path q; +q = pa; +q.scale(.5, .5); +q.unfill(); +current_picture.output(Projections::PARALLEL_X_Y); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(17); +current_picture.clear(); + +beginfig(18); +pa.fill(gray); +q.unfilldraw(white, "", "pensquare xscaled 3mm yscaled 1mm"); +current_picture.output(Projections::PARALLEL_X_Y); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(18); +current_picture.clear(); + +beginfig(19); +p0.dotlabel(Point::WORLD_VALUES, "bot"); +p1.dotlabel(Point::WORLD_VALUES, "bot"); +p0.draw(p1); +pa.fill(gray); +q.unfilldraw(black, "", "pensquare xscaled 3mm yscaled 1mm"); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(19); +current_picture.clear(); + +beginfig(20); +{ +default_focus.set(2, 3, -10, 2, 3, 10, 10); +Reg_Polygon p(origin, 5, 3); +p.draw(); +Point shift_z(0, -.1); +draw_axes(0, "d", "d", "rt", gray, +"", "", origin, origin, shift_z); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(20); +current_picture.clear(); + +beginfig(21); +{ +Reg_Polygon p(origin, 5, 3, 90); +p.draw(); +Point shift_z(0, -.1); +draw_axes(0, "d", "d", "d", gray, "", "", origin, origin, shift_z); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(21); +current_picture.clear(); + +beginfig(22); +{ +Reg_Polygon p(origin, 5, 3, 0, 36); +p.draw(); +Point shift_z(0, -.1); +draw_axes(0, "d", "d", "rt", gray, "", "", origin, origin, shift_z); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(22); +current_picture.clear(); + +beginfig(23); +{ +Reg_Polygon p(origin, 5, 3, 0, 0, 90); +p.draw(); +Point shift_z(0, -.1); +draw_axes(0, "d", "d", "rt", gray, "", "", origin, origin, shift_z); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(23); +current_picture.clear(); + +beginfig(24); +{ +Reg_Polygon p(origin, 5, 3, 45, 45, 45); +p.draw(); +Point shift_z(0, -.1); +draw_axes(0, "d", "d", "d", gray, "", "", origin, origin, shift_z); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(24); +current_picture.clear(); + +beginfig(25); +{ +Point P(-2, 1, 1); +P.dotlabel("P"); +Reg_Polygon hex(P, 6, 4, 60, 30, 30); +hex.draw(); +Point shift_z(0, -.1); +draw_axes(0, "d", "d", "d", gray, "", "", origin, origin, shift_z); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(25); +current_picture.clear(); + +beginfig(26); +{ +Point p(0, -3); +Reg_Polygon polygon; +for (int i = 3; i < 9; ++i){ +polygon.set(p, i, 3); +polygon.draw(); +p.shift(0, 1);} +Point shift_z(0, -.1); +draw_axes(0, "d", "d", "rt", gray, "", "", origin, origin, shift_z); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(26); +current_picture.clear(); + +beginfig(27); +{ +Rectangle r(origin, 2, 3); +r.draw(); +Point shift_z(0, -.1); +draw_axes(0, "d", "d", "rt", gray, "", "", origin, origin, shift_z); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(27); +current_picture.clear(); + +beginfig(28); +{ +Rectangle r(origin, 2, 3, 30, 45, 15); +r.draw(); +Point shift_z(0, -.1); +draw_axes(0, "d", "d", "d", gray, "", "", origin, origin, shift_z); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(28); +current_picture.clear(); + +beginfig(29); +{ +Point p0(.5, 1, 3); +p0.dotlabel("$p_0$"); +Point pt1(p0); +pt1.shift(2); +pt1.label("$p_0 = (0.5, 1, 3)$", "rt"); +Rectangle r(p0, 4, 2, 30, 30, 30); +r.draw(); +Point shift_z(0, -.1); +draw_axes(0, "d", "d", "d", gray, "", "", origin, origin, shift_z); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(29); +current_picture.clear(); + +beginfig(30); +{ +default_focus.set(5, 3, -10, 5, 3, 10, 10); +Rectangle r; +for (int i = 0; i < 180; i += 30){ +r.set(origin, 4, 2, i); + r.draw();} +Point shift_z(0, -.1); +draw_axes(3, "d", "d", "d", gray, "", "", origin, origin, shift_z); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(30); +current_picture.clear(); + + + +beginfig(31); +{ +Point pt[4]; +pt[0].shift(-1, -2); +pt[2] = pt[1] = pt[0]; +pt[1].rotate(180); +pt[3] = pt[1]; +pt[2] *= pt[3].rotate(0, 180); +Rectangle r(pt[0], pt[2], pt[3], pt[1]); +r.draw(); +r.get_point(0).dotlabel(Point::WORLD_VALUES_X_Y, "llft"); +r.get_point(1).dotlabel(Point::WORLD_VALUES_X_Y, "lrt"); +r.get_point(2).dotlabel(Point::WORLD_VALUES_X_Y, "urt"); +r.get_point(3).dotlabel(Point::WORLD_VALUES_X_Y, "ulft"); +Point shift_z(0, -.1); +draw_axes(0, "d", "d", "", gray, "", "", origin, origin, shift_z); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(31); +current_picture.clear(); + +beginfig(32); +{ +Point pt[4]; +pt[0].shift(-1, -2); +pt[2] = pt[1] = pt[0]; +pt[1].rotate(180); +pt[3] = pt[1]; +pt[2] *= pt[3].rotate(0, 180); +pt[0].shift(0, -1); +pt[3].shift(0, 1); +Rectangle r(pt[0], pt[2], pt[3], pt[1]); +r.draw(); +r.get_point(0).dotlabel(Point::WORLD_VALUES_X_Y, "llft"); +r.get_point(1).dotlabel(Point::WORLD_VALUES_X_Y, "lrt"); +r.get_point(2).dotlabel(Point::WORLD_VALUES_X_Y, "urt"); +r.get_point(3).dotlabel(Point::WORLD_VALUES_X_Y, "ulft"); +Point shift_z(0, -.1); +draw_axes(0, "d", "ulft", "", gray, "", "", origin, origin, shift_z); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(32); +current_picture.clear(); + +beginfig(33); +{ +Point pt(-1, 1, 1); +pt.dotlabel(Point::WORLD_VALUES, "bot"); +Ellipse e(pt, 3, 6, 90); +e.draw(); +Point shift_z(0, -.1); +draw_axes(0, "d", "d", "", gray, ""); +current_picture.output(PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(33); +current_picture.clear(); + +beginfig(34); +{ +Ellipse e; +real h_save = 1.5; +real v_save = 2; +real h = h_save; +real v = v_save; +Point p(-1); +for (int i = 0; i < 5; ++i){ +e.set(p, h, v, 90); +e.draw(); +h_save += .25; +v_save += .25; +h *= sqrt(h_save); +v *= sqrt(v_save); +p.shift(0, 0, 2);} +Point shift_z(0, -.1); +draw_axes(0, "d", "d", "d", gray, "", "", origin, origin, shift_z); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(34); +current_picture.clear(); + +beginfig(35); +{ +Point P(0, 2, 1); +P.dotlabel(Point::WORLD_VALUES); +Circle c(P, 3.5, 90, 90); +c.draw(); +Point shift_z(0, -.1); +draw_axes(0, "", "lft", "bot", gray, ""); +current_picture.output(PARALLEL_Z_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(35); +current_picture.clear(); + +beginfig(36); +{ +default_focus.set(2, 5, -10, 2, 5, 10, 10); +Circle c; +Point p(0, 0, 1); +p.dotlabel("p", "bot"); +for (int i = 0; i < 16; ++i){ +c.set(p, 5, i * 22.5, 0, 0, 64); +c.draw();} +Point shift_z(0, -.1); +draw_axes(3.5, "d", "d", "d", gray, "", "", origin, origin, shift_z); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(36); +current_picture.clear(); + +beginfig(37); +{ +default_focus.set(2, 5, -10, 2, 5, 10, 10); +Cuboid c0(origin, 3, 3, 3, 0, 30); +c0.draw(); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(37); +current_picture.clear(); + +beginfig(38); +{ +Cuboid c1(origin, 3, 4, 5, 0, 30); +c1.filldraw(); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(38); +current_picture.clear(); + +beginfig(39); +{ +Tetrahedron t(origin, 4); +t.draw(); +t.get_center().dotlabel("$c$"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(39); +current_picture.clear(); + +beginfig(40); +{ +Dodecahedron d(origin, 3); +d.draw(); +Point P(0, -2.5); +P.label("Parallel projection, x-y plane", "bot"); +current_picture.output(PARALLEL_X_Y); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(40); +current_picture.clear(); + +beginfig(41); +d.draw(); +P.set(0, 0, -3); +P.label("Parallel projection, x-z plane", "bot"); +current_picture.output(PARALLEL_X_Z); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(41); +current_picture.clear(); + +beginfig(42); +d.draw(); +P.set(0, -2.5); +P.label("Parallel projection, z-y plane", "bot"); +current_picture.output(PARALLEL_Z_Y); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(42); +current_picture.clear(); + +beginfig(43); +d.draw(); +P.set(0, -3.5); +P.label("Perspective projection", "bot"); +current_picture.output(); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(43); +current_picture.clear(); + +beginfig(44); +d.filldraw(); +P.label("Perspective projection", "bot"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(44); +current_picture.clear(); + +beginfig(45); +{ +Icosahedron i(origin, 3); +i.draw(); +Point P(0, -2.5); +P.label("Parallel projection, x-y plane", "bot"); +current_picture.output(PARALLEL_X_Y); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(45); +current_picture.clear(); + +beginfig(46); +i.draw(); +P.set(0, 0, -3); +P.label("Parallel projection, x-z plane", "bot"); +current_picture.output(PARALLEL_X_Z); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(46); +current_picture.clear(); + +beginfig(47); +i.draw(); +P.set(0, -2.5); +P.label("Parallel projection, z-y plane", "bot"); +current_picture.output(PARALLEL_Z_Y); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(47); +current_picture.clear(); + +beginfig(48); +default_focus.set(3, 0, -10, 2, 0, 10, 10); +i.draw(); +P.set(0, -3.5); +P.label("Perspective projection---drawn", "bot"); +current_picture.output(); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(48); +current_picture.clear(); + +beginfig(49); +i.filldraw(); +P.label("Perspective projection---filldrawn", "bot"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(49); +current_picture.clear(); + +beginfig(50); +{ +default_focus.set(0, 0, -10, 0, 0, 10, 10); +Circle c(origin, 3, 90); +c.draw(); +c.shift(1.5); +c.draw(); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(50); +current_picture.clear(); + +beginfig(51); +{ +Picture my_picture; +default_focus.set(0, 0, -10, 0, 0, 10, 10); +Circle c(origin, 3, 90); +c.draw(my_picture); +my_picture.output(); +c.shift(1.5); +c.fill(light_gray); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(51); +current_picture.clear(); + +beginfig(52); +{ +default_focus.set(7, 5, -10, 7, 5, 10, 10); +Cuboid c0(origin, 5, 5, 5); +c0.shift(0, 0, 3); +c0.draw(); +Circle z0(c0.get_rectangle_center(0), 2.5, 90, 0, 0, 64); +z0.draw(); +Circle z1(z0); +z1.shift(0, 0, -1); +z1.draw(); +int i; +int j = z0.get_size(); +for (i = 0; i < 8; ++i) + z0.get_point(i * j/8).draw(z1.get_point(i * j/8)); +Cuboid c1(c0.get_rectangle_center(4), 5, 3, 3); +c1.shift(0, 2.5); +c1.draw(); +Rectangle r0 = *c1.get_rectangle_ptr(3); +Point p[10]; +for (i = 0; i < 4; ++i) + p[i] = r0.get_point(i); +p[4] = r0.get_mid_point(0); +p[5] = r0.get_mid_point(2); +p[6] = p[4].mediate(p[5], 2/3.0); +Circle z2(p[6], 2, 90, 90, 0, 64); +z2.draw(); +Circle z3 = z2; +z3.shift(3); +z3.draw(); +j = z2.get_size(); +for (i = 0; i < 8; ++i) + z2.get_point(i * j/8).draw(z3.get_point(i * j/8)); +p[7] = c0.get_rectangle_center(2); +p[7].shift(-4); +p[8] = c0.get_rectangle_center(3); +p[8].shift(4); +current_picture.output(); +current_picture.rotate(45, 45); +current_picture.shift(10, 0, 3); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(52); +current_picture.clear(); + +beginfig(53); +{ +Rectangle r(origin, 3, 3, 90); +Circle c(origin, 3, 90); +c *= r.shift(0, 0, 5); +r.filldraw(black, gray); +c.unfilldraw(black); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(53); +current_picture.clear(); + +beginfig(54); +{ +Rectangle r(origin, 3, 3, 90, 60); +Circle c(origin, 3, 90, 60); +c *= r.shift(0, 0, 5); +r.filldraw(black, gray); +c.unfilldraw(black); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(54); +current_picture.clear(); + +beginfig(55); +{ +Rectangle r(origin, 4, 4, 90, 60); +Circle c(origin, 4, 90, 60); +c *= r.shift(0, 0, 5); +r.filldraw(black, gray); +c.unfilldraw(black); +Point p(origin); +p.label("$.5\\times$", ""); +current_picture.output(Projections::PARALLEL_X_Y, .5); +current_picture.kill_labels(); +p.label("Normal size", ""); +p *= current_picture.shift(2.5); +current_picture.output(Projections::PARALLEL_X_Y); +current_picture.kill_labels(); +p.label("$2\\times$", ""); +current_picture.shift(1); +current_picture.output(Projections::PARALLEL_X_Y, 2); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(55); +current_picture.clear(); + +beginfig(56); +{ +persp_0(2, 1.5, 5, 2, 40, 6, 4, 6, 9, 6, 9); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(56); +current_picture.clear(); + +beginfig(57); +{ +default_focus.set(0, 4, -6, 0, 4, 6, 6); +Rectangle R(origin, 2, 5, 0, 40); +Point p(2, 0, 1.5); +R.shift(p - R.get_point(0)); +R.get_point(0).dotlabel("$r_0$", "bot"); +R.get_point(1).dotlabel("$r_1$", "rt"); +R.get_point(2).dotlabel("$r_2$"); +R.get_point(3).dotlabel("$r_3$", "lft"); +R.get_center().label("$R$", ""); +R.draw(); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(57); +current_picture.clear(); + +beginfig(58); +{ +vector vps; +vps.push_back(.5); +vps.push_back(5); +for (real r = 10; r < 90; r+=10) +vps.push_back(r); +vector points = +make_perspective_frame(vps, 5, 4, 1, 16); +Point f(*points[0]); +Point vp_pt_5r(*points[7]); +Point vp5r(*points[8]); +Point vp10r(*points[9]); +Point p10r(vp10r - f); +Point p_pt_5r(vp_pt_5r - f); +Point p5r(vp5r - f); +p_pt_5r.unit_vector(true); +p5r.unit_vector(true); +p10r.unit_vector(true); +p_pt_5r *= p5r *= p10r *= 13.5; +stringstream s; +f.drawarrow(p_pt_5r, black, "evenly"); +s << "VP $0.5^\\circ$ $(x=" +<< vp_pt_5r.get_x() << "{{}\\rm cm}{})$"; +p_pt_5r.label(s.str(), "rt"); +s.str(""); +f.drawarrow(p5r, black, "evenly"); +s << "VP $5^\\circ$ $(x=" +<< vp5r.get_x() << "{{}\\rm cm}{})$"; +p5r.label(s.str(), "rt"); +s.str(""); +f.drawarrow(p10r, black, "evenly"); +s << "VP $10^\\circ$ $(x=" +<< vp10r.get_x() << "{{}\\rm cm}{})$"; +p10r.label(s.str(), "rt"); +s.str(""); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "b.dx=.25cm; b.dy=.5cm;" << endl; +out_stream << "b.c := b.c shifted (0cm, 0cm);" << endl; + +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(58); +current_picture.clear(); + +beginfig(59); +{ +default_focus.set(0, 4, -6, 0, 4, 6, 6); +Rectangle r; +Point center(0, 2); +stringstream s; +r.set(center, 2, 5, 0, 0, 0.5); +r.draw(); +s << "$" << .5 << "^\\circ$"; +center.label(s.str(), ""); +s.str(""); +center.shift(4); +r.set(center, 2, 5, 0, 0, 2.5); +r.draw(); +s << "$" << 2.5 << "^\\circ$"; +center.label(s.str(), ""); +s.str(""); +center.shift(4); +r.set(center, 2, 5, 0, 0, 5); +r.draw(); +s << "$" << 5 << "^\\circ$"; +center.label(s.str(), ""); +s.str(""); +center.shift(4); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(59); +current_picture.clear(); + +beginfig(60); +{ +Point pos(0, 5, -10); +Point dir(0, 5, 10); +Focus f(pos, dir, 10); +Point center(2, 0, 3); +Rectangle r(center, 3, 3); +r.draw(); +center.label("$r$", ""); +draw_axes(gray); +current_picture.output(f); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(60); +current_picture.clear(); + +beginfig(61); +{ +Point pos(0, 5, -10); +Point dir(0, 5, 10); +Focus f(pos, dir, 10, 30); +Point center(2, 0, 3); +Rectangle r(center, 3, 3); +r.draw(); +center.label("$r$", ""); +draw_axes(gray); +current_picture.output(f); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(61); +current_picture.clear(); + +beginfig(62); +{ +Focus f(3, 5, -5, 0, 3, 0, 10, 10); +Point center(2, 0, 3); +Rectangle r(center, 3, 3); +r.draw(); +center.label("$r$", ""); +draw_axes(gray); +current_picture.output(f); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(62); +current_picture.clear(); + +beginfig(63); +{ +Point pos(2, 10, 3); +Point dir(2, -10, 3); +Focus f; +Point center(2, 0, 3); +for (int i = 0; i < 5; ++i) +{ +f.set(pos, dir, 10, (15 * i)); +Rectangle r(center, 3, 3); +r.get_point(0).label(i, "lft"); +r.draw(); + current_picture.output(f); + current_picture.clear(); + pos.shift(1, 1, 0); + dir.rotate(0, 0, 10); + } +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(63); +current_picture.clear(); + +beginfig(64); +{ +default_focus.set(1, 3, -5, 0, 3, 5, 10); +Point p(0, -2, 5); +Rectangle r(p, 3, 4, 90); +p.label("$r$", ""); +r.draw(); +Point q(2, -2, 3); +Circle c(q, 3, 90); +q.label("$c$", ""); +c.draw(); +current_picture.output(); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(64); +current_picture.clear(); + +beginfig(65); +p.label("$r$", ""); +q.label("$c$", ""); +r.draw(); +c.filldraw(); +current_picture.output(); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(65); +current_picture.clear(); + +beginfig(66); +default_focus.set(8, 0, -5, 5, 3, 5, 10); +r.get_point(3).mediate(p, .333).label("$r$", ""); +q.label("$c$", ""); +r.draw(); +c.filldraw(); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(66); +current_picture.clear(); + +beginfig(67); +{ +default_focus.set(5, 3, -10, 3, 1, 1, 10, 180); +Rectangle r0(origin, 3, 4, 45); +Rectangle r1(origin, 2, 6, -45); +r0.draw(); +r1.draw(); +r0.get_point(0).label(Point::WORLD_VALUES_Z, "lft"); +r0.get_point(1).label(Point::WORLD_VALUES_Z, "rt"); +r0.get_point(2).label(Point::WORLD_VALUES_Z, "lrt"); +r0.get_point(3).label(Point::WORLD_VALUES_Z, "llft"); +r1.get_point(0).label(Point::WORLD_VALUES_Z, "lft"); +r1.get_point(1).label(Point::WORLD_VALUES_Z, "rt"); +r1.get_point(2).label(Point::WORLD_VALUES_Z, "rt"); +r1.get_point(3).label(Point::WORLD_VALUES_Z, "lft"); +r0.get_mid_point(0).label("$r_0$", "bot"); +r1.get_mid_point(0).label("$r_1$"); +draw_axes(gray); +current_picture.output(default_focus, PERSP, 1, MAX_Z); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(67); +current_picture.clear(); + +beginfig(68); +{ +default_focus.set(5, 3, -10, 3, 1, 1, 10, 180); +Rectangle r0(origin, 3, 4, 45); +Rectangle r1(origin, 2, 6, -45); +r0.filldraw(); +r1.filldraw(black, gray); +r0.get_mid_point(0).label("$r_0$", "bot"); +r1.get_mid_point(0).label("$r_1$"); +draw_axes(gray); +current_picture.output(default_focus, PERSP, 1, MAX_Z); +current_picture.clear(); +draw_axes(gray); +current_picture.output(default_focus, PERSP, 1, MAX_Z); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(68); +current_picture.clear(); + +beginfig(69); +{ +default_focus.set(5, 3, -10, 3, 1, 1, 10, 180); +Rectangle r0(origin, 3, 4, 45); +Rectangle r1(origin, 2, 6, -45); +r0.get_mid_point(0).label("$r_0$", "bot"); +r1.get_mid_point(0).label("$r_1$"); +r0.filldraw(); +r1.filldraw(black, gray); +draw_axes(gray); +current_picture.output(default_focus, PERSP, 1, MIN_Z); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(69); +current_picture.clear(); + + + +beginfig(70); +{ +default_focus.set(5, 3, -10, 3, 1, 1, 10, 180); +Rectangle r(origin, 3, 4, 45); +Circle c(origin, 2, -45); +r.filldraw(); +c.filldraw(black, gray); +draw_axes(gray); +current_picture.output(default_focus, PERSP, 1, NO_SORT); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(70); +current_picture.clear(); + +beginfig(71); +{ +Rectangle r0(origin, 2, .5, 90); +r0.draw(); +Point p0(r0.get_center()); +p0.label("{\\tt Shapes}", ""); +Rectangle r1(origin, 3, .5, 90); +r1.shift(r0.get_point(1) - r1.get_point(0)); +r1.draw(); +Point p1(r1.get_center()); +p1.label("Comparisons", ""); +Transform t; +t.shift(r0.get_point(0) - r0.get_point(3)); +p0 *= p1 *= r0 *= r1 *= t; +r0.draw(); +r1.draw(); +real w0 = r0.get_point(1).get_x() - r0.get_point(0).get_x(); +real w1 = r1.get_point(1).get_x() - r1.get_point(0).get_x(); +p0.shift(.375 * w0); +p1.shift(.375 * w1); +p0.label("10", "lft"); +p1.label("45", "lft"); +p0 *= p1 *= r0 *= r1 *= t; +r0.draw(); +r1.draw(); +p0.label("100", "lft"); +p1.label("4950", "lft"); +p0 *= p1 *= r0 *= r1 *= t; +r0.draw(); +r1.draw(); +p0.label("1000", "lft"); +p1.label("499,500", "lft"); +p0 *= p1 *= r0 *= r1 *= t; +r0.draw(); +r1.draw(); +p0.label("10,000", "lft"); +p1.label("49,995,000", "lft"); +p0 *= p1 *= r0 *= r1 *= t; +r0.draw(); +r1.draw(); +p0.label("100,000", "lft"); +p1.label("$4.99995\\times 10^9$", "lft"); +current_picture.output(Projections::PARALLEL_X_Y); +} +endfig(71); +current_picture.clear(); + +beginfig(72); +{ +default_focus.set(2, 3, -10, 2, 3, 10, 20); +Rectangle R(origin, 5, 3); +Circle C(origin, 3, 90); +C.half(180).filldraw(black, light_gray); +R.filldraw(); +C.half().filldraw(black, light_gray); +Point p = C.get_point(4); +p.shift(0, -.5 * p.get_y()); +p.label("$C$", ""); +Point q = R.get_mid_point(0); +q.shift(0, 0, -.5 * q.get_z()); +q.label("$R$", ""); +current_picture.output(default_focus, PERSP, 1, NO_SORT); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(72); +current_picture.clear(); + +beginfig(73); +{ +Rectangle r[4]; +r[0].set(origin, 1, 1, 90); +r[3] = r[2] = r[1] = r[0]; +Transform t; +t.reset(); +t.shift(1.5, 1.5); +r[0] *= t; +r[0].draw(); +r[0].get_center().label("$r_0$", ""); +t.shift_times(1.5, 1.5); +r[1] *= t; +r[1].get_center().label("$r_1$", ""); +r[1].draw(); +t.shift_times(1.5, 1.5); +r[2] *= t; +r[2].get_center().label("$r_2$", ""); +r[2].draw(); +t.shift_times(1.5, 1.5); +r[3] *= t; +r[3].get_center().label("$r_3$", ""); +r[3].draw(); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(73); +current_picture.clear(); + +beginfig(74); +{ +default_focus.set(2, 3, -10, 2, 3, 10, 10); +Cuboid c(origin, 1, 1, 1); +c.draw(); +Transform t; +t.rotate(30, 30, 30); +t.shift(1, 0, 1); +c *= t; +c.draw(); +t.shift_times(1.5, 0, 1.5); +c *= t; +c.draw(); +t.shift_times(1.5, 0, 1.5); +c *= t; +c.draw(); +t.shift_times(1.5, 0, 1.5); +c *= t; +c.draw(); +t.shift_times(1.5, 0, 1.5); +c *= t; +c.draw(); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(74); +current_picture.clear(); + + + + +beginfig(75); +{ +default_focus.set(2, 3, -10, 2, 3, 10, 10); +Circle c(origin, 3, 75, 25, 6); +c.shift(2, 3); +c.draw(); +c.get_center().label("$c$", "llft"); +Point n = c.get_normal(); +n.shift(c.get_center()); +n.label("$\\vec{n}$", "urt"); +c.get_center().drawarrow(n); +Transform t; +t.align_with_axis(c.get_center(), n, 'y'); +n *= c *= t; +c.draw(); +c.get_center().label("$c$", "lrt"); +n.label("$\\vec{n}$", "rt"); +draw_axes(gray, 0, "d", "d", "rt"); +c.get_center().drawarrow(n); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(75); +current_picture.clear(); + +beginfig(76); +{ +default_focus.set(2, 1, -10, 2, 1, 10, 10); +Point P(1, 1, 2); +origin.drawarrow(P); +P.label("$\\vec{{}P}{}$"); +draw_axes(gray); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(76); +current_picture.clear(); + + + +beginfig(77); +Circle c(origin, 3); +c.draw(); +Picture new_picture(current_picture); +new_picture.shift(2); +new_picture.output(Projections::PARALLEL_X_Z); +Point p1(c.get_point(8)); +Point p0(p1); +p0.shift(-1); +p0.dotlabel("current$\\underline{\\hbox to 1ex{\\hfil}}$picture", "ulft"); +p0.drawarrow(p1); +Point p2(c.get_point(0)); +p2.shift(2); +Point p3(p2); p3.shift(1); +p3.drawarrow(p2); +p3.dotlabel("new$\\underline{\\hbox to 1ex{\\hfil}}$picture", "urt"); +current_picture.output(Projections::PARALLEL_X_Z); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(77); +current_picture.clear(); + +beginfig(78); +Transform t; +t.rotate(0, 0, 180); +t.shift(5); +Reg_Polygon pl(origin, 5, 3, 90); +pl.draw(); +pl.label(); +current_picture.output(Projections::PARALLEL_X_Y); +current_picture *= t; +current_picture.output(Projections::PARALLEL_X_Y); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(78); +current_picture.clear(); + +beginfig(79); +Ellipse e(origin, 3, 5); +e.label(); +e.draw(); +Point pt0(-3); +Point pt1(3); +pt0.draw(pt1); +Point pt2(0, 0, -4); +Point pt3(0, 0, 4); +pt2.draw(pt3); +pt0.dotlabel("0", "lft"); +pt1.dotlabel("1", "rt"); +pt2.dotlabel("2", "bot"); +pt3.dotlabel("3"); +current_picture.output(Projections::PARALLEL_X_Z); +current_picture.rotate(0, 60); +current_picture.suppress_labels(); +current_picture.output(Projections::PARALLEL_X_Z); +current_picture.rotate(0, 60); +current_picture.output(Projections::PARALLEL_X_Z); +current_picture.unsuppress_labels(); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(79); +current_picture.clear(); + +beginfig(80); +{ +default_focus.set(4, 3, -10, 0, 3, 10, 10); +Point P(1, 1, 1); +P.dotlabel("$P$", "bot"); +Rectangle r(P, 4, 4, 20, 45, 35); +r.filldraw(black, light_gray); +Plane q = r.get_plane(); +P.mediate(r.get_point(1), .25).label("$r$", ""); +Point A(2, 0, 2); +Point B(2, 1.64143, 2); +A.dotlabel("$A$", "rt"); +B.dotlabel("$B$", "rt"); +Point C(0.355028, 2.2185, 6.48628); +C.dotlabel("$C$"); +draw_axes(0, "d", "d", "d", black, "evenly"); +current_picture.output(default_focus, Projections::PERSP, 1, Sorting::NO_SORT); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(80); +current_picture.clear(); + + + + + +beginfig(81); +{ +default_focus.set(3, 2, -10, 3, 2, 10, 10); +Point p0_b(1, 0, 2); +p0_b.dotlabel(Point::WORLD_VALUES, "bot"); +Point p0_a(p0_b); +p0_a.rotate(90); +p0_a.label(Point::WORLD_VALUES); +p0_b.drawarrow(p0_a, black, "evenly"); +p0_b.mediate(p0_a).label("$p0$", "rt"); +Point p1_b(-1, 1, 1); +p1_b.dotlabel(Point::WORLD_VALUES); +Point p1_a(p1_b); +p1_a.rotate(-90, 90, 90); +p1_a.label(Point::WORLD_VALUES, "bot"); +p1_b.mediate(p1_a, .3).label("$p_1$", "llft"); +p1_b.drawarrow(p1_a, black, "evenly"); +draw_axes(gray); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(81); +current_picture.clear(); + +beginfig(82); +{ +default_focus.set(4, 3, -10, 4, 3, 10, 10); +Point P(2, 0, 0); +Point R(P); +P.dotlabel("$P_{\\rm{{}initial}}$", "urt"); +P.label(Point::WORLD_VALUES, "bot"); +Path q; +q.set_connectors(".."); +Point A; +A.dotlabel("$A$", "lrt"); +Point B(2, 2, 2); +B.dotlabel("$B$"); +A.draw(B); +P.rotate(A, B, 180); +P.dotlabel("$P_{\\rm{{}rotated}}$", "ulft"); +P.label(Point::WORLD_VALUES, "llft"); +q += R; +for (int i = 10; i <= 180; i+=10) + { + R.rotate(A, B, 10); + q += R; + } +q.draw(black, "evenly"); +draw_axes(gray, 3.5, "rt"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(82); +current_picture.clear(); + +beginfig(83); +{ +default_focus.set(3, 2, -10, 3, 2, 10, 10); +Point p0_b(1, 0, 3); +p0_b.dotlabel(Point::WORLD_VALUES); +Point p0_a(p0_b); +p0_a.scale(4); +p0_a.label(Point::WORLD_VALUES); +p0_b.drawarrow(p0_a, black, "evenly"); +p0_b.mediate(p0_a).label("$p_0$"); +Point p1_b(-2, -1, -2); +p1_b.dotlabel(Point::WORLD_VALUES, "bot"); +Point p1_a(p1_b); +p1_a.scale(-2, -3, -4); +p1_a.label(Point::WORLD_VALUES); +p1_b.drawarrow(p1_a, black, "evenly"); +p1_b.mediate(p1_a, .25).label("$p_1$"); +draw_axes(gray); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(83); +current_picture.clear(); + +beginfig(84); +{ +Point P0; +Point P1(3); +Point P2(3, 3); +Point P3(0, 3); +Rectangle r(P0, P1, P2, P3); +r.draw(); +r.get_point(0).dotlabel("$P_0$ = $Q_0$ = (0, 0)", "llft"); +r.get_point(1).dotlabel("$P_1$ = $Q_1$ = (3, 0)", "lrt"); +r.get_point(2).dotlabel("$P_2$ = (3, 3)", "ulft"); +r.get_point(3).dotlabel("$P_3$ = (0, 3)", "ulft"); +r.get_center().label("$r$", ""); +Point q_center(r.get_center()); +q_center *= r.shear(1.5); +q_center.label("$q$", ""); +r.get_point(2).dotlabel("$Q_2$ = (7.5, 3)"); +r.get_point(3).dotlabel("$Q_3$ = (4.5, 3)"); +r.draw(black, "evenly"); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(84); +current_picture.clear(); + +beginfig(85); +{ +default_focus.set(4, 3, -10, 4, 3, 10, 10); +Point P; +Path q; +q.set_connectors(".."); +q += P; +P.dotlabel(Point::WORLD_VALUES, "lrt"); +P.shift(1, 1, 1); +q += P; +P.dotlabel(Point::WORLD_VALUES, "rt"); +P.shift_times(2, 2, 2); +q += P; +P.dotlabel(Point::WORLD_VALUES, "rt"); +P.shift_times(2, 2, 2); +q += P; +P.dotlabel(Point::WORLD_VALUES, "rt"); +P.shift_times(2, 2, 2); +q += P; +P.label(Point::WORLD_VALUES); +q.drawarrow(black, "evenly"); +draw_axes(gray); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(85); +current_picture.clear(); + + + +beginfig(86); +{ +default_focus.set(4, 1, -10, 4, 1, 10, 10); +Point P(1, -1, -1); +origin.drawarrow(P); +P.label("$P$", "rt"); +P.label(Point::WORLD_VALUES, "bot"); +Point Q(3, 2, 5); +origin.drawarrow(Q); +Q.label("$Q$"); +Q.label(Point::WORLD_VALUES, "rt"); +real P_Q_angle = (180.0 / PI) + * acos(P.dot_product(Q) / (P.magnitude() * Q.magnitude())); +Path r; +r.set_connectors("--"); +r += origin; +r += P; +r += Q; +Point N = r.get_normal(); +Point T(P); +T *= .75; +Path u; +u.set_connectors(".."); +u += T; +Point V(T); +V.rotate(origin, N, -P_Q_angle / 2); +V.label("$\\theta$", "lft"); +V.shift(.75); +stringstream s; +s << "$\\theta = " << P_Q_angle << "^\\circ$"; +V.label(s.str(), "urt"); +s.str(""); +s << "$P\\bullet Q = " << P.dot_product(Q) << "$"; +V.label(s.str(), "lrt"); +for (int i = 0; i < 10; ++i) + { + T.rotate(origin, N, -P_Q_angle/10); + u += T; + } +u.draw(black, "evenly"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(86); +current_picture.clear(); + +beginfig(87); +{ +default_focus.set(4, 1, -10, 4, 1, 10, 10); +Point P(2); +Point Q(P); +real dist = .75; +Point P0(dist); +Point R0(dist, dist); +Point Q0(P0); +Q0 *= Q.rotate(0, 0, 90); +R0 *= P0 *= Q0 *= P *= Q.rotate(0, 45, 45); +R0 *= P0 *= Q0 *= P *= Q.rotate(45); +origin.drawarrow(P); +P.label("$P$"); +P.label(Point::WORLD_VALUES, "rt"); +origin.drawarrow(Q); +Q.label("$Q$"); +Q.label(Point::WORLD_VALUES, "llft"); +origin.mediate(R0).label("$90^\\circ$", ""); +Path s("--", false, &P0, &R0, &Q0, 0); +s.draw(black, "evenly"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(87); +current_picture.clear(); + +beginfig(88); +{ +default_focus.set(4, 1, -10, 4, 1, 10, 10); +Point P(2, 2, 2); +Point Q(-2, 2, 2); +Point n = P.cross_product(Q); +real angle_deg = P.angle(Q); +real theta = (PI / 180.0) * angle_deg; +real n_mag = P.magnitude() * Q.magnitude() * sin(theta); +P.label("$P$"); +P.label(Point::WORLD_VALUES, "rt"); +Q.label("$Q$"); +Q.label(Point::WORLD_VALUES, "lft"); +n.label("$\\vec{{}n}{}$", "bot"); +n.label(Point::WORLD_VALUES, "urt"); +origin.drawarrow(n); +origin.drawarrow(P); +origin.drawarrow(Q); +Point R(origin.mediate(P)); +Point T(R); +Path s; +s.set_connectors(".."); +s += R; +real angle = P.angle(Q); +for (int i = 0; i < 10; ++i) + { + R.rotate(origin, n, angle/10); + s += R; + } +s.draw(black, "evenly"); +T.rotate(origin, n, angle/2); +T = origin.mediate(T, .5); +T.label("$\\theta$", ""); +T.shift(1.5); +stringstream u; +u << "$\\theta = " << angle_deg << "^\\circ$"; +T.label(u.str(), "rt"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(88); +current_picture.clear(); + +beginfig(89); +{ +default_focus.set(4, 1, -10, 4, 1, 10, 10); +Point P(1, 2, 1); +Point Q(P); +Point R; +R *= Q.shift(-3, -1, 1); +origin.drawarrow(P); +R.drawarrow(Q); +Point s(Q - R); +R.mediate(Q).label("$\\vec{{}s}$", "ulft"); +Point n = P.cross_product(s); +origin.dotlabel("origin", "bot"); +P.label("$P$"); +Q.label("$Q$"); +R.dotlabel("$R$", "bot"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(89); +current_picture.clear(); + + + +beginfig(90); +{ +default_focus.set(3, 3, -10, 2, 2, 10, 10, 180); +Point P(3.75, -1.25, 6.25); +P.label("$P$"); +origin.drawarrow(P, black); +Point Q(-5, 2.5, 6.25); +Q.label("$Q$"); +origin.drawarrow(Q, black); +real angle = P.angle(Q); +Point n = origin.get_normal(P, Q); +n.label("$\\vec{{}n}$", "lft"); +origin.drawarrow(n); +Point a(P); +a *= .75; +Path b; +b += ".."; +b += a; +for (int i = 0; i < 10; ++i) + { + a.rotate(origin, n, -angle/10); + b += a; + } +a.rotate(origin, n, angle/2); +a.label("$\\theta$", "bot"); +a.shift(1.5, 1); +stringstream c; +c << "$\\theta = " << angle << "^\\circ$"; +a.label(c.str(), ""); +b.draw(black, "evenly"); +draw_axes(gray, 0, "d", "d", "rt"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(90); +current_picture.clear(); + +beginfig(91); +{ +default_focus.set(2, 2, -10, 2, 2, 10, 10); +Point p0(-1, -2, 1); +Point p1(3, 2, 5); +Point p2(p0.mediate(p1, .75)); +Point p3(p0.mediate(p1, 1.5)); +Point p4(p2); +p4.shift(-2, 1, -1); +p0.dotlabel("$p_0$", "bot"); +p1.dotlabel("$p_1$"); +p2.dotlabel("$p_2$", "lft"); +p3.dotlabel("$p_3$"); +p4.dotlabel("$p_4$"); +p0.draw(p1); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(91); +current_picture.clear(); + +beginfig(92); +{ +Point A(-1, -2); +A.dotlabel("$A$", "rt"); +Point B(2, 3); +B.dotlabel("$B$", "lft"); +A.draw(B); +Point C(B.mediate(A, 1.25)); +C.dotlabel("$C$", "ulft"); +stringstream s; +bool_real br = C.is_on_line(A, B); +s << "$r \\equiv " << br.second << "$"; +C.label(s.str(), "bot"); +C.draw(A, black, "evenly"); +s.str(""); +Point D(A.mediate(B)); +br = D.is_on_line(A, B); +D.dotlabel("$D$", "lft"); +s << "$r \\equiv " << br.second << "$"; +D.label(s.str(), "rt"); +s.str(""); +Point E(A.mediate(B, 1.25)); +br = E.is_on_line(A, B); +E.dotlabel("$E$", "lft"); +s << "$r \\equiv " << br.second << "$"; +E.label(s.str(), "rt"); +B.draw(E, black, "evenly"); +s.str(""); +Point F(D); +F.shift(-1, 1); +F.dotlabel("$F$"); +F.label("$r\\equiv$ {\\tt INVALID$\\underline{\\hbox to 1ex{\\hfil}}$REAL}", "llft"); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(92); +current_picture.clear(); + +beginfig(93); +{ +default_focus.set(2, 5, -10, 1, 3, 10, 10, 180); +Point p0(-1, 0, -1); +Point p1(10, 0, 10); +p0.draw(p1); +Point p2(5, 5, 5); +p0.draw(p2); +Point p3 = p0.mediate(p1, 1.5); +p1.draw(p3, black, "evenly"); +Point p4 = p0.mediate(p2, 1/3.0); +p0.dotlabel("$p_0$", "bot"); +p1.dotlabel("$p_1$"); +p2.dotlabel("$p_2$"); +p3.dotlabel("$p_3$"); +p4.dotlabel("$p_4$", "rt"); +draw_axes(gray); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(93); +current_picture.clear(); + +beginfig(94); +{ +Point A(-1, -1); +Point B(1, 1); +Point C(-1, 1); +Point D(1, -1); +A.draw(B); +C.draw(D); +A.dotlabel("$A$", "bot"); +B.dotlabel("$B$"); +C.dotlabel("$C$"); +D.dotlabel("$D$", "bot"); +bool_point bp = Point::intersection_point(A, B, C, D); +bp.pt.dotlabel("$i$"); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(94); +current_picture.clear(); + +beginfig(95); +{ +Point A(.5, .5); +Point B(1.5, 1.5); +Point C(-1, 1); +Point D(1, -1); +A.draw(B); +C.draw(D); +A.dotlabel("$A$"); +B.dotlabel("$B$"); +C.dotlabel("$C$"); +D.dotlabel("$D$"); +bool_point bp = Point::intersection_point(A, B, C, D); +bp.pt.dotlabel("$i$"); +Point E(A.mediate(bp.pt, 2)); +A.draw(E, black, "evenly"); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(95); +current_picture.clear(); + +beginfig(96); +{ +Point P(1, 1); +P.drawdot(gray, "pensquare scaled 1cm"); +P.label("$P$", ""); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(96); +current_picture.clear(); + +beginfig(97); +{ +Point P(1, 1); +P.drawdot(gray, "pensquare scaled 1cm"); +P.undrawdot("pencircle scaled .5cm"); +P.label("$P$", ""); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(97); +current_picture.clear(); + +beginfig(98); +{ +default_focus.set(4, 3, -10, 0, 3, 10, 10); +Point P(-1, -1, -1); +P.dotlabel("$P$", "bot"); +Point Q(2, 3, 5); +Q.dotlabel("$Q$"); +P.draw(Q, Colors::gray, "", "pensquare scaled .5cm"); +draw_axes(); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(98); +current_picture.clear(); + +beginfig(99); +{ +default_focus.set(4, 3, -10, 0, 3, 10, 10); +Point P(-1, -1, -1); +P.dotlabel("$P$", "bot"); +Point Q(2, 3, 5); +Q.dotlabel("$Q$"); +P.draw(Q, gray, "", "pensquare scaled .5cm"); +P.undraw(Q, "evenly scaled 6", "pencircle scaled .3cm"); +draw_axes(); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(99); +current_picture.clear(); + + + + +beginfig(100); +{ +default_focus.set(4, 3, -10, 0, 3, 10, 10); +Point P(-3, -2, 1); +P.dotlabel("$P$", "bot"); +Point Q(3, 3, 5); +Q.label("$Q$"); +P.drawarrow(Q); +Point R(P.mediate(Q)); +R.label("$\\overrightarrow{{}PQ}{}$", "ulft"); +draw_axes(gray); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(100); +current_picture.clear(); + +beginfig(101); +{ +Point p0(2, 3); +p0.label("$p_0$"); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(101); +current_picture.clear(); + +beginfig(102); +{ +Point P; +Point Q(2, 2); +P.drawarrow(Q); +P.dotlabel("$P$", "bot"); +Q.label("$Q$"); +Point R(P.mediate(Q)); +R.label("$\\overrightarrow{PQ}$", "ulft"); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(102); +current_picture.clear(); + +beginfig(103); +{ +Point p0(2, 3); +p0.dotlabel("$p_0$"); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(103); +current_picture.clear(); + +beginfig(104); +{ +default_focus.set(2, 3, -10, 0, 3, 10, 10); +draw_axes(gray); +stringstream s; +Point p(2, 1, 2); +Point d(-3, 3, 3.5); +p.dotlabel("$p$"); +p.label(Point::WORLD_VALUES, "bot"); +p.draw(d, black, "evenly"); +Line L0(p, d); +s << "$d \\equiv L_0.{\\tt direction}\\equiv (" + << L0.direction.get_x() + << ", " << L0.direction.get_y() << ", " << L0.direction.get_z() + << ")$"; +L0.direction.label(s.str()); +origin.drawarrow(L0.direction); +Line L1 = p.get_line(d); +s.str(""); +s << "$L_1.{\\tt direction}\\equiv (" << L1.direction.get_x() + << ", " << L1.direction.get_y() << ", " << L1.direction.get_z() + << ")$"; +L1.direction.label(s.str()); +origin.drawarrow(L1.direction); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(104); +current_picture.clear(); + +beginfig(105); +{ +default_focus.set(4, 3, -10, 0, 3, 10, 10); +Circle c(origin, 5); +Point N(0, 1); +c *= N.rotate(-35, 30, 20); +N.label("$N$"); +Point N_save(N); +Point P(1, 1, 1); +Plane q(P, N); +P.dotlabel("$P$", "lrt"); +c *= N.shift(P); +N.label("$\\vec{n}$"); +c.filldraw(black, light_gray, "evenly"); +Point pt[7]; +P.drawarrow(N); +pt[0] = c.get_center(); +for (int i = 0; i < 16; i+=2) + { + pt[1] = c.get_point(i); + pt[2] = pt[1]- pt[0]; + pt[2] *= .5; + pt[2].shift(pt[1]); + pt[0].drawarrow(pt[2], black, "evenly"); + } +pt[3] = c.get_center().mediate(c.get_point(15), .667); +pt[4] = c.get_center().mediate(c.get_point(0), .667); +pt[5] = pt[3].mediate(pt[4]); +pt[5].label("$q$"); +pt[6].shift(0, -.1); +draw_axes(0,"d","d","d",black,"","",0,0,pt[6]); +origin.drawarrow(N_save); +current_picture.output(default_focus, Projections::PERSP, 1, Sorting::NO_SORT); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(105); +current_picture.clear(); + +beginfig(106); +{ +default_focus.set(-3, 4, -10, -3, 4, 10, 10); +Circle c(origin, 5); +Point N(0, 1); +c *= N.rotate(-10, 20, 20); +Point P(1, 1, 1); +Plane q(P, N); +P.dotlabel("$P$", "lrt"); +c *= N.shift(P); +N.label("$\\vec{n}$", "rt"); +c.filldraw(black, light_gray, "evenly"); +Point pt[7]; +P.drawarrow(N); +pt[0] = c.get_center(); +for (int i = 0; i < 16; i+=2) + { + pt[1] = c.get_point(i); + pt[2] = pt[1]- pt[0]; + pt[2] *= .5; + pt[2].shift(pt[1]); + pt[0].drawarrow(pt[2], black, "evenly"); + } +pt[3] = c.get_point(12).mediate(c.get_point(14), .4); +pt[4] = pt[0].mediate(pt[3], .8); +pt[4].label("$q$", ""); +pt[6].shift(0, -.1); +Point A(4, -2, 4); +Point B(-1, 3, 2); +A.dotlabel("$A$", "bot"); +B.dotlabel("$B$"); +A.draw(B, black, "evenly"); +Point C = q.intersection_point(A, B).pt; +C.dotlabel("$C$", "bot"); +real_short bp; +draw_axes(0,"d","d","d",black,"","",0,0,pt[6]); +current_picture.output(default_focus, Projections::PERSP, 1, Sorting::NO_SORT); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(106); +current_picture.clear(); + +beginfig(107); +{ +default_focus.set(3, 2, -10, 3, 2, 10, 10); +Point center(2, 2, 3.5); +center.drawdot(); +Reg_Polygon h(center, 6, 4, 80, 30, 10); +h.draw(); +Plane q = h.get_plane(); +Point N = q.normal; +N.shift(center); +Point N_temp(N); +N_temp *= 1.1; +center.drawarrow(N_temp); +N_temp.label("$\\vec{n}$", "rt"); +Point P0 = center.mediate(h.get_point(2)); +P0.shift(5 * (N - center)); +P0.dotlabel("$P_0$"); +Point P1(P0); +P1.rotate(h.get_point(1), h.get_point(4)); +P1 = 3 * (P1 - P0); +P1.shift(P0); +P1.shift(3, -.5, -2); +P1.dotlabel("$P_1$"); +bool_point bp = q.intersection_point(P0, P1); +Point i_P = bp.pt; +i_P.dotlabel("$i_P$", "bot"); +P0.draw(P1, black, "evenly"); +Point P4 = h.get_point(3).mediate(h.get_point(0), .75); +P4.shift(N - center); +Point P5(P4); +P5.rotate(h.get_point(3), h.get_point(0)); +P4.shift(-1, 2); +Path theta(P4, P5); +P4.drawdot(black, "pencircle scaled .75mm"); +theta.get_point(0).mediate(theta.get_point(1), .1).label("$\\theta$", "rt"); +theta.drawarrow(black); +bp = q.intersection_point(theta); +Point i_theta = bp.pt; +i_theta.dotlabel("$i_\\theta$", "rt"); +draw_axes(); +current_picture.output(default_focus, Projections::PERSP, 1, Sorting::NO_SORT); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(107); +current_picture.clear(); + +beginfig(108); +{ +default_focus.set(3, 2, -10, 3, 2, 10, 10); +Rectangle r0(origin, 5, 5, 10, 15, 6); +Rectangle r1(origin, 5, 5, 90, 50, 10); +r1 *= r0.rotate(30, 30, 30); +r1 *= r0.shift(1, -1, 3); +r1.filldraw(black, gray); +r0.draw(black, "", "pencircle scaled .5mm"); +r0.get_point(1).label("$r_0$"); +r1.get_point(2).label("$r_1$", "lft"); +Plane q0 = r0.get_plane(); +Plane q1 = r1.get_plane(); +Line l = q0.intersection_line(q1); +Point P0(l.direction); +P0.shift(l.position); +Point P1(-l.direction); +P1.shift(l.position); +Point P2(P0 - P1); +P2 *= 12.5; +P2.shift(P0); +Point P3(P0 - P1); +P3 *= 7; +P3.shift(P0); +P2.label("$P_2$", "rt"); +P3.label("$P_3$", "rt"); +P2.drawarrow(P3, black, "evenly"); +P3.drawarrow(P2, black, "evenly"); +P2.mediate(P3, .8).label("$l$", "rt"); +draw_axes(); +current_picture.output(default_focus, Projections::PERSP, 1, Sorting::NO_SORT); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(108); +current_picture.clear(); + +beginfig(109); +{ +Point p0; +p0.dotlabel("$p_0$", "bot"); +Point p1(1, 1); +p1.dotlabel("$p_1$"); +Point p2(2, 3); +p2.dotlabel("$p_2$"); +Path q0(p0, p1); +Path q1; +q1 = q0; +Path q2 = p0.draw(p1); +Path q3("..", false, &p1, &p2, &p0, 0); +q3.draw(black, "evenly"); +Point p4(p0.mediate(p1)); +p4.label("$q_0 \\equiv q_1 \\equiv q_2$", "rt"); +Point p5(p2); +p5.shift(-3, -1); +p5.label("$q_3$"); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(109); +current_picture.clear(); + +beginfig(110); +{ +default_focus.set(2, 2, -10, 2, 2, 10, 10); +Point A(-2, -2.5, -1); +Point B(3, 2, 2.5); +A.dotlabel("$A$", "llft"); +A.label(Point::WORLD_VALUES, "lrt"); +B.dotlabel("$B$", "ulft"); +B.label(Point::WORLD_VALUES, "urt"); +Path p(A, B); +p.draw(); +draw_axes(gray); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(110); +current_picture.clear(); + +beginfig(111); +{ +Point P0; +Point P1(2); +Point P2(2,2); +Point P3(0,2); +Path p("..", true, &P0, &P1, &P2, &P3, 0); +p.draw(); +P0.dotlabel("$P_0$", "llft"); +P1.dotlabel("$P_1$", "lrt"); +P2.dotlabel("$P_2$"); +P3.dotlabel("$P_3$"); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(111); +current_picture.clear(); + +beginfig(112); +{ +default_focus.set(2, 2, -10, 2, 2, 10, 10); +Point P[4]; +P[0].set(2, 1, 3); +P[3] = P[2] = P[1] = P[0]; +P[3] *= P[2] *= P[1].rotate(3, 12, 18); +P[3] *= P[2].shift(-2, -1, 3); +P[3].shear(1.5, .5, 3.5); +Path q("...", false, &P[0], &P[1], &P[2], &P[3], 0); +q.dotlabel(); +q.draw(); +draw_axes(gray); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(112); +current_picture.clear(); + +beginfig(113); +{ +Point A; +Point B(2, 0); +Point C(3, 2); +Point D(1, 3); +A.dotlabel("A", "llft"); +B.dotlabel("B", "lrt"); +C.dotlabel("C"); +D.dotlabel("D"); +Path p(&A, "..", &B, "..", &C, "--", &D, "...", 0); +p.draw(); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(113); +current_picture.clear(); + +beginfig(114); +{ +Point A(-2, 2); +Point B(-2, -2); +Point C(2, -2); +Point D(2, 2); +A.dotlabel("$A$", "ulft"); +B.dotlabel("$B$", "llft"); +C.dotlabel("$C$", "lrt"); +D.dotlabel("$D$", "urt"); +Path q("--", false, &A, &B, &C, &D, 0); +Point E(1, 2); +Point F(0, 4); +Point G(-.5, 3); +E.dotlabel("$E$", "urt"); +F.dotlabel("$F$"); +G.dotlabel("$G$", "rt"); +Path r("..", false, &E, &F, &G, 0); +q.append(r, "..", true); +q += ".."; +q += "--"; +q.set_cycle(); +q.draw(); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(114); +current_picture.clear(); + +beginfig(115); +{ +origin.dotlabel("(0, 0, 0)", "bot"); +Point pt[8]; +pt[0] = (-1, -1); +for (int i = 1; i < 8; ++i) +{ +pt[i] = pt[0]; +pt[i].rotate(0, 0, i * 45); +} +Path p("--", true, &pt[0], &pt[1], &pt[2], &pt[3], +&pt[4], &pt[5], &pt[6], +&pt[7], 0); +p.draw(); +p.scale(2, 2); +p.draw(); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(115); +current_picture.clear(); + +beginfig(116); +{ +default_focus.set(3, 3, -10, 3, 3, 10, 10); +Point p0; +Point p1(1); +Point p2(1, 1); +Point p3(0, 1); +Path q("--", true, &p0, &p1, &p2, &p3, 0); +q.rotate(0, 45); +q.shift(1); +q.filldraw(black, light_gray); +q.get_point(0).dotlabel(Point::WORLD_VALUES, "llft"); +q.get_point(1).dotlabel(Point::WORLD_VALUES, "rt"); +q.get_point(2).dotlabel(Point::WORLD_VALUES, "rt"); +q.get_point(3).dotlabel(Point::WORLD_VALUES, "lft"); +q.shear(1.5, 2, 2.5, 3, 3.5, 5); +q.filldraw(black, light_gray); +q.get_point(0).dotlabel(Point::WORLD_VALUES, "ulft"); +q.get_point(1).dotlabel(Point::WORLD_VALUES, "lft"); +q.get_point(2).dotlabel(Point::WORLD_VALUES, "rt"); +q.get_point(3).dotlabel(Point::WORLD_VALUES, "rt"); +draw_axes(gray); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(116); +current_picture.clear(); + +beginfig(117); +{ +default_focus.set(5, 10, -10, 0, 10, 10, 10); +draw_axes(2.5, "bot", "lft", "rt", gray); +Point pt[6]; +pt[0].set(-2, -2); +pt[1].set(0, -3); +pt[2].set(2, -2); +pt[3].set(2, 2); +pt[4].set(0, 3); +pt[5].set(-2, 2); +Path p("--", true, &pt[0], &pt[1], &pt[2], &pt[3], &pt[4], &pt[5], 0); +Point p_center(origin); +origin.label("$p$", "lrt"); +p.draw(); +p_center *= p.shift(3, 3, 3); +origin.drawarrow(p_center, black, "evenly"); +p_center.label("$p$"); +p.draw(); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(117); +current_picture.clear(); + +beginfig(118); +{ +default_focus.set(5, 10, -10, 0, 10, 10, 10); +draw_axes(2.5, "bot", "lft", "rt", gray); +Point pt[6]; +pt[0].set(-2, -2); +pt[1].set(0, -3); +pt[2].set(2, -2); +pt[3].set(2, 2); +pt[4].set(0, 3); +pt[5].set(-2, 2); +Path p("--", true, &pt[0], &pt[1], &pt[2], +&pt[3], &pt[4], &pt[5], 0); +p.draw(); +Point A; +A.label("$p$", "lrt"); +Point s(2, -2, 4); +A *= p.shift(s); +origin.drawarrow(A, black, "evenly"); +A.label("$p$"); +p.draw(); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(118); +current_picture.clear(); + +beginfig(119); +{ +default_focus.set(2, 2, -10, 2, 2, 10, 10); +Point A(2, 3, 2); +Point B(-1, 1, 3); +Path p(A, B); +A.dotlabel("$A$", "urt"); +B.dotlabel("$B$", "lft"); +A.mediate(B).label("$p$"); +p.draw(); +Transform t = p.align_with_axis(true, 'z'); +p *= t; +Point C(1); +C *= t.inverse(); +Path q; +q += ".."; +q += C; +for (int i = 0; i < 15; ++i) + { + C.rotate(A, B, 360.0/16); + q += C; + } +q.set_cycle(true); +q.draw(); +q.get_point(14).label("$q$", "ulft"); +q.align_with_axis(A, B, 'z'); +q.draw(); +origin.mediate(q.get_point(6)).label("$q$"); +draw_axes(gray); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(119); +current_picture.clear(); + +beginfig(120); +{ +Point A; +Point B(2); +Point C(3, 3); +Point D(1, 2); +Point E(-1, 1); +A.dotlabel("A", "bot"); +B.dotlabel("B", "bot"); +C.dotlabel("C"); +D.dotlabel("D"); +E.dotlabel("E", "lft"); +Path p("..", true, &A, &B, &C, &D, &E, 0); +p.draw(); +current_picture.output(Projections::PARALLEL_X_Y); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(120); +current_picture.clear(); + +beginfig(121); +A.dotlabel("A", "bot"); +B.dotlabel("B", "bot"); +C.dotlabel("C"); +D.dotlabel("D"); +E.dotlabel("E", "lft"); +out_stream << "pickup pencircle scaled 2mm;" << endl; +p.draw(Colors::gray); +current_picture.output(Projections::PARALLEL_X_Y); +out_stream << "pickup pencircle scaled .25mm;" << endl; +current_picture.output(Projections::PARALLEL_X_Y); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(121); +current_picture.clear(); + +beginfig(122); +A.dotlabel("A", "bot"); +B.dotlabel("B", "bot"); +C.dotlabel("C"); +D.dotlabel("D"); +E.dotlabel("E", "lft"); +p.draw(black, "evenly"); +current_picture.output(Projections::PARALLEL_X_Y); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(122); +current_picture.clear(); + +beginfig(123); +Point A0(A); +Point B0(B); +Point C0(C); +Point D0(D); +Point E0(E); +A0 *= B0.shift(0, -.1); +C0.shift(0, .05); +D0.shift(0, .15); +E0.shift(-.175); +A0.label("A", "bot"); +B0.label("B", "bot"); +C0.label("C"); +D0.label("D"); +E0.label("E", "lft"); +p.draw(black, "", "pensquare xscaled 3mm yscaled .25mm scaled .5mm"); +current_picture.output(Projections::PARALLEL_X_Y); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(123); +current_picture.clear(); + +beginfig(124); +Picture temp_picture; +A.dotlabel("A", "bot", temp_picture); +B.dotlabel("B", "bot", temp_picture); +C.dotlabel("C", "top", temp_picture); +D.dotlabel("D", "top", temp_picture); +E.dotlabel("E", "lft", temp_picture); +p.draw(temp_picture); +temp_picture.output(Projections::PARALLEL_X_Y); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(124); +current_picture.clear(); + +beginfig(125); +{ +Point m; +Point n(2, 2); +m.dotlabel("$m$", "bot"); +n.label("$n$"); +m.drawarrow(n); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(125); +current_picture.clear(); + +beginfig(126); +{ +draw_axes(0, "bot", "rt", ""); +current_picture.output(PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(126); +current_picture.clear(); + +beginfig(127); +{ +draw_axes(); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(127); +current_picture.clear(); + +beginfig(128); +{ +Point P(.5, .5, .5); +draw_axes(0, "d", "d", "d", black, "", "", P, -P, P); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(128); +current_picture.clear(); + +beginfig(129); +A.dotlabel("A", "bot"); +B.dotlabel("B", "bot"); +C.dotlabel("C"); +D.dotlabel("D"); +E.dotlabel("E", "lft"); +p.fill(gray); +current_picture.output(Projections::PARALLEL_X_Y); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(129); +current_picture.clear(); + +beginfig(130); +A0.label("A", "bot"); +B0.label("B", "bot"); +C0.label("C"); +D0.label("D"); +E0.label("E", "lft"); +p.filldraw(black, gray, "", "pencircle scaled 2mm"); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(130); +current_picture.clear(); + +beginfig(131); +{ +default_focus.set(3, 0, -10, 3, 0, 10, 10); +Point p[8]; +p[0] = p[1] = p[2] = p[3] = p[4] = p[5] = p[6] = p[7].set(-1,-1, 5); +p[1] *= p[2] *= p[3] *= p[4] *= p[5] *= p[6] *= p[7].rotate(0, 0, 45); +p[2] *= p[3] *= p[4] *= p[5] *= p[6] *= p[7].rotate(0, 0, 45); +p[3] *= p[4] *= p[5] *= p[6] *= p[7].rotate(0, 0, 45); +p[4] *= p[5] *= p[6] *= p[7].rotate(0, 0, 45); +p[5] *= p[6] *= p[7].rotate(0, 0, 45); +p[6] *= p[7].rotate(0, 0, 45); +p[7].rotate(0, 0, 45); +Path r0("..", true, &p[0], &p[1], &p[2], &p[3], &p[4], &p[5], &p[6], &p[7], 0); +r0.filldraw(black, light_gray); +r0.scale(2, .5); +r0.shift(0, 0, -2.5); +r0.filldraw(black, gray, "evenly scaled 4", +"pencircle scaled .5mm"); +r0.scale(.25, 3); +r0.shift(0, 0, -2.5); +r0.filldraw(); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(131); +current_picture.clear(); + +beginfig(132); +{ +Point P0(1, 1); +Point P1(2, 1); +Point P2(2, 3); +Point P3(-1, 1); +Path p("--", false, &origin, &P0, &P1, &P2, &P3, 0); +p.draw(black, "", "pencircle scaled 3mm"); +p.undraw("", "pencircle scaled 1mm"); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(132); +current_picture.clear(); + +beginfig(133); +{ +Point pt[4]; +pt[0].set(-2, -2); +pt[1].set(2, -2); +pt[2].set(2, 2); +pt[3].set(-2, 2); +Path p("--", true, &pt[0], &pt[1], &pt[2], &pt[3], 0); +p.draw(); +p.filldraw(black, gray); +p.scale(.5, .5); +p.unfill(); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(133); +current_picture.clear(); + +beginfig(134); +{ +Point pt[6]; +pt[0].set(-2, -2); +pt[1].set(0, -3); +pt[2].set(2, -2); +pt[3].set(2, 2); +pt[4].set(0, 3); +pt[5].set(-2, 2); +Path p("--", true, &pt[0], &pt[1], &pt[2], &pt[3], &pt[4], &pt[5], 0); +p.fill(gray); +p.scale(.5, .5); +p.unfilldraw(black, "", "pensquare xscaled 3mm"); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(134); +current_picture.clear(); + +beginfig(135); +{ +default_focus.set(0, 3, -10, 0, 3, 10, 10); +Reg_Polygon r(origin, 5, 3, 45); +r.fill(gray); +Point p[10]; +for (int i = 0; i < 5; ++i) + p[i] = r.get_point(i); +p[0].dotlabel(0); +p[1].dotlabel(1, "ulft"); +p[2].dotlabel(2, "llft"); +p[3].dotlabel(3, "lrt"); +p[4].dotlabel(4, "urt"); +p[5] = Point::intersection_point(p[4], p[0], p[2], p[1]).pt; +p[5].dotlabel(5); +p[6] = Point::intersection_point(p[0], p[1], p[2], p[3]).pt; +p[6].dotlabel(6, "lft"); +p[7] = Point::intersection_point(p[1], p[2], p[4], p[3]).pt; +p[7].dotlabel(7, "bot"); +p[8] = Point::intersection_point(p[2], p[3], p[0], p[4]).pt; +p[8].dotlabel(8, "rt"); +p[9] = Point::intersection_point(p[3], p[4], p[0], p[1]).pt; +p[9].dotlabel(9); +Path q("--", true, &p[0], &p[5], &p[1], &p[6], &p[2], &p[7], + &p[3], &p[8], &p[4], &p[9], 0); +q.draw(); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(135); +current_picture.clear(); + +beginfig(136); +{ +default_focus.set(2, 3, -10, 0, 3, 10, 10); +Point P(1, 1, 1); +P.dotlabel("$P$", "bot"); +Rectangle r(P, 4, 4, 30, 30, 30); +r.get_point(0).dotlabel(0, "bot"); +r.get_point(1).dotlabel(1, "rt"); +r.get_point(2).dotlabel(2); +r.get_point(3).dotlabel(3, "lft"); +r.filldraw(black, light_gray); +Point N = r.get_normal(); +N.label("$\\vec{N}$"); +origin.drawarrow(N); +N.shift(P); +P.drawarrow(N); +N.label("$\\vec{N}$", "rt"); +draw_axes(0, "d", "d", "d", black, "evenly"); +current_picture.output(default_focus, Projections::PERSP, 1, Sorting::NO_SORT); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(136); +current_picture.clear(); + +beginfig(137); +{ +default_focus.set(4, 3, -10, 0, 3, 10, 10); +Point P(1, 1, 1); +P.dotlabel("$P$", "bot"); +Rectangle r(P, 4, 4, 45, 20, 15); +r.filldraw(black, light_gray); +Plane q = r.get_plane(); +q.point.dotlabel("{\\tt q.point}", "bot"); +origin.drawarrow(q.normal); +q.normal.label("{\\tt q.normal}", "lft"); +P.mediate(r.get_point(2), .5).label("$r$", ""); +draw_axes(0, "d", "d", "d", black, "evenly"); +current_picture.output(default_focus, Projections::PERSP, 1, Sorting::NO_SORT); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(137); +current_picture.clear(); + +beginfig(138); +{ +default_focus.set(2, 10, -10, 2, 10, 10, 10); +Point A(-1, -1, -1); +Point B(1, 1, 1); +Path p0(A, B); +p0.draw(); +Point C(-2, 1, 1); +Point D(1.75, 0.25, 0.25); +Path p1(C, D); +p1.draw(); +bool_point bp = p0.intersection_point(p1); +bp.pt.dotlabel("$i$"); +A.dotlabel("$A$", "bot"); +B.dotlabel("$B$"); +C.dotlabel("$C$", "lft"); +D.dotlabel("$D$", "rt"); +draw_axes(gray, 0, "d", "d", "rt"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(138); +current_picture.clear(); + +beginfig(139); +{ +default_focus.set(2, 10, -10, 2, 10, 10, 10); +Point A(1, 1, 1); +Reg_Polygon r(origin, 5, 3); +Transform t; +t.rotate(15, 12, 11); +t.shift(A); +Point P(-2, 0, -1); +Point Q(2, 0, 1); +P *= Q *= r *= t; +P.dotlabel("$P$"); +Q.dotlabel("$Q$"); +P.draw(Q); +r.draw(); +bool_point_pair bpp = r.intersection_points(P, Q); +bpp.first.pt.dotlabel("$f$", "rt"); +bpp.second.pt.dotlabel("$s$"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(139); +current_picture.clear(); + +beginfig(140); +{ +default_focus.set(2, 10, -10, 2, 10, 10, 10); +Point A(1, 1, 1); +Reg_Polygon r(origin, 5, 3); +Transform t; +t.rotate(15, 12, 11); +t.shift(A); +Point B(r.get_point(3).mediate(r.get_point(4))); +Point C(B); +B.shift(0, 2, .5); +C.shift(0, -2, -.5); +Point P(-1, -2, -1); +Point Q(0, 2, 1); +B *= C *= P *= Q *= r *= t; +B.dotlabel("$B$"); +C.dotlabel("$C$", "bot"); +B.draw(C); +r.draw(); +P.dotlabel("$P$", "bot"); +Q.dotlabel("$Q$"); +P.draw(Q); +bool_point_pair bpp = r.intersection_points(B, C); +bpp.first.pt.dotlabel("$i_0$", "rt"); +bpp = r.intersection_points(P, Q); +bpp.first.pt.dotlabel("$i_1$", "rt"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(140); +current_picture.clear(); + +beginfig(141); +{ +default_focus.set(2, 10, -10, 2, 10, 10, 10); +Point A(1, 1, 1); +Reg_Polygon r(origin, 5, 3); +Transform t; +t.rotate(10, 0, 60); +t.shift(A); +Point P(0, 1); +Point Q(0, 3); +P *= Q *= r *= t; +r.draw(); +P.dotlabel("$P$"); +Q.dotlabel("$Q$"); +P.draw(Q); +bool_point_pair bpp = r.intersection_points(P, Q); +bpp.first.pt.dotlabel("$i$"); +Point S(P.mediate(bpp.first.pt, 2.25)); +P.draw(S, black, "evenly"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(141); +current_picture.clear(); + +beginfig(142); +{ +Rectangle r(origin, 4, 4); +Reg_Polygon rp(origin, 5, 5, 0, 36); +rp.shift(0, 0, .25); +r.draw(); +rp.draw(); +vector v = r.intersection_points(rp); +v[0].dotlabel(0, "llft"); +v[1].dotlabel(1, "lrt"); +v[2].dotlabel(2, "lrt"); +v[3].dotlabel(3, "rt"); +v[4].dotlabel(4, "ulft"); +v[5].dotlabel(5, "urt"); +v[6].dotlabel(6, "lft"); +v[7].dotlabel(7, "llft"); +current_picture.output(Projections::PARALLEL_X_Z); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(142); +current_picture.clear(); + +beginfig(143); +{ +default_focus.set(2, 5, -10, 2, 5, 10, 10); +Point A(1, 1, 1); +Rectangle r(A, 4, 4); +Reg_Polygon p(A, 5, 5); +p.rotate(90, 30); +p.shift(2, 0, 3); +A.mediate(r.get_point(3)).label("$r$", ""); +p.get_center().mediate(p.get_point(0)).label("$p$", ""); +r.draw(); +p.draw(); +vector v = r.intersection_points(p); +int i = 0; +v[0].dotlabel("0", "llft"); +v[1].dotlabel("1", "lft"); +v[2].dotlabel("2", "llft"); +v[3].dotlabel("3", "rt"); +v[1].draw(v[2], black, "evenly"); +v[0].draw(v[3], black, "evenly"); +v[2].draw(v[0]); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(143); +current_picture.clear(); + +beginfig(144); +{ +default_focus.set(2, 5, -10, 2, 5, 10, 10); +Point A(1, 1, 1); +Rectangle r(A, 4, 4); +Reg_Polygon p(A, 5, 5); +p.rotate(90, 30); +p.shift(4, 3, 3); +r.draw(); +p.draw(); +A.label("$r$", ""); +p.get_center().label("$p$", ""); +vector v = r.intersection_points(p); +v[0].dotlabel("0", "bot"); +v[1].dotlabel("1", "rt"); +v[0].draw(v[1], black, "evenly"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(144); +current_picture.clear(); + +beginfig(145); +{ +default_focus.set(-5, 10, -10, -5, 10, 10, 10); +Reg_Polygon r(origin, 3, 2.75, 10, 15, 12.5); +r.draw(); +draw_axes(gray, 0, "d", "d", "rt"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(145); +current_picture.clear(); + +beginfig(146); +{ +Reg_Polygon r; +real j = .5; +for (int i = 3; i <= 16; ++i) + { + r.set(origin, i, j); + r.draw(); + j += .5; + } +current_picture.output(Projections::PARALLEL_X_Z); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(146); +current_picture.clear(); + +beginfig(147); +{ +default_focus.set(3, 5, -5, 3, 0, 1, 10); +Point P(0, -1, 1); +Reg_Polygon h(P, 6, 4, 15, 12, 11.5); +h.filldraw(black, gray); +h.get_point(4).mediate(h.get_point(5)).label("$h$", "urt"); +Circle c = h.in_circle(); +c.unfilldraw(black); +P.label("$c$"); +draw_axes(gray, 0, "d", "d", "top"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(147); +current_picture.clear(); + +beginfig(148); +{ +default_focus.set(2, 3, -10, 2, 3, 10, 10); +Point P(0, 1, 1); +Reg_Polygon h(P, 7, 4, 80, 2, 5); +h.draw(black, "evenly"); +h.get_point(0).label("$h$"); +h.draw_in_circle(); +P.label("$c$", ""); +draw_axes(gray, 0, "d", "d", "top"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(148); +current_picture.clear(); + +beginfig(149); +{ +default_focus.set(3, 5, -5, 3, 0, 1, 10); +Point P(0, -1, 1); +Reg_Polygon h(P, 6, 4, 15, 12, 11.5); +Circle c = h.out_circle(); +c.filldraw(black, gray); +h.unfilldraw(black); +P.label("$h$"); +c.get_point(7).label("$c$"); +draw_axes(gray, 0, "d", "d", "top"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(149); +current_picture.clear(); + +beginfig(150); +{ +default_focus.set(2, 3, -10, 2, 3, 10, 10); +Point P(0, 1, 1); +Reg_Polygon h(P, 7, 4, 80, 2, 5); +h.draw(black, "evenly"); +Circle c = h.draw_out_circle(); +c.get_point(0).label("$c$"); +P.label("$h$", ""); +draw_axes(gray, 0, "d", "d", "top"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(150); +current_picture.clear(); + +beginfig(151); +{ +default_focus.set(1, 3, -10, 1, 3, -9, 10); +Point C(-1, -1, 1); +Rectangle r(C, 3, 4, 30, 30, 30); +C.label("$r$", ""); +r.draw(); +draw_axes(gray, 0, "d", "d", "rt"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(151); +current_picture.clear(); + +beginfig(152); +{ +default_focus.set(4, 3, -10, 2, 2, 10, 10, 180); +Point P(-1, -1, 3); +Rectangle r(P, 3, 4, 60, 30, 15); +Ellipse e = r.out_ellipse(); +e.filldraw(black, gray); +r.unfilldraw(black); +draw_axes(gray, 3.5); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(152); +current_picture.clear(); + +beginfig(153); +{ +default_focus.set(4, 3, -10, 2, 2, 10, 10, 180); +Point P(-1, -1, 3); +Rectangle r(P, 3, 4, 60, 30, 15); +Ellipse e = r.in_ellipse(); +r.filldraw(black, gray); +e.unfilldraw(black); +draw_axes(gray, 3.5); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(153); +current_picture.clear(); + +beginfig(154); +{ +Point p0(2, 2, 3); +p0.label("$e$", ""); +Ellipse e(p0, 3, 4, 30, -60, -5.2); +e.draw(); +Point p1 = p0.mediate(e.get_point(11), .5); +Point A = e.get_normal(); +A *= 2.5; +A.shift(p1); +A.dotlabel("$A$"); +Point B = A.mediate(p1, 2); +B.dotlabel("$B$", "bot"); +A.draw(B, black, "evenly"); +bool_point_pair bpp = e.intersection_points(A, B); +bpp.first.pt.dotlabel("$i_0$", "rt"); +Point C(0, 2, 0); +Point D(0, -3.5, 0); +C *= D.rotate(2, 0, -5); +C *= D.shift(e.get_point(4)); +C.dotlabel("$C$"); +D.dotlabel("$D$", "bot"); +C.draw(D, black, "evenly"); +bpp = e.intersection_points(C, D); +bpp.first.pt.dotlabel("$i_1$", "rt"); +current_picture.output(); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(154); +current_picture.clear(); + +beginfig(155); +e.draw(); +p0.label("$e$"); +A = p0.mediate(e.get_point(3), 1.5); +B = p0.mediate(e.get_point(11), 1.5); +Path q(A, B); +q.get_point(0).dotlabel("$q_0$", "rt"); +q.get_point(1).dotlabel("$q_1$", "lft"); +q.draw(black, "evenly"); +bpp = e.intersection_points(q); +bpp.first.pt.dotlabel("$i_0$"); +bpp.second.pt.dotlabel("$i_1$", "ulft"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(155); +current_picture.clear(); + +beginfig(156); +{ +default_focus.set(2, 5, -10, 2, 5, 10, 10); +Circle c(origin, 4, 30, 30, 30); +c.draw(); +origin.label("$c$", ""); +Path p = c.segment(3, 130); +(.75 * p.get_point(2)).label("$p$", "rt"); +p.filldraw(black, light_gray, "", "pencircle scaled .75mm"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(156); +current_picture.clear(); + +beginfig(157); +{ +default_focus.set(3, 5, -10, 3, 3, 10, 10); +Ellipse e(origin, 3, 5, 20, 15, 12.5); +e.fill(light_gray); +origin.label("$e$", ""); +Path p = e.half(0, false); +p.get_point(p.get_size() / 2).label("$p$"); +p.draw(black, "", "pencircle scaled .75mm"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(157); +current_picture.clear(); + +beginfig(158); +{ +default_focus.set(3, 5, -10, 3, 3, 10, 10); +Ellipse e(origin, 3, 5, 60, 5, 2.5); +e.fill(light_gray); +origin.label("$e$", ""); +Path p = e.quarter(180, false); +p.get_point(p.get_size() / 2).label("$p$", "llft"); +p.draw(black, "", "pencircle scaled .75mm"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(158); +current_picture.clear(); + +beginfig(159); +{ +Ellipse e(origin, 6, 4); +e.draw(); +draw_axes(gray, 3.5, "d", "", "rt"); +current_picture.output(Projections::PARALLEL_X_Z); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(159); +current_picture.clear(); + +beginfig(160); +{ +default_focus.set(3, 5, -10, 2, 4, 10, 10, 180); +Point P(1, 1, 1); +Ellipse e(P, 6, 4, 15, 12, 11); +e.draw(); +draw_axes(gray, 0, "d", "d", "rt"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(160); +current_picture.clear(); + +beginfig(161); +{ +Ellipse e(origin, 6, 4); +e.draw(); +e.label(); +draw_axes(gray, 3.5, "d", "", "rt"); +current_picture.output(Projections::PARALLEL_X_Z); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(161); +current_picture.clear(); + +beginfig(162); +{ +Ellipse e(origin, 6, 4); +e.draw(); +e.dotlabel(); +draw_axes(gray, 3.5, "d", "", "rt"); +current_picture.output(Projections::PARALLEL_X_Z); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(162); +current_picture.clear(); + +beginfig(163); +{ +Ellipse e(origin, 5, 2, 90); +e.draw(); +Point P(e.angle_point(-35)); +stringstream s; +s << "$P=(" << P.get_x() << ", " << P.get_y() << ")$"; +P.dotlabel(s.str(), "urt"); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(163); +current_picture.clear(); + +beginfig(164); +{ +default_focus.set(2, 5, -10, 2, 5, 10, 10); +Ellipse e(origin, 3, 5, 45, 15, 3); +e.shift(2, 1, 1); +e.draw(); +Point center = e.get_center(); +center.label("$e$", ""); +Point A = e.get_point(7); +A.dotlabel("$A$", "lft"); +Point B = center.mediate(e.get_point(2)); +B.dotlabel("$B$"); +Point C = center.mediate(e.get_point(2), 1.5); +C.dotlabel("$C$"); +Point D = A; +D.shift(-2, 0, 4); +D.dotlabel("$D$"); +e.scale(1.5, 0, 1.5); +draw_axes(gray, 0, "d", "d", "lft"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(164); +current_picture.clear(); + +beginfig(165); +{ +Ellipse e(origin, 6, 4); +e.draw(); +Point center = e.get_center(); +center.label("$e$", "bot"); +Point e0 = e.get_point(0); +e0.label(0, "rt"); +center.drawarrow(e0); +Point P = e.angle_point(135); +Point Q = e.angle_point(135/2.0); +center.mediate(Q, .25).label("$\\theta = 135^\\circ$", "rt"); +center.drawarrow(P); +P.label("$P$"); +Point R(e.get_point(12)); +R.shift(0, 0, -.75); +R.label("x-z plane"); +current_picture.output(Projections::PARALLEL_X_Z); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(165); +current_picture.clear(); + +beginfig(166); +{ +Ellipse e(origin, 6, 4, 90); +e.draw(); +Point center = e.get_center(); +center.mediate(e.get_point(8), .25).label("$e$", ""); +Point e0 = e.get_point(0); +e0.label(0, "rt"); +e.get_point(1).dotlabel(1); +e.get_point(2).dotlabel(2); +center.drawarrow(e0); +Point P = e.angle_point(135); +Point R = e.angle_point(135/2.0); +center.mediate(R, .25).label("$\\theta = 135^\\circ$", "rt"); +center.drawarrow(P); +P.label("$P$", "bot"); +Point Q = e.angle_point(-135); +R = e.angle_point(-135/2.0); +center.mediate(R, .25).label("$\\phi = -135^\\circ$", "rt"); +center.drawarrow(Q); +Q.label("$Q$"); +Point S(e.get_point(12)); +S.shift(0, -.75); +S.label("x-y plane"); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(166); +current_picture.clear(); + +beginfig(167); +{ +default_focus.set(2, 5, -10, 2, 5, 10, 10); +Ellipse e(origin, 5, 7, 30, 30, 30); +e.shift(3, 0, 3); +e.get_center().label("$e$", ""); +e.draw(); +Point p0 = e.get_center().mediate(e.get_point(3)); +Point normal = e.get_normal(); +Point A = normal; +A *= 2.5; +A.shift(p0); +Point B = normal; +B *= -2.5; +B.shift(p0); +A.dotlabel("$A$"); +B.dotlabel("$B$", "bot"); +bool_point_pair bpp = e.intersection_points(A, B); +bpp.first.pt.dotlabel("$i_0$", "rt"); +A.draw(bpp.first.pt); +bpp.first.pt.draw(B, black, "evenly"); +Point C = e.get_point(15).mediate(e.get_point(11), 1.25); +C.dotlabel("$C$", "bot"); +Point D = e.get_point(11).mediate(e.get_point(15), 1.5); +D.dotlabel("$D$"); +Path q = C.draw(D); +bpp = e.intersection_points(q); +bpp.first.pt.dotlabel("$i_1$", "llft"); +bpp.second.pt.dotlabel("$i_2$", "ulft"); +draw_axes(gray, 0, "d", "d", "lft"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(167); +current_picture.clear(); + +beginfig(168); +{ +Ellipse e(origin, 5, 2); +Point pt_e(origin.mediate(e.get_point(0), .75)); +pt_e.shift(0, 0, .2); +pt_e.label("$e$", ""); +Ellipse f(origin, 2, 5); +Point pt_f(origin.mediate(f.get_point(4), .75)); +pt_f.shift(.2); +pt_f.label("$f$", ""); +e.draw(); +f.draw(); +bool_point_quadruple bpq = e.intersection_points(f); +bpq.first.pt.dotlabel(1, "llft"); +bpq.second.pt.dotlabel(2, "urt"); +bpq.third.pt.dotlabel(3, "ulft"); +bpq.fourth.pt.dotlabel(4, "lrt"); +draw_axes(gray, 3.5, "d", "", "rt"); +current_picture.output(Projections::PARALLEL_X_Z); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(168); +current_picture.clear(); + +beginfig(169); +{ +default_focus.set(2, 5, -10, 2, 5, 10, 15); +Ellipse e(origin, 4, 2); +Ellipse f(origin, 2, 5); +f.shift(0, 0, 1); +f.rotate(0, 15); +f.shift(1, 0, 1); +e *= f.shift(-.25, 1, -1); +e *= f.rotate(10, -12.5, 3); +e.get_center().label("$e$", ""); +f.get_center().mediate(f.get_point(4)).label("$f$", ""); +e.draw(); +f.draw(); +bool_point_quadruple bpq = e.intersection_points(f, true); +bpq.first.pt.dotlabel(1, "rt"); +bpq.second.pt.dotlabel(2, "ulft"); +draw_axes(gray, 0, "d", "d", "urt"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(169); +current_picture.clear(); + +beginfig(170); +{ +default_focus.set(2, 5, -10, 2, 5, 10, 10); +Ellipse e(origin, 5, 3); +Ellipse f(origin, 2, 5); +f.rotate(0, 0, 30); +f.rotate(0, 10); +f.rotate(45); +f.shift(1.5, 1); +e.draw(); +f.draw(); +bool_point_quadruple bpq = e.intersection_points(f, true); +bpq.first.pt.dotlabel(1); +bpq.second.pt.dotlabel(2); +bpq.third.pt.dotlabel(3, "rt"); +bpq.fourth.pt.dotlabel(4, "urt"); +e.get_center().label("$e$", ""); +f.get_center().label("$f$", ""); +bpq.second.pt.draw(bpq.third.pt, black, "evenly"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(170); +current_picture.clear(); + +beginfig(171); +{ +default_focus.set(2, 5, -10, 2, 5, 10, 10); +Ellipse e(origin, 5, 3); +Ellipse f(origin, 2, 5, 45); +f.shift(0, 2.5, 3); +e.draw(); +f.draw(); +bool_point_quadruple bpq = e.intersection_points(f, true); +bpq.first.pt.dotlabel(1); +bpq.second.pt.dotlabel(2); +bpq.first.pt.draw(bpq.second.pt, black, "evenly"); +e.get_center().label("$e$", ""); +f.get_center().label("$f$", ""); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(171); +current_picture.clear(); + +beginfig(172); +{ +Ellipse e(origin, 3, 4, 45, 30, 17); +e.shift(1, -1, 2); +e.get_center().label("$e$", ""); +Rectangle r = e.out_rectangle(); +r.filldraw(black, gray); +e.unfilldraw(black); +r.get_point(2).mediate(r.get_point(3)).label("$r$"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(172); +current_picture.clear(); + +beginfig(173); +{ +Ellipse e(origin, 3, 4, 45, 30, 17); +e.shift(1, -1, 2); +e.get_point(4).label("$e$"); +Rectangle r = e.in_rectangle(); +r.get_center().label("$r$", ""); +e.filldraw(black, gray); +r.unfilldraw(black); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(173); +current_picture.clear(); + +beginfig(174); +{ +default_focus.set(2, 3, -10, 1, 2, 10, 10); +Ellipse e(origin, 2.5, 5, 10, 12, 15.5); +e.shift(-1, 1, 1); +e.filldraw(black, gray); +Rectangle r = e.draw_out_rectangle(black, "evenly", "pencircle scaled .3mm"); +e.get_center().label("$e$", ""); +r.get_point(0).mediate(r.get_point(1), .25).label("$r$"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(174); +current_picture.clear(); + +beginfig(175); +{ +default_focus.set(2, 3, -10, 1, 2, 10, 10); +Ellipse e(origin, 3.5, 6, 10, 12, 15.5); +e.shift(-1, 1, 1); +e.draw(); +Rectangle r = e.draw_in_rectangle +(black, "evenly", "pencircle scaled .3mm"); +r.get_center().label("$r$", ""); +e.get_point(12).label("$e$"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(175); +current_picture.clear(); + +beginfig(176); +{ +Circle c(origin, 3, 90); +Circle d = c; +d.shift(2.5); +c.draw(); +c.get_center().label("$c$", ""); +d.scale(2, 3); +d.draw(); +d.get_center().label("$d$", ""); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(176); +current_picture.clear(); + +beginfig(177); +{ +Circle t(origin, 5, 90); +Circle c(origin, 3, 90); +c.shift(3); +c.rotate(0, 0, 45); +t.draw(); +c.draw(); +t.get_center().label("t", ""); +c.get_center().label("c", ""); +bool_point_quadruple bpq = t.intersection_points(c); +bpq.first.pt.dotlabel("$f$", "lrt"); +bpq.second.pt.dotlabel("$s$", "llft"); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(177); +current_picture.clear(); + +beginfig(178); +{ +default_focus.set(0, 10, -10, 0, 10, 25, 10); +hex_pattern_1(1, 0, 0, 5, 5); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(178); +current_picture.clear(); + +beginfig(179); +{ +default_focus.set(-5, 5, -10, 0, 10, 25, 10); +hex_pattern_1(2, 1.5, 1, 2, 5, 2, black, gray, black, light_gray, black); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(179); +current_picture.clear(); + +beginfig(180); +{ +epicycloid_pattern_1(5, 3, 3, 1, 72); +current_picture.output(Projections::PARALLEL_X_Z); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(180); +current_picture.clear(); + +beginfig(181); +{ +default_focus.set(2, 5, -10, 2, 5, 10, 10); +epicycloid_pattern_1(5, 3, 3, 1, 36); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(181); +current_picture.clear(); + +beginfig(182); +{ +default_focus.set(2, 2, -10, 0, 2, 10, 10); +Dodecahedron d(origin, 3); +d.filldraw(); +Point C = d.get_shape_center(Solid::REG_POLYGON, 1); +C.dotlabel("C"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(182); +current_picture.clear(); + +beginfig(183); +{ +Cuboid c(origin, 3, 4, 5, 0, 30); +c.draw(); +for (int i = 0; i < 6; ++i) + c.get_rectangle_center(i).label(i, ""); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(183); +current_picture.clear(); + +beginfig(184); +{ +Icosahedron I(origin, 3); +I.filldraw(); +Reg_Polygon* t = +static_cast(I.get_shape_ptr(Solid::REG_POLYGON, 9)); +t->fill(gray); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(184); +current_picture.clear(); + +beginfig(185); +{ +default_focus.set(2, 2, -10, 0, 2, 10, 10); +Dodecahedron d(origin, 3); +d.draw(); +const Reg_Polygon* ptr = d.get_reg_polygon_ptr(0); +ptr->fill(gray); +Reg_Polygon A = *d.get_reg_polygon_ptr(5); +A.draw(black, "evenly scaled 4", "pencircle scaled 1mm"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(185); +current_picture.clear(); + +beginfig(186); +{ +default_focus.set(3, 3, -10, 3, 3, 10, 20); +Point P(-3, -2, 12); +P.dotlabel("$P$"); +Cuboid c(P, 3, 5, 2.93, 35, 10, 60); +c.draw(); +draw_axes(gray); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(186); +current_picture.clear(); + +beginfig(187); +{ +default_focus.set(3, 3, -10, 3, 3, 10, 20); +Tetrahedron t(origin, 3); +t.draw(); +draw_axes(gray); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(187); +current_picture.clear(); + +beginfig(188); +{ +default_focus.set(3, 3, -10, 3, 3, 10, 20); +Point P(1, 0, 1); +P.dotlabel("$P$", "bot"); +Tetrahedron t(P, 2.75, 30, 32.5, 20); +t.draw(); +draw_axes(gray); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(188); +current_picture.clear(); + +beginfig(189); +{ +vector vrp = Tetrahedron::get_net(2); +for (vector::iterator iter = vrp.begin(); + iter != vrp.end(); + ++iter) + { + (**iter).draw(); + } +draw_axes(gray, 0, "d", "", "rt"); +current_picture.output(Projections::PARALLEL_X_Z); +current_picture.output(Projections::PARALLEL_X_Z ); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(189); +current_picture.clear(); + +beginfig(190); +{ +Tetrahedron::draw_net(3, true); +current_picture.output(Projections::PARALLEL_X_Y); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(190); +current_picture.clear(); + +beginfig(191); +{ +default_focus.set(2, 5, -10, 2, 5, 10, 10); +Point P(-1, -2, 4); +P.dotlabel("$P$"); +Dodecahedron d(P, 3, 12.5, 16, 2); +d.draw(); +draw_axes(gray, 0, "d", "d", "top"); +current_picture.output(); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(191); +current_picture.clear(); + +beginfig(192); +d.filldraw(); +draw_axes(gray, 0, "d", "d", "top"); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(192); +current_picture.clear(); + +beginfig(193); +{ +vector vrp = Dodecahedron::get_net(1); +for(vector::iterator iter = vrp.begin(); + iter != vrp.end(); ++iter) + (**iter).draw(); +current_picture.output(Projections::PARALLEL_X_Z); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(193); +current_picture.clear(); + +beginfig(194); +{ +Dodecahedron::draw_net(1, false); +current_picture.output(Projections::PARALLEL_X_Z); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(194); +current_picture.clear(); + +beginfig(195); +{ +default_focus.set(3, 5, -10, 3, 5, 10, 10); +Icosahedron i(origin, 3, 0, 10); +i.draw(); +current_picture.output(); +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(195); +current_picture.clear(); + +beginfig(196); +i.filldraw(); +current_picture.output(); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(196); +current_picture.clear(); + +beginfig(197); +{ +vector vrp = Icosahedron::get_net(1.5); +for (vector::iterator iter = vrp.begin(); + iter != vrp.end(); ++iter) + (**iter).draw(); +current_picture.output(Projections::PARALLEL_X_Z); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(197); +current_picture.clear(); + +beginfig(198); +{ +Icosahedron::draw_net(2, false); +current_picture.output(Projections::PARALLEL_X_Z); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(198); +current_picture.clear(); + +beginfig(199); +{ +persp_0(3, 2, 10, 5, 47.5, 7, 5, 8.5, 9.5, 8.5, 9.5); +} +out_stream << "boxit.b(currentpicture);" << endl; +out_stream << "draw bpath b withpen pencircle scaled .25mm;" << endl; +endfig(199); +current_picture.clear(); + +@i subex2.web + + diff -Naur 3DLDF-1.1.4/CWEB/gsltmplt.web 3DLDF-1.1.5.1/CWEB/gsltmplt.web --- 3DLDF-1.1.4/CWEB/gsltmplt.web 1970-01-01 01:00:00.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/gsltmplt.web 2004-01-12 22:29:56.000000000 +0100 @@ -0,0 +1,453 @@ +@q gsltmplt.web @> + +@q * Copyright and License.@> + +@q This file is part of 3DLDF, a package for three-dimensional drawing. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> + +@q 3DLDF is free software; you can redistribute it and/or modify @> +@q it under the terms of the GNU General Public License as published by @> +@q the Free Software Foundation; either version 2 of the License, or @> +@q (at your option) any later version. @> + +@q 3DLDF is distributed in the hope that it will be useful, @> +@q but WITHOUT ANY WARRANTY; without even the implied warranty of @> +@q MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the @> +@q GNU General Public License for more details. @> + +@q You should have received a copy of the GNU General Public License @> +@q along with 3DLDF; if not, write to the Free Software @> +@q Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA @> + +@q 3DLDF is a GNU package. @> +@q It is part of the GNU Project of the @> +@q Free Software Foundation @> +@q and is published under the GNU General Public License. @> +@q See the website http://www.gnu.org @> +@q for more information. @> +@q 3DLDF is available for downloading from @> +@q http://www.gnu.org/3DLDF. @> +@q It is also available from @> +@q http://www.dante.de/software/ctan/, the Dante www-server @> +@q and from http://wwwuser.gwdg.de/~lfinsto1, @> +@q the author's website. @> + +@q (``@@'' stands for a single at-sign in the following paragraph.) @> + +@q Please send bug reports to bug-3DLDF@@gnu.org @> +@q The mailing list help-3DLDF@@gnu.org is available for people to @> +@q ask other users for help. @> +@q The mailing list info-3DLDF@@gnu.org is for sending @> +@q announcements to users. To subscribe to these mailing lists, send an @> +@q email with ``subscribe '' as the subject. @> + +@q The author can be contacted at: @> + +@q Laurence D. Finston @> +@q Kreuzbergring 41 @> +@q D-37075 Goettingen @> +@q Germany @> + +@q lfinsto1@@gwdg.de (@@ stands for a single ``at'' sign.)@> +@q s246794@@stud.uni-goettingen.de @> + + +@q * Get second-largest |real| value. @> +@** Get second-largest {\bf real} value. +@= +static string rcs_id + = "$Id: gsltmplt.web,v 1.4 2004/01/12 21:29:56 lfinsto1 Exp $"; + +@q * Include files.@> +@* Include files. +@= +#include "loader.h" +#include "pspglb.h" + + + +@q * Declare |namespace System|. @> +@* Declare {\bf namespace System}. @> +\LOG +\initials{LDF 2004.1.2.} Added this section. +\ENDLOG +@+= +namespace +System +{ + @@; +} + +@q * Get second largest. @> +@* Get second largest. +This function calculates the second-largest |real| value. +It should be called using |float| or |double| as a parameter, e.g., +|get_second_largest(FLT_MAX)| or +|get_second_largest(DBL_MAX)|. +|FLT_MAX| or |DBL_MAX| must be +passed as an argument. +On systems with the |numeric_limits| template, +|real_limits.max()| could be used instead. +\initials{LDF 2003.12.29.} + +|get_second_largest()| determines which +unsigned integral type has the same size as the template parameter +|Real|. The locally declared type |i_type| is defined to be a synonym +for this type using |typedef|. +|ip| is a pointer to |i_type|. It is assigned a value by +casting a pointer to |MAX_VAL| to the type of |ip|, i.e., a pointer to +|i_type|. Then, 1 is subtracted from |*ip|, and the |ip| +is cast back to a pointer to |Real|. This is the second largest +|Real| value. +\initials{LDF 2003.12.29.} + +This algorithm works on all of the machines I've tested. It doesn't +matter whether they are big or little-endian, whether they have 32 or +64-bit processors. If the exponent of a floating point type is stored +in its low order byte or bytes, then this will fail. +I haven't run into this problem yet, though. +The commented-out code in |@| may help in +finding the second-largest |Real| value in this case. +\initials{LDF 2003.12.29.} + + +\LOG +\initials{LDF 2003.12.29.} Added this function. + +\initials{LDF 2004.1.2.} Moved this section from +\filename{pspglb.web} to \filename{creatnew.web}. +\ENDLOG + +@q ** Declaration. @> +@= +template +Real +get_second_largest (Real MAX_VAL, bool verbose = false); + +float get_second_largest (float, bool); +double get_second_largest (double, bool); + +@ +@= + + +@q ** Definition. @> +@ +@= +template +Real +System::get_second_largest (Real MAX_VAL, bool verbose) +{ + const unsigned short USHORT_SIZE = sizeof(unsigned short); + const unsigned short UINT_SIZE = sizeof(unsigned int); + const unsigned short ULONG_SIZE = sizeof(unsigned long); + const unsigned short ULONG_LONG_SIZE = sizeof(unsigned long long); + + const unsigned short Real_SIZE = sizeof(Real); + const unsigned short FLT_SIZE = sizeof(float); + const unsigned short DBL_SIZE = sizeof(double); + const unsigned short LONG_DBL_SIZE = sizeof(long double); + + + const bool Real_EQ_USHORT = (Real_SIZE == USHORT_SIZE); + const bool Real_EQ_UINT = (Real_SIZE == UINT_SIZE); + const bool Real_EQ_ULONG = (Real_SIZE == ULONG_SIZE); + const bool Real_EQ_ULONG_LONG = (Real_SIZE == ULONG_LONG_SIZE); + + if (verbose) + { + cout << "USHORT_SIZE == " << USHORT_SIZE << endl << flush; + cout << "UINT_SIZE == " << UINT_SIZE << endl << flush; + cout << "ULONG_SIZE == " << ULONG_SIZE << endl << flush; + cout << "ULONG_LONG_SIZE == " << ULONG_LONG_SIZE << endl << flush; + cout << "FLT_SIZE == " << FLT_SIZE << endl << flush; + cout << "DBL_SIZE == " << DBL_SIZE << endl << flush; + cout << "LONG_DBL_SIZE == " << LONG_DBL_SIZE << endl << flush; + cout << "Real_SIZE == " << Real_SIZE << endl << flush; + } + + + Real* rp; + + if (Real_EQ_USHORT) + { + if (verbose) + cout << "Real_EQ_USHORT\n"; + typedef unsigned short i_type; + @@; + } + + else if (Real_EQ_UINT) + { + if (verbose) + cout << "Real_EQ_UINT \n"; + typedef unsigned int i_type; + @@; + } + + else if (Real_EQ_ULONG) + { + if (verbose) + cout << "Real_EQ_ULONG \n"; + typedef unsigned long i_type; + @@; + } + else if (Real_EQ_ULONG_LONG) + { + if (verbose) + cout << "Real_EQ_ULONG_LONG\n"; + typedef unsigned long long i_type; + @@; + } + + else + { + cerr << "ERROR! In main():\n" + << "Apparently, Real doesn't have the same size " + << "as any unsigned integral type.\n" + << "There must be some mistake.\n" + << "Exiting with return value -1.\n\n" << flush; + return -1; + } + + if (verbose) + { + cout.precision(25); + cout << "MAX_VAL == " << MAX_VAL << endl + << "*rp == " << *rp << endl + << "(MAX_VAL == *rp) == " + << (MAX_VAL == *rp) + << endl + << "(MAX_VAL - *rp) == " + << (MAX_VAL - *rp) << endl + << "MAX_VAL > *rp == " + << (MAX_VAL > *rp) << endl + << "MAX_VAL < *rp == " + << (MAX_VAL < *rp) << endl << flush; + } + + + if (MAX_VAL == *rp) + { + cerr << "ERROR! In System::get_second_largest():\n" + << "MAX_VAL == *rp. Exiting with return value 1" + << endl << endl << flush; + exit(1); + } + + else if (MAX_VAL < *rp) + { + cerr << "ERROR! In System::get_second_largest():\n" + << "MAX_VAL < *rp. Exiting with return value 1" + << endl << endl << flush; + exit(1); + } + + return *rp; +} + +@q *** Calculate second-largest |Real|. @> +@*2 Calculate second-largest {\bf Real}. +@= +{ + i_type* ip = reinterpret_cast(&MAX_VAL); + + if (verbose) + cout << "*ip == " << *ip << endl << flush; + + i_type bit_pattern_i_type; + i_type result; + + + bit_pattern_i_type = 1; + + bitset b; + + b = *ip; + + if (verbose) + cout << "b (MAX_VAL) == " << b << endl << flush; + + b = bit_pattern_i_type; + + if (verbose) + cout << "b (bit_pattern_i_type) == " << b << endl << flush; + + result = bit_pattern_i_type ^ *ip; + + if (verbose) + cout << "result == " << result << endl << flush; + + b = result; + + if (verbose) + cout << "b (result) == " << b << endl << flush; + + rp = reinterpret_cast(&result); + + if (verbose) + cout << "*rp == " << *rp << endl << flush; + } + + +@q *** Loop for testing bits. @> +@*2 Loop for testing bits. +@= +#if 0 + int counter; + + for (int i = 0; i < (sizeof(Real) * CHAR_BIT); ++i) + { + if (verbose) + cout << "i == " << i << endl << flush; + + + // This has only been needed on the DEC Alpha, so far. + // This is the case that the highest-order bit of the + // mantissa is 1, and all of the other bits (in particular, + // all the bits of the exponent) are 0. In this case, |*rp| + // is not a number (NAN). The GNU compiler copes with this, + // the DEC compiler signals a floating point error and dumps + // core (I believe). I wasn't able to catch the error with + // |try| and |catch|. + // START HERE. Change |(8 + 1)| to |(FLT_EXP + 1)|, except + // |FLT_EXP| + // isn't the right name. Find it, and put here. This + // assumes the exponent is at the left, which may not be + // true. Skipping this bit pattern is necessary on the DEC + // ALPHA, because the float is not a number. + + // It must be 23 for float, and 52 for double. + if (i == (sizeof(Real) * CHAR_BIT) - (12)) + { + if (verbose) + cout << "i == " << i << ". This produces NAN. Continuing.\n\n" << flush; + continue; + } + + + bit_pattern_i_type = 1; + bit_pattern_i_type <<= i; + if (verbose) + cout << "bit_pattern_i_type (1 << " << i << ") == " + << bit_pattern_i_type << endl << flush; + + b = bit_pattern_i_type; + + if (verbose) + cout << "b (bit_pattern_i_type) == " << b << endl << flush; + + result = bit_pattern_i_type ^ *ip; + + + if (verbose) + cout << "result == " << result << endl << flush; + + b = result; + + if (verbose) + cout << "b (result) == " << b << endl << flush; + + rp = reinterpret_cast(&result); + + if (verbose) + cout << "*rp == " << *rp << endl << flush; + + + if (*rp <= 0) + { + if (verbose) + cout << "*rp <= 0.\nContinuing.\n\n" << flush; + continue; + } + + else if (*rp >= MAX_VAL) + { + if (verbose) + cout << "*rp >= MAX_VAL\nContinuing." + << endl << flush; + continue; + } + + else if (second_largest_real >= *rp) + { + if (verbose) + cout << "second_largest_real >= *rp\nContinuing." + << "\n" << flush; + continue; + } + else if (*rp > second_largest_real && *rp < MAX_VAL) + { + if (verbose) + cout << "*rp > second_largest_real && " + << "*rp < MAX_VAL" << endl + << "Setting second_largest_real to *rp" + << " and counter to i (" << i << ").\n" << flush; + + second_largest_real = *rp; + counter = i; + } + else + { + if (verbose) + cout << "Some other condition. Continuing.\n"; + continue; + } + + } /* |for| */ + +#endif + +@q * Template function instantiations. @> +@* Template function instantiations. +\LOG +\initials{LDF 2003.12.29.} Added this section. +\ENDLOG +@= +float +get_second_largest (float MAX_VAL, bool verbose); + +@ +@= +double +get_second_largest (double MAX_VAL, bool verbose); + + +@q * Putting gsltmplt together.@> +@* Putting {\tt gsltmplt} together. + +@q ** This is what's compiled.@> +@ This is what's compiled. +I don't really need to compile the definition of |get_second_largest()| here, +because it must be included in all of the files that instantiate it, +anyway. However, that may become unnecessary later, in which case it +will have to be compiled here. In addition, if there's something +wrong with the definition, it may be helpful to catch the error here. +\initials{LDF 2004.1.2.} +@c +@@; +@@; +@@; +@@; + +@q ** This is what's written to \filename{gsltmplt.h}.@> +@ This is what's written to the \filename{gsltmplt.h}. +The file \filename{gsltmplt.h} must be included by all files that +define specializations of |get_second_largest()|. +\initials{LDF 2003.12.29.} +@(gsltmplt.h@>= +@@; +@@; +@@; + + + +@q Local Variables: @> +@q mode:CWEB @> +@q eval:(display-time) @> +@q run-cweb-on-file:"3DLDF.web" @> +@q eval:(read-abbrev-file) @> +@q indent-tabs-mode:nil @> +@q eval:(outline-minor-mode) @> +@q End: @> + diff -Naur 3DLDF-1.1.4/CWEB/io.web 3DLDF-1.1.5.1/CWEB/io.web --- 3DLDF-1.1.4/CWEB/io.web 2003-12-10 16:39:40.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/io.web 2004-01-12 22:30:03.000000000 +0100 @@ -3,7 +3,7 @@ @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -52,8 +52,6 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: io.web,v 1.2 2003/12/10 15:39:40 lfinsto1 Exp $ @> - @q * I/O.@> @** I/O\quad ({\tt io\PERIOD web}).\hfil @@ -69,7 +67,7 @@ \ENDLOG @= static string rcs_id - = "$Id: io.web,v 1.2 2003/12/10 15:39:40 lfinsto1 Exp $"; + = "$Id: io.web,v 1.4 2004/01/12 21:30:03 lfinsto1 Exp $"; @q * Include files.@> diff -Naur 3DLDF-1.1.4/CWEB/lines.web 3DLDF-1.1.5.1/CWEB/lines.web --- 3DLDF-1.1.4/CWEB/lines.web 2003-12-10 16:40:48.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/lines.web 2004-01-12 22:30:20.000000000 +0100 @@ -3,7 +3,7 @@ @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -52,8 +52,6 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: lines.web,v 1.2 2003/12/10 15:40:48 lfinsto1 Exp $ @> - @q * Line.@> @** Line\quad ({\tt lines\PERIOD web}).\hfil \initials{LDF 2002.10.29.} |Lines| are not |Shapes|. They are used for @@ -79,7 +77,7 @@ \ENDLOG @= static string rcs_id - = "$Id: lines.web,v 1.2 2003/12/10 15:40:48 lfinsto1 Exp $"; + = "$Id: lines.web,v 1.4 2004/01/12 21:30:20 lfinsto1 Exp $"; @q * Include files.@> @* Include files. diff -Naur 3DLDF-1.1.4/CWEB/loader.web 3DLDF-1.1.5.1/CWEB/loader.web --- 3DLDF-1.1.4/CWEB/loader.web 2003-12-10 16:42:10.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/loader.web 2004-01-12 22:30:27.000000000 +0100 @@ -3,7 +3,7 @@ @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -52,21 +52,8 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: loader.web,v 1.2 2003/12/01 19:17:18 lfinsto1 Exp $ @> - @q * Preprocessor variables and library files.@> @** Preprocessor variables and library files\quad ({\tt loader\PERIOD web}).\hfil -This \CWEB/ file generates no \CPLUSPLUS/ code, but only the header -file \filename{loader.h}, -which loads the library header files. The latter is -included in all of the web files. - -This seemed like a good idea at the time, but now I don't think it -was. @:!! TO DO@> TO DO: Change this, so that the individual CWEB -files load the library header files that they need. Only the ones -that all of the CWEB files really need should remain in this file. -\initials{LDF 2003.08.25.} - \initials{LDF 2002.10.15.} It would, of course, be possible to put this code into a \.{.h} file directly, but it's convenient to have a \CWEB/ file so that it can be @@ -101,9 +88,7 @@ stream formatting. \initials{LDF 2003.08.29.} Removed \filename{getopt.h} to \filename{main.web}, -because it's only used there. @:!! TO DO@> TO DO: Move the rest of -the include commands to the files where they're needed, -{\bf and get rid of this file}. +because it's only used there. \initials{LDF 2003.09.03.} Added |@[#define@]| |LDF_PUBLIC| in order to be able to conditionally include \filename{plfmvar.h}. The latter is not @@ -115,6 +100,10 @@ development versions. \ENDLOG +@= +static string rcs_id + = "$Id: loader.web,v 1.4 2004/01/12 21:30:27 lfinsto1 Exp $"; + @q * Configuration file.@> @* Configuration file.@> This section includes \filename{config.h}, which is generated by @@ -144,24 +133,37 @@ \LOG \initials{LDF 2003.11.12.} Added this section. + +\initials{LDF 2003.12.17.} \filename{config.h} is now not included if +I'm with the DEC \CPLUSPLUS/ compiler. This is because because +building with Autoconf, etc., +doesn't work on the DEC Alpha machine I'm using. \ENDLOG -@(loader.h@>= +@= +#ifndef __DECCXX #include "config.h" +#endif @q * Library files.@> @* Library files.@> -@(loader.h@>= -#define LDF_PUBLIC +\LOG +\initials{LDF 2003.12.17.} Changed the conditional in which +|_GNU_SOURCE|, |LDF_GCC_3_3|, and |LDF_GCC_2_95| are defined or +undefined. Working on compiling with the DEC \CPLUSPLUS/ compiler. +\ENDLOG +@= + -#ifdef LDF_PUBLIC +#define LDF_PUBLIC + +#ifndef __DECCXX +#ifndef _GNU_SOURCE #define _GNU_SOURCE +#endif #define LDF_GCC_3_3 #undef LDF_GCC_2_95 -#undef __DECCXX /* Just to be extra sure. \initials{LDF 2003.09.03.} */ -#else -/* Do nothing. */ -#endif +#endif #ifdef __DECCXX #define __USE_STD_IOSTREAM /* Needed for "sstream" below. */ @@ -192,21 +194,6 @@ #include #include -#ifdef __DECCXX -#include -#else -#ifdef LDF_GCC_3_3 -#include -#else -#ifdef LDF_GCC_2_95 -#if HAVE_LIMITS_H -#include -#endif -#endif -#endif -#endif - -#include #include #ifdef LDF_GCC_3_3 #include @@ -224,14 +211,16 @@ #include #endif -#if HAVE_STDLIB_H +#ifdef __DECCXX +#include +#elif HAVE_STDLIB_H #include #endif @ \filename{streambuf.h} is included above, if |LDF_GCC_2_95| is defined, instead of \filename{ios}, which is included in all other cases. \initials{LDF 2003.08.14.} -@(loader.h@>= +@= #include #include #include @@ -242,9 +231,44 @@ ``|using namespace std|''. This is needed with GCC 3.3, but not with GCC 2.95 or the DEC C++ compiler. \ENDLOG -@(loader.h@>= +@= using namespace std; +@q * Putting loader together.@> +@* Putting {\tt loader} together. + +@q ** This is what's compiled.@> +@ This is what's compiled. +It's not necessary to include \filename{stdlib.h} when using GCC 3.3, +but I think it's safer. +\initials{LDF 2004.01.06.} + +\LOG +\initials{LDF 2004.01.06.} Added this section. It simplifies the +rules for building the executable \.{3dldf} if \filename{loader.c} is +compiled. +\ENDLOG +@c +#ifdef __DECCXX +#include +#elif HAVE_STDLIB_H +#include +#endif + +#include + +using namespace std; +@@; + +@q ** This is what's written to \filename{loader.h}.@> +@ This is what's written to the \filename{loader.h}. +\LOG +\initials{LDF 2004.01.06.} Added this section. +\ENDLOG +@(loader.h@>= +@@; + + diff -Naur 3DLDF-1.1.4/CWEB/main.web 3DLDF-1.1.5.1/CWEB/main.web --- 3DLDF-1.1.4/CWEB/main.web 2003-12-10 16:44:47.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/main.web 2004-01-12 22:30:34.000000000 +0100 @@ -3,7 +3,7 @@ @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -52,8 +52,6 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: main.web,v 1.9 2003/12/09 15:33:08 lfinsto1 Exp $ @> - @q * Main.@> @** Main\quad ({\tt main\PERIOD web}).\hfil \LOG @@ -77,20 +75,25 @@ @= static string rcs_id - = "$Id: main.web,v 1.9 2003/12/09 15:33:08 lfinsto1 Exp $"; + = "$Id: main.web,v 1.12 2004/01/12 21:30:34 lfinsto1 Exp $"; @q * Include files.@> @* Include files. +\filename{getopt.h} is included for +processing the command line options. +\initials{LDF 2003.08.14.} @= #include "loader.h" -#ifdef __GNUC__ +#include -#include /* For processing the command line options. - \initials{LDF 2003.08.14.} */ +#ifdef __GNUC__ +#include #endif #include "pspglb.h" +#include "creatnew.h" +#include "gsltmplt.h" #include "io.h" #include "colors.h" #include "transfor.h" @@ -131,10 +134,15 @@ using namespace Colors; using namespace Projections; - -vector v; +if (ldf_real_float) + MAX_REAL = System::get_second_largest(FLT_MAX, false); +else if (ldf_real_double) + MAX_REAL = System::get_second_largest(DBL_MAX, false); + +MAX_REAL_SQRT = sqrt(MAX_REAL); + -#if 1 +vector v; v.push_back(&red); v.push_back(&green); v.push_back(&blue); @@ -160,7 +168,7 @@ v.push_back(&blue_violet); v.push_back(&violet_red); #endif -#endif + @ Your code here! @= @@ -419,13 +427,6 @@ @q * Main itself.@> @* Main itself. -\initials{LDF 2002.12.11.} @:!! KLUDGE@> !! KLUDGE: I test whether -|INVALID_REAL| and |MAX_REAL| are equal here, because I've had to set -them in a way I don't like in \filename{pspglb.web}. If they are -equal, it's possible that a problem will occur before we get here, but -this is the soonest I can test it. -See the place where |INVALID_REAL| and |MAX_REAL| are declared in -\filename{pspglb.web} for more information. @= int main(int argc, char *argv[]) @@ -433,84 +434,6 @@ @q Currently not used@> @q - - /* \initials{LDF 2002.12.11.} Kludge. See {\TeX} section above. */@; - -@ Error handling. -@= -#if LDF_REAL_FLOAT - if (sizeof(float) != sizeof(unsigned long)) - { - cerr << "sizeof(float) != sizeof(unsigned long)!" << endl; - << "This will probably cause |MAX_REAL| to have a bad value." - << endl << "Continuing, with finger's crossed." << endl << endl; - } -#elif LDF_REAL_DOUBLE - if (sizeof(double) != sizeof(unsigned long long)) - { - cerr << "sizeof(double) != sizeof(unsigned long long)!" << endl; - << "This will probably cause |MAX_REAL| to have a bad value." - << endl << "Proceding with fingers crossed." - << endl << endl << flush; - } -#endif - - if (INVALID_REAL == MAX_REAL) - { - cerr << "ERROR! In main():\nINVALID_REAL == MAX_REAL.\n."; - cerr << "You must set MAX_REAL to a smaller value in pspglb.web " - << " and recompile." << endl << "Exiting with return value 1." - << endl << endl << flush; - exit(1); - } - -@ @^system dependencies@> -This tests whether |MAX_REAL| has a reasonable value. This is -system dependent, so it may need to be fiddled with when 3DLDF is ported. -\initials{LDF 2003.12.08.} - -@:!! TO DO@> TO DO: If |LDF_REAL_DOUBLE|, |threshold| must be set -to a smaller value. \initials{LDF 2003.12.08.} -@= - -#ifdef WORDS_BIGENDIAN - { - cerr << "ERROR! In main():\nThis is a big-endian computer.\n" - << "You will have to change the way MAX_REAL is calculated\n" - << "in pspglb.web and recompile. Sorry about this.\n" - << "Exiting with return value 1\n\n" << flush; - exit(1); - } -#endif - - - { - real threshold = 1e35; -#if LDF_REAL_DOUBLE - cerr << "WARNING! In main():" << endl - << "threshold must be set to a smaller value, " - << "because real is a synonym for double." << endl - << "Proceding with fingers crossed." << endl << endl << flush; -#endif - - if ((INVALID_REAL - MAX_REAL) > threshold) - { - cerr << "ERROR! In main():\nINVALID_REAL - MAX_REAL > 1e35.\n." - << "INVALID_REAL == " << INVALID_REAL << endl - << "MAX_REAL == " << MAX_REAL << endl - << "INVALID_REAL - MAX_REAL == " << (INVALID_REAL - MAX_REAL) - << endl - << "This may mean that your computer represents floating point\n" - << "numbers differently from the one 3DLDF was developed on.\n" - << "You'll have to change the way MAX_REAL is set in pspglb.web." - << endl << "Exiting with return value 1." - << endl << endl << flush; - exit(1); - } - -} -@ -@= @; @ @@ -566,7 +489,6 @@ @@; @@; @@; - - + diff -Naur 3DLDF-1.1.4/CWEB/parser.web 3DLDF-1.1.5.1/CWEB/parser.web --- 3DLDF-1.1.4/CWEB/parser.web 2003-12-10 16:47:42.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/parser.web 2004-01-12 22:30:44.000000000 +0100 @@ -3,7 +3,7 @@ @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -52,8 +52,6 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: parser.web,v 1.2 2003/12/10 15:47:41 lfinsto1 Exp $ @> - @q * Parsing.@> @** Parsing\quad ({\tt parser\PERIOD web}).\hfil \LOG @@ -69,12 +67,16 @@ them back in, now I'm doing the rest of them. However, the release versions are now in their own RCS repository. \ENDLOG + @= static string rcs_id - = "$Id: parser.web,v 1.2 2003/12/10 15:47:41 lfinsto1 Exp $"; + = "$Id: parser.web,v 1.4 2004/01/12 21:30:44 lfinsto1 Exp $"; @q * Include files.@> @ Include files. +\filename{map.h} is currently not needed, but I plan to use it for the +input routine. +\initials{LDF 2004.01.06.} @= #include "loader.h" #include "pspglb.h" diff -Naur 3DLDF-1.1.4/CWEB/paths.web 3DLDF-1.1.5.1/CWEB/paths.web --- 3DLDF-1.1.4/CWEB/paths.web 2003-12-10 17:10:57.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/paths.web 2004-01-12 22:30:52.000000000 +0100 @@ -3,7 +3,7 @@ @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -52,8 +52,6 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: paths.web,v 1.3 2003/12/10 16:10:57 lfinsto1 Exp $ @> - @q * Path.@> @** Path\quad ({\tt paths\PERIOD web}).\hfil \LOG @@ -70,13 +68,14 @@ @f Path Shape @= static string rcs_id - = "$Id: paths.web,v 1.3 2003/12/10 16:10:57 lfinsto1 Exp $"; + = "$Id: paths.web,v 1.7 2004/01/12 21:30:51 lfinsto1 Exp $"; @q * Include files. @> @* Include files. @= #include "loader.h" #include "pspglb.h" +#include "creatnew.h" #include "io.h" #include "colors.h" #include "transfor.h" @@ -176,11 +175,13 @@ derived classes resize |projective_extremes|; at least, I thought they did. \ENDLOG +@q ** Declaration. @> @= virtual Path& operator=(const Path& p); +@q ** Definition. @> @ @= Path& @@ -216,7 +217,7 @@ for (vector ::const_iterator p_iter = p.points.begin(); p_iter != p.points.end(); p_iter++) - points.push_back(Point::create_new_point(*p_iter)); + points.push_back(create_new(*p_iter)); for (vector ::const_iterator c_iter = p.connectors.begin(); c_iter != p.connectors.end(); @@ -335,9 +336,9 @@ arrow = false; - points.push_back(Point::create_new_point(p0)); + points.push_back(create_new(p0)); - points.push_back(Point::create_new_point(p1)); + points.push_back(create_new(p1)); connectors.push_back("--"); if (DEBUG) @@ -373,8 +374,8 @@ projective_extremes = 0; /* LDF 2002.09.18. Added this line. */ - points.push_back(Point::create_new_point(p0)); - points.push_back(Point::create_new_point(p1)); + points.push_back(create_new(p0)); + points.push_back(create_new(p1)); connectors.push_back("--"); line_switch = true; } @@ -441,7 +442,7 @@ Point* arg_ptr; while ((arg_ptr = va_arg(ap, Point*)) != static_cast(0)) - points.push_back(Point::create_new_point(arg_ptr)); + points.push_back(create_new(arg_ptr)); va_end(ap); if (DEBUG) @@ -490,7 +491,7 @@ Point* arg_ptr; while ((arg_ptr = va_arg(ap, Point*)) != static_cast(0)) - points.push_back(Point::create_new_point(arg_ptr)); + points.push_back(create_new(arg_ptr)); va_end(ap); @@ -542,7 +543,7 @@ pen = ""; arrow = false; - points.push_back(Point::create_new_point(first_point_ptr)); + points.push_back(create_new(first_point_ptr)); va_list ap; /* For the variable length argument list. */ va_start(ap, first_point_ptr); @@ -560,7 +561,7 @@ cycle_switch = true; break; } - points.push_back(Point::create_new_point(point_ptr)); + points.push_back(create_new(point_ptr)); } va_end(ap); @@ -599,7 +600,7 @@ pen = ""; arrow = false; - points.push_back(Point::create_new_point(first_point_ptr)); + points.push_back(create_new(first_point_ptr)); va_list ap; /* For the variable length argument list. */ va_start(ap, first_point_ptr); @@ -618,7 +619,7 @@ cycle_switch = true; break; } - points.push_back(Point::create_new_point(point_ptr)); + points.push_back(create_new(point_ptr)); } va_end(ap); } @@ -664,78 +665,43 @@ @q * Pseudo-constructor for dynamic allocation. @> @* Pseudo-constructor for dynamic allocation. -@q ** Optional pointer argument.@> -@*1 Optional pointer argument.@> +@q ** Pointer argument.@> +@*1 Pointer argument.@> \LOG \initials{LDF 2002.10.29.} Added argument |const Path* p|. If |p != 0|, the new |Path| is assigned to using the values from |p|. -\ENDLOG -@^\cfunc{Path}{create\_new\_path}@> -@= -static +\initials{LDF 2003.12.30.} Replaced this version of +|Path::create_new_path()| with +a specialization of |template C* create_new()|. + +\initials{LDF 2003.12.30.} Changed the argument. It's now a +|const Path*|. + +\initials{LDF 2003.12.30.} Removed default argument ``0'', because +this caused a compiler error when using the DEC \CPLUSPLUS/ compiler. +Apparently, it suffices to declare a default argument in the template +declaration. +\ENDLOG +@= Path* -create_new_path(const Path* p = 0); +create_new(const Path* p); -@ -@= -Path* -Path::create_new_path(const Path* p) -{ - bool DEBUG = false; /* |true| */ - if (DEBUG) - cout << "Entering create_new_path().\n" << flush; - - Path* a = new(Path); - a->on_free_store = true; - - if (p != 0) - { - *a = *p; - } - else - { - a->fill_draw_value = 0; - a->draw_color = 0; - a->fill_color = 0; - } - - if (DEBUG) - cout << "Exiting create_new_path().\n" << flush; - - return a; -} - -@q ** Required Path argument.@> -@*1 Required {\bf Path} argument.@> -@^\cfunc{Path}{create\_new\_path}@> +@q ** Reference argument.@> +@*1 Reference argument.@> \LOG \initials{LDF 2002.10.29.} Added this function. -\ENDLOG -@= -static -Path* -create_new_path(const Path& p); - -@ -@= -Path* -Path::create_new_path(const Path& p) -{ - bool DEBUG = false; /* |true| */ - if (DEBUG) - cout << "Entering create_new_path().\n" << flush; - Path* a = new(Path); - a->on_free_store = true; +\initials{LDF 2003.12.30.} Replaced this version of +|Path::create_new_path()| with +a specialization of |template C* create_new()|. - *a = p; +\initials{LDF 2003.12.30.} Changed argument from |Path| to |const Path&|. - if (DEBUG) - cout << "Exiting create_new_path().\n" << flush; - - return a; -} +\ENDLOG +@= +Path* +create_new(const Path& p); @q * Destructor. @> @* Destructor. @@ -902,18 +868,26 @@ Shape* Path::get_copy() const { - Path* p = create_new_path(this); + Path* p = create_new(0); + *p = *this; return static_cast(p); } @q * Set on free store.@> @* Set on free store. @^\cfunc{Path}{set\_on\_free\_store}@> +\LOG +\initials{LDF 2004.01.06.} Made non-inline. +\ENDLOG @= -inline virtual bool -set_on_free_store(bool b = true) +set_on_free_store(bool b = true); + +@ +@= +bool +Path::set_on_free_store(bool b) { on_free_store = b; return b; @@ -1582,7 +1556,7 @@ void Path::operator+=(const Point& pt) { - points.push_back(Point::create_new_point(pt)); + points.push_back(create_new(pt)); return; } @@ -1604,7 +1578,7 @@ Path::operator+(const Point& pt) const { Path pa(*this); - pa.points.push_back(Point::create_new_point(pt)); + pa.points.push_back(create_new(pt)); return pa; } @@ -1706,7 +1680,7 @@ copies onto |points|. */ iter != pa.points.end(); iter++) - points.push_back(Point::create_new_point(*iter)); + points.push_back(create_new(*iter)); @ \initials{LDF 2002.4.6.} Put the connectors from |pa| onto the new |Path|. Since they're @@ -1802,7 +1776,7 @@ for(vector::const_iterator iter = pa.points.begin(); iter != pa.points.end(); iter++) - r.points.push_back(Point::create_new_point(*iter)); + r.points.push_back(create_new(*iter)); @ Put the connectors from |pa| onto the new |Path|. Since they're |strings|, and not pointers, we don't have to copy them. I tested @@ -1867,7 +1841,7 @@ return; } - Path* p = create_new_path(*this); + Path* p = create_new(*this); p->fill_draw_value = DRAW; p->arrow = aarrow; @@ -1881,7 +1855,7 @@ { if (DEBUG) cout << "Allocating memory for Color.\n" << flush; - Color* c = Color::create_new_color(); + Color* c = create_new(0); *c = ddraw_color; p->draw_color = c; } @@ -2196,7 +2170,8 @@ return; } - Path* p = create_new_path(this); + Path* p = create_new(0); + *p = *this; p->fill_draw_value = FILL; @@ -2209,7 +2184,7 @@ { if (DEBUG) cout << "Allocating memory for Color.\n" << flush; - Color* c = Color::create_new_color(); + Color* c = create_new(0); *c = ffill_color; p->fill_color = c; } @@ -2307,7 +2282,8 @@ return; } - Path* p = create_new_path(this); + Path* p = create_new(0); + *p = *this; p->fill_draw_value = FILLDRAW; @@ -2325,7 +2301,7 @@ { if (DEBUG) cout << "Allocating memory for Color.\n" << flush; - Color* c = Color::create_new_color(); + Color* c = create_new(0); *c = ddraw_color; p->draw_color = c; } @@ -2341,7 +2317,7 @@ { if (DEBUG) cout << "Allocating memory for Color.\n" << flush; - Color* c = Color::create_new_color(); + Color* c = create_new(0); *c = ffill_color; p->fill_color = c; } @@ -2410,7 +2386,7 @@ return; } - Path* p = create_new_path(this); + Path* p = create_new(this); p->fill_draw_value = UNDRAW; p->draw_color = 0; @@ -2506,7 +2482,7 @@ return; } - Path* p = create_new_path(this); + Path* p = create_new(this); p->fill_draw_value = UNFILL; p->draw_color = 0; @@ -2549,7 +2525,7 @@ return; } - Path* p = create_new_path(this); + Path* p = create_new(this); p->fill_draw_value = UNFILLDRAW; @@ -2562,7 +2538,7 @@ { if (DEBUG) cout << "Allocating memory for Color.\n" << flush; - Color* c = Color::create_new_color(); + Color* c = create_new(0); *c = ddraw_color; p->draw_color = c; } @@ -3575,10 +3551,17 @@ @q ** Is on free store.@> @*1 Is on free store. @^\cfunc{Path}{is\_on\_free\_store}@> +\LOG +\initials{LDF 2004.01.06.} Made non-inline. +\ENDLOG @= -inline bool -is_on_free_store() const +is_on_free_store() const; + +@ +@= +bool +Path::is_on_free_store() const { return on_free_store; } @@ -3922,7 +3905,7 @@ << "Breaking out of loop.\n\n" << flush; break; } - p.points.push_back(Point::create_new_point(points[i])); + p.points.push_back(create_new(points[i])); } p.connectors.push_back(connector); p.set_cycle(cycle); @@ -3962,7 +3945,7 @@ for (size_t i = start; i < end; i++) { - q.points.push_back(Point::create_new_point(p.points[i])); + q.points.push_back(create_new(p.points[i])); if (i < p.connectors.size()) q.connectors.push_back(p.connectors[i]); } @@ -5111,10 +5094,12 @@ @@; @@; @@; +@@; @ This is what's written to \filename{paths.h}. @(paths.h@>= @@; @@; +@@; diff -Naur 3DLDF-1.1.4/CWEB/patterns.web 3DLDF-1.1.5.1/CWEB/patterns.web --- 3DLDF-1.1.4/CWEB/patterns.web 2003-12-10 17:12:59.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/patterns.web 2004-01-12 22:31:19.000000000 +0100 @@ -3,7 +3,7 @@ @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -52,8 +52,6 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: patterns.web,v 1.2 2003/12/10 16:12:59 lfinsto1 Exp $ @> - @q * Patterns.@> @** Patterns\quad ({\tt patterns\PERIOD web}).\hfil \initials{LDF 2002.09.21.} @@ -82,7 +80,7 @@ @= static string rcs_id - = "$Id: patterns.web,v 1.2 2003/12/10 16:12:59 lfinsto1 Exp $"; + = "$Id: patterns.web,v 1.4 2004/01/12 21:31:19 lfinsto1 Exp $"; @q * Include files.@> @* Include files. diff -Naur 3DLDF-1.1.4/CWEB/pictures.web 3DLDF-1.1.5.1/CWEB/pictures.web --- 3DLDF-1.1.4/CWEB/pictures.web 2003-12-10 17:17:07.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/pictures.web 2004-01-12 22:31:45.000000000 +0100 @@ -3,7 +3,7 @@ @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -52,8 +52,6 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: pictures.web,v 1.2 2003/12/10 16:17:06 lfinsto1 Exp $ @> - @q * Picture and Label.@> @** Picture and Label\quad ({\tt pictures\PERIOD web}).\hfil @@ -69,7 +67,7 @@ \ENDLOG @= static string rcs_id - = "$Id: pictures.web,v 1.2 2003/12/10 16:17:06 lfinsto1 Exp $"; + = "$Id: pictures.web,v 1.4 2004/01/12 21:31:45 lfinsto1 Exp $"; @q * Include files.@> @* Include files. @@ -157,7 +155,8 @@ \initials{LDF 2003.05.11.} Added |AXON|. \ENDLOG @= -namespace Projections +namespace +Projections { extern const unsigned short PERSP = 0; extern const unsigned short PARALLEL_X_Y = 1; diff -Naur 3DLDF-1.1.4/CWEB/planes.web 3DLDF-1.1.5.1/CWEB/planes.web --- 3DLDF-1.1.4/CWEB/planes.web 2003-12-10 17:18:26.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/planes.web 2004-01-12 22:31:54.000000000 +0100 @@ -3,7 +3,7 @@ @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -52,8 +52,6 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: planes.web,v 1.2 2003/12/10 16:18:26 lfinsto1 Exp $ @> - @q * Plane.@> @** Plane\quad ({\tt planes\PERIOD web}).\hfil \initials{LDF 2002.10.29.} |Planes| are not |Shapes|. They are used for @@ -76,7 +74,7 @@ \ENDLOG @= static string rcs_id - = "$Id: planes.web,v 1.2 2003/12/10 16:18:26 lfinsto1 Exp $"; + = "$Id: planes.web,v 1.4 2004/01/12 21:31:54 lfinsto1 Exp $"; @q * Include files.@> @* Include files. diff -Naur 3DLDF-1.1.4/CWEB/points.web 3DLDF-1.1.5.1/CWEB/points.web --- 3DLDF-1.1.4/CWEB/points.web 2003-12-10 17:21:48.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/points.web 2004-01-12 22:32:01.000000000 +0100 @@ -3,7 +3,7 @@ @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -52,8 +52,6 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: points.web,v 1.3 2003/12/10 16:21:48 lfinsto1 Exp $ @> - @q * Point.@> @** Point\quad ({\tt points\PERIOD web}).\hfil @@ -79,7 +77,7 @@ \ENDLOG @= static string rcs_id - = "$Id: points.web,v 1.3 2003/12/10 16:21:48 lfinsto1 Exp $"; + = "$Id: points.web,v 1.6 2004/01/12 21:32:01 lfinsto1 Exp $"; @q * Include files.@> @* Include files. @@ -87,6 +85,7 @@ #include "loader.h" #include "pspglb.h" +#include "creatnew.h" #include "io.h" #include "colors.h" #include "transfor.h" @@ -611,7 +610,7 @@ @q * Pseudo-constructor for dynamic allocation.@> @* Pseudo-constructor for dynamic allocation. -|create_new_point()| is meant to be used instead of |new()| for +|create_new()| is meant to be used instead of |new()| for dynamic allocation of |Points|. It calls the default constructor (without arguments) and then sets |on_free_store| to |true|. @@ -621,78 +620,41 @@ classes derived from |Path|, currently |Ellipse|, |Reg_Polygon|, and |Rectangle|. It is intended that objects of these types be declared, i.e., unlike |Reg_Cl_Plane_Curve|, they are not meant to be used only as base -classes. |Reg_Cl_Plane_Curve| does not use |create_new_point()| and it is +classes. |Reg_Cl_Plane_Curve| does not use |create_new()| and it is unlikely that other classes of this kind will use it. - -@q ** Optional pointer argument.@> -@*1 Optional pointer argument.@> -@^\cfunc{Point}{create\_new\_point}@> -\LOG -\initials{LDF 2002.10.29.} Made this function non-|inline|. -Added argument |const Point* p|. If |p != 0|, the new |Point| is -assigned to using the values from |p|. -\ENDLOG -@= -static -Point* -create_new_point(const Point* p = 0); - -@ -@= -Point* -Point::create_new_point(const Point* p) -{ - Point* a = new(Point); - a->on_free_store = true; - if (p != 0) - *a = *p; - return a; -} - -@q ** Required Point argument.@> -@*1 Required {\bf Point} argument.@> -@^\cfunc{Point}{create\_new\_point}@> -@= -static +\LOG +\initials{LDF 2003.12.30.} Replaced the non-template +|create_new_point()| functions with versions of the |create_new()| +template function. I believe the definitions shouldn't be necessary, +but at present they are. Without them, the templates aren't +instantiated. + +\initials{LDF 2003.12.30.} Changed the argument. It's now a +|const Point*|. + +\initials{LDF 2003.12.30.} Removed default argument ``0'', because +this caused a compiler error when using the DEC \CPLUSPLUS/ compiler. +Apparently, it suffices to declare a default argument in the template +declaration. +\ENDLOG + +@q ** Pointer argument.@> +@*1 Pointer argument.@> +@= Point* -create_new_point(const Point& p); +create_new(const Point* p); +@q ** Reference argument.@> +@*1 Referece argument.@> -@ -@= -Point* -Point::create_new_point(const Point& p) -{ - Point* a = new(Point); - a->on_free_store = true; - *a = p; - return a; -} - -@q ** real arguments.@> -@*1 {\bf real} arguments.@> -@^\cfunc{Point}{create\_new\_point}@> \LOG -\initials{LDF 2002.11.06.} Added this function. +\initials{LDF 2003.12.30.} Changed argument from |Point| to |const Point&|. \ENDLOG -@= -static + +@= Point* -create_new_point(const real x, const real y = 0, const real z = 0); - - -@ -@= -Point* -Point::create_new_point(const real x, const real y, const real z) -{ - Point* a = new(Point); - a->on_free_store = true; - a->set(x, y, z); - return a; -} - +create_new(const Point& p); @q * Destructor.@> @* Destructor. @@ -758,11 +720,18 @@ @q * Set on free store.@> @* Set on free store. @^\cfunc{Point}{set\_on\_free\_store}@> +\LOG +\initials{LDF 2003.12.29.} Made non-inline. +\ENDLOG @= -inline virtual bool -set_on_free_store(bool b = true) +set_on_free_store(bool b = true); + +@ +@= +bool +Point::set_on_free_store(bool b) { on_free_store = b; return b; @@ -836,13 +805,30 @@ @q ** Epsilon.@> @*1 Epsilon. @^\cfunc{Point}{epsilon}@> +\LOG +\initials{LDF 2004.1.2.} Now returning different values, depending on +whether |real| is |float| or |double|. +@:!! TO DO@> TO DO: Try to find out what values would be best. It +will be necessary to check how good the value for |double| is. + + +\initials{LDF 2004.1.2.} Made |epsilon()| non-inline. +\ENDLOG @= -inline static real -epsilon() +epsilon(); + +@ +@= +real +Point::epsilon() { +#if LDF_REAL_DOUBLE + return .000000001; +#else return .00001; +#endif } @q ** Get Line.@> @@ -1253,17 +1239,25 @@ Shape* Point::get_copy() const { - Point* p = create_new_point(); + Point* p = create_new(0); *p = *this; return static_cast(p); } @q ** Is on free store.@> @*1 Is on free store. + +\LOG +\initials{LDF 2004.01.06.} Made non-inline. +\ENDLOG @= -inline bool -is_on_free_store() const +is_on_free_store() const; + +@ +@= +bool +Point::is_on_free_store() const { return on_free_store; } @@ -2681,7 +2675,7 @@ if (DEBUG) cout << "Entering drawdot()" << "\n" << flush; - Point* pt = create_new_point(); + Point* pt = create_new(0); *pt = *this; pt->drawdot_value = DRAWDOT; pt->drawdot_color = &ddrawdot_color; @@ -2735,7 +2729,7 @@ void Point::undrawdot(string ppen, Picture& picture) { - Point* pt = create_new_point(); + Point* pt = create_new(0); *pt = *this; pt->drawdot_value = UNDRAWDOT; pt->drawdot_color = Colors::background_color; @@ -3109,11 +3103,11 @@ \initials{LDF 2002.09.16.} Removed calls to |apply_transform()| and |project()|. \ENDLOG -@= +@= ostream& operator<<(ostream& o, Point& p); @ -@= +@= ostream& operator<<(ostream& o, Point& p) { @@ -3660,7 +3654,7 @@ Label* lbl = new(Label); - lbl->pt = Point::create_new_point(); + lbl->pt = create_new(0); *(lbl->pt) = *this; @@ -3884,7 +3878,7 @@ Label::get_copy() const { Label* lbl = new(Label); - lbl->pt = Point::create_new_point(); + lbl->pt = create_new(0); *(lbl->pt) = *pt; lbl->dot = dot; lbl->text = text; @@ -4111,11 +4105,11 @@ @q *** Non-member version. @> @*2 Non-member version (scalar first). @^\ofunc{*}@> -@= +@= Point operator*(const real, const Point& p); @ -@= +@= Point operator*(const real r, const Point& p) { @@ -4292,8 +4286,10 @@ real Point::magnitude() const { - real r; - real temp; + bool DEBUG = true; /* |false| */ + + real r; + real temp; Point a(*this); @@ -6350,11 +6346,13 @@ @q * Putting Point and Focus together.@> @* Putting {\bf Point} and {\bf Focus} together. -@ This is what's compiled. +@q ** This is what's compiled.@> +@*1 This is what's compiled. @c @@; @@; @@; +@@; @@; @@; @@; @@ -6364,7 +6362,7 @@ @@; @@; @@; -@@; +@@; @@; @@; @@; @@ -6373,12 +6371,14 @@ @@; -@ This is what's written to \filename{points.h}. +@q ** This is what's written to \filename{points.h}. @> +@*1 This is what's written to \filename{points.h}. @(points.h@>= @@; @@; @@; - @@; + @@; + @@; @@; @@; diff -Naur 3DLDF-1.1.4/CWEB/polygons.web 3DLDF-1.1.5.1/CWEB/polygons.web --- 3DLDF-1.1.4/CWEB/polygons.web 2003-12-10 17:24:07.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/polygons.web 2004-01-12 22:32:09.000000000 +0100 @@ -3,7 +3,7 @@ @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -52,8 +52,6 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: polygons.web,v 1.2 2003/12/10 16:24:07 lfinsto1 Exp $ @> - @q * Polygon.@> @** Polygon\quad ({\tt polygons\PERIOD web}).\hfil \LOG @@ -74,13 +72,14 @@ @f Polygon Path @= static string rcs_id - = "$Id: polygons.web,v 1.2 2003/12/10 16:24:07 lfinsto1 Exp $"; + = "$Id: polygons.web,v 1.4 2004/01/12 21:32:08 lfinsto1 Exp $"; @q * Include files.@> @* Include files. @= #include "loader.h" #include "pspglb.h" +#include "creatnew.h" #include "io.h" #include "colors.h" #include "transfor.h" @@ -1147,7 +1146,8 @@ @= for (int i = 0; i < sides; i++) { - Point* vertex = Point::create_new_point(0, 0, radius); + Point* vertex = create_new(0); + vertex->set(0, 0, radius); if (sides % 2 == 0) vertex->rotate(0, internal_angle / 2, 0); @@ -1217,59 +1217,33 @@ @q * Pseudo-constructor for dynamic allocation.@> @* Pseudo-constructor for dynamic allocation. -@q ** Optional pointer argument.@> -@*1 Optional pointer argument.@> -@^\cfunc{Reg\_Polygon}{create\_new\_reg\_polygon}@> +@q ** Pointer argument.@> +@*1 Pointer argument.@> \LOG \initials{LDF 2002.11.06.} Added optional |Reg_Polygon| pointer argument. Made non-|inline|. + +\initials{LDF 2003.12.30.} Replaced |Reg_Polygon::create_new_reg_polygon()| +with a specialization of |template C* create_new()| for +|Reg_Polygon|. \ENDLOG -@= -static -Reg_Polygon* -create_new_reg_polygon(const Reg_Polygon* r = 0); -@ -@= -Reg_Polygon* -Reg_Polygon::create_new_reg_polygon(const Reg_Polygon* r) -{ - Reg_Polygon* p = new(Reg_Polygon); - if (r != 0) - *p = *r; - p->on_free_store = true; - p->cycle_switch = true; - p->line_switch = false; - p->projective_extremes.resize(6, 0); /* LDF 2003.04.09. Added this - line. */ - return p; -} +@= +Reg_Polygon* +create_new(const Reg_Polygon* r); -@q ** Required Reg_Polygon argument.@> -@*1 Required {\bf Reg\_Polygon} argument.@> -@^\cfunc{Reg\_Polygon}{create\_new\_Reg\_Polygon}@> +@q ** Reference argument.@> +@*1 Reference argument.@> \LOG \initials{LDF 2002.11.06.} Added this function. -\ENDLOG -@= -static -Reg_Polygon* -create_new_reg_polygon(const Reg_Polygon& r); -@ -@= -Reg_Polygon* -Reg_Polygon::create_new_reg_polygon(const Reg_Polygon& r) -{ - Reg_Polygon* p = new(Reg_Polygon); - *p = r; - p->on_free_store = true; - p->cycle_switch = true; - p->line_switch = false; - p->projective_extremes.resize(6, 0); /* LDF 2003.04.09. Added this - line. */ - return p; -} +\initials{LDF 2003.12.30.} Replaced |Reg_Polygon::create_new_reg_polygon()| +with a specialization of |template C* create_new()| for +|Reg_Polygon|. +\ENDLOG +@= +Reg_Polygon* +create_new(const Reg_Polygon& r); @q * Destructor. @> @* Destructor. @@ -1408,12 +1382,14 @@ @@; @@; @@; +@@; @ This is what's written to \filename{polygons.h}. @(polygons.h@>= @@; @@; +@@; diff -Naur 3DLDF-1.1.4/CWEB/polyhed.web 3DLDF-1.1.5.1/CWEB/polyhed.web --- 3DLDF-1.1.4/CWEB/polyhed.web 2003-12-10 17:27:16.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/polyhed.web 2004-01-12 22:32:19.000000000 +0100 @@ -3,7 +3,7 @@ @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -52,8 +52,6 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: polyhed.web,v 1.3 2003/12/10 16:27:16 lfinsto1 Exp $ @> - @q * Polyhedra.@> @** Polyhedra\quad ({\tt polyhedra\PERIOD web}).\hfil \initials{LDF 2002.11.12.} @@ -79,13 +77,14 @@ \ENDLOG @= static string rcs_id - = "$Id: polyhed.web,v 1.3 2003/12/10 16:27:16 lfinsto1 Exp $"; + = "$Id: polyhed.web,v 1.5 2004/01/12 21:32:19 lfinsto1 Exp $"; @q * Include files.@> @* Include files. @= #include "loader.h" #include "pspglb.h" +#include "creatnew.h" #include "io.h" #include "colors.h" #include "transfor.h" @@ -464,7 +463,7 @@ int i; for(i = 0; i < 4; i++) - triangles.push_back(Reg_Polygon::create_new_reg_polygon()); + triangles.push_back(create_new(0)); triangles[0]->set(origin, 3, triangle_diameter, 0, 180); @@ -883,7 +882,7 @@ for (i = 0; i < 6; ++i) { - reg_polygons.push_back(Reg_Polygon::create_new_reg_polygon()); + reg_polygons.push_back(create_new(0)); *reg_polygons.back() = *reg_polygons[i]; reg_polygons.back()->rotate(180); } @@ -973,7 +972,7 @@ vector pents; for (i = 0; i < 6; ++i) - pents.push_back(Reg_Polygon::create_new_reg_polygon()); + pents.push_back(create_new(0)); pents[0]->set(origin, 5, pentagon_diameter, 0, 180); /* The middle pentagon. */ @@ -1023,7 +1022,7 @@ for (i = 6; i < 12; i++) { - pents.push_back(Reg_Polygon::create_new_reg_polygon()); + pents.push_back(create_new(0)); *pents[i] = *pents[i - 6]; pents[i]->rotate(0, 180); } @@ -1225,7 +1224,7 @@ triangle_radius = triangle_diameter / 2.0; int i; - reg_polygons.push_back(Reg_Polygon::create_new_reg_polygon()); + reg_polygons.push_back(create_new(0)); reg_polygons.front()->set(origin, 3, triangle_diameter); @@ -1236,7 +1235,7 @@ for (i = 1; i < 6; ++i) { - reg_polygons.push_back(Reg_Polygon::create_new_reg_polygon(reg_polygons.front())); + reg_polygons.push_back(create_new(reg_polygons.front())); } reg_polygons[1]->shift(pts[2] - pts[1]); @@ -1253,7 +1252,7 @@ for (i = 6; i < 10; ++i) { - reg_polygons.push_back(Reg_Polygon::create_new_reg_polygon(reg_polygons[5])); + reg_polygons.push_back(create_new(reg_polygons[5])); } reg_polygons[6]->shift(pts[2] - pts[1]); @@ -1290,7 +1289,7 @@ for (i = 10; i < 20; ++i) { - reg_polygons.push_back(Reg_Polygon::create_new_reg_polygon(reg_polygons[i - 10])); + reg_polygons.push_back(create_new(reg_polygons[i - 10])); reg_polygons.back()->rotate(180); reg_polygons.back()->shift(0, 12); } @@ -1367,7 +1366,7 @@ vector triangles; int i; for (i = 0; i < 10; ++i) - triangles.push_back(Reg_Polygon::create_new_reg_polygon()); + triangles.push_back(create_new(0)); @,@/ /* The bottom left triangle. */ triangles[0]->set(origin, 3, triangle_diameter, 0, 180); @@ -1426,7 +1425,7 @@ cout << "Doing the second half.\n"; for (i = 0; i < 10; ++i) - triangles.push_back(Reg_Polygon::create_new_reg_polygon()); + triangles.push_back(create_new(0)); for (int j = 8; j <= 16; j += 4) for (i = 0; i < 4; ++i) @@ -1735,31 +1734,31 @@ /* 7 */ reg_polygons.push_back - (Reg_Polygon::create_new_reg_polygon(reg_polygons[0])); + (create_new(reg_polygons[0])); /* 8 */ reg_polygons.push_back - (Reg_Polygon::create_new_reg_polygon(reg_polygons[1])); + (create_new(reg_polygons[1])); /* 9 */ reg_polygons.push_back - (Reg_Polygon::create_new_reg_polygon(reg_polygons[2])); + (create_new(reg_polygons[2])); /* 10 */ reg_polygons.push_back - (Reg_Polygon::create_new_reg_polygon(reg_polygons[3])); + (create_new(reg_polygons[3])); /* 11 */ reg_polygons.push_back - (Reg_Polygon::create_new_reg_polygon(reg_polygons[4])); + (create_new(reg_polygons[4])); /* 12 */ reg_polygons.push_back - (Reg_Polygon::create_new_reg_polygon(reg_polygons[5])); + (create_new(reg_polygons[5])); /* 13 */ reg_polygons.push_back - (Reg_Polygon::create_new_reg_polygon(reg_polygons[6])); + (create_new(reg_polygons[6])); Transform t; t.rotate(180); @@ -1823,20 +1822,20 @@ int i; - reg_polygons.push_back(Reg_Polygon::create_new_reg_polygon()); + reg_polygons.push_back(create_new(0)); reg_polygons[0]->set(origin, 6, hexagon_diameter); Point pts[24]; for (i = 0; i < 6; i++) pts[i] = reg_polygons[0]->get_point(i); - reg_polygons.push_back(Reg_Polygon::create_new_reg_polygon(reg_polygons[0])); + reg_polygons.push_back(create_new(reg_polygons[0])); reg_polygons[1]->shift(pts[4] - pts[2]); - reg_polygons.push_back(Reg_Polygon::create_new_reg_polygon(reg_polygons[0])); + reg_polygons.push_back(create_new(reg_polygons[0])); reg_polygons[2]->shift(pts[3] - pts[5]); - reg_polygons.push_back(Reg_Polygon::create_new_reg_polygon(reg_polygons[0])); + reg_polygons.push_back(create_new(reg_polygons[0])); reg_polygons[3]->shift(pts[1] - pts[3]); real side_length = pts[5].get_x() - pts[0].get_x(); @@ -1848,7 +1847,7 @@ Rectangle r(pts[0], pts[5], pts[7], pts[6]); - reg_polygons.push_back(Reg_Polygon::create_new_reg_polygon(r)); + reg_polygons.push_back(create_new(r)); pts[8] = pts[2]; pts[9] = pts[1]; @@ -1859,7 +1858,7 @@ pts[10].shift(pts[2] - pts[1]); r.set(pts[10], pts[2], pts[1], pts[8]); - reg_polygons.push_back(Reg_Polygon::create_new_reg_polygon(r)); + reg_polygons.push_back(create_new(r)); pts[11] = pts[3]; @@ -1871,7 +1870,7 @@ pts[13].shift(pts[3] - pts[4]); r.set(pts[11], pts[4], pts[3], pts[13]); - reg_polygons.push_back(Reg_Polygon::create_new_reg_polygon(r)); + reg_polygons.push_back(create_new(r)); if (do_half) @@ -1899,11 +1898,11 @@ reg_polygons.push_back - (Reg_Polygon::create_new_reg_polygon + (create_new (reg_polygons[0])); /* 7 */ reg_polygons.push_back - (Reg_Polygon::create_new_reg_polygon + (create_new (reg_polygons[4])); /* 8 */ @@ -1912,27 +1911,27 @@ reg_polygons.push_back - (Reg_Polygon::create_new_reg_polygon + (create_new (reg_polygons[0])); /* 9 */ reg_polygons[9]->shift(pts[4] + pts[0] - (2 * pts[2])); reg_polygons.push_back - (Reg_Polygon::create_new_reg_polygon + (create_new (reg_polygons[4])); /* 10 */ reg_polygons.push_back - (Reg_Polygon::create_new_reg_polygon + (create_new (reg_polygons[0])); /* 11 */ reg_polygons.push_back - (Reg_Polygon::create_new_reg_polygon + (create_new (reg_polygons[1])); /* 12 */ reg_polygons.push_back - (Reg_Polygon::create_new_reg_polygon + (create_new (reg_polygons[6])); /* 13 */ diff -Naur 3DLDF-1.1.4/CWEB/pspglb.web 3DLDF-1.1.5.1/CWEB/pspglb.web --- 3DLDF-1.1.4/CWEB/pspglb.web 2003-12-10 17:34:02.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/pspglb.web 2004-01-16 17:30:41.000000000 +0100 @@ -3,7 +3,7 @@ @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -52,8 +52,6 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: pspglb.web,v 1.10 2003/12/10 16:34:02 lfinsto1 Exp $ @> - @q * Global items (pspglb).@> @** Global items\quad ({\tt pspglb\PERIOD web}).\hfil Typedefs, global variables and constants, @@ -65,17 +63,37 @@ files for the distribution of 3DLDF 1.1.1. They're still used in my development versions. -\initials{LDF 2003.12.01.} Put the version control identifiers back -into the release versions, because I've put them in their own RCS repository. +\initials{LDF 2003.12.10.} Put the version control identifiers back +into my release versions for 3DLDF 1.1.4. I've already put some of +them back in, now I'm doing the rest of them. However, the release +versions are now in their own RCS repository. \ENDLOG @= static string rcs_id - = "$Id: pspglb.web,v 1.10 2003/12/10 16:34:02 lfinsto1 Exp $"; + = "$Id: pspglb.web,v 1.14 2004/01/16 16:30:41 lfinsto1 Exp $"; @q * Include files.@> @* Include files. @= #include "loader.h" + +#ifdef __DECCXX +#include +#else +#ifdef LDF_GCC_3_3 +#include +#else +#ifdef LDF_GCC_2_95 +#if HAVE_LIMITS_H +#include +#endif +#endif +#endif +#endif + + + + #include @q * Type definitions.@> @@ -103,6 +121,12 @@ \initials{LDF 2003.06.03.} Added |real_short|. It's the return type of |Plane::get_distance()|. +\initials{LDF 2003.12.30.} Now using |#define| instead of |@@d| for +the definitions of |LDF_REAL_FLOAT| and |LDF_REAL_DOUBLE|. If |@@d| +is used, the definitions are only written to \filename{pspglb.c}. +Using |#define|, and writing |@| to +\filename{pspglb.h} makes the definitions available to the files that +include \filename{pspglb.h}. \ENDLOG @f real float @@ -110,14 +134,15 @@ @f bool_pair real_pair @f real_pair real_short @f Matrix int -@d LDF_REAL_FLOAT 1 -@d LDF_REAL_DOUBLE 0 @= +#define LDF_REAL_FLOAT 1 +#define LDF_REAL_DOUBLE 0 + #if LDF_REAL_FLOAT typedef float real; #elif LDF_REAL_DOUBLE typedef double real; -#else +#else /* Default. LDF 2003.12.17. */ typedef float real; #endif @@ -165,39 +190,9 @@ -@ |MAX_REAL| is the second largest |real| value on a -little-endian platform where |sizeof(float) == sizeof(unsigned long)| and -|sizeof(double) == sizeof(unsigned long long)|. -The terms -``endianness'', ``big-endian'', and ``little-endian'' refer to the way -in which data is stored in ``words'' in a particular computer -architecture. In a big-endian architecture, the most significant byte -is stored first. \initials{LDF 2003.12.09.} - -@:!! TO DO@> TO DO: Write conditionally compiled code for processors, -where this is not the case! -The endianness of the processor and the value |MAX_REAL| are tested in -\filename{main.web}. If the processor is big-endian, or -|MAX_REAL == INVALID_REAL|, or |INVALID_REAL - MAX_REAL| is greater -than a threshold value (currently |1e35|), 3DLDF will issue an error -message and exit with return value 1. \initials{LDF 2003.12.09.} -\initials{LDF 2003.12.09.} - - -|reinterpret_cast()| is used, because neither |static_cast()| nor -|dynamic_cast()| work. Stroustrup, -{\it The \CPLUSPLUS/ Programming Language}, \S 6.2.7, p.~130, goes -into this. He explicitly mentions that |reinterpret_cast()| -``$\ldots$ generally $\lbrack\ldots\rbrack$ produces a value of a new -type that has the same bit pattern as its argument.'' -\initials{LDF 2003.12.08.} - -The method I'm using now to calculate |MAX_REAL| may fail on systems -that represent floating point numbers differently from the platform -I'm using. LDF 2003.12.08. - - - +@ |MAX_REAL| is the second largest |real| value. +|MAX_REAL_SQRT| is convenient to have for testing when computing +distances. @:!! KLUDGE@> !! KLUDGE: Using the macros |FLT_MAX| or |DBL_MAX| because the |numeric_limits| template doesn't seem to be available @@ -209,6 +204,18 @@ Changed the definition of |MAX_REAL|. Previously, it was calculated using |.00000003 * FLT_MAX|, which was a kludge. + + +\initials{LDF 2003.12.29.} Changed the way |MAX_REAL| and +|MAX_REAL_SQRT| are declared. They can no longer be |const|, because +the value of |MAX_REAL| is set at the beginning of |main()| using +|get_second_largest()|. +The value of |MAX_REAL_SQRT| is set +after this. Their values should never change after this! + +|MAX_REAL_SQRT| must be initialized here, +because it's used in |Point::magnitude()|. +\initials{LDF 2003.12.29.} \ENDLOG @= @@ -222,24 +229,9 @@ extern const real INVALID_REAL = FLT_MAX; #endif #endif - -#if LDF_REAL_DOUBLE -real d = INVALID_REAL; -real *dp = &d; -unsigned long long* ip = reinterpret_cast(dp); -unsigned long long i = (*ip) -= 1; -bitset<8*sizeof(unsigned long long)> b = i; -extern const real MAX_REAL = *(reinterpret_cast(&i)); - -#else /* |LDF_REAL_FLOAT|, or not specified. LDF 2003.12.08. */ -real f = INVALID_REAL; -real *fp = &f; -unsigned long* ip = reinterpret_cast(fp); -unsigned long i = (*ip) -= 1; -bitset<8*sizeof(unsigned long)> b = i; -extern const real MAX_REAL = *(reinterpret_cast(&i)); -#endif +real MAX_REAL = 0; +real MAX_REAL_SQRT = 0; @ \initials{LDF 2003.08.14.} |VERBOSE_GLOBAL| is |false| by default. It is set to |true| by the command line option ``{\tt --verbose}''. @@ -256,18 +248,34 @@ @= extern bool VERBOSE_GLOBAL; extern bool SILENT_GLOBAL; +extern const bool ldf_real_float; +extern const bool ldf_real_double; +extern real MAX_REAL; +extern real MAX_REAL_SQRT; @ \LOG \initials{LDF 2003.08.14.} Added |VERSION_3DLDF| and |COPYRIGHT_3DLDF|. \ENDLOG @= -extern const string VERSION_3DLDF = "1.1.4"; -extern const string COPYRIGHT_3DLDF = "Copyright (C) 2003 by Laurence D. Finston."; + +#if LDF_REAL_FLOAT + extern const bool ldf_real_float = 1; + extern const bool ldf_real_double = 0; +#elif LDF_REAL_DOUBLE + extern const bool ldf_real_float = 0; + extern const bool ldf_real_double = 1; +#else /* Defaults. LDF 2003.12.17. */ + extern const bool ldf_real_float = 1; + extern const bool ldf_real_double = 0; +#endif + +extern const string VERSION_3DLDF = "1.1.5.1"; +extern const string COPYRIGHT_3DLDF = "Copyright (C) 2003, 2004 by Laurence D. Finston."; extern const string DISCLAIMER_3DLDF = "3DLDF comes with ABSOLUTELY NO WARRANTY;\n\ for details see the file COPYING,\n\ which you should have received\n\ -in the distribution of 3DLDF 1.1.4\n\ +in the distribution of 3DLDF 1.1.5.1\n\ This is free software, and you are welcome\n\ to redistribute it under certain conditions;\n\ for details, again, see the file COPYING.\n\n\ @@ -286,6 +294,8 @@ extern const string VERSION_3DLDF; extern const string COPYRIGHT_3DLDF; extern const string DISCLAIMER_3DLDF; +extern const bool ldf_real_float; +extern const bool ldf_real_double; @ @:!! TO DO@> TO DO: Find out why the library version of |trunc()| can't be found in the version for @@ -357,9 +367,6 @@ \initials{LDF 2002.10.16.} Modified \initials{LDF 2002.10.20.} -|MAX_REAL| is the largest permitted |real| value. -|MAX_REAL_SQRT| is convenient to have for testing when computing -distances. \LOG \initials{LDF 2002.09.25.} Added this section. Previously, I declared and @@ -385,16 +392,7 @@ -#ifdef __DECCXX -extern const real MAX_REAL_SQRT = sqrt(MAX_REAL); -#endif -@ \initials{LDF 2002.12.10.} -@:!! URGENT@> URGENT: Find out why |sqrt()| doesn't work. -@= -#ifdef __GNUC__ -extern const real MAX_REAL_SQRT = 1.84467e+19; -#endif @q ** For the header file.@> @*1 For the header file. @@ -403,8 +401,6 @@ extern const real INVALID_REAL; extern const real_pair INVALID_REAL_PAIR; extern const real_short INVALID_REAL_SHORT; -extern const real MAX_REAL; -extern const real MAX_REAL_SQRT; @q * Utility functions.@> @@ -453,34 +449,198 @@ return p; } -@q ** Dynamic allocation.@> -@*1 Dynamic allocation. -\initials{LDF 2002.10.02.} @:!! TO DO@> TO DO: Try to get this to work. I -haven't been able to get this template function to instantiate -correctly. -@= -#if 0 -template -C* -create_new(C* c = 0); -#endif + + + + +@q * System information.@> +@* System information. +\LOG +\initials{LDF 2003.12.29.} Added this section. +\ENDLOG + + +@q ** Declare |namespace System|. @> +@*1 Declare {\bf namespace System}. @> +\LOG +\initials{LDF 2003.12.29.} Added this section. +\ENDLOG +@= +namespace +System +{ + @@; +} + + +@q ** Endianness. @> +@*1 Endianness. +\LOG +\initials{LDF 2003.12.29.} Added this section. +\ENDLOG + +@q *** Get endianness. @> +@*2 Get endianness. +|get_endianness()| returns the following values: + +\item{0} if the processor is little-endian. +\item{1} if the processor is big-endian. +\item{-1} if the endianness cannot be determined. + +It is called by |is_little_endian()| and |is_big_endian()|. +\initials{LDF 2003.12.21.} + +This function has been adapted from +Harbison, Samuel~P., and Guy~L. Steele Jr. +{\it C, A Reference Manual}, pp.~163--164. +\initials{LDF 2003.12.29.} + + +\LOG +\initials{LDF 2003.12.29.} Added this function. +\ENDLOG +@= +signed short +get_endianness(const bool verbose = false); + @ -@= -#if 0 -template -C* -create_new(C* c) +@= +signed short +System::get_endianness(const bool verbose) { - cout << "In create_new.\n" << flush; - C* new_shape_ptr = new(C); - if (c != 0) - *new_shape_ptr = *c; - new_shape_ptr->set_on_free_store(true); - return new_shape_ptr; -} -#endif + union { + long Long; + char Char[sizeof(long)]; + } u; + u.Long = 1; + if (u.Char[0] == 1) + { + if (verbose) + cout << "Processor is little-endian." << endl << endl + << flush; + return 0; + } + else if (u.Char[sizeof(long) - 1] == 1) + { + if (verbose) + cout << "Processor is big-endian." << endl << endl + << flush; + return 1; + } + else + { + cerr << "ERROR! In System::get_endianness():\n" + << "Can't determine endianness. Returning -1" + << endl << endl << flush; + return -1; + } +} + + + +@q *** Is big endian. @> +@*2 Is big endian. +\LOG +\initials{LDF 2003.12.29.} Added this function. +\ENDLOG +@= +bool +is_big_endian(const bool verbose = false); + +@ +@= +bool +System::is_big_endian(const bool verbose) +{ + return (get_endianness(verbose) == 1); +} + +@q *** Is little endian. @> +@*2 Is little endian. +\LOG +\initials{LDF 2003.12.29.} Added this function. +\ENDLOG +@= +bool +is_little_endian(const bool verbose = false); + +@ +@= +bool +System::is_little_endian(const bool verbose) +{ + return (get_endianness(verbose) == 0); +} + + +@q ** Register width. @> +@*1 Register width. +\LOG +\initials{LDF 2003.12.29.} Added this section. +\ENDLOG + +@q *** Get register width. @> +@*2 Get register width. +\LOG +\initials{LDF 2003.12.29.} Added this function. + +\initials{LDF 2004.1.2.} Changed the name of this function from +|get_processor_size()| to |get_register_width()|. +\ENDLOG +@= +unsigned short +get_register_width(); + + +@ +@= +unsigned short +System::get_register_width() +{ + return (sizeof(void*) * CHAR_BIT); +} + + +@q *** Is 32 bit. @> +@*2 Is 32 bit. +\LOG +\initials{LDF 2003.12.29.} Added this function. +\ENDLOG +@= +bool +is_32_bit(); + +@ +@= +bool +System::is_32_bit() +{ + return (get_register_width() == 32); +} + + +@q *** Is 64 bit. @> +@*2 Is 64 bit. + +\LOG +\initials{LDF 2003.12.29.} Added this function. +\ENDLOG +@= +bool +is_64_bit(); + + +@ +@= +bool +System::is_64_bit() +{ + return (get_register_width() == 64); +} + + @q * Forward declarations.@> @* Forward declarations. \initials{LDF 2002.10.16.} In the files that are compiled first, some classes @@ -528,6 +688,9 @@ @@; @@; @@; +@@; +@@; +@@; @q ** This is what's written to \filename{pspglb.h}.@> @ This is what's written to the \filename{pspglb.h}. @@ -535,6 +698,7 @@ @@; @@; @@; +@@; /* This doesn't work, apparently because it's incompatible with the use of \filename{sstream}. */ @@ -546,6 +710,7 @@ @@; @@; +@@; diff -Naur 3DLDF-1.1.4/CWEB/rectangs.web 3DLDF-1.1.5.1/CWEB/rectangs.web --- 3DLDF-1.1.4/CWEB/rectangs.web 2003-12-10 17:36:58.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/rectangs.web 2004-01-12 22:32:24.000000000 +0100 @@ -3,7 +3,7 @@ @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -52,8 +52,6 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: rectangs.web,v 1.3 2003/12/10 16:36:58 lfinsto1 Exp $ @> - @q * Rectangle.@> @** Rectangle\quad ({\tt rectangles\PERIOD web}).\hfil @@ -78,13 +76,14 @@ @f Rectangle Reg_Polygon @= static string rcs_id - = "$Id: rectangs.web,v 1.3 2003/12/10 16:36:58 lfinsto1 Exp $"; + = "$Id: rectangs.web,v 1.5 2004/01/12 21:32:24 lfinsto1 Exp $"; @q * Include files.@> @* Include files. @= #include "loader.h" #include "pspglb.h" +#include "creatnew.h" #include "io.h" #include "colors.h" #include "transfor.h" @@ -193,7 +192,7 @@ top_rt.shift(center); for(int i = 0; i < 4; i++) - points.push_back(Point::create_new_point()); + points.push_back(create_new(0)); *points[0] = bot_lft; *points[1] = bot_rt; @@ -266,10 +265,10 @@ axis_h = (pt1 - pt0).magnitude(); axis_v = (pt2 - pt1).magnitude(); - points.push_back(Point::create_new_point(pt0)); - points.push_back(Point::create_new_point(pt1)); - points.push_back(Point::create_new_point(pt2)); - points.push_back(Point::create_new_point(pt3)); + points.push_back(create_new(pt0)); + points.push_back(create_new(pt1)); + points.push_back(create_new(pt2)); + points.push_back(create_new(pt3)); connectors.push_back("--"); } @@ -303,52 +302,31 @@ @q * Pseudo-constructor for dynamic allocation.@> @* Pseudo-constructor for dynamic allocation. -@q ** Optional pointer argument.@> -@*1 Optional pointer argument. - -@^\cfunc{Rectangle}{create\_new\_rectangle}@> -@= -static -Rectangle* -create_new_rectangle(const Rectangle* p = 0); -@ -@= -Rectangle* -Rectangle::create_new_rectangle(const Rectangle* p) -{ - Rectangle* r = new(Rectangle); - if (p != 0) - *r = *p; - - r->on_free_store = true; - r->line_switch = false; - r->cycle_switch = true; - return r; -} +@q ** Pointer argument.@> +@*1 Pointer argument. +\LOG +\initials{LDF 2003.12.30.} Replaced |Rectangle::create_new_rectangle()| +with a specialization of |template C* create_new()| for +|Rectangle|. +\ENDLOG +@= +Rectangle* +create_new(const Rectangle* c); -@q ** Required Rectangle argument.@> -@*1 Required Rectangle argument. -@^\cfunc{Rectangle}{create\_new\_rectangle}@> -@= -static -Rectangle* -create_new_rectangle(const Rectangle& p); +@q ** Reference argument.@> +@*1 Reference argument. -@ -@= -Rectangle* -Rectangle::create_new_rectangle(const Rectangle& p) -{ - Rectangle* r = new(Rectangle); - *r = p; +\LOG +\initials{LDF 2003.12.30.} Replaced |Rectangle::create_new_rectangle()| +with a specialization of |template C* create_new()| for +|Rectangle|. +\ENDLOG - r->on_free_store = true; - r->line_switch = false; - r->cycle_switch = true; - return r; -} +@= +Rectangle* +create_new(const Rectangle& c); @q * Destructor. @> @* Destructor. @@ -615,10 +593,12 @@ @@; @@; @@; +@@; @ This is what's written to \filename{rectangs.h}. @(rectangs.h@>= @@; +@@; diff -Naur 3DLDF-1.1.4/CWEB/shapes.web 3DLDF-1.1.5.1/CWEB/shapes.web --- 3DLDF-1.1.4/CWEB/shapes.web 2003-12-10 17:44:36.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/shapes.web 2004-01-12 22:32:30.000000000 +0100 @@ -3,7 +3,7 @@ @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -52,8 +52,6 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: shapes.web,v 1.2 2003/12/10 16:44:36 lfinsto1 Exp $ @> - @q ** Shape.@> @** Shape\quad ({\tt shapes\PERIOD web}). \hfil \initials{LDF 2002.10.20.} |Shape| is an abstract class. This means that no @@ -74,7 +72,7 @@ \ENDLOG @= static string rcs_id - = "$Id: shapes.web,v 1.2 2003/12/10 16:44:36 lfinsto1 Exp $"; + = "$Id: shapes.web,v 1.4 2004/01/12 21:32:30 lfinsto1 Exp $"; @q * Include files.@> @* Include files. diff -Naur 3DLDF-1.1.4/CWEB/solfaced.web 3DLDF-1.1.5.1/CWEB/solfaced.web --- 3DLDF-1.1.4/CWEB/solfaced.web 2003-12-10 17:45:17.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/solfaced.web 2004-01-12 22:33:15.000000000 +0100 @@ -3,7 +3,7 @@ @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -52,8 +52,6 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: solfaced.web,v 1.2 2003/12/10 16:45:17 lfinsto1 Exp $ @> - @q * Solid_Faced.@> @** Solid\_Faced\quad ({\tt solfaced\PERIOD web}).\hfil \LOG @@ -70,7 +68,7 @@ \ENDLOG @= static string rcs_id - = "$Id: solfaced.web,v 1.2 2003/12/10 16:45:17 lfinsto1 Exp $"; + = "$Id: solfaced.web,v 1.4 2004/01/12 21:33:15 lfinsto1 Exp $"; @q * Include files.@> @* Include files. diff -Naur 3DLDF-1.1.4/CWEB/solids.web 3DLDF-1.1.5.1/CWEB/solids.web --- 3DLDF-1.1.4/CWEB/solids.web 2003-12-10 17:46:34.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/solids.web 2004-01-12 22:33:23.000000000 +0100 @@ -3,7 +3,7 @@ @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -52,8 +52,6 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: solids.web,v 1.2 2003/12/10 16:46:34 lfinsto1 Exp $ @> - @q * Solid.@> @** Solid\quad ({\tt solids\PERIOD web}).\hfil \initials{LDF 2002.11.12.} @:!! TO DO@> TO DO: Add |get_center()|. Must set @@ -74,13 +72,14 @@ @= static string rcs_id - = "$Id: solids.web,v 1.2 2003/12/10 16:46:34 lfinsto1 Exp $"; + = "$Id: solids.web,v 1.5 2004/01/12 21:33:23 lfinsto1 Exp $"; @q * Include files.@> @* Include files. @= #include "loader.h" #include "pspglb.h" +#include "creatnew.h" #include "io.h" #include "colors.h" #include "transfor.h" @@ -172,7 +171,7 @@ |Solid| will not normally be used in user code, since it is intended to be a base class only. Therefore, objects of type |Solid| will not normally be declared as automatic variables and there will be no -|static| global |Solids|. However, |Solid::create_new_solid()| is +|static| global |Solids|. However, |create_new()| is used in the drawing and filling functions, in order to put |Solids| onto |Pictures|. If we didn't have a constructor, |projective_extremes| wouldn't initially have the right size and @@ -212,35 +211,35 @@ for (vector::const_iterator iter = s.paths.begin(); iter != s.paths.end(); ++iter) { - paths.push_back(Path::create_new_path()); + paths.push_back(create_new(0)); *(paths.back()) = **iter; } for (vector::const_iterator iter = s.circles.begin(); iter != s.circles.end(); ++iter) { - circles.push_back(Circle::create_new_circle()); + circles.push_back(create_new(0)); *(circles.back()) = **iter; } for (vector::const_iterator iter = s.ellipses.begin(); iter != s.ellipses.end(); ++iter) { - ellipses.push_back(Ellipse::create_new_ellipse()); + ellipses.push_back(create_new(0)); *(ellipses.back()) = **iter; } for (vector::const_iterator iter = s.reg_polygons.begin(); iter != s.reg_polygons.end(); ++iter) { - reg_polygons.push_back(Reg_Polygon::create_new_reg_polygon()); + reg_polygons.push_back(create_new(0)); *(reg_polygons.back()) = **iter; } for (vector::const_iterator iter = s.rectangles.begin(); iter != s.rectangles.end(); ++iter) { - rectangles.push_back(Rectangle::create_new_rectangle()); + rectangles.push_back(create_new(0)); *(rectangles.back()) = **iter; } @@ -249,26 +248,30 @@ @q * Pseudo-constructor for dynamic allocation. @> @* Pseudo-constructor for dynamic allocation. -@^\cfunc{Solid}{create\_new\_solid}@> -\initials{LDF 2003.05.06.} @:!! TO DO@> TO DO: Add an optional |Solid*| -argument, and a version with a required |const Solid&| argument. -@= -static -Solid* -create_new_solid(); +@q ** Pointer argument.@> +@*1 Pointer argument. -@ -@= +\LOG +\initials{LDF 2003.12.30.} Replaced |Solid::create_new_solid()| +with a specialization of |template C* create_new()| for +|Solid|. The argument is now |const|. +\ENDLOG + + +@= Solid* -Solid::create_new_solid() -{ - Solid* s = new(Solid); - s->on_free_store = true; - s->do_output = true; - return s; -} +create_new(const Solid* c); + +@q ** Reference argument.@> +@*1 Reference argument. +\LOG +LDF 2003.12.30. Added this function. +\ENDLOG +@= +Solid* +create_new(const Solid& c); @q * Destructor.@> @* Destructor. @@ -359,44 +362,46 @@ (**iter).clear(); rectangles.clear(); } - - /* \initials{LDF 2002.10.02.} Now, create new |Path|, |Circle|, |Ellipse|, - |Reg_Polygon|, and |Rectangle| pointers, allocate memory for them, - assign values to the objects they point to from |s|, and - push them onto the appropriate vectors. */ - - for (vector::const_iterator iter = s.paths.begin(); +@ Now, create new |Path|, |Circle|, |Ellipse|, +|Reg_Polygon|, and |Rectangle| pointers, allocate memory for them, +assign values to the objects they point to from |s|, and +push them onto the appropriate vectors. +\initials{LDF 2002.10.02.} +@= + Path* p; + for (vector::const_iterator iter = s.paths.begin(); iter != s.paths.end(); ++iter) { - paths.push_back(Path::create_new_path()); + p = create_new(0); + paths.push_back(p); *(paths.back()) = **iter; } for (vector::const_iterator iter = s.circles.begin(); iter != s.circles.end(); ++iter) { - circles.push_back(Circle::create_new_circle()); + circles.push_back(create_new(0)); *(circles.back()) = **iter; } for (vector::const_iterator iter = s.ellipses.begin(); iter != s.ellipses.end(); ++iter) { - ellipses.push_back(Ellipse::create_new_ellipse()); + ellipses.push_back(create_new(0)); *(ellipses.back()) = **iter; } for (vector::const_iterator iter = s.reg_polygons.begin(); iter != s.reg_polygons.end(); ++iter) { - reg_polygons.push_back(Reg_Polygon::create_new_reg_polygon()); + reg_polygons.push_back(create_new(0)); *(reg_polygons.back()) = **iter; } for (vector::const_iterator iter = s.rectangles.begin(); iter != s.rectangles.end(); ++iter) { - rectangles.push_back(Rectangle::create_new_rectangle()); + rectangles.push_back(create_new(0)); *(rectangles.back()) = **iter; } @@ -439,7 +444,7 @@ Shape* Solid::get_copy() const { - Solid* s = create_new_solid(); + Solid* s = create_new(0); *s = *this; return dynamic_cast(s); } @@ -447,11 +452,18 @@ @q * Set on free store.@> @* Set on free store. @^\cfunc{Solid}{set\_on\_free\_store}@> +\LOG +\initials{LDF 2004.01.06.} Made non-inline. +\ENDLOG @= -inline virtual bool -set_on_free_store(bool b = true) +set_on_free_store(bool b = true); + +@ +@= +bool +Solid::set_on_free_store(bool b) { on_free_store = b; return b; @@ -1893,7 +1905,7 @@ { if (DEBUG) cout << "Allocating memory for Color.\n" << flush; - Color* c = Color::create_new_color(); + Color* c = create_new(0); *c = *color_ptr; (**iter).set_draw_color(c); } @@ -1932,7 +1944,7 @@ if (DEBUG) cout << "Entering Solid::draw():" << "\n" << flush; - Solid* s = create_new_solid(); + Solid* s = create_new(0); *s = *this; const Color* color_ptr = Colors::default_color; @@ -2023,7 +2035,7 @@ { if (DEBUG) cout << "Allocating memory for Color.\n" << flush; - Color* c = Color::create_new_color(); + Color* c = create_new(0); *c = *color_ptr; (**iter).set_fill_color(c); } @@ -2066,7 +2078,7 @@ if (DEBUG) cout << "Entering Solid::fill():" << "\n" << flush; - Solid* s = create_new_solid(); + Solid* s = create_new(0); *s = *this; const Color* color_ptr = Colors::default_color; @@ -2154,7 +2166,7 @@ { if (DEBUG) cout << "Allocating memory for Color.\n" << flush; - Color* c = Color::create_new_color(); + Color* c = create_new(0); *c = *draw_color_ptr; (**iter).set_draw_color(c); } @@ -2176,7 +2188,7 @@ { if (DEBUG) cout << "Allocating memory for Color.\n" << flush; - Color* c = Color::create_new_color(); + Color* c = create_new(0); *c = *fill_color_ptr; (**iter).set_fill_color(c); } @@ -2219,7 +2231,7 @@ if (DEBUG) cout << "Entering Solid::filldraw():" << "\n" << flush; - Solid* s = create_new_solid(); + Solid* s = create_new(0); *s = *this; const Color* draw_color_ptr; @@ -2315,7 +2327,7 @@ if (DEBUG) cout << "Entering Solid::undraw():" << "\n" << flush; - Solid* s = create_new_solid(); + Solid* s = create_new(0); *s = *this; @@ -2405,7 +2417,7 @@ if (DEBUG) cout << "Entering Solid::unfill():" << "\n" << flush; - Solid* s = create_new_solid(); + Solid* s = create_new(0); *s = *this; @@ -2499,7 +2511,7 @@ if (DEBUG) cout << "Entering Solid::unfilldraw():" << "\n" << flush; - Solid* s = create_new_solid(); + Solid* s = create_new(0); *s = *this; for (vector::const_iterator iter = s->paths.begin(); @@ -2556,9 +2568,11 @@ @@; @@; @@; +@@; @ This is what's written to \filename{solids.h}. @(solids.h@>= @@; +@@; diff -Naur 3DLDF-1.1.4/CWEB/transfor.web 3DLDF-1.1.5.1/CWEB/transfor.web --- 3DLDF-1.1.4/CWEB/transfor.web 2003-12-10 17:52:21.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/transfor.web 2004-01-12 22:33:44.000000000 +0100 @@ -3,7 +3,7 @@ @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -52,8 +52,6 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: transfor.web,v 1.3 2003/12/10 16:52:21 lfinsto1 Exp $ @> - @q * Transformations.@> @** Transformations\quad ({\tt transform\PERIOD web}).\hfil @@ -69,7 +67,7 @@ \ENDLOG @= static string rcs_id - = "$Id: transfor.web,v 1.3 2003/12/10 16:52:21 lfinsto1 Exp $"; + = "$Id: transfor.web,v 1.5 2004/01/12 21:33:44 lfinsto1 Exp $"; @q * Include files. @> @* Include files. @@ -303,12 +301,31 @@ functions. In the latter case, I would have to truncate the |doubles| to |floats| eventually, so I don't know if this would have any benefit. + +\LOG +\initials{LDF 2004.1.2.} Now returning different values, depending on +whether |real| is |float| or |double|. +@:!! TO DO@> TO DO: Try to find out what values would be best. It +will be necessary to check how good the value for |double| is. + +\initials{LDF 2004.1.2.} Made |epsilon() static| and non-inline. +\ENDLOG + @= -inline +static +real +epsilon(); + +@ +@= real -epsilon() +Transform::epsilon() { +#if LDF_REAL_DOUBLE + return .000000001; +#else return .00001; +#endif } @q * Test for identity matrix. @> diff -Naur 3DLDF-1.1.4/CWEB/tsthdweb 3DLDF-1.1.5.1/CWEB/tsthdweb --- 3DLDF-1.1.4/CWEB/tsthdweb 2003-12-10 17:56:19.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/tsthdweb 2004-01-12 22:33:50.000000000 +0100 @@ -4,7 +4,7 @@ #### Created by Laurence D. Finston (LDF). # This file is part of 3DLDF, a package for three-dimensional drawing. -# Copyright (C) 2003 Laurence D. Finston. +# Copyright (C) 2003, 2004 Laurence D. Finston. # 3DLDF is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by @@ -30,7 +30,7 @@ # lfinsto1@gwdg.de # s246794@stud.uni-goettingen.de -# $Id: tsthdweb,v 1.6 2003/12/10 16:56:19 lfinsto1 Exp $ +# $Id: tsthdweb,v 1.9 2004/01/12 21:33:50 lfinsto1 Exp $ ## tsthdweb is a shell script that compares to files with the same ## name and different extensions using diff. It is used for comparing @@ -114,8 +114,7 @@ if test $2 -eq 0 || test $2 -eq 1 # Test C++ file. then - diff -q -w -B -I '^[[:space:]]*\(#\|/\*\)' $file_a $file_b > diff_res - + diff -q -w -B -I '^[[:space:]]*\(#line\|/\*\)' $file_a $file_b > diff_res # cat diff_res if test -s diff_res then @@ -136,7 +135,7 @@ if test $2 -eq 0 || test $2 -eq 2 # Test header file. then - diff -q -w -B -I '^[[:space:]]*\(#\|/\*\)' $file_c $file_d > diff_res + diff -q -w -B -I '^[[:space:]]*\(#line\|/\*\)' $file_c $file_d > diff_res if test -s diff_res then #cat diff_res diff -Naur 3DLDF-1.1.4/CWEB/utility.web 3DLDF-1.1.5.1/CWEB/utility.web --- 3DLDF-1.1.4/CWEB/utility.web 2003-12-10 17:57:28.000000000 +0100 +++ 3DLDF-1.1.5.1/CWEB/utility.web 2004-01-12 22:33:56.000000000 +0100 @@ -3,7 +3,7 @@ @q * Copyright and License.@> @q This file is part of 3DLDF, a package for three-dimensional drawing. @> -@q Copyright (C) 2003 Laurence D. Finston. @> +@q Copyright (C) 2003, 2004 Laurence D. Finston. @> @q 3DLDF is free software; you can redistribute it and/or modify @> @q it under the terms of the GNU General Public License as published by @> @@ -52,8 +52,6 @@ @q s246794@@stud.uni-goettingen.de @> -@q $Id: utility.web,v 1.2 2003/12/10 16:57:28 lfinsto1 Exp $ @> - @q * Utility functions.@> @** Utility functions\quad ({\tt utility\PERIOD web}).\hfil \initials{LDF 2003.05.13.} @@ -74,9 +72,10 @@ them back in, now I'm doing the rest of them. However, the release versions are now in their own RCS repository. \ENDLOG + @= static string rcs_id - = "$Id: utility.web,v 1.2 2003/12/10 16:57:28 lfinsto1 Exp $"; + = "$Id: utility.web,v 1.4 2004/01/12 21:33:56 lfinsto1 Exp $"; @q * Include files.@> @@ -84,6 +83,7 @@ @= #include "loader.h" #include "pspglb.h" +#include "creatnew.h" #include "io.h" #include "colors.h" #include "transfor.h" @@ -103,7 +103,6 @@ #include "cuboid.h" #include "polyhed.h" - @q * Perspective functions.@> @* Perspective functions. \initials{LDF 2003.05.13.} These functions can be used to make perspective @@ -194,13 +193,13 @@ @= vector points; - points.push_back(Point::create_new_point(f)); - points.push_back(Point::create_new_point(cv)); - points.push_back(Point::create_new_point(origin)); - points.push_back(Point::create_new_point(horizon_l)); - points.push_back(Point::create_new_point(horizon_r)); - points.push_back(Point::create_new_point(gl_l)); - points.push_back(Point::create_new_point(gl_r)); + points.push_back(create_new(f)); + points.push_back(create_new(cv)); + points.push_back(create_new(origin)); + points.push_back(create_new(horizon_l)); + points.push_back(create_new(horizon_r)); + points.push_back(create_new(gl_l)); + points.push_back(create_new(gl_r)); @ Calculate the vanishing points on the right side, and put them onto @@ -228,7 +227,7 @@ << "]. Angle = " << *iter <<". x = " << q.get_x() << endl << flush; #endif - points.push_back(Point::create_new_point(q)); + points.push_back(create_new(q)); if (*iter == 60 || *iter == 80) /* KLUDGE. \initials{LDF 2003.05.14.} */ { q_super = q; diff -Naur 3DLDF-1.1.4/ChangeLog 3DLDF-1.1.5.1/ChangeLog --- 3DLDF-1.1.4/ChangeLog 2003-12-10 18:34:16.000000000 +0100 +++ 3DLDF-1.1.5.1/ChangeLog 2004-01-16 19:05:57.000000000 +0100 @@ -1,5 +1,62 @@ +2004-01-16 Laurence Finston + + * configure.ac: LDF 2004.01.16. + Changed release number to 1.1.5.1. + + * ldfr, NEWS, AUTHORS: LDF 2004.01.16. + Updated copyright date. + + * Makefile.am: LDF 2004.01.16. + Updated copyright date. + Changed release number to 1.1.5.1. + + * README: LDF 2004.01.16. + Changed release number to 1.1.5.1. + Edited patch instructions accordingly. + + * INSTALL: LDF 2004.01.16. + Updated copyright date. + + Changed release number to 1.1.5.1. + + * NEWS: LDF 2004.01.16. + Added items for Release 1.1.5.1. + +2004-01-14 Laurence Finston + + * configure.ac: LDF 2004.01.14. + Changed release number to 1.1.5. + Changed copyright date to "2003, 2004". + + * README: LDF 2004.01.14. + Edited for Release 1.1.5. + + * NEWS: LDF 2004.01.14. + Added entries for Release 1.1.5. + + Changed "Version" to "Release". + + * Makefile.am: LDF 2004.01.14. + + Added `GRAPHICSDIR' and `PNGDIR'. They are exported, along with + `EPSDIR'. + + Added phony `show' target. + +2004-01-12 Laurence Finston + + * INSTALL: LDF 2004.01.12. + Changed version number from `1.1.4' to `1.1.5'. + 2003-12-10 Laurence Finston + * README: LDF 2003.12.10. + Added information about the system dependency I've introduced by + changing the way |MAX_REAL| is calculated. + + I forgot to check this file in before making the distribution of release 1.1.4, but + this version in it. + * NEWS: LDF 2003.12.10. Added items for version 1.1.4. diff -Naur 3DLDF-1.1.4/DOC/.rcsfreeze.log 3DLDF-1.1.5.1/DOC/.rcsfreeze.log --- 3DLDF-1.1.4/DOC/.rcsfreeze.log 2003-12-10 18:38:15.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/.rcsfreeze.log 2004-01-14 21:53:48.000000000 +0100 @@ -1,3 +1,8 @@ +Version: C_4(C_4), Date: Wed Jan 14 21:53:43 MET 2004 +----------- + Release 1.1.5. +----------- + Version: C_3(C_3), Date: Wed Dec 10 18:38:08 MET 2003 ----------- Release 1.1.4. diff -Naur 3DLDF-1.1.4/DOC/ChangeLog 3DLDF-1.1.5.1/DOC/ChangeLog --- 3DLDF-1.1.4/DOC/ChangeLog 2003-12-10 18:34:32.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/ChangeLog 2004-01-16 18:11:25.000000000 +0100 @@ -1,3 +1,20 @@ +2004-01-16 Laurence Finston + + * Makefile.am: LDF 2004.01.16. + Changed release number to 1.1.5.1. + +2004-01-14 Laurence Finston + + * Makefile.am: LDF 2004.01.14. + Added phony `show' target. + +2004-01-12 Laurence Finston + + * Makefile.am: LDF 2004.01.12. + Changed version number from `1.1.4' to `1.1.5'. + + Changed copyright date from ``2003'' to ``2003, 2004''. + 2003-12-10 Laurence Finston * Makefile.am: LDF 2003.12.10. diff -Naur 3DLDF-1.1.4/DOC/Makefile.am 3DLDF-1.1.5.1/DOC/Makefile.am --- 3DLDF-1.1.4/DOC/Makefile.am 2003-12-10 18:03:03.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/Makefile.am 2004-01-16 17:31:53.000000000 +0100 @@ -1,7 +1,7 @@ -## 3DLDF-1.1.4/DOC/Makefile.am - +## 3DLDF-1.1.5.1/DOC/Makefile.am + # This file is part of 3DLDF, a package for three-dimensional drawing. -# Copyright (C) 2003 Laurence D. Finston. +# Copyright (C) 2003, 2004 Laurence D. Finston. # 3DLDF is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by @@ -28,7 +28,7 @@ # s246794@stud.uni-goettingen.de -# $Id: Makefile.am,v 1.7 2003/12/10 17:03:03 lfinsto1 Exp $ +# $Id: Makefile.am,v 1.10 2004/01/16 16:31:53 lfinsto1 Exp $ TEXINFODIR := TEXINFO @@ -50,6 +50,12 @@ TAGS: $(MAKE) TAGS -C $(TEXINFODIR) +.PHONY : show +show: + $(MAKE) show -C $(TEXINFODIR) + + + ## Local Variables: ## mode:Makefile ## End: diff -Naur 3DLDF-1.1.4/DOC/Makefile.in 3DLDF-1.1.5.1/DOC/Makefile.in --- 3DLDF-1.1.4/DOC/Makefile.in 2003-12-10 18:41:53.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/Makefile.in 2004-01-16 19:18:52.000000000 +0100 @@ -15,7 +15,7 @@ @SET_MAKE@ # This file is part of 3DLDF, a package for three-dimensional drawing. -# Copyright (C) 2003 Laurence D. Finston. +# Copyright (C) 2003, 2004 Laurence D. Finston. # 3DLDF is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by @@ -41,7 +41,7 @@ # lfinsto1@gwdg.de # s246794@stud.uni-goettingen.de -# $Id: Makefile.am,v 1.7 2003/12/10 17:03:03 lfinsto1 Exp $ +# $Id: Makefile.am,v 1.10 2004/01/16 16:31:53 lfinsto1 Exp $ srcdir = @srcdir@ top_srcdir = @top_srcdir@ @@ -414,6 +414,10 @@ TAGS: $(MAKE) TAGS -C $(TEXINFODIR) + +.PHONY : show +show: + $(MAKE) show -C $(TEXINFODIR) # Tell versions [3.59,3.63) of GNU make to not export all variables. # Otherwise a system limit (for SysV at least) may be exceeded. .NOEXPORT: diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/.rcsfreeze.log 3DLDF-1.1.5.1/DOC/TEXINFO/.rcsfreeze.log --- 3DLDF-1.1.4/DOC/TEXINFO/.rcsfreeze.log 2003-12-10 18:38:28.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/.rcsfreeze.log 2004-01-14 21:55:47.000000000 +0100 @@ -1,3 +1,45 @@ +Version: C_9(C_9), Date: Wed Jan 14 21:55:22 MET 2004 +----------- + Release 1.1.5. The last frozen configuration was missing a couple of things. +----------- + +Version: C_8(C_8), Date: Wed Jan 14 21:53:56 MET 2004 +----------- + Release 1.1.5. +----------- + +Version: C_7(C_7), Date: Fri Dec 19 19:20:55 MET 2003 +----------- + Edition 1.1.4.2. + Illustrations are now included in the HTML output. They are scaled to + \magstep3. + + A few changes to the text that mentions HTML output. Previously, I said it + couldn't be generated. + +----------- + +Version: C_5(C_5), Date: Tue Dec 16 19:10:57 MET 2003 +----------- + Changed `EDITION' to `1.1.4.1'. + The difference is, that I've added `@ifhtml' and `@ifinfo' code for the + illustrations. + + PNG files are included in the HTML output. They are of the correct size and + use the same fonts as in the TeX output, i.e., Computer Modern. It wasn't + easy to get this to work! + + Graphics are not displayed in Info output. Instead, text indicates that + ``Fig. X'' is not displayed. + + + I've put the figure numbers for HTML and Info output into the Texinfo files + explicitly using Emacs-Lisp. These numbers are also used to identify the PNG + files. This isn't necessary in the TeX output, because I can use `figcnt'. + The HTML and Info formats currently don't support incrementing numerical + variables. +----------- + Version: C_4(C_4), Date: Wed Dec 10 18:38:24 MET 2003 ----------- Release 1.1.4. diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info --- 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info 2003-12-10 18:44:55.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info 2004-01-16 19:03:28.000000000 +0100 @@ -1,11 +1,11 @@ This is 3DLDF.info, produced by makeinfo version 4.5 from 3DLDF.texi. -This is the 3DLDF User and Reference Manual, edition 1.1.4 for 3DLDF -1.1.4. This manual was last updated on 10 December 2003. 3DLDF is a +This is the 3DLDF User and Reference Manual, edition 1.1.5.1 for 3DLDF +1.1.5.1. This manual was last updated on 16 January 2004. 3DLDF is a GNU package for three-dimensional drawing with MetaPost output. The author is Laurence D. Finston. - Copyright (C) 2003 Laurence D. Finston. + Copyright (C) 2003, 2004 Laurence D. Finston. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, @@ -21,333 +21,362 @@  Indirect: -3DLDF.info-1: 891 -3DLDF.info-2: 49349 -3DLDF.info-3: 98223 -3DLDF.info-4: 147834 -3DLDF.info-5: 191157 -3DLDF.info-6: 240632 -3DLDF.info-7: 286566 -3DLDF.info-8: 330973 -3DLDF.info-9: 380375 -3DLDF.info-10: 429106 -3DLDF.info-11: 471365 -3DLDF.info-12: 509440 +3DLDF.info-1: 900 +3DLDF.info-2: 49782 +3DLDF.info-3: 99750 +3DLDF.info-4: 148401 +3DLDF.info-5: 198234 +3DLDF.info-6: 244013 +3DLDF.info-7: 294005 +3DLDF.info-8: 334208 +3DLDF.info-9: 383246 +3DLDF.info-10: 432796 +3DLDF.info-11: 481734 +3DLDF.info-12: 512705 +3DLDF.info-13: 550926  Tag Table: (Indirect) -Node: Top891 -Node: Introduction8912 -Node: Sources of Information11349 -Node: About This Manual12651 -Node: Manual Conventions15861 -Node: Illustrations18949 -Ref: Illustrations-Footnote-123171 -Ref: Illustrations-Footnote-223367 -Node: CWEB Documentation23709 -Node: Metafont and MetaPost26132 -Ref: Metafont and MetaPost-Footnote-129714 -Ref: Metafont and MetaPost-Footnote-229848 -Ref: Metafont and MetaPost-Footnote-329982 -Node: Caveats30196 -Node: Accuracy30356 -Ref: Accuracy-Footnote-132487 -Ref: Accuracy-Footnote-232815 -Node: No Input Routine32870 -Ref: No Input Routine-Footnote-133858 -Node: Ports33993 -Node: Contributing to 3DLDF36804 -Node: Using 3DLDF37416 -Node: Points37936 -Node: Declaring and Initializing Points38128 -Node: Setting and Assigning to Points42184 -Node: Transforming Points43647 -Ref: Transforming Points-Footnote-144918 -Ref: Transforming Points-Footnote-245406 -Node: Shifting Points45737 -Node: Scaling Points47224 -Node: Shearing Points48204 -Node: Rotating Points49349 -Node: Transforms51929 -Ref: Transforms-Footnote-155640 -Ref: Transforms-Footnote-255927 -Node: Applying Transforms to Points Intro56676 -Node: Inverting Transforms58619 -Node: Drawing and Labeling Points60669 -Node: Drawing Points Intro60886 -Ref: Drawing Points Intro-Footnote-163584 -Ref: Drawing Points Intro-Footnote-263855 -Ref: Drawing Points Intro-Footnote-364149 -Node: Labeling Points Intro64433 -Node: Paths66235 -Ref: Paths-Footnote-168264 -Node: Declaring and Initializing Paths68386 -Ref: Declaring and Initializing Paths-Footnote-171573 -Ref: Declaring and Initializing Paths-Footnote-271999 -Node: Drawing and Filling Paths Intro72054 -Node: Plane Figures75605 -Node: Regular Polygons Getstart76993 -Node: Rectangles Getstart79141 -Node: Ellipses Getstart81591 -Node: Circles Getstart82875 -Node: Solid Figures83917 -Node: Cuboid Getstart84091 -Node: Polyhedron Getstart85394 -Node: Tetrahedron Getstart86652 -Node: Dodecahedron Getstart87138 -Node: Icosahedron Getstart87756 -Node: Pictures88254 -Node: Projections94784 -Ref: Projections-Footnote-196477 -Node: Parallel Projections96569 -Node: The Perspective Projection98223 -Ref: The Perspective Projection-Footnote-1102232 -Ref: The Perspective Projection-Footnote-2102500 -Node: Focuses Getstart103107 -Ref: Focuses Getstart-Footnote-1108286 -Node: Surface Hiding108347 -Node: Intersections116298 -Ref: Intersections-Footnote-1119441 -Node: Installing and Running 3DLDF119688 -Node: Installing 3DLDF119925 -Node: Running 3DLDF121465 -Node: Command Line Arguments126738 -Node: Typedefs and Utility Structures127670 -Node: Global Constants and Variables129931 -Ref: Global Constants and Variables-Footnote-1133293 -Node: Color Reference133345 -Node: Color Data Members133758 -Node: Color Constructors and Setting Functions134802 -Node: Color Operators136855 -Node: Modifying Colors138211 -Node: Showing Colors139197 -Node: Querying Colors139638 -Node: Defining and Initializing Colors140751 -Node: Namespace Colors141356 -Node: Input and Output143075 -Node: I/O Global Variables143266 -Node: I/O Functions144260 -Node: Shape Reference145449 -Node: Shape Data Members146502 -Node: Shape Operators147136 -Node: Copying Shapes147342 -Node: Modifying Shapes147834 -Node: Affine Transformations for Shapes148857 -Node: Applying Transformations to Shapes149495 -Node: Clearing Shapes149975 -Node: Querying Shapes150421 -Node: Showing Shapes150708 -Node: Outputting Shapes151258 -Node: Transform Reference154390 -Node: Transform Data Members155034 -Node: Transform Global Variables and Constants155334 -Node: Transform Constructors156290 -Node: Transform Operators157272 -Node: Matrix Inversion162053 -Node: Setting Values Transforms162774 -Node: Querying Transforms163380 -Node: Returning Information for Transforms164648 -Node: Showing Transforms165989 -Node: Affine Transformations for Transforms167066 -Ref: Affine Transformations for Transforms-Footnote-1173282 -Node: Alignment with an Axis for Transforms173360 -Node: Resetting Transforms175666 -Node: Cleaning Transforms175911 -Node: Label Reference176145 -Node: Label Data Members177553 -Node: Copying Labels179246 -Node: Outputting Labels179997 -Node: Picture Reference180917 -Node: Picture Data Members181327 -Ref: Picture Data Members-Footnote-1183211 -Node: Picture Global Variables183379 -Node: Picture Constructors183678 -Node: Picture Operators184256 -Node: Affine Transformations for Pictures185774 -Node: Modifying Pictures187360 -Node: Showing Pictures188186 -Ref: Showing Pictures-Footnote-1189388 -Node: Outputting Pictures189493 -Node: Picture Output Namespaces189682 -Node: Namespace Projections189904 -Node: Namespace Sorting190601 -Node: Picture Output Functions191157 -Node: Point Reference199743 -Node: Point Data Members200664 -Node: Point Typedefs and Utility Structures206748 -Node: Point Global Constants and Variables209306 -Node: Point Constructors and Setting Functions210230 -Node: Point Destructor213398 -Node: Point Operators213809 -Node: Copying Points218824 -Node: Querying Points219337 -Ref: Querying Points-Footnote-1221465 -Node: Returning Coordinates221721 -Node: Returning Information for Points226760 -Node: Modifying Points227482 -Node: Affine Transformations for Points228618 -Node: Applying Transformations to Points234132 -Node: Projecting Points234507 -Node: Vector Operations235527 -Node: Points and Lines240632 -Node: Point Intersections244577 -Node: Point Drawing Functions246407 -Node: Labelling Points251302 -Node: Showing Points254434 -Node: Outputting Points255780 -Node: Focus Reference258773 -Node: Focus Data Members259297 -Node: Focus Global Variables260989 -Node: Focus Constructors and Setting Functions261991 -Node: Focus Operators263747 -Node: Modifying Focuses264002 -Node: Querying Focuses264285 -Node: Showing Focuses265376 -Node: Line Reference265888 -Node: Line Data Members266537 -Node: Line Global Constants266860 -Node: Line Constructors267114 -Node: Line Operators267766 -Node: Get Path267974 -Node: Showing268291 -Node: Plane Reference269183 -Node: Planes Data Members270168 -Node: Planes Global Constants270667 -Node: Planes Constructors271100 -Node: Planes Operators272916 -Node: Planes Returning Information274177 -Node: Plane Intersections276361 -Node: Planes Showing279816 -Node: Path Reference280786 -Node: Path Data Members281458 -Ref: Path Data Members-Footnote-1286506 -Node: Path Constructors and Setting Functions286566 -Ref: Path Constructors and Setting Functions-Footnote-1292317 -Ref: Path Constructors and Setting Functions-Footnote-2292956 -Ref: Path Constructors and Setting Functions-Footnote-3293016 -Node: Path Destructor293330 -Node: Path Operators294020 -Node: Appending to Paths295765 -Node: Copying Paths296860 -Node: Clearing Paths297437 -Node: Modifying Paths298238 -Node: Affine Transformations for Paths300741 -Node: Aligning Paths with an Axis305389 -Node: Applying Transformations to Paths308508 -Node: Drawing and Filling Paths308932 -Ref: Drawing and Filling Paths-Footnote-1325270 -Ref: Drawing and Filling Paths-Footnote-2325324 -Ref: Drawing and Filling Paths-Footnote-3325426 -Node: Labelling Paths325784 -Node: Showing Paths327235 -Ref: Showing Paths-Footnote-1330827 -Node: Querying Paths330973 -Node: Outputting Paths336918 -Node: Path Intersections339406 -Node: Polygon Reference340848 -Node: Polygon Data Members341497 -Node: Polygon Operators341850 -Node: Querying Polygons342272 -Node: Affine Transformations for Polygons342674 -Node: Polygon Intersections344785 -Ref: Polygon Intersections-Footnote-1349714 -Node: Regular Polygon Reference349807 -Node: Regular Polygon Data Members350832 -Node: Regular Polygon Constructors and Setting Functions351877 -Node: Regular Polygon Operators354126 -Node: Querying Regular Polygons354434 -Node: Circles for Regular Polygons354685 -Node: Rectangle Reference356704 -Node: Rectangle Data Members357723 -Node: Rectangle Constructors and Setting Functions358651 -Node: Rectangle Operators360927 -Node: Returning Points for Rectangles361228 -Node: Querying Rectangles361699 -Node: Ellipses for Rectangles362387 -Node: Regular Closed Plane Curve Reference363994 -Ref: Regular Closed Plane Curve Reference-Footnote-1366365 -Node: Regular Closed Plane Curve Data Members366564 -Node: Querying Regular Closed Plane Curves367012 -Node: Regular Closed Plane Curve Intersections369668 -Node: Regular Closed Plane Curve Segments372086 -Node: Ellipse Reference374419 -Node: Ellipse Data Members375056 -Node: Ellipse Constructors and Setting Functions376788 -Node: Performing Transformations on Ellipses378744 -Node: Ellipse Operators379867 -Node: Labeling Ellipses380375 -Node: Affine Transformations for Ellipses381198 -Node: Querying Ellipses383368 -Node: Returning Elements and Information for Ellipses384616 -Node: Ellipse Intersections388999 -Node: Solving Ellipses394679 -Node: Rectangles for Ellipses396967 -Node: Circle Reference398828 -Node: Circle Data Members399614 -Node: Circle Constructors and Setting Functions399854 -Node: Circle Operators401351 -Node: Querying Circles401887 -Node: Circle Intersections402617 -Node: Pattern Reference403677 -Node: Plane Tesselations404049 -Node: Roulettes and Involutes409594 -Node: Epicycloids410565 -Node: Solid Reference413431 -Node: Solid Data Members414222 -Node: Solid Constructors and Setting Functions416391 -Node: Solid Destructor416890 -Node: Solid Operators417301 -Node: Copying Solids417772 -Node: Setting Solid Members418346 -Node: Querying Solids418759 -Node: Returning Elements and Information Solids419120 -Node: Getting Shape Centers Solids419589 -Node: Getting Shapes Solids421917 -Node: Showing Solids424913 -Node: Affine Transformations for Solids425789 -Node: Applying Transformations to Solids426698 -Node: Outputting Solids427039 -Node: Drawing and Filling Solids429106 -Node: Clearing Solids433895 -Node: Faced Solid Reference434418 -Node: Solid_Faced Data Members434944 -Node: Cuboid Reference435364 -Node: Cuboid Data Members435720 -Node: Cuboid Constructors and Setting Functions436183 -Node: Cuboid Operators437664 -Node: Polyhedron Reference437981 -Node: Polyhedron Data Members438636 -Node: Regular Platonic Polyhedra439494 -Node: Tetrahedron440128 -Node: Tetrahedron Data Members440503 -Node: Tetrahedron Constructors and Setting Functions441180 -Node: Tetrahedron Net442554 -Ref: Tetrahedron Net-Footnote-1445407 -Node: Dodecahedron445479 -Node: Dodecahedron Data Members445895 -Node: Dodecahedron Constructors and Setting Functions446368 -Node: Dodecahedron Net447375 -Node: Icosahedron449296 -Node: Icosahedron Data Members449685 -Node: Icosahedron Constructors and Setting Functions450154 -Node: Icosahedron Net451126 -Node: Semi-Regular Archimedean Polyhedra453023 -Node: Truncated Octahedron453424 -Node: Truncated Octahedron Data Members453992 -Node: Truncated Octahedron Constructors and Setting Functions454684 -Node: Truncated Octahedron Net455715 -Node: Utility Functions456651 -Node: Perspective Functions457992 -Node: Adding a File460115 -Ref: Adding a File-Footnote-1464626 -Ref: Adding a File-Footnote-2464722 -Node: Future Plans464878 -Ref: Future Plans-Footnote-1466770 -Node: Changes466855 -Node: Bibliography468845 -Node: GNU Free Documentation License471365 -Node: Data Type and Variable Index493802 -Node: Function Index509440 -Node: Concept Index536053 +Node: Top900 +Node: Introduction10289 +Node: Sources of Information12726 +Node: About This Manual14028 +Node: Manual Conventions16867 +Node: Illustrations19955 +Ref: Illustrations-Footnote-124921 +Ref: Illustrations-Footnote-225117 +Node: CWEB Documentation25459 +Node: Metafont and MetaPost27895 +Ref: Metafont and MetaPost-Footnote-131477 +Ref: Metafont and MetaPost-Footnote-231611 +Ref: Metafont and MetaPost-Footnote-331745 +Node: Caveats31959 +Node: Accuracy32119 +Ref: Accuracy-Footnote-134250 +Ref: Accuracy-Footnote-234578 +Node: No Input Routine34633 +Ref: No Input Routine-Footnote-135621 +Node: Ports35756 +Node: Contributing to 3DLDF38372 +Node: Using 3DLDF38984 +Node: Points39504 +Node: Declaring and Initializing Points39696 +Node: Setting and Assigning to Points43752 +Node: Transforming Points45215 +Ref: Transforming Points-Footnote-146486 +Ref: Transforming Points-Footnote-246974 +Node: Shifting Points47305 +Node: Scaling Points48802 +Node: Shearing Points49782 +Node: Rotating Points50957 +Node: Transforms53567 +Ref: Transforms-Footnote-157278 +Ref: Transforms-Footnote-257565 +Node: Applying Transforms to Points Intro58314 +Node: Inverting Transforms60257 +Node: Drawing and Labeling Points62307 +Node: Drawing Points Intro62524 +Ref: Drawing Points Intro-Footnote-165372 +Ref: Drawing Points Intro-Footnote-265643 +Ref: Drawing Points Intro-Footnote-365937 +Node: Labeling Points Intro66221 +Node: Paths68053 +Ref: Paths-Footnote-170082 +Node: Declaring and Initializing Paths70204 +Ref: Declaring and Initializing Paths-Footnote-173483 +Ref: Declaring and Initializing Paths-Footnote-273909 +Node: Drawing and Filling Paths Intro73964 +Node: Plane Figures77763 +Node: Regular Polygons Getstart79151 +Node: Rectangles Getstart81516 +Node: Ellipses Getstart84152 +Node: Circles Getstart85498 +Node: Solid Figures86602 +Node: Cuboid Getstart86776 +Node: Polyhedron Getstart88141 +Node: Tetrahedron Getstart89399 +Node: Dodecahedron Getstart89916 +Node: Icosahedron Getstart90689 +Node: Pictures91342 +Node: Projections97965 +Ref: Projections-Footnote-199658 +Node: Parallel Projections99750 +Node: The Perspective Projection101497 +Ref: The Perspective Projection-Footnote-1105630 +Ref: The Perspective Projection-Footnote-2105898 +Node: Focuses Getstart106505 +Ref: Focuses Getstart-Footnote-1111808 +Node: Surface Hiding111869 +Node: Intersections120068 +Ref: Intersections-Footnote-1123211 +Node: Installing and Running 3DLDF123458 +Node: Installing 3DLDF123695 +Node: Template Functions125294 +Ref: Template Functions-Footnote-1127647 +Node: Running 3DLDF127733 +Node: Converting EPS Files133072 +Ref: Converting EPS Files-Footnote-1136366 +Ref: Converting EPS Files-Footnote-2136424 +Node: Converting EPS Files ELISP136489 +Node: Command Line Arguments138925 +Node: Typedefs and Utility Structures139864 +Node: Global Constants and Variables142089 +Ref: Global Constants and Variables-Footnote-1146516 +Node: Dynamic Allocation of Shapes146568 +Node: System Information148401 +Node: Endianness149893 +Node: Register Width152058 +Node: Get Second Largest Real153112 +Ref: Get Second Largest Real-Footnote-1154484 +Node: Color Reference154950 +Node: Color Data Members155351 +Node: Color Constructors and Setting Functions156396 +Node: Color Operators158805 +Node: Modifying Colors160161 +Node: Showing Colors161147 +Node: Querying Colors161588 +Node: Defining and Initializing Colors162694 +Node: Namespace Colors163299 +Node: Input and Output165018 +Node: I/O Global Variables165209 +Node: I/O Functions166203 +Node: Shape Reference167392 +Node: Shape Data Members168445 +Node: Shape Operators169079 +Node: Copying Shapes169285 +Node: Modifying Shapes169777 +Node: Affine Transformations for Shapes170285 +Node: Applying Transformations to Shapes170923 +Node: Clearing Shapes171403 +Node: Querying Shapes171849 +Node: Showing Shapes172136 +Node: Outputting Shapes172686 +Node: Transform Reference175818 +Node: Transform Data Members176462 +Node: Transform Global Variables and Constants176762 +Node: Transform Constructors177718 +Node: Transform Operators178700 +Node: Matrix Inversion183481 +Node: Setting Values Transforms184202 +Node: Querying Transforms184808 +Node: Returning Information for Transforms186076 +Ref: Returning Information for Transforms-Footnote-1188108 +Node: Showing Transforms188213 +Node: Affine Transformations for Transforms189290 +Ref: Affine Transformations for Transforms-Footnote-1195572 +Node: Alignment with an Axis for Transforms195650 +Node: Resetting Transforms197989 +Node: Cleaning Transforms198234 +Node: Label Reference198468 +Node: Label Data Members199876 +Node: Copying Labels201602 +Node: Outputting Labels202353 +Node: Picture Reference203273 +Node: Picture Data Members203683 +Ref: Picture Data Members-Footnote-1205567 +Node: Picture Global Variables205735 +Node: Picture Constructors206034 +Node: Picture Operators206645 +Node: Affine Transformations for Pictures208196 +Node: Modifying Pictures209782 +Node: Showing Pictures210608 +Ref: Showing Pictures-Footnote-1211810 +Node: Outputting Pictures211915 +Node: Picture Output Namespaces212104 +Node: Namespace Projections212326 +Node: Namespace Sorting213023 +Node: Picture Output Functions213579 +Node: Point Reference222198 +Node: Point Data Members223119 +Node: Point Typedefs and Utility Structures229434 +Node: Point Global Constants and Variables231992 +Node: Point Constructors and Setting Functions232916 +Node: Point Destructor235555 +Node: Point Operators235966 +Node: Copying Points240981 +Node: Querying Points241495 +Ref: Querying Points-Footnote-1243757 +Node: Returning Coordinates244013 +Node: Returning Information for Points249052 +Ref: Returning Information for Points-Footnote-1251310 +Node: Modifying Points251415 +Node: Affine Transformations for Points252643 +Node: Applying Transformations to Points258322 +Node: Projecting Points258697 +Node: Vector Operations259717 +Node: Points and Lines264987 +Node: Point Intersections269031 +Node: Point Drawing Functions270927 +Node: Labelling Points275988 +Node: Showing Points279222 +Node: Outputting Points280568 +Node: Focus Reference283561 +Node: Focus Data Members284085 +Node: Focus Global Variables285777 +Node: Focus Constructors and Setting Functions286779 +Node: Focus Operators288535 +Node: Modifying Focuses288790 +Node: Querying Focuses289073 +Node: Showing Focuses290164 +Node: Line Reference290676 +Node: Line Data Members291325 +Node: Line Global Constants291648 +Node: Line Constructors291902 +Node: Line Operators292588 +Node: Get Path292796 +Node: Showing293113 +Node: Plane Reference294005 +Node: Planes Data Members294990 +Node: Planes Global Constants295489 +Node: Planes Constructors295922 +Node: Planes Operators297772 +Node: Planes Returning Information299033 +Node: Plane Intersections301251 +Node: Planes Showing304774 +Node: Path Reference305744 +Node: Path Data Members306416 +Ref: Path Data Members-Footnote-1311499 +Node: Path Constructors and Setting Functions311559 +Ref: Path Constructors and Setting Functions-Footnote-1317499 +Ref: Path Constructors and Setting Functions-Footnote-2318138 +Ref: Path Constructors and Setting Functions-Footnote-3318198 +Node: Path Destructor318512 +Node: Path Operators319202 +Node: Appending to Paths320947 +Node: Copying Paths322076 +Node: Clearing Paths322654 +Node: Modifying Paths323455 +Node: Affine Transformations for Paths325847 +Node: Aligning Paths with an Axis330631 +Node: Applying Transformations to Paths333784 +Node: Drawing and Filling Paths334208 +Ref: Drawing and Filling Paths-Footnote-1351091 +Ref: Drawing and Filling Paths-Footnote-2351145 +Ref: Drawing and Filling Paths-Footnote-3351247 +Node: Labelling Paths351605 +Node: Showing Paths353056 +Ref: Showing Paths-Footnote-1356682 +Node: Querying Paths356828 +Node: Outputting Paths362834 +Node: Path Intersections365322 +Node: Polygon Reference366798 +Node: Polygon Data Members367447 +Node: Polygon Operators367800 +Node: Querying Polygons368222 +Node: Affine Transformations for Polygons368624 +Node: Polygon Intersections370735 +Ref: Polygon Intersections-Footnote-1375868 +Node: Regular Polygon Reference375961 +Node: Regular Polygon Data Members376986 +Node: Regular Polygon Constructors and Setting Functions378032 +Node: Regular Polygon Operators380532 +Node: Querying Regular Polygons380840 +Node: Circles for Regular Polygons381091 +Node: Rectangle Reference383246 +Node: Rectangle Data Members384265 +Node: Rectangle Constructors and Setting Functions385194 +Node: Rectangle Operators387698 +Node: Returning Points for Rectangles387999 +Node: Querying Rectangles388470 +Node: Ellipses for Rectangles389158 +Node: Regular Closed Plane Curve Reference390833 +Ref: Regular Closed Plane Curve Reference-Footnote-1393204 +Node: Regular Closed Plane Curve Data Members393403 +Node: Querying Regular Closed Plane Curves393851 +Node: Regular Closed Plane Curve Intersections396507 +Node: Regular Closed Plane Curve Segments398993 +Node: Ellipse Reference401428 +Node: Ellipse Data Members402065 +Node: Ellipse Constructors and Setting Functions403797 +Node: Performing Transformations on Ellipses406004 +Node: Ellipse Operators407127 +Node: Labeling Ellipses407635 +Node: Affine Transformations for Ellipses408526 +Node: Querying Ellipses410696 +Node: Returning Elements and Information for Ellipses411978 +Node: Ellipse Intersections416463 +Node: Solving Ellipses422928 +Node: Rectangles for Ellipses425216 +Node: Circle Reference427213 +Node: Circle Data Members427999 +Node: Circle Constructors and Setting Functions428239 +Node: Circle Operators430030 +Node: Querying Circles430566 +Node: Circle Intersections431330 +Node: Pattern Reference432424 +Node: Plane Tesselations432796 +Node: Roulettes and Involutes438409 +Node: Epicycloids439380 +Node: Solid Reference442314 +Node: Solid Data Members443105 +Node: Solid Constructors and Setting Functions445274 +Node: Solid Destructor446285 +Node: Solid Operators446696 +Node: Copying Solids447167 +Node: Setting Solid Members447742 +Node: Querying Solids448174 +Node: Returning Elements and Information Solids448826 +Node: Getting Shape Centers Solids449295 +Node: Getting Shapes Solids451691 +Node: Showing Solids454755 +Node: Affine Transformations for Solids455631 +Node: Applying Transformations to Solids456540 +Node: Outputting Solids456881 +Node: Drawing and Filling Solids458948 +Node: Clearing Solids463737 +Node: Faced Solid Reference464260 +Node: Solid_Faced Data Members464786 +Node: Cuboid Reference465206 +Node: Cuboid Data Members465562 +Node: Cuboid Constructors and Setting Functions466025 +Node: Cuboid Operators467932 +Node: Polyhedron Reference468249 +Node: Polyhedron Data Members468904 +Node: Regular Platonic Polyhedra469762 +Node: Tetrahedron470396 +Node: Tetrahedron Data Members470771 +Node: Tetrahedron Constructors and Setting Functions471448 +Node: Tetrahedron Net472890 +Ref: Tetrahedron Net-Footnote-1475811 +Node: Dodecahedron475883 +Node: Dodecahedron Data Members476299 +Node: Dodecahedron Constructors and Setting Functions476772 +Node: Dodecahedron Net477847 +Node: Icosahedron479836 +Node: Icosahedron Data Members480225 +Node: Icosahedron Constructors and Setting Functions480694 +Node: Icosahedron Net481734 +Node: Semi-Regular Archimedean Polyhedra483699 +Node: Truncated Octahedron484100 +Node: Truncated Octahedron Data Members484626 +Node: Truncated Octahedron Constructors and Setting Functions485318 +Node: Truncated Octahedron Net486349 +Node: Utility Functions487285 +Node: Perspective Functions488626 +Node: Adding a File490783 +Ref: Adding a File-Footnote-1495302 +Ref: Adding a File-Footnote-2495398 +Node: Future Plans495554 +Node: Geometry496319 +Ref: Geometry-Footnote-1498397 +Ref: Geometry-Footnote-2498499 +Node: Curves and Surfaces498584 +Ref: Curves and Surfaces-Footnote-1500084 +Ref: Curves and Surfaces-Footnote-2500263 +Ref: Curves and Surfaces-Footnote-3500335 +Node: Shadows500502 +Node: Multi-Threading502440 +Node: Changes503565 +Node: Changes in 3DLDF 1.1.5.1503867 +Node: Changes in 3DLDF 1.1.5504476 +Node: Changes in 3DLDF 1.1.4.2507053 +Node: Changes in 3DLDF 1.1.4.1507286 +Node: Changes in 3DLDF 1.1.4507496 +Node: Initial version508185 +Node: Bibliography509590 +Node: GNU Free Documentation License512705 +Node: Data Type and Variable Index535142 +Node: Function Index550926 +Node: Concept Index578144  End Tag Table diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-1 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-1 --- 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-1 2003-12-10 18:44:55.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-1 2004-01-16 19:03:28.000000000 +0100 @@ -1,11 +1,11 @@ This is 3DLDF.info, produced by makeinfo version 4.5 from 3DLDF.texi. -This is the 3DLDF User and Reference Manual, edition 1.1.4 for 3DLDF -1.1.4. This manual was last updated on 10 December 2003. 3DLDF is a +This is the 3DLDF User and Reference Manual, edition 1.1.5.1 for 3DLDF +1.1.5.1. This manual was last updated on 16 January 2004. 3DLDF is a GNU package for three-dimensional drawing with MetaPost output. The author is Laurence D. Finston. - Copyright (C) 2003 Laurence D. Finston. + Copyright (C) 2003, 2004 Laurence D. Finston. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, @@ -22,12 +22,12 @@  File: 3DLDF.info, Node: Top, Next: Introduction, Prev: (dir), Up: (dir) -This is the 3DLDF User and Reference Manual, edition 1.1.4 for 3DLDF -1.1.4. This manual was last updated on 10 December 2003. 3DLDF is a +This is the 3DLDF User and Reference Manual, edition 1.1.5.1 for 3DLDF +1.1.5.1. This manual was last updated on 16 January 2004. 3DLDF is a GNU package for three-dimensional drawing with MetaPost output. The author is Laurence D. Finston. - Copyright (C) 2003 Laurence D. Finston. + Copyright (C) 2003, 2004 Laurence D. Finston. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, @@ -36,8 +36,8 @@ no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License". - Please note that the figures cannot be shown in the Info or HTML -output formats! + Please note that the figures cannot be shown in the Info output +format. * Menu: @@ -56,6 +56,8 @@ * Installing and Running 3DLDF:: * Typedefs and Utility Structures:: * Global Constants and Variables:: +* Dynamic Allocation of Shapes:: +* System Information:: * Color Reference:: * Input and Output:: * Shape Reference:: @@ -88,7 +90,6 @@ * Function Index:: * Concept Index:: ---- The Detailed Node Listing --- Introduction @@ -109,15 +110,83 @@ * Accuracy:: * No Input Routine:: +Points + +* Declaring and Initializing Points:: +* Setting and Assigning to Points:: +* Shifting Points:: +* Scaling Points:: +* Shearing Points:: +* Rotating Points:: + +Transforms + +* Applying Transforms to Points Intro:: +* Inverting Transforms:: + +Drawing and Labeling Points + +* Drawing Points Intro:: +* Labeling Points Intro:: + +Paths + +* Declaring and Initializing Paths:: +* Drawing and Filling Paths Intro:: + +Plane Figures + +* Regular Polygons Getstart:: +* Rectangles Getstart:: +* Ellipses Getstart:: +* Circles Getstart:: + +Solid Figures + +* Cuboid Getstart:: +* Polyhedron Getstart:: + +Polyhedron + +* Tetrahedron Getstart:: +* Dodecahedron Getstart:: +* Icosahedron Getstart:: + +Pictures + +* Projections:: +* Focuses Getstart:: +* Surface Hiding:: + +Projections + +* Parallel Projections:: +* The Perspective Projection:: + Installing and Running 3DLDF * Installing 3DLDF:: * Running 3DLDF:: +Installing 3DLDF + +* Template Functions:: + Running 3DLDF +* Converting EPS Files:: * Command Line Arguments:: +Converting EPS Files + +* Converting EPS Files ELISP:: + +System Information + +* Endianness:: +* Register Width:: +* Get Second Largest Real:: + Color Reference * Color Data Members:: @@ -305,6 +374,7 @@ * Affine Transformations for Ellipses:: * Querying Ellipses:: * Returning Elements and Information for Ellipses:: +* Ellipse Intersections:: * Solving Ellipses:: * Rectangles for Ellipses:: @@ -394,12 +464,29 @@ Truncated Octahedron * Truncated Octahedron Data Members:: +* Truncated Octahedron Constructors and Setting Functions:: * Truncated Octahedron Net:: Utility Functions * Perspective Functions:: +Future Plans + +* Geometry:: +* Curves and Surfaces:: +* Shadows:: +* Multi-Threading:: + +Changes + +* Changes in 3DLDF 1.1.5.1:: +* Changes in 3DLDF 1.1.5:: +* Changes in 3DLDF 1.1.4.2:: +* Changes in 3DLDF 1.1.4.1:: +* Changes in 3DLDF 1.1.4:: +* Initial version:: +  File: 3DLDF.info, Node: Introduction, Next: Contributing to 3DLDF, Prev: Top, Up: Top @@ -507,7 +594,8 @@ This manual has been created using Texinfo, a documentation system which is part of the GNU Project, whose main sponsor is the Free -Software Foundation. +Software Foundation. Texinfo can be used to generate online and +printed documentation from the same input files. For more information about Texinfo, see: @@ -518,23 +606,15 @@ For more information about the GNU Project and the Free Software Foundation, see the following web site: `http://www.gnu.org'. - Texinfo can be used to generate online and printed documentation from -the same input files. This manual is currently designed for printing -_only_. It contains a large amount of TeX text, including the -illustrations, which would be lost if the input files were used to -generate an online version of this manual in its current form. I plan -to make the changes necessary in order to make it possible to generate -online documentation in the not-too-distant future. - - The edition of this manual is 1.1.4 and it documents version 1.1.4 -of 3DLDF. The edition number of the manual and the version number of -the program are the same (as of 10 December 2003), but may diverge at a -later date. + The edition of this manual is 1.1.5.1 and it documents version +1.1.5.1 of 3DLDF. The edition number of the manual and the version +number of the program are the same (as of 16 January 2004), but may +diverge at a later date. Note that "I", "me", etc., in this manual refers to Laurence D. Finston, so far the sole author of both 3DLDF and this manual. -"Currently" and similar formulations refer to version 1.1.4 of 3DLDF as -of 10 December 2003. +"Currently" and similar formulations refer to version 1.1.5.1 of 3DLDF +as of 16 January 2004. This manual is intended for both beginning and advanced users of 3DLDF. So, if there's something you don't understand, it's probably @@ -676,8 +756,22 @@ possible to make use of the latter's facility for writing ASCII text to files using TeX's `\write' command. - Please note that the figures cannot be shown in the Info or HTML -output formats! + The file `3DLDF-1.1.5.1/CWEB/exampman.web' contains the C++ code, +and the file `3DLDF-1.1.5.1/CWEB/examples.mp' contains the MetaPost +code for generating the illustrations. 3DLDF was built using GCC 2.95 +when the illustrations were generated. For some reason, GCC 3.3 has +difficulty with them. It works to generate them in batches of about 50 +with GCC 3.3. + + MetaPost outputs Encapsulated PostScript files. These can be +included in TeX files, as explained below. However, in order to +display the illustrations in the HTML version of this manual, I had to +convert them to PNG ("Portable Network Graphics") format +(http://www.libpng.org/pub/png/index.html). *Note Converting EPS +Files::, for instructions on how to do this. + + Please note that the illustrations cannot be shown in the Info output +format! If you have problems including the illustrations in the printed version, for example, if your installation doesn't have `dvips', look @@ -703,7 +797,7 @@ don't understand it, it's meaning should become clear after reading the manual and some experience with using 3DLDF. - The file `3DLDF.texi' in the directory `3DLDF-1.1.4/DOC/TEXINFO', + The file `3DLDF.texi' in the directory `3DLDF-1.1.5.1/DOC/TEXINFO', the driver file for this manual, contains the following TeX code: \newif\ifmakeexamples @@ -713,7 +807,7 @@ When `texi2dvi' is run on `3DLDF.texi', `\makeexamplestrue' is not commented-out, and `\makeexamplesfalse' is, the C++ code for the illustrations is written to the file `examples.web'. If the EPS files -don't already exist (in the directory `3DLDF-1.1.4/DOC/TEXINFO/EPS'), +don't already exist (in the directory `3DLDF-1.1.5.1/DOC/TEXINFO/EPS'), the TeX macro `\PEX', which includes them in the Texinfo files, will signal an error each time it can't find one. Just type `s' at the command line to tell TeX to keep going. If you want to be sure that @@ -723,7 +817,7 @@ `texi2dvi 3DLDF.texi' also generates the file `extext.tex', which contains TeX code for including the illustrations by themselves. - `examples.web' must now be moved to `3DLDF-1.1.4/CWEB/' and + `examples.web' must now be moved to `3DLDF-1.1.5.1/CWEB/' and ctangled, `examples.c' must compiled, and 3DLDF must be relinked. `ctangle examples' also generates the header file `example.h', which is included in `main.web'. Therefore, if the contents of `examples.h' have @@ -733,7 +827,7 @@ Running `3dldf' and MetaPost now generates the EPS (Encapsulated PostScript) files `3DLDFmp.1' through (currently) `3DLDFmp.199' for the -illustrations. They must be moved to `3DLDF-1.1.4/DOC/TEXINFO/EPS'. +illustrations. They must be moved to `3DLDF-1.1.5.1/DOC/TEXINFO/EPS'. Now, when `texi2dvi 3DLDF.texi' is run again, the `dvips' command `\epsffile' includes the EPS files for the illustrations in the manual. `3DLDF.texi' includes the line `\input epsf', so that `\epsffile' @@ -747,10 +841,10 @@ won't be, because the EPS files for the illustrations are included in the distribution. - The version of `examples.web' in `3DLDF-1.1.4/CWEB' merely includes -the files `subex1.web' and `subex2.web'. If you rename -`3DLDF-1.1.4/CWEB/exampman.web' to `examples.web', you can generate the -illustrations. + The version of `examples.web' in `3DLDF-1.1.5.1/CWEB' merely +includes the files `subex1.web' and `subex2.web'. If you rename +`3DLDF-1.1.5.1/CWEB/exampman.web' to `examples.web', you can generate +the illustrations. ---------- Footnotes ---------- @@ -786,21 +880,21 @@ to compilation, but these are taken care of by `make'. *Note Adding a File::, and *Note Changes::, for more information. - The CWEB files in the directory `3DLDF-1.1.4/CWEB/' contain the + The CWEB files in the directory `3DLDF-1.1.5.1/CWEB/' contain the source code for 3DLDF. The file `3DLDFprg.web' in this directory is only ever used for cweaving; it is never ctangled and contains no C++ code for compilation. It does, however, include all of the other CWEB files, so that `cweave 3DLDFprg.web' generates the TeX file containing the complete documentation of the source code of 3DLDF. - The files `3DLDF-1.1.4/CWEB/3DLDFprg.tex', -`3DLDF-1.1.4/CWEB/3DLDFprg.dvi', and `3DLDF-1.1.4/CWEB/3DLDFprg.ps' are -included in the distribution of 3DLDF as a convenience. However, users -may generate them themselves, should there be some reason for doing so, -by entering `make ps' from the command line of a shell from the working -directory `3DLDF-1.1.4/' or `3DLDF-1.1.4/CWEB'. Alternatively, the -user may generate them by hand from the working directory -`3DLDF-1.1.4/CWEB/' in the following way: + The files `3DLDF-1.1.5.1/CWEB/3DLDFprg.tex', +`3DLDF-1.1.5.1/CWEB/3DLDFprg.dvi', and `3DLDF-1.1.5.1/CWEB/3DLDFprg.ps' +are included in the distribution of 3DLDF as a convenience. However, +users may generate them themselves, should there be some reason for +doing so, by entering `make ps' from the command line of a shell from +the working directory `3DLDF-1.1.5.1/' or `3DLDF-1.1.5.1/CWEB'. +Alternatively, the user may generate them by hand from the working +directory `3DLDF-1.1.5.1/CWEB/' in the following way: 1. `cweave 3DLDFprg.web' generates `3DLDFprg.tex'. @@ -976,7 +1070,7 @@ ---------- Footnotes ---------- (1) Flex is a program for generating text scanners and Bison is a -parser generator. They are available from . +parser generator. They are available from `http://www.gnu.org'.  File: 3DLDF.info, Node: Ports, Prev: Caveats, Up: Introduction @@ -985,26 +1079,15 @@ ===== I originally developed 3DLDF on a DECalpha Personal Workstation with -two processors, under Tru64 Unix 5.1, using the DEC C++ compiler. I -then ported it to a PC Pentium 4 under Linux 2.4, using GCC 2.95.3, and -a PC Pentium II XEON under Linux 2.4, using GCC 3.3. I am currently -only maintaining the last version. I do not believe that it's -worthwhile to maintain a version for GCC 2.95. While I would like -3DLDF to run on as many platforms as possible, I would rather spend my -time developing it than porting it. This is something where I would be -grateful for help from other programmers. - - The global constant `MAX_REAL', defined in `pspglb.web', is -initialized using system dependent code. *Note Global Constants and -Variables::. Currently, 3DLDF can only be built correctly on a 32-bit -little-endian architecture. You don't necessarily need to know what -this means; If `MAX_REAL' cannot be set correctly, 3DLDF will exit -with an error message when you try to run it. Intel and VAX are -little-endian, while Motorola and SPARC are big-endian, as is the -DECalpha mentioned above. If your computer is big-endian, you will need -to fix the way `MAX_REAL' is initialized, or get somebody to do it for -you. I plan to fix this soon, so that it will work on other -architectures soon. When I have, I will supply a patch. +two processors running under the operating system Tru64 Unix 5.1, using +the DEC C++ compiler. I then ported it to a PC Pentium 4 running +under Linux 2.4, using the GNU C++ compiler GCC 2.95.3, and a PC +Pentium II XEON under Linux 2.4, using GCC 3.3. I am currently only +maintaining the last version. I do not believe that it's worthwhile to +maintain a version for GCC 2.95. While I would like 3DLDF to run on as +many platforms as possible, I would rather spend my time developing it +than porting it. This is something where I would be grateful for help +from other programmers. Although I am no longer supporting ports to other systems, I have left some conditionally compiled code for managing platform @@ -1023,7 +1106,7 @@ undefined, so if you want to try using GCC 2.95, you'll have to change this (it's not guaranteed to work). - 3DLDF 1.1.4 now uses Autoconf and Automake, and the `configure' + 3DLDF 1.1.5.1 now uses Autoconf and Automake, and the `configure' script generates a `config.h' file, which is now included in `loader.web'. Some of the preprocessor macros defined in `config.h' are used to conditionally include library header files, but so far, @@ -1031,6 +1114,16 @@ included. I hope to improve the way 3DLDF works together with Autoconf and Automake in the near future. + 3DLDF 1.1.5 is the first release that contains template functions. +Template instantiation differs from compiler to compiler, so using +template functions will tend to make 3DLDF less portable. *Note +Template Functions::, for more information. I am no longer able to +build 3DLDF on the DECalpha Personal Workstation. I'm fairly sure that +it would be possible to port it, but I don't plan to do this, since +Tru64 Unix 5.1 and the DEC C++ + + compiler are non-free software. +  File: 3DLDF.info, Node: Contributing to 3DLDF, Next: Using 3DLDF, Prev: Introduction, Up: Top @@ -1267,7 +1360,7 @@ Shifting ======== - The function adds its arguments to the corresponding + The function `shift()' adds its arguments to the corresponding `world_coordinates' of a `Point'. In the following example, the function `show()' is used to print the `world_coordinates' of `p0' to standard output. @@ -1342,43 +1435,3 @@ p0.show("p0:"); -| p0: (4, 18, 36) - -File: 3DLDF.info, Node: Shearing Points, Next: Rotating Points, Prev: Scaling Points, Up: Transforming Points - -Shearing -======== - - Shearing is more complicated than shifting or scaling. The function -`shear()' takes six `real' arguments. If p is a `Point', then -`p.shear(a, b, c, d, e, f)' sets x_p to x_p + ay_p + bz_p, y_p to y_p + -cx_p + dz_p, and z_p to z_p + ex_p + fy_p. In this way, each -coordinate of a `Point' is modified based on the values of the other -two coordinates, whereby the influence of the other coordinates on the -new value is weighted according to the arguments. - - Point p(1, 1, 1); - p.shear(1); - p.show("p:"); - -| p: (2, 1, 1) - p.set(1, 1, 1); - p.shear(1, 1); - p.show("p:"); - -| p: (3, 1, 1) - p.set(1, 1, 1); - p.shear(1, 1, 2, 2, 3, 3); - p.show("p:"); - -| p: (3, 5, 7) - - [next figure] demonstrates the effect of shearing the points of a -rectangle in the x-y plane. - - Point P0; - Point P1(3); - Point P2(3, 3); - Point P3(0, 3); - Rectangle r(p0, p1, p2, p3); - r.draw(); - Rectangle q(r); - q.shear(1.5); - q.draw(black, "evenly"); - diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-10 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-10 --- 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-10 2003-12-10 18:44:55.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-10 2004-01-16 19:03:28.000000000 +0100 @@ -1,11 +1,11 @@ This is 3DLDF.info, produced by makeinfo version 4.5 from 3DLDF.texi. -This is the 3DLDF User and Reference Manual, edition 1.1.4 for 3DLDF -1.1.4. This manual was last updated on 10 December 2003. 3DLDF is a +This is the 3DLDF User and Reference Manual, edition 1.1.5.1 for 3DLDF +1.1.5.1. This manual was last updated on 16 January 2004. 3DLDF is a GNU package for three-dimensional drawing with MetaPost output. The author is Laurence D. Finston. - Copyright (C) 2003 Laurence D. Finston. + Copyright (C) 2003, 2004 Laurence D. Finston. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, @@ -20,6 +20,644 @@ END-INFO-DIR-ENTRY  +File: 3DLDF.info, Node: Plane Tesselations, Next: Roulettes and Involutes, Prev: Pattern Reference, Up: Pattern Reference + +Plane Tesselations +================== + + 3DLDF can be used to make perspective projections of plane +tesselations and other two-dimensional patterns. These can be used for +drawing tiled floors and other architectural items, among other things. +While patterns can be generated by using the basic facilities of C++ +and 3DLDF without any specially defined functions, it can be useful to +define such functions. + + 3DLDF currently contains only one function for drawing patterns +based on a plane tessellation. I plan to add more soon. + + - Function: unsigned int hex_pattern_1 ([real DIAMETER_OUTER = 5, + [real DIAMETER_MIDDLE = 0, [real DIAMETER_INNER = 0, + [unsigned short FIRST_ROW = 5, [unsigned short DOUBLE_ROWS = + 10, [unsigned short ROW_SHIFT = 2, [Color DRAW_COLOR_OUTER = + `*Colors::default_color', [Color FILL_COLOR_OUTER = + `*Colors::background_color', [Color DRAW_COLOR_MIDDLE = + `*Colors::default_color', [Color FILL_COLOR_MIDDLE = + `*Colors::background_color', [Color DRAW_COLOR_INNER = + `*Colors::default_color', [Color FILL_COLOR_INNER = + `*Colors::background_color', [string PEN_OUTER = "pencircle + scaled .5mm", [string PEN_MIDDLE = "pencircle scaled .3mm", + [string PEN_INNER = "pencircle scaled .3mm", [Picture& + PICTURE = `current_picture', [unsigned int MAX_HEXAGONS = + 1000]]]]]]]]]]]]]]]]]) + Draws a pattern consisting of hexagons forming a tesselation of + the x-z plane, with additional hexagons within them. + + The arguments: + `real' DIAMETER_OUTER + Default: 5. The diameter of the outer hexagon in each set + of three hexagons. The outer hexagons form a tessellation of + the plane. + + `real' DIAMETER_MIDDLE + Default: 0. The diameter of the middle hexagon in a set of + three hexagons. + + `real' DIAMETER_INNER + Default: 0. The diameter of the inner hexagon in a set of + three hexagons. + + `unsigned short' FIRST_ROW + Default: 5. The number of sets of hexagons in the first + single row. The second single row will have FIRST_ROW + 1 + sets of hexagons. + + `unsigned short' DOUBLE_ROWS + Default: 10. The number of double rows drawn. + + `unsigned short' ROW_SHIFT + Default: 2. For ROW_SHIFT != 0, the number of sets of + hexagons in each (single) row is increased by 2 every + ROW_SHIFT rows. If ROW_SHIFT == 0, the number sets of + hexagons remains constant. The rows remain centered around + the z-axis. + + `Color' DRAW_COLOR_OUTER + Default: `*Colors::default_color'. The `Color' used for + drawing the outer hexagons. + + `Color' FILL_COLOR_OUTER + Default: `*Colors::background_color'. The `Color' used for + filling the outer hexagons. + + `Color' DRAW_COLOR_MIDDLE + Default: `*Colors::default_color'. The `Color' used for + drawing the middle hexagon. + + `Color' fill_color_middle + Default: `*Colors::background_color'. The `Color' used for + filling the middle hexagons. + + `Color' DRAW_COLOR_INNER + Default: `*Colors::default_color'. The `Color' used for + drawing the inner hexagons. + + `Color' FILL_COLOR_INNER + Default: `*Colors::background_color'. The `Color' used for + filling the inner hexagons. + + `string' PEN_OUTER + Default: `"pencircle scaled .5mm"'. The pen used for drawing + the outer hexagons. + + `string' PEN_MIDDLE + Default: `"pencircle scaled .3mm"'. The pen used for + drawing the middle hexagons. + + `string' pen_inner + Default: `"pencircle scaled .3mm"'. The pen used for + drawing the inner hexagons. + + `Picture&' PICTURE + Default: `current_picture'. The `Picture' onto which the + pattern is put. + + `unsigned int' MAX_HEXAGONS + Default: 1000. The maximum number of hexagons that will be + drawn. + + + Draws a pattern in the x-z plane consisting of hexagons. The outer + hexagons form a tessellation. The middle and inner hexagons fit + within the outer hexagons. The hexagons are drawn in double rows. + The tessellation can be repeated by copying a double row and + shifting the copy to lie directly behind the first double row. If + the `Picture' with the pattern is projected with the `Focus' in + front of the pattern, looking in the direction of the back of the + pattern, the first row of hexagons will appear larger than the rows + behind it. Therefore, in order for the perspective projection of + the pattern to fill a rectangular area on the plane of projection, + it will generally be necessary to increase the number of sets of + hexagons in each double row. On the other hand, if the same + number of sets of hexagons were used in the front double row, as + will be needed for the back double row, many of them would + probably be unprojectable. + + The return value of this function is the number of hexagons drawn. + + default_focus.set(0, 10, -10, 0, 10, 25, 10); + hex_pattern_1(1, 0, 0, 5, 5); + + [Figure 178 not displayed.] + + default_focus.set(-5, 5, -10, 0, 10, 25, 10); + hex_pattern_1(2, 1.5, 1, 2, 5, 2, black, gray, black, + light_gray, black); + + [Figure 179 not displayed.] + + + +File: 3DLDF.info, Node: Roulettes and Involutes, Prev: Plane Tesselations, Up: Pattern Reference + +Roulettes and Involutes +======================= + + "A "roulette" is the curve generated by a point which is carried by + a curve which rolls on a fixed curve. [...] The locus of a point + carried by a circle rolling on a straight line is a "trochoid". If + the point is inside the circle the trochoid has inflexions; if it + is outside the circle, but rigidly attached to it, the trochoid + has loops. [...] In the particular case when the point is on the + circumference of the rolling circle the roulette is a "cycloid". + When the circle rolls on the outside of another circle the + corresponding curves are the "epitrochoids" and "epicycloids"; if + it rolls on the inside, they are the "hypotrochoids" and + "hypocycloids"." + H. Martyn Cundy and A. P. Rollett, _Mathematical Models_, p. 46. + +* Menu: + +* Epicycloids:: + + +File: 3DLDF.info, Node: Epicycloids, Prev: Roulettes and Involutes, Up: Roulettes and Involutes + +Epicycloids +----------- + + - Function: unsigned int epicycloid_pattern_1 (real DIAMETER_INNER, + real DIAMETER_OUTER_START, real DIAMETER_OUTER_END, real + STEP, int ARC_DIVISIONS, unsigned int OFFSETS, [vector COLORS = `Colors::default_color_vector']) + Draws a pattern consisting of epicycloids. The outer circle rolls + around the circumference of the inner circle and a `Point' on the + outer circle traces an epicycloid. + + If OFFSETS is greater than 1, the outer circle is rotated OFFSET + times around the center of the inner circle by 360 / offsets + (starting from the outer circle's original position). From each + of these new positions, an epicycloid is drawn. + + While DIAMETER_OUTER_START is greater than or equal to + DIAMETER_OUTER_END, the diameter of the outer circle is reduced by + STEP, and another set of epicycloids is traced, as described + above. Each time the diameter of the outer circle is reduced, a + new `Color' is taken from COLORS for the drawing commands. If + there are more iterations than `Colors', the last `Color' on + COLORS is used for the remaining iterations. + + The arguments: + `real' DIAMETER_INNER + The diameter of the inner circle. + + `real' DIAMETER_OUTER_START + The diameter of the outer circle for the first iteration. It + must be greater than or equal to DIAMETER_OUTER_END. + + `real' DIAMETER_OUTER_END + The diameter of the outer circle for the last iteration. It + must be less than or equal to DIAMETER_OUTER_START. + + `real' STEP + The amount by which the diameter of the outer circle is + _reduced_ upon each iteration. + + `int' ARC_DIVISIONS + The number of divisions of the circle used for calculating + `Points' on the epicycloid. For instance, if ARC_DIVISIONS + is 90, then the `Path' for each epicycloid will only have 4 + `Points', since 360 / 90 = 4. + + `unsigned int' OFFSETS + The number of epicycloids drawn upon each iteration. Each + one is rotated by 360 / OFFSETS around the center of the + inner circle. OFFSETS must be greater than or equal to 1. + + `vector' COLORS + Default: `Colors::default_color_vector'. The `Colors' pointed + to by the pointers on this vector are used for drawing the + epicycloids. One `Color' is used for each iteration. + + + Example: + epicycloid_pattern_1(5, 3, 3, 1, 72); + current_picture.output(Projections::PARALLEL_X_Z); + + [Figure 180 not displayed.] + + Example: + default_focus.set(2, 5, -10, 2, 5, 10, 10); + epicycloid_pattern_1(5, 3, 3, 1, 36); + current_picture.output(); + + [Figure 181 not displayed.] + + + +File: 3DLDF.info, Node: Solid Reference, Next: Faced Solid Reference, Prev: Pattern Reference, Up: Top + +Solid Reference +*************** + + Class `Solid' is defined in `solids.web'. It's derived from `Shape' +using public derivation. It is intended to be used as a base class for +more specialized classes representing solid figures, e.g., cuboids, +polyhedra, solids of rotation, etc. + +* Menu: + +* Solid Data Members:: +* Solid Constructors and Setting Functions:: +* Solid Destructor:: +* Solid Operators:: +* Copying Solids:: +* Setting Solid Members:: +* Querying Solids:: +* Returning Elements and Information Solids:: +* Showing Solids:: +* Affine Transformations for Solids:: +* Applying Transformations to Solids:: +* Outputting Solids:: +* Drawing and Filling Solids:: +* Clearing Solids:: + + +File: 3DLDF.info, Node: Solid Data Members, Next: Solid Constructors and Setting Functions, Prev: Solid Reference, Up: Solid Reference + +Data Members +============ + + - Protected variable: bool on_free_store + `true', if the `Solid' was dynamically allocated on the free + store, otherwise `false'. `Solids' should only be allocated on + the free store by `create_new()', or analogous functions + for derived classes. *Note Solid Reference; Constructors and + Setting Functions: Solid Constructors and Setting Functions. + + - Protected variable: Point center + The center of the `Solid'. An object of a type derived from + `Solid' need not have a meaningful `center'. However, many do, so + it's convenient to be able to access it using the member functions + of `Solid'. + + - Protected variable: bool do_output + Set to `false' in `Picture::output()', if the `Solid' cannot be + projected using the arguments of that particular invocation of + `output()'. Reset to `true' at the end of `Picture::output()', so + that the `Solid' will be tested for projectability again, if + `output()' is called on the `Picture' again. + + - Protected variables: vector paths + - : vector circles + - : vector ellipses + - : vector reg_polygons + - : vector rectangles + Vectors of pointers to the `Paths', `Circles', `Ellipses', + `Reg_Polygons', and `Rectangles', respectively, belonging to the + `Solid', if any exist. + + - Protected variable: valarray projective_extremes + The maximum and minimum values for the x, y, and z-coordinates of + the `Points' belonging to the `Solid'. Used in + `Picture::output()' for testing whether a `Solid' is projectable + using a particular set of arguments. + + - Public static `const' variables: unsigned short CIRCLE + - : unsigned short ELLIPSE + - : unsigned short PATH + - : unsigned short RECTANGLE + - : unsigned short REG_POLYGON + Used as arguments in the functions `get_shape_ptr()' and + `get_shape_center()' (*note Returning Elements and Information: + Returning Elements and Information Solids.). + + +File: 3DLDF.info, Node: Solid Constructors and Setting Functions, Next: Solid Destructor, Prev: Solid Data Members, Up: Solid Reference + +Constructors and Setting Functions +================================== + + - Default constructor: `void' Solid (`void') + Creates an empty `Solid'. + + - Copy constructor: `void' Solid (const Solid& S) + Creates a new `Solid' and makes it a copy of S. + + - Template specializations: Solid* create_new (const Solid* S) + - : Solid* create_new (const Solid& S) + Pseudo-constructors for dynamic allocation of `Solids'. They + create a `Solid' on the free store and allocate memory for it using + `new(Solid)'. They return a pointer to the new `Solid'. + + If S is a non-zero pointer or a reference, the new `Solid' will be + a copy of S. If the new object is not meant to be a copy of an + existing one, `0' must be passed to `create_new()' as its + argument. *Note Dynamic Allocation of Shapes::, for more + information. + + +File: 3DLDF.info, Node: Solid Destructor, Next: Solid Operators, Prev: Solid Constructors and Setting Functions, Up: Solid Reference + +Destructor +========== + + - `virtual' Destructor: void ~Solid (`void') + This function currently has an empty definition, but its existence + prevents GCC 3.3 from issuing the following warning: "`class + Solid' has virtual functions but non-virtual destructor". + + +File: 3DLDF.info, Node: Solid Operators, Next: Copying Solids, Prev: Solid Destructor, Up: Solid Reference + +Operators +========= + + - Virtual function: const Solid& operator= (const Solid& S) + Assignment operator. Makes `*this' a copy of S, discarding the + old contents of `*this'. + + - Virtual function: Transform operator*= (const Transform& T) + Multiplication by a `Transform'. All of the `Shapes' that make up + the `Solid' are transformed by T. + + +File: 3DLDF.info, Node: Copying Solids, Next: Setting Solid Members, Prev: Solid Operators, Up: Solid Reference + +Copying +======= + + - `const' virtual function: Shape* get_copy (`void') + Dynamically allocates a new `Solid' on the free store, using + `create_new()', and makes it a copy of `*this'. Then, a + pointer to `Shape' is pointed at the copy and returned. Used for + putting `Solids' onto `Picture::shapes' in the drawing and filling + functions for `Solid'. *Note Solid Reference; Drawing and + Filling: Drawing and Filling Solids. + + +File: 3DLDF.info, Node: Setting Solid Members, Next: Querying Solids, Prev: Copying Solids, Up: Solid Reference + +Setting Members +=============== + + - Virtual function: bool set_on_free_store ([bool B = `true']) + Sets `on_free_store' to B. This function is called in the + template function `create_new()'. *Note Solid Reference; + Constructors and Setting Functions: Solid Constructors and Setting + Functions. + + +File: 3DLDF.info, Node: Querying Solids, Next: Returning Elements and Information Solids, Prev: Setting Solid Members, Up: Solid Reference + +Querying +======== + + - `const' virtual function: bool is_on_free_store (`void') + Returns the value of `on_free_store'; `true', if the `Solid' was + dynamically allocated on the free store, otherwise `false'. + `Solids', and objects of classes derived from `Solid', should only + ever be allocated on the free store by a specialization of the + template function `create_new()'. *Note Solid Reference; + Constructors and Setting Functions: Solid Constructors and Setting + Functions. + + +File: 3DLDF.info, Node: Returning Elements and Information Solids, Next: Showing Solids, Prev: Querying Solids, Up: Solid Reference + +Returning Elements and Information +================================== + + - `const' virtual function: const Point& get_center (void) + Returns `center'. If the `Solid' doesn't have a meaningful + center, the return value will probably be `INVALID_POINT'. + +* Menu: + +* Getting Shape Centers Solids:: +* Getting Shapes Solids:: + + +File: 3DLDF.info, Node: Getting Shape Centers Solids, Next: Getting Shapes Solids, Prev: Returning Elements and Information Solids, Up: Returning Elements and Information Solids + +Getting Shape Centers +--------------------- + + - `const' virtual function: const Point& get_shape_center (const + unsigned short SHAPE_TYPE, const unsigned short S) + Returns the `center' of a `Shape' belonging to the `Solid'. + Currently, the object can be a `Circle', `Ellipse', `Rectangle', + or `Reg_Polygon', and it is accessed through a pointer on one of + the following vectors of pointers to `Shape': `circles', + `ellipses', `rectangles', or `reg_polygons'. The type of object + is specified using the SHAPE_TYPE argument. The following `public + static const' data members of `Solid' can (and probably should) be + passed as the SHAPE_TYPE argument: `CIRCLE', `ELLIPSE', + `RECTANGLE', and `REG_POLYGON'. + + The argument S is used to index the vector. + + This function is called within the more specialized functions in + this section, namely: `get_circle_center()', + `get_ellipse_center()', ``get_rectangle_center()'', and + `get_reg_polygon_center()'. I don't expect it to be needed in user + code very often. + + Dodecahedron d(origin, 3); + d.filldraw(); + Point C = d.get_shape_center(Solid::REG_POLYGON, 1); + C.dotlabel("C"); + + [Figure 182 not displayed.] + + Note that this function will have to be changed, if new vectors of + `Shape' pointers are added to `class Solid'! + + - `const' virtual functions: const Point& get_circle_center (const + unsigned short S) + - : const Point& get_ellipse_center (const unsigned short S) + - : const Point& get_rectangle_center (const unsigned short S) + - : const Point& get_reg_polygon_center (const unsigned short S) + These functions all return the center of the `Shape' pointed to by + a pointer on one of the vectors of `Shapes' belonging to the + `Solid'. The argument S indicates which element on the vector is + to be accessed. For example, `get_rectangle_center(2)' returns + the center of the `Rectangle' pointed to by `rectangles[2]'. + + Cuboid c(origin, 3, 4, 5, 0, 30); + c.draw(); + for (int i = 0; i < 6; ++i) + c.get_rectangle_center(i).label(i, ""); + + [Figure 183 not displayed.] + + + +File: 3DLDF.info, Node: Getting Shapes Solids, Prev: Getting Shape Centers Solids, Up: Returning Elements and Information Solids + +Getting Shapes +-------------- + + The functions in this section all return `const' pointers to +`Shape', or one of its derived classes. Therefore, they must be invoked +in such a way, that the `const' qualifier is not discarded. See the +description of `get_reg_polygon_ptr()' below, for an example. + + - `const' virtual function: Shape* get_shape_ptr (const unsigned short + shape_type, const unsigned short s) + Copies one of the objects belonging to the `Solid', and returns a + pointer to `Shape' that points to the copy. The object is found + by dereferencing one of the pointers on one of the vectors of + pointers belonging to the `Solid'. Currently, these vectors are + `circles', `ellipses', `paths', `rectangles', and `reg_polygons'. + The argument SHAPE_TYPE specifies the vector, and the argument S + specifies which element of the vector should be accessed. The + following `public static const' data members of `Solid' can (and + probably should) be passed as the SHAPE_TYPE argument: `CIRCLE', + `ELLIPSE', `PATH', `RECTANGLE', and `REG_POLYGON'. + + This function was originally intended to be called within the more + specialized functions in this section, namely: `get_circle_ptr()', + `get_ellipse_ptr()', `get_path_ptr()', `get_rectangle_ptr', and + `get_reg_polygon_ptr'. However, these functions no longer use + `get_shape_ptr()', so this function is probably no longer needed. + + Icosahedron I(origin, 3); + I.filldraw(); + Reg_Polygon* t = + static_cast(I.get_shape_ptr(Solid::REG_POLYGON, 9)); + t->fill(gray); + + [Figure 184 not displayed.] + + + - `const' virtual functions: const Reg_Polygon* get_circle_ptr (const + unsigned short S) + - : const Reg_Polygon* get_ellipse_ptr (const unsigned short S) + - : const Reg_Polygon* get_path_ptr (const unsigned short S) + - : const Reg_Polygon* get_rectangle_ptr (const unsigned short S) + - : const Reg_Polygon* get_reg_polygon_ptr (const unsigned short S) + Each of these functions returns a pointer from one of the vectors + of `Shape' pointers belonging to the `Solid'. The argument S + specifies which element of the appropriate vector should be + returned. For example, `get_reg_polygon_ptr(2)' returns the + `Reg_Polygon*' in `reg_polygons[2]'. + + Since these functions return `const' pointers, they must be invoked + in such a way, that the `const' qualifier is not discarded, as + noted at the beginning of this section. The following example + demonstrates two ways of invoking `get_reg_polygon_ptr()': + + Dodecahedron d(origin, 3); + d.draw(); + const Reg_Polygon* ptr = d.get_reg_polygon_ptr(0); + ptr->draw(black, "evenly scaled 4", "pencircle scaled 1mm"); + Reg_Polygon A = *d.get_reg_polygon_ptr(5); + A.fill(gray); + + [Figure 185 not displayed.] + + + +File: 3DLDF.info, Node: Showing Solids, Next: Affine Transformations for Solids, Prev: Returning Elements and Information Solids, Up: Solid Reference + +Showing +======= + + - `const' virtual function: `void' show ([string TEXT = "", [char + COORDS = 'w', [const bool DO_PERSP = `true', [const bool + DO_APPLY = `true', [Focus* f = 0, [const unsigned short PROJ + = `Projections::PERSP', [const real FACTOR = 1]]]]]]]) + Prints TEXT and the value of `on_free_store' to the standard + output (`stdout'), and then calls `show()' on the objects pointed + to by the pointers on `paths', `circles', `ellipses', + `reg_polygons', and `rectangles', unless the vectors are empty. + The arguments are passed to `Path::show()', `Ellipse::show()', + etc. If a vector is empty, a message to this effect is printed to + the standard output. + + +File: 3DLDF.info, Node: Affine Transformations for Solids, Next: Applying Transformations to Solids, Prev: Showing Solids, Up: Solid Reference + +Affine Transformations +====================== + + - Virtual functions: Transform scale (real X, [real Y = 0, [real Z = + 0]]) + `Solid'. + + - : Transform shear (real XY, [real XZ = 0, [real YX = 0, [real YZ = + 0, [real ZX = 0, [real ZY = 0]]]]]) + - : Transform shift (real X, [real Y = 0, [real Z = 0]]) + - : Transform shift (const Point& PT) + - : Transform rotate (const real X, [const real Y = 0, [const real Z = + 0]]) + - : Transform rotate (const Point& P0, const Point& P1, [const real + ANGLE = 180]) + These functions perform the corresponding transformations on all + of the `Shapes' belonging to the `Solid'. *Note Transform + Reference; Affine Transformations: Affine Transformations for + Transforms. + + +File: 3DLDF.info, Node: Applying Transformations to Solids, Next: Outputting Solids, Prev: Affine Transformations for Solids, Up: Solid Reference + +Applying Transformations +======================== + + - Virtual function: void apply_transform (`void') + Calls `apply_transform()' on all of the `Shapes' belonging to the + `Solid'. + + +File: 3DLDF.info, Node: Outputting Solids, Next: Drawing and Filling Solids, Prev: Applying Transformations to Solids, Up: Solid Reference + +Outputting +========== + + The functions in this section are are called, directly or +indirectly, by `Picture::output()'. *Note Picture Reference; +Outputting: Outputting Pictures. + + - Virtual function: void output (`void') + Writes the MetaPost code for drawing, filling, filldrawing, + undrawing, unfilling, or unfilldrawing the `Solid' to `out_stream'. + + - Virtual function: void suppress_output (`void') + Used in `Picture::output()'. Sets `do_output' to `false', if the + `Solid' cannot be projected using a particular set of arguments to + `Picture::output()'. + + - Virtual function: void unsuppress_output (`void') + Used in `Picture::output()'. Resets `do_output' to `true', so + that the `Solid' will be tested for projectability again, if the + `Picture' it's on is output again. + + - Virtual function: vector extract (const Focus& F, const + unsigned short PROJ, real FACTOR) + Tests whether all of the `Shapes' belonging to the `Solid' are + projectable, using the arguments passed to `output()'. If it is, + this function returns a vector of pointers to `Shape' containing a + single pointer to the `Solid'. If not, an empty vector is + returned. + + - Virtual function: bool set_extremes (`void') + Sets `projective_extremes' to contain the maximum and minimum + values for the x, y, and z-coordinates of the `Points' on the + `Shape'. Used for determining projectability of a `Solid' using a + particular set of arguments. + + - `const' inline virtual function: const valarray get_extremes + (`void') + Returns `projective_extremes'. + + - `const' virtual functions: real get_minimum_z (`void') + - : real get_maximum_z (`void') + - : real get_mean_z (`void') + Returns the minimum, maximum, or mean z-value, respectively, of the + `Points' belonging to the `Solid'. Used for surface hiding. + *Note Surface Hiding::. + + File: 3DLDF.info, Node: Drawing and Filling Solids, Next: Clearing Solids, Prev: Outputting Solids, Up: Solid Reference Drawing and Filling @@ -227,11 +865,21 @@ Point P(-3, -2, 12); Cuboid c(P, 3, 5, 2.93, 35, 10, 60); + [Figure 186 not displayed.] + - - Static function: Cuboid* create_new_cuboid ([const Cuboid* C = 0]) - Dynamically allocates a new `Cuboid' on the free store and returns - a pointer to it. If a non-zero argument C is used, the new - `Cuboid' will be a copy of *C. + - Template specializations: Cuboid* create_new (const Cuboid* + C) + - : Cuboid* create_new (const Cuboid& C) + Pseudo-constructors for dynamic allocation of `Cuboids'. They + create a `Cuboid' on the free store and allocate memory for it + using `new(Cuboid)'. They return a pointer to the new `Cuboid'. + + If C is a non-zero pointer or a reference, the new `Cuboid' will + be a copy of C. If the new object is not meant to be a copy of an + existing one, `0' must be passed to `create_new()' as its + argument. *Note Dynamic Allocation of Shapes::, for more + information. - Destructor: void ~Cuboid (`void') Deallocates the `Rectangles' pointed to by the pointers on @@ -369,10 +1017,14 @@ Tetrahedron t(origin, 3); t.draw(); + [Figure 187 not displayed.] + Point P(1, 0, 1); Tetrahedron t(P, 2.75, 30, 32.5, 20); t.draw(); + [Figure 188 not displayed.] + - Setting function: void set (const Point& P, const real DIAMETER_OF_TRIANGLE, [real ANGLE_X = 0, [real ANGLE_Y = 0, @@ -401,6 +1053,8 @@ (**iter).draw(); } + [Figure 189 not displayed.] + This function is used in the non-default constructor. *Note Polyhedron Reference; Regular Platonic Polyhedra; Tetrahedron; Constructors and Setting Functions: Tetrahedron Constructors and @@ -434,6 +1088,8 @@ Tetrahedron::draw_net(3, true); + [Figure 190 not displayed.] + The net is drawn in the x-y plane, because it currently doesn't work to draw it in the x-z plane. I haven't gotten around to fixing this problem yet. @@ -496,8 +1152,12 @@ Dodecahedron d(P, 3, 12.5, 16, 2); d.draw(); + [Figure 191 not displayed.] + d.filldraw(); + [Figure 192 not displayed.] +  File: 3DLDF.info, Node: Dodecahedron Net, Prev: Dodecahedron Constructors and Setting Functions, Up: Dodecahedron @@ -522,6 +1182,8 @@ iter != vrp.end(); ++iter) (**iter).draw(); + [Figure 193 not displayed.] + - Static function: void draw_net (const real PENTAGON_DIAMETER, [bool PORTRAIT = `true', [bool MAKE_TABS = `true']]) @@ -540,6 +1202,8 @@ Dodecahedron::draw_net(1, false); + [Figure 194 not displayed.] +  File: 3DLDF.info, Node: Icosahedron, Prev: Dodecahedron, Up: Regular Platonic Polyhedra @@ -594,508 +1258,10 @@ Icosahedron i(origin, 3, 0, 10); i.draw(); - i.filldraw(); - - - -File: 3DLDF.info, Node: Icosahedron Net, Prev: Icosahedron Constructors and Setting Functions, Up: Icosahedron - -Net -... - - - Static function: vector get_net (const real - TRIANGLE_DIAMETER, [bool DO_HALF = `false']) - Returns the "net", i.e., the two-dimensional pattern of triangles - that can be folded into a model of an icosahedron. The net lies - in the x-z plane. The triangles have enclosing circles of diameter - TRIANGLE_DIAMETER. If the argument DO_HALF = `true', only the - first half of the net is created. This is used in the non-default - constructor. *Note Polyhedron Reference; Regular Platonic - Polyhedra; Icosahedron; Constructors and Setting Functions: - Icosahedron Constructors and Setting Functions. - - vector vrp = Icosahedron::get_net(1.5); - for (vector::iterator iter = vrp.begin(); - iter != vrp.end(); ++iter) - (**iter).draw(); - - - - Static function: void draw_net (const real TRIANGLE_DIAMETER, [bool - PORTRAIT = TRUE, [bool MAKE_TABS = `true']]) - Draws the net for an `Icosahedron' in the x-z plane. The triangles - have enclosing circles of diameter TRIANGLE_DIAMETER. If the - argument PORTRAIT is `true' (the default), the net will be - arranged for printing in portrait format. If it's `false', it - will be arranged for printing in landscape format. In portrait - format, the center of the bottom right triangle is at the origin. - In landscape format, the center of the bottom left triangle is at - the origin. The triangles are numbered. - - The argument MAKE_TABS currently has no effect. When I get around - to programming this, it will be used for specifying whether tabs - for gluing and/or sewing a cardboard model should be drawn, too. - - Icosahedron::draw_net(2, false); - - - -File: 3DLDF.info, Node: Semi-Regular Archimedean Polyhedra, Prev: Regular Platonic Polyhedra, Up: Polyhedron Reference - -Semi-Regular Archimedean Polyhedra -================================== - - Once I've added `class Octahedron', the only Platonic polyhedron I -haven't programmed yet, I plan to start adding classes for the -semi-regular Archimedean polyhedra. - -* Menu: - -* Truncated Octahedron:: - - -File: 3DLDF.info, Node: Truncated Octahedron, Next: Truncated Octahedron Data Members, Prev: Semi-Regular Archimedean Polyhedra, Up: Semi-Regular Archimedean Polyhedra - -Truncated Octahedron --------------------- - - Class `Trunc_Octahedron' is defined in `polyhed.web'. It is derived -from `Polyhedron' using public derivation. - - `Trunc_Octahedron' does not yet have a functioning constructor, so -it cannot be used as yet. - -* Menu: - -* Truncated Octahedron Data Members:: -* Truncated Octahedron Net:: -* Truncated Octahedron Constructors and Setting Functions:: - - -File: 3DLDF.info, Node: Truncated Octahedron Data Members, Next: Truncated Octahedron Constructors and Setting Functions, Prev: Truncated Octahedron, Up: Truncated Octahedron - -Data Members -............ - - - Protected static `const' variable: real angle_hex_square - The angle between the hexagonal and the square faces of the - truncated octahedron, namely 125 degrees 16' . - - - Protected static `const' variable: real angle_hex_hex - The angle between the hexagonal faces of the truncated octahedron, - namely 109 degrees 28' . - - - Protected variable: real hexagon_radius - The radius of the circle enclosing a hexagonal or square face of - the `Trunc_Octahedron'. - - -File: 3DLDF.info, Node: Truncated Octahedron Constructors and Setting Functions, Next: Truncated Octahedron Net, Prev: Truncated Octahedron Data Members, Up: Truncated Octahedron - -Constructors and Setting Functions -.................................. - - - Default constructor: void Trunc_Octahedron (`void') - Creates an empty `Trunc_Octahedron'. - - - Constructor: void Trunc_Octahedron (const Point& P, const real - DIAMETER_OF_HEXAGON, [real ANGLE_X = 0, [real ANGLE_Y = 0, - [real ANGLE_Z = 0]]]) - This function does not yet exist! When it does, it will create a - `Trunc_Octahedron' with its center at the origin, where the - hexagonal and square faces have enclosing circles of diameter - DIAMETER_OF_HEXAGON. If any of ANGLE_X, ANGLE_Y, or ANGLE_Z is - non-zero, the `Trunc_Octahedron' will be rotated by the amounts - specified around the corresponding axes. Finally, if P is not the - origin, the `Trunc_Octahedron' will be shifted such that `center' - comes to lie at P. - - -File: 3DLDF.info, Node: Truncated Octahedron Net, Prev: Truncated Octahedron Constructors and Setting Functions, Up: Truncated Octahedron - -Net -... - - - Static function: vector get_net (const real - HEXAGON_DIAMETER, [bool DO_HALF = `false']) - This function does not yet exist! When it does, it will return - the "net", i.e., the two-dimensional pattern of hexagons and - squares that can be folded into a model of a truncated octahedron. - The net will lie in the x-z plane. The hexagons and squares will - have enclosing circles of diameter HEXAGON_DIAMETER. If the - argument DO_HALF is `true', only the first half of the net will be - created. This will be used in the non-default constructor. *Note - Polyhedron Reference; Regular Platonic Polyhedra; Truncated - Octahedron Constructors and Setting Functions: Truncated - Octahedron Constructors and Setting Functions. - - -File: 3DLDF.info, Node: Utility Functions, Next: Adding a File, Prev: Polyhedron Reference, Up: Top - -Utility Functions -***************** - - - Function: double trunc (double d) - Defined in `pspglb.web'. For some reason, when I compile 3DLDF - using GNU CC on a PC Pentium II XEON under Linux 2.4.4 i686, the - standard library function `trunc()' is not available. Therefore, - I've had to write one. This is a kludge! Someday, I'll have to - try to find a better solution to this problem. - - - Function: pair solve_quadratic (real A, real B, real C) - Defined in `pspglb.web'. This function tries to find the - solutions S_0 and S_1 to the quadratic equation ax^2 + bx + c - according to the formulae S_0 == -b + sqrt(b^2 - 4ac) / 2a) and - S_1 == -b - sqrt( b^2 - 4ac) / 2a. Let `r' stand for the return - value. If S_0 cannot be found, `r.first' will be `INVALID_REAL', - otherwise S_0. If S_1 cannot be found, `r.second' will be - `INVALID_REAL', otherwise S_1. - - (x + 4)(x + 2) = x^2 + 6x + 8 = 0 - - real_pair r = solve_quadratic(1, 6, 8); - => r.first == -2 - => r.second == -4 - - real_pair r = solve_quadratic(1, -2, 4); - => r.first == INVALID_REAL - => r.second == INVALID_REAL - - -* Menu: - -* Perspective Functions:: - - -File: 3DLDF.info, Node: Perspective Functions, Prev: Utility Functions, Up: Utility Functions - -Perspective Functions -===================== - - - Function: void persp_0 (const real FRONT_CORNER_X, const real - FRONT_CORNER_Z, const real SIDE_LFT, const real SIDE_RT, - const real ANGLE_RT, const real F_2_CV, const real GL_2_CV, - [const real HORIZON_LFT = 6, [real HORIZON_RT = 0, [real - GL_LFT = 0, [real GL_RT = 0]]]]) - Defined in `utility.web'. This function is used for the figure in - *Note The Perspective Projection::, illustrating a perspective - projection as it could be done by hand. It draws a rectangle in - the ground plane and the construction lines used for putting it - into perspective. It also labels the vanishing and measuring - points. - - The arguments: - `CONST REAL' FRONT_CORNER_X - The x-coordinate of the front corner of the rectangle. - - `CONST REAL' FRONT_CORNER_Z - The z-coordinate of the front corner of the rectangle. - - `CONST REAL' SIDE_LFT - The length of the left side of the rectangle. - - `CONST REAL' SIDE_RT - The length of the right side of the rectangle. - - `CONST REAL' ANGLE_RT - The angle at which the right side of the rectangle recedes to - the horizon. - - `CONST REAL' F_2_CV - The distance from the focus to the center of vision. - - `CONST REAL' GL_2_CV - The distance of the ground line to the center of vision. - - `CONST REAL' HORIZON_LFT - Default: 6. The length of the horizon line leftwards of the - center of vision. - - `REAL' HORIZON_RT - Default: 0. The length of the horizon line rightwards of the - center of vision. - - `REAL' GL_LFT - Default: 0. The length of the ground line leftwards of the - line from the focus to the center of vision. - - `REAL' GL_RT - Default: 0. The length of the ground line rightwards of the - line from the focus to the center of vision. - - Example: - - persp_0(3, 2, 10, 5, 47.5, 7, 5, 8.5, 9.5, 8.5, 9.5); - + [Figure 195 not displayed.] - -File: 3DLDF.info, Node: Adding a File, Next: Future Plans, Prev: Utility Functions, Up: Top - -Adding a File -************* - - Version 1.1.1 was the first version of 3DLDF since it became a GNU -package (the current version is 1.1.4). In previous versions, -recompilation was controlled by an auxilliary program, which I wrote in -C++ using CWEB. However, in the course of making 3DLDF conformant to -the GNU Coding Standards(1), this has been changed. Recompilation is -now controlled by `make', as is customary. The chapter "Compiling" in -previous editions of this manual, is therefore no longer needed. - - Nonetheless, using CWEB still has consequences for the way -recompilation must be handled, and it was fairly tricky getting `make' -to work for 3DLDF. Users who only put code in `main.web' and/or change -code in existing files won't have to worry about this; for others, this -chapter explains how to add files to 3DLDF. - - Let's say you want to add a file `widgets.web' that defines a `class -Widget', and that the latter needs access to `class Rectangle', and is -in turn required by `class Ellipse'. Code must be added to -`3DLDF-1.1.4/CWEB/Makefile' for ctangling `widgets.web', compiling -`widgets.cxx', and linking `widgets.o' with the other object files to -make the executable `3dldf'. - - The best way to do this is to change `3DLDF-1.1.4/CWEB/Makefile.am' -and use Automake to generate a new `Makefile.in'. Then, `configure' -can be used to generate a new `Makefile'. It would be possible to -modify `Makefile' by hand, but I don't recommend it. The following -assumes that the user has access to Automake. If he or she is using a -GNU/Linux system, this is probably true.(2) - - `widgets.web' must be added between `rectangs.web' and -`ellipses.web' in the following variable declaration in -`3DLDF-1.1.4/CWEB/Makefile.am': - - 3dldf_SOME_CWEBS = pspglb.web io.web colors.web transfor.web \ - shapes.web pictures.web points.web \ - lines.web planes.web paths.web curves.web \ - polygons.web rectangs.web ellipses.web \ - circles.web patterns.web solids.web - solfaced.web cuboid.web polyhed.web \ - utility.web parser.web examples.web - - Now, add `widgets.o' between `ellipses.o' and `rectangs.o' in the -following variable declaration: - - 3dldf_OBS_REVERSED = main.o examples.o parser.o utility.o \ - polyhed.o cuboid.o solfaced.o solids.o \ - patterns.o circles.o ellipses.o rectangs.o \ - polygons.o curves.o paths.o \ - planes.o lines.o points.o pictures.o shapes.o - transfor.o colors.o io.o pspglb.o - - `3dldf_OBS_REVERSED' is needed, because 3DLDF fails with a -"Segmentation fault", if the executable is linked using -`$(3dldf_OBJECTS)'. This may cause problems, if `3dldf' isn't built -using the GNU C++ compiler (GCC). - - Now add a target for `widgets.o' between the targets for -`rectangs.o' and `ellipses.o', and add `widgets.tim' after -`rectangs.tim' in the list of prerequisites for `ellipses.o': - - rectangs.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.cxx - - ellipses.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.tim ellipses.cxx - - This is the result: - rectangs.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.cxx - - widgets.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.tim \ - widgets.cxx - - ellipses.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ - shapes.tim pictures.tim points.tim lines.tim planes.tim \ - paths.tim curves.tim polygons.tim rectangs.tim widgets.tim \ - ellipses.cxx - - In addition, `widgets.tim' must be added to the list of -prerequisites in all of the following targets up to and including -`examples.o'. - - ---------- Footnotes ---------- - - (1) The GNU Coding Standards are available at -`http://www.gnu.org/prep/standards_toc.html'. - - (2) Automake is available for downloading from -`http://ftp.gnu.org/gnu/automake/'. The Automake website is at -`http://www.gnu.org/software/automake/'. - - -File: 3DLDF.info, Node: Future Plans, Next: Changes, Prev: Adding a File, Up: Top - -Future Plans -************ - - 3DLDF is a work-in-progress. In fact, it can never be finished, -because the supply of interesting geometric constructions is -inexhaustible. However, presently 3DLDF still has a number of major -gaps. The following is a list of matters that I plan to address sooner -rather than later: - - * Program an input routine. The lack of one is the most significant - defect in 3DLDF, as mentioned in *Note No Input Routine::. - - * Port to other platforms. - - * Add `class Octahedron' to complete the set of regular Platonic - polyhedra. - - * Improve the polyhedra, by storing the vertices as `Points', rather - than `Reg_Polygons'. Find a better way of generating them, if - possible, without using rotations. - - * Add classes for the Kepler-Poinsot polyhedra, the semi-regular - Archimedean polyhedra, the dual solids, the stellated Archimedean - polyhedra, and the regular compounds.(1) - - * Add more functions for finding the intersections of objects of - various types, starting with the plane figures. In particular, I - believe I've found an algebraic solution for the intersection of - an `Ellipse' and a `Circle' in a plane, but I haven't had a chance - to try implementing it yet. - - * Add constructors with a normal vector argument rather than angles - of rotation about the main axes. - - * Add the classes `Sphere' and `Ellipsoid'. - - * Provide a means for calculating triangle solutions, perhaps using a - `class Triangle'. - - * Provide a means of producing shadows and reflections. - - * Improve the indexes in the manual. - - If you're interesting in contributing to 3DLDF, with respect to one -of these ideas, or if you have others of your own, see *Note -Contributing to 3DLDF::. - - ---------- Footnotes ---------- - - (1) Cundy and Rollet, `Mathematical Models', Chapter 3, "Polyhedra", -pp. 76-160. - - -File: 3DLDF.info, Node: Changes, Next: Bibliography, Prev: Future Plans, Up: Top - -Changes -******* - -Updated 10 December 2003. - - Changes in 3DLDF 1.1.4: - * `MAX_REAL' is now the second largest float value. However, the - calculation is system dependent, and will only work on 32-bit - little-endian architectures. I will start working on porting this - soon. - - * Fixed bug in `tsthdweb', that caused files to be compiled more - often than necessary. It will be necessary to keep an eye on this. - - * Added `Rectangle::is_rectangular()'. - - * Made `mediate()' a member function of `Point'. - - * It is now possible to generate this manual in the Info and HTML - formats. - - 3DLDF 1.1.1 was the first version of 3DLDF since it became a GNU -package (the current version is 1.1.4). It is now conformant to the -GNU Coding Standards, except that a functioning `3DLDF.info' cannot be -generated from `3DLDF.texi'. The distribution now includes a -`configure' script, `Makefile.in' files, and other files generated by -Autoconf and Automake. Recompilation is now handled by `make' rather -than the auxilliary program `3DLDFcpl'. The files `3DLDFcpl.web' and -`3DLDFprc.web' have been removed from the distribution. - - The extension of the C++ files generated by `ctangle' is changed -from `c' to `cxx' before they are compiled. After `ctangle' is run on -a CWEB file, `.c' is compared to the old `.cxx' -using `diff'. Whitespace, comments, and `#line' preprocessor commands -are ignored. The `.c' is only renamed to `.cxx' -and compiled if they differ. This way, changes to the TeX text only in -a CWEB file no longer cause recompilation and relinking. - - The main Texinfo file is now called `3DLDF.texi'. It was formerly -called `3DLDFman.texi'. This is because Automake expects this name. -For this reason, the CWEB file passed as an argument to cweave has been -renamed `3DLDFprg.web'. It was formerly called `3DLDF.web'. - - -File: 3DLDF.info, Node: Bibliography, Next: GNU Free Documentation License, Prev: Changes, Up: Top - -Bibliography -************ - - Cundy, H. Martyn and A.P. Rollet. Mathematical Models. Oxford 1961. -Oxford University Press. - - Unfortunately out of print. - - -Finston, Laurence D. 3DLDF: The Program. Go"ttingen 2003. - -Fischer, Gerd. Ebene algebraische Kurven. Vieweg Studium. Aufbaukurs -Mathematik. Friedr. Vieweg & Sohn Verlagsgesellschaft mbH. -Braunschweig/Wiesbaden 1994. - -Gill, Robert W. Creative Perspective. London 1975. Thames and Hudson -Ltd. ISBN 0-500-27056-2. - -Hobby, John D. A User's Manual for MetaPost. AT & T Bell Laboratories. -Murray Hill, NJ. No date. - -Jones, Huw. Computer Graphics through Key Mathematics. -Springer-Verlag London Limited 2001. ISBN 1-85233-422-3. - -Knuth, Donald Ervin. Metafont: The Program. Computers and -Typesetting; D. Addison Wesley Publishing Company, Inc. Reading, -Massachusetts 1986. ISBN 0-201-13438-1. - -Knuth, Donald Ervin. The METAFONTbook. Computers and Typesetting; C. -Addison Wesley Publishing Company, Inc. Reading, Massachusetts 1986. - -Knuth, Donald Ervin. TeX: The Program. Computers and Typesetting; B. -Addison Wesley Publishing Company, Inc. Reading, Massachusetts 1986. -ISBN 0-201-13437-3. - -Knuth, Donald E. The TeXbook. Computers and Typesetting; A. Addison -Wesley Publishing Company, Inc. Reading, Massachusetts 1986. - -Knuth, Donald E. and Silvio Levy. The CWEB System of Structured -Documentation. Version 3.64--February 2002. - -Salomon, David. Computer Graphics and Geometric Modeling. Berlin 1999. -Springer-Verlag. ISBN: 0-387-98682-0. - -Stallman, Richard M. and Roland McGrath. GNU Make. A Program for -Directing Recompilation. make Version 3.79. Boston 2000. Free -Software Foundation, Inc. ISBN: 1-882114-80-9. - -Stroustrup, Bjarne. The C++ Programming Language. Special Edition. -Reading, Massachusetts 2000. Addison-Wesley. ISBN 0-201-70073-5. - -Stroustrup, Bjarne. The Design and Evolution of C++ . Reading, -Massachusetts 1994. Addison-Wesley Publishing Company. -ISBN 0-201-54330-3. - -Vredeman de Vries, Jan. Perspective. New York 1968. Dover -Publications, Inc. Standard Book Number: 486-21086-4. - - The beautiful perspective constructions in this volume are taken from - the original work, first published by Henricus Hondius in Leiden in 1604 - and 1605. + i.filldraw(); + [Figure 196 not displayed.] -White, Gwen. Perspective. A Guide for Artists, Architects and -Designers. London 1968 and 1982. B T Batsford Ltd. -ISBN 0-7134-3412-0. diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-11 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-11 --- 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-11 2003-12-10 18:44:55.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-11 2004-01-16 19:03:28.000000000 +0100 @@ -1,11 +1,11 @@ This is 3DLDF.info, produced by makeinfo version 4.5 from 3DLDF.texi. -This is the 3DLDF User and Reference Manual, edition 1.1.4 for 3DLDF -1.1.4. This manual was last updated on 10 December 2003. 3DLDF is a +This is the 3DLDF User and Reference Manual, edition 1.1.5.1 for 3DLDF +1.1.5.1. This manual was last updated on 16 January 2004. 3DLDF is a GNU package for three-dimensional drawing with MetaPost output. The author is Laurence D. Finston. - Copyright (C) 2003 Laurence D. Finston. + Copyright (C) 2003, 2004 Laurence D. Finston. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, @@ -20,683 +20,773 @@ END-INFO-DIR-ENTRY  -File: 3DLDF.info, Node: GNU Free Documentation License, Next: Data Type and Variable Index, Prev: Bibliography, Up: Top +File: 3DLDF.info, Node: Icosahedron Net, Prev: Icosahedron Constructors and Setting Functions, Up: Icosahedron -GNU Free Documentation License -****************************** +Net +... - Version 1.2, November 2002 - Copyright (C) 2000,2001,2002 Free Software Foundation, Inc. - 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA + - Static function: vector get_net (const real + TRIANGLE_DIAMETER, [bool DO_HALF = `false']) + Returns the "net", i.e., the two-dimensional pattern of triangles + that can be folded into a model of an icosahedron. The net lies + in the x-z plane. The triangles have enclosing circles of diameter + TRIANGLE_DIAMETER. If the argument DO_HALF = `true', only the + first half of the net is created. This is used in the non-default + constructor. *Note Polyhedron Reference; Regular Platonic + Polyhedra; Icosahedron; Constructors and Setting Functions: + Icosahedron Constructors and Setting Functions. + + vector vrp = Icosahedron::get_net(1.5); + for (vector::iterator iter = vrp.begin(); + iter != vrp.end(); ++iter) + (**iter).draw(); + + [Figure 197 not displayed.] + + + - Static function: void draw_net (const real TRIANGLE_DIAMETER, [bool + PORTRAIT = TRUE, [bool MAKE_TABS = `true']]) + Draws the net for an `Icosahedron' in the x-z plane. The triangles + have enclosing circles of diameter TRIANGLE_DIAMETER. If the + argument PORTRAIT is `true' (the default), the net will be + arranged for printing in portrait format. If it's `false', it + will be arranged for printing in landscape format. In portrait + format, the center of the bottom right triangle is at the origin. + In landscape format, the center of the bottom left triangle is at + the origin. The triangles are numbered. + + The argument MAKE_TABS currently has no effect. When I get around + to programming this, it will be used for specifying whether tabs + for gluing and/or sewing a cardboard model should be drawn, too. + + Icosahedron::draw_net(2, false); + + [Figure 198 not displayed.] + + + +File: 3DLDF.info, Node: Semi-Regular Archimedean Polyhedra, Prev: Regular Platonic Polyhedra, Up: Polyhedron Reference + +Semi-Regular Archimedean Polyhedra +================================== + + Once I've added `class Octahedron', the only Platonic polyhedron I +haven't programmed yet, I plan to start adding classes for the +semi-regular Archimedean polyhedra. + +* Menu: + +* Truncated Octahedron:: + + +File: 3DLDF.info, Node: Truncated Octahedron, Prev: Semi-Regular Archimedean Polyhedra, Up: Semi-Regular Archimedean Polyhedra + +Truncated Octahedron +-------------------- + + Class `Trunc_Octahedron' is defined in `polyhed.web'. It is derived +from `Polyhedron' using public derivation. + + `Trunc_Octahedron' does not yet have a functioning constructor, so +it cannot be used as yet. + +* Menu: + +* Truncated Octahedron Data Members:: +* Truncated Octahedron Constructors and Setting Functions:: +* Truncated Octahedron Net:: + + +File: 3DLDF.info, Node: Truncated Octahedron Data Members, Next: Truncated Octahedron Constructors and Setting Functions, Prev: Truncated Octahedron, Up: Truncated Octahedron + +Data Members +............ + + - Protected static `const' variable: real angle_hex_square + The angle between the hexagonal and the square faces of the + truncated octahedron, namely 125 degrees 16' . + + - Protected static `const' variable: real angle_hex_hex + The angle between the hexagonal faces of the truncated octahedron, + namely 109 degrees 28' . + + - Protected variable: real hexagon_radius + The radius of the circle enclosing a hexagonal or square face of + the `Trunc_Octahedron'. + + +File: 3DLDF.info, Node: Truncated Octahedron Constructors and Setting Functions, Next: Truncated Octahedron Net, Prev: Truncated Octahedron Data Members, Up: Truncated Octahedron + +Constructors and Setting Functions +.................................. + + - Default constructor: void Trunc_Octahedron (`void') + Creates an empty `Trunc_Octahedron'. + + - Constructor: void Trunc_Octahedron (const Point& P, const real + DIAMETER_OF_HEXAGON, [real ANGLE_X = 0, [real ANGLE_Y = 0, + [real ANGLE_Z = 0]]]) + This function does not yet exist! When it does, it will create a + `Trunc_Octahedron' with its center at the origin, where the + hexagonal and square faces have enclosing circles of diameter + DIAMETER_OF_HEXAGON. If any of ANGLE_X, ANGLE_Y, or ANGLE_Z is + non-zero, the `Trunc_Octahedron' will be rotated by the amounts + specified around the corresponding axes. Finally, if P is not the + origin, the `Trunc_Octahedron' will be shifted such that `center' + comes to lie at P. + + +File: 3DLDF.info, Node: Truncated Octahedron Net, Prev: Truncated Octahedron Constructors and Setting Functions, Up: Truncated Octahedron + +Net +... + + - Static function: vector get_net (const real + HEXAGON_DIAMETER, [bool DO_HALF = `false']) + This function does not yet exist! When it does, it will return + the "net", i.e., the two-dimensional pattern of hexagons and + squares that can be folded into a model of a truncated octahedron. + The net will lie in the x-z plane. The hexagons and squares will + have enclosing circles of diameter HEXAGON_DIAMETER. If the + argument DO_HALF is `true', only the first half of the net will be + created. This will be used in the non-default constructor. *Note + Polyhedron Reference; Regular Platonic Polyhedra; Truncated + Octahedron Constructors and Setting Functions: Truncated + Octahedron Constructors and Setting Functions. + + +File: 3DLDF.info, Node: Utility Functions, Next: Adding a File, Prev: Polyhedron Reference, Up: Top + +Utility Functions +***************** + + - Function: double trunc (double d) + Defined in `pspglb.web'. For some reason, when I compile 3DLDF + using GNU CC on a PC Pentium II XEON under Linux 2.4.4 i686, the + standard library function `trunc()' is not available. Therefore, + I've had to write one. This is a kludge! Someday, I'll have to + try to find a better solution to this problem. + + - Function: pair solve_quadratic (real A, real B, real C) + Defined in `pspglb.web'. This function tries to find the + solutions S_0 and S_1 to the quadratic equation ax^2 + bx + c + according to the formulae S_0 == -b + sqrt(b^2 - 4ac) / 2a) and + S_1 == -b - sqrt( b^2 - 4ac) / 2a. Let `r' stand for the return + value. If S_0 cannot be found, `r.first' will be `INVALID_REAL', + otherwise S_0. If S_1 cannot be found, `r.second' will be + `INVALID_REAL', otherwise S_1. + + (x + 4)(x + 2) = x^2 + 6x + 8 = 0 + + real_pair r = solve_quadratic(1, 6, 8); + => r.first == -2 + => r.second == -4 + + real_pair r = solve_quadratic(1, -2, 4); + => r.first == INVALID_REAL + => r.second == INVALID_REAL + + +* Menu: + +* Perspective Functions:: + + +File: 3DLDF.info, Node: Perspective Functions, Prev: Utility Functions, Up: Utility Functions + +Perspective Functions +===================== + + - Function: void persp_0 (const real FRONT_CORNER_X, const real + FRONT_CORNER_Z, const real SIDE_LFT, const real SIDE_RT, + const real ANGLE_RT, const real F_2_CV, const real GL_2_CV, + [const real HORIZON_LFT = 6, [real HORIZON_RT = 0, [real + GL_LFT = 0, [real GL_RT = 0]]]]) + Defined in `utility.web'. This function is used for the figure in + *Note The Perspective Projection::, illustrating a perspective + projection as it could be done by hand. It draws a rectangle in + the ground plane and the construction lines used for putting it + into perspective. It also labels the vanishing and measuring + points. + + The arguments: + `CONST REAL' FRONT_CORNER_X + The x-coordinate of the front corner of the rectangle. + + `CONST REAL' FRONT_CORNER_Z + The z-coordinate of the front corner of the rectangle. + + `CONST REAL' SIDE_LFT + The length of the left side of the rectangle. + + `CONST REAL' SIDE_RT + The length of the right side of the rectangle. + + `CONST REAL' ANGLE_RT + The angle at which the right side of the rectangle recedes to + the horizon. + + `CONST REAL' F_2_CV + The distance from the focus to the center of vision. + + `CONST REAL' GL_2_CV + The distance of the ground line to the center of vision. + + `CONST REAL' HORIZON_LFT + Default: 6. The length of the horizon line leftwards of the + center of vision. + + `REAL' HORIZON_RT + Default: 0. The length of the horizon line rightwards of the + center of vision. + + `REAL' GL_LFT + Default: 0. The length of the ground line leftwards of the + line from the focus to the center of vision. + + `REAL' GL_RT + Default: 0. The length of the ground line rightwards of the + line from the focus to the center of vision. + + Example: + + persp_0(3, 2, 10, 5, 47.5, 7, 5, 8.5, 9.5, 8.5, 9.5); + + [Figure 199 not displayed.] + + + +File: 3DLDF.info, Node: Adding a File, Next: Future Plans, Prev: Utility Functions, Up: Top + +Adding a File +************* + + Version 1.1.1 was the first version of 3DLDF since it became a GNU +package (the current version is 1.1.5.1). In previous versions, +recompilation was controlled by an auxilliary program, which I wrote in +C++ using CWEB. However, in the course of making 3DLDF conformant to +the GNU Coding Standards(1), this has been changed. Recompilation is +now controlled by `make', as is customary. The chapter "Compiling" in +previous editions of this manual, is therefore no longer needed. + + Nonetheless, using CWEB still has consequences for the way +recompilation must be handled, and it was fairly tricky getting `make' +to work for 3DLDF. Users who only put code in `main.web' and/or change +code in existing files won't have to worry about this; for others, this +chapter explains how to add files to 3DLDF. + + Let's say you want to add a file `widgets.web' that defines a `class +Widget', and that the latter needs access to `class Rectangle', and is +in turn required by `class Ellipse'. Code must be added to +`3DLDF-1.1.5.1/CWEB/Makefile' for ctangling `widgets.web', compiling +`widgets.cxx', and linking `widgets.o' with the other object files to +make the executable `3dldf'. + + The best way to do this is to change +`3DLDF-1.1.5.1/CWEB/Makefile.am' and use Automake to generate a new +`Makefile.in'. Then, `configure' can be used to generate a new +`Makefile'. It would be possible to modify `Makefile' by hand, but I +don't recommend it. The following assumes that the user has access to +Automake. If he or she is using a GNU/Linux system, this is probably +true.(2) + + `widgets.web' must be added between `rectangs.web' and +`ellipses.web' in the following variable declaration in +`3DLDF-1.1.5.1/CWEB/Makefile.am': + + 3dldf_SOME_CWEBS = pspglb.web io.web colors.web transfor.web \ + shapes.web pictures.web points.web \ + lines.web planes.web paths.web curves.web \ + polygons.web rectangs.web ellipses.web \ + circles.web patterns.web solids.web + solfaced.web cuboid.web polyhed.web \ + utility.web parser.web examples.web + + Now, add `widgets.o' between `ellipses.o' and `rectangs.o' in the +following variable declaration: + + 3dldf_OBS_REVERSED = main.o examples.o parser.o utility.o \ + polyhed.o cuboid.o solfaced.o solids.o \ + patterns.o circles.o ellipses.o rectangs.o \ + polygons.o curves.o paths.o \ + planes.o lines.o points.o pictures.o shapes.o + transfor.o colors.o io.o pspglb.o + + `3dldf_OBS_REVERSED' is needed, because 3DLDF fails with a +"Segmentation fault", if the executable is linked using +`$(3dldf_OBJECTS)'. This may cause problems, if `3dldf' isn't built +using the GNU C++ compiler (GCC). + + Now add a target for `widgets.o' between the targets for +`rectangs.o' and `ellipses.o', and add `widgets.tim' after +`rectangs.tim' in the list of prerequisites for `ellipses.o': + + rectangs.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.cxx + + ellipses.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.tim ellipses.cxx + + This is the result: + rectangs.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.cxx - Everyone is permitted to copy and distribute verbatim copies - of this license document, but changing it is not allowed. + widgets.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.tim \ + widgets.cxx + + ellipses.o: loader.tim pspglb.tim io.tim colors.tim transfor.tim \ + shapes.tim pictures.tim points.tim lines.tim planes.tim \ + paths.tim curves.tim polygons.tim rectangs.tim widgets.tim \ + ellipses.cxx + + In addition, `widgets.tim' must be added to the list of +prerequisites in all of the following targets up to and including +`examples.o'. + + ---------- Footnotes ---------- + + (1) The GNU Coding Standards are available at +`http://www.gnu.org/prep/standards_toc.html'. + + (2) Automake is available for downloading from +`http://ftp.gnu.org/gnu/automake/'. The Automake website is at +`http://www.gnu.org/software/automake/'. + + +File: 3DLDF.info, Node: Future Plans, Next: Changes, Prev: Adding a File, Up: Top + +Future Plans +************ + + 3DLDF is a work-in-progress. In fact, it can never be finished, +because the supply of interesting geometric constructions is +inexhaustible. However, presently 3DLDF still has a number of major +gaps. + + If you're interesting in contributing to 3DLDF, with respect to one +of the topics below and in the following sections, or if you have ideas +of your own, see *Note Contributing to 3DLDF::. + + * Input routine. The lack of one is the most significant defect in + 3DLDF, as mentioned in *Note No Input Routine::. + + * Port to other platforms. *Note Ports::. + +* Menu: + +* Geometry:: +* Curves and Surfaces:: +* Shadows:: +* Multi-Threading:: + + +File: 3DLDF.info, Node: Geometry, Next: Curves and Surfaces, Prev: Future Plans, Up: Future Plans + +Geometry +======== + + 3DLDF currently provides a set of basic plane and solid geometrical +figures. However, some important ones are still missing. There are +many useful geometrical data types and functions whose implementation +would require no more than elementary geometry. + + * Add constructors with a normal vector argument rather than angles + of rotation about the main axes. + + * I have started defining `class Triangle', which can be used for + calculating triangle solutions. - 0. PREAMBLE + * Add a class `Conic_Section' and derive `Ellipse' from it. This + will be the first case of "multiple inheritance"(1) in 3DLDF, + since `Ellipse' is already derived from `Path'. *Note Ellipse + Reference::. Add the classes `Parabola' and `Hyperbola'. - The purpose of this License is to make a manual, textbook, or other - functional and useful document "free" in the sense of freedom: to - assure everyone the effective freedom to copy and redistribute it, - with or without modifying it, either commercially or - noncommercially. Secondarily, this License preserves for the - author and publisher a way to get credit for their work, while not - being considered responsible for modifications made by others. - - This License is a kind of "copyleft", which means that derivative - works of the document must themselves be free in the same sense. - It complements the GNU General Public License, which is a copyleft - license designed for free software. - - We have designed this License in order to use it for manuals for - free software, because free software needs free documentation: a - free program should come with manuals providing the same freedoms - that the software does. But this License is not limited to - software manuals; it can be used for any textual work, regardless - of subject matter or whether it is published as a printed book. - We recommend this License principally for works whose purpose is - instruction or reference. - - 1. 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A copy of the license is included in the section entitled - ``GNU Free Documentation License''. - - If you have Invariant Sections, Front-Cover Texts and Back-Cover -Texts, replace the "with...Texts." line with this: - - with the Invariant Sections being LIST THEIR TITLES, with - the Front-Cover Texts being LIST, and with the Back-Cover Texts - being LIST. - - If you have Invariant Sections without Cover Texts, or some other -combination of the three, merge those two alternatives to suit the -situation. - - If your document contains nontrivial examples of program code, we -recommend releasing these examples in parallel under your choice of -free software license, such as the GNU General Public License, to -permit their use in free software. + * Add more functions for finding the intersections of objects of + various types, starting with the plane figures. In particular, I + believe I've found an algebraic solution for the intersection of + an `Ellipse' and a `Circle' in a plane, but I haven't had a chance + to try implementing it yet. + + If this works, I think it will make it possible to find the + intersection of two coplanar ellipses algebraically, because it + will be possible to transform them both such that one of them + becomes circular. + + * Class `Octahedron' will complete the set of regular Platonic + polyhedra. + + * Add classes for the Kepler-Poinsot polyhedra, the semi-regular + Archimedean polyhedra, the dual solids, the stellated Archimedean + polyhedra, and the regular compounds.(2) + + * Add class `Ellipsoid' and a derived class `Sphere'. + + * Improve the specification of `Solid' and `Solid_Faced'. In + particular, it would help to store the vertices of `Polyhedra' as + individual `Points', rather than using `Reg_Polygons'. I'd also + like to find a better way of generating `Solids', without using + rotations, if possible. + + + ---------- Footnotes ---------- + + (1) Stroustrup, `The C++ Programming Language', section 15.2 +"Multiple Inheritance", pp. 390-92. + + (2) Cundy and Rollet, `Mathematical Models', Chapter 3, "Polyhedra", +pp. 76-160. + + +File: 3DLDF.info, Node: Curves and Surfaces, Next: Shadows, Prev: Geometry, Up: Future Plans + +Curves and Surfaces +=================== + + 3D modelling software usually supports the creation and manipulation +of various kinds of "spline curves": "Be'zier curves", "B-splines", and +"non-uniform rational B-splines" or "NURBS". These curves can be used +for generating surfaces.(1) + + `paths' in Metafont and MetaPost are Be'zier curves. It would be +possible to implement three-dimensional Be'zier curves in 3DLDF, but +unfortunately they are not "projectively invariant": + + Let c_0 represent a Be'zier curve in three dimensions, P the control +points of c_0, and t a projection transformation. Further, let Q +represent the points generated from applying t to P, and c_1 the curve +generated from Q. Finally, let R represent the points generated from +applying t to all of the points on c_0, and c_2 the curve through R: +c_1 \not\equiv c_2. + + NURBS, on the other hand, are projectively invariant,(2) so I will +probably concentrate on implementing them. On the other hand, it would +be nice to be able to implement Metafont's way of specifying `paths' +using ``curl'', ``tension'', and ``dir'' in 3DLDF. This may prove to +be difficult or impossible. I do not yet know whether Metafont's +`path' creation algorithm can be generalized to three dimensions.(3) + + Curves and surfaces are advanced topics, so it may be a while before +I implement them in 3DLDF. + + ---------- Footnotes ---------- + + (1) Huw Jones, Computer Graphics through Key Mathematics, and David +Salomon, Computer Graphics and Geometric Modeling, are my main sources +of information about spline curves. + + (2) Jones, Huw. Computer Graphics through Key Mathematics, p. 282. + + (3) Knuth, Donald Ervin. The METAFONTbook, p. 130, and Hobby, John +D. Smooth, Easy to Compute Interpolating Splines. Discrete and +Computational Geometery 1(2). + + +File: 3DLDF.info, Node: Shadows, Next: Multi-Threading, Prev: Curves and Surfaces, Up: Future Plans + +Shadows, Reflections, and Rendering +=================================== + + Shadows and reflections are closely related to transformations and +projections. A shadow is the projection of the outline of an object +onto a surface or surfaces, and reflection in a plane is an affine +transformation. + + 3D rendering software generally implements shadows, or more +generally, "shading", reflections, and certain other effects using +methods involving the calculation of individual pixel values. Surface +hiding is also often implemented at the pixel level. 3DLDF does no +scan converting ((*note Accuracy::), and hence no calculation of pixel +values at all, so these methods cannot be used in 3DLDF at present. + + However, it is possible to define functions for generating shadows +and reflections within 3DLDF by other means. + + I have defined the function `Point::reflect()' for reflecting a +`Point' in a `Plane', and have begun definining versions for other +classes. + + However, in order for reflections to work, I must define functions +for breaking up objects into smaller units. This is also necessary for +surface hiding to work properly. + + For MetaPost output, I will have to implement shadows, reflections, +and surface hiding in this way. However, 3DLDF could be made to produce +output in other formats. There are two possibilities: implementing +rendering functionality within 3DLDF, or interfacing to existing +rendering software. If I decide to do the latter, there are again two +possibilities: having 3DLDF write output in a format that a renderer +can input, or linking to a library supplied by a rendering package. + + I haven't yet decided which course to pursue. However, in the long +run, I'd like it to be possible to use 3DLDF for fancier graphics than +is currently possible using MetaPost and PostScript alone. + + +File: 3DLDF.info, Node: Multi-Threading, Prev: Shadows, Up: Future Plans + +Multi-Threading +=============== + + When 3DLDF is run, there is only one thread of execution. However, +it could benefit from the use of multiple threads. In particular, it +may be faster and more efficient to have `Picture::output()' run in its +own thread. In this case, it will no longer be possible to share +`current_picture' among figures. + + It may also be worthwhile to execute the code for "figures", i.e., +the code between `beginfig()' and `endfig()', inclusive, in their own +threads. This will require some changes in the way data are handled. +For example, if non-constant objects are shared among figures, there +may be no advantage to multi-threading because of the need to +coordinate the access of the threads to the objects. If threads are +used, then non-constant objects should be declared locally within the +figure. They may be locally declared copies of global objects. +Alternatively, `beginfig()' could be changed so that objects could be +passed to it as arguments, perhaps as a `vector' and/or a +`vector'.  -File: 3DLDF.info, Node: Data Type and Variable Index, Next: Function Index, Prev: GNU Free Documentation License, Up: Top +File: 3DLDF.info, Node: Changes, Next: Bibliography, Prev: Future Plans, Up: Top + +Changes +******* -Data Type and Variable Index -**************************** +Updated 16 January 2004. * Menu: -* angle: Focus Data Members. -* angle_hex_hex: Truncated Octahedron Data Members. -* angle_hex_square: Truncated Octahedron Data Members. -* arrow: Path Data Members. -* axis: Focus Data Members. -* axis_h <1>: Ellipse Data Members. -* axis_h: Rectangle Data Members. -* axis_v <1>: Ellipse Data Members. -* axis_v: Rectangle Data Members. -* AXON: Namespace Projections. -* background_color: Namespace Colors. -* background_color_vector: Namespace Colors. -* black: Namespace Colors. -* blue: Namespace Colors. -* blue_part: Color Data Members. -* blue_violet: Namespace Colors. -* bool_pair: Typedefs and Utility Structures. -* bool_point: Point Typedefs and Utility Structures. -* bool_point_pair: Point Typedefs and Utility Structures. -* bool_point_quadruple: Point Typedefs and Utility Structures. -* bool_real: Typedefs and Utility Structures. -* bool_real_point: Point Typedefs and Utility Structures. -* center <1>: Solid Data Members. -* center <2>: Regular Closed Plane Curve Data Members. -* center: Polygon Data Members. -* CIRCLE: Solid Data Members. -* Circle <1>: Circle Reference. -* Circle: Plane Figures. -* circles: Solid Data Members. -* Color: Color Reference. -* connectors: Path Data Members. -* Cuboid <1>: Cuboid Reference. -* Cuboid: Cuboid Getstart. -* CURR_Y: Point Data Members. -* CURR_Z: Point Data Members. -* cyan: Namespace Colors. -* cycle_switch: Path Data Members. -* dashed: Path Data Members. -* default_background: Namespace Colors. -* default_color: Namespace Colors. -* default_color_vector: Namespace Colors. -* default_focus: Focus Global Variables. -* DEFAULT_NUMBER_OF_POINTS: Ellipse Data Members. -* depth: Cuboid Data Members. -* dihedral_angle <1>: Icosahedron Data Members. -* dihedral_angle <2>: Dodecahedron Data Members. -* dihedral_angle: Tetrahedron Data Members. -* direction <1>: Line Data Members. -* direction: Focus Data Members. -* distance <1>: Planes Data Members. -* distance: Focus Data Members. -* do_help_lines: Path Data Members. -* do_labels: Picture Data Members. -* DO_LABELS: Label Data Members. -* do_output <1>: Solid Data Members. -* do_output <2>: Path Data Members. -* do_output: Point Data Members. -* Dodecahedron <1>: Dodecahedron. -* Dodecahedron: Dodecahedron Getstart. -* dot: Label Data Members. -* DRAW: Shape Data Members. -* draw_color: Path Data Members. -* DRAWDOT: Shape Data Members. -* drawdot_color: Point Data Members. -* drawdot_value: Point Data Members. -* edge_radius: Polyhedron Data Members. -* edges: Solid_Faced Data Members. -* ELLIPSE: Solid Data Members. -* Ellipse <1>: Ellipse Reference. -* Ellipse: Plane Figures. -* ellipses: Solid Data Members. -* face_radius: Polyhedron Data Members. -* faces: Solid_Faced Data Members. -* FILL: Shape Data Members. -* fill_color: Path Data Members. -* fill_draw_value: Path Data Members. -* FILLDRAW: Shape Data Members. -* Focus: Focus Reference. -* focus: Focuses Getstart. -* focus0: Ellipse Data Members. -* focus1: Ellipse Data Members. -* gray: Namespace Colors. -* green: Namespace Colors. -* green_part: Color Data Members. -* green_yellow: Namespace Colors. -* height: Cuboid Data Members. -* help_color <1>: Path Data Members. -* help_color: Namespace Colors. -* help_color_vector: Namespace Colors. -* help_dash_pattern: Path Data Members. -* hexagon_radius: Truncated Octahedron Data Members. -* Icosahedron <1>: Icosahedron. -* Icosahedron: Icosahedron Getstart. -* IDENTITY_TRANSFORM: Transform Global Variables and Constants. -* in_stream: I/O Global Variables. -* internal_angle: Regular Polygon Data Members. -* INVALID_BOOL_POINT: Point Global Constants and Variables. -* INVALID_BOOL_POINT_PAIR: Point Global Constants and Variables. -* INVALID_BOOL_POINT_QUADRUPLE: Point Global Constants and Variables. -* INVALID_BOOL_REAL_POINT: Point Global Constants and Variables. -* INVALID_LINE: Line Global Constants. -* INVALID_PLANE: Planes Global Constants. -* INVALID_POINT: Point Global Constants and Variables. -* INVALID_REAL: Global Constants and Variables. -* INVALID_REAL_PAIR: Global Constants and Variables. -* INVALID_REAL_SHORT: Global Constants and Variables. -* INVALID_TRANSFORM: Transform Global Variables and Constants. -* ISO: Namespace Projections. -* Label: Label Reference. -* labels: Picture Data Members. -* light_gray: Namespace Colors. -* Line: Line Reference. -* line_switch: Path Data Members. -* linear_eccentricity: Ellipse Data Members. -* magenta: Namespace Colors. -* matrix: Transform Data Members. -* Matrix: Typedefs and Utility Structures. -* MAX_REAL: Global Constants and Variables. -* MAX_REAL_SQRT: Global Constants and Variables. -* MAX_Z: Namespace Sorting. -* MEAN_Z: Namespace Sorting. -* measurement_units: Point Data Members. -* measurement_units (Point): Declaring and Initializing Points. -* MIN_Z: Namespace Sorting. -* name: Color Data Members. -* NO_SORT: Namespace Sorting. -* normal: Planes Data Members. -* null_coordinates: Global Constants and Variables. -* number_of_points: Regular Closed Plane Curve Data Members. -* number_of_polygon_types: Polyhedron Data Members. -* numerical_eccentricity: Ellipse Data Members. -* on_free_store <1>: Solid Data Members. -* on_free_store <2>: Rectangle Data Members. -* on_free_store <3>: Regular Polygon Data Members. -* on_free_store <4>: Path Data Members. -* on_free_store <5>: Point Data Members. -* on_free_store: Color Data Members. -* orange: Namespace Colors. -* orange_red: Namespace Colors. -* origin: Point Global Constants and Variables. -* out_stream <1>: I/O Global Variables. -* out_stream: Pictures. -* PARALLEL_X_Y: Namespace Projections. -* PARALLEL_X_Z: Namespace Projections. -* PARALLEL_Z_Y: Namespace Projections. -* PATH: Solid Data Members. -* Path <1>: Path Reference. -* Path: Paths. -* paths: Solid Data Members. -* pen <1>: Path Data Members. -* pen: Point Data Members. -* pentagon_radius: Dodecahedron Data Members. -* persp: Focus Data Members. -* PERSP: Namespace Projections. -* PI: Global Constants and Variables. -* Picture <1>: Picture Global Variables. -* Picture <2>: Picture Reference. -* Picture: Pictures. -* pink: Namespace Colors. -* Plane: Plane Reference. -* point: Planes Data Members. -* Point <1>: Point Reference. -* Point: Declaring and Initializing Points. -* Point::measurement_units: Declaring and Initializing Points. -* Point::projective_coordinates: Declaring and Initializing Points. -* Point::user_coordinates: Declaring and Initializing Points. -* Point::view_coordinates: Declaring and Initializing Points. -* Point::world_coordinates: Declaring and Initializing Points. -* point_pair: Point Typedefs and Utility Structures. -* points: Path Data Members. -* Polygon <1>: Polygon Reference. -* Polygon: Plane Figures. -* Polyhedron <1>: Polyhedron Reference. -* Polyhedron: Polyhedron Getstart. -* position <1>: Line Data Members. -* position <2>: Focus Data Members. -* position: Label Data Members. -* projective_coordinates: Point Data Members. -* projective_coordinates (Point): Declaring and Initializing Points. -* projective_extremes <1>: Solid Data Members. -* projective_extremes <2>: Path Data Members. -* projective_extremes: Point Data Members. -* pt: Label Data Members. -* purple: Namespace Colors. -* radius <1>: Circle Data Members. -* radius: Regular Polygon Data Members. -* real: Typedefs and Utility Structures. -* real_pair: Typedefs and Utility Structures. -* real_short: Typedefs and Utility Structures. -* real_triple: Typedefs and Utility Structures. -* RECTANGLE: Solid Data Members. -* Rectangle <1>: Rectangle Reference. -* Rectangle: Plane Figures. -* rectangles: Solid Data Members. -* red: Namespace Colors. -* red_part: Color Data Members. -* Reg_Cl_Plane_Curve <1>: Regular Closed Plane Curve Reference. -* Reg_Cl_Plane_Curve: Plane Figures. -* REG_POLYGON: Solid Data Members. -* Reg_Polygon <1>: Regular Polygon Reference. -* Reg_Polygon: Plane Figures. -* reg_polygons: Solid Data Members. -* Shape: Shape Reference. -* shapes: Picture Data Members. -* short: Regular Polygon Data Members. -* Solid: Solid Reference. -* Solid_Faced: Faced Solid Reference. -* Tetrahedron <1>: Tetrahedron. -* Tetrahedron: Tetrahedron Getstart. -* tex_stream: I/O Global Variables. -* text: Label Data Members. -* transform <1>: Focus Data Members. -* transform <2>: Point Data Members. -* transform: Picture Data Members. -* Transform <1>: Transform Reference. -* Transform: Transforms. -* triangle_radius <1>: Icosahedron Data Members. -* triangle_radius: Tetrahedron Data Members. -* Trunc_Octahedron: Truncated Octahedron. -* Truncated Octahedron: Truncated Octahedron. -* UNDRAW: Shape Data Members. -* UNDRAWDOT: Shape Data Members. -* UNFILL: Shape Data Members. -* UNFILLDRAW: Shape Data Members. -* up: Focus Data Members. -* use_name: Color Data Members. -* user_coordinates: Point Data Members. -* user_coordinates (Point): Declaring and Initializing Points. -* user_transform: Transform Global Variables and Constants. -* vertex_radius: Polyhedron Data Members. -* vertices: Solid_Faced Data Members. -* view_coordinates: Point Data Members. -* view_coordinates (Point): Declaring and Initializing Points. -* violet: Namespace Colors. -* violet_red: Namespace Colors. -* white: Namespace Colors. -* width: Cuboid Data Members. -* world_coordinates: Point Data Members. -* world_coordinates (Point): Declaring and Initializing Points. -* yellow: Namespace Colors. -* yellow_green: Namespace Colors. +* Changes in 3DLDF 1.1.5.1:: +* Changes in 3DLDF 1.1.5:: +* Changes in 3DLDF 1.1.4.2:: +* Changes in 3DLDF 1.1.4.1:: +* Changes in 3DLDF 1.1.4:: +* Initial version:: + + +File: 3DLDF.info, Node: Changes in 3DLDF 1.1.5.1, Next: Changes in 3DLDF 1.1.5, Prev: Changes, Up: Changes + +3DLDF 1.1.5.1 +============= + + * Added missing Texinfo files to the `3dldf_TEXINFOS' variable in + `3DLDF-1.1.5.1/DOC/TEXINFO/Makefile.am', and reordered the + filenames. + + * Changed the names of the PNG (Portable Network Graphics) files + included in the HTML version of this manual. Changed the names in + the commands for including these files in the Texinfo files. I + wasn't able to write some of the files with the old names to a + CD-R (Compact Disk, Recordable). + + +File: 3DLDF.info, Node: Changes in 3DLDF 1.1.5, Next: Changes in 3DLDF 1.1.4.2, Prev: Changes in 3DLDF 1.1.5.1, Up: Changes + +3DLDF 1.1.5 +=========== + + In release 1.1.5, I've tied up some loose ends. I wanted to do this +before starting on the input routine. + + * Added `const real' STEP argument to the version of + `Ellipse::intersection_points()' that takes an `Ellipse' argument. + *Note Ellipse Reference; Intersections: Ellipse Intersections. + + * It is now possible to "typedef" `real' to either `float' or + `double'. This means that `real' can now be made a synonym for + either `float' or `double' by using a `typedef' declaration. + `real' is typedeffed to `float' by default. + + * Added `const bool ldf_real_float' and `extern const bool + ldf_real_double' for use in non-conditionally compiled code. They + are set according to the values of `LDF_REAL_FLOAT' and + `LDF_REAL_DOUBLE'. + + * `Transform::epsilon()' and `Point::epsilon()' now return different + values, depending on the values of the preprocessor macros + `LDF_REAL_FLOAT' and `LDF_REAL_DOUBLE'. I have not yet tested + whether good values are returned when `real' is `double'. + + * `MAX_REAL' and `MAX_REAL_SQRT' are no longer constants. Their + values are set at the beginning of `main()'. However, users + should not change their values. `MAX_REAL' is the second-largest + `float' or `double' on a given machine. This now works for all + common architectures. + + * Added `namespace System' containing the following functions: + `get_endianness()', `is_big_endian()', `is_little_endian()', + `get_register_width()', `is_32_bit()', `is_64_bit()', and the + template function `get_second_largest()'. + + `namespace System' and its functions are documented in + `system.texi', which is new in edition 1.1.5.1. + + * Replaced the various `create_new_'`()' functions with the + template function `create_new()'. The latter is documented in + `creatnew.texi', which is new in edition 1.1.5.1. + + * Added the file `3DLDF-1.1.5.1/CWEB/cnepspng.el' to the + distribution. It contains the definitions of the Emacs-Lisp + functions `convert-eps' and `convert-eps-loop'. *Note Running + 3DLDF; Converting EPS Files; Emacs-Lisp Functions: Converting EPS + Files ELISP. + + * Added the files `3DLDF-1.1.5.1/CWEB/exampman.web' and + `3DLDF-1.1.5.1/CWEB/examples.mp' to the distribution. They + contain the C++ and MetaPost code, respectively, for generating + the illustrations in this manual. + + + +File: 3DLDF.info, Node: Changes in 3DLDF 1.1.4.2, Next: Changes in 3DLDF 1.1.4.1, Prev: Changes in 3DLDF 1.1.5, Up: Changes + +3DLDF 1.1.4.2 +============= + + * The illustrations in the HTML output are now scaled to `magstep3'. + + +File: 3DLDF.info, Node: Changes in 3DLDF 1.1.4.1, Next: Changes in 3DLDF 1.1.4, Prev: Changes in 3DLDF 1.1.4.2, Up: Changes + +3DLDF 1.1.4.1 +============= + + * The HTML output now includes illustrations. + + +File: 3DLDF.info, Node: Changes in 3DLDF 1.1.4, Next: Initial version, Prev: Changes in 3DLDF 1.1.4.1, Up: Changes + +3DLDF 1.1.4 +=========== + + * `MAX_REAL' is now the second largest float value. However, the + calculation is system dependent, and will only work on 32-bit + little-endian architectures. I will start working on porting this + soon. + + * Fixed bug in `tsthdweb', that caused files to be compiled more + often than necessary. It will be necessary to keep an eye on this. + + * Added `Rectangle::is_rectangular()'. + + * Made `mediate()' a member function of `Point'. + + * It is now possible to generate this manual in the Info and HTML + formats. + + +File: 3DLDF.info, Node: Initial version, Prev: Changes in 3DLDF 1.1.4, Up: Changes + +3DLDF 1.1.1 +=========== + + 3DLDF 1.1.1 was the first version of 3DLDF since it became a GNU +package (the current version is 1.1.5.1). It is now conformant to the +GNU Coding Standards, except that a functioning `3DLDF.info' cannot be +generated from `3DLDF.texi'. The distribution now includes a +`configure' script, `Makefile.in' files, and other files generated by +Autoconf and Automake. Recompilation is now handled by `make' rather +than the auxilliary program `3DLDFcpl'. The files `3DLDFcpl.web' and +`3DLDFprc.web' have been removed from the distribution. + + The extension of the C++ files generated by `ctangle' is changed +from `c' to `cxx' before they are compiled. After `ctangle' is run on +a CWEB file, `.c' is compared to the old `.cxx' +using `diff'. Whitespace, comments, and `#line' preprocessor commands +are ignored. The `.c' is only renamed to `.cxx' +and compiled if they differ. This way, changes to the TeX text only in +a CWEB file no longer cause recompilation and relinking. + + The main Texinfo file is now called `3DLDF.texi'. It was formerly +called `3DLDFman.texi'. This is because Automake expects this name. +For this reason, the CWEB file passed as an argument to cweave has been +renamed `3DLDFprg.web'. It was formerly called `3DLDF.web'. + + +File: 3DLDF.info, Node: Bibliography, Next: GNU Free Documentation License, Prev: Changes, Up: Top + +Bibliography +************ + + Cundy, H. Martyn and A.P. Rollet. Mathematical Models. Oxford 1961. +Oxford University Press. + + Unfortunately out of print. + + +Finston, Laurence D. 3DLDF: The Program. Go"ttingen 2003. + +Fischer, Gerd. Ebene algebraische Kurven. Vieweg Studium. Aufbaukurs +Mathematik. Friedr. Vieweg & Sohn Verlagsgesellschaft mbH. +Braunschweig/Wiesbaden 1994. + +Gill, Robert W. Creative Perspective. London 1975. Thames and Hudson +Ltd. ISBN 0-500-27056-2. + +Harbison, Samuel P., and Guy L. Steele Jr. C, A Reference Manual. +Prentice Hall. Englewood Cliffs, New Jersey 1995. +ISBN 0-13-326232-4 {Case}. ISBN~0-13-326224-3 {Paperback}. + +Hobby, John D. Smooth, Easy to Compute Interpolating Splines. +Discrete and Computational Geometery 1(2). Springer-Verlag. New York +1986. + +Hobby, John D. A User's Manual for MetaPost. AT & T Bell Laboratories. +Murray Hill, NJ. No date. + +Jones, Huw. Computer Graphics through Key Mathematics. +Springer-Verlag London Limited 2001. ISBN 1-85233-422-3. + +Knuth, Donald Ervin. Metafont: The Program. Computers and +Typesetting; D. Addison Wesley Publishing Company, Inc. Reading, +Massachusetts 1986. ISBN 0-201-13438-1. + +Knuth, Donald Ervin. The METAFONTbook. Computers and Typesetting; C. +Addison Wesley Publishing Company, Inc. Reading, Massachusetts 1986. + +Knuth, Donald Ervin. TeX: The Program. Computers and Typesetting; B. +Addison Wesley Publishing Company, Inc. Reading, Massachusetts 1986. +ISBN 0-201-13437-3. + +Knuth, Donald E. The TeXbook. Computers and Typesetting; A. Addison +Wesley Publishing Company, Inc. Reading, Massachusetts 1986. + +Knuth, Donald E. and Silvio Levy. The CWEB System of Structured +Documentation. Version 3.64--February 2002. + +Rokicki, Tomas. Dvips: A DVI-to-PostScript Translator for version +5.66a. February 1997. `http://dante.ctan.org/CTAN/dviware/dvips/' + +Salomon, David. Computer Graphics and Geometric Modeling. Berlin 1999. +Springer-Verlag. ISBN: 0-387-98682-0. + +Stallman, Richard M. and Roland McGrath. GNU Make. A Program for +Directing Recompilation. make Version 3.79. Boston 2000. Free +Software Foundation, Inc. ISBN: 1-882114-80-9. + +Stallman, Richard M. Using and Porting the GNU Compiler Collection. +For GCC Version 3.3.2. Boston 2003. Free Software Foundation, Inc. + +Stroustrup, Bjarne. The C++ Programming Language. Special Edition. +Reading, Massachusetts 2000. Addison-Wesley. ISBN 0-201-70073-5. + +Stroustrup, Bjarne. The Design and Evolution of C++ . Reading, +Massachusetts 1994. Addison-Wesley Publishing Company. +ISBN 0-201-54330-3. + +Vredeman de Vries, Jan. Perspective. New York 1968. Dover +Publications, Inc. Standard Book Number: 486-21086-4. + + The beautiful perspective constructions in this volume are taken from + the original work, first published by Henricus Hondius in Leiden in 1604 + and 1605. + + +White, Gwen. Perspective. A Guide for Artists, Architects and +Designers. London 1968 and 1982. B T Batsford Ltd. +ISBN 0-7134-3412-0. diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-12 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-12 --- 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-12 2003-12-10 18:44:55.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-12 2004-01-16 19:03:28.000000000 +0100 @@ -1,11 +1,11 @@ This is 3DLDF.info, produced by makeinfo version 4.5 from 3DLDF.texi. -This is the 3DLDF User and Reference Manual, edition 1.1.4 for 3DLDF -1.1.4. This manual was last updated on 10 December 2003. 3DLDF is a +This is the 3DLDF User and Reference Manual, edition 1.1.5.1 for 3DLDF +1.1.5.1. This manual was last updated on 16 January 2004. 3DLDF is a GNU package for three-dimensional drawing with MetaPost output. The author is Laurence D. Finston. - Copyright (C) 2003 Laurence D. Finston. + Copyright (C) 2003, 2004 Laurence D. Finston. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, @@ -20,484 +20,685 @@ END-INFO-DIR-ENTRY  -File: 3DLDF.info, Node: Function Index, Next: Concept Index, Prev: Data Type and Variable Index, Up: Top +File: 3DLDF.info, Node: GNU Free Documentation License, Next: Data Type and Variable Index, Prev: Bibliography, Up: Top -Function Index -************** +GNU Free Documentation License +****************************** -* Menu: - -* align_with_axis <1>: Aligning Paths with an Axis. -* align_with_axis: Alignment with an Axis for Transforms. -* angle: Vector Operations. -* angle_point <1>: Returning Elements and Information for Ellipses. -* angle_point: Querying Regular Closed Plane Curves. -* append: Appending to Paths. -* apply_transform <1>: Applying Transformations to Solids. -* apply_transform <2>: Applying Transformations to Paths. -* apply_transform <3>: Applying Transformations to Points. -* apply_transform: Applying Transformations to Shapes. -* beginfig: I/O Functions. -* bool_point: Point Typedefs and Utility Structures. -* bool_point::operator=: Point Typedefs and Utility Structures. -* bool_point_quadruple: Point Typedefs and Utility Structures. -* bool_point_quadruple::operator=: Point Typedefs and Utility Structures. -* bool_real_point: Point Typedefs and Utility Structures. -* bool_real_point::operator=: Point Typedefs and Utility Structures. -* Circle: Circle Constructors and Setting Functions. -* clean <1>: Modifying Points. -* clean: Cleaning Transforms. -* clear <1>: Clearing Solids. -* clear <2>: Clearing Paths. -* clear <3>: Modifying Points. -* clear <4>: Modifying Pictures. -* clear: Clearing Shapes. -* Color: Color Constructors and Setting Functions. -* corner: Returning Points for Rectangles. -* create_new_circle: Circle Constructors and Setting Functions. -* create_new_color: Color Constructors and Setting Functions. -* create_new_cuboid: Cuboid Constructors and Setting Functions. -* create_new_ellipse: Ellipse Constructors and Setting Functions. -* create_new_path: Path Constructors and Setting Functions. -* create_new_point: Point Constructors and Setting Functions. -* create_new_rectangle: Rectangle Constructors and Setting Functions. -* create_new_reg_polygon: Regular Polygon Constructors and Setting Functions. -* create_new_solid: Solid Constructors and Setting Functions. -* cross_product: Vector Operations. -* Cuboid: Cuboid Constructors and Setting Functions. -* define_color_mp: Defining and Initializing Colors. -* do_transform: Performing Transformations on Ellipses. -* Dodecahedron: Dodecahedron Constructors and Setting Functions. -* dot_product: Vector Operations. -* dotlabel <1>: Labeling Ellipses. -* dotlabel <2>: Labelling Paths. -* dotlabel: Labelling Points. -* draw <1>: Drawing and Filling Solids. -* draw <2>: Drawing and Filling Paths. -* draw: Point Drawing Functions. -* draw_axes: Drawing and Filling Paths. -* draw_help <1>: Drawing and Filling Paths. -* draw_help: Point Drawing Functions. -* draw_in_circle: Circles for Regular Polygons. -* draw_in_ellipse: Ellipses for Rectangles. -* draw_in_rectangle: Rectangles for Ellipses. -* draw_net <1>: Icosahedron Net. -* draw_net <2>: Dodecahedron Net. -* draw_net: Tetrahedron Net. -* draw_out_circle: Circles for Regular Polygons. -* draw_out_ellipse: Ellipses for Rectangles. -* draw_out_rectangle: Rectangles for Ellipses. -* drawarrow <1>: Drawing and Filling Paths. -* drawarrow: Point Drawing Functions. -* drawdot: Point Drawing Functions. -* Ellipse: Ellipse Constructors and Setting Functions. -* endfig: I/O Functions. -* epicycloid_pattern_1: Epicycloids. -* epsilon <1>: Returning Information for Points. -* epsilon: Returning Information for Transforms. -* extract <1>: Outputting Solids. -* extract <2>: Outputting Paths. -* extract <3>: Outputting Points. -* extract: Outputting Shapes. -* fill <1>: Drawing and Filling Solids. -* fill: Drawing and Filling Paths. -* filldraw <1>: Drawing and Filling Solids. -* filldraw: Drawing and Filling Paths. -* Focus: Focus Constructors and Setting Functions. -* get_all_coords: Returning Coordinates. -* get_axis_h <1>: Returning Elements and Information for Ellipses. -* get_axis_h: Querying Rectangles. -* get_axis_v <1>: Returning Elements and Information for Ellipses. -* get_axis_v: Querying Rectangles. -* get_blue_part: Querying Colors. -* get_center <1>: Returning Elements and Information Solids. -* get_center <2>: Returning Elements and Information for Ellipses. -* get_center: Querying Polygons. -* get_circle_center: Getting Shape Centers Solids. -* get_circle_ptr: Getting Shapes Solids. -* get_coefficients <1>: Solving Ellipses. -* get_coefficients: Querying Regular Closed Plane Curves. -* get_coord: Returning Coordinates. -* get_copy <1>: Copying Solids. -* get_copy <2>: Copying Paths. -* get_copy <3>: Copying Points. -* get_copy <4>: Copying Labels. -* get_copy: Copying Shapes. -* get_diameter: Querying Circles. -* get_direction: Querying Focuses. -* get_distance <1>: Planes Returning Information. -* get_distance: Querying Focuses. -* get_element: Querying Transforms. -* get_ellipse_center: Getting Shape Centers Solids. -* get_ellipse_ptr: Getting Shapes Solids. -* get_extremes <1>: Outputting Solids. -* get_extremes <2>: Outputting Paths. -* get_extremes <3>: Outputting Points. -* get_extremes: Outputting Shapes. -* get_focus: Returning Elements and Information for Ellipses. -* get_green_part: Querying Colors. -* get_last_point: Querying Paths. -* get_line <1>: Querying Paths. -* get_line: Points and Lines. -* get_line_switch: Querying Paths. -* get_linear_eccentricity: Returning Elements and Information for Ellipses. -* get_maximum_z <1>: Outputting Solids. -* get_maximum_z <2>: Outputting Paths. -* get_maximum_z <3>: Outputting Points. -* get_maximum_z: Outputting Shapes. -* get_mean_z <1>: Outputting Solids. -* get_mean_z <2>: Outputting Paths. -* get_mean_z <3>: Outputting Points. -* get_mean_z: Outputting Shapes. -* get_minimum_z <1>: Outputting Solids. -* get_minimum_z <2>: Outputting Paths. -* get_minimum_z <3>: Outputting Points. -* get_minimum_z: Outputting Shapes. -* get_name: Querying Colors. -* get_net <1>: Truncated Octahedron Net. -* get_net <2>: Icosahedron Net. -* get_net <3>: Dodecahedron Net. -* get_net: Tetrahedron Net. -* get_normal: Querying Paths. -* get_numerical_eccentricity: Returning Elements and Information for Ellipses. -* get_path: Get Path. -* get_path_ptr: Getting Shapes Solids. -* get_persp: Querying Focuses. -* get_persp_element: Querying Focuses. -* get_plane: Querying Paths. -* get_point: Querying Paths. -* get_position: Querying Focuses. -* get_radius <1>: Querying Circles. -* get_radius: Querying Regular Polygons. -* get_rectangle_center: Getting Shape Centers Solids. -* get_rectangle_ptr: Getting Shapes Solids. -* get_red_part: Querying Colors. -* get_reg_polygon_center: Getting Shape Centers Solids. -* get_reg_polygon_ptr: Getting Shapes Solids. -* get_shape_center: Getting Shape Centers Solids. -* get_shape_ptr: Getting Shapes Solids. -* get_size: Querying Paths. -* get_transform <1>: Querying Focuses. -* get_transform: Querying Points. -* get_transform_element: Querying Focuses. -* get_up: Querying Focuses. -* get_use_name: Querying Colors. -* get_w: Returning Coordinates. -* get_x: Returning Coordinates. -* get_y: Returning Coordinates. -* get_z: Returning Coordinates. -* half: Regular Closed Plane Curve Segments. -* hex_pattern_1: Plane Tesselations. -* Icosahedron: Icosahedron Constructors and Setting Functions. -* in_circle: Circles for Regular Polygons. -* in_ellipse: Ellipses for Rectangles. -* in_rectangle: Rectangles for Ellipses. -* initialize_colors: Defining and Initializing Colors. -* initialize_io: I/O Functions. -* intersection_line: Plane Intersections. -* intersection_point <1>: Path Intersections. -* intersection_point <2>: Plane Intersections. -* intersection_point: Point Intersections. -* intersection_points <1>: Circle Intersections. -* intersection_points <2>: Ellipse Intersections. -* intersection_points <3>: Regular Closed Plane Curve Intersections. -* intersection_points: Polygon Intersections. -* inverse: Matrix Inversion. -* is_circular: Querying Circles. -* is_cubic <1>: Querying Ellipses. -* is_cubic: Querying Regular Closed Plane Curves. -* is_cycle: Querying Paths. -* is_elliptical: Querying Ellipses. -* is_identity <1>: Querying Points. -* is_identity: Querying Transforms. -* is_in_triangle: Querying Points. -* is_linear: Querying Paths. -* is_on_free_store <1>: Querying Solids. -* is_on_free_store <2>: Querying Paths. -* is_on_free_store <3>: Querying Points. -* is_on_free_store <4>: Querying Shapes. -* is_on_free_store: Querying Colors. -* is_on_line: Points and Lines. -* is_on_plane: Querying Points. -* is_on_segment: Points and Lines. -* is_planar: Querying Paths. -* is_quadratic <1>: Querying Ellipses. -* is_quadratic: Querying Regular Closed Plane Curves. -* is_quartic <1>: Querying Ellipses. -* is_quartic: Querying Regular Closed Plane Curves. -* is_rectangular: Querying Rectangles. -* kill_labels: Modifying Pictures. -* label <1>: Labeling Ellipses. -* label <2>: Labelling Paths. -* label: Labelling Points. -* Line: Line Constructors. -* location <1>: Returning Elements and Information for Ellipses. -* location: Querying Regular Closed Plane Curves. -* magnitude: Vector Operations. -* mediate: Points and Lines. -* mid_point: Returning Points for Rectangles. -* modify: Modifying Colors. -* operator!= <1>: Planes Operators. -* operator!= <2>: Point Operators. -* operator!=: Color Operators. -* operator&: Path Operators. -* operator&=: Path Operators. -* operator* <1>: Point Operators. -* operator*: Transform Operators. -* operator*= <1>: Solid Operators. -* operator*= <2>: Ellipse Operators. -* operator*= <3>: Polygon Operators. -* operator*= <4>: Path Operators. -* operator*= <5>: Point Operators. -* operator*= <6>: Picture Operators. -* operator*= <7>: Transform Operators. -* operator*=: Shape Operators. -* operator+ <1>: Path Operators. -* operator+: Point Operators. -* operator+= <1>: Path Operators. -* operator+= <2>: Point Operators. -* operator+=: Picture Operators. -* operator-: Point Operators. -* operator-=: Point Operators. -* operator/: Point Operators. -* operator/=: Point Operators. -* operator<< <1>: Outputting Points. -* operator<<: Color Operators. -* operator= <1>: Cuboid Operators. -* operator= <2>: Solid Operators. -* operator= <3>: Circle Operators. -* operator= <4>: Ellipse Operators. -* operator= <5>: Rectangle Operators. -* operator= <6>: Regular Polygon Operators. -* operator= <7>: Planes Operators. -* operator= <8>: Line Operators. -* operator= <9>: Focus Operators. -* operator= <10>: Point Operators. -* operator= <11>: Picture Operators. -* operator= <12>: Transform Operators. -* operator=: Color Operators. -* operator= (for Points): Setting and Assigning to Points. -* operator== <1>: Planes Operators. -* operator== <2>: Point Operators. -* operator==: Color Operators. -* out_circle: Circles for Regular Polygons. -* out_ellipse: Ellipses for Rectangles. -* out_rectangle: Rectangles for Ellipses. -* output <1>: Outputting Solids. -* output <2>: Outputting Paths. -* output <3>: Outputting Points. -* output <4>: Picture Output Functions. -* output <5>: Outputting Labels. -* output: Outputting Shapes. -* Path: Path Constructors and Setting Functions. -* persp_0: Perspective Functions. -* Picture: Picture Constructors. -* Plane: Planes Constructors. -* Point: Point Constructors and Setting Functions. -* Point::intersection_points: Intersections. -* Point::operator=: Setting and Assigning to Points. -* Point::set: Setting and Assigning to Points. -* project <1>: Outputting Paths. -* project: Projecting Points. -* quarter: Regular Closed Plane Curve Segments. -* real_triple: Typedefs and Utility Structures. -* Rectangle: Rectangle Constructors and Setting Functions. -* Reg_Polygon: Regular Polygon Constructors and Setting Functions. -* reset: Resetting Transforms. -* reset_angle: Modifying Focuses. -* reset_transform <1>: Modifying Points. -* reset_transform: Modifying Pictures. -* reverse: Querying Paths. -* rotate <1>: Affine Transformations for Solids. -* rotate <2>: Affine Transformations for Ellipses. -* rotate <3>: Affine Transformations for Polygons. -* rotate <4>: Affine Transformations for Paths. -* rotate <5>: Affine Transformations for Points. -* rotate <6>: Affine Transformations for Pictures. -* rotate <7>: Affine Transformations for Transforms. -* rotate: Affine Transformations for Shapes. -* scale <1>: Affine Transformations for Solids. -* scale <2>: Affine Transformations for Ellipses. -* scale <3>: Affine Transformations for Polygons. -* scale <4>: Affine Transformations for Paths. -* scale <5>: Affine Transformations for Points. -* scale <6>: Affine Transformations for Pictures. -* scale <7>: Affine Transformations for Transforms. -* scale: Affine Transformations for Shapes. -* segment: Regular Closed Plane Curve Segments. -* set <1>: Tetrahedron Constructors and Setting Functions. -* set <2>: Circle Constructors and Setting Functions. -* set <3>: Ellipse Constructors and Setting Functions. -* set <4>: Rectangle Constructors and Setting Functions. -* set <5>: Regular Polygon Constructors and Setting Functions. -* set <6>: Path Constructors and Setting Functions. -* set <7>: Focus Constructors and Setting Functions. -* set <8>: Point Constructors and Setting Functions. -* set: Color Constructors and Setting Functions. -* set (for Points): Setting and Assigning to Points. -* set_blue_part: Modifying Colors. -* set_connectors: Modifying Paths. -* set_cycle: Querying Paths. -* set_dash_pattern: Modifying Paths. -* set_draw_color: Modifying Paths. -* set_element: Setting Values Transforms. -* set_extremes <1>: Outputting Solids. -* set_extremes <2>: Outputting Paths. -* set_extremes <3>: Outputting Points. -* set_extremes: Outputting Shapes. -* set_fill_color: Modifying Paths. -* set_fill_draw_value: Modifying Paths. -* set_green_part: Modifying Colors. -* set_name: Modifying Colors. -* set_on_free_store <1>: Setting Solid Members. -* set_on_free_store <2>: Modifying Paths. -* set_on_free_store <3>: Modifying Points. -* set_on_free_store: Modifying Shapes. -* set_pen: Modifying Paths. -* set_red_part: Modifying Colors. -* set_transform: Modifying Pictures. -* set_use_name: Modifying Colors. -* shear <1>: Affine Transformations for Solids. -* shear <2>: Affine Transformations for Ellipses. -* shear <3>: Affine Transformations for Polygons. -* shear <4>: Affine Transformations for Paths. -* shear <5>: Affine Transformations for Points. -* shear <6>: Affine Transformations for Transforms. -* shear: Affine Transformations for Shapes. -* shift <1>: Affine Transformations for Solids. -* shift <2>: Affine Transformations for Ellipses. -* shift <3>: Affine Transformations for Polygons. -* shift <4>: Affine Transformations for Paths. -* shift <5>: Affine Transformations for Points. -* shift <6>: Affine Transformations for Pictures. -* shift <7>: Affine Transformations for Transforms. -* shift: Affine Transformations for Shapes. -* shift_times <1>: Affine Transformations for Ellipses. -* shift_times <2>: Affine Transformations for Polygons. -* shift_times <3>: Affine Transformations for Paths. -* shift_times <4>: Affine Transformations for Points. -* shift_times: Affine Transformations for Transforms. -* show <1>: Showing Solids. -* show <2>: Showing Paths. -* show <3>: Planes Showing. -* show <4>: Showing. -* show <5>: Showing Focuses. -* show <6>: Showing Points. -* show <7>: Showing Pictures. -* show <8>: Showing Transforms. -* show <9>: Showing Shapes. -* show: Showing Colors. -* show_colors: Showing Paths. -* show_transform <1>: Showing Points. -* show_transform: Showing Pictures. -* size: Querying Paths. -* slope <1>: Querying Paths. -* slope: Points and Lines. -* Solid: Solid Constructors and Setting Functions. -* solve <1>: Solving Ellipses. -* solve: Querying Regular Closed Plane Curves. -* solve_quadratic: Utility Functions. -* subpath: Querying Paths. -* suppress_labels: Picture Output Functions. -* suppress_output <1>: Outputting Solids. -* suppress_output <2>: Outputting Paths. -* suppress_output <3>: Outputting Points. -* suppress_output: Outputting Shapes. -* Tetrahedron: Tetrahedron Constructors and Setting Functions. -* Transform: Transform Constructors. -* trunc: Utility Functions. -* Trunc_Octahedron: Truncated Octahedron Constructors and Setting Functions. -* undraw <1>: Drawing and Filling Solids. -* undraw <2>: Drawing and Filling Paths. -* undraw: Point Drawing Functions. -* undrawdot: Point Drawing Functions. -* unfill <1>: Drawing and Filling Solids. -* unfill: Drawing and Filling Paths. -* unfilldraw <1>: Drawing and Filling Solids. -* unfilldraw: Drawing and Filling Paths. -* unit_vector: Vector Operations. -* unsuppress_labels: Picture Output Functions. -* unsuppress_output <1>: Outputting Solids. -* unsuppress_output <2>: Outputting Paths. -* unsuppress_output: Outputting Shapes. -* void: Outputting Points. -* write_footers: I/O Functions. -* ~Cuboid: Cuboid Constructors and Setting Functions. -* ~Path: Path Destructor. -* ~Point: Point Destructor. -* ~Solid: Solid Destructor. + Version 1.2, November 2002 + Copyright (C) 2000,2001,2002 Free Software Foundation, Inc. + 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA + + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + 0. PREAMBLE + + The purpose of this License is to make a manual, textbook, or other + functional and useful document "free" in the sense of freedom: to + assure everyone the effective freedom to copy and redistribute it, + with or without modifying it, either commercially or + noncommercially. Secondarily, this License preserves for the + author and publisher a way to get credit for their work, while not + being considered responsible for modifications made by others. + + This License is a kind of "copyleft", which means that derivative + works of the document must themselves be free in the same sense. + It complements the GNU General Public License, which is a copyleft + license designed for free software. + + We have designed this License in order to use it for manuals for + free software, because free software needs free documentation: a + free program should come with manuals providing the same freedoms + that the software does. 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FUTURE REVISIONS OF THIS LICENSE + + The Free Software Foundation may publish new, revised versions of + the GNU Free Documentation License from time to time. Such new + versions will be similar in spirit to the present version, but may + differ in detail to address new problems or concerns. See + `http://www.gnu.org/copyleft/'. + + Each version of the License is given a distinguishing version + number. If the Document specifies that a particular numbered + version of this License "or any later version" applies to it, you + have the option of following the terms and conditions either of + that specified version or of any later version that has been + published (not as a draft) by the Free Software Foundation. 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A copy of the license is included in the section entitled + ``GNU Free Documentation License''. + + If you have Invariant Sections, Front-Cover Texts and Back-Cover +Texts, replace the "with...Texts." line with this: + + with the Invariant Sections being LIST THEIR TITLES, with + the Front-Cover Texts being LIST, and with the Back-Cover Texts + being LIST. + + If you have Invariant Sections without Cover Texts, or some other +combination of the three, merge those two alternatives to suit the +situation. + + If your document contains nontrivial examples of program code, we +recommend releasing these examples in parallel under your choice of +free software license, such as the GNU General Public License, to +permit their use in free software.  -File: 3DLDF.info, Node: Concept Index, Prev: Function Index, Up: Top +File: 3DLDF.info, Node: Data Type and Variable Index, Next: Function Index, Prev: GNU Free Documentation License, Up: Top -Concept Index -************* +Data Type and Variable Index +**************************** * Menu: -* animation: Focuses Getstart. -* arbitrary Path: Intersections. -* bugs: Rotating Points. -* Comprehensive TeX Archive Network (CTAN): Sources of Information. -* connecting Points: Drawing Points Intro. -* connectors <1>: Intersections. -* connectors: Paths. -* contributing to 3DLDF: Intersections. -* control points: Paths. -* controls: Paths. -* CTAN (Comprehensive TeX Archive Network): Sources of Information. -* curl: Paths. -* drawing and filling: Drawing Points Intro. -* Emacs: I/O Functions. -* Encapsulated PostScript (EPS): Metafont and MetaPost. -* EPS (Encapsulated PostScript): Metafont and MetaPost. -* FDL, GNU Free Documentation License: GNU Free Documentation License. -* figures: Illustrations. -* file, output: Point Drawing Functions. -* function, member: Manual Conventions. -* future plans: Intersections. -* help lines: Point Drawing Functions. -* hidden surface algorithm: Surface Hiding. -* homogeneous coordinates: Transforms. -* identity matrix: Transforms. -* input routine: Declaring and Initializing Points. -* intersection: Intersections. -* intersection points: Intersections. -* intersection theory: Intersections. -* inversion: Inverting Transforms. -* kludge: Utility Functions. -* linear Paths: Path Data Members. -* lines, drawing: Drawing Points Intro. -* local variable lists: I/O Functions. -* matrix inversion: Inverting Transforms. -* matrix operations: Transforms. -* matrix, identity: Transforms. -* measurement units: Declaring and Initializing Points. -* member function: Manual Conventions. -* Metafont: Metafont and MetaPost. -* MetaPost: Metafont and MetaPost. -* non-arbitrary Path: Intersections. -* operations, matrix: Transforms. -* output file <1>: Point Drawing Functions. -* output file <2>: Intersections. -* output file: Pictures. -* output files: Pictures. -* painter's algorithm: Surface Hiding. -* Path connectors: Intersections. -* Path intersections: Intersections. -* paths: Paths. -* pen expression: Point Drawing Functions. -* pens: Drawing Points Intro. -* Points, connecting: Drawing Points Intro. -* raw MetaPost code: Pictures. -* RGB (red-green-blue): Color Data Members. -* surface hiding: Surface Hiding. -* symbols: Manual Conventions. -* system dependencies: Global Constants and Variables. -* tension: Paths. -* theory of intersection: Intersections. -* TO DO <1>: Global Constants and Variables. -* TO DO: Projections. -* units of measurement: Declaring and Initializing Points. - +* angle: Focus Data Members. +* angle_hex_hex: Truncated Octahedron Data Members. +* angle_hex_square: Truncated Octahedron Data Members. +* arrow: Path Data Members. +* axis: Focus Data Members. +* axis_h <1>: Ellipse Data Members. +* axis_h: Rectangle Data Members. +* axis_v <1>: Ellipse Data Members. +* axis_v: Rectangle Data Members. +* AXON: Namespace Projections. +* background_color: Namespace Colors. +* background_color_vector: Namespace Colors. +* black: Namespace Colors. +* blue: Namespace Colors. +* blue_part: Color Data Members. +* blue_violet: Namespace Colors. +* bool_pair: Typedefs and Utility Structures. +* bool_point: Point Typedefs and Utility Structures. +* bool_point_pair: Point Typedefs and Utility Structures. +* bool_point_quadruple: Point Typedefs and Utility Structures. +* bool_real: Typedefs and Utility Structures. +* bool_real_point: Point Typedefs and Utility Structures. +* center <1>: Solid Data Members. +* center <2>: Regular Closed Plane Curve Data Members. +* center: Polygon Data Members. +* CIRCLE: Solid Data Members. +* Circle <1>: Circle Reference. +* Circle: Plane Figures. +* circles: Solid Data Members. +* Color: Color Reference. +* connectors: Path Data Members. +* Cuboid <1>: Cuboid Reference. +* Cuboid: Cuboid Getstart. +* CURR_Y: Point Data Members. +* CURR_Z: Point Data Members. +* cyan: Namespace Colors. +* cycle_switch: Path Data Members. +* dashed: Path Data Members. +* default_background: Namespace Colors. +* default_color: Namespace Colors. +* default_color_vector: Namespace Colors. +* default_focus: Focus Global Variables. +* DEFAULT_NUMBER_OF_POINTS: Ellipse Data Members. +* depth: Cuboid Data Members. +* dihedral_angle <1>: Icosahedron Data Members. +* dihedral_angle <2>: Dodecahedron Data Members. +* dihedral_angle: Tetrahedron Data Members. +* direction <1>: Line Data Members. +* direction: Focus Data Members. +* distance <1>: Planes Data Members. +* distance: Focus Data Members. +* do_help_lines: Path Data Members. +* do_labels: Picture Data Members. +* DO_LABELS: Label Data Members. +* do_output <1>: Solid Data Members. +* do_output <2>: Path Data Members. +* do_output: Point Data Members. +* Dodecahedron <1>: Dodecahedron. +* Dodecahedron: Dodecahedron Getstart. +* dot: Label Data Members. +* DRAW: Shape Data Members. +* draw_color: Path Data Members. +* DRAWDOT: Shape Data Members. +* drawdot_color: Point Data Members. +* drawdot_value: Point Data Members. +* edge_radius: Polyhedron Data Members. +* edges: Solid_Faced Data Members. +* ELLIPSE: Solid Data Members. +* Ellipse <1>: Ellipse Reference. +* Ellipse: Plane Figures. +* ellipses: Solid Data Members. +* face_radius: Polyhedron Data Members. +* faces: Solid_Faced Data Members. +* FILL: Shape Data Members. +* fill_color: Path Data Members. +* fill_draw_value: Path Data Members. +* FILLDRAW: Shape Data Members. +* Focus: Focus Reference. +* focus: Focuses Getstart. +* focus0: Ellipse Data Members. +* focus1: Ellipse Data Members. +* gray: Namespace Colors. +* green: Namespace Colors. +* green_part: Color Data Members. +* green_yellow: Namespace Colors. +* height: Cuboid Data Members. +* help_color <1>: Path Data Members. +* help_color: Namespace Colors. +* help_color_vector: Namespace Colors. +* help_dash_pattern: Path Data Members. +* hexagon_radius: Truncated Octahedron Data Members. +* Icosahedron <1>: Icosahedron. +* Icosahedron: Icosahedron Getstart. +* IDENTITY_TRANSFORM: Transform Global Variables and Constants. +* in_stream: I/O Global Variables. +* internal_angle: Regular Polygon Data Members. +* INVALID_BOOL_POINT: Point Global Constants and Variables. +* INVALID_BOOL_POINT_PAIR: Point Global Constants and Variables. +* INVALID_BOOL_POINT_QUADRUPLE: Point Global Constants and Variables. +* INVALID_BOOL_REAL_POINT: Point Global Constants and Variables. +* INVALID_LINE: Line Global Constants. +* INVALID_PLANE: Planes Global Constants. +* INVALID_POINT: Point Global Constants and Variables. +* INVALID_REAL: Global Constants and Variables. +* INVALID_REAL_PAIR: Global Constants and Variables. +* INVALID_REAL_SHORT: Global Constants and Variables. +* INVALID_TRANSFORM: Transform Global Variables and Constants. +* ISO: Namespace Projections. +* Label: Label Reference. +* labels: Picture Data Members. +* ldf_real_double: Global Constants and Variables. +* ldf_real_float: Global Constants and Variables. +* light_gray: Namespace Colors. +* Line: Line Reference. +* line_switch: Path Data Members. +* linear_eccentricity: Ellipse Data Members. +* magenta: Namespace Colors. +* matrix: Transform Data Members. +* Matrix: Typedefs and Utility Structures. +* MAX_REAL: Global Constants and Variables. +* MAX_REAL_SQRT: Global Constants and Variables. +* MAX_Z: Namespace Sorting. +* MEAN_Z: Namespace Sorting. +* measurement_units: Point Data Members. +* measurement_units (Point): Declaring and Initializing Points. +* MIN_Z: Namespace Sorting. +* name: Color Data Members. +* NO_SORT: Namespace Sorting. +* normal: Planes Data Members. +* null_coordinates: Global Constants and Variables. +* number_of_points: Regular Closed Plane Curve Data Members. +* number_of_polygon_types: Polyhedron Data Members. +* numerical_eccentricity: Ellipse Data Members. +* on_free_store <1>: Solid Data Members. +* on_free_store <2>: Rectangle Data Members. +* on_free_store <3>: Regular Polygon Data Members. +* on_free_store <4>: Path Data Members. +* on_free_store <5>: Point Data Members. +* on_free_store: Color Data Members. +* orange: Namespace Colors. +* orange_red: Namespace Colors. +* origin: Point Global Constants and Variables. +* out_stream <1>: I/O Global Variables. +* out_stream: Pictures. +* PARALLEL_X_Y: Namespace Projections. +* PARALLEL_X_Z: Namespace Projections. +* PARALLEL_Z_Y: Namespace Projections. +* PATH: Solid Data Members. +* Path <1>: Path Reference. +* Path: Paths. +* paths: Solid Data Members. +* pen <1>: Path Data Members. +* pen: Point Data Members. +* pentagon_radius: Dodecahedron Data Members. +* persp: Focus Data Members. +* PERSP: Namespace Projections. +* PI: Global Constants and Variables. +* Picture <1>: Picture Global Variables. +* Picture <2>: Picture Reference. +* Picture: Pictures. +* pink: Namespace Colors. +* Plane: Plane Reference. +* point: Planes Data Members. +* Point <1>: Point Reference. +* Point: Declaring and Initializing Points. +* Point::measurement_units: Declaring and Initializing Points. +* Point::projective_coordinates: Declaring and Initializing Points. +* Point::user_coordinates: Declaring and Initializing Points. +* Point::view_coordinates: Declaring and Initializing Points. +* Point::world_coordinates: Declaring and Initializing Points. +* point_pair: Point Typedefs and Utility Structures. +* points: Path Data Members. +* Polygon <1>: Polygon Reference. +* Polygon: Plane Figures. +* Polyhedron <1>: Polyhedron Reference. +* Polyhedron: Polyhedron Getstart. +* position <1>: Line Data Members. +* position <2>: Focus Data Members. +* position: Label Data Members. +* projective_coordinates: Point Data Members. +* projective_coordinates (Point): Declaring and Initializing Points. +* projective_extremes <1>: Solid Data Members. +* projective_extremes <2>: Path Data Members. +* projective_extremes: Point Data Members. +* pt: Label Data Members. +* purple: Namespace Colors. +* radius <1>: Circle Data Members. +* radius: Regular Polygon Data Members. +* real: Typedefs and Utility Structures. +* real_pair: Typedefs and Utility Structures. +* real_short: Typedefs and Utility Structures. +* real_triple: Typedefs and Utility Structures. +* RECTANGLE: Solid Data Members. +* Rectangle <1>: Rectangle Reference. +* Rectangle: Plane Figures. +* rectangles: Solid Data Members. +* red: Namespace Colors. +* red_part: Color Data Members. +* Reg_Cl_Plane_Curve <1>: Regular Closed Plane Curve Reference. +* Reg_Cl_Plane_Curve: Plane Figures. +* REG_POLYGON: Solid Data Members. +* Reg_Polygon <1>: Regular Polygon Reference. +* Reg_Polygon: Plane Figures. +* reg_polygons: Solid Data Members. +* Shape: Shape Reference. +* shapes: Picture Data Members. +* short: Regular Polygon Data Members. +* Solid: Solid Reference. +* Solid_Faced: Faced Solid Reference. +* Tetrahedron <1>: Tetrahedron. +* Tetrahedron: Tetrahedron Getstart. +* tex_stream: I/O Global Variables. +* text: Label Data Members. +* transform <1>: Focus Data Members. +* transform <2>: Point Data Members. +* transform: Picture Data Members. +* Transform <1>: Transform Reference. +* Transform: Transforms. +* triangle_radius <1>: Icosahedron Data Members. +* triangle_radius: Tetrahedron Data Members. +* Trunc_Octahedron: Truncated Octahedron. +* Truncated Octahedron: Truncated Octahedron. +* UNDRAW: Shape Data Members. +* UNDRAWDOT: Shape Data Members. +* UNFILL: Shape Data Members. +* UNFILLDRAW: Shape Data Members. +* up: Focus Data Members. +* use_name: Color Data Members. +* user_coordinates: Point Data Members. +* user_coordinates (Point): Declaring and Initializing Points. +* user_transform: Transform Global Variables and Constants. +* vertex_radius: Polyhedron Data Members. +* vertices: Solid_Faced Data Members. +* view_coordinates: Point Data Members. +* view_coordinates (Point): Declaring and Initializing Points. +* violet: Namespace Colors. +* violet_red: Namespace Colors. +* white: Namespace Colors. +* width: Cuboid Data Members. +* world_coordinates: Point Data Members. +* world_coordinates (Point): Declaring and Initializing Points. +* yellow: Namespace Colors. +* yellow_green: Namespace Colors. diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-13 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-13 --- 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-13 1970-01-01 01:00:00.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-13 2004-01-16 19:03:28.000000000 +0100 @@ -0,0 +1,564 @@ +This is 3DLDF.info, produced by makeinfo version 4.5 from 3DLDF.texi. + +This is the 3DLDF User and Reference Manual, edition 1.1.5.1 for 3DLDF +1.1.5.1. This manual was last updated on 16 January 2004. 3DLDF is a +GNU package for three-dimensional drawing with MetaPost output. The +author is Laurence D. Finston. + + Copyright (C) 2003, 2004 Laurence D. Finston. + + Permission is granted to copy, distribute and/or modify this + document under the terms of the GNU Free Documentation License, + Version 1.2 or any later version published by the Free Software + Foundation; with no Invariant Sections, no Front-Cover Texts, and + no Back-Cover Texts. A copy of the license is included in the + section entitled "GNU Free Documentation License". + +INFO-DIR-SECTION GNU packages +START-INFO-DIR-ENTRY +* 3DLDF: (3DLDF). 3D drawing with MetaPost output. +END-INFO-DIR-ENTRY + + +File: 3DLDF.info, Node: Function Index, Next: Concept Index, Prev: Data Type and Variable Index, Up: Top + +Function Index +************** + +* Menu: + +* align_with_axis <1>: Aligning Paths with an Axis. +* align_with_axis: Alignment with an Axis for Transforms. +* angle: Vector Operations. +* angle_point <1>: Returning Elements and Information for Ellipses. +* angle_point: Querying Regular Closed Plane Curves. +* append: Appending to Paths. +* apply_transform <1>: Applying Transformations to Solids. +* apply_transform <2>: Applying Transformations to Paths. +* apply_transform <3>: Applying Transformations to Points. +* apply_transform: Applying Transformations to Shapes. +* beginfig: I/O Functions. +* bool_point: Point Typedefs and Utility Structures. +* bool_point::operator=: Point Typedefs and Utility Structures. +* bool_point_quadruple: Point Typedefs and Utility Structures. +* bool_point_quadruple::operator=: Point Typedefs and Utility Structures. +* bool_real_point: Point Typedefs and Utility Structures. +* bool_real_point::operator=: Point Typedefs and Utility Structures. +* Circle: Circle Constructors and Setting Functions. +* clean <1>: Modifying Points. +* clean: Cleaning Transforms. +* clear <1>: Clearing Solids. +* clear <2>: Clearing Paths. +* clear <3>: Modifying Points. +* clear <4>: Modifying Pictures. +* clear: Clearing Shapes. +* Color: Color Constructors and Setting Functions. +* convert-eps: Converting EPS Files ELISP. +* convert-eps-loop: Converting EPS Files ELISP. +* corner: Returning Points for Rectangles. +* create_new: Dynamic Allocation of Shapes. +* create_new: Circle Constructors and Setting Functions. +* create_new: Color Constructors and Setting Functions. +* create_new: Cuboid Constructors and Setting Functions. +* create_new: Ellipse Constructors and Setting Functions. +* create_new: Path Constructors and Setting Functions. +* create_new: Point Constructors and Setting Functions. +* create_new: Rectangle Constructors and Setting Functions. +* create_new: Regular Polygon Constructors and Setting Functions. +* create_new: Solid Constructors and Setting Functions. +* cross_product: Vector Operations. +* Cuboid: Cuboid Constructors and Setting Functions. +* define_color_mp: Defining and Initializing Colors. +* do_transform: Performing Transformations on Ellipses. +* Dodecahedron: Dodecahedron Constructors and Setting Functions. +* dot_product: Vector Operations. +* dotlabel <1>: Labeling Ellipses. +* dotlabel <2>: Labelling Paths. +* dotlabel: Labelling Points. +* draw <1>: Drawing and Filling Solids. +* draw <2>: Drawing and Filling Paths. +* draw: Point Drawing Functions. +* draw_axes: Drawing and Filling Paths. +* draw_help <1>: Drawing and Filling Paths. +* draw_help: Point Drawing Functions. +* draw_in_circle: Circles for Regular Polygons. +* draw_in_ellipse: Ellipses for Rectangles. +* draw_in_rectangle: Rectangles for Ellipses. +* draw_net <1>: Icosahedron Net. +* draw_net <2>: Dodecahedron Net. +* draw_net: Tetrahedron Net. +* draw_out_circle: Circles for Regular Polygons. +* draw_out_ellipse: Ellipses for Rectangles. +* draw_out_rectangle: Rectangles for Ellipses. +* drawarrow <1>: Drawing and Filling Paths. +* drawarrow: Point Drawing Functions. +* drawdot: Point Drawing Functions. +* Ellipse: Ellipse Constructors and Setting Functions. +* endfig: I/O Functions. +* epicycloid_pattern_1: Epicycloids. +* epsilon <1>: Returning Information for Points. +* epsilon: Returning Information for Transforms. +* extract <1>: Outputting Solids. +* extract <2>: Outputting Paths. +* extract <3>: Outputting Points. +* extract: Outputting Shapes. +* fill <1>: Drawing and Filling Solids. +* fill: Drawing and Filling Paths. +* filldraw <1>: Drawing and Filling Solids. +* filldraw: Drawing and Filling Paths. +* Focus: Focus Constructors and Setting Functions. +* get_all_coords: Returning Coordinates. +* get_axis_h <1>: Returning Elements and Information for Ellipses. +* get_axis_h: Querying Rectangles. +* get_axis_v <1>: Returning Elements and Information for Ellipses. +* get_axis_v: Querying Rectangles. +* get_blue_part: Querying Colors. +* get_center <1>: Returning Elements and Information Solids. +* get_center <2>: Returning Elements and Information for Ellipses. +* get_center: Querying Polygons. +* get_circle_center: Getting Shape Centers Solids. +* get_circle_ptr: Getting Shapes Solids. +* get_coefficients <1>: Solving Ellipses. +* get_coefficients: Querying Regular Closed Plane Curves. +* get_coord: Returning Coordinates. +* get_copy <1>: Copying Solids. +* get_copy <2>: Copying Paths. +* get_copy <3>: Copying Points. +* get_copy <4>: Copying Labels. +* get_copy: Copying Shapes. +* get_diameter: Querying Circles. +* get_direction: Querying Focuses. +* get_distance <1>: Planes Returning Information. +* get_distance: Querying Focuses. +* get_element: Querying Transforms. +* get_ellipse_center: Getting Shape Centers Solids. +* get_ellipse_ptr: Getting Shapes Solids. +* get_endianness: Endianness. +* get_extremes <1>: Outputting Solids. +* get_extremes <2>: Outputting Paths. +* get_extremes <3>: Outputting Points. +* get_extremes: Outputting Shapes. +* get_focus: Returning Elements and Information for Ellipses. +* get_green_part: Querying Colors. +* get_last_point: Querying Paths. +* get_line <1>: Querying Paths. +* get_line: Points and Lines. +* get_line_switch: Querying Paths. +* get_linear_eccentricity: Returning Elements and Information for Ellipses. +* get_maximum_z <1>: Outputting Solids. +* get_maximum_z <2>: Outputting Paths. +* get_maximum_z <3>: Outputting Points. +* get_maximum_z: Outputting Shapes. +* get_mean_z <1>: Outputting Solids. +* get_mean_z <2>: Outputting Paths. +* get_mean_z <3>: Outputting Points. +* get_mean_z: Outputting Shapes. +* get_minimum_z <1>: Outputting Solids. +* get_minimum_z <2>: Outputting Paths. +* get_minimum_z <3>: Outputting Points. +* get_minimum_z: Outputting Shapes. +* get_name: Querying Colors. +* get_net <1>: Truncated Octahedron Net. +* get_net <2>: Icosahedron Net. +* get_net <3>: Dodecahedron Net. +* get_net: Tetrahedron Net. +* get_normal: Querying Paths. +* get_numerical_eccentricity: Returning Elements and Information for Ellipses. +* get_path: Get Path. +* get_path_ptr: Getting Shapes Solids. +* get_persp: Querying Focuses. +* get_persp_element: Querying Focuses. +* get_plane: Querying Paths. +* get_point: Querying Paths. +* get_position: Querying Focuses. +* get_radius <1>: Querying Circles. +* get_radius: Querying Regular Polygons. +* get_rectangle_center: Getting Shape Centers Solids. +* get_rectangle_ptr: Getting Shapes Solids. +* get_red_part: Querying Colors. +* get_reg_polygon_center: Getting Shape Centers Solids. +* get_reg_polygon_ptr: Getting Shapes Solids. +* get_register_width: Register Width. +* get_second_largest: Get Second Largest Real. +* get_shape_center: Getting Shape Centers Solids. +* get_shape_ptr: Getting Shapes Solids. +* get_size: Querying Paths. +* get_transform <1>: Querying Focuses. +* get_transform: Querying Points. +* get_transform_element: Querying Focuses. +* get_up: Querying Focuses. +* get_use_name: Querying Colors. +* get_w: Returning Coordinates. +* get_x: Returning Coordinates. +* get_y: Returning Coordinates. +* get_z: Returning Coordinates. +* half: Regular Closed Plane Curve Segments. +* hex_pattern_1: Plane Tesselations. +* Icosahedron: Icosahedron Constructors and Setting Functions. +* in_circle: Circles for Regular Polygons. +* in_ellipse: Ellipses for Rectangles. +* in_rectangle: Rectangles for Ellipses. +* initialize_colors: Defining and Initializing Colors. +* initialize_io: I/O Functions. +* intersection_line: Plane Intersections. +* intersection_point <1>: Path Intersections. +* intersection_point <2>: Plane Intersections. +* intersection_point: Point Intersections. +* intersection_points <1>: Circle Intersections. +* intersection_points <2>: Ellipse Intersections. +* intersection_points <3>: Regular Closed Plane Curve Intersections. +* intersection_points: Polygon Intersections. +* inverse: Matrix Inversion. +* is_32_bit: Register Width. +* is_64_bit: Register Width. +* is_big_endian: Endianness. +* is_circular: Querying Circles. +* is_cubic <1>: Querying Ellipses. +* is_cubic: Querying Regular Closed Plane Curves. +* is_cycle: Querying Paths. +* is_elliptical: Querying Ellipses. +* is_identity <1>: Querying Points. +* is_identity: Querying Transforms. +* is_in_triangle: Querying Points. +* is_linear: Querying Paths. +* is_little_endian: Endianness. +* is_on_free_store <1>: Querying Solids. +* is_on_free_store <2>: Querying Paths. +* is_on_free_store <3>: Querying Points. +* is_on_free_store <4>: Querying Shapes. +* is_on_free_store: Querying Colors. +* is_on_line: Points and Lines. +* is_on_plane: Querying Points. +* is_on_segment: Points and Lines. +* is_planar: Querying Paths. +* is_quadratic <1>: Querying Ellipses. +* is_quadratic: Querying Regular Closed Plane Curves. +* is_quartic <1>: Querying Ellipses. +* is_quartic: Querying Regular Closed Plane Curves. +* is_rectangular: Querying Rectangles. +* kill_labels: Modifying Pictures. +* label <1>: Labeling Ellipses. +* label <2>: Labelling Paths. +* label: Labelling Points. +* Line: Line Constructors. +* location <1>: Returning Elements and Information for Ellipses. +* location: Querying Regular Closed Plane Curves. +* magnitude: Vector Operations. +* mediate: Points and Lines. +* mid_point: Returning Points for Rectangles. +* modify: Modifying Colors. +* operator!= <1>: Planes Operators. +* operator!= <2>: Point Operators. +* operator!=: Color Operators. +* operator&: Path Operators. +* operator&=: Path Operators. +* operator* <1>: Point Operators. +* operator*: Transform Operators. +* operator*= <1>: Solid Operators. +* operator*= <2>: Ellipse Operators. +* operator*= <3>: Polygon Operators. +* operator*= <4>: Path Operators. +* operator*= <5>: Point Operators. +* operator*= <6>: Picture Operators. +* operator*= <7>: Transform Operators. +* operator*=: Shape Operators. +* operator+ <1>: Path Operators. +* operator+: Point Operators. +* operator+= <1>: Path Operators. +* operator+= <2>: Point Operators. +* operator+=: Picture Operators. +* operator-: Point Operators. +* operator-=: Point Operators. +* operator/: Point Operators. +* operator/=: Point Operators. +* operator<< <1>: Outputting Points. +* operator<<: Color Operators. +* operator= <1>: Cuboid Operators. +* operator= <2>: Solid Operators. +* operator= <3>: Circle Operators. +* operator= <4>: Ellipse Operators. +* operator= <5>: Rectangle Operators. +* operator= <6>: Regular Polygon Operators. +* operator= <7>: Planes Operators. +* operator= <8>: Line Operators. +* operator= <9>: Focus Operators. +* operator= <10>: Point Operators. +* operator= <11>: Picture Operators. +* operator= <12>: Transform Operators. +* operator=: Color Operators. +* operator= (for Points): Setting and Assigning to Points. +* operator== <1>: Planes Operators. +* operator== <2>: Point Operators. +* operator==: Color Operators. +* out_circle: Circles for Regular Polygons. +* out_ellipse: Ellipses for Rectangles. +* out_rectangle: Rectangles for Ellipses. +* output <1>: Outputting Solids. +* output <2>: Outputting Paths. +* output <3>: Outputting Points. +* output <4>: Picture Output Functions. +* output <5>: Outputting Labels. +* output: Outputting Shapes. +* Path: Path Constructors and Setting Functions. +* persp_0: Perspective Functions. +* Picture: Picture Constructors. +* Plane: Planes Constructors. +* Point: Point Constructors and Setting Functions. +* Point::intersection_points: Intersections. +* Point::operator=: Setting and Assigning to Points. +* Point::set: Setting and Assigning to Points. +* project <1>: Outputting Paths. +* project: Projecting Points. +* quarter: Regular Closed Plane Curve Segments. +* real_triple: Typedefs and Utility Structures. +* Rectangle: Rectangle Constructors and Setting Functions. +* Reg_Polygon: Regular Polygon Constructors and Setting Functions. +* reset: Resetting Transforms. +* reset_angle: Modifying Focuses. +* reset_transform <1>: Modifying Points. +* reset_transform: Modifying Pictures. +* reverse: Querying Paths. +* rotate <1>: Affine Transformations for Solids. +* rotate <2>: Affine Transformations for Ellipses. +* rotate <3>: Affine Transformations for Polygons. +* rotate <4>: Affine Transformations for Paths. +* rotate <5>: Affine Transformations for Points. +* rotate <6>: Affine Transformations for Pictures. +* rotate <7>: Affine Transformations for Transforms. +* rotate: Affine Transformations for Shapes. +* scale <1>: Affine Transformations for Solids. +* scale <2>: Affine Transformations for Ellipses. +* scale <3>: Affine Transformations for Polygons. +* scale <4>: Affine Transformations for Paths. +* scale <5>: Affine Transformations for Points. +* scale <6>: Affine Transformations for Pictures. +* scale <7>: Affine Transformations for Transforms. +* scale: Affine Transformations for Shapes. +* segment: Regular Closed Plane Curve Segments. +* set <1>: Tetrahedron Constructors and Setting Functions. +* set <2>: Circle Constructors and Setting Functions. +* set <3>: Ellipse Constructors and Setting Functions. +* set <4>: Rectangle Constructors and Setting Functions. +* set <5>: Regular Polygon Constructors and Setting Functions. +* set <6>: Path Constructors and Setting Functions. +* set <7>: Focus Constructors and Setting Functions. +* set <8>: Point Constructors and Setting Functions. +* set: Color Constructors and Setting Functions. +* set (for Points): Setting and Assigning to Points. +* set_blue_part: Modifying Colors. +* set_connectors: Modifying Paths. +* set_cycle: Querying Paths. +* set_dash_pattern: Modifying Paths. +* set_draw_color: Modifying Paths. +* set_element: Setting Values Transforms. +* set_extremes <1>: Outputting Solids. +* set_extremes <2>: Outputting Paths. +* set_extremes <3>: Outputting Points. +* set_extremes: Outputting Shapes. +* set_fill_color: Modifying Paths. +* set_fill_draw_value: Modifying Paths. +* set_green_part: Modifying Colors. +* set_name: Modifying Colors. +* set_on_free_store <1>: Setting Solid Members. +* set_on_free_store <2>: Modifying Paths. +* set_on_free_store <3>: Modifying Points. +* set_on_free_store: Modifying Shapes. +* set_pen: Modifying Paths. +* set_red_part: Modifying Colors. +* set_transform: Modifying Pictures. +* set_use_name: Modifying Colors. +* shear <1>: Affine Transformations for Solids. +* shear <2>: Affine Transformations for Ellipses. +* shear <3>: Affine Transformations for Polygons. +* shear <4>: Affine Transformations for Paths. +* shear <5>: Affine Transformations for Points. +* shear <6>: Affine Transformations for Transforms. +* shear: Affine Transformations for Shapes. +* shift <1>: Affine Transformations for Solids. +* shift <2>: Affine Transformations for Ellipses. +* shift <3>: Affine Transformations for Polygons. +* shift <4>: Affine Transformations for Paths. +* shift <5>: Affine Transformations for Points. +* shift <6>: Affine Transformations for Pictures. +* shift <7>: Affine Transformations for Transforms. +* shift: Affine Transformations for Shapes. +* shift_times <1>: Affine Transformations for Ellipses. +* shift_times <2>: Affine Transformations for Polygons. +* shift_times <3>: Affine Transformations for Paths. +* shift_times <4>: Affine Transformations for Points. +* shift_times: Affine Transformations for Transforms. +* show <1>: Showing Solids. +* show <2>: Showing Paths. +* show <3>: Planes Showing. +* show <4>: Showing. +* show <5>: Showing Focuses. +* show <6>: Showing Points. +* show <7>: Showing Pictures. +* show <8>: Showing Transforms. +* show <9>: Showing Shapes. +* show: Showing Colors. +* show_colors: Showing Paths. +* show_transform <1>: Showing Points. +* show_transform: Showing Pictures. +* size: Querying Paths. +* slope <1>: Querying Paths. +* slope: Points and Lines. +* Solid: Solid Constructors and Setting Functions. +* solve <1>: Solving Ellipses. +* solve: Querying Regular Closed Plane Curves. +* solve_quadratic: Utility Functions. +* subpath: Querying Paths. +* suppress_labels: Picture Output Functions. +* suppress_output <1>: Outputting Solids. +* suppress_output <2>: Outputting Paths. +* suppress_output <3>: Outputting Points. +* suppress_output: Outputting Shapes. +* Tetrahedron: Tetrahedron Constructors and Setting Functions. +* Transform: Transform Constructors. +* trunc: Utility Functions. +* Trunc_Octahedron: Truncated Octahedron Constructors and Setting Functions. +* undraw <1>: Drawing and Filling Solids. +* undraw <2>: Drawing and Filling Paths. +* undraw: Point Drawing Functions. +* undrawdot: Point Drawing Functions. +* unfill <1>: Drawing and Filling Solids. +* unfill: Drawing and Filling Paths. +* unfilldraw <1>: Drawing and Filling Solids. +* unfilldraw: Drawing and Filling Paths. +* unit_vector: Vector Operations. +* unsuppress_labels: Picture Output Functions. +* unsuppress_output <1>: Outputting Solids. +* unsuppress_output <2>: Outputting Paths. +* unsuppress_output: Outputting Shapes. +* void: Outputting Points. +* write_footers: I/O Functions. +* ~Cuboid: Cuboid Constructors and Setting Functions. +* ~Path: Path Destructor. +* ~Point: Point Destructor. +* ~Solid: Solid Destructor. + + +File: 3DLDF.info, Node: Concept Index, Prev: Function Index, Up: Top + +Concept Index +************* + +* Menu: + +* animation: Focuses Getstart. +* arbitrary Path: Intersections. +* B-splines: Curves and Surfaces. +* Be'zier curves: Curves and Surfaces. +* bugs: Rotating Points. +* CD-R (Compact Disk, Recordable): Converting EPS Files. +* Compact Disk, Recordable (CD-R): Converting EPS Files. +* Comprehensive TeX Archive Network (CTAN): Sources of Information. +* connecting Points: Drawing Points Intro. +* connectors <1>: Intersections. +* connectors: Paths. +* contributing to 3DLDF: Intersections. +* control points: Paths. +* controls: Paths. +* convert (ImageMagick): Converting EPS Files. +* CTAN (Comprehensive TeX Archive Network): Sources of Information. +* curl: Paths. +* derivation: Geometry. +* derived classes: Geometry. +* display (ImageMagick): Converting EPS Files. +* drawing and filling: Drawing Points Intro. +* Emacs: I/O Functions. +* Emacs-Lisp: Converting EPS Files ELISP. +* Encapsulated PostScript (EPS) <1>: Converting EPS Files ELISP. +* Encapsulated PostScript (EPS) <2>: Converting EPS Files. +* Encapsulated PostScript (EPS) <3>: Metafont and MetaPost. +* Encapsulated PostScript (EPS): Illustrations. +* EPS (Encapsulated PostScript) <1>: Converting EPS Files ELISP. +* EPS (Encapsulated PostScript) <2>: Converting EPS Files. +* EPS (Encapsulated PostScript) <3>: Metafont and MetaPost. +* EPS (Encapsulated PostScript): Illustrations. +* FDL, GNU Free Documentation License: GNU Free Documentation License. +* file, output: Point Drawing Functions. +* function templates: Template Functions. +* function, member: Manual Conventions. +* future plans: Intersections. +* help lines: Point Drawing Functions. +* hidden surface algorithm: Surface Hiding. +* homogeneous coordinates: Transforms. +* identity matrix: Transforms. +* ImageMagick: Converting EPS Files. +* ImageMagick convert: Converting EPS Files. +* ImageMagick display: Converting EPS Files. +* input routine: Declaring and Initializing Points. +* intersection: Intersections. +* intersection points: Intersections. +* intersection theory: Intersections. +* invariance, projective: Curves and Surfaces. +* inversion: Inverting Transforms. +* kludge: Utility Functions. +* linear Paths: Path Data Members. +* lines, drawing: Drawing Points Intro. +* local variable lists: I/O Functions. +* matrix inversion: Inverting Transforms. +* matrix operations: Transforms. +* matrix, identity: Transforms. +* measurement units: Declaring and Initializing Points. +* member function: Manual Conventions. +* Metafont: Metafont and MetaPost. +* MetaPost: Metafont and MetaPost. +* multi-threading: Multi-Threading. +* multiple inheritance: Geometry. +* non-arbitrary Path: Intersections. +* non-uniform rational B-splines (NURBS): Curves and Surfaces. +* NURBS (non-uniform rational B-splines): Curves and Surfaces. +* operations, matrix: Transforms. +* output file <1>: Point Drawing Functions. +* output file <2>: Intersections. +* output file: Pictures. +* output files: Pictures. +* painter's algorithm: Surface Hiding. +* patches: Curves and Surfaces. +* Path connectors: Intersections. +* Path intersections: Intersections. +* paths: Paths. +* pen expression: Point Drawing Functions. +* pens: Drawing Points Intro. +* PNG (Portable Network Graphics) <1>: Changes in 3DLDF 1.1.5.1. +* PNG (Portable Network Graphics) <2>: Converting EPS Files ELISP. +* PNG (Portable Network Graphics) <3>: Converting EPS Files. +* PNG (Portable Network Graphics): Illustrations. +* Points, connecting: Drawing Points Intro. +* Portable Network Graphics (PNG) <1>: Changes in 3DLDF 1.1.5.1. +* Portable Network Graphics (PNG) <2>: Converting EPS Files ELISP. +* Portable Network Graphics (PNG) <3>: Converting EPS Files. +* Portable Network Graphics (PNG): Illustrations. +* PostScript (PS) <1>: Converting EPS Files ELISP. +* PostScript (PS) <2>: Converting EPS Files. +* PostScript (PS): Illustrations. +* PostScript, structured <1>: Converting EPS Files ELISP. +* PostScript, structured: Converting EPS Files. +* projective invariance: Curves and Surfaces. +* PS (PostScript) <1>: Converting EPS Files ELISP. +* PS (PostScript) <2>: Converting EPS Files. +* PS (PostScript): Illustrations. +* raw MetaPost code: Pictures. +* reflections: Shadows. +* RGB (red-green-blue): Color Data Members. +* shading: Shadows. +* shadows: Shadows. +* spline curves: Curves and Surfaces. +* splines: Curves and Surfaces. +* structured PostScript <1>: Converting EPS Files ELISP. +* structured PostScript: Converting EPS Files. +* surface hiding: Surface Hiding. +* surface patches: Curves and Surfaces. +* symbols: Manual Conventions. +* system dependencies: Global Constants and Variables. +* template functions: Template Functions. +* templates: Template Functions. +* tension: Paths. +* theory of intersection: Intersections. +* TO DO <1>: Global Constants and Variables. +* TO DO: Projections. +* units of measurement: Declaring and Initializing Points. + + diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-2 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-2 --- 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-2 2003-12-10 18:44:55.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-2 2004-01-16 19:03:28.000000000 +0100 @@ -1,11 +1,11 @@ This is 3DLDF.info, produced by makeinfo version 4.5 from 3DLDF.texi. -This is the 3DLDF User and Reference Manual, edition 1.1.4 for 3DLDF -1.1.4. This manual was last updated on 10 December 2003. 3DLDF is a +This is the 3DLDF User and Reference Manual, edition 1.1.5.1 for 3DLDF +1.1.5.1. This manual was last updated on 16 January 2004. 3DLDF is a GNU package for three-dimensional drawing with MetaPost output. The author is Laurence D. Finston. - Copyright (C) 2003 Laurence D. Finston. + Copyright (C) 2003, 2004 Laurence D. Finston. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, @@ -20,6 +20,48 @@ END-INFO-DIR-ENTRY  +File: 3DLDF.info, Node: Shearing Points, Next: Rotating Points, Prev: Scaling Points, Up: Transforming Points + +Shearing +======== + + Shearing is more complicated than shifting or scaling. The function +`shear()' takes six `real' arguments. If p is a `Point', then +`p.shear(a, b, c, d, e, f)' sets x_p to x_p + ay_p + bz_p, y_p to y_p + +cx_p + dz_p, and z_p to z_p + ex_p + fy_p. In this way, each +coordinate of a `Point' is modified based on the values of the other +two coordinates, whereby the influence of the other coordinates on the +new value is weighted according to the arguments. + + Point p(1, 1, 1); + p.shear(1); + p.show("p:"); + -| p: (2, 1, 1) + p.set(1, 1, 1); + p.shear(1, 1); + p.show("p:"); + -| p: (3, 1, 1) + p.set(1, 1, 1); + p.shear(1, 1, 2, 2, 3, 3); + p.show("p:"); + -| p: (3, 5, 7) + + [next figure] demonstrates the effect of shearing the points of a +rectangle in the x-y plane. + + Point P0; + Point P1(3); + Point P2(3, 3); + Point P3(0, 3); + Rectangle r(p0, p1, p2, p3); + r.draw(); + Rectangle q(r); + q.shear(1.5); + q.draw(black, "evenly"); + + [Figure 1 not displayed.] + + File: 3DLDF.info, Node: Rotating Points, Prev: Shearing Points, Up: Transforming Points Rotating @@ -96,6 +138,8 @@ p6.show("p6:"); -| p6: (0.276332, 1.44889, -1.47433) + [Figure 2 not displayed.] + I have sometimes gotten erroneous results using `rotate()' for rotation about two `Points'. It's usually worked to reverse the order of the `Point' arguments, or to change sign of the angle argument. I @@ -378,6 +422,8 @@ Point P(0, 1); P.drawdot(Colors::black, "pencircle scaled 3mm"); + [Figure 3 not displayed.] + In `drawdot()', a `Color' argument precedes the `string' argument for the pen, so "`Colors::black'" must be specified as a placeholder in the call to `drawdot()'.(2) @@ -387,6 +433,8 @@ p.undrawdot("pencircle scaled 2mm"); + [Figure 4 not displayed.] + For complete descriptions of `drawdot()' and `undrawdot()', see *Note Point Reference; Drawing: Point Drawing Functions. @@ -399,6 +447,8 @@ Point p1(2, 2); p0.draw(p1); + [Figure 5 not displayed.] + `p0.draw(p1)' is equivalent in its effect to `p1.draw(p0)'. The function `Point::draw()' takes a required `Point&' argument (a @@ -410,6 +460,8 @@ p0.draw(p1, Colors::gray, "", "pensquare scaled .5cm rotated 45"); + [Figure 6 not displayed.] + The function `Point::undraw()' takes a required `Point&' argument and optional `string' arguments for the dash pattern and the pen. Unlike `Point::draw()', a `Color' argument would have no meaning for @@ -422,6 +474,8 @@ p0.undraw(p1, "evenly scaled 6", "pencircle scaled .2cm"); + [Figure 7 not displayed.] + For complete descriptions of `draw()' and `undraw()', see *Note Point Reference; Drawing: Point Drawing Functions. @@ -490,6 +544,8 @@ p4.label(4); p5.label("$\\leftarrow p_5$", "rt"); + [Figure 8 not displayed.] + For complete descriptions of `Point::label()' and `Point::dotlabel()', see *Note Points; Labelling: Labelling Points. @@ -561,6 +617,8 @@ Path p(A, B); p.draw(); + [Figure 9 not displayed.] + `Paths' created in this way are important, because they are guaranteed to be linear, as long as no operations are performed on them that cause them to become non-linear. Linear `Paths' can be used to @@ -579,6 +637,8 @@ Path pa("--", true, &p[0], &p[1], &p[2], 0); pa.draw(); + [Figure 10 not displayed.] + Another constructor must be used for `Paths' with more than one connector and an arbitrary number of `Points'. The argument list starts with a pointer to `Point', followed by `string' for the first @@ -603,6 +663,8 @@ "...", &p[3], "..", &p[7], "...", 0); pa.draw(); + [Figure 11 not displayed.] + As mentioned above (*note Accuracy::), specifying connectors is problematic for three-dimensional `Paths', because MetaPost ultimately calculates the "most pleasing curve" based on the two-dimensional @@ -649,6 +711,8 @@ Path pa("..", true, &pt[0], &pt[1], &pt[2], &pt[3], &pt[4], 0); pa.draw(); + [Figure 12 not displayed.] + Since `pa' is closed, it can be filled as well as drawn. The following example uses `fill()' with a `Color' argument, in order to avoid having a large splotch of black on the page. Common `Colors' are @@ -656,6 +720,8 @@ pa.fill(Colors::gray); + [Figure 13 not displayed.] + Closed `Paths' can be filled and drawn, using the function `filldraw()'. This function draws the `Path' using the pen specified, or MetaPost's `currentpen' by default. A `Color' for drawing the @@ -673,6 +739,8 @@ p0.draw(p1); pa.filldraw(); + [Figure 14 not displayed.] + The following example uses arguments for the `Colors' used for drawing and filling, and the pen. The empty string argument before the pen argument is a placeholder for the dash pattern argument. @@ -680,18 +748,24 @@ pa.filldraw(black, gray, "", "pensquare xscaled 3mm yscaled 1mm rotated 60"); + [Figure 15 not displayed.] + `Paths' can also be "undrawn", "unfilled", and "unfilldrawn", using the corresponding functions: pa.fill(gray); p0.undraw(p1, "", "pencircle scaled 3mm"); + [Figure 16 not displayed.] + pa.fill(gray); Path q; q = pa; q.scale(.5, .5); q.unfill(); + [Figure 17 not displayed.] + The function `unfilldraw()' takes a `Color' argument for drawing the `Path', which is `*Colors::background_color' by default. This makes it possible to unfill the `Path' while drawing the outline with a visible @@ -702,6 +776,8 @@ pa.fill(gray); q.unfilldraw(white, "", "pensquare xscaled 3mm yscaled 1mm"); + [Figure 18 not displayed.] + The following example demonstrates the use of `unfilldraw()' with `black' as its `Color' argument. Unfortunately, it also demonstrates one of the limitations of the surface hiding algorith: The line from @@ -718,6 +794,8 @@ pa.fill(gray); q.unfilldraw(black, "", "pensquare xscaled 3mm yscaled 1mm"); + [Figure 19 not displayed.] + *Note Paths; Drawing and Filling: Drawing and Filling Paths, for more information, and complete descriptions of the functions. @@ -766,6 +844,8 @@ Reg_Polygon p(origin, 5, 3); p.draw(); + [Figure 20 not displayed.] + Three additional arguments cause the pentagon to be rotated about the x, y, and z axes by the amount indicated. In this example, it's rotated 90 degrees @@ -775,6 +855,8 @@ Reg_Polygon p(origin, 5, 3, 90); p.draw(); + [Figure 21 not displayed.] + In this example, it's rotated 36 degrees about the y-axis, so that it appears to point in the opposite @@ -782,6 +864,8 @@ Reg_Polygon p(origin, 5, 3, 0, 36); p.draw(); + [Figure 22 not displayed.] + In this example, it's rotated 90 degrees about the z-axis, so that it lies in the z-y plane: @@ -789,6 +873,8 @@ Reg_Polygon p(origin, 5, 3, 0, 0, 90); p.draw(); + [Figure 23 not displayed.] + In this example, it's rotated 45 degrees about the x, y, and z-axes in that order: @@ -796,6 +882,8 @@ Reg_Polygon p(origin, 5, 3, 45, 45, 45); p.draw(); + [Figure 24 not displayed.] + `Reg_Polygons' need not be centered about the `origin'. If another `Point' PT is used as the first argument, the `Reg_Polygon' is first created with its center at the origin, then the specified rotations, if @@ -806,6 +894,8 @@ Reg_Polygon hex(P, 6, 4, 60, 30, 30); hex.draw(); + [Figure 25 not displayed.] + In the following example, the `Reg_Polygon' `polygon' is first declared using the default constructor, which creates an empty `Reg_Polygon'. Then, the `polygon' is repeatedly changed using the @@ -822,6 +912,8 @@ p.shift(0, 1); } + [Figure 26 not displayed.] +  File: 3DLDF.info, Node: Rectangles Getstart, Next: Ellipses Getstart, Prev: Regular Polygons Getstart, Up: Plane Figures @@ -834,12 +926,16 @@ Rectangle r(origin, 2, 3); r.draw(); + [Figure 27 not displayed.] + Three additional arguments can be used to specify rotation about the x, y, and z-axes respectively: Rectangle r(origin, 2, 3, 30, 45, 15); r.draw(); + [Figure 28 not displayed.] + If a `Point' P other than the origin is specified as the center of the `Rectangle', the latter is first created in the x-z plane, centered about the origin, as above. Then, any rotations specified are @@ -850,6 +946,8 @@ Rectangle r(p0, 4, 2, 30, 30, 30); r.draw(); + [Figure 29 not displayed.] + This constructor has a corresponding setting function: Rectangle r; @@ -859,6 +957,8 @@ r.draw(); } + [Figure 30 not displayed.] + `Rectangles' can also be specified using four `Points' as arguments, whereby they must be ordered so that they are contiguous in the resulting `Rectangle': @@ -872,6 +972,8 @@ Rectangle r(pt[0], pt[2], pt[3], pt[1]); r.draw(); + [Figure 31 not displayed.] + This constructor checks whether the `Point' arguments are coplanar, however, it does not check whether they are really the corners of a valid rectangle; the user, or the code that calls this function, must @@ -883,6 +985,8 @@ Rectangle q(pt[0], pt[2], pt[3], pt[1]); q.draw(); + [Figure 32 not displayed.] + This constructor is not really intended to be used directly, but should mostly be called from within other functions, that should ensure that the arguments produce a rectangular `Rectangle'. There is also no @@ -913,6 +1017,8 @@ Ellipse e(pt, 3, 6, 90); e.draw(); + [Figure 33 not displayed.] + As you may expect, this constructor has a corresponding setting function: @@ -933,6 +1039,8 @@ p.shift(0, 0, 2); } + [Figure 34 not displayed.] +  File: 3DLDF.info, Node: Circles Getstart, Prev: Ellipses Getstart, Up: Plane Figures @@ -948,6 +1056,8 @@ Circle c(P, 3.5, 90, 90); c.draw(); + [Figure 35 not displayed.] + This constructor, too, has a corresponding setting function: Circle c; @@ -958,6 +1068,8 @@ c.draw(); } + [Figure 36 not displayed.] + In the preceding example, the last argument to `set()', namely "64", is for the number of `Points' used for constructing the perimeter of the `Circle'. The default value is 16, however, if it is used, @@ -1002,12 +1114,16 @@ Cuboid c0(origin, 3, 3, 3, 0, 30); c0.draw(); + [Figure 37 not displayed.] + In the following example, the `Cuboid' is "filldrawn", so that the lines dilineating the hidden surfaces of the `Cuboid' are covered. Cuboid c1(origin, 3, 4, 5, 0, 30); c1.filldraw(); + [Figure 38 not displayed.] +  File: 3DLDF.info, Node: Polyhedron Getstart, Prev: Cuboid Getstart, Up: Solid Figures @@ -1055,6 +1171,8 @@ t.draw(); t.get_center().dotlabel("$c$"); + [Figure 39 not displayed.] +  File: 3DLDF.info, Node: Dodecahedron Getstart, Next: Icosahedron Getstart, Prev: Tetrahedron Getstart, Up: Polyhedron Getstart @@ -1069,12 +1187,22 @@ Dodecahedron d(origin, 3); d.draw(); + [Figure 40 not displayed.] + + [Figure 41 not displayed.] + Please note that the `Dodecahedron' in [next figure] is drawn, and not filldrawn! + [Figure 42 not displayed.] + + [Figure 43 not displayed.] + In [next figure] , `d' is filldrawn. In this case, the surface hiding algorithm has worked properly. *Note Surface Hiding::. + [Figure 44 not displayed.] +  File: 3DLDF.info, Node: Icosahedron Getstart, Prev: Dodecahedron Getstart, Up: Polyhedron Getstart @@ -1089,9 +1217,19 @@ Icosahedron i(origin, 3); i.draw(); + [Figure 45 not displayed.] + + [Figure 46 not displayed.] + + [Figure 47 not displayed.] + + [Figure 48 not displayed.] + In [next figure] , `i' is filldrawn. In this case, the surface hiding algorithm has worked properly. *Note Surface Hiding::. + [Figure 49 not displayed.] +  File: 3DLDF.info, Node: Pictures, Next: Intersections, Prev: Solid Figures, Up: Top @@ -1134,6 +1272,8 @@ current_picture.output(); endfig(1); + [Figure 50 not displayed.] + The C++ code for [the previous figure] starts with the command `beginfig(1)' and ends with the command `endfig(1)'. They simply write "`beginfig( )'" and "`endfig()'" to `out_stream', The optional @@ -1171,6 +1311,8 @@ current_picture.output(); endfig(1); + [Figure 51 not displayed.] + Multiple objects, or complex objects made up of sub-objects, can be stored in a `Picture', so that operations can be applied to them as a group: @@ -1215,6 +1357,8 @@ current_picture.shift(10, 0, 3); current_picture.output(); + [Figure 52 not displayed.] + Let's say the complex object in [the previous figure] represents a furnace. From the point of view of 3DLDF, however, it's not an object at all, and the drawing consists of a collection of unrelated @@ -1314,46 +1458,3 @@ (1) Namespaces are described in Stroustrup, `The C++ Programming Language', Chapter 8. - -File: 3DLDF.info, Node: Parallel Projections, Next: The Perspective Projection, Prev: Projections, Up: Projections - -Parallel Projections --------------------- - - When a `Picture' is projected onto the x-y plane, the x and y-values -from the `world_coordinates' of the `Points' belonging to the objects -on the `Picture' are copied to their `projective_coordinates', which are -used in the MetaPost code written to `out_stream'. If a `Picture' P -contains an object in the x-y plane, or in a plane parallel to the x-y -plane, then the result of `P.output(Projections::PARALLEL_X_Y)' is -more-or-less equivalent to just using MetaPost without 3DLDF. - - Rectangle r(origin, 3, 3, 90); - Circle c(origin, 3, 90); - c *= r.shift(0, 0, 5); - r.draw(); - c.draw(); - current_picture.output(Projections::PARALLEL_X_Y); - - If the objects do not lie in the x-y plane, or a plane parallel to -the x-y plane, then the projection will be distorted: - - current_picture.output(Projections::PARALLEL_X_Y); - - `Picture::output()' can be called with an additional `real' argument -FACTOR for magnifying or shrinking the `Picture'. - - Rectangle r(origin, 4, 4, 90, 60); - Circle c(origin, 4, 90, 60); - c *= r.shift(0, 0, 5); - r.filldraw(black, gray); - c.unfilldraw(black); - current_picture.output(Projections::PARALLEL_X_Y, .5); - current_picture.shift(2.5); - current_picture.output(Projections::PARALLEL_X_Y); - current_picture.shift(1); - current_picture.output(Projections::PARALLEL_X_Y, 2); - - Parallel projection onto the x-z and z-y planes are completely -analogous to parallel projection onto the x-y plane. - diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-3 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-3 --- 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-3 2003-12-10 18:44:55.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-3 2004-01-16 19:03:28.000000000 +0100 @@ -1,11 +1,11 @@ This is 3DLDF.info, produced by makeinfo version 4.5 from 3DLDF.texi. -This is the 3DLDF User and Reference Manual, edition 1.1.4 for 3DLDF -1.1.4. This manual was last updated on 10 December 2003. 3DLDF is a +This is the 3DLDF User and Reference Manual, edition 1.1.5.1 for 3DLDF +1.1.5.1. This manual was last updated on 16 January 2004. 3DLDF is a GNU package for three-dimensional drawing with MetaPost output. The author is Laurence D. Finston. - Copyright (C) 2003 Laurence D. Finston. + Copyright (C) 2003, 2004 Laurence D. Finston. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, @@ -20,6 +20,55 @@ END-INFO-DIR-ENTRY  +File: 3DLDF.info, Node: Parallel Projections, Next: The Perspective Projection, Prev: Projections, Up: Projections + +Parallel Projections +-------------------- + + When a `Picture' is projected onto the x-y plane, the x and y-values +from the `world_coordinates' of the `Points' belonging to the objects +on the `Picture' are copied to their `projective_coordinates', which are +used in the MetaPost code written to `out_stream'. If a `Picture' P +contains an object in the x-y plane, or in a plane parallel to the x-y +plane, then the result of `P.output(Projections::PARALLEL_X_Y)' is +more-or-less equivalent to just using MetaPost without 3DLDF. + + Rectangle r(origin, 3, 3, 90); + Circle c(origin, 3, 90); + c *= r.shift(0, 0, 5); + r.draw(); + c.draw(); + current_picture.output(Projections::PARALLEL_X_Y); + + [Figure 53 not displayed.] + + If the objects do not lie in the x-y plane, or a plane parallel to +the x-y plane, then the projection will be distorted: + + current_picture.output(Projections::PARALLEL_X_Y); + + [Figure 54 not displayed.] + + `Picture::output()' can be called with an additional `real' argument +FACTOR for magnifying or shrinking the `Picture'. + + Rectangle r(origin, 4, 4, 90, 60); + Circle c(origin, 4, 90, 60); + c *= r.shift(0, 0, 5); + r.filldraw(black, gray); + c.unfilldraw(black); + current_picture.output(Projections::PARALLEL_X_Y, .5); + current_picture.shift(2.5); + current_picture.output(Projections::PARALLEL_X_Y); + current_picture.shift(1); + current_picture.output(Projections::PARALLEL_X_Y, 2); + + [Figure 55 not displayed.] + + Parallel projection onto the x-z and z-y planes are completely +analogous to parallel projection onto the x-y plane. + + File: 3DLDF.info, Node: The Perspective Projection, Prev: Parallel Projections, Up: Projections The Perspective Projection @@ -46,6 +95,8 @@ = 5cm, at an angle of 90 degrees - 40 degrees = 50 degrees to the ground line. + [Figure 56 not displayed.] + While it's possible to use 3DLDF to make a perspective construction in the traditional way, as [the previous figure] shows, the code for [next figure] @@ -58,6 +109,8 @@ r.shift(p - r.get_point(0)); r.draw(); + [Figure 57 not displayed.] + In [the second-to-last figure] , it was convenient to start with the corner point r_0; if we needed the center of R, it would have to be found from the corner points. However, in 3DLDF, `Rectangles' are most @@ -80,6 +133,8 @@ angle of a vanishing point, the further away it is from the center of vision, as [next figure] shows: + [Figure 58 not displayed.] + In [the previous figure] , the 0.5 degrees vanishing point is nearly 5 and 3/4 meters away from the CV, and a line receding to it will be very nearly horizontal. However, the distance from the focus to the CV @@ -107,6 +162,8 @@ r.draw(); current_picture.output(); + [Figure 59 not displayed.] + ---------- Footnotes ---------- (1) There are many books on linear perspective for artists. I've @@ -168,6 +225,8 @@ r.draw(); current_picture.output(f); + [Figure 60 not displayed.] + The "up" direction is calculated by the `Focus' constructor automatically. An optional argument can be used to specify the angle by which to rotate the `Focus' about the line PD. @@ -180,6 +239,8 @@ r.draw(); current_picture.output(f); + [Figure 61 not displayed.] + Alternatively, a `Focus' can be declared using three `real' arguments each for the x, y, and z-coordinates of `position' and `direction', respectively, followed by the `real' arguments for @@ -191,6 +252,8 @@ r.draw(); current_picture.output(f); + [Figure 62 not displayed.] + `Focuses' contain two `Transforms', `transform' and `persp'. A `Focus' can be located anywhere in 3DLDF's coordinate system. However, performing the perspective projection is more convenient, if `position' @@ -227,6 +290,8 @@ } endfig(1); + [Figure 63 not displayed.] + In [the previous figure] , `current_picture' is output 5 times within a single MetaPost figure. Since the file passed to MetaPost is called `persp.mp', the file of Encapsulated PostScript (EPS) code @@ -277,17 +342,23 @@ c.draw(); current_picture.output(); + [Figure 64 not displayed.] + If instead, C is filled or filldrawn, only the parts of R that are not covered by C should be visible: r.draw(); c.filldraw(); + [Figure 65 not displayed.] + What parts of `r' are covered depend on the point of view, i.e., the position and direction of the `Focus' used for outputting the `Picture': default_focus.set(8, 0, -5, 5, 3, 5, 10); + [Figure 66 not displayed.] + Determining what objects cover other objects in a program for 3D graphics is called "surface hiding", and is performed by a "hidden surface algorithm". 3DLDF currently has a very primitive hidden @@ -366,6 +437,8 @@ (-1.39791, -4.05125, 0.208945) -- (-2.87319, -3.93975, 0.230717) -- cycle; + [Figure 67 not displayed.] + In [the previous figure] , the `Rectangles' r_0 and r_1 intersect along the x-axis. The z-values of the `world_coordinates' of r_0 are -1.41421 and 1.41421 (two `Points' each), while those of r_1 are @@ -386,6 +459,8 @@ current_picture.output(default_focus, PERSP, 1, MAX_Z); + [Figure 68 not displayed.] + In [next figure] , the `Shapes' on `current_picture' are sorted according to the minimum z-values of the `projective_coordinates' of the `Points' belonging to the `Shapes'. `r1' is drawn and filled last, @@ -395,6 +470,8 @@ current_picture.output(default_focus, PERSP, 1, MIN_Z); + [Figure 69 not displayed.] + Neither sorting by the mean z-value in the `projective_coordinates', nor suppressing sorting does any good. In each case, one `Rectangle' is always drawn and filled last, covering parts of the other that lie @@ -410,6 +487,8 @@ c.filldraw(black, gray); current_picture.output(default_focus, PERSP, 1, NO_SORT); + [Figure 70 not displayed.] + Even where objects don't intersect, their projections may. In order to handle these cases properly, it is necessary to break up the `Shapes' on a `Picture' into smaller `Shapes', until there are none @@ -428,6 +507,8 @@ Therefore, for n `Shapes', there will be n! / ((n - r)! r!) (possibly time-consuming) comparisons. + [Figure 71 not displayed.] + Clearly, such a hidden surface algorithm would considerably increase run-time. @@ -535,36 +616,94 @@ 3DLDF is available for downloading from `http://ftp.gnu.org/gnu/3dldf'. The official 3DLDF website is `http://www.gnu.org/software/3dldf'. The "tarball", i.e., the -compressed archive file `3DLDF-1.1.4.tar.gz' unpacks into a directory -called `/3DLDF-1.1.4/'. +compressed archive file `3DLDF-1.1.5.1.tar.gz' unpacks into a directory +called `/3DLDF-1.1.5.1/'. On a typical Unix-like system, entering the following commands at the command line in a shell will unpack the 3DLDF distribution. Please note that the form of the commands may differ on your system. - gunzip 3DLDF-1.1.4.tar.gz - tar xpvf 3DLDF-1.1.4.tar + gunzip 3DLDF-1.1.5.1.tar.gz + tar xpvf 3DLDF-1.1.5.1.tar The `p' option to `tar' ensures that the files will have the same permissions as when they were packed. - The directory `3DLDF-1.1.4/' contains a `configure' script, which + The directory `3DLDF-1.1.5.1/' contains a `configure' script, which should be called from the command line in the shell, using the absolute -path of `3DLDF-1.1.4/' as the prefix argument. For example, if the -path is `/usr/local/mydir/3DLDF-1.1.4/', `configure' should be invoked -as follows: +path of `3DLDF-1.1.5.1/' as the prefix argument. For example, if the +path is `/usr/local/mydir/3DLDF-1.1.5.1/', `configure' should be +invoked as follows: - cd 3DLDF-1.1.4 - configure --prefix=/usr/local/mydir/3DLDF-1.1.4/ + cd 3DLDF-1.1.5.1 + configure --prefix=/usr/local/mydir/3DLDF-1.1.5.1/ `configure' generates a `Makefile' from the `Makefile.in' in -`3DLDF-1.1.4/', and in each of the subdirectories `3DLDF-1.1.4/CWEB', -`3DLDF-1.1.4/DOC', and `3DLDF-1.1.4/DOC/TEXINFO'. Now, `make install' -causes the 3DLDF to be built. The executable is called `3dldf'. +`3DLDF-1.1.5.1/', and in each of the subdirectories +`3DLDF-1.1.5.1/CWEB', `3DLDF-1.1.5.1/DOC', and +`3DLDF-1.1.5.1/DOC/TEXINFO'. Now, `make install' causes the 3DLDF to +be built. The executable is called `3dldf'. See the files `README' and `INSTALL' in the 3DLDF distribution for more information. +* Menu: + +* Template Functions:: + + +File: 3DLDF.info, Node: Template Functions, Prev: Installing 3DLDF, Up: Installing 3DLDF + +Template Functions +------------------ + + 3DLDF 1.1.5 is the first release that contains "template functions", +namely `template C* create_new()', which is defined in +`creatnew.web', and `template Real get_second_largest()', +which is defined in `gsltmplt.web'. *Note Dynamic Allocation of +Shapes::, and *Note Get Second Largest Real::. + + In order for template functions to be instantiated correctly, their +_definitions_ must be available in each compilation unit where +specializations are declared or used. For non-template functions, it +suffices for their _declarations_ to be available, and their +definitions are found at link-time. For this reason, the definitions +of `create_new()' and `get_second_largest()' are in their own CWEB +files, and are written to their own header files. The latter are +included in the other CWEB files that need them. + + In addition, `AM_CXXFLAGS = -frepo' has been added to the file +`Makefile.am' in `3DLDF-1.1.5/CWEB/', so that the C++ + + compiler is called using the `-frepo' option. The manual `Using and +Porting the GNU Compiler Collection' explains this as follows: + + "Compile your template-using code with `-frepo'. The compiler will + generate files with the extension `.rpo' listing all of the + template instantiations used in the corresponding object files + which could be instantiated there; the link wrapper, `collect2', + will then update the `.rpo' files to tell the compiler where to + place those instantiations and rebuild any affected object files. + The link-time overhead is negligible after the first pass, as the + compiler will continue to place the instantiations in the same + files."(1) + + The first time the executable `3dldf' is built, the files that use +the template functions are recompiled one or more times, and the linker +is also called several times. This doesn't happen anymore, once the +`.rpo' files exist. + + Template instantiation differs from compiler to compiler, so using +template functions will tend to make 3DLDF less portable. I am no +longer able to compile it on the DECalpha Personal Workstation I had +been using with the DEC C++ compiler. *Note Ports::, for more +information. + + ---------- Footnotes ---------- + + (1) Stallman, Richard M. `Using and Porting the GNU Compiler +Collection', p. 285. +  File: 3DLDF.info, Node: Running 3DLDF, Prev: Installing 3DLDF, Up: Installing and Running 3DLDF @@ -572,15 +711,15 @@ ============= To use 3DLDF, call `make run' from the command line in the shell. -The working directory should be `3DLDF-1.1.4/' or `3DLDF-1.1.4/CWEB'. -Either will work, but the latter may be more convenient, because this -is the location of the CWEB, TeX and MetaPost files that you'll be -editing. Alternatively, call `ldfr', which is merely a shell script -that calls `make run'. This takes care of running `3dldf', MetaPost, -TeX, and `dvips', producing a PostScript file containing your drawings. -You can display the latter on your terminal using Ghostview or some -other PostScript viewer, print it out, and whatever else you like to do -with PostScript files. +The working directory should be `3DLDF-1.1.5.1/' or +`3DLDF-1.1.5.1/CWEB'. Either will work, but the latter may be more +convenient, because this is the location of the CWEB, TeX and MetaPost +files that you'll be editing. Alternatively, call `ldfr', which is +merely a shell script that calls `make run'. This takes care of +running `3dldf', MetaPost, TeX, and `dvips', producing a PostScript +file containing your drawings. You can display the latter on your +terminal using Ghostview or some other PostScript viewer, print it out, +and whatever else you like to do with PostScript files. However, you can also perform the actions performed by `make run' by hand, by writing your own shell scripts, by defining Emacs-Lisp @@ -589,12 +728,12 @@ this by hand. The CWEB source files for 3DLDF are in the subdirectory -`3DLDF-1.1.4/CWEB/'. They must be `ctangled', and the resulting C++ +`3DLDF-1.1.5.1/CWEB/'. They must be `ctangled', and the resulting C++ files must be compiled and linked, in order to create the executable file `3dldf'. The C++ files and header files generated by `ctangle', the object files generated by the compiler, and the executable `3dldf' -all reside in `3DLDF-1.1.4/CWEB/'. Therefore, the latter must be your -working directory. +all reside in `3DLDF-1.1.5.1/CWEB/'. Therefore, the latter must be +your working directory. Since 3DLDF has no input routine as yet, as explained in *Note No Input Routine::, it is necessary to add C++ code to the function @@ -621,6 +760,8 @@ current_picture.output(default_focus, PERSP, 1, NO_SORT); endfig(1); + [Figure 72 not displayed.] + 1. Save `main.web', and any other CWEB files you've changed. Since these files have changed, they must be `ctangled', and the resulting C++ files must be recompiled. If you've changed any @@ -688,10 +829,152 @@ * Menu: +* Converting EPS Files:: * Command Line Arguments::  -File: 3DLDF.info, Node: Command Line Arguments, Prev: Running 3DLDF, Up: Running 3DLDF +File: 3DLDF.info, Node: Converting EPS Files, Next: Command Line Arguments, Prev: Running 3DLDF, Up: Running 3DLDF + +Converting EPS Files +-------------------- + + ImageMagick (http://www.imagemagick.org) is a "collection of tools +and libraries" for image manipulation. It provides a `convert' utility +which can convert images from one format to another. It can convert +structured PostScript (PS) to to Portable Network Graphics (PNG) +(http://www.libpng.org/pub/png/index.html), but _not_ EPS (Encapsulated +PostScript) to PNG. Nor can it convert EPS to structured PostScript. + + It is possible to have MetaPost generate structured PostScript +directly by including the command `prologues:=1;' at the beginning of +the MetaPost input. However, this "generally doesn't work when you use +TeX fonts."(1) This is a significant problem if your labels contain +math mode material, and you haven't already taken steps to ensure that +appropriate fonts will be used in the PS output. + + In the following, I describe the _only way_ I've found to convert an +EPS image to PNG format while still using TeX fonts. There may be +other and better ways of doing this, but I haven't found them. + + 1. Assume the EPS image is in the file `3DLDFmp.1' Include the EPS + image in a TeX file which looks like this: + + \advance\voffset by -1in + \advance\hoffset by -1in + \nopagenumbers + \input epsf + \epsfverbosetrue + \def\epsfsize#1#2{#1} + \setbox0=\vbox{\epsffile{3DLDFmp.1}} + \vsize=\ht0 + \hsize=\wd0 + \special{papersize=\the\wd0,\the\ht0} + \box0 + \bye + + Do not name this file `3DLDFmp.1.tex'! While this worked fine for + me on a DECalpha Personal Workstation running under Tru64 Unix + 5.1, with TeX, Version 3.1415 (C version 6.1), and dvipsk 5.58f, + it failed on a PC Pentium II XEON under Linux 2.4, with TeX, + Version 3.14159 (Web2C 7.4.5), and dvips(k) 5.92b, kpathsea + version 3.4.5, with the following error message: + ``No BoundingBox comment found in file examples.1; using defaults'' + + The resulting PS image had the wrong size and the the graphic was + positioned improperly. + + Apparently, it confuses the EPSF macros when the name of an + included image is the same as `\jobname'. So, for this example, + let's call it `3DLDFmp.1_.tex'. + + You don't really need to call the macro `\epsfverbosetrue'. If you + do, it will print the measurements of the bounding box and other + information to standard output.(2) + + 2. Run `tex 3DLDFmp.1_.tex'. + + 3. Run `dvips -o 3DLDF.1.ps 3DLDFmp.1_.dvi'. + + 4. Run `convert 3DLDF.1.ps 3DLDFmp.1.png'. + + ImageMagick supplies a ``display'' utility, which can be used to +display the PNG image: + + display 3DLDFmp.1.png + + It can be included in an HTML document as follows: + + [Fig. 1]..png' to a CD-R (Compact +Disk, Recordable), when `number' had more than one digit. + +* Menu: + +* Converting EPS Files ELISP:: + + ---------- Footnotes ---------- + + (1) Hobby, `A User's Manual for MetaPost', pp. 21-22. + + (2) Rokicki, `Dvips: A DVI-to-PostScript Translator', p. 24. + + +File: 3DLDF.info, Node: Converting EPS Files ELISP, Prev: Converting EPS Files, Up: Converting EPS Files + +Emacs-Lisp Functions +.................... + + The file `3DLDF-1.1.5.1/CWEB/cnepspng.el' contains definitions of +two Emacs-Lisp functions that can be used to convert Encapsulated +PostScript (EPS) files to structured PostScript (PS) and Portable +Network Graphics (PNG) files. + + - Emacs-Lisp function: convert-eps filename do-not-delete-files + Converts an EPS image file to the PS and PNG formats. + + If called interactively, `convert-eps' prompts for the filename, + including the extension, of an EPS image file. It follows the + procedure described above in *Note Converting EPS Files::, to + create `FILENAME.ps' and `FILENAME.png'. + + If DO-NOT-DELETE-FILES is `nil', the `.tex', `.dvi', and `.log' + files will be deleted. This is the case when `convert-eps' is + called interactively with no prefix argument. If `convert-eps' is + called interactively with a prefix argument, or non-interactively + with a non-`nil' DO-NOT-DELETE-FILES argument, these files will + not be deleted. + + - Emacs-Lisp function: convert-eps-loop arg start end + Converts a set of EPS image files to the PS and PNG formats. The + files must all have the same filename, and the extensions must + form a range of positive integers. For example, + `convert-eps-loop' can be used to convert the files `3DLDFmp.1', + `3DLDFmp.2', and `3DLDFmp.3' to `3DLDFmp.1.ps', `3DLDFmp.2.ps', and + `3DLDFmp.3.ps' on the one hand, and `3DLDFmp.1.png', + `3DLDFmp.2.png', `3DLDFmp.3.png' on the other. + + If `convert-eps-loop' is called interactively, it prompts for + FILENAME _with no extension_ and the starting and ending numbers + of the range. + + For all i \in \INT and START \le i \le END, `convert-eps-loop' + checks whether a file named `FILENAME.I' exists. If it does, it + calls `convert-eps', passing `FILENAME.I' as the latter's FILENAME + argument. + + DO-NOT-DELETE-FILES is also passed to `convert-eps'. If it's + `nil', the `.tex', `.dvi', and `.log' files will be deleted. This + is the case when `convert-eps-loop' is called interactively with + no prefix argument. If `convert-eps-loop' is called interactively + with a prefix argument, or non-interactively with a non-`nil' + DO-NOT-DELETE-FILES argument, these files will not be deleted. + + +File: 3DLDF.info, Node: Command Line Arguments, Prev: Converting EPS Files, Up: Running 3DLDF Command Line Arguments ---------------------- @@ -741,10 +1024,8 @@ `LDF_REAL_DOUBLE'. The meaning of `real' is determined by means of conditional compilation. If `real' is `float', 3DLDF will require less memory than if `real' is `double', but its - calculations will be less precise. - - Please note that it currently does not work to define `real' to be - `double'! + calculations will be less precise. `real' is "typedeffed" to + `float' by default. - typedef: real_pair first second Synonymous with `pair'. @@ -777,7 +1058,7 @@ Synonymous with `pair'.  -File: 3DLDF.info, Node: Global Constants and Variables, Next: Color Reference, Prev: Typedefs and Utility Structures, Up: Top +File: 3DLDF.info, Node: Global Constants and Variables, Next: Dynamic Allocation of Shapes, Prev: Typedefs and Utility Structures, Up: Top Global Constants and Variables ****************************** @@ -786,6 +1067,17 @@ found in `pspglb.web'. Others, of types defined in 3DLDF, are described in subsequent chapters. + - Constants: bool ldf_real_float + - : bool ldf_real_double + Set to 0 or 1 to match the values of the preprocessor macros + `LDF_REAL_FLOAT' and `LDF_REAL_DOUBLE'. The latter are used for + conditional compilation and determine whether `real' is + "typedeffed" to `float' or `double', i.e., whether `real' is made + to be a synonym of `float' or `double' using `typedef'. + + `ldf_real_float' and `ldf_real_double' can be used to control + conditional expressions in non-conditionally compiled code. + - Constant: real PI The value of `PI' is calculated as 4.0 * arctan(1.0). I believe that a preprocessor macro "`PI'" was available when I compiled @@ -816,26 +1108,35 @@ - Constant: real INVALID_REAL_SHORT `first' is `INVALID_REAL' and `second' is 0. - - Constant: real MAX_REAL - The largest `real' value permitted in 3DLDF. It is the second + - Variable: real MAX_REAL + The largest `real' value permitted in the the elements of + `Transforms' and the coordinates of `Points'. It is the second largest `real' value (i.e., `float' or `double') on a given machine (`INVALID_REAL' is the largest). - However, the way it's calculated depends on the system's floating - point representation and the size of certain data types. - Currently, `MAX_REAL' can only be calculated correctly for 32-bit, - little-endian architectures. I plan to fix this soon, so that it - will work on other architectures soon. When I have, I will supply - a patch. *Note Ports::. - - - - Constant: real MAX_REAL_SQRT - The square root of `MAX_REAL'. Used in `Point::magnitude()' - (*note Vector Operations::). The magnitude of a `Point' is found - by using the formula \sqrtx^2 + y^2 + z^2. x, y, and z are all - tested against `MAX_REAL_SQRT' to ensure that x^2, y^2, and z^2 - will all be less than or equal to `MAX_REAL' before trying to - calculate them. + `MAX_REAL' is a variable, but it should be used like a constant. + In other words, users should never reset its value. It can't be + declared `const' because its value must be calculated using + function calls, which can't be done before the entry point of the + program, i.e., `main()'. Therefore, the value of `MAX_REAL' is + calculated at the beginning of `main()'. + + - Variable: real MAX_REAL_SQRT + The square root of `MAX_REAL'. + + `MAX_REAL_SQRT' is a variable, but it should be used like a + constant. In other words, users should never reset its value. It + can't be declared `const' because its value is calculated using the + `sqrt()' function, which can't be done before the entry point of + the program, i.e., `main()'. Therefore, the value of + `MAX_REAL_SQRT' is set after `MAX_REAL' is calculated, at the + beginning of `main()'. + + `MAX_REAL_SQRT' is used in `Point::magnitude()' (*note Vector + Operations::). The magnitude of a `Point' is found by using the + formula \sqrtx^2 + y^2 + z^2. x, y, and z are all tested against + `MAX_REAL_SQRT' to ensure that x^2, y^2, and z^2 will all be less + than or equal to `MAX_REAL' before trying to calculate them. Metafont implements an operation called "Pythagorean addition", notated as "`++'"which can be used to calculate distances without @@ -853,399 +1154,56 @@ (1) Knuth, Donald E. `The Metafontbook', p. 66.  -File: 3DLDF.info, Node: Color Reference, Next: Input and Output, Prev: Global Constants and Variables, Up: Top - -Color Reference -*************** - - Class `Color' is defined in `colors.web'. - -* Menu: - -* Color Data Members:: -* Color Constructors and Setting Functions:: -* Color Operators:: -* Modifying Colors:: -* Showing Colors:: -* Querying Colors:: -* Defining and Initializing Colors:: -* Namespace Colors:: - - -File: 3DLDF.info, Node: Color Data Members, Next: Color Constructors and Setting Functions, Prev: Color Reference, Up: Color Reference - -Data Members -============ - - - Variable: string name - The name of the `Color'. - - - Variable: bool use_name - If `true', `name' is written to `out_stream' when the `Color' is - used for drawing or filling. Otherwise, the RGB (red-green-blue) - values are written to `out_stream'. - - - Variable: bool on_free_store - `true', if the `Color' has been created by `create_new_color()', - which allocates memory for the `Color' on the free store. - Otherwise `false'. `Colors' should only ever be dynamically - allocated by using `create_new_color()' (*note Color - Reference;;Constructors and Setting Functions: Color Constructors - and Setting Functions.). - - - Variable: real red_part - - Variable: real green_part - - Variable: real blue_part - The RGB (red-green-blue) values of the `Color'. A `real' value r - is valid for these variables if and only if 0 <= r <= 1. - - -File: 3DLDF.info, Node: Color Constructors and Setting Functions, Next: Color Operators, Prev: Color Data Members, Up: Color Reference - -Constructors and Setting Functions -================================== +File: 3DLDF.info, Node: Dynamic Allocation of Shapes, Next: System Information, Prev: Global Constants and Variables, Up: Top - - Default constructor: void Color (void) - Creates a `Color' and initializes its `red_part', `green_part', - and `blue_part' to 0. `use_name' and `on_free_store' are set to - `false'. - - - Copy constructor: void Color (const Color& C, [const string N = "", - [const bool U = `true']]) - Creates a `Color' and makes it a copy of C. If N is not the empty - string and U is `true', `use_name' is set to `true'. Otherwise, - its set to `false'. - - - Constructor: void Color (const string N, const unsigned short R, - const unsigned short G, const unsigned short B, [const bool U - = `true']) - Creates a `Color' with name N. Its `red_part', `green_part', and - `blue_part' are set to r/255.0, g/255.0, and b/255.0, respectively. - `use_name' is set to U. - - - Setting function: void set (const string N, const unsigned short R, - const unsigned short G, const unsigned short B, [const bool U - = `false']) - Corresponds to the constructor above, except that U is `false' by - default. - - - Constructor: void Color (const real R, const real G, const real B) - Creates an unnamed `Color' using the `real' values R, G, and B for - its `red_part', `green_part', and `blue_part', respectively. - - - Setting function: void set (const real R, const real G, const real B) - Corresponds to the constructor above. - - - Inline static function: Color* create_new_color (void) - Pseudo-constructor for dynamic allocation of `Colors'. It creates - a `Color' on the free store and allocate memory for it using - `new(Color)'. It returns a pointer to the new `Color'. - - This function is used in the drawing and filling functions for - `Path' and `Solid'. `Point::drawdot()' should be changed to use - it too, but I haven't gotten around to doing this yet. - - -File: 3DLDF.info, Node: Color Operators, Next: Modifying Colors, Prev: Color Constructors and Setting Functions, Up: Color Reference - -Operators -========= - - - Assignment operator: void operator= (const Color& C) - Sets `name' to the empty `string', `use_name' to `false', and - `red_part', `green_part', and `blue_part' to C.`red_part', - C.`green_part', and C.`blue_part', respectively. - - - `const' operator: bool operator== (const Color& C) - Equality operator. Returns `true', if the `red_parts', - `green_parts', and `blue_parts' of `*this' and C are equal, - otherwise `false'. The `names' and `use_names' are not compared. - - - `const' operator: bool operator!= (const Color& C) - Inequality operator. Returns `false', if the `red_parts', - `green_parts', and `blue_parts' of `*this' and C are equal, - otherwise `true'. The `names' and `use_names' are not compared. - - - Non-member function: ostream& operator<< (ostream& O, const Color& C) - Output operator. Writes the MetaPost code for the `Color' to - `out_stream' when a `Picture' is output. This occurs when the - `Color' has been used as an argument to drawing or filling - functions. - - If `use_name' is `true', `name' is written to `out_stream'. - Otherwise, "(`red_part', `green_part', `blue_part')" is written to - `out_stream'. - - -File: 3DLDF.info, Node: Modifying Colors, Next: Showing Colors, Prev: Color Operators, Up: Color Reference - -Modifying -========= - - - Function: void set_name (const string S) - Sets `name' to S. `use_name' is not reset. - - - Function: void set_use_name (const bool B) - Sets `use_name' to B. - - - Function: void modify (const real R, [const real G = 0, [const real - B = 0]]) - Adds R, G, and B to `red_part', `green_part', and `blue_part', - respectively. Following the addition, if `red_part', - `green_part', and/or `blue_part' is greater than 1, it is reduced - to 1. If it is less than 0, it is increased to 0. - - - Function: void set_red_part (const real Q) - - Function: void set_green_part (const real Q) - - Function: void set_blue_part (const real Q) - Let p stand for `red_part', `green_part', or `blue_part', - depending upon which function is used. If 0 <= q <= 1, p is set - to q. If q < 0, p is set to 0. If q > 1, p is set to 1. - - -File: 3DLDF.info, Node: Showing Colors, Next: Querying Colors, Prev: Modifying Colors, Up: Color Reference - -Showing -======= - - - `const' function: void show ([string TEXT = ""]) - Prints information about the `Color' to standard output. If TEXT - is not the empty `string', prints TEXT on a line of its own. - Otherwise, it prints "Color:". Then it prints `name', `use_name', - `red_part', `green_part', and `blue_part'. - - -File: 3DLDF.info, Node: Querying Colors, Next: Defining and Initializing Colors, Prev: Showing Colors, Up: Color Reference - -Querying -======== - - - Inline `const' function: bool is_on_free_store (void) - Returns `on_free_store'. This will only be true, if the `Color' - was created by `create_new_color()' (*note Color Reference; - Constructors and Setting Functions: Color Constructors and Setting - Functions.). - - - Inline `const' function: real get_red_part ([bool DECIMAL = `false']) - - Inline `const' function: real get_green_part ([bool DECIMAL = - `false']) - - Inline `const' function: real get_blue_part ([bool DECIMAL = - `false']) - These functions return the `red_part', `green_part', or - `blue_part' of the `Color', respectively. If DECIMAL is `false' - (the default), the actual `real' value of the "part" is returned. - Otherwise, the corresponding whole number n such that 0 <= n <= 255 - is returned. - - - `const' function: bool get_use_name (void) - Returns `use_name'. - - - Inline `const' function: string get_name (void) - Returns `name'. - - -File: 3DLDF.info, Node: Defining and Initializing Colors, Next: Namespace Colors, Prev: Querying Colors, Up: Color Reference - -Defining and Initializing Colors -================================ - - - `const' function: void define_color_mp () - Writes MetaPost code to `out_stream', in order to define objects of - type `color' within MetaPost, and set their `redparts', - `greenparts', and `blueparts'. - - - Static function: void initialize_colors (void) - Calls `define_color_mp()' (described above) for the `Colors' that - are defined in `namespace Colors' (*note Namespace Colors::). - - -File: 3DLDF.info, Node: Namespace Colors, Prev: Defining and Initializing Colors, Up: Color Reference - -Namespace Colors. -================= - - - Constant: const Color red - - Constant: const Color green - - Constant: const Color blue - - Constant: const Color cyan - - Constant: const Color yellow - - Constant: const Color magenta - - Constant: const Color orange_red - - Constant: const Color violet_red - - Constant: const Color pink - - Constant: const Color green_yellow - - Constant: const Color orange - - Constant: const Color violet - - Constant: const Color purple - - Constant: const Color blue_violet - - Constant: const Color yellow_green - - Constant: const Color black - - Constant: const Color white - - Constant: const Color gray - - Constant: const Color light_gray - These constant `Colors' can be used in drawing and filling - commands. - - - Constant: const Color default_background - The default background color. Equal to `white' per default. - - - Pointer: const Color* background_color - Points to `default_background' by default. - - - Pointer: const Color* default_color - Points to `black' by default. - - - Pointer: const Color* help_color - Points to `green' by default. - - The following vectors of pointers to `Color' can be used in the -drawing and filling functions for `Solid' (*note Solid Reference; -Drawing and Filling: Drawing and Filling Solids.). - - - Vector: const vector default_color_vector - Contains one pointer, namely `default_color'. - - - Vector: const vector help_color_vector - Contains one pointer, namely `help_color'. - - - Vector: const vector background_color_vector - Contains one pointer, namely `background_color'. - - -File: 3DLDF.info, Node: Input and Output, Next: Shape Reference, Prev: Color Reference, Up: Top - -Input and Output -**************** - -* Menu: - -* I/O Global Variables:: -* I/O Functions:: - - -File: 3DLDF.info, Node: I/O Global Variables, Next: I/O Functions, Prev: Input and Output, Up: Input and Output - -Global Variables -================ - - - Variable: ifstream in_stream - Intended for inputting files of input code. However, 3DLDF does - not currently have a routine for reading input code. `in_stream' - is currently attached to the file `ldfinput.ldf' by - `initialize_io()' (*note I/O Functions::). `in_stream' is read in - character-by-character in `main()', however this serves no useful - purpose as yet. - - - Variable: ofstream out_stream - Used for writing the file of MetaPost code, which is 3DLDF's - output. Currently attached to the file `subpersp.mp' by - `initialize_io()' (*note I/O Functions::). - - - Variable: ofstream tex_stream - TeX code can be written to a file through `tex_stream', if - desired. 3DLDF makes no use of it itself. Currently attached to - `subpersp.tex' by `initialize_io()' (*note I/O Functions::). - - -File: 3DLDF.info, Node: I/O Functions, Prev: I/O Global Variables, Up: Input and Output - -I/O Functions -============= - - - Function: void initialize_io (string IN_STREAM_NAME, string - OUT_STREAM_NAME, string TEX_STREAM_NAME, char* PROGRAM_NAME) - Opens files with names specified by the first three arguments, and - attaches them to the file streams `in_stream', `out_stream', and - `tex_stream', respectively. Comments are written at the beginning - of the files, containing their names, a datestamp, and the name of - the program used to generate them. - - - Function: void write_footers (void) - Writes code at the end of the files attached to `in_stream', - `out_stream', and `tex_stream', before the streams are closed. - Currently, they write comments containing local variable lists for - use in Emacs. - - - Inline function: void beginfig (unsigned short I) - Writes "`beginfig(I)'" to `out_stream'. - - - Inline function: void endfig ([unsigned short I = 0]) - Writes "`endfig()'" to `out_stream'. The argument I is "syntactic - sugar"; it's ignored by `endfig()', but may help the user keep - track of what figure is being ended. - - -File: 3DLDF.info, Node: Shape Reference, Next: Transform Reference, Prev: Input and Output, Up: Top - -Shape Reference -*************** - - Class `Shape' is defined in `shapes.web'. - - `Shape' is an "abstract class", which means that all of its member -functions are pure virtual functions, and that it's only used as a base -class, i.e., no objects of type `Shape' may be declared. - - All of the "drawable" types in 3DLDF, `Point', `Path', `Ellipse', -etc., are derived from `Shape'. - - Deriving all of the drawable types from `Shape' makes it possible to -handle objects of different types in the same way. This is especially -important in the `Picture' functions, where objects of various types -(but all derived from `Shape') are accessed through pointers to -`Shape'. *Note Picture Reference::. - -* Menu: - -* Shape Data Members:: -* Shape Operators:: -* Copying Shapes:: -* Modifying Shapes:: -* Affine Transformations for Shapes:: -* Applying Transformations to Shapes:: -* Clearing Shapes:: -* Querying Shapes:: -* Showing Shapes:: -* Outputting Shapes:: - - -File: 3DLDF.info, Node: Shape Data Members, Next: Shape Operators, Prev: Shape Reference, Up: Shape Reference - -Data Members -============ - - - Protected static constants: signed short DRAWDOT - - : signed short DRAW - - : signed short FILL - - : signed short FILLDRAW - - : signed short UNDRAWDOT - - : signed short UNDRAW - - : signed short UNFILL - - : signed short UNFILLDRAW - Values used in the `output()' functions of the classes derived from - `Shape'. For example, in `Path', if the data member - `fill_draw_value' = `DRAW', then the MetaPost command `draw' is - written to `out_stream' when that `Path' is output. - - -File: 3DLDF.info, Node: Shape Operators, Next: Copying Shapes, Prev: Shape Data Members, Up: Shape Reference - -Operators -========= - - - Pure virtual function: Transform operator*= (const Transform& T) - - -File: 3DLDF.info, Node: Copying Shapes, Next: Modifying Shapes, Prev: Shape Operators, Up: Shape Reference - -Copying -======= +Dynamic Allocation of Shapes +**************************** - - `const' pure virtual function: Shape* get_copy (void) - Copies an object, allocating memory on the free store for the copy, - and returns a pointer to `Shape' for accessing the copy. - - Used in the drawing and filling functions for copying the `Shape', - and putting a pointer to the copy onto the `vector shapes' - of the `Picture'. + - Template function: `template C*' create_new (const C* ARG) + - Template function: `template C*' create_new (const C& ARG) + These functions dynamically allocate an object derived from + `Shape' on the free store, returning a pointer to the type of the + `Shape' and setting `on_free_store' to `true'. + + If a non-zero pointer or a reference is passed to `create_new()', + the new object will be a copy of ARG. + + It is not possible to instantiate more than one specialization of + `create_new()' that takes no argument, because calls to these + functions would be ambiguous. If the new object is not meant to + be a copy of an existing one, `0' must be passed to `create_new()' + as its argument. + + `create_new' is called like this: + + Point* p = create_new(0); + p->show("*p:"); + -| *p: (0, 0, 0) + + Color c(.3, .5, .25); + Color* d = create_new(c); + d->show("*d:"); + -| + *d: + name == + use_name == 0 + red_part == 0.3 + green_part == 0.5 + blue_part == 0.25 + + + Point a0(3, 2.5, 6); + Point a1(10, 11, 14); + Path q(a0, a1); + Path* r = create_new(&q); + r->show("*r:"); + -| + *r: + points.size() == 2 + connectors.size() == 1 + (3, 2.5, 6) -- (10, 11, 14); + + Specializations of this template function are currently declared + for `Color', `Point', `Path', `Reg_Polygon', `Rectangle', + `Ellipse', `Circle', `Solid', and `Cuboid'. diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-4 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-4 --- 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-4 2003-12-10 18:44:55.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-4 2004-01-16 19:03:28.000000000 +0100 @@ -1,11 +1,11 @@ This is 3DLDF.info, produced by makeinfo version 4.5 from 3DLDF.texi. -This is the 3DLDF User and Reference Manual, edition 1.1.4 for 3DLDF -1.1.4. This manual was last updated on 10 December 2003. 3DLDF is a +This is the 3DLDF User and Reference Manual, edition 1.1.5.1 for 3DLDF +1.1.5.1. This manual was last updated on 16 January 2004. 3DLDF is a GNU package for three-dimensional drawing with MetaPost output. The author is Laurence D. Finston. - Copyright (C) 2003 Laurence D. Finston. + Copyright (C) 2003, 2004 Laurence D. Finston. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, @@ -20,6 +20,584 @@ END-INFO-DIR-ENTRY  +File: 3DLDF.info, Node: System Information, Next: Color Reference, Prev: Dynamic Allocation of Shapes, Up: Top + +System Information +****************** + + The functions described in this chapter are all declared in the +`namespace System'. They are for finding out information about the +system on which 3DLDF is being run. They are declared and defined in +`pspglb.web', except for the template function `get_second_largest()', +which is declared and defined in `gsltmplt.web'. + + There are two reasons for this. The first is that template +definitions must be available in the compilation units where +specializations are instantiated. I therefore write the template +definition of `get_second_largest()' to `gsltmplt.h', so it can be +included by the CWEB files that need it, currently `main.web' only. If +I wrote it to `pspglb.h', it would be included by all of the CWEB files +except for `loader.web', causing unnecessarily bloated object code. + + The other reason is because of the way way 3DLDF is built using +Automake and make. I originally tried to define `get_second_largest()' +in `pspglb.web' and wrote the definition to `gsltmplt.cc', which is no +problem with CWEB. However, I was unable to express the dependencies +among the CWEB, C++ , and object files in such a way that 3DLDF was +built properly. + + Therefore all template functions will be put into files either by +themselves, or in small groups. + +* Menu: + +* Endianness:: +* Register Width:: +* Get Second Largest Real:: + + +File: 3DLDF.info, Node: Endianness, Next: Register Width, Prev: System Information, Up: System Information + +Endianness +========== + + - Function: signed short get_endianness ([const bool VERBOSE = + `false']) + Returns the following values: + + 0 + if the processor is little-endian. + + 1 + if the processor is big-endian. + + -1 + if the endianness cannot be determined. + + + It is called by `is_little_endian()' and `is_big_endian()'. + + If VERBOSE is `true', messages are printed to standard output. + + This function has been adapted from Harbison, Samuel P., and + Guy L. Steele Jr. `C, A Reference Manual', pp. 163-164. This + book has the clearest explanation of endianness that I've found so + far. + + This is the C++ code: + + signed short + System::get_endianness(const bool verbose) + { + union { + long Long; + char Char[sizeof(long)]; + } u; + u.Long = 1; + if (u.Char[0] == 1) + { + if (verbose) + cout << "Processor is little-endian." + << endl << endl << flush; + return 0; + } + else if (u.Char[sizeof(long) - 1] == 1) + { + if (verbose) + cout << "Processor is big-endian." + << endl << endl << flush; + return 1; + } + else + { + cerr << "ERROR! In System::get_endianness():\n" + << "Can't determine endianness. Returning -1" + << endl << endl << flush; + return -1; + } + } + + - Function: bool is_big_endian ([const bool VERBOSE = `false']) + Returns `true' if the processor is big-endian, otherwise `false'. + If VERBOSE is `true', messages are printed to standard output. + + - Function: bool is_little_endian ([const bool VERBOSE = `false']) + Returns `true' if the processor is little-endian, otherwise + `false'. If VERBOSE is `true', messages are printed to standard + output. + + +File: 3DLDF.info, Node: Register Width, Next: Get Second Largest Real, Prev: Endianness, Up: System Information + +Register Width +============== + + - Function: unsigned short get_register_width (void) + Returns the register width of the CPU of the system on which 3DLDF + is being run. This will normally be either 32 or 64 bits. + + This is the C++ code: + + return (sizeof(void*) * CHAR_BIT); + + This assumes that an address will be the same size as the + processor's registers, and that `CHAR_BIT' will be the number of + bits in a byte. These are reasonable assumptions that apply to + all architectures I know about. + + This function is called by `is_32_bit()' and `is_64_bit()'. + + - Function: bool is_32_bit (void) + Returns `true' if the CPU of the system on which 3DLDF is being run + has a register width of 32 bits, otherwise `false'. + + - Function: bool is_64_bit (void) + Returns `true' if the CPU of the system on which 3DLDF is being run + has a register width of 64 bits, otherwise `false'. + + +File: 3DLDF.info, Node: Get Second Largest Real, Prev: Register Width, Up: System Information + +Get Second Largest Real +======================= + + - Template function: template Real get_second_largest + (Real MAX_VAL, [bool VERBOSE = `false']) + - Template specialization: float get_second_largest (float, bool) + - Template specialization: double get_second_largest (double, bool) + `get_second_largest' returns the second largest floating point + number of the type specified the template paramater REAL. If + VERBOSE is `true', messages are printed to standard output. + + This function is used for setting the value of `MAX_REAL'. *Note + Global Constants and Variables::. + + `get_second_largest' depends on there being an unsigned integer + type with the same length as REAL. This should always be the case + for `float' and `double', but may not be `long double'. + + MAX_VAL should be the largest number of type REAL on a given + architecture. The GNU C++ compiler GCC 3.3 does not currently + supply the `numeric_limits' template, so it is necessary to pass + one of the macros `FLT_MAX' or `DBL_MAX' explicitly, depending on + which specialization you use(1). When and if GCC supplies the + `numeric_limits' template, I will eliminate the MAX_REAL argument. + + ---------- Footnotes ---------- + + (1) If your system supplies an unsigned integer type with the same +length as `long double', then you can instantiate +`get_second_largest()' and call `get_second_largest(LDBL_MAX)'. However, I doubt that this amount of precision +would be worthwhile. If it ever were required, 3DLDF would have to be +changed in other ways, too. In particular, it would have to use more +precise trigonometric functions for rotations. *Note Accuracy::. + + +File: 3DLDF.info, Node: Color Reference, Next: Input and Output, Prev: System Information, Up: Top + +Color Reference +*************** + + Class `Color' is defined in `colors.web'. + +* Menu: + +* Color Data Members:: +* Color Constructors and Setting Functions:: +* Color Operators:: +* Modifying Colors:: +* Showing Colors:: +* Querying Colors:: +* Defining and Initializing Colors:: +* Namespace Colors:: + + +File: 3DLDF.info, Node: Color Data Members, Next: Color Constructors and Setting Functions, Prev: Color Reference, Up: Color Reference + +Data Members +============ + + - Variable: string name + The name of the `Color'. + + - Variable: bool use_name + If `true', `name' is written to `out_stream' when the `Color' is + used for drawing or filling. Otherwise, the RGB (red-green-blue) + values are written to `out_stream'. + + - Variable: bool on_free_store + `true', if the `Color' has been created by `create_new()', + which allocates memory for the `Color' on the free store. + Otherwise `false'. `Colors' should only ever be dynamically + allocated by using `create_new()'. *Note Color + Reference;;Constructors and Setting Functions: Color Constructors + and Setting Functions. + + - Variable: real red_part + - Variable: real green_part + - Variable: real blue_part + The RGB (red-green-blue) values of the `Color'. A `real' value r + is valid for these variables if and only if 0 <= r <= 1. + + +File: 3DLDF.info, Node: Color Constructors and Setting Functions, Next: Color Operators, Prev: Color Data Members, Up: Color Reference + +Constructors and Setting Functions +================================== + + - Default constructor: void Color (void) + Creates a `Color' and initializes its `red_part', `green_part', + and `blue_part' to 0. `use_name' and `on_free_store' are set to + `false'. + + - Copy constructor: void Color (const Color& C, [const string N = "", + [const bool U = `true']]) + Creates a `Color' and makes it a copy of C. If N is not the empty + string and U is `true', `use_name' is set to `true'. Otherwise, + its set to `false'. + + - Constructor: void Color (const string N, const unsigned short R, + const unsigned short G, const unsigned short B, [const bool U + = `true']) + Creates a `Color' with name N. Its `red_part', `green_part', and + `blue_part' are set to r/255.0, g/255.0, and b/255.0, respectively. + `use_name' is set to U. + + - Setting function: void set (const string N, const unsigned short R, + const unsigned short G, const unsigned short B, [const bool U + = `false']) + Corresponds to the constructor above, except that U is `false' by + default. + + - Constructor: void Color (const real R, const real G, const real B) + Creates an unnamed `Color' using the `real' values R, G, and B for + its `red_part', `green_part', and `blue_part', respectively. + + - Setting function: void set (const real R, const real G, const real B) + Corresponds to the constructor above. + + - Template specializations: Color* create_new (const Color* C) + - : Color* create_new (const Color& C) + Pseudo-constructors for dynamic allocation of `Colors'. They + create a `Color' on the free store and allocate memory for it using + `new(Color)'. They return a pointer to the new `Color'. + + If C is a non-zero pointer or a reference, the new `Color' will be + a copy of C. If the new object is not meant to be a copy of an + existing one, `0' must be passed to `create_new()' as its + argument. *Note Dynamic Allocation of Shapes::, for more + information. + + This function is used in the drawing and filling functions for + `Path' and `Solid'. `Point::drawdot()' should be changed to use + it too, but I haven't gotten around to doing this yet. + + +File: 3DLDF.info, Node: Color Operators, Next: Modifying Colors, Prev: Color Constructors and Setting Functions, Up: Color Reference + +Operators +========= + + - Assignment operator: void operator= (const Color& C) + Sets `name' to the empty `string', `use_name' to `false', and + `red_part', `green_part', and `blue_part' to C.`red_part', + C.`green_part', and C.`blue_part', respectively. + + - `const' operator: bool operator== (const Color& C) + Equality operator. Returns `true', if the `red_parts', + `green_parts', and `blue_parts' of `*this' and C are equal, + otherwise `false'. The `names' and `use_names' are not compared. + + - `const' operator: bool operator!= (const Color& C) + Inequality operator. Returns `false', if the `red_parts', + `green_parts', and `blue_parts' of `*this' and C are equal, + otherwise `true'. The `names' and `use_names' are not compared. + + - Non-member function: ostream& operator<< (ostream& O, const Color& C) + Output operator. Writes the MetaPost code for the `Color' to + `out_stream' when a `Picture' is output. This occurs when the + `Color' has been used as an argument to drawing or filling + functions. + + If `use_name' is `true', `name' is written to `out_stream'. + Otherwise, "(`red_part', `green_part', `blue_part')" is written to + `out_stream'. + + +File: 3DLDF.info, Node: Modifying Colors, Next: Showing Colors, Prev: Color Operators, Up: Color Reference + +Modifying +========= + + - Function: void set_name (const string S) + Sets `name' to S. `use_name' is not reset. + + - Function: void set_use_name (const bool B) + Sets `use_name' to B. + + - Function: void modify (const real R, [const real G = 0, [const real + B = 0]]) + Adds R, G, and B to `red_part', `green_part', and `blue_part', + respectively. Following the addition, if `red_part', + `green_part', and/or `blue_part' is greater than 1, it is reduced + to 1. If it is less than 0, it is increased to 0. + + - Function: void set_red_part (const real Q) + - Function: void set_green_part (const real Q) + - Function: void set_blue_part (const real Q) + Let p stand for `red_part', `green_part', or `blue_part', + depending upon which function is used. If 0 <= q <= 1, p is set + to q. If q < 0, p is set to 0. If q > 1, p is set to 1. + + +File: 3DLDF.info, Node: Showing Colors, Next: Querying Colors, Prev: Modifying Colors, Up: Color Reference + +Showing +======= + + - `const' function: void show ([string TEXT = ""]) + Prints information about the `Color' to standard output. If TEXT + is not the empty `string', prints TEXT on a line of its own. + Otherwise, it prints "Color:". Then it prints `name', `use_name', + `red_part', `green_part', and `blue_part'. + + +File: 3DLDF.info, Node: Querying Colors, Next: Defining and Initializing Colors, Prev: Showing Colors, Up: Color Reference + +Querying +======== + + - `const' function: bool is_on_free_store (void) + Returns `on_free_store'. This will only be true, if the `Color' + was created by `create_new()'. *Note Color Reference; + Constructors and Setting Functions: Color Constructors and Setting + Functions. + + - Inline `const' function: real get_red_part ([bool DECIMAL = `false']) + - Inline `const' function: real get_green_part ([bool DECIMAL = + `false']) + - Inline `const' function: real get_blue_part ([bool DECIMAL = + `false']) + These functions return the `red_part', `green_part', or + `blue_part' of the `Color', respectively. If DECIMAL is `false' + (the default), the actual `real' value of the "part" is returned. + Otherwise, the corresponding whole number n such that 0 <= n <= 255 + is returned. + + - `const' function: bool get_use_name (void) + Returns `use_name'. + + - Inline `const' function: string get_name (void) + Returns `name'. + + +File: 3DLDF.info, Node: Defining and Initializing Colors, Next: Namespace Colors, Prev: Querying Colors, Up: Color Reference + +Defining and Initializing Colors +================================ + + - `const' function: void define_color_mp () + Writes MetaPost code to `out_stream', in order to define objects of + type `color' within MetaPost, and set their `redparts', + `greenparts', and `blueparts'. + + - Static function: void initialize_colors (void) + Calls `define_color_mp()' (described above) for the `Colors' that + are defined in `namespace Colors' (*note Namespace Colors::). + + +File: 3DLDF.info, Node: Namespace Colors, Prev: Defining and Initializing Colors, Up: Color Reference + +Namespace Colors. +================= + + - Constant: const Color red + - Constant: const Color green + - Constant: const Color blue + - Constant: const Color cyan + - Constant: const Color yellow + - Constant: const Color magenta + - Constant: const Color orange_red + - Constant: const Color violet_red + - Constant: const Color pink + - Constant: const Color green_yellow + - Constant: const Color orange + - Constant: const Color violet + - Constant: const Color purple + - Constant: const Color blue_violet + - Constant: const Color yellow_green + - Constant: const Color black + - Constant: const Color white + - Constant: const Color gray + - Constant: const Color light_gray + These constant `Colors' can be used in drawing and filling + commands. + + - Constant: const Color default_background + The default background color. Equal to `white' per default. + + - Pointer: const Color* background_color + Points to `default_background' by default. + + - Pointer: const Color* default_color + Points to `black' by default. + + - Pointer: const Color* help_color + Points to `green' by default. + + The following vectors of pointers to `Color' can be used in the +drawing and filling functions for `Solid' (*note Solid Reference; +Drawing and Filling: Drawing and Filling Solids.). + + - Vector: const vector default_color_vector + Contains one pointer, namely `default_color'. + + - Vector: const vector help_color_vector + Contains one pointer, namely `help_color'. + + - Vector: const vector background_color_vector + Contains one pointer, namely `background_color'. + + +File: 3DLDF.info, Node: Input and Output, Next: Shape Reference, Prev: Color Reference, Up: Top + +Input and Output +**************** + +* Menu: + +* I/O Global Variables:: +* I/O Functions:: + + +File: 3DLDF.info, Node: I/O Global Variables, Next: I/O Functions, Prev: Input and Output, Up: Input and Output + +Global Variables +================ + + - Variable: ifstream in_stream + Intended for inputting files of input code. However, 3DLDF does + not currently have a routine for reading input code. `in_stream' + is currently attached to the file `ldfinput.ldf' by + `initialize_io()' (*note I/O Functions::). `in_stream' is read in + character-by-character in `main()', however this serves no useful + purpose as yet. + + - Variable: ofstream out_stream + Used for writing the file of MetaPost code, which is 3DLDF's + output. Currently attached to the file `subpersp.mp' by + `initialize_io()' (*note I/O Functions::). + + - Variable: ofstream tex_stream + TeX code can be written to a file through `tex_stream', if + desired. 3DLDF makes no use of it itself. Currently attached to + `subpersp.tex' by `initialize_io()' (*note I/O Functions::). + + +File: 3DLDF.info, Node: I/O Functions, Prev: I/O Global Variables, Up: Input and Output + +I/O Functions +============= + + - Function: void initialize_io (string IN_STREAM_NAME, string + OUT_STREAM_NAME, string TEX_STREAM_NAME, char* PROGRAM_NAME) + Opens files with names specified by the first three arguments, and + attaches them to the file streams `in_stream', `out_stream', and + `tex_stream', respectively. Comments are written at the beginning + of the files, containing their names, a datestamp, and the name of + the program used to generate them. + + - Function: void write_footers (void) + Writes code at the end of the files attached to `in_stream', + `out_stream', and `tex_stream', before the streams are closed. + Currently, they write comments containing local variable lists for + use in Emacs. + + - Inline function: void beginfig (unsigned short I) + Writes "`beginfig(I)'" to `out_stream'. + + - Inline function: void endfig ([unsigned short I = 0]) + Writes "`endfig()'" to `out_stream'. The argument I is "syntactic + sugar"; it's ignored by `endfig()', but may help the user keep + track of what figure is being ended. + + +File: 3DLDF.info, Node: Shape Reference, Next: Transform Reference, Prev: Input and Output, Up: Top + +Shape Reference +*************** + + Class `Shape' is defined in `shapes.web'. + + `Shape' is an "abstract class", which means that all of its member +functions are pure virtual functions, and that it's only used as a base +class, i.e., no objects of type `Shape' may be declared. + + All of the "drawable" types in 3DLDF, `Point', `Path', `Ellipse', +etc., are derived from `Shape'. + + Deriving all of the drawable types from `Shape' makes it possible to +handle objects of different types in the same way. This is especially +important in the `Picture' functions, where objects of various types +(but all derived from `Shape') are accessed through pointers to +`Shape'. *Note Picture Reference::. + +* Menu: + +* Shape Data Members:: +* Shape Operators:: +* Copying Shapes:: +* Modifying Shapes:: +* Affine Transformations for Shapes:: +* Applying Transformations to Shapes:: +* Clearing Shapes:: +* Querying Shapes:: +* Showing Shapes:: +* Outputting Shapes:: + + +File: 3DLDF.info, Node: Shape Data Members, Next: Shape Operators, Prev: Shape Reference, Up: Shape Reference + +Data Members +============ + + - Protected static constants: signed short DRAWDOT + - : signed short DRAW + - : signed short FILL + - : signed short FILLDRAW + - : signed short UNDRAWDOT + - : signed short UNDRAW + - : signed short UNFILL + - : signed short UNFILLDRAW + Values used in the `output()' functions of the classes derived from + `Shape'. For example, in `Path', if the data member + `fill_draw_value' = `DRAW', then the MetaPost command `draw' is + written to `out_stream' when that `Path' is output. + + +File: 3DLDF.info, Node: Shape Operators, Next: Copying Shapes, Prev: Shape Data Members, Up: Shape Reference + +Operators +========= + + - Pure virtual function: Transform operator*= (const Transform& T) + + +File: 3DLDF.info, Node: Copying Shapes, Next: Modifying Shapes, Prev: Shape Operators, Up: Shape Reference + +Copying +======= + + - `const' pure virtual function: Shape* get_copy (void) + Copies an object, allocating memory on the free store for the copy, + and returns a pointer to `Shape' for accessing the copy. + + Used in the drawing and filling functions for copying the `Shape', + and putting a pointer to the copy onto the `vector shapes' + of the `Picture'. + + File: 3DLDF.info, Node: Modifying Shapes, Next: Affine Transformations for Shapes, Prev: Copying Shapes, Up: Shape Reference Modifying @@ -30,16 +608,9 @@ from `Shape' must therefore also have a data member `on_free_store'. - This function was intended for use with a `create_new' - template function, however, I was unable to get it to work. I - _was_ able to get a template function to work when a program was - generated from a single compilation unit, so I suspect the problem - has something to do with linkage when there are several - compilation units. However, I haven't bothered to try to solve - this problem yet. Therefore, each class that needs one has a - function for creating a new object of that class, and allocating - memory for it on the free store, e.g., - `Point::create_new_point()', `Path::create_new_path()', etc. + This function is used in the template function `create_new'. + *Note Dynamic Allocation of Shapes::, for more information. +  File: 3DLDF.info, Node: Affine Transformations for Shapes, Next: Applying Transformations to Shapes, Prev: Modifying Shapes, Up: Shape Reference @@ -484,27 +1055,43 @@ Returning Information ===================== - - Inline function: real epsilon (void) - Returns the smallest `real' value which a `Transform' should - contain. This value is used for comparing `Transforms' and in the - function `clean()' (*note Transform Reference; Cleaning: Cleaning - Transforms.). It is currently 0.00001. - - The value of `epsilon()' should be smaller when `real' is `double' - than when `real' is `float'. Currently, it doesn't work to have - `real' be `double'. + - Static function: real epsilon (void) + Returns the positive `real' value of smallest magnitude \epsilon + which an element of a `Transform' should contain. An element of a + `Transform' may also contain -\epsilon. + + The value \epsilon is used for in the function `clean()' (*note + Transform Reference; Cleaning: Cleaning Transforms.). It will + also be used for comparing `Transforms', when I've added the + equality operator `Transform::operator==()'. + + `epsilon()' returns different values, depending on whether `real' + is `float' or `double': If `real' is `float' (the default), + `epsilon()' returns 0.00001. If `real' is `double', it returns + 0.000000001. + + Please note: I haven't tested whether 0.000000001 is a good value + yet, so users should be aware of this if they set `real' to + `double'!(1) The way to test this is to transform two different + `Transforms' t_1 and t_2 using different rotations in such a way + that the end result should be the same for both `Transforms'. Let + \epsilon stand for the value returned by `epsilon()'. If for all + sets of corresponding elements E_1 and E_2 of t_1 and t_2, ||E_1| + - |E_2|| \le \epsilon, then \epsilon is a good value. It will be + easier to test this when I've added `Transform::operator==()'. Rotation causes a significant loss of precision to due to the use of the `sin()' and `cos()' functions. Therefore, neither `Transform::epsilon()' nor `Point::epsilon()' (*note Point Reference; Returning Information: Returning Information for Points.) can be as small as I'd like them to be. If they are two - small, the operations that test for equality of `Transforms' and + small, operations that test for equality of `Transforms' and `Points' will return `false' for objects that should be equal. - Another problem is how to determine what value `epsilon()' should - return. A good value on one computer may not be good on another, - especially if one has a 32-bit, and the other a 64-bit processor. + ---------- Footnotes ---------- + + (1) For that matter, I haven't really tested whether 0.00001 is a +good value when `real' is `float'.  File: 3DLDF.info, Node: Showing Transforms, Next: Affine Transformations for Transforms, Prev: Returning Information for Transforms, Up: Transform Reference @@ -684,6 +1271,8 @@ r[3] *= t; r[3].draw(); + [Figure 73 not displayed.] + Cuboid c(origin, 1, 1, 1); c.draw(); Transform t; @@ -704,6 +1293,8 @@ c *= t; c.draw(); + [Figure 74 not displayed.] + - Function: Transform rotate (real X, [real Y = 0, [real Z = 0]]) Rotation around the main axes. Creates a `Transform t' @@ -792,6 +1383,8 @@ n.show("n:"); -| n: (0, 1, 0) + [Figure 75 not displayed.] +  File: 3DLDF.info, Node: Resetting Transforms, Next: Cleaning Transforms, Prev: Alignment with an Axis for Transforms, Up: Transform Reference @@ -802,410 +1395,3 @@ - Function: void reset (void) Resets MATRIX to the identity matrix. - -File: 3DLDF.info, Node: Cleaning Transforms, Prev: Resetting Transforms, Up: Transform Reference - -Cleaning -======== - - - Function: void clean (void) - Sets elements in MATRIX whose absolute values are < `epsilon()' to - 0. - - -File: 3DLDF.info, Node: Label Reference, Next: Picture Reference, Prev: Transform Reference, Up: Top - -Label Reference -*************** - - Class `Label' is defined in `pictures.web'. `Point' and `Picture' -are `friends' of `Label'. - - Labels can be included in drawings by using the `label()' and -`dotlabel()' functions, which are currently defined for the classes -`Point' and `Path', and the classes derived from them. *Note Point -Reference; Labelling: Labelling Points, and *Note Path Reference; -Labelling: Labelling Paths. They are currently not defined for -`Solid', and its derived classes. I plan to add them for `Solid' soon. - - Users will normally never need to declare objects of type `Label', -access its data members or call its member functions directly. - - When `label()' or `dotlabel()' is invoked, one or more `Labels' is -allocated dynamically and pointers to the new `Labels' are placed onto -the `vector labels' of a `Picture': `current_picture', by -default. There are no explicitly defined constructors for `Label', nor -is it intended that `Labels' ever be created in any way other than -through `label()' or `dotlabel()'. When a `Picture' is copied, the -`Labels' are copied, too, and when a `Picture' is cleared (using -`Picture::clear()') or destroyed, the `Labels' are deallocated and -destroyed. - -* Menu: - -* Label Data Members:: -* Copying Labels:: -* Outputting Labels:: - - -File: 3DLDF.info, Node: Label Data Members, Next: Copying Labels, Prev: Label Reference, Up: Label Reference - -Data Members -============ - - - Private variable: Point* pt - A pointer to the `Point' representing the location of the `Label'. - - - Private variable: bool dot - `true' if the label should be dotted, otherwise `false'. - - `dot' will be `false', if the label was generated by a call to - `label()' with the "`dot'" argument `false' (the default), `true', - if the label was generated by a call to `dotlabel()', or to - `label()' with the "`dot'" argument `true'. - - - Private variable: string text - The text of the label. TEXT is always put between "`btex'" and - "`etex'" in the MetaPost code, so that TeX will be used to format - the labels. In particular, this means that TeX's math mode can be - used. However, double backslashes must be used instead of single - backslashes, in order that single backslashes be written to - `out_stream'. - - Point P(1, 1, 2); - origin.drawarrow(P); - P.label("$\\vec{P}$"); - - - - Private variable: string position - The position of the text with respect to `*pt'. Valid values are - as in MetaPost: "top", "bot" (bottom), "lft" (left), "rt" (right), - "ulft" (upper left), "llft" (lower left), "urt" (upper right), - "lrt" (lower right). - - - Public static variable: bool DO_LABELS - Enables or disables creation of `Labels'. If `true', `label' and - `dotlabel()' cause `Labels' to be created and put onto a - `Picture'. If `false', they are not. Note that it is also - possible to suppress output of existing `Labels' when outputting a - `Picture'. - - -File: 3DLDF.info, Node: Copying Labels, Next: Outputting Labels, Prev: Label Data Members, Up: Label Reference - -Copying -======= - - - `const' Function: Label* get_copy (void) - Creates a copy of the `Label' and returns a pointer to the copy. - Called in `Picture::operator=()' and `Picture::operator+=()' where - `Pictures' are copied. Users should never need to call this - function directly. *Note Picture Reference; Operators: Picture - Operators. - - This function dynamically allocates a new `Label' and a new - `Point' within the `Label', and copies the `strings' from `*this' - to the new `Label'. The standard library functions for `strings' - take care of the allocation for the `string' members of `Label'. - - -File: 3DLDF.info, Node: Outputting Labels, Prev: Copying Labels, Up: Label Reference - -Outputting -========== - - - Function: void output (const Focus& F, const unsigned short PROJ, - real FACTOR, const Transform& T) - Writes MetaPost code for the labels to `out_stream'. It is called - in `Picture::output()' (*note Picture Reference; Outputting: - Outputting Pictures.). Users should never need to call this - function directly. - - When `Picture::output()' is invoked, the MetaPost code for - `Labels' is written to `out_stream' after the code for the drawing - and filling commands. This prevents the `Labels' from being - covered up. However, they can still be covered by other `Labels', - or by `Shapes' or `Labels' from subsequent invocations of - `Picture::output()' within the same figure (*note I/O Functions::, - for descriptions of `beginfig() and `endfig()''). - - -File: 3DLDF.info, Node: Picture Reference, Next: Point Reference, Prev: Label Reference, Up: Top - -Picture Reference -***************** - - Class `Picture' is defined in `pictures.web'. - -* Menu: - -* Picture Data Members:: -* Picture Global Variables:: -* Picture Constructors:: -* Picture Operators:: -* Affine Transformations for Pictures:: -* Modifying Pictures:: -* Showing Pictures:: -* Outputting Pictures:: - - -File: 3DLDF.info, Node: Picture Data Members, Next: Picture Global Variables, Prev: Picture Reference, Up: Picture Reference - -Data Members -============ - - - Private variable: Transform transform - Applied to the `Shapes' on the `Picture' when the latter is - output. It is initialized as the identity `Transform', and can be - modified by the transformation functions, by - `Picture::operator*=(const Transform&)' (*note Picture Reference; - Operators: Picture Operators.), and by `Picture::set_transform()' - (*note Picture Reference; Modifying: Modifying Pictures.). - - - Private variable: vector shapes - Contains pointers to the `Shapes' on the `Picture'. When a - drawing or filling function is invoked for a `Shape', a copy is - dynamically allocated and a pointer to the copy is placed onto - `shapes'. - - - Private variable: vector labels - Contains pointers to the `Labels' on the `Picture'. When a - `Point' is labelled, either directly or through a call to - `label()' or `dotlabel()' for another type of `Shape'(1), a - `Label' is dynamically allocated, the `Point' is copied to - `*Label::pt', and a pointer to the `Label' is placed onto `labels'. - - - Private variable: bool do_labels - Used for enabling or disabling output of `Labels' when outputting a - `Picture'. The default value is `true'. It is set to `false' by - using `suppress_labels()' and can be reset to `true' by using - `unsuppress_labels()'. *Note Picture Reference; Output Functions: - Picture Output Functions. - - Often, when a `Picture' is copied, transformed, and output again in - a single figure, it's undesirable to have the `Labels' output again - in their new positions. To avoid this, use `suppress_labels()' - after outputting the `Picture' the first time. - - ---------- Footnotes ---------- - - (1) `label()' and `dotlabel()' are currently only defined for -`Point' and `Path' (and the latter's derived classes), i.e., not for -`Solid' and its derived classes. - - -File: 3DLDF.info, Node: Picture Global Variables, Next: Picture Constructors, Prev: Picture Data Members, Up: Picture Reference - -Global Variables -================ - - - Variable: Variable Picture current_picture - The `Picture' used as the default by the drawing and filling - functions. - - -File: 3DLDF.info, Node: Picture Constructors, Next: Picture Operators, Prev: Picture Global Variables, Up: Picture Reference - -Constructors -============ - - - Default constructor: void Picture (void) - Creates an empty `Picture'. - - - Copy constructor: void Picture (const Picture& P) - Creates a copy of `Picture' P. - - Circle c(origin, 3); - c.draw(); - current_picture.output(Projections::PARALLEL_X_Z); - Picture new_picture(current_picture); - new_picture.shift(2); - new_picture.output(Projections::PARALLEL_X_Z); - - - -File: 3DLDF.info, Node: Picture Operators, Next: Affine Transformations for Pictures, Prev: Picture Constructors, Up: Picture Reference - -Operators -========= - - - Assignment operator: void operator= (const Picture& P) - Makes `*this' a copy of P, destroying the old contents of `*this'. - - - Operator: void operator+= (const Picture& P) - Adds the contents of P to `*this'. P remains unchanged. - - - Operator: void operator+= (Shape* S) - Puts S onto `shapes'. Note that the pointer S itself is put onto - `shapes', so any allocation and copying must be performed first. - This is a low-level function that users normally won't need to use - directly. - - - Operator: void operator+= (Label* LABEL) - Puts LABEL onto `labels'. Note that the pointer LABEL itself is - put onto `labels', so any allocation and copying must be performed - first. This is a low-level function that users normally won't - need to invoke directly. - - - Operator: Transform operator*= (const Transform& T) - Multiplies `transform' by T. This has the effect of transforming - all of the `Shapes' on `shapes' and all of the `Points' of the - `Labels' on `labels' by T upon output. - - Transform t; - t.rotate(0, 0, 180); - t.shift(3); - Reg_Polygon pl(origin, 5, 3, 90); - pl.draw(); - pl.label(); - current_picture.output(Projections::PARALLEL_X_Y); - current_picture *= t; - current_picture.output(Projections::PARALLEL_X_Y); - - - -File: 3DLDF.info, Node: Affine Transformations for Pictures, Next: Modifying Pictures, Prev: Picture Operators, Up: Picture Reference - -Affine Transformations -====================== - - The functions in this section all operate on the `transform' data -member of the `Picture' and return a `Transform' representing the -transformation--_not_ `transform'. - - - Function: Transform scale (real X, [real Y = 1, [real Z = 1]]) - Performs `transform.scale(X, Y, Z)' and returns the result. This - has the effect of scaling all of the elements of `shapes' and - `labels'. - - - Function: Transform shift (real x, [real Y = 0, [real Z = 0]]) - Performs `transform.shift(X, Y, Z)' and returns the result. This - has the effect of shifting all of the `Shapes' and `Labels' on the - `Picture'. - - - Function: Transform shift (const Point& P) - Performs `transform.shift(P)' and returns the result. This has - the effect of shifting all of the `Shapes' and `Labels' on the - `Picture' by the x, y, and z-coordinates of P. - - - Function: Transform rotate (const real X, [const real Y = 0, [const - real Z = 0]]) - Performs `transform.rotate(X, Y, Z)' and returns the result. This - has the effect of rotating all of the elements of `shapes' and - `labels'. - - - Function: Transform rotate (const Point& P0, const Point& P1, [const - real ANGLE = 180]); - Performs `transform.rotate(P0, P1, ANGLE)' and returns the result. - This has the effect of rotating all of the elements of `shapes' - and `labels' about the line from p_0 to p_1. - - -File: 3DLDF.info, Node: Modifying Pictures, Next: Showing Pictures, Prev: Affine Transformations for Pictures, Up: Picture Reference - -Modifying -========= - - - Function: void clear (void) - Destroys the `Shapes' and `Labels' on the `Picture' and removes - all the `Shape' pointers from `shapes' and the `Label' pointers - from `labels'. All dynamically allocated objects are deallocated, - namely the `Shapes', the `Labels', and the `Points' belonging to - the `Labels'. `transform' is reset to the identity `Transform'. - - - Function: void reset_transform (void) - Resets `transform' to the identity `Transform'. - - - Function: Transform set_transform (const Transform& T) - Sets `transform' to `t' and returns `t'. - - - Function: void kill_labels (void) - Removes the `Labels' from the `Picture'. - - -File: 3DLDF.info, Node: Showing Pictures, Next: Outputting Pictures, Prev: Modifying Pictures, Up: Picture Reference - -Showing -======= - - - Function: void show ([string TEXT = "", [bool STOP = `false']]) - Prints information about the `Picture' to standard output. - - `show()' first prints the string `"Showing Picture:"' to standard - output, followed by TEXT, if the latter is not the empty string - (`""')(1). Then it calls `transform.show()', prints the size of - `shapes' and `labels', and the value of `do_labels'. Then it calls - `show()' on each of the `Shapes' on `shapes'. Since `show()' is a - `virtual' function in `class Shape', the appropriate `show()' is - called for each `Shape', i.e., `Point::show()' for a `Point', - `Path::show()' for a `Path', etc. If STOP is `true', execution - stops and the user is requested to type to continue. - Finally, the string `"Done showing picture."' is printed to - standard output. - - - Function: void show_transform ([string TEXT = "Transform from - Picture:"]) - Calls `transform.show()', passing TEXT as the argument to the - latter function. - - ---------- Footnotes ---------- - - (1) Actually, it's printed to standard output even if it is the -empty string, you just don't see it. - - -File: 3DLDF.info, Node: Outputting Pictures, Prev: Showing Pictures, Up: Picture Reference - -Outputting -========== - -* Menu: - -* Picture Output Namespaces:: -* Picture Output Functions:: - - -File: 3DLDF.info, Node: Picture Output Namespaces, Next: Picture Output Functions, Prev: Outputting Pictures, Up: Outputting Pictures - -Namespaces ----------- - -* Menu: - -* Namespace Projections:: -* Namespace Sorting:: - - -File: 3DLDF.info, Node: Namespace Projections, Next: Namespace Sorting, Prev: Picture Output Namespaces, Up: Picture Output Namespaces - -Namespace Projections -..................... - - The namespace `Projections' is defined in `pictures.web'. - - - Constant: const unsigned short PERSP - - Constant: const unsigned short PARALLEL_X_Y - - Constant: const unsigned short PARALLEL_X_Z - - Constant: const unsigned short PARALLEL_Z_Y - - Constant: const unsigned short AXON - - Constant: const unsigned short ISO - These constants can be used for the PROJECTION argument in - `Picture::output()', described in *Note Picture Reference; - Outputting; Functions: Picture Output Functions, below. - - -File: 3DLDF.info, Node: Namespace Sorting, Prev: Namespace Projections, Up: Picture Output Namespaces - -Namespace Sorting -................. - - The namespace `Sorting' is defined in `pictures.web'. - - - Constant: const unsigned short NO_SORT - - Constant: const unsigned short MAX_Z - - Constant: const unsigned short MIN_Z - - Constant: const unsigned short MEAN_Z - These constants can be used for the SORT_VALUE argument in - `Picture::output()', described in *Note Picture Reference; - Outputting; Functions: Picture Output Functions, below. - diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-5 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-5 --- 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-5 2003-12-10 18:44:55.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-5 2004-01-16 19:03:28.000000000 +0100 @@ -1,11 +1,11 @@ This is 3DLDF.info, produced by makeinfo version 4.5 from 3DLDF.texi. -This is the 3DLDF User and Reference Manual, edition 1.1.4 for 3DLDF -1.1.4. This manual was last updated on 10 December 2003. 3DLDF is a +This is the 3DLDF User and Reference Manual, edition 1.1.5.1 for 3DLDF +1.1.5.1. This manual was last updated on 16 January 2004. 3DLDF is a GNU package for three-dimensional drawing with MetaPost output. The author is Laurence D. Finston. - Copyright (C) 2003 Laurence D. Finston. + Copyright (C) 2003, 2004 Laurence D. Finston. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, @@ -20,6 +20,419 @@ END-INFO-DIR-ENTRY  +File: 3DLDF.info, Node: Cleaning Transforms, Prev: Resetting Transforms, Up: Transform Reference + +Cleaning +======== + + - Function: void clean (void) + Sets elements in MATRIX whose absolute values are < `epsilon()' to + 0. + + +File: 3DLDF.info, Node: Label Reference, Next: Picture Reference, Prev: Transform Reference, Up: Top + +Label Reference +*************** + + Class `Label' is defined in `pictures.web'. `Point' and `Picture' +are `friends' of `Label'. + + Labels can be included in drawings by using the `label()' and +`dotlabel()' functions, which are currently defined for the classes +`Point' and `Path', and the classes derived from them. *Note Point +Reference; Labelling: Labelling Points, and *Note Path Reference; +Labelling: Labelling Paths. They are currently not defined for +`Solid', and its derived classes. I plan to add them for `Solid' soon. + + Users will normally never need to declare objects of type `Label', +access its data members or call its member functions directly. + + When `label()' or `dotlabel()' is invoked, one or more `Labels' is +allocated dynamically and pointers to the new `Labels' are placed onto +the `vector labels' of a `Picture': `current_picture', by +default. There are no explicitly defined constructors for `Label', nor +is it intended that `Labels' ever be created in any way other than +through `label()' or `dotlabel()'. When a `Picture' is copied, the +`Labels' are copied, too, and when a `Picture' is cleared (using +`Picture::clear()') or destroyed, the `Labels' are deallocated and +destroyed. + +* Menu: + +* Label Data Members:: +* Copying Labels:: +* Outputting Labels:: + + +File: 3DLDF.info, Node: Label Data Members, Next: Copying Labels, Prev: Label Reference, Up: Label Reference + +Data Members +============ + + - Private variable: Point* pt + A pointer to the `Point' representing the location of the `Label'. + + - Private variable: bool dot + `true' if the label should be dotted, otherwise `false'. + + `dot' will be `false', if the label was generated by a call to + `label()' with the "`dot'" argument `false' (the default), `true', + if the label was generated by a call to `dotlabel()', or to + `label()' with the "`dot'" argument `true'. + + - Private variable: string text + The text of the label. TEXT is always put between "`btex'" and + "`etex'" in the MetaPost code, so that TeX will be used to format + the labels. In particular, this means that TeX's math mode can be + used. However, double backslashes must be used instead of single + backslashes, in order that single backslashes be written to + `out_stream'. + + Point P(1, 1, 2); + origin.drawarrow(P); + P.label("$\\vec{P}$"); + + [Figure 76 not displayed.] + + + - Private variable: string position + The position of the text with respect to `*pt'. Valid values are + as in MetaPost: "top", "bot" (bottom), "lft" (left), "rt" (right), + "ulft" (upper left), "llft" (lower left), "urt" (upper right), + "lrt" (lower right). + + - Public static variable: bool DO_LABELS + Enables or disables creation of `Labels'. If `true', `label' and + `dotlabel()' cause `Labels' to be created and put onto a + `Picture'. If `false', they are not. Note that it is also + possible to suppress output of existing `Labels' when outputting a + `Picture'. + + +File: 3DLDF.info, Node: Copying Labels, Next: Outputting Labels, Prev: Label Data Members, Up: Label Reference + +Copying +======= + + - `const' Function: Label* get_copy (void) + Creates a copy of the `Label' and returns a pointer to the copy. + Called in `Picture::operator=()' and `Picture::operator+=()' where + `Pictures' are copied. Users should never need to call this + function directly. *Note Picture Reference; Operators: Picture + Operators. + + This function dynamically allocates a new `Label' and a new + `Point' within the `Label', and copies the `strings' from `*this' + to the new `Label'. The standard library functions for `strings' + take care of the allocation for the `string' members of `Label'. + + +File: 3DLDF.info, Node: Outputting Labels, Prev: Copying Labels, Up: Label Reference + +Outputting +========== + + - Function: void output (const Focus& F, const unsigned short PROJ, + real FACTOR, const Transform& T) + Writes MetaPost code for the labels to `out_stream'. It is called + in `Picture::output()' (*note Picture Reference; Outputting: + Outputting Pictures.). Users should never need to call this + function directly. + + When `Picture::output()' is invoked, the MetaPost code for + `Labels' is written to `out_stream' after the code for the drawing + and filling commands. This prevents the `Labels' from being + covered up. However, they can still be covered by other `Labels', + or by `Shapes' or `Labels' from subsequent invocations of + `Picture::output()' within the same figure (*note I/O Functions::, + for descriptions of `beginfig() and `endfig()''). + + +File: 3DLDF.info, Node: Picture Reference, Next: Point Reference, Prev: Label Reference, Up: Top + +Picture Reference +***************** + + Class `Picture' is defined in `pictures.web'. + +* Menu: + +* Picture Data Members:: +* Picture Global Variables:: +* Picture Constructors:: +* Picture Operators:: +* Affine Transformations for Pictures:: +* Modifying Pictures:: +* Showing Pictures:: +* Outputting Pictures:: + + +File: 3DLDF.info, Node: Picture Data Members, Next: Picture Global Variables, Prev: Picture Reference, Up: Picture Reference + +Data Members +============ + + - Private variable: Transform transform + Applied to the `Shapes' on the `Picture' when the latter is + output. It is initialized as the identity `Transform', and can be + modified by the transformation functions, by + `Picture::operator*=(const Transform&)' (*note Picture Reference; + Operators: Picture Operators.), and by `Picture::set_transform()' + (*note Picture Reference; Modifying: Modifying Pictures.). + + - Private variable: vector shapes + Contains pointers to the `Shapes' on the `Picture'. When a + drawing or filling function is invoked for a `Shape', a copy is + dynamically allocated and a pointer to the copy is placed onto + `shapes'. + + - Private variable: vector labels + Contains pointers to the `Labels' on the `Picture'. When a + `Point' is labelled, either directly or through a call to + `label()' or `dotlabel()' for another type of `Shape'(1), a + `Label' is dynamically allocated, the `Point' is copied to + `*Label::pt', and a pointer to the `Label' is placed onto `labels'. + + - Private variable: bool do_labels + Used for enabling or disabling output of `Labels' when outputting a + `Picture'. The default value is `true'. It is set to `false' by + using `suppress_labels()' and can be reset to `true' by using + `unsuppress_labels()'. *Note Picture Reference; Output Functions: + Picture Output Functions. + + Often, when a `Picture' is copied, transformed, and output again in + a single figure, it's undesirable to have the `Labels' output again + in their new positions. To avoid this, use `suppress_labels()' + after outputting the `Picture' the first time. + + ---------- Footnotes ---------- + + (1) `label()' and `dotlabel()' are currently only defined for +`Point' and `Path' (and the latter's derived classes), i.e., not for +`Solid' and its derived classes. + + +File: 3DLDF.info, Node: Picture Global Variables, Next: Picture Constructors, Prev: Picture Data Members, Up: Picture Reference + +Global Variables +================ + + - Variable: Variable Picture current_picture + The `Picture' used as the default by the drawing and filling + functions. + + +File: 3DLDF.info, Node: Picture Constructors, Next: Picture Operators, Prev: Picture Global Variables, Up: Picture Reference + +Constructors +============ + + - Default constructor: void Picture (void) + Creates an empty `Picture'. + + - Copy constructor: void Picture (const Picture& P) + Creates a copy of `Picture' P. + + Circle c(origin, 3); + c.draw(); + current_picture.output(Projections::PARALLEL_X_Z); + Picture new_picture(current_picture); + new_picture.shift(2); + new_picture.output(Projections::PARALLEL_X_Z); + + [Figure 77 not displayed.] + + + +File: 3DLDF.info, Node: Picture Operators, Next: Affine Transformations for Pictures, Prev: Picture Constructors, Up: Picture Reference + +Operators +========= + + - Assignment operator: void operator= (const Picture& P) + Makes `*this' a copy of P, destroying the old contents of `*this'. + + - Operator: void operator+= (const Picture& P) + Adds the contents of P to `*this'. P remains unchanged. + + - Operator: void operator+= (Shape* S) + Puts S onto `shapes'. Note that the pointer S itself is put onto + `shapes', so any allocation and copying must be performed first. + This is a low-level function that users normally won't need to use + directly. + + - Operator: void operator+= (Label* LABEL) + Puts LABEL onto `labels'. Note that the pointer LABEL itself is + put onto `labels', so any allocation and copying must be performed + first. This is a low-level function that users normally won't + need to invoke directly. + + - Operator: Transform operator*= (const Transform& T) + Multiplies `transform' by T. This has the effect of transforming + all of the `Shapes' on `shapes' and all of the `Points' of the + `Labels' on `labels' by T upon output. + + Transform t; + t.rotate(0, 0, 180); + t.shift(3); + Reg_Polygon pl(origin, 5, 3, 90); + pl.draw(); + pl.label(); + current_picture.output(Projections::PARALLEL_X_Y); + current_picture *= t; + current_picture.output(Projections::PARALLEL_X_Y); + + [Figure 78 not displayed.] + + + +File: 3DLDF.info, Node: Affine Transformations for Pictures, Next: Modifying Pictures, Prev: Picture Operators, Up: Picture Reference + +Affine Transformations +====================== + + The functions in this section all operate on the `transform' data +member of the `Picture' and return a `Transform' representing the +transformation--_not_ `transform'. + + - Function: Transform scale (real X, [real Y = 1, [real Z = 1]]) + Performs `transform.scale(X, Y, Z)' and returns the result. This + has the effect of scaling all of the elements of `shapes' and + `labels'. + + - Function: Transform shift (real x, [real Y = 0, [real Z = 0]]) + Performs `transform.shift(X, Y, Z)' and returns the result. This + has the effect of shifting all of the `Shapes' and `Labels' on the + `Picture'. + + - Function: Transform shift (const Point& P) + Performs `transform.shift(P)' and returns the result. This has + the effect of shifting all of the `Shapes' and `Labels' on the + `Picture' by the x, y, and z-coordinates of P. + + - Function: Transform rotate (const real X, [const real Y = 0, [const + real Z = 0]]) + Performs `transform.rotate(X, Y, Z)' and returns the result. This + has the effect of rotating all of the elements of `shapes' and + `labels'. + + - Function: Transform rotate (const Point& P0, const Point& P1, [const + real ANGLE = 180]); + Performs `transform.rotate(P0, P1, ANGLE)' and returns the result. + This has the effect of rotating all of the elements of `shapes' + and `labels' about the line from p_0 to p_1. + + +File: 3DLDF.info, Node: Modifying Pictures, Next: Showing Pictures, Prev: Affine Transformations for Pictures, Up: Picture Reference + +Modifying +========= + + - Function: void clear (void) + Destroys the `Shapes' and `Labels' on the `Picture' and removes + all the `Shape' pointers from `shapes' and the `Label' pointers + from `labels'. All dynamically allocated objects are deallocated, + namely the `Shapes', the `Labels', and the `Points' belonging to + the `Labels'. `transform' is reset to the identity `Transform'. + + - Function: void reset_transform (void) + Resets `transform' to the identity `Transform'. + + - Function: Transform set_transform (const Transform& T) + Sets `transform' to `t' and returns `t'. + + - Function: void kill_labels (void) + Removes the `Labels' from the `Picture'. + + +File: 3DLDF.info, Node: Showing Pictures, Next: Outputting Pictures, Prev: Modifying Pictures, Up: Picture Reference + +Showing +======= + + - Function: void show ([string TEXT = "", [bool STOP = `false']]) + Prints information about the `Picture' to standard output. + + `show()' first prints the string `"Showing Picture:"' to standard + output, followed by TEXT, if the latter is not the empty string + (`""')(1). Then it calls `transform.show()', prints the size of + `shapes' and `labels', and the value of `do_labels'. Then it calls + `show()' on each of the `Shapes' on `shapes'. Since `show()' is a + `virtual' function in `class Shape', the appropriate `show()' is + called for each `Shape', i.e., `Point::show()' for a `Point', + `Path::show()' for a `Path', etc. If STOP is `true', execution + stops and the user is requested to type to continue. + Finally, the string `"Done showing picture."' is printed to + standard output. + + - Function: void show_transform ([string TEXT = "Transform from + Picture:"]) + Calls `transform.show()', passing TEXT as the argument to the + latter function. + + ---------- Footnotes ---------- + + (1) Actually, it's printed to standard output even if it is the +empty string, you just don't see it. + + +File: 3DLDF.info, Node: Outputting Pictures, Prev: Showing Pictures, Up: Picture Reference + +Outputting +========== + +* Menu: + +* Picture Output Namespaces:: +* Picture Output Functions:: + + +File: 3DLDF.info, Node: Picture Output Namespaces, Next: Picture Output Functions, Prev: Outputting Pictures, Up: Outputting Pictures + +Namespaces +---------- + +* Menu: + +* Namespace Projections:: +* Namespace Sorting:: + + +File: 3DLDF.info, Node: Namespace Projections, Next: Namespace Sorting, Prev: Picture Output Namespaces, Up: Picture Output Namespaces + +Namespace Projections +..................... + + The namespace `Projections' is defined in `pictures.web'. + + - Constant: const unsigned short PERSP + - Constant: const unsigned short PARALLEL_X_Y + - Constant: const unsigned short PARALLEL_X_Z + - Constant: const unsigned short PARALLEL_Z_Y + - Constant: const unsigned short AXON + - Constant: const unsigned short ISO + These constants can be used for the PROJECTION argument in + `Picture::output()', described in *Note Picture Reference; + Outputting; Functions: Picture Output Functions, below. + + +File: 3DLDF.info, Node: Namespace Sorting, Prev: Namespace Projections, Up: Picture Output Namespaces + +Namespace Sorting +................. + + The namespace `Sorting' is defined in `pictures.web'. + + - Constant: const unsigned short NO_SORT + - Constant: const unsigned short MAX_Z + - Constant: const unsigned short MIN_Z + - Constant: const unsigned short MEAN_Z + These constants can be used for the SORT_VALUE argument in + `Picture::output()', described in *Note Picture Reference; + Outputting; Functions: Picture Output Functions, below. + + File: 3DLDF.info, Node: Picture Output Functions, Prev: Picture Output Namespaces, Up: Outputting Pictures Output Functions @@ -187,6 +600,8 @@ current_picture.rotate(0, 60); current_picture.output(Projections::PARALLEL_X_Z); + [Figure 79 not displayed.] + - Inline function: void unsuppress_labels (void) Sets `do_labels' to `true'. If a `Picture' contains `Labels', @@ -276,10 +691,13 @@ Applying Transformations: Applying Transformations to Points. - Private variable: bool on_free_store - Indicates whether a `Point' has been dynamically allocated on the - free store or not. `Points' should only ever be dynamically - allocated by `create_new_point()', which sets `on_free_store' to - `true'. + Returns `on_free_store'. This should only be `true' if the + `Point' was dynamically allocated on the free store. `Points' + should only ever be dynamically allocated by + `create_new()', which uses `set_on_free_store()' to set + `on_free_store' to `true'. *Note Point Reference; Constructors + and Setting Functions: Point Constructors and Setting Functions, + and *Note Point Reference; Modifying: Modifying Points. - Private variable: signed short drawdot_value Used to tell `Point::output()' what MetaPost drawing command @@ -488,35 +906,27 @@ Point Reference; Operators: Point Operators.) performs exactly the same function. - - Static function: Point* create_new_point ([const Point* P = 0]) - - Static function: Point* create_new_point (const Point& P) - - Static function: Point* create_new_point (const real X, [const real - Y = 0, [const real Z = 0]]) - Pseudo-constructors for dynamic allocation of `Points'. These - functions create a `Point' on the free store and allocate memory - for it using `new(Point)'. They return a pointer to the new - `Point'. One use is in the constructors for `classes' of objects - that can contain a variable number of `Points', such as `Path' and - `Polygon'. Another use is in the drawing and filling functions, - where objects are copied and the copies put onto a `Picture'. + - Template specializations: Point* create_new (const Point* P) + - : Point* create_new (const Point& P) + Pseudo-constructors for dynamic allocation of `Points'. They + create a `Point' on the free store and allocate memory for it using + `new(Point)'. They return a pointer to the new `Point'. + + If P is a non-zero pointer or a reference, the new `Point' will be + a copy of P. If the new object is not meant to be a copy of an + existing one, `0' must be passed to `create_new()' as its + argument. *Note Dynamic Allocation of Shapes::, for more + information. + + One use for `create_new' is in the constructors for + `classes' of objects that can contain a variable number of + `Points', such as `Path' and `Polygon'. Another use is in the + drawing and filling functions, where objects are copied and the + copies put onto a `Picture'. Programmers who dynamically allocate `Points' must ensure that they are deallocated properly using `delete'! - In the first version, the optional argument P can be a pointer to - `Point'. If an argument is present, the x, y, and z-coordinates - of the new `Point' are copied from `*p' (after they've been - updated, if necessary). Otherwise, they are all set to 0. - - In the second version, P is a reference to a `Point', and the x, - y, and z-coordinates of the new `Point' are copied from P. - - In the third version, at least one `real' value is passed as an - argument. The coordinates of the new `Point' are set using the - values of the arguments X, Y, and Z. Please note, that if Z or Y - and Z are not specified, the corresponding coordinates are set to - 0, not `CURR_Y' or `CURR_Z'. -  File: 3DLDF.info, Node: Point Destructor, Next: Point Operators, Prev: Point Constructors and Setting Functions, Up: Point Reference @@ -656,7 +1066,7 @@ - `const' function: Shape* get_copy (void) Creates a copy of the `Point', and allocates memory for it on the - free store using `create_new_point()'. It returns a pointer to + free store using `create_new()'. It returns a pointer to `Shape' that points to the new `Point'. This function is used in the drawing commands for putting `Points' onto `Pictures'. *Note Point Reference; Drawing: Point Drawing Functions. @@ -673,10 +1083,11 @@ - `const' inline function: Transform get_transform (void) Returns `transform'. - - `const' inline function: bool is_on_free_store (void) + - `const' function: bool is_on_free_store (void) Returns `true' if memory for the `Point' has been dynamically allocated on the free store, i.e., if the `Point' has been created - using `create_new_point()'. + using `create_new()'. *Note Point Reference; Constructors + and Setting Functions: Point Constructors and Setting Functions. - `const' function: bool is_on_plane (const Plane& P) Returns `true', if the `Point' lies on the `Plane' P, otherwise @@ -699,6 +1110,8 @@ cout << "C.is_on_plane(q)"; -| 1 + [Figure 80 not displayed.] + - `const' function: bool is_in_triangle (const Point& P0, const Point& P1, const Point& P2, [bool VERBOSE = `false', [bool @@ -725,478 +1138,3 @@ for B and C were found by using `Plane::intersection_point()'. *Note Planes; Intersections: Plane Intersections. - -File: 3DLDF.info, Node: Returning Coordinates, Next: Returning Information for Points, Prev: Querying Points, Up: Point Reference - -Returning Coordinates -===================== - - The functions in this section return either a single coordinate or a -set of coordinates. Each has a `const' and a non-`const' version. - - The arguments are the same, with one exception: - -`CHAR' C - Only in `get_coord()'. Indicates which coordinate should be - returned. Valid values are `'x'', `'X'', `'y'', `'Y'', `'z'', - `'Z'', `'w'', and `'W''. - -`CHAR COORDS' - Indicates the set of coordinates which should be returned or from - which the coordinate to be returned should be chosen from. Valid - values are `'w'' for `world_coordinates' (the default), `'p'' for - `projective_coordinates', `'u'' for `user_coordinates', and `'v'' - for `view_coordinates'. - -`CONST BOOL' DO_PERSP - Only relevant if `projective_coordinates', or one of its elements - is to be returned. If `true', the default, then `project()' is - called, thereby generating values for `projective_coordinates'. - If DO_PERSP is `false', then `projective_coordinates', or one of - its elements, is returned unchanged, which may sometimes be useful. - -`CONST BOOL' DO_APPLY - If `true' (the default), `apply_transform()' is called, thereby - updating the `world_coordinates'. Otherwise, it's not, so that - the values stored in `world_coordinates' remain unchanged. Note - that if COORDS is `'p'' and DO_PERSP is `true', - `apply_transform()' will be called in `project()' whether - `do_apply' is `true' or `false'. If for some reason, one wanted - get `projective_coordinates', or one of its values, based on the - projection of `world_coordinates' without first updating them, one - would have to call `reset_transform()' before calling one of these - functions. It would probably be a good idea to save `transform' - before doing so. - -`FOCUS*' F - Indicates what `Focus' is to be used for projection. Only - relevant if `coords' is `'p'', i.e., `projective_coordinates', or - one of its elements, is to be returned. The default is 0, in - which case F points to the global variable `default_focus'. - -`CONST UNSIGNED SHORT' PROJ - Indicates what form of projection is to be used. Only relevant if - `coords' is `'p'', i.e., `projective_coordinates', or one of its - elements, is to be returned. The default is `Projections::PERSP', - which causes the perspective projection to be applied. - -`REAL' FACTOR - Passed to `project()'. The values of the x and y coordinates in - `projective_coordinates' are multiplied by FACTOR. Only relevant - if `coords' is `'p'', i.e., `projective_coordinates', or one of - its elements, is to be returned. The default is 1. - - - Function: valarray get_all_coords ([char COORDS = 'w', [const - bool DO_PERSP = true, [const bool DO_APPLY = true, [Focus* F - = 0, [const unsigned short PROJ = Projections::PERSP, [real - factor = 1]]]]]]) - Returns one of the sets of coordinates; `world_coordinates' by - default. Returns a complete set of coordinates: `'w'' for - `world_coordinates', `'p'' for `projective_coordinates', `'u'' for - `user_coordinates', or`'v'' for `view_coordinates'. - - - Function: real get_coord (char C, [char COORDS = 'w', [const bool - DO_PERSP = true, [const bool DO_APPLY = true, [Focus* F = 0, - [const unsigned short PROJ = `Projections::PERSP', [real - FACTOR = 1]]]]]]) - Returns one `coordinate', x, y, z, or w, from the set of - coordinates indicated (or `world_coordinates', by default). - - - Function: real get_x ([char COORDS = 'w', [const bool DO_PERSP = - true, [const bool DO_APPLY = true, [Focus* F = 0, [const - unsigned short PROJ = Projections::PERSP, [real FACTOR = - 1]]]]]]) - Returns the x-coordinate from the set of coordinates indicated (or - `world_coordinates', by default). - - - Function: real get_y ([char COORDS = 'w', [const bool DO_PERSP = - true, [const bool DO_APPLY = true, [Focus* F = 0, [const - unsigned short PROJ = Projections::PERSP, [real FACTOR = - 1]]]]]]) - Returns the y-coordinate from the set of coordinates indicated (or - `world_coordinates', by default). - - - Function: real get_z ([char COORDS = 'w', [const bool DO_PERSP = - true, [const bool DO_APPLY = true, [Focus* F = 0, [const - unsigned short PROJ = Projections::PERSP, [real FACTOR = - 1]]]]]]) - Returns the z-coordinate from the set of coordinates indicated (or - `world_coordinates', by default). - - - Function: real get_w ([char COORDS = 'w', [const bool DO_PERSP = - true, [const bool DO_APPLY = true, [Focus* F = 0, [const - unsigned short PROJ = Projections::PERSP, [real FACTOR = - 1]]]]]]) - Returns the w-coordinate from the set of coordinates indicated (or - `world_coordinates', by default). - - -File: 3DLDF.info, Node: Returning Information for Points, Next: Modifying Points, Prev: Returning Coordinates, Up: Point Reference - -Returning Information -===================== - - - Inline static function: real epsilon (void) - Returns the absolute value of the `real' number of smallest - magnitude that should be used as a coordinate value in a `Point'. - This value is also used for testing the equality of `Points': - - Let e be the value returned by `epsilon()', P and Q be `Points', - and P_x, Q_x, P_y, Q_y, P_z, and Q_z the updated x, y, and - z-coordinates of P and Q, respectively. If and only if ||P_x| - - |Q_x|| < e$, $||P_y| - |Q_y|| < e, and ||P_z| - |Q_z|| < e, then P - == Q. - - -File: 3DLDF.info, Node: Modifying Points, Next: Affine Transformations for Points, Prev: Returning Information for Points, Up: Point Reference - -Modifying -========= - - - `inline' virtual function: bool set_on_free_store ([bool B = true]) - This function was intended to be used in the template function - `create_new()', which I haven't been able to get to work yet. - Otherwise, there is currently no need for it. - - - Function: void clear (void) - Sets all of the coordinates in all of the sets of coordinates - (i.e., `world_coordinates', `user_coordinates', - `view_coordinates', and `projective_coordinates') to 0 and resets - `transform' - - - Function: void clean ([int FACTOR = 1]) - Calls `apply_transform()' and sets the values of - `world_coordinates' to 0, whose absolute values are less than - `epsilon()' * FACTOR . - - - Function: void reset_transform (void) - Sets `Transform' to the identity `Transform'. Performed in - `apply_transform()', after the latter updates `world_coordinates'. - *Note Point Reference; Applying Transformations: Applying - Transformations to Points. - - -File: 3DLDF.info, Node: Affine Transformations for Points, Next: Applying Transformations to Points, Prev: Modifying Points, Up: Point Reference - -Affine Transformations -====================== - - - Function: Transform rotate (const real X, [const real Y = 0, [const - real Z = 0]]) - - Function: Transform rotate (const Point& P0, const Point& P1, [const - real ANGLE = 180]) - - Function: Transform rotate (const Path& P, [const real ANGLE = 180]) - Each of these functions calls the corresponding version of - `Transform::rotate()', and returns its return value, namely, a - `Transform' representing the rotation only. - - In the first version, taking three `real' arguments, the `Point' - is rotated X degrees around the x-axis, Y degrees around the - y-axis, and Z degrees around the z-axis in that order. - - Point p0(1, 0, 2); - p0.rotate(90); - p0.show("p0:") - -| p0: (1, 2, 0) - Point p1(-1, 1, 1); - p1.rotate(-90, 90, 90); - p1.show("pt1:"); - -| p1: (1, -1, -1) - - Please note that rotations are not commutative operations. Nor - are they commutative with other transformations. So, if you want - to rotate a `Point' about the x, y and z-axes in that order, you - can do so with a single invocation of `rotate()', as in the - previous example. However, if you want to rotate a `Point' first - about the y-axis and then about the x-axis, you must invoke - `rotate()' twice. - - Point pt0(1, 1, 1); - pt0.rotate(0, 45); - pt0.rotate(45); - pt0.show("pt0:"); - -| pt0: (0, 1.70711, 0.292893) - - In the version taking two `Point' arguments P0 and P1, and a - `real' argument ANGLE, the `Point' is rotated `angle' degrees - around the axis determined by P0 and P1, 180 degrees by default. - - Point P(2, 0, 0); - Point A; - Point B(2, 2, 2); - P.rotate(A, B, 180); - - - - Function: Transform scale (real X, [real Y = 1, [real Z = 1]]) - Calls `transform.scale(X, Y, Z)' and returns its return value, - namely, a `Transform' representing the scaling operation only. - - Scaling causes the x-coordinate of the `Point' to be multiplied by - X, the y-coordinate of the `Point' to be multiplied by Y, and the - z-coordinate of the `Point' to be multiplied by Z. - - Point p0(1, 0, 3); - p0.scale(4); - p0.show("p0:"); - -| p0: (4, 0, 3) - Point p1(-2, -1, -2); - p1.scale(-2, -3, -4); - p1.show("p1:"); - -| p1: (4, 3, 8) - - - - Function: Transform shear (real XY, [real XZ = 0, [real YX = 0, - [real YZ = 0, [real ZX = 0, [real ZY = 0]]]]]) - Calls `transform.shear()' with the same arguments and returns its - return value, namely, a `Transform' representing the shearing - operation only. - - Shearing modifies each coordinate of a `Point' proportionately to - the values of the other two coordinates. Let x_0, y_0, and z_0 - stand for the coordinates of a `Point' P before `P.shear('\alpha, - \beta, \gamma, \delta, \epsilon, \zeta `)', and x_1, y_1, and z_1 - for its coordinates afterwards. - - x_1 == x_0 + \alpha y + \beta z - y_1 == y_0 + \gamma x + \delta z - z_1 == z_0 + \epsilon x + \zeta y - - [next figure] demonstrates the effect of shearing the four - `Points' of a 3 * 3 - - `Rectangle' (i.e., a square) r in the x-y plane using only an XY - argument, making it non-rectangular. - - Point P0; - Point P1(3); - Point P2(3, 3); - Point P3(0, 3); - Rectangle r(p0, p1, p2, p3); - r.draw(); - r.shear(1.5); - r.draw(black, "evenly"); - - - - Function: Transform shift (real X, [real Y = 0, [real Z = 0]]) - - Function: Transform shift (const Point& P) - Each of these functions calls the corresponding version of - `Transform::shift()' on `transform', and returns its return value, - namely, a `Transform' representing the shifting operation only. - - The `Point' is shifted X units in the direction of the positive - x-axis, Y units in the direction of the positive y-axis, and Z - units in the direction of the positive z-axis. - - p0(1, 2, 3); - p0.shift(2, 3, 5); - p0.show("p0:"); - -| p0: (3, 5, 8) - - - - Function: Transform shift_times (real X, [real Y = 1, [real Z = 1]]) - - Function: Transform shift_times (const Point& P) - Each of these functions calls the corresponding version of - `Transform::shift_times()' on `transform' and returns its return - value, namely the new value of `transform'. - - `shift_times()' makes it possible to increase the magnitude of a - shift applied to a `Point', while maintaining its direction. - Please note that `shift_times()' will only have an effect if it's - called after a call to `shift()' and before `transform' is reset. - This is performed by `reset_transform()', which is called in - `apply_transform()', and can also be called directly. *Note - Transform Reference; Resetting: Resetting Transforms, and *Note - Point Reference; Applying Transformations: Applying - Transformations to Points. - - Point P; - P.drawdot(); - P.shift(1, 1, 1); - P.drawdot(); - P.shift_times(2, 2, 2); - P.drawdot(); - P.shift_times(2, 2, 2); - P.drawdot(); - P.shift_times(2, 2, 2); - P.drawdot(); - - - -File: 3DLDF.info, Node: Applying Transformations to Points, Next: Projecting Points, Prev: Affine Transformations for Points, Up: Point Reference - -Applying Transformations -======================== - - - Function: void apply_transform (void) - Updates `world_coordinates' by multiplying it by `transform', - which is subsequently reset to the identity `Transform'. - - -File: 3DLDF.info, Node: Projecting Points, Next: Vector Operations, Prev: Applying Transformations to Points, Up: Point Reference - -Projecting -========== - - - Function: bool project (const Focus& F, [const unsigned short PROJ = - Projections::PERSP, [real FACTOR = 1]]) - - Function: bool project ([const unsigned short& PROJ = - Projections::PERSP, [real FACTOR = 1]]) - These functions calculate `projective_coordinates'. PROJ - indicates which projection is to be performed. If it is - `Projections::PERSP', then F indicates which `Focus' is to be used - (in the first version), or the global variable `default_focus' is - used (in the second). If `Projections::PARALLEL_X_Y', - `Projections::PARALLEL_X_Z', or `Projections::PARALLEL_Z_Y' is - used, F is ignored, since these projections don't use a `Focus'. - Currently, no other projections are defined. The x and y - coordinates in `projective_coordinates' are multiplied by FACTOR - with the default being 1. - - -File: 3DLDF.info, Node: Vector Operations, Next: Points and Lines, Prev: Projecting Points, Up: Point Reference - -Vector Operations -================= - - Mathematically speaking, vectors and points are not the same. -However, they can both be represented as triples of real numbers (in a -three-dimensional Cartesian space). It is sometimes convenient to treat -points as though they were vectors, and vice versa. In particular, it -is convenient to use the same data type, namely `class Point', to -represent both points and vectors in 3DLDF. - - - `const' function: real dot_product (Point P) - Returns the dot or scalar product of `*this' and P. - - If P and Q are `Points', - P \dot Q = x_P * x_Q + y_P * y_Q + z_P * z_Q = |P||Q| * cos(\theta) - where |P| and |Q| are the magnitudes of P and Q, respectively, - and \theta is the angle between P and Q. - - Since - \theta = arccos(P \dot Q / |P||Q|), - the dot product can be used for finding the angle between two - vectors. - - Point P(1, -1, -1); - Point Q(3, 2, 5); - cout << P.angle(Q); - -| 112.002 - cout << P.dot_product(Q); - -| -4 - real P_Q_angle = (180.0 / PI) - * acos(P.dot_product(Q) - / (P.magnitude() * Q.magnitude())); - cout << P_Q_angle; - -| 112.002 - - If the angle \theta between two vectors P and Q is 90 degrees , - then \cos(\theta) is 0, so P \dot Q will also be 0. Therefore, - `dot_product()' can be used as a test for the orthogonality of - vectors. - - Point P(2); - Point Q(P); - Point Q0(P0); - Q0 *= Q.rotate(0, 0, 90); - P *= Q.rotate(0, 45, 45); - P *= Q.rotate(45); - cout << P.angle(Q); - -| 90 - cout << P.dot_product(Q); - -| 0 - - - - `const' function: Point cross_product (Point P) - Returns the cross or vector product of `*this' and P. - - If P and Q are `Points', - - P * Q = ((y_P * z_Q - z_P * y_Q), (z_P * x_Q - x_P * z_Q), - (x_P * y_Q - y_P * x_Q)) = |P||Q| * sin(\theta) * n, - - where |P| and |Q| are the magnitudes of P and Q, respectively, - \theta is the angle between P and Q, and n is a unit vector - perpendicular to both P and Q in the direction of a right-hand - screw from P towards Q. Therefore, `cross_product()' can be used - to find the normals to planes. - - Point P(2, 2, 2); - Point Q(-2, 2, 2); - Point n = P.cross_product(Q); - n.show("n:"); - -| n: (0, -8, 8) - real theta = (PI / 180.0) * P.angle(Q); - cout << theta; - -| 1.23096 - real n_mag = P.magnitude() * Q.magnitude() * sin(theta); - cout << n_mag; - -| 11.3137 - n /= n_mag; - cout << n.magnitude(); - -| 1 - - If \theta = 0 degrees or 180 degrees, \sin(\theta) will be 0, and - P * Q will be (0, 0, 0). The cross product thus provides a test - for parallel vectors. - - Point P(1, 2, 1); - Point Q(P); - Point R; - R *= Q.shift(-3, -1, 1); - Point s(Q - R); - Point n = P.cross_product(s); - n.show("n:"); - -| n: (0, 0, 0) - - - - `const' function: real magnitude (void) - Returns the magnitude of the `Point'. This is its distance from - `origin' and is equal to sqrt(x^2 + y^2 + z^2). - - Point P(13, 15.7, 22); - cout << P.magnitude(); - -| 29.9915 - - - `const' function: real angle (Point P) - Returns the angle in degrees between two `Points'. - - Point P(3.75, -1.25, 6.25); - Point Q(-5, 2.5, 6.25); - real angle = P.angle(Q); - cout << angle; - -| 73.9084 - Point n = origin.get_normal(P, Q); - n.show("n:"); - -| n: (0.393377, 0.91788, -0.0524503) - - - - Function: Point unit_vector (const bool ASSIGN, [const bool SILENT = - FALSE]) - - `const' function: Point unit_vector (void) - These functions return a `Point' with the x, y, and z-coordinates - of `world_coordinates' divided by the magnitude of the `Point'. - The magnitude of the resulting `Point' is thus 1. The first - version assigns the result to `*this' and should only ever be - called with ASSIGN = `true'. Calling it with the argument `false' - is equivalent to calling the `const' version, with no assignment. - If `unit_vector()' is called with ASSIGN and SILENT both `false', - it issues a warning message is issued and the `const' version is - called. If SILENT is `true', the message is suppressed. - - Point P(21, 45.677, 91); - Point Q = P.unit_vector(); - Q.show("Q:"); - -| Q: (0.201994, 0.439357, 0.875308) - P.rotate(30, 25, 10); - P.show("P:"); - P: (-19.3213, 82.9627, 59.6009) - cout << P.magnitude(); - -| 103.963 - P.unit_vector(true); - P.show("P:"); - -| P: (-0.185847, 0.797999, 0.573287) - cout << P.magnitude(); - -| 1 - - diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-6 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-6 --- 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-6 2003-12-10 18:44:55.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-6 2004-01-16 19:03:28.000000000 +0100 @@ -1,11 +1,11 @@ This is 3DLDF.info, produced by makeinfo version 4.5 from 3DLDF.texi. -This is the 3DLDF User and Reference Manual, edition 1.1.4 for 3DLDF -1.1.4. This manual was last updated on 10 December 2003. 3DLDF is a +This is the 3DLDF User and Reference Manual, edition 1.1.5.1 for 3DLDF +1.1.5.1. This manual was last updated on 16 January 2004. 3DLDF is a GNU package for three-dimensional drawing with MetaPost output. The author is Laurence D. Finston. - Copyright (C) 2003 Laurence D. Finston. + Copyright (C) 2003, 2004 Laurence D. Finston. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, @@ -20,6 +20,535 @@ END-INFO-DIR-ENTRY  +File: 3DLDF.info, Node: Returning Coordinates, Next: Returning Information for Points, Prev: Querying Points, Up: Point Reference + +Returning Coordinates +===================== + + The functions in this section return either a single coordinate or a +set of coordinates. Each has a `const' and a non-`const' version. + + The arguments are the same, with one exception: + +`CHAR' C + Only in `get_coord()'. Indicates which coordinate should be + returned. Valid values are `'x'', `'X'', `'y'', `'Y'', `'z'', + `'Z'', `'w'', and `'W''. + +`CHAR COORDS' + Indicates the set of coordinates which should be returned or from + which the coordinate to be returned should be chosen from. Valid + values are `'w'' for `world_coordinates' (the default), `'p'' for + `projective_coordinates', `'u'' for `user_coordinates', and `'v'' + for `view_coordinates'. + +`CONST BOOL' DO_PERSP + Only relevant if `projective_coordinates', or one of its elements + is to be returned. If `true', the default, then `project()' is + called, thereby generating values for `projective_coordinates'. + If DO_PERSP is `false', then `projective_coordinates', or one of + its elements, is returned unchanged, which may sometimes be useful. + +`CONST BOOL' DO_APPLY + If `true' (the default), `apply_transform()' is called, thereby + updating the `world_coordinates'. Otherwise, it's not, so that + the values stored in `world_coordinates' remain unchanged. Note + that if COORDS is `'p'' and DO_PERSP is `true', + `apply_transform()' will be called in `project()' whether + `do_apply' is `true' or `false'. If for some reason, one wanted + get `projective_coordinates', or one of its values, based on the + projection of `world_coordinates' without first updating them, one + would have to call `reset_transform()' before calling one of these + functions. It would probably be a good idea to save `transform' + before doing so. + +`FOCUS*' F + Indicates what `Focus' is to be used for projection. Only + relevant if `coords' is `'p'', i.e., `projective_coordinates', or + one of its elements, is to be returned. The default is 0, in + which case F points to the global variable `default_focus'. + +`CONST UNSIGNED SHORT' PROJ + Indicates what form of projection is to be used. Only relevant if + `coords' is `'p'', i.e., `projective_coordinates', or one of its + elements, is to be returned. The default is `Projections::PERSP', + which causes the perspective projection to be applied. + +`REAL' FACTOR + Passed to `project()'. The values of the x and y coordinates in + `projective_coordinates' are multiplied by FACTOR. Only relevant + if `coords' is `'p'', i.e., `projective_coordinates', or one of + its elements, is to be returned. The default is 1. + + - Function: valarray get_all_coords ([char COORDS = 'w', [const + bool DO_PERSP = true, [const bool DO_APPLY = true, [Focus* F + = 0, [const unsigned short PROJ = Projections::PERSP, [real + factor = 1]]]]]]) + Returns one of the sets of coordinates; `world_coordinates' by + default. Returns a complete set of coordinates: `'w'' for + `world_coordinates', `'p'' for `projective_coordinates', `'u'' for + `user_coordinates', or`'v'' for `view_coordinates'. + + - Function: real get_coord (char C, [char COORDS = 'w', [const bool + DO_PERSP = true, [const bool DO_APPLY = true, [Focus* F = 0, + [const unsigned short PROJ = `Projections::PERSP', [real + FACTOR = 1]]]]]]) + Returns one `coordinate', x, y, z, or w, from the set of + coordinates indicated (or `world_coordinates', by default). + + - Function: real get_x ([char COORDS = 'w', [const bool DO_PERSP = + true, [const bool DO_APPLY = true, [Focus* F = 0, [const + unsigned short PROJ = Projections::PERSP, [real FACTOR = + 1]]]]]]) + Returns the x-coordinate from the set of coordinates indicated (or + `world_coordinates', by default). + + - Function: real get_y ([char COORDS = 'w', [const bool DO_PERSP = + true, [const bool DO_APPLY = true, [Focus* F = 0, [const + unsigned short PROJ = Projections::PERSP, [real FACTOR = + 1]]]]]]) + Returns the y-coordinate from the set of coordinates indicated (or + `world_coordinates', by default). + + - Function: real get_z ([char COORDS = 'w', [const bool DO_PERSP = + true, [const bool DO_APPLY = true, [Focus* F = 0, [const + unsigned short PROJ = Projections::PERSP, [real FACTOR = + 1]]]]]]) + Returns the z-coordinate from the set of coordinates indicated (or + `world_coordinates', by default). + + - Function: real get_w ([char COORDS = 'w', [const bool DO_PERSP = + true, [const bool DO_APPLY = true, [Focus* F = 0, [const + unsigned short PROJ = Projections::PERSP, [real FACTOR = + 1]]]]]]) + Returns the w-coordinate from the set of coordinates indicated (or + `world_coordinates', by default). + + +File: 3DLDF.info, Node: Returning Information for Points, Next: Modifying Points, Prev: Returning Coordinates, Up: Point Reference + +Returning Information +===================== + + - Static function: real epsilon (void) + Returns the positive `real' value of smallest magnitude \epsilon + that should be used as a coordinate value in a `Point'. A + coordinate of a `Point' may also contain -\epsilon. + + The value \epsilon is used for testing the equality of `Points' in + `Point::operator==()' (*note Point Reference; Operators: Point + Operators.): + + Let \epsilon be the value returned by `epsilon()', P and Q be + `Points', and P_x, Q_x, P_y, Q_y, P_z, and Q_z the updated x, y, + and z-coordinates of P and Q, respectively. If and only if ||P_x| + - |Q_x|| < \epsilon, ||P_y| - |Q_y|| < \epsilon, and ||P_z| - + |Q_z|| < \epsilon, then P = Q. + + `epsilon()' returns different values, depending on whether `real' + is `float' or `double': If `real' is `float' (the default), + `epsilon()' returns 0.00001. If `real' is `double', it returns + 0.000000001. + + Please note: I haven't tested whether 0.000000001 is a good value + yet, so users should be aware of this if they set `real' to + `double'!(1) The way to test this is to start with two `Points' P + and Q at different locations. Then they should be transformed + using different rotations in such a way that they should end up at + the same location. Let \epsilon stand for the value returned by + `epsilon()', and let x, y, and y stand for the `world_coordinates' + of the `Points' after `apply_transform()' has been called on them. + If x_P = x_Q, y_P = y_Q, and z_P = z_Q, \epsilon is a good value. + + Rotation causes a significant loss of precision to due to the use + of the `sin()' and `cos()' functions. Therefore, neither + `Point::epsilon()' nor `Transform::epsilon()' (*note Tranform + Reference; Returning Information: Returning Information for + Transforms.) can be as small as I'd like them to be. If they are + two small, operations that test for equality of `Transforms' and + `Points' will return `false' for objects that should be equal. + + ---------- Footnotes ---------- + + (1) For that matter, I haven't really tested whether 0.00001 is a +good value when `real' is `float'. + + +File: 3DLDF.info, Node: Modifying Points, Next: Affine Transformations for Points, Prev: Returning Information for Points, Up: Point Reference + +Modifying +========= + + - Virtual function: bool set_on_free_store ([bool B = true]) + This function is used in the template function `create_new()'. It + sets `on_free_store' to `true'. *Note Point Reference; Data + Members: Point Data Members, and *Note Point Reference; + Constructors and Setting Functions: Point Constructors and Setting + Functions. + + - Function: void clear (void) + Sets all of the coordinates in all of the sets of coordinates + (i.e., `world_coordinates', `user_coordinates', + `view_coordinates', and `projective_coordinates') to 0 and resets + `transform' + + - Function: void clean ([int FACTOR = 1]) + Calls `apply_transform()' and sets the values of + `world_coordinates' to 0, whose absolute values are less than + `epsilon()' * FACTOR . + + - Function: void reset_transform (void) + Sets `Transform' to the identity `Transform'. Performed in + `apply_transform()', after the latter updates `world_coordinates'. + *Note Point Reference; Applying Transformations: Applying + Transformations to Points. + + +File: 3DLDF.info, Node: Affine Transformations for Points, Next: Applying Transformations to Points, Prev: Modifying Points, Up: Point Reference + +Affine Transformations +====================== + + - Function: Transform rotate (const real X, [const real Y = 0, [const + real Z = 0]]) + - Function: Transform rotate (const Point& P0, const Point& P1, [const + real ANGLE = 180]) + - Function: Transform rotate (const Path& P, [const real ANGLE = 180]) + Each of these functions calls the corresponding version of + `Transform::rotate()', and returns its return value, namely, a + `Transform' representing the rotation only. + + In the first version, taking three `real' arguments, the `Point' + is rotated X degrees around the x-axis, Y degrees around the + y-axis, and Z degrees around the z-axis in that order. + + Point p0(1, 0, 2); + p0.rotate(90); + p0.show("p0:") + -| p0: (1, 2, 0) + Point p1(-1, 1, 1); + p1.rotate(-90, 90, 90); + p1.show("pt1:"); + -| p1: (1, -1, -1) + + [Figure 81 not displayed.] + + Please note that rotations are not commutative operations. Nor + are they commutative with other transformations. So, if you want + to rotate a `Point' about the x, y and z-axes in that order, you + can do so with a single invocation of `rotate()', as in the + previous example. However, if you want to rotate a `Point' first + about the y-axis and then about the x-axis, you must invoke + `rotate()' twice. + + Point pt0(1, 1, 1); + pt0.rotate(0, 45); + pt0.rotate(45); + pt0.show("pt0:"); + -| pt0: (0, 1.70711, 0.292893) + + In the version taking two `Point' arguments P0 and P1, and a + `real' argument ANGLE, the `Point' is rotated `angle' degrees + around the axis determined by P0 and P1, 180 degrees by default. + + Point P(2, 0, 0); + Point A; + Point B(2, 2, 2); + P.rotate(A, B, 180); + + [Figure 82 not displayed.] + + + - Function: Transform scale (real X, [real Y = 1, [real Z = 1]]) + Calls `transform.scale(X, Y, Z)' and returns its return value, + namely, a `Transform' representing the scaling operation only. + + Scaling causes the x-coordinate of the `Point' to be multiplied by + X, the y-coordinate of the `Point' to be multiplied by Y, and the + z-coordinate of the `Point' to be multiplied by Z. + + Point p0(1, 0, 3); + p0.scale(4); + p0.show("p0:"); + -| p0: (4, 0, 3) + Point p1(-2, -1, -2); + p1.scale(-2, -3, -4); + p1.show("p1:"); + -| p1: (4, 3, 8) + + [Figure 83 not displayed.] + + + - Function: Transform shear (real XY, [real XZ = 0, [real YX = 0, + [real YZ = 0, [real ZX = 0, [real ZY = 0]]]]]) + Calls `transform.shear()' with the same arguments and returns its + return value, namely, a `Transform' representing the shearing + operation only. + + Shearing modifies each coordinate of a `Point' proportionately to + the values of the other two coordinates. Let x_0, y_0, and z_0 + stand for the coordinates of a `Point' P before `P.shear('\alpha, + \beta, \gamma, \delta, \epsilon, \zeta `)', and x_1, y_1, and z_1 + for its coordinates afterwards. + + x_1 == x_0 + \alpha y + \beta z + y_1 == y_0 + \gamma x + \delta z + z_1 == z_0 + \epsilon x + \zeta y + + [next figure] demonstrates the effect of shearing the four + `Points' of a 3 * 3 + + `Rectangle' (i.e., a square) r in the x-y plane using only an XY + argument, making it non-rectangular. + + Point P0; + Point P1(3); + Point P2(3, 3); + Point P3(0, 3); + Rectangle r(p0, p1, p2, p3); + r.draw(); + r.shear(1.5); + r.draw(black, "evenly"); + + [Figure 84 not displayed.] + + + - Function: Transform shift (real X, [real Y = 0, [real Z = 0]]) + - Function: Transform shift (const Point& P) + Each of these functions calls the corresponding version of + `Transform::shift()' on `transform', and returns its return value, + namely, a `Transform' representing the shifting operation only. + + The `Point' is shifted X units in the direction of the positive + x-axis, Y units in the direction of the positive y-axis, and Z + units in the direction of the positive z-axis. + + p0(1, 2, 3); + p0.shift(2, 3, 5); + p0.show("p0:"); + -| p0: (3, 5, 8) + + + - Function: Transform shift_times (real X, [real Y = 1, [real Z = 1]]) + - Function: Transform shift_times (const Point& P) + Each of these functions calls the corresponding version of + `Transform::shift_times()' on `transform' and returns its return + value, namely the new value of `transform'. + + `shift_times()' makes it possible to increase the magnitude of a + shift applied to a `Point', while maintaining its direction. + Please note that `shift_times()' will only have an effect if it's + called after a call to `shift()' and before `transform' is reset. + This is performed by `reset_transform()', which is called in + `apply_transform()', and can also be called directly. *Note + Transform Reference; Resetting: Resetting Transforms, and *Note + Point Reference; Applying Transformations: Applying + Transformations to Points. + + Point P; + P.drawdot(); + P.shift(1, 1, 1); + P.drawdot(); + P.shift_times(2, 2, 2); + P.drawdot(); + P.shift_times(2, 2, 2); + P.drawdot(); + P.shift_times(2, 2, 2); + P.drawdot(); + + [Figure 85 not displayed.] + + + +File: 3DLDF.info, Node: Applying Transformations to Points, Next: Projecting Points, Prev: Affine Transformations for Points, Up: Point Reference + +Applying Transformations +======================== + + - Function: void apply_transform (void) + Updates `world_coordinates' by multiplying it by `transform', + which is subsequently reset to the identity `Transform'. + + +File: 3DLDF.info, Node: Projecting Points, Next: Vector Operations, Prev: Applying Transformations to Points, Up: Point Reference + +Projecting +========== + + - Function: bool project (const Focus& F, [const unsigned short PROJ = + Projections::PERSP, [real FACTOR = 1]]) + - Function: bool project ([const unsigned short& PROJ = + Projections::PERSP, [real FACTOR = 1]]) + These functions calculate `projective_coordinates'. PROJ + indicates which projection is to be performed. If it is + `Projections::PERSP', then F indicates which `Focus' is to be used + (in the first version), or the global variable `default_focus' is + used (in the second). If `Projections::PARALLEL_X_Y', + `Projections::PARALLEL_X_Z', or `Projections::PARALLEL_Z_Y' is + used, F is ignored, since these projections don't use a `Focus'. + Currently, no other projections are defined. The x and y + coordinates in `projective_coordinates' are multiplied by FACTOR + with the default being 1. + + +File: 3DLDF.info, Node: Vector Operations, Next: Points and Lines, Prev: Projecting Points, Up: Point Reference + +Vector Operations +================= + + Mathematically speaking, vectors and points are not the same. +However, they can both be represented as triples of real numbers (in a +three-dimensional Cartesian space). It is sometimes convenient to treat +points as though they were vectors, and vice versa. In particular, it +is convenient to use the same data type, namely `class Point', to +represent both points and vectors in 3DLDF. + + - `const' function: real dot_product (Point P) + Returns the dot or scalar product of `*this' and P. + + If P and Q are `Points', + P \dot Q = x_P * x_Q + y_P * y_Q + z_P * z_Q = |P||Q| * cos(\theta) + where |P| and |Q| are the magnitudes of P and Q, respectively, + and \theta is the angle between P and Q. + + Since + \theta = arccos(P \dot Q / |P||Q|), + the dot product can be used for finding the angle between two + vectors. + + Point P(1, -1, -1); + Point Q(3, 2, 5); + cout << P.angle(Q); + -| 112.002 + cout << P.dot_product(Q); + -| -4 + real P_Q_angle = (180.0 / PI) + * acos(P.dot_product(Q) + / (P.magnitude() * Q.magnitude())); + cout << P_Q_angle; + -| 112.002 + + [Figure 86 not displayed.] + + If the angle \theta between two vectors P and Q is 90 degrees , + then \cos(\theta) is 0, so P \dot Q will also be 0. Therefore, + `dot_product()' can be used as a test for the orthogonality of + vectors. + + Point P(2); + Point Q(P); + Point Q0(P0); + Q0 *= Q.rotate(0, 0, 90); + P *= Q.rotate(0, 45, 45); + P *= Q.rotate(45); + cout << P.angle(Q); + -| 90 + cout << P.dot_product(Q); + -| 0 + + [Figure 87 not displayed.] + + + - `const' function: Point cross_product (Point P) + Returns the cross or vector product of `*this' and P. + + If P and Q are `Points', + + P * Q = ((y_P * z_Q - z_P * y_Q), (z_P * x_Q - x_P * z_Q), + (x_P * y_Q - y_P * x_Q)) = |P||Q| * sin(\theta) * n, + + where |P| and |Q| are the magnitudes of P and Q, respectively, + \theta is the angle between P and Q, and n is a unit vector + perpendicular to both P and Q in the direction of a right-hand + screw from P towards Q. Therefore, `cross_product()' can be used + to find the normals to planes. + + Point P(2, 2, 2); + Point Q(-2, 2, 2); + Point n = P.cross_product(Q); + n.show("n:"); + -| n: (0, -8, 8) + real theta = (PI / 180.0) * P.angle(Q); + cout << theta; + -| 1.23096 + real n_mag = P.magnitude() * Q.magnitude() * sin(theta); + cout << n_mag; + -| 11.3137 + n /= n_mag; + cout << n.magnitude(); + -| 1 + + [Figure 88 not displayed.] + + If \theta = 0 degrees or 180 degrees, \sin(\theta) will be 0, and + P * Q will be (0, 0, 0). The cross product thus provides a test + for parallel vectors. + + Point P(1, 2, 1); + Point Q(P); + Point R; + R *= Q.shift(-3, -1, 1); + Point s(Q - R); + Point n = P.cross_product(s); + n.show("n:"); + -| n: (0, 0, 0) + + [Figure 89 not displayed.] + + + - `const' function: real magnitude (void) + Returns the magnitude of the `Point'. This is its distance from + `origin' and is equal to sqrt(x^2 + y^2 + z^2). + + Point P(13, 15.7, 22); + cout << P.magnitude(); + -| 29.9915 + + - `const' function: real angle (Point P) + Returns the angle in degrees between two `Points'. + + Point P(3.75, -1.25, 6.25); + Point Q(-5, 2.5, 6.25); + real angle = P.angle(Q); + cout << angle; + -| 73.9084 + Point n = origin.get_normal(P, Q); + n.show("n:"); + -| n: (0.393377, 0.91788, -0.0524503) + + [Figure 90 not displayed.] + + + - Function: Point unit_vector (const bool ASSIGN, [const bool SILENT = + FALSE]) + - `const' function: Point unit_vector (void) + These functions return a `Point' with the x, y, and z-coordinates + of `world_coordinates' divided by the magnitude of the `Point'. + The magnitude of the resulting `Point' is thus 1. The first + version assigns the result to `*this' and should only ever be + called with ASSIGN = `true'. Calling it with the argument `false' + is equivalent to calling the `const' version, with no assignment. + If `unit_vector()' is called with ASSIGN and SILENT both `false', + it issues a warning message is issued and the `const' version is + called. If SILENT is `true', the message is suppressed. + + Point P(21, 45.677, 91); + Point Q = P.unit_vector(); + Q.show("Q:"); + -| Q: (0.201994, 0.439357, 0.875308) + P.rotate(30, 25, 10); + P.show("P:"); + P: (-19.3213, 82.9627, 59.6009) + cout << P.magnitude(); + -| 103.963 + P.unit_vector(true); + P.show("P:"); + -| P: (-0.185847, 0.797999, 0.573287) + cout << P.magnitude(); + -| 1 + + + File: 3DLDF.info, Node: Points and Lines, Next: Point Intersections, Prev: Vector Operations, Up: Point Reference Points and Lines @@ -84,6 +613,8 @@ cout << (br.second == INVALID_REAL) -| 1 + [Figure 91 not displayed.] + - `const' function: bool_real is_on_line (const Point& P0, const Point& P1) @@ -117,6 +648,8 @@ F.shift(-1, 1); br = F.is_on_line(A, B); + [Figure 92 not displayed.] + - `const' function: Point mediate (Point P, [const real R = .5]) Returns a `Point' R of the way from `*this' to P. @@ -131,6 +664,8 @@ p4.show("p4:"); -| p4: (1, 1.66667, 1) + [Figure 93 not displayed.] +  File: 3DLDF.info, Node: Point Intersections, Next: Point Drawing Functions, Prev: Points and Lines, Up: Point Reference @@ -168,6 +703,8 @@ cout << "bp.b == " << bp.b << endl << flush; -| bp.b == 1 + [Figure 94 not displayed.] + Point A(.5, .5); Point B(1.5, 1.5); Point C(-1, 1); @@ -177,6 +714,8 @@ cout << "bp.b == " << bp.b << endl << flush; -| bp.b == 0 + [Figure 95 not displayed.] +  File: 3DLDF.info, Node: Point Drawing Functions, Next: Labelling Points, Prev: Point Intersections, Up: Point Reference @@ -213,6 +752,8 @@ Point P(1, 1); P.drawdot(gray, "pensquare scaled 1cm"); + [Figure 96 not displayed.] + - Function: void undrawdot ([string PEN = "", [Picture& PICTURE = `current_picture']]) @@ -226,6 +767,8 @@ P.drawdot(gray, "pensquare scaled 1cm"); P.undrawdot("pencircle scaled .5cm"); + [Figure 97 not displayed.] + - Function: void draw (const Point& P, [const Color& DDRAW_COLOR = `*Colors::default_color', [string DDASHED = "", [string PPEN @@ -243,6 +786,8 @@ Point Q(2, 3, 5); P.draw(Q, Colors::gray, "", "pensquare scaled .5cm"); + [Figure 98 not displayed.] + - Function: void undraw (const Point& P, [string DDASHED = "", [string PPEN = "", [Picture& PICTURE = `current_picture']]]) @@ -257,6 +802,8 @@ P.draw(Q, Colors::gray, "", "pensquare scaled .5cm"); P.undraw(Q, "evenly scaled 6", "pencircle scaled .3cm"); + [Figure 99 not displayed.] + - Function: Path draw_help (const Point& P, [const Color& DDRAW_COLOR = *Colors::help_color, [string DDASHED = "", [string PPEN = @@ -285,6 +832,8 @@ Point Q(3, 3, 5); P.drawarrow(Q); + [Figure 100 not displayed.] +  File: 3DLDF.info, Node: Labelling Points, Next: Showing Points, Prev: Point Drawing Functions, Up: Point Reference @@ -321,6 +870,8 @@ Point p0(2, 3); p0.label("$p_0$"); + [Figure 101 not displayed.] + If backslashes are needed in the text of the label, then TEXT_STR must contain double backslashes, so that single backslashes will be written to `out_stream'. @@ -330,6 +881,8 @@ Point R(P.mediate(Q)); R.label("$\\overrightarrow{PQ}$", "ulft"); + [Figure 102 not displayed.] + The POSITION argument indicates where the text of the label should be located relative to the `Point'. The valid values are the strings used in MetaPost for this purpose, i.e., `top', `bot', @@ -355,6 +908,8 @@ Point p0(2, 3); p0.dotlabel("$p_0$"); + [Figure 103 not displayed.] +  File: 3DLDF.info, Node: Showing Points, Next: Outputting Points, Prev: Labelling Points, Up: Point Reference @@ -716,6 +1271,8 @@ Line L0(p, d); Line L1 = p.get_line(d); + [Figure 104 not displayed.] + - Copy constructor: void Line (const Line& L) Creates a `Line', making it a copy of L. @@ -770,482 +1327,3 @@ fill_draw_value == 0 (1, -2, 3) -- (-12.3, 21, 36.002); - -File: 3DLDF.info, Node: Plane Reference, Next: Path Reference, Prev: Line Reference, Up: Top - -Plane Reference -*************** - - The `struct Plane' is defined in `planes.web'. `Planes' are not -`Shapes'. They are used for performing vector operations. A `Plane' -is defined by a `Point' representing a point on the plane, a `Point' -representing the normal to the plane, and the distance of the plane from -the origin. - - The most common use of `Planes' is to represent the plane in which -an existing plane figure lies. Therefore, they most likely to be -created by using `Path::get_plane()'. *Note Path Reference; Querying: -Querying Paths. However, `class Plane' does have constructors for -creating `Planes' directly, if desired. *Note Planes Reference; -Constructors: Planes Constructors. - -* Menu: - -* Planes Data Members:: -* Planes Global Constants:: -* Planes Constructors:: -* Planes Operators:: -* Planes Returning Information:: -* Plane Intersections:: -* Planes Showing:: - - -File: 3DLDF.info, Node: Planes Data Members, Next: Planes Global Constants, Prev: Plane Reference, Up: Plane Reference - -Data Members -============ - - Because the main purpose of `Plane' is to provide information about -`Shapes', its data members are all `public'. - - - Public variable: Point point - Represents a point on the plane. - - - Public variable: Point normal - Represents the normal to the plane. - - - Public variable: real distance - The distance of the plane from the origin. - - -File: 3DLDF.info, Node: Planes Global Constants, Next: Planes Constructors, Prev: Planes Data Members, Up: Plane Reference - -Global Constants -================ - - - Constant: const Plane INVALID_PLANE - A `Plane' with `point' == `normal', and `distance' == - `INVALID_REAL'. - - `INVALID_PLANE' is returned from `Path::get_plane()', if the - `Path' is not planar. *Note Path Reference; Querying: Querying - Paths. - - -File: 3DLDF.info, Node: Planes Constructors, Next: Planes Operators, Prev: Planes Global Constants, Up: Plane Reference - -Constructors -============ - - - Default constructor: void Plane (void) - Creates a degenerate `Plane' with `point' == `normal' == `origin', - and `distance' == 0. - - `Planes' constructed using this constructor will probably be set - using the assignment operator or `Path::get_plane()' immediately, - or very soon after being declared. *Note Planes Reference; - Operators: Planes Operators, and *Note Paths Reference; Querying: - Querying Paths. - - - Copy constructor: void Plane (const Plane& p) - Creates a new `Plane', making it a copy of P. - - - Constructor: void Plane (const Point& P, const Point& N) - If P is not equal to N, this constructor creates a `Plane' and - sets `point' to P. `normal' is set to N, and made a unit vector. - `distance' is calculated according to the following formula: Let n - stand for `normal', p for `point', and d for `distance': d = -p - \dot n. If d = 0, `origin' lies in the `Plane'. If d > 0, - `origin' lies on the side of the `Plane' that `normal' points to, - considered to be "outside". If d<0, `origin' lies on the side of - the `Plane' that `normal' does not point to, considered to be - "inside". - - However, if P == N, `point' and `normal' are both set to - `INVALID_POINT', and `distance' is set to `INVALID_REAL', i.e., - `*this' will be equal to `INVALID_PLANE' (*note Planes Reference; - Global Constants: Planes Global Constants.). - - Point P(1, 1, 1); - Point N(0, 1); - N.rotate(-35, 30, 20); - N.show("N:"); - -| N: (-0.549659, 0.671664, 0.496732) - Plane q(P, N); - cout << q.distance; - -| -0.618736 - - - -File: 3DLDF.info, Node: Planes Operators, Next: Planes Returning Information, Prev: Planes Constructors, Up: Plane Reference - -Operators -========= - - - Assignment operator: const Plane& operator= (const Plane& P) - Sets `point' to P.`point', `normal' to P.`normal', and `distance' - to P.`distance'. The return value is P, so that invocations of - this function can be chained. - - Point pt(2, 2.3, 6); - Point norm(-1, 12, -36); - Plane A(pt, norm); - Plane B; - Plane C; - B = C = A; - A.show("A:"); - -| A: - normal: (-0.0263432, 0.316118, -0.948354) - point: (2, 2.3, 6) - distance == 5.01574 - cout << (A == B && A == C && B == C); - -| 1 - - - `const' operator: bool operator== (const Plane& P) - Equality operator. Compares `*this' and P, and returns `true', if - `point' == P.`point', `normal' == P.`normal', and `distance' == - P.`distance', otherwise `false'. - - - `const' operator: bool operator!= (const Plane& P) - Inequality operator. Compares `*this' and P and returns `true', - if `point' != P.`point', or `normal' != P.`normal', or - `distance' != P.`distance'. Otherwise, it returns `false'. - - -File: 3DLDF.info, Node: Planes Returning Information, Next: Plane Intersections, Prev: Planes Operators, Up: Plane Reference - -Returning Information -===================== - - - `const' function: real_short get_distance (const Point& P) - - `const' function: real_short get_distance (void) - The version of this function taking a `Point' argument returns a - `real_short' R, whose `real' part (R.`first') represents the - distance of P from the `Plane'. This value is always positive. - R.`second' can take on three values: - - 0 - If the `Point' lies in the `Plane'. - - 1 - If it lies on the side of the `Plane' pointed at by the - normal to the `Plane', considered to be the "outside". - - -1 - If it lies on the side of the `Plane' _not_ pointed at by the - normal to the `Plane', considered to be the "inside". - - The version taking no argument returns the absolute of the data - member `distance' and its sign, i.e., the distance of `origin' to - the `Plane', and which side of the `Plane' it lies on. - - It would have been possible to use `origin' as the default for an - optional `Point' argument, but I've chosen to overload this - function, because of problems that may arise, when I implement - `user_coordinates' and `view_coordinates' (*note Point Reference; - Data Members: Point Data Members.). - - Point N(0, 1); - N.rotate(-10, 20, 20); - Point P(1, 1, 1); - Plane q(P, N); - Point A(4, -2, 4); - Point B(-1, 3, 2); - Point C = q.intersection_point(A, B).pt; - real_short bp; - - bp = q.get_distance(); - cout << bp.first; - -| 0.675646 - cout << bp.second - -| -1 - - bp = q.get_distance(A) - cout << bp.first; - -| 3.40368 - cout << bp.second; - -| -1 - - bp = q.get_distance(B) - cout << bp.first; - -| 2.75865 - cout << bp.second; - -| 1 - - bp = q.get_distance(C) - cout << bp.first; - -| 0 - cout << bp.second; - -| 0 - - - -File: 3DLDF.info, Node: Plane Intersections, Next: Planes Showing, Prev: Planes Returning Information, Up: Plane Reference - -Intersections -============= - - - `const' function: bool_point intersection_point (const Point& P0, - const Point& P1) - - `const' function: bool_point intersection_point (const Path& P) - These functions find the intersection point of the `Plane' and a - line. In the first version, the line is defined by the two - `Point' arguments. In the second version, the `Path' P must be - linear, i.e., P.`is_linear()' must be `true'. - - Both versions of `intersection_point()' return a `bool_point' BP, - where BP.`pt' is the intersection point, or `INVALID_POINT', if - there is none. If an intersection point is found, BP.`b' will be - `true', otherwise `false'. Returning a `bool_point' makes it - possible to test for success without comparing the `Point' - returned against `INVALID_POINT'. - - Point center(2, 2, 3.5); - Reg_Polygon h(center, 6, 4, 80, 30, 10); - Plane q = h.get_plane(); - Point P0 = center.mediate(h.get_point(2)); - P0.shift(5 * (N - center)); - Point P1(P0); - P1.rotate(h.get_point(1), h.get_point(4)); - P1 = 3 * (P1 - P0); - P1.shift(P0); - P1.shift(3, -.5, -2); - bool_point bp = q.intersection_point(P0, P1); - Point i_P = bp.pt; - Point P4 = h.get_point(3).mediate(h.get_point(0), .75); - P4.shift(N - center); - Point P5(P4); - P5.rotate(h.get_point(3), h.get_point(0)); - P4.shift(-1, 2); - Path theta(P4, P5); - bp = q.intersection_point(theta); - Point i_theta = bp.pt; - draw_axes(); - - - - `const' function: Line intersection_line (const Plane& P) - Returns a `Line' L. representing the line of intersection of two - `Planes'. *Note Line Reference::. - - In [next figure] , `intersection_line()' is used to find the line - of intersection of the `Planes' derived from the `Rectangles' r_0 - and r_1 using `get_plane()' (*note Paths Reference; Querying: - Querying Paths.). Please note that there is no guarantee that - L.`position' will be in a convenient place for your drawing. A - bit of fiddling was needed to find the `Points' P_2 and P_3. I - plan to add functions for finding the intersection lines of plane - figures, but haven't done so yet. - - Rectangle r0(origin, 5, 5, 10, 15, 6); - Rectangle r1(origin, 5, 5, 90, 50, 10); - r1 *= r0.rotate(30, 30, 30); - r1 *= r0.shift(1, -1, 3); - Plane q0 = r0.get_plane(); - Plane q1 = r1.get_plane(); - Line l = q0.intersection_line(q1); - l.show("l:"); - -| l: - position: (0, 11.2193, 20.0759) - direction: (0.0466595, -0.570146, -0.796753) - Point P0(l.direction); - P0.shift(l.position); - P0.show("P0:"); - -| P0: (0.0466595, 10.6491, 19.2791) - Point P1(-l.direction); - P1.shift(l.position); - Point P2(P0 - P1); - P2 *= 12.5; - P2.shift(P0); - cout << P2.is_on_plane(q0); - -| 1 - cout << P2.is_on_plane(q1); - -| 1 - Point P3(P0 - P1); - P3 *= 7; - P3.shift(P0); - cout << P3.is_on_plane(q0); - -| 1 - cout << P3.is_on_plane(q1); - -| 1 - - - -File: 3DLDF.info, Node: Planes Showing, Prev: Plane Intersections, Up: Plane Reference - -Showing -======= - - - `const' function: void show ([string TEXT = ""]) - Prints information about the `Plane' to standard output. If TEXT - is not the empty `string', it is printed to the standard output. - Otherwise, `Plane:' is printed. Following this, if the `Plane' is - equal to `INVALID_PLANE' (*note Planes Reference; Global - Constants: Planes Global Constants.), a message to this effect is - printed to standard output. Otherwise, `normal' and `point' are - shown using `Point::show()' (*note Point Reference; Showing: - Showing Points.). Finally, `distance' is printed. - - Point A(1, 3, 2.5); - Rectangle r0(A, 5, 5, 10, 15, 6); - Plane p = r0.get_plane(); - -| p: - normal: (-0.0582432, 0.984111, -0.167731) - point: (-0.722481, 2.38245, -0.525176) - distance == -2.47476 - - - -File: 3DLDF.info, Node: Path Reference, Next: Polygon Reference, Prev: Plane Reference, Up: Top - -Path Reference -************** - - Class `Path' is defined in `paths.web'. It is derived from `Shape' -using `protected' derivation. - -* Menu: - -* Path Data Members:: -* Path Constructors and Setting Functions:: -* Path Destructor:: -* Path Operators:: -* Appending to Paths :: -* Copying Paths:: -* Clearing Paths :: -* Modifying Paths :: -* Affine Transformations for Paths:: -* Aligning Paths with an Axis:: -* Applying Transformations to Paths:: -* Drawing and Filling Paths:: -* Labelling Paths:: -* Showing Paths:: -* Querying Paths:: -* Outputting Paths:: -* Path Intersections:: - - -File: 3DLDF.info, Node: Path Data Members, Next: Path Constructors and Setting Functions, Prev: Path Reference, Up: Path Reference - -Data Members -============ - - - Protected variable: bool line_switch - `true' if the `Path' was created using the constructor `Path(const - Point& p0, const Point& p1)', directly or indirectly. *Note Path - Reference; Constructors and Setting Functions: Path Constructors - and Setting Functions. - - Point p0; - Point p1(1, 1); - Point p2(2, 3); - Path q0(p0, p1); - cout << q0.get_line_switch(); - -| 1 - Path q1; - q1 = q0; - cout << q1.get_line_switch(); - -| 1 - Path q2 = p0.draw(p1); - cout << q2.get_line_switch(); - -| 1 - Path q3("..", false, &p1, &p2, &p0, 0); - cout << q3.get_line_switch(); - -| 0 - - Some `Path' functions only work on _linear `Paths'_, so it's - necessary to be able to distinguish them from non-linear ones. - The function `is_linear()' should be enough to ensure that all of - these functions work, so I plan to make `line_switch' obsolete - soon. However, at the moment, it's still needed. *Note Path - Reference; Querying: Querying Paths. - - - Protected variable: bool cycle_switch - `true' if the `Path' is cyclical, otherwise `false'. - - - Protected variable: bool on_free_store - `true' if the `Path' was dynamically allocated on the free store. - Otherwise `false'. Set to `true' only in `create_new_path()', - which should be the only way `Paths' are ever dynamically - allocated. *Note Path Reference; Constructors and Setting - Functions: Path Constructors and Setting Functions. - - - Protected variable: bool do_output - Used in `Picture::output()'. Set to `false' if the `Path' isn't - projectable using the arguments passed to `Picture::output()'. - *Note Picture Reference; Outputting: Outputting Pictures. - - - Protected variable: signed short fill_draw_value - Set in the drawing and filling functions, and used in - `Path::output()', to determine what MetaPost code to write to - `out_stream'. *Note Path Reference; Drawing and Filling: Drawing - and Filling Paths, and *Note Path Reference; Outputting: - Outputting Paths. - - - Protected variable: const Color* draw_color - Pointer to the `Color' used if the `Path' is drawn. - - - Protected variable: const Color* fill_color - Pointer to the `Color' used if the `Path' is filled. - - - Protected variable: string dashed - String written to `out_stream' for the "dash pattern" in a - MetaPost `draw' or `undraw' command. If and only if `dashed' is - not the empty string, "`dashed' <_dash pattern_>" is written to - `out_stream'. - - Dash patterns have no meaning inside 3DLDF; `dashed', if - non-empty, is written unchanged to `out_stream'. I may change this - in the future. - - - Protected variable: string pen - String written to `out_stream' for the `pen' to be used in a - MetaPost `draw', `undraw', `filldraw', or `unfilldraw' command. - If and only if `pen' is not the empty string, "`withpen' <...>" is - written to `out_stream'. - - Pens have no meaning inside 3DLDF; `pen', if non-empty, is - written unchanged to `out_stream'. I may change this in the - future. - - - Protected variable: bool arrow - Indicates whether an arrow should be drawn when outputting a - `Path'. Set to `true' on a `Path' created on the free store and - put onto a `Picture' by `drawarrow()'. - - - Protected variable: valarray projective_extremes - Contains the maxima and minima of the x, y, and z-coordinates of - the _projections_ of `Points' on a `Path' using a particular - `Focus'. Set in `set_extremes()' and used in `Picture::output()' - for surface hiding. - - - Protected variable: vector points - Pointers to the `Points' on the `Path'. - - - Protected variable: vector connectors - The connectors between the `Points' on the `Path'. Connectors are - simply `strings' in 3DLDF, they are written unchanged to - `out_stream'. - - - Public static variable: const Color* help_color - Pointer to a `const Color', which becomes the default for - `draw_help()'. *Note Path Reference; Drawing and Filling: Drawing - and Filling Paths. - - Please note that `help_color' is a pointer to a `const Color', not - a `const' pointer to a `Color' or a `const' pointer to a `const - Color'! It's easy to get confused by the syntax for these types - of pointers.(1) - - - Public static variable: string help_dash_pattern - The default dash pattern for `draw_help()'. - - - Public static variable: bool do_help_lines - `true' if help lines should be output, otherwise `false'. If - `false', a call to `draw_help()' does not cause a copy of the - `Path' to be created and put onto a `Picture'. *Note Path - Reference; Drawing and Filling: Drawing and Filling Paths. - - ---------- Footnotes ---------- - - (1) Stroustrup, `The C++ Programming Language', p. 96. - diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-7 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-7 --- 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-7 2003-12-10 18:44:55.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-7 2004-01-16 19:03:28.000000000 +0100 @@ -1,11 +1,11 @@ This is 3DLDF.info, produced by makeinfo version 4.5 from 3DLDF.texi. -This is the 3DLDF User and Reference Manual, edition 1.1.4 for 3DLDF -1.1.4. This manual was last updated on 10 December 2003. 3DLDF is a +This is the 3DLDF User and Reference Manual, edition 1.1.5.1 for 3DLDF +1.1.5.1. This manual was last updated on 16 January 2004. 3DLDF is a GNU package for three-dimensional drawing with MetaPost output. The author is Laurence D. Finston. - Copyright (C) 2003 Laurence D. Finston. + Copyright (C) 2003, 2004 Laurence D. Finston. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, @@ -20,6 +20,495 @@ END-INFO-DIR-ENTRY  +File: 3DLDF.info, Node: Plane Reference, Next: Path Reference, Prev: Line Reference, Up: Top + +Plane Reference +*************** + + The `struct Plane' is defined in `planes.web'. `Planes' are not +`Shapes'. They are used for performing vector operations. A `Plane' +is defined by a `Point' representing a point on the plane, a `Point' +representing the normal to the plane, and the distance of the plane from +the origin. + + The most common use of `Planes' is to represent the plane in which +an existing plane figure lies. Therefore, they most likely to be +created by using `Path::get_plane()'. *Note Path Reference; Querying: +Querying Paths. However, `class Plane' does have constructors for +creating `Planes' directly, if desired. *Note Planes Reference; +Constructors: Planes Constructors. + +* Menu: + +* Planes Data Members:: +* Planes Global Constants:: +* Planes Constructors:: +* Planes Operators:: +* Planes Returning Information:: +* Plane Intersections:: +* Planes Showing:: + + +File: 3DLDF.info, Node: Planes Data Members, Next: Planes Global Constants, Prev: Plane Reference, Up: Plane Reference + +Data Members +============ + + Because the main purpose of `Plane' is to provide information about +`Shapes', its data members are all `public'. + + - Public variable: Point point + Represents a point on the plane. + + - Public variable: Point normal + Represents the normal to the plane. + + - Public variable: real distance + The distance of the plane from the origin. + + +File: 3DLDF.info, Node: Planes Global Constants, Next: Planes Constructors, Prev: Planes Data Members, Up: Plane Reference + +Global Constants +================ + + - Constant: const Plane INVALID_PLANE + A `Plane' with `point' == `normal', and `distance' == + `INVALID_REAL'. + + `INVALID_PLANE' is returned from `Path::get_plane()', if the + `Path' is not planar. *Note Path Reference; Querying: Querying + Paths. + + +File: 3DLDF.info, Node: Planes Constructors, Next: Planes Operators, Prev: Planes Global Constants, Up: Plane Reference + +Constructors +============ + + - Default constructor: void Plane (void) + Creates a degenerate `Plane' with `point' == `normal' == `origin', + and `distance' == 0. + + `Planes' constructed using this constructor will probably be set + using the assignment operator or `Path::get_plane()' immediately, + or very soon after being declared. *Note Planes Reference; + Operators: Planes Operators, and *Note Paths Reference; Querying: + Querying Paths. + + - Copy constructor: void Plane (const Plane& p) + Creates a new `Plane', making it a copy of P. + + - Constructor: void Plane (const Point& P, const Point& N) + If P is not equal to N, this constructor creates a `Plane' and + sets `point' to P. `normal' is set to N, and made a unit vector. + `distance' is calculated according to the following formula: Let n + stand for `normal', p for `point', and d for `distance': d = -p + \dot n. If d = 0, `origin' lies in the `Plane'. If d > 0, + `origin' lies on the side of the `Plane' that `normal' points to, + considered to be "outside". If d<0, `origin' lies on the side of + the `Plane' that `normal' does not point to, considered to be + "inside". + + However, if P == N, `point' and `normal' are both set to + `INVALID_POINT', and `distance' is set to `INVALID_REAL', i.e., + `*this' will be equal to `INVALID_PLANE' (*note Planes Reference; + Global Constants: Planes Global Constants.). + + Point P(1, 1, 1); + Point N(0, 1); + N.rotate(-35, 30, 20); + N.show("N:"); + -| N: (-0.549659, 0.671664, 0.496732) + Plane q(P, N); + cout << q.distance; + -| -0.618736 + + [Figure 105 not displayed.] + + + +File: 3DLDF.info, Node: Planes Operators, Next: Planes Returning Information, Prev: Planes Constructors, Up: Plane Reference + +Operators +========= + + - Assignment operator: const Plane& operator= (const Plane& P) + Sets `point' to P.`point', `normal' to P.`normal', and `distance' + to P.`distance'. The return value is P, so that invocations of + this function can be chained. + + Point pt(2, 2.3, 6); + Point norm(-1, 12, -36); + Plane A(pt, norm); + Plane B; + Plane C; + B = C = A; + A.show("A:"); + -| A: + normal: (-0.0263432, 0.316118, -0.948354) + point: (2, 2.3, 6) + distance == 5.01574 + cout << (A == B && A == C && B == C); + -| 1 + + - `const' operator: bool operator== (const Plane& P) + Equality operator. Compares `*this' and P, and returns `true', if + `point' == P.`point', `normal' == P.`normal', and `distance' == + P.`distance', otherwise `false'. + + - `const' operator: bool operator!= (const Plane& P) + Inequality operator. Compares `*this' and P and returns `true', + if `point' != P.`point', or `normal' != P.`normal', or + `distance' != P.`distance'. Otherwise, it returns `false'. + + +File: 3DLDF.info, Node: Planes Returning Information, Next: Plane Intersections, Prev: Planes Operators, Up: Plane Reference + +Returning Information +===================== + + - `const' function: real_short get_distance (const Point& P) + - `const' function: real_short get_distance (void) + The version of this function taking a `Point' argument returns a + `real_short' R, whose `real' part (R.`first') represents the + distance of P from the `Plane'. This value is always positive. + R.`second' can take on three values: + + 0 + If the `Point' lies in the `Plane'. + + 1 + If it lies on the side of the `Plane' pointed at by the + normal to the `Plane', considered to be the "outside". + + -1 + If it lies on the side of the `Plane' _not_ pointed at by the + normal to the `Plane', considered to be the "inside". + + The version taking no argument returns the absolute of the data + member `distance' and its sign, i.e., the distance of `origin' to + the `Plane', and which side of the `Plane' it lies on. + + It would have been possible to use `origin' as the default for an + optional `Point' argument, but I've chosen to overload this + function, because of problems that may arise, when I implement + `user_coordinates' and `view_coordinates' (*note Point Reference; + Data Members: Point Data Members.). + + Point N(0, 1); + N.rotate(-10, 20, 20); + Point P(1, 1, 1); + Plane q(P, N); + Point A(4, -2, 4); + Point B(-1, 3, 2); + Point C = q.intersection_point(A, B).pt; + real_short bp; + + bp = q.get_distance(); + cout << bp.first; + -| 0.675646 + cout << bp.second + -| -1 + + bp = q.get_distance(A) + cout << bp.first; + -| 3.40368 + cout << bp.second; + -| -1 + + bp = q.get_distance(B) + cout << bp.first; + -| 2.75865 + cout << bp.second; + -| 1 + + bp = q.get_distance(C) + cout << bp.first; + -| 0 + cout << bp.second; + -| 0 + + [Figure 106 not displayed.] + + + +File: 3DLDF.info, Node: Plane Intersections, Next: Planes Showing, Prev: Planes Returning Information, Up: Plane Reference + +Intersections +============= + + - `const' function: bool_point intersection_point (const Point& P0, + const Point& P1) + - `const' function: bool_point intersection_point (const Path& P) + These functions find the intersection point of the `Plane' and a + line. In the first version, the line is defined by the two + `Point' arguments. In the second version, the `Path' P must be + linear, i.e., P.`is_linear()' must be `true'. + + Both versions of `intersection_point()' return a `bool_point' BP, + where BP.`pt' is the intersection point, or `INVALID_POINT', if + there is none. If an intersection point is found, BP.`b' will be + `true', otherwise `false'. Returning a `bool_point' makes it + possible to test for success without comparing the `Point' + returned against `INVALID_POINT'. + + Point center(2, 2, 3.5); + Reg_Polygon h(center, 6, 4, 80, 30, 10); + Plane q = h.get_plane(); + Point P0 = center.mediate(h.get_point(2)); + P0.shift(5 * (N - center)); + Point P1(P0); + P1.rotate(h.get_point(1), h.get_point(4)); + P1 = 3 * (P1 - P0); + P1.shift(P0); + P1.shift(3, -.5, -2); + bool_point bp = q.intersection_point(P0, P1); + Point i_P = bp.pt; + Point P4 = h.get_point(3).mediate(h.get_point(0), .75); + P4.shift(N - center); + Point P5(P4); + P5.rotate(h.get_point(3), h.get_point(0)); + P4.shift(-1, 2); + Path theta(P4, P5); + bp = q.intersection_point(theta); + Point i_theta = bp.pt; + draw_axes(); + + [Figure 107 not displayed.] + + + - `const' function: Line intersection_line (const Plane& P) + Returns a `Line' L. representing the line of intersection of two + `Planes'. *Note Line Reference::. + + In [next figure] , `intersection_line()' is used to find the line + of intersection of the `Planes' derived from the `Rectangles' r_0 + and r_1 using `get_plane()' (*note Paths Reference; Querying: + Querying Paths.). Please note that there is no guarantee that + L.`position' will be in a convenient place for your drawing. A + bit of fiddling was needed to find the `Points' P_2 and P_3. I + plan to add functions for finding the intersection lines of plane + figures, but haven't done so yet. + + Rectangle r0(origin, 5, 5, 10, 15, 6); + Rectangle r1(origin, 5, 5, 90, 50, 10); + r1 *= r0.rotate(30, 30, 30); + r1 *= r0.shift(1, -1, 3); + Plane q0 = r0.get_plane(); + Plane q1 = r1.get_plane(); + Line l = q0.intersection_line(q1); + l.show("l:"); + -| l: + position: (0, 11.2193, 20.0759) + direction: (0.0466595, -0.570146, -0.796753) + Point P0(l.direction); + P0.shift(l.position); + P0.show("P0:"); + -| P0: (0.0466595, 10.6491, 19.2791) + Point P1(-l.direction); + P1.shift(l.position); + Point P2(P0 - P1); + P2 *= 12.5; + P2.shift(P0); + cout << P2.is_on_plane(q0); + -| 1 + cout << P2.is_on_plane(q1); + -| 1 + Point P3(P0 - P1); + P3 *= 7; + P3.shift(P0); + cout << P3.is_on_plane(q0); + -| 1 + cout << P3.is_on_plane(q1); + -| 1 + + [Figure 108 not displayed.] + + + +File: 3DLDF.info, Node: Planes Showing, Prev: Plane Intersections, Up: Plane Reference + +Showing +======= + + - `const' function: void show ([string TEXT = ""]) + Prints information about the `Plane' to standard output. If TEXT + is not the empty `string', it is printed to the standard output. + Otherwise, `Plane:' is printed. Following this, if the `Plane' is + equal to `INVALID_PLANE' (*note Planes Reference; Global + Constants: Planes Global Constants.), a message to this effect is + printed to standard output. Otherwise, `normal' and `point' are + shown using `Point::show()' (*note Point Reference; Showing: + Showing Points.). Finally, `distance' is printed. + + Point A(1, 3, 2.5); + Rectangle r0(A, 5, 5, 10, 15, 6); + Plane p = r0.get_plane(); + -| p: + normal: (-0.0582432, 0.984111, -0.167731) + point: (-0.722481, 2.38245, -0.525176) + distance == -2.47476 + + + +File: 3DLDF.info, Node: Path Reference, Next: Polygon Reference, Prev: Plane Reference, Up: Top + +Path Reference +************** + + Class `Path' is defined in `paths.web'. It is derived from `Shape' +using `protected' derivation. + +* Menu: + +* Path Data Members:: +* Path Constructors and Setting Functions:: +* Path Destructor:: +* Path Operators:: +* Appending to Paths :: +* Copying Paths:: +* Clearing Paths :: +* Modifying Paths :: +* Affine Transformations for Paths:: +* Aligning Paths with an Axis:: +* Applying Transformations to Paths:: +* Drawing and Filling Paths:: +* Labelling Paths:: +* Showing Paths:: +* Querying Paths:: +* Outputting Paths:: +* Path Intersections:: + + +File: 3DLDF.info, Node: Path Data Members, Next: Path Constructors and Setting Functions, Prev: Path Reference, Up: Path Reference + +Data Members +============ + + - Protected variable: bool line_switch + `true' if the `Path' was created using the constructor `Path(const + Point& p0, const Point& p1)', directly or indirectly. *Note Path + Reference; Constructors and Setting Functions: Path Constructors + and Setting Functions. + + Point p0; + Point p1(1, 1); + Point p2(2, 3); + Path q0(p0, p1); + cout << q0.get_line_switch(); + -| 1 + Path q1; + q1 = q0; + cout << q1.get_line_switch(); + -| 1 + Path q2 = p0.draw(p1); + cout << q2.get_line_switch(); + -| 1 + Path q3("..", false, &p1, &p2, &p0, 0); + cout << q3.get_line_switch(); + -| 0 + + [Figure 109 not displayed.] + + Some `Path' functions only work on _linear `Paths'_, so it's + necessary to be able to distinguish them from non-linear ones. + The function `is_linear()' should be enough to ensure that all of + these functions work, so I plan to make `line_switch' obsolete + soon. However, at the moment, it's still needed. *Note Path + Reference; Querying: Querying Paths. + + - Protected variable: bool cycle_switch + `true' if the `Path' is cyclical, otherwise `false'. + + - Protected variable: bool on_free_store + `true' if the `Path' was dynamically allocated on the free store. + Otherwise `false'. Set to `true' only in `create_new()', + which should be the only way `Paths' are ever dynamically + allocated. *Note Path Reference; Constructors and Setting + Functions: Path Constructors and Setting Functions. + + - Protected variable: bool do_output + Used in `Picture::output()'. Set to `false' if the `Path' isn't + projectable using the arguments passed to `Picture::output()'. + *Note Picture Reference; Outputting: Outputting Pictures. + + - Protected variable: signed short fill_draw_value + Set in the drawing and filling functions, and used in + `Path::output()', to determine what MetaPost code to write to + `out_stream'. *Note Path Reference; Drawing and Filling: Drawing + and Filling Paths, and *Note Path Reference; Outputting: + Outputting Paths. + + - Protected variable: const Color* draw_color + Pointer to the `Color' used if the `Path' is drawn. + + - Protected variable: const Color* fill_color + Pointer to the `Color' used if the `Path' is filled. + + - Protected variable: string dashed + String written to `out_stream' for the "dash pattern" in a + MetaPost `draw' or `undraw' command. If and only if `dashed' is + not the empty string, "`dashed' <_dash pattern_>" is written to + `out_stream'. + + Dash patterns have no meaning inside 3DLDF; `dashed', if + non-empty, is written unchanged to `out_stream'. I may change this + in the future. + + - Protected variable: string pen + String written to `out_stream' for the `pen' to be used in a + MetaPost `draw', `undraw', `filldraw', or `unfilldraw' command. + If and only if `pen' is not the empty string, "`withpen' <...>" is + written to `out_stream'. + + Pens have no meaning inside 3DLDF; `pen', if non-empty, is + written unchanged to `out_stream'. I may change this in the + future. + + - Protected variable: bool arrow + Indicates whether an arrow should be drawn when outputting a + `Path'. Set to `true' on a `Path' created on the free store and + put onto a `Picture' by `drawarrow()'. + + - Protected variable: valarray projective_extremes + Contains the maxima and minima of the x, y, and z-coordinates of + the _projections_ of `Points' on a `Path' using a particular + `Focus'. Set in `set_extremes()' and used in `Picture::output()' + for surface hiding. + + - Protected variable: vector points + Pointers to the `Points' on the `Path'. + + - Protected variable: vector connectors + The connectors between the `Points' on the `Path'. Connectors are + simply `strings' in 3DLDF, they are written unchanged to + `out_stream'. + + - Public static variable: const Color* help_color + Pointer to a `const Color', which becomes the default for + `draw_help()'. *Note Path Reference; Drawing and Filling: Drawing + and Filling Paths. + + Please note that `help_color' is a pointer to a `const Color', not + a `const' pointer to a `Color' or a `const' pointer to a `const + Color'! It's easy to get confused by the syntax for these types + of pointers.(1) + + - Public static variable: string help_dash_pattern + The default dash pattern for `draw_help()'. + + - Public static variable: bool do_help_lines + `true' if help lines should be output, otherwise `false'. If + `false', a call to `draw_help()' does not cause a copy of the + `Path' to be created and put onto a `Picture'. *Note Path + Reference; Drawing and Filling: Drawing and Filling Paths. + + ---------- Footnotes ---------- + + (1) Stroustrup, `The C++ Programming Language', p. 96. + + File: 3DLDF.info, Node: Path Constructors and Setting Functions, Next: Path Destructor, Prev: Path Data Members, Up: Path Reference Constructors and Setting Functions @@ -43,6 +532,8 @@ -| p: (-2, -2.5, -1) -- (3, 2, 2.5); + [Figure 110 not displayed.] + - Setting function: void set (const Point& P0, const Point& P1) Corresponds to the constructor above. @@ -98,6 +589,8 @@ Path p("..", true, &P0, &P1, &P2, &P3, 0); p.draw(); + [Figure 111 not displayed.] + - Setting function: void set (string CONNECTOR, bool CYCLE, Point* P, [...], 0) @@ -115,6 +608,8 @@ (2, 1, 3) ... (0.92139, 1.51449, 3.29505) ... (-1.07861, 0.514487, 6.29505) ... (2.84065, -3.26065, 6.29505); + [Figure 112 not displayed.] + - Constructor: void Path (Point* FIRST_POINT_PTR, char* S, Point* P, [...], 0) @@ -136,6 +631,8 @@ Point D(1, 3); Path p(&A, "..", &B, "..", &C, "--", &D, "...", 0); + [Figure 113 not displayed.] + - Setting function: void set (Point *FIRST_POINT_PTR, string S, Point *P, [...], 0) @@ -144,18 +641,19 @@ - Copy constructor: void Path (const Path& P) Creates a new `Path', making it a copy of P. - - Static function: Path* create_new_path ([const Path* P = 0]) - - Static function: Path* create_new_path (const Path& P) - Pseudo-constructors for dynamic allocation of `Paths'. `Paths' - should never be dynamically allocated, except by means of - `create_new_path()'. Sets `on_free_store' to `true'. *Note Path - Reference; Data Members: Path Data Members. - - In the first version, if P is 0, the new `Path' will be empty. - Otherwise, it will be a copy of *P. In the second version, the - new `Path' will be a copy of P. + - Template specializations: Path* create_new (const Path* P) + - : Path* create_new (const Path& P) + Pseudo-constructors for dynamic allocation of `Paths'. They + create a `Path' on the free store and allocate memory for it using + `new(Path)'. They return a pointer to the new `Path'. + + If P is a non-zero pointer or a reference, the new `Path' will be + a copy of P. If the new object is not meant to be a copy of an + existing one, `0' must be passed to `create_new()' as its + argument. *Note Dynamic Allocation of Shapes::, for more + information. - `create_new_path()' is used in the drawing and filling functions + `create_new()' is used in the drawing and filling functions for copying a `Path' and putting the copy onto a `Picture'. *Note Path Reference; Drawing and Filling: Drawing and Filling Paths. @@ -188,13 +686,13 @@ - `virtual' Destructor: void ~Path (`void') All of the `Points' on a `Path' are created by - `create_new_point()', which allocates them dynamically on the free - store. Therefore, the destructor calls `delete()' on all of the - pointers on `points'. Following this, it calls `points.clear()' - and `connectors.clear()'. `draw_color' and `fill_color' may or - may not have been allocated on the free store, so `~Path()' checks - this first, and deletes them, if they were. Then, it sets them to - 0. + `create_new()', which allocates them dynamically on the + free store. Therefore, the destructor calls `delete()' on all of + the pointers on `points'. Following this, it calls + `points.clear()' and `connectors.clear()'. `draw_color' and + `fill_color' may or may not have been allocated on the free store, + so `~Path()' checks this first, and deletes them, if they were. + Then, it sets them to 0.  File: 3DLDF.info, Node: Path Operators, Next: Appending to Paths, Prev: Path Destructor, Up: Path Reference @@ -276,6 +774,8 @@ (1, 2, 0) .. (0, 4, 0) .. (-0.5, 3, 0) -- cycle; + [Figure 114 not displayed.] +  File: 3DLDF.info, Node: Copying Paths, Next: Clearing Paths, Prev: Appending to Paths, Up: Path Reference @@ -284,7 +784,7 @@ ======= - `const' virtual function: Shape* get_copy (void) - Creates a copy of the `Path' using `create_new_path()', which + Creates a copy of the `Path' using `create_new()', which returns a pointer to `Path'. `get_copy()' then casts this pointer to a pointer to `Shape' and returns it. @@ -318,12 +818,10 @@ Modifying ========= - - Inline virtual function: bool set_on_free_store ([bool B = `true']) - Sets `on_free_store' to B. This function is never used, but it's - a pure virtual function in `class Shape', so every class derived - from `Shape' must have one. It was intended for use in the - template function `create_new()', but I haven't been able to get - the latter to work. + - Virtual function: bool set_on_free_store ([bool B = `true']) + Sets `on_free_store' to B. This is used in the template function + `create_new()'. *Note Path Reference; Constructors and Setting + Functions: Path Constructors and Setting Functions. - Virtual function: void set_fill_draw_value (const signed short S) Sets `fill_draw_value' to S, which should be one of `Shape::DRAW', @@ -401,6 +899,8 @@ p.scale(2, 2); p.draw(); + [Figure 115 not displayed.] + - Function: Transform shear (real XY, [real XZ = 0, [real YX = 0, [real YZ = 0, [real ZX = 0, [real ZY = 0]]]]]) @@ -419,6 +919,8 @@ q.shear(1.5, 2, 2.5, 3, 3.5, 5); q.filldraw(black, light_gray); + [Figure 116 not displayed.] + - Function: Transform shift (real X, [real Y = 0, [real Z = 0]]) Creates a `Transform t' locally and calls `t.shift(X, Y, Z)'. `t' @@ -442,6 +944,8 @@ p.shift(3, 3, 3); p.draw(); + [Figure 117 not displayed.] + - Function: Transform shift (const Point& P) Creates a `Transform t' locally and calls `t.shift(P)'. `t' is @@ -466,6 +970,8 @@ p.shift(s); p.draw(); + [Figure 118 not displayed.] + - Virtual function: void shift_times (real X, [real Y = 1, [real Z = 1]]) @@ -572,6 +1078,8 @@ (0, -1, 0) .. (0.383, -0.924, 0) .. (0.707, -0.707, 0) .. (0.924, -0.383, 0) .. cycle; + [Figure 119 not displayed.] +  File: 3DLDF.info, Node: Applying Transformations to Paths, Next: Drawing and Filling Paths, Prev: Aligning Paths with an Axis, Up: Path Reference @@ -584,503 +1092,3 @@ `points'. *Note Point Reference; Applying Transformations: Applying Transformations to Points. - -File: 3DLDF.info, Node: Drawing and Filling Paths, Next: Labelling Paths, Prev: Applying Transformations to Paths, Up: Path Reference - -Drawing and Filling -=================== - - - `const' virtual function: void draw ([const Color& DDRAW_COLOR = - `*Colors::default_color', [const string DDASHED = "", [const - string PPEN = "", [Picture& PICTURE = `current_picture']]]]) - - `const' Virtual function: void draw (Picture& PICTURE, [const Color& - DDRAW_COLOR = *Colors::default_color, [string DDASHED = "", - [string PPEN = ""]]]) - Allocates a copy of the `Path' on the free store, puts a pointer to - the copy on PICTURE.`shapes', sets its `fill_draw_value' to - `DRAW', and the values of its `draw_color', `dashed', and `pen' - according to the arguments. - - The second version is convenient for passing a `Picture' argument - without having to specify all of the other arguments. - - All of the arguments to `draw()' are optional, so it can be invoked - as follows: - - Point A; - Point B(2); - Point C(3, 3); - Point D(1, 2); - Point E(-1, 1); - Path p("..", true, &A, &B, &C, &D, &E, 0); - p.draw(); - - The arguments: - - DDRAW_COLOR - Used to specify a color for the `Path'. DDRAW_COLOR is a - reference to a `Color'. Colors are described in *Note Color - Reference::. - - The most basic `Colors' are predefined in 3DLDF (in the - `namespace Colors'), and users may create new `Colors' and - specify their red-green-blue values. - - The `Path p' could be drawn in red by calling - `p.draw(Colors::red)'. This manual isn't intended to be - printed in color, so there's no figure to demonstrate this. - However, gray values can be printed on non-color printers. - - using namespace Colors; - p.draw(gray, "", "pencircle scaled .25mm"); - - DDASHED - A `string' representing a "dash pattern", as defined in - MetaPost(1). Dash patterns have no meaning in 3DLDF, they - are simply `strings' that are written unchanged to - `out_stream'. - - p.draw(black, "evenly"); - - PPEN - A `string' representing a "pen", as defined in Metafont and - MetaPost(2). Pens have no meaning in 3DLDF, they are simply - `strings' that are written unchanged to `out_stream'. - - p.draw(black, "", "pensquare xscaled 3mm - yscaled .25mm scaled .5mm"); - - PICTURE - Indicates the `Picture' on which the `Path' should be drawn. - - The two versions of `draw()' differ in the position of the - PICTURE argument: In the first version, it's the last - argument, while in the second version, it's the first - argument. If a PICTURE argument is used, it's often more - convenient to use the second version. - - The following example puts `Path p' onto `temp_picture'. It - also demonstrates how the labels are put onto `temp_picture', - and how `temp_picture' is output. In the previous examples, - the commands for making the labels and outputting - `current_picture' were left out in order to reduce clutter. - *Note Point Reference; Labelling: Labelling Points, and *Note - Picture Reference; Outputting; Output Functions: Picture - Output Functions. - - Picture temp_picture; - p.draw(temp_picture); - A.dotlabel("A", "bot", temp_picture); - B.dotlabel("B", "bot", temp_picture); - C.dotlabel("C", "top", temp_picture); - D.dotlabel("D", "top", temp_picture); - E.dotlabel("E", "lft", temp_picture); - temp_picture.output(Projections::PARALLEL_X_Y); - - - - `const' function: void draw_help ([const Color& DDRAW_COLOR = - *help_color, [string DDASHED = help_dash_pattern, [string - PPEN = "", [Picture& PICTURE = `current_picture']]]]) - - `const' function: void draw_help (Picture& PICTURE, [const Color& - DDRAW_COLOR = `*help_color', [string DDASHED = - `help_dash_pattern', [string PPEN = ""]]]) - This functions are for drawing help lines. They are like - `draw()', except that `draw_help()' returns immediately, if - `do_help_lines' (a static data member in `Path') is `false'. - Also, the defaults for DDRAW_COLOR and DDASHED differ from those - for `draw()'. - - - `const' virtual function: void drawarrow ([const Color& DDRAW_COLOR - = `*Colors::default_color', [string DDASHED = "", [string - PPEN = "", [Picture& PICTURE = `current_picture']]]]) - - `const' virtual function: void drawarrow (Picture& PICTURE, [const - Color& DDRAW_COLOR = `*Colors::default_color', [string - DDASHED = "", [string PPEN = ""]]]) - Like `draw()', except that the MetaPost command `drawarrow' is - written to `out_stream' when `picture' is output. The second - version is convenient for passing a `Picture' argument without - having to specify all of the other arguments. - - Point m; - Point n(2, 2); - m.dotlabel("$m$", "bot"); - n.dotlabel("$n$"); - m.drawarrow(n); - - - - Non-member function: void draw_axes ([real DIST = 2.5, [string POS_X - = "bot", [string POS_Y = "lft", [string POS_Z = "bot", [const - Color& DDRAW_COLOR = `*Colors::default_color', [const string - DDASHED = "", [const string PPEN = "", [const Point& SHIFT_X - = `origin', [const Point& SHIFT_Y = `origin', [const Point& - SHIFT_Z = `origin', [Picture& PICTURE = - `current_picture']]]]]]]]]]]) - - Non-member function: void draw_axes (const Color& DDRAW_COLOR, [real - DIST = 2.5, [string POS_X = "bot", [string POS_Y = "lft", - [string POS_Z = "bot", [const string DDASHED = "", [const - string PPEN = "", [const Point& SHIFT_X = `origin', [const - Point& SHIFT_Y = `origin', [const Point& SHIFT_Z = `origin', - [Picture& PICTURE = `current_picture']]]]]]]]]]) - These functions draw lines centered on the origin, and ending in - arrows in the directions of the positive x, y, and z-axes, and - labels them with the appropriate letters. `draw_axes()' is used in - many of the figures in this handbook. It can be helpful in - determining whether a `Focus' has a good "`up'" direction. *Note - Focus Reference; Data Members: Focus Data Members. - - In the first version, all of the arguments are optional. In the - second version, DDRAW_COLOR is required and has been moved to the - front of the argument list. This version is often convenient, - when a `Color' other than the default is desired. - - The arguments: - DIST - The length of the lines drawn. The default is 2.5. The - value 0 can be used as a dummy argument, if the default for - DIST is desired, but other arguments must be specified. - - - POS_X - POS_Y - POS_Z - The position arguments for the labelling commands for each of - the axes. The defaults are `"bot"' for the x and z-axes, and - `"lft"' for the y-axis. The usual `strings' for the position - of labels can be used, namely: `"top"', `"bot"', `"lft"', - `"rt"', `"ulft"', `"urt"', `"llft"', `"lrt"', and `""'. If - `""' is used, that axis is not drawn. This can be useful for - parallel projections onto one of the major planes(3). In - addition, `"d"' can be used to indicate that the default - should be used for that label. This can be useful if one - needs a placeholder, but doesn't remember what the default is - for that label. - - draw_axes(0, "bot", "rt", ""); - current_picture.output(Projections::PARALLEL_X_Y); - - In addition, the arguments SHIFT_X, SHIFT_Y, and SHIFT_Z can - be used to adjust the positions of the labels further (see - below). - - DDRAW_COLOR - DDASHED - PPEN - Arguments for the `drawarrow()' command, described above, in - this section. - - SHIFT_X - SHIFT_Y - SHIFT_Z - Offsets for the labels. These arguments make it possible to - adjust the positions of the labels. The defaults are - `origin', so no shifting takes place, if they are used. In - [next figure] , `draw_axes' is called without any arguments, - so the defaults are used. - - draw_axes(); - - In [next figure] , the `Point P' is used to shift the labels. - Please note that placeholders must be used for the first - arguments. - - Point P(.5, .5, .5); - draw_axes(0, "d", "d", "d", black, "", "", P, -P, P); - - Please note that the `Points' used for placing the labels are - three-dimensional `Points', whether the SHIFT_X, SHIFT_Y, - and/or SHIFT_Z arguments are used or not. It is not - currently possible to adjust the positions of the labels on - the two-dimensional projection itself. This would probably - be more useful, but would require changing the way - `Picture::output()' functions. - - PICTURE - The `Picture', onto which the `Paths' and `Labels' are put. - - - `const' function: void fill ([const Color& FFILL_COLOR = - `*Colors::default_color', [Picture& PICTURE = - `current_picture']]) - - Function: void fill (Picture& PICTURE, [const Color& FFILL_COLOR = - `*Colors::default_color']) - Allocates a copy of the `Path' on the free store, puts a pointer to - it onto PICTURE.`shapes', sets its `fill_draw_value' to `FILL', and - its `fill_color' to `*FFILL_COLOR'. - - The second version is convenient for passing a `Picture' argument - without having to specify all of the other arguments. - - The arguments are similar to those of `draw()', except that the - `Color' argument is called FFILL_COLOR instead of DDRAW_COLOR. - - p.fill(gray); - - - - `const' function: void filldraw ([const Color& DDRAW_COLOR = - `*Colors::default_color', [const Color& FFILL_COLOR = - `*Colors::background_color', [string DDASHED = "", [string - PPEN = "", [Picture& PICTURE = `current_picture']]]]]) - - `const' function: void filldraw (Picture& PICTURE, [const Color& - DDRAW_COLOR = `*Colors::default_color', [const Color& - FFILL_COLOR = `*Colors::background_color', [string DDASHED = - "", [string PPEN = ""]]]]) - Allocates a copy of the `Path' on the free store, puts a pointer to - the copy onto PICTURE.`shapes', sets its `fill_draw_value' to - `FILLDRAW', its `draw_color' and `fill_color' to `*DDRAW_COLOR' - and `*FFILL_COLOR', respectively, its `dashed' to DDASHED, and its - `pen' to PPEN. - - The second version is convenient for passing a `Picture' argument - without having to specify all of the other arguments. - - The arguments are similar to those of `draw()' and `fill()', - except that both DDRAW_COLOR and FFILL_COLOR are used. - - 3DLDF's `filldraw()' differs from Metafont's and MetaPost's - `filldraw' commands: In Metafont and MetaPost, `filldrawing' is - equivalent to filling a `path' and then drawing its border using - the `pen'. Metafont does not have colors. While MetaPost does, - its `filldraw' command does not foresee the use of different - colors for drawing and filling. - - p.filldraw(black, gray, "", "pencircle scaled 2mm"); - - It can often be useful to draw the outline of a `Path', but to have - it hide objects that lie behind it. This is why the default for - FFILL_COLOR is `*Colors::background_color'. - - default_focus.set(3, 0, -10, 3, 10, 10, 10); - Point p[8]; - p[0] = p[1] = p[2] = p[3] = p[4] - = p[5] = p[6] = p[7].set(-1,-1, 5); - p[1] *= p[2] *= p[3] *= p[4] *= p[5] - *= p[6] *= p[7].rotate(0, 0, 45); - p[2] *= p[3] *= p[4] - *= p[5] *= p[6] *= p[7].rotate(0, 0, 45); - p[3] *= p[4] *= p[5] *= p[6] - *= p[7].rotate(0, 0, 45); - p[4] *= p[5] *= p[6] *= p[7].rotate(0, 0, 45); - p[5] *= p[6] *= p[7].rotate(0, 0, 45); - p[6] *= p[7].rotate(0, 0, 45); - p[7].rotate(0, 0, 45); - Path r0("..", true, &p[0], &p[1], &p[2], - &p[3], &p[4], &p[5], &p[6], &p[7], 0); - r0.filldraw(black, light_gray); - r0.scale(2, .5); - r0.shift(0, 0, -2.5); - r0.filldraw(black, gray); - r0.scale(.25, 3); - r0.shift(0, 0, -2.5); - r0.filldraw(); - - - - Function: void undraw ([string DDASHED = "", [string PPEN = "", - [Picture& PICTURE = `current_picture']]]) - - Function: void undraw (Picture& PICTURE, [string DDASHED = "", - [string PPEN = ""]]) - Allocates a copy of the `Path' on the free store, puts a pointer to - it on PICTURE.`shapes', sets its `fill_draw_value' to `UNDRAW', and - the values of its `dashed' and `pen' according to the arguments. - - The second version is convenient for passing a `Picture' argument - without having to specify all of the other arguments. - - This function "undraws" a `Path'. This is equivalent to drawing - the `Path' using the background color - (`*Colors::background_color'). - - Undrawing is useful for removing a portion of a `Path'. - - Point P0(1, 1); - Point P1(2, 1); - Point P2(2, 3); - Point P3(-1, 1); - Path p("--", false, &origin, &P0, &P1, &P2, &P3, 0); - p.draw(black, "", "pencircle scaled 3mm"); - p.undraw("", "pencircle scaled 1mm"); - - - - Function: void unfill ([Picture& PICTURE = `current_picture']) - Allocates a copy of the `Path' on the free store, puts a pointer to - it on PICTURE.`shapes' and sets its `fill_draw_value' to `UNFILL' - - This function is useful for removing a portion of a filled region. - - Point pt[4]; - pt[0].set(-2, -2); - pt[1].set(2, -2); - pt[2].set(2, 2); - pt[3].set(-2, 2); - Path p("--", true, &pt[0], &pt[1], &pt[2], &pt[3], 0); - p.draw(); - p.dotlabel(); - p.filldraw(black, gray); - p.scale(.5, .5); - p.unfill(); - - - - Function: void unfilldraw ([const Color& DDRAW_COLOR = - `*Colors::background_color', [string DDASHED = "", [string - PPEN = "", [Picture& PICTURE = current_picture]]]]) - - Function: void unfilldraw (Picture& PICTURE, [const Color& - DDRAW_COLOR = `*Colors::background_color', [string DDASHED = - "", [string PPEN = ""]]]) - Allocates a copy of the `Path' on the free store, puts a pointer to - it on PICTURE.`shapes', sets its `fill_draw_value' to - `UNFILLDRAW', and the values of its `draw_color', `dashed', and - `pen' according to the arguments. While the default for - DDRAW_COLOR is `*Colors::background_color', any other `Color' can - be used, so that `unfilldraw()' can unfill a `Path' and draw an - outline around it. - - The second version is convenient for passing a `Picture' argument - without having to specify all of the other arguments. - - This function is similar to `unfill()' (*note Path Reference; - Drawing and Filling: Drawing and Filling Paths.), except that the - outline of the `Path' will be "undrawn" using the pen specified - with the PPEN argument, or MetaPost's `currentpen', if no PPEN - argument is specified. In addition, the `Path' will be drawn - using the `Color' specified in the DDRAW_COLOR argument. Since - the default is `*Colors::background_color', the `Path' will be - "undrawn" unless a different `Color' is specified. - - Point pt[6]; - pt[0].set(-2, -2); - pt[1].set(0, -3); - pt[2].set(2, -2); - pt[3].set(2, 2); - pt[4].set(0, 3); - pt[5].set(-2, 2); - Path p("--", true, &pt[0], &pt[1], &pt[2], - &pt[3], &pt[4], &pt[5], 0); - p.fill(gray); - p.scale(.5, .5); - p.unfilldraw(black, "", "pensquare xscaled 3mm"); - - - ---------- Footnotes ---------- - - (1) Hobby, `A User's Manual for MetaPost', p. 32. - - (2) Knuth, `The METAFONTbook', Chapter 4, p. 21ff. Hobby, `A User's -Manual for MetaPost', p. 32. - - (3) The usual interpretation of `""' as a position argument to a -labelling command would be to put it directly onto `*(Label.pt)', which -in this case would put it onto the arrowhead. Since this will probably -never be desirable, I've decided to use `""' to suppress drawing axes. -Formerly, `draw_axes()' used three additional arguments for this -purpose. - - -File: 3DLDF.info, Node: Labelling Paths, Next: Showing Paths, Prev: Drawing and Filling Paths, Up: Path Reference - -Labelling -========= - - - `const' function: void label ([unsigned int I = 0, [string - POSITION_STRING = "top", [short TEXT_SHORT = 0, [bool DOT = - `false', [Picture& PICTURE = `current_picture']]]]]) - - `const' function: void label (Picture& PICTURE, [unsigned int I = 0, - [string POSITION_STRING = "top", [short TEXT_SHORT = 0, [bool - DOT = `false']]]]) - Calls `Point::label()' on all of the `Points' on `points'. They - are numbered consecutively starting with I. The other arguments - are used for all of the `Points', so it's not possible to specify - different positions for the labels for different `Points'. DOT - will normally not be specified, unless a PICTURE argument is used - in the first version. `dotlabel()' calls `label()' with DOT = - `true'. - - The second version is convenient for passing a `Picture' argument - without having to specify all of the other arguments. - - - `const' function: void dotlabel ([unsigned int I = 0, [string - POSITION_STRING = "top", [short TEXT_SHORT = 0, Picture& - PICTURE = `current_picture']]]) - - `const' function: void dotlabel (Picture& PICTURE, [unsigned int I = - 0, [string POSITION_STRING = "top", [short TEXT_SHORT = 0]]]) - Like `label()', except that the `Points' are dotted. - - -File: 3DLDF.info, Node: Showing Paths, Next: Querying Paths, Prev: Labelling Paths, Up: Path Reference - -Showing -======= - - - `const' function: void show ([string TEXT = "", [char COORDS = 'w', - [const bool DO_PERSP = `true', [const bool DO_APPLY = `true', - [Focus* F = 0, [const unsigned short PROJ = - `Projections::PERSP', [const real FACTOR = 1]]]]]]]) - Prints information about the `Path' to standard output (`stdout'). - TEXT is simply printed out, unless it's the empty string, in - which case `"Path:"' is printed out. COORDS indicates which set - of coordinates should be shown. Valid values are `'w'' for the - `world_coordinates', `'p'' for the `projective_coordinates', `'u'' - for the `user_coordinates', and `'v'' for the `view_coordinates', - whereby the latter two are currently not in use (*note Point - Reference; Data Members: Point Data Members.). If DO_APPLY is - `true', `apply_transform()' is called on each `Point', updating - its `world_coordinates' and resetting its `transform'. Otherwise, - it's not. The arguments DO_PERSP, F, PROJ, and FACTOR are only - relevant when showing `projective_coordinates'. If `do_persp' is - `true', the `Points' are projected using the values of F, PROJ, - and FACTOR (*note Path Reference; Outputting: Outputting Paths.). - Otherwise, the values currently stored in `projective_coordinates' - are shown. The `Points' and connectors are printed out - alternately to standard output, followed by the word "cycle", if - `cycle_switch = true'.(1) - - default_focus.set(0, 3, -10, 0, 3, 10, 10); - Reg_Polygon r(origin, 5, 3, 45); - r.fill(gray); - Point p[10]; - for (int i = 0; i < 5; ++i) - p[i] = r.get_point(i); - p[5] = Point::intersection_point(p[4], p[0], p[2], p[1]).pt; - p[6] = Point::intersection_point(p[0], p[1], p[2], p[3]).pt; - p[7] = Point::intersection_point(p[1], p[2], p[4], p[3]).pt; - p[8] = Point::intersection_point(p[2], p[3], p[0], p[4]).pt; - p[9] = Point::intersection_point(p[3], p[4], p[0], p[1]).pt; - Path q("--", true, &p[0], &p[5], &p[1], &p[6], &p[2], &p[7], - &p[3], &p[8], &p[4], &p[9], 0); - q.draw(); - q.show("q:"); - -| q: - fill_draw_value == 0 - (0, 1.06066, 1.06066) - -- (-2.30826, 2.24651, 2.24651) - -- (-1.42658, 0.327762, 0.327762) - -- (-3.73485, -0.858092, -0.858092) - -- (-0.881678, -0.858092, -0.858092) - -- (4.92996e-07, -2.77684, -2.77684) - -- (0.881678, -0.858092, -0.858092) - -- (3.73485, -0.858092, -0.858092) - -- (1.42658, 0.327762, 0.327762) - -- (2.30826, 2.24651, 2.24651) -- cycle; - q.show("q:", 'p'); - -| q: - fill_draw_value == 0 - Projective coordinates. - (0, -1.75337, 0.0958948) - -- (-1.88483, -0.615265, 0.183441) - -- (-1.38131, -2.58743, 0.031736) - -- (-4.08541, -4.22023, -0.0938636) - -- (-0.964435, -4.22023, -0.0938636) - -- (0, -7.99767, -0.384436) - -- (0.964436, -4.22023, -0.0938636) - -- (4.08541, -4.22023, -0.0938636) - -- (1.38131, -2.58743, 0.031736) - -- (1.88483, -0.615266, 0.183441) -- cycle; - - - - Function: void show_colors ([bool = `false']) - Shows the values of `draw_color' and `fill_color'. These will - normally be 0, unless the `Path' is on a `Picture'. - - ---------- Footnotes ---------- - - (1) The following example shows only one `Point' per line. In -actual use, two `Points' are shown, but this causes overfull boxes in -Texinfo. - diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-8 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-8 --- 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-8 2003-12-10 18:44:55.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-8 2004-01-16 19:03:28.000000000 +0100 @@ -1,11 +1,11 @@ This is 3DLDF.info, produced by makeinfo version 4.5 from 3DLDF.texi. -This is the 3DLDF User and Reference Manual, edition 1.1.4 for 3DLDF -1.1.4. This manual was last updated on 10 December 2003. 3DLDF is a +This is the 3DLDF User and Reference Manual, edition 1.1.5.1 for 3DLDF +1.1.5.1. This manual was last updated on 16 January 2004. 3DLDF is a GNU package for three-dimensional drawing with MetaPost output. The author is Laurence D. Finston. - Copyright (C) 2003 Laurence D. Finston. + Copyright (C) 2003, 2004 Laurence D. Finston. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, @@ -20,12 +20,544 @@ END-INFO-DIR-ENTRY  +File: 3DLDF.info, Node: Drawing and Filling Paths, Next: Labelling Paths, Prev: Applying Transformations to Paths, Up: Path Reference + +Drawing and Filling +=================== + + - `const' virtual function: void draw ([const Color& DDRAW_COLOR = + `*Colors::default_color', [const string DDASHED = "", [const + string PPEN = "", [Picture& PICTURE = `current_picture']]]]) + - `const' Virtual function: void draw (Picture& PICTURE, [const Color& + DDRAW_COLOR = *Colors::default_color, [string DDASHED = "", + [string PPEN = ""]]]) + Allocates a copy of the `Path' on the free store, puts a pointer to + the copy on PICTURE.`shapes', sets its `fill_draw_value' to + `DRAW', and the values of its `draw_color', `dashed', and `pen' + according to the arguments. + + The second version is convenient for passing a `Picture' argument + without having to specify all of the other arguments. + + All of the arguments to `draw()' are optional, so it can be invoked + as follows: + + Point A; + Point B(2); + Point C(3, 3); + Point D(1, 2); + Point E(-1, 1); + Path p("..", true, &A, &B, &C, &D, &E, 0); + p.draw(); + + [Figure 120 not displayed.] + + The arguments: + + DDRAW_COLOR + Used to specify a color for the `Path'. DDRAW_COLOR is a + reference to a `Color'. Colors are described in *Note Color + Reference::. + + The most basic `Colors' are predefined in 3DLDF (in the + `namespace Colors'), and users may create new `Colors' and + specify their red-green-blue values. + + The `Path p' could be drawn in red by calling + `p.draw(Colors::red)'. This manual isn't intended to be + printed in color, so there's no figure to demonstrate this. + However, gray values can be printed on non-color printers. + + using namespace Colors; + p.draw(gray, "", "pencircle scaled .25mm"); + + [Figure 121 not displayed.] + + DDASHED + A `string' representing a "dash pattern", as defined in + MetaPost(1). Dash patterns have no meaning in 3DLDF, they + are simply `strings' that are written unchanged to + `out_stream'. + + p.draw(black, "evenly"); + + [Figure 122 not displayed.] + + PPEN + A `string' representing a "pen", as defined in Metafont and + MetaPost(2). Pens have no meaning in 3DLDF, they are simply + `strings' that are written unchanged to `out_stream'. + + p.draw(black, "", "pensquare xscaled 3mm + yscaled .25mm scaled .5mm"); + + [Figure 123 not displayed.] + + PICTURE + Indicates the `Picture' on which the `Path' should be drawn. + + The two versions of `draw()' differ in the position of the + PICTURE argument: In the first version, it's the last + argument, while in the second version, it's the first + argument. If a PICTURE argument is used, it's often more + convenient to use the second version. + + The following example puts `Path p' onto `temp_picture'. It + also demonstrates how the labels are put onto `temp_picture', + and how `temp_picture' is output. In the previous examples, + the commands for making the labels and outputting + `current_picture' were left out in order to reduce clutter. + *Note Point Reference; Labelling: Labelling Points, and *Note + Picture Reference; Outputting; Output Functions: Picture + Output Functions. + + Picture temp_picture; + p.draw(temp_picture); + A.dotlabel("A", "bot", temp_picture); + B.dotlabel("B", "bot", temp_picture); + C.dotlabel("C", "top", temp_picture); + D.dotlabel("D", "top", temp_picture); + E.dotlabel("E", "lft", temp_picture); + temp_picture.output(Projections::PARALLEL_X_Y); + + [Figure 124 not displayed.] + + + - `const' function: void draw_help ([const Color& DDRAW_COLOR = + *help_color, [string DDASHED = help_dash_pattern, [string + PPEN = "", [Picture& PICTURE = `current_picture']]]]) + - `const' function: void draw_help (Picture& PICTURE, [const Color& + DDRAW_COLOR = `*help_color', [string DDASHED = + `help_dash_pattern', [string PPEN = ""]]]) + This functions are for drawing help lines. They are like + `draw()', except that `draw_help()' returns immediately, if + `do_help_lines' (a static data member in `Path') is `false'. + Also, the defaults for DDRAW_COLOR and DDASHED differ from those + for `draw()'. + + - `const' virtual function: void drawarrow ([const Color& DDRAW_COLOR + = `*Colors::default_color', [string DDASHED = "", [string + PPEN = "", [Picture& PICTURE = `current_picture']]]]) + - `const' virtual function: void drawarrow (Picture& PICTURE, [const + Color& DDRAW_COLOR = `*Colors::default_color', [string + DDASHED = "", [string PPEN = ""]]]) + Like `draw()', except that the MetaPost command `drawarrow' is + written to `out_stream' when `picture' is output. The second + version is convenient for passing a `Picture' argument without + having to specify all of the other arguments. + + Point m; + Point n(2, 2); + m.dotlabel("$m$", "bot"); + n.dotlabel("$n$"); + m.drawarrow(n); + + [Figure 125 not displayed.] + + + - Non-member function: void draw_axes ([real DIST = 2.5, [string POS_X + = "bot", [string POS_Y = "lft", [string POS_Z = "bot", [const + Color& DDRAW_COLOR = `*Colors::default_color', [const string + DDASHED = "", [const string PPEN = "", [const Point& SHIFT_X + = `origin', [const Point& SHIFT_Y = `origin', [const Point& + SHIFT_Z = `origin', [Picture& PICTURE = + `current_picture']]]]]]]]]]]) + - Non-member function: void draw_axes (const Color& DDRAW_COLOR, [real + DIST = 2.5, [string POS_X = "bot", [string POS_Y = "lft", + [string POS_Z = "bot", [const string DDASHED = "", [const + string PPEN = "", [const Point& SHIFT_X = `origin', [const + Point& SHIFT_Y = `origin', [const Point& SHIFT_Z = `origin', + [Picture& PICTURE = `current_picture']]]]]]]]]]) + These functions draw lines centered on the origin, and ending in + arrows in the directions of the positive x, y, and z-axes, and + labels them with the appropriate letters. `draw_axes()' is used in + many of the figures in this handbook. It can be helpful in + determining whether a `Focus' has a good "`up'" direction. *Note + Focus Reference; Data Members: Focus Data Members. + + In the first version, all of the arguments are optional. In the + second version, DDRAW_COLOR is required and has been moved to the + front of the argument list. This version is often convenient, + when a `Color' other than the default is desired. + + The arguments: + DIST + The length of the lines drawn. The default is 2.5. The + value 0 can be used as a dummy argument, if the default for + DIST is desired, but other arguments must be specified. + + + POS_X + POS_Y + POS_Z + The position arguments for the labelling commands for each of + the axes. The defaults are `"bot"' for the x and z-axes, and + `"lft"' for the y-axis. The usual `strings' for the position + of labels can be used, namely: `"top"', `"bot"', `"lft"', + `"rt"', `"ulft"', `"urt"', `"llft"', `"lrt"', and `""'. If + `""' is used, that axis is not drawn. This can be useful for + parallel projections onto one of the major planes(3). In + addition, `"d"' can be used to indicate that the default + should be used for that label. This can be useful if one + needs a placeholder, but doesn't remember what the default is + for that label. + + draw_axes(0, "bot", "rt", ""); + current_picture.output(Projections::PARALLEL_X_Y); + + [Figure 126 not displayed.] + + In addition, the arguments SHIFT_X, SHIFT_Y, and SHIFT_Z can + be used to adjust the positions of the labels further (see + below). + + DDRAW_COLOR + DDASHED + PPEN + Arguments for the `drawarrow()' command, described above, in + this section. + + SHIFT_X + SHIFT_Y + SHIFT_Z + Offsets for the labels. These arguments make it possible to + adjust the positions of the labels. The defaults are + `origin', so no shifting takes place, if they are used. In + [next figure] , `draw_axes' is called without any arguments, + so the defaults are used. + + draw_axes(); + + [Figure 127 not displayed.] + + In [next figure] , the `Point P' is used to shift the labels. + Please note that placeholders must be used for the first + arguments. + + Point P(.5, .5, .5); + draw_axes(0, "d", "d", "d", black, "", "", P, -P, P); + + [Figure 128 not displayed.] + + Please note that the `Points' used for placing the labels are + three-dimensional `Points', whether the SHIFT_X, SHIFT_Y, + and/or SHIFT_Z arguments are used or not. It is not + currently possible to adjust the positions of the labels on + the two-dimensional projection itself. This would probably + be more useful, but would require changing the way + `Picture::output()' functions. + + PICTURE + The `Picture', onto which the `Paths' and `Labels' are put. + + - `const' function: void fill ([const Color& FFILL_COLOR = + `*Colors::default_color', [Picture& PICTURE = + `current_picture']]) + - Function: void fill (Picture& PICTURE, [const Color& FFILL_COLOR = + `*Colors::default_color']) + Allocates a copy of the `Path' on the free store, puts a pointer to + it onto PICTURE.`shapes', sets its `fill_draw_value' to `FILL', and + its `fill_color' to `*FFILL_COLOR'. + + The second version is convenient for passing a `Picture' argument + without having to specify all of the other arguments. + + The arguments are similar to those of `draw()', except that the + `Color' argument is called FFILL_COLOR instead of DDRAW_COLOR. + + p.fill(gray); + + [Figure 129 not displayed.] + + + - `const' function: void filldraw ([const Color& DDRAW_COLOR = + `*Colors::default_color', [const Color& FFILL_COLOR = + `*Colors::background_color', [string DDASHED = "", [string + PPEN = "", [Picture& PICTURE = `current_picture']]]]]) + - `const' function: void filldraw (Picture& PICTURE, [const Color& + DDRAW_COLOR = `*Colors::default_color', [const Color& + FFILL_COLOR = `*Colors::background_color', [string DDASHED = + "", [string PPEN = ""]]]]) + Allocates a copy of the `Path' on the free store, puts a pointer to + the copy onto PICTURE.`shapes', sets its `fill_draw_value' to + `FILLDRAW', its `draw_color' and `fill_color' to `*DDRAW_COLOR' + and `*FFILL_COLOR', respectively, its `dashed' to DDASHED, and its + `pen' to PPEN. + + The second version is convenient for passing a `Picture' argument + without having to specify all of the other arguments. + + The arguments are similar to those of `draw()' and `fill()', + except that both DDRAW_COLOR and FFILL_COLOR are used. + + 3DLDF's `filldraw()' differs from Metafont's and MetaPost's + `filldraw' commands: In Metafont and MetaPost, `filldrawing' is + equivalent to filling a `path' and then drawing its border using + the `pen'. Metafont does not have colors. While MetaPost does, + its `filldraw' command does not foresee the use of different + colors for drawing and filling. + + p.filldraw(black, gray, "", "pencircle scaled 2mm"); + + [Figure 130 not displayed.] + + It can often be useful to draw the outline of a `Path', but to have + it hide objects that lie behind it. This is why the default for + FFILL_COLOR is `*Colors::background_color'. + + default_focus.set(3, 0, -10, 3, 10, 10, 10); + Point p[8]; + p[0] = p[1] = p[2] = p[3] = p[4] + = p[5] = p[6] = p[7].set(-1,-1, 5); + p[1] *= p[2] *= p[3] *= p[4] *= p[5] + *= p[6] *= p[7].rotate(0, 0, 45); + p[2] *= p[3] *= p[4] + *= p[5] *= p[6] *= p[7].rotate(0, 0, 45); + p[3] *= p[4] *= p[5] *= p[6] + *= p[7].rotate(0, 0, 45); + p[4] *= p[5] *= p[6] *= p[7].rotate(0, 0, 45); + p[5] *= p[6] *= p[7].rotate(0, 0, 45); + p[6] *= p[7].rotate(0, 0, 45); + p[7].rotate(0, 0, 45); + Path r0("..", true, &p[0], &p[1], &p[2], + &p[3], &p[4], &p[5], &p[6], &p[7], 0); + r0.filldraw(black, light_gray); + r0.scale(2, .5); + r0.shift(0, 0, -2.5); + r0.filldraw(black, gray); + r0.scale(.25, 3); + r0.shift(0, 0, -2.5); + r0.filldraw(); + + [Figure 131 not displayed.] + + + - Function: void undraw ([string DDASHED = "", [string PPEN = "", + [Picture& PICTURE = `current_picture']]]) + - Function: void undraw (Picture& PICTURE, [string DDASHED = "", + [string PPEN = ""]]) + Allocates a copy of the `Path' on the free store, puts a pointer to + it on PICTURE.`shapes', sets its `fill_draw_value' to `UNDRAW', and + the values of its `dashed' and `pen' according to the arguments. + + The second version is convenient for passing a `Picture' argument + without having to specify all of the other arguments. + + This function "undraws" a `Path'. This is equivalent to drawing + the `Path' using the background color + (`*Colors::background_color'). + + Undrawing is useful for removing a portion of a `Path'. + + Point P0(1, 1); + Point P1(2, 1); + Point P2(2, 3); + Point P3(-1, 1); + Path p("--", false, &origin, &P0, &P1, &P2, &P3, 0); + p.draw(black, "", "pencircle scaled 3mm"); + p.undraw("", "pencircle scaled 1mm"); + + [Figure 132 not displayed.] + + + - Function: void unfill ([Picture& PICTURE = `current_picture']) + Allocates a copy of the `Path' on the free store, puts a pointer to + it on PICTURE.`shapes' and sets its `fill_draw_value' to `UNFILL' + + This function is useful for removing a portion of a filled region. + + Point pt[4]; + pt[0].set(-2, -2); + pt[1].set(2, -2); + pt[2].set(2, 2); + pt[3].set(-2, 2); + Path p("--", true, &pt[0], &pt[1], &pt[2], &pt[3], 0); + p.draw(); + p.dotlabel(); + p.filldraw(black, gray); + p.scale(.5, .5); + p.unfill(); + + [Figure 133 not displayed.] + + + - Function: void unfilldraw ([const Color& DDRAW_COLOR = + `*Colors::background_color', [string DDASHED = "", [string + PPEN = "", [Picture& PICTURE = current_picture]]]]) + - Function: void unfilldraw (Picture& PICTURE, [const Color& + DDRAW_COLOR = `*Colors::background_color', [string DDASHED = + "", [string PPEN = ""]]]) + Allocates a copy of the `Path' on the free store, puts a pointer to + it on PICTURE.`shapes', sets its `fill_draw_value' to + `UNFILLDRAW', and the values of its `draw_color', `dashed', and + `pen' according to the arguments. While the default for + DDRAW_COLOR is `*Colors::background_color', any other `Color' can + be used, so that `unfilldraw()' can unfill a `Path' and draw an + outline around it. + + The second version is convenient for passing a `Picture' argument + without having to specify all of the other arguments. + + This function is similar to `unfill()' (*note Path Reference; + Drawing and Filling: Drawing and Filling Paths.), except that the + outline of the `Path' will be "undrawn" using the pen specified + with the PPEN argument, or MetaPost's `currentpen', if no PPEN + argument is specified. In addition, the `Path' will be drawn + using the `Color' specified in the DDRAW_COLOR argument. Since + the default is `*Colors::background_color', the `Path' will be + "undrawn" unless a different `Color' is specified. + + Point pt[6]; + pt[0].set(-2, -2); + pt[1].set(0, -3); + pt[2].set(2, -2); + pt[3].set(2, 2); + pt[4].set(0, 3); + pt[5].set(-2, 2); + Path p("--", true, &pt[0], &pt[1], &pt[2], + &pt[3], &pt[4], &pt[5], 0); + p.fill(gray); + p.scale(.5, .5); + p.unfilldraw(black, "", "pensquare xscaled 3mm"); + + [Figure 134 not displayed.] + + + ---------- Footnotes ---------- + + (1) Hobby, `A User's Manual for MetaPost', p. 32. + + (2) Knuth, `The METAFONTbook', Chapter 4, p. 21ff. Hobby, `A User's +Manual for MetaPost', p. 32. + + (3) The usual interpretation of `""' as a position argument to a +labelling command would be to put it directly onto `*(Label.pt)', which +in this case would put it onto the arrowhead. Since this will probably +never be desirable, I've decided to use `""' to suppress drawing axes. +Formerly, `draw_axes()' used three additional arguments for this +purpose. + + +File: 3DLDF.info, Node: Labelling Paths, Next: Showing Paths, Prev: Drawing and Filling Paths, Up: Path Reference + +Labelling +========= + + - `const' function: void label ([unsigned int I = 0, [string + POSITION_STRING = "top", [short TEXT_SHORT = 0, [bool DOT = + `false', [Picture& PICTURE = `current_picture']]]]]) + - `const' function: void label (Picture& PICTURE, [unsigned int I = 0, + [string POSITION_STRING = "top", [short TEXT_SHORT = 0, [bool + DOT = `false']]]]) + Calls `Point::label()' on all of the `Points' on `points'. They + are numbered consecutively starting with I. The other arguments + are used for all of the `Points', so it's not possible to specify + different positions for the labels for different `Points'. DOT + will normally not be specified, unless a PICTURE argument is used + in the first version. `dotlabel()' calls `label()' with DOT = + `true'. + + The second version is convenient for passing a `Picture' argument + without having to specify all of the other arguments. + + - `const' function: void dotlabel ([unsigned int I = 0, [string + POSITION_STRING = "top", [short TEXT_SHORT = 0, Picture& + PICTURE = `current_picture']]]) + - `const' function: void dotlabel (Picture& PICTURE, [unsigned int I = + 0, [string POSITION_STRING = "top", [short TEXT_SHORT = 0]]]) + Like `label()', except that the `Points' are dotted. + + +File: 3DLDF.info, Node: Showing Paths, Next: Querying Paths, Prev: Labelling Paths, Up: Path Reference + +Showing +======= + + - `const' function: void show ([string TEXT = "", [char COORDS = 'w', + [const bool DO_PERSP = `true', [const bool DO_APPLY = `true', + [Focus* F = 0, [const unsigned short PROJ = + `Projections::PERSP', [const real FACTOR = 1]]]]]]]) + Prints information about the `Path' to standard output (`stdout'). + TEXT is simply printed out, unless it's the empty string, in + which case `"Path:"' is printed out. COORDS indicates which set + of coordinates should be shown. Valid values are `'w'' for the + `world_coordinates', `'p'' for the `projective_coordinates', `'u'' + for the `user_coordinates', and `'v'' for the `view_coordinates', + whereby the latter two are currently not in use (*note Point + Reference; Data Members: Point Data Members.). If DO_APPLY is + `true', `apply_transform()' is called on each `Point', updating + its `world_coordinates' and resetting its `transform'. Otherwise, + it's not. The arguments DO_PERSP, F, PROJ, and FACTOR are only + relevant when showing `projective_coordinates'. If `do_persp' is + `true', the `Points' are projected using the values of F, PROJ, + and FACTOR (*note Path Reference; Outputting: Outputting Paths.). + Otherwise, the values currently stored in `projective_coordinates' + are shown. The `Points' and connectors are printed out + alternately to standard output, followed by the word "cycle", if + `cycle_switch = true'.(1) + + default_focus.set(0, 3, -10, 0, 3, 10, 10); + Reg_Polygon r(origin, 5, 3, 45); + r.fill(gray); + Point p[10]; + for (int i = 0; i < 5; ++i) + p[i] = r.get_point(i); + p[5] = Point::intersection_point(p[4], p[0], p[2], p[1]).pt; + p[6] = Point::intersection_point(p[0], p[1], p[2], p[3]).pt; + p[7] = Point::intersection_point(p[1], p[2], p[4], p[3]).pt; + p[8] = Point::intersection_point(p[2], p[3], p[0], p[4]).pt; + p[9] = Point::intersection_point(p[3], p[4], p[0], p[1]).pt; + Path q("--", true, &p[0], &p[5], &p[1], &p[6], &p[2], &p[7], + &p[3], &p[8], &p[4], &p[9], 0); + q.draw(); + q.show("q:"); + -| q: + fill_draw_value == 0 + (0, 1.06066, 1.06066) + -- (-2.30826, 2.24651, 2.24651) + -- (-1.42658, 0.327762, 0.327762) + -- (-3.73485, -0.858092, -0.858092) + -- (-0.881678, -0.858092, -0.858092) + -- (4.92996e-07, -2.77684, -2.77684) + -- (0.881678, -0.858092, -0.858092) + -- (3.73485, -0.858092, -0.858092) + -- (1.42658, 0.327762, 0.327762) + -- (2.30826, 2.24651, 2.24651) -- cycle; + q.show("q:", 'p'); + -| q: + fill_draw_value == 0 + Projective coordinates. + (0, -1.75337, 0.0958948) + -- (-1.88483, -0.615265, 0.183441) + -- (-1.38131, -2.58743, 0.031736) + -- (-4.08541, -4.22023, -0.0938636) + -- (-0.964435, -4.22023, -0.0938636) + -- (0, -7.99767, -0.384436) + -- (0.964436, -4.22023, -0.0938636) + -- (4.08541, -4.22023, -0.0938636) + -- (1.38131, -2.58743, 0.031736) + -- (1.88483, -0.615266, 0.183441) -- cycle; + + [Figure 135 not displayed.] + + + - Function: void show_colors ([bool = `false']) + Shows the values of `draw_color' and `fill_color'. These will + normally be 0, unless the `Path' is on a `Picture'. + + ---------- Footnotes ---------- + + (1) The following example shows only one `Point' per line. In +actual use, two `Points' are shown, but this causes overfull boxes in +Texinfo. + + File: 3DLDF.info, Node: Querying Paths, Next: Outputting Paths, Prev: Showing Paths, Up: Path Reference Querying ======== - - `const' inline function: bool is_on_free_store (void) + - `const' function: bool is_on_free_store (void) Returns `true', if the `Path' was dynamically allocated on the free store, otherwise `false'. @@ -100,6 +632,8 @@ Rectangle r(P, 4, 4, 30, 30, 30); Point N = r.get_normal(); + [Figure 136 not displayed.] + In 3DLDF, plane figures generally have constructors taking a |Point| argument for the center, a variable number of |real| arguments for the dimensions, and three |real| arguments for the @@ -131,6 +665,8 @@ point: (0.0178869, -0.727258, -1.01297) distance == -0.131735 + [Figure 137 not displayed.] + - Function: void set_cycle ([const bool C = `true']) Sets `cycle_switch' to C. @@ -239,6 +775,8 @@ bp.pt.show("bp.pt:"); -| bp.pt: (0.5, 0.5, 0.5) + [Figure 138 not displayed.] +  File: 3DLDF.info, Node: Polygon Reference, Next: Regular Polygon Reference, Prev: Path Reference, Up: Top @@ -380,6 +918,8 @@ bpp.first.pt.dotlabel("$f$", "rt"); bpp.second.pt.dotlabel("$s$"); + [Figure 139 not displayed.] + In [next figure] , the lines BC and PQ are not coplanar with the `Reg_Polygon' r. In each case, only one @@ -399,6 +939,8 @@ bpp = r.intersection_points(P, Q); bpp.first.pt.dotlabel("$i_1$", "rt"); + [Figure 140 not displayed.] + In [next figure] , the intersection point of r with the line PQ does not lie on the line _segment_ PQ. @@ -408,6 +950,8 @@ cout << "bpp.first.b == " << bpp.first.b << endl << flush; -| bpp.first.b == 0 + [Figure 141 not displayed.] + - `const' function: vector intersection_points (const Polygon& R) @@ -421,6 +965,8 @@ rp.shift(0, 0, .25); vector v = r.intersection_points(rp); + [Figure 142 not displayed.] + If the `Polygons' lie in parallel planes, there can be no intersection points. If they lie in non-parallel, non-coplanar planes, `intersection_points()' first finds the intersection line @@ -439,6 +985,8 @@ p.shift(2, 0, 3); vector v = r.intersection_points(p); + [Figure 143 not displayed.] + In [next figure] , the `Rectangle' r and the `Reg_Polygon' p don't overlap at all, nor does the intersection line of the two planes intersect with p. However, it does intersect with p at the @@ -455,6 +1003,8 @@ iter != v.end(); ++iter) iter->dotlabel(i++, "bot"); + [Figure 144 not displayed.] + ---------- Footnotes ---------- @@ -509,7 +1059,7 @@ - Private variable: bool on_free_store `true', if the `Reg_Polygon' was dynamically allocated on the free store, otherwise `false'. Dynamic allocation of `Reg_Polygons' - should only be performed by `create_new_reg_polygon()', which sets + should only be performed by `create_new()', which sets `on_free_store' to `true'.  @@ -537,6 +1087,8 @@ Reg_Polygon r(origin, 3, 2.75, 10, 15, 12.5); r.draw(); + [Figure 145 not displayed.] + - Setting function: void set (const Point& CCENTER, const unsigned short SSIDES, const real DDIAMETER, [const real ANGLE_X = 0, @@ -557,17 +1109,20 @@ j += .5; } + [Figure 146 not displayed.] - - Static function: Reg_Polygon* create_new_reg_polygon ([const - Reg_Polygon* R = 0]) - - Static function: Reg_Polygon* create_new_reg_polygon (const - Reg_Polygon& R) - Pseudo-constructors for dynamic allocation. In the first version, - R is an optional pointer argument. If R is non-zero, the new - `Reg_Polygon' will be a copy of *R. Otherwise, it will be empty. - In the second version, R is a required reference argument, and the - new `Reg_Polygon' will be a copy of R. + - Template specializations: Reg_Polygon* create_new + (const Reg_Polygon* R) + - : Reg_Polygon* create_new (const Reg_Polygon& R) + Pseudo-constructors for dynamic allocation of `Reg_Polygons'. + They create a `Reg_Polygon' on the free store and allocate memory + for it using `new(Reg_Polygon)'. They return a pointer to the new + `Reg_Polygon'. If R is a non-zero pointer or a reference, the new + `Reg_Polygon' will be a copy of R. If the new object is not meant + to be a copy of an existing one, `0' must be passed to + `create_new()' as its argument. *Note Dynamic + Allocation of Shapes::, for more information.  File: 3DLDF.info, Node: Regular Polygon Operators, Next: Querying Regular Polygons, Prev: Regular Polygon Constructors and Setting Functions, Up: Regular Polygon Reference @@ -602,6 +1157,8 @@ Circle c = h.in_circle(); c.unfilldraw(black); + [Figure 147 not displayed.] + - `const' function: Circle draw_in_circle ([const Color& DDRAW_COLOR = `*Colors::default_color', [const string DDASHED = "", [const @@ -617,6 +1174,8 @@ h.draw(black, "evenly"); h.draw_in_circle(); + [Figure 148 not displayed.] + - `const' function: Circle out_circle (void) Returns the surrounding `Circle' of the `Reg_Polygon'. @@ -627,6 +1186,8 @@ c.filldraw(black, gray); h.unfilldraw(black); + [Figure 149 not displayed.] + - `const' function: Circle draw_out_circle ([const Color& DDRAW_COLOR = `*Colors::default_color', [const string DDASHED = "", @@ -643,592 +1204,6 @@ h.draw(black, "evenly"); h.draw_out_circle(); + [Figure 150 not displayed.] - -File: 3DLDF.info, Node: Rectangle Reference, Next: Regular Closed Plane Curve Reference, Prev: Regular Polygon Reference, Up: Top - -Rectangle Reference -******************* - - Class `Rectangle' is defined in `rectangs.web', and is derived from -`Polygon', using public derivation. - - As noted above in *Note Polygon Reference; Affine Transformations: -Affine Transformations for Polygons, `class Rectangle', like `class -Reg_Polygon', currently inherits its transformation functions and -`operator*=(const Transform&)' from `Polygon'. Consequently, the data -members of a `Rectangle', except for `center', are not recalculated -when it's transformed. I plan to change this soon! It will also be -necessary to add the function `Rectangle::is_rectangular()', in order -to test whether a `Rectangle' is still rectangular. - -* Menu: - -* Rectangle Data Members:: -* Rectangle Constructors and Setting Functions:: -* Rectangle Operators:: -* Returning Points for Rectangles:: -* Querying Rectangles:: -* Ellipses for Rectangles:: - - -File: 3DLDF.info, Node: Rectangle Data Members, Next: Rectangle Constructors and Setting Functions, Prev: Rectangle Reference, Up: Rectangle Reference - -Data Members -============ - - - Private variables: real axis_h - - : real axis_v - The lengths of the horizontal and vertical axes, respectively, of - the `Rectangle'. Actually, they are merely the horizontal and - vertical axes by convention, since there are no restrictions on - the orientation of an `Rectangle'. - - Please note that `axis_h' and `axis_v' are currently not - recalculated, when a `Rectangle' is transformed. I plan to do - something about this soon. - - - Private variable: bool on_free_store - `true', if the `Rectangle' was dynamically allocated on the free - store, otherwise `false'. Dynamic allocation of `Rectangles' - should only be performed by `create_new_rectangle()', which sets - `on_free_store' to `true'. - - -File: 3DLDF.info, Node: Rectangle Constructors and Setting Functions, Next: Rectangle Operators, Prev: Rectangle Data Members, Up: Rectangle Reference - -Constructors and Setting Functions -================================== - - - Default constructor: void Rectangle (void) - Creates an empty `Rectangle'. - - - Constructor: void Rectangle (const Point& CCENTER, const real - AAXIS_H, const real AAXIS_V, [const real ANGLE_X = 0, [const - real ANGLE_Y = 0, [const real ANGLE_Z = 0]]]) - Creates a `Rectangle' in the x-z plane, centered at the origin, - with width == AAXIS_H (in the + or - x direction), and height == - AAXIS_V (in the + or - z direction). If one or more of the - arguments ANGLE_X, ANGLE_Y, or ANGLE_Z are used, it is rotated by - those amounts around the appropriate axes. Finally, the - `Rectangle' is shifted such that its center lies at CCENTER. - - Point C(-1, -1, 1); - Rectangle r(C, 3, 4, 30, 30, 30); - - - - Setting function: void set (const Point& CCENTER, const real - AAXIS_H, const real AAXIS_V, [const real ANGLE_X = 0, [const - real ANGLE_Y = 0, [const real ANGLE_Z = 0]]]) - Corresponds to the constructor described above. - - - Constructor: void Rectangle (const Point& P0, const Point& P1, const - Point& P2, const Point& P3) - Creates `Rectangle' using four `Point' arguments. The order of - the arguments must correspond with a path around the `Rectangle'. - - This function does not currently check that the arguments yield a - valid `Rectangle', therefore all code using it must ensure that - they do. - - - Setting function: void set (const Point& PT0, const Point& PT1, - const Point& PT2, const Point& PT3) - Corresponds to the constructor above. - - - Static functions: Rectangle* create_new_rectangle ([const Rectangle* - @var{r} = 0]) - - : Rectangle* create_new_rectangle (const Rectangle& R) - Pseudo-constructors for dynamic allocation. - - In the first version, R is an optional pointer argument. If R is - non-zero, the new `Rectangle' will be a copy of *R. Otherwise, it - will be empty. - - In the second version, R is a required reference argument, and the - new `Rectangle' will be a copy of R. - - -File: 3DLDF.info, Node: Rectangle Operators, Next: Returning Points for Rectangles, Prev: Rectangle Constructors and Setting Functions, Up: Rectangle Reference - -Operators -========= - - - Assignment Operator: const Rectangle& operator= (const Rectangle& R) - Makes the `Rectangle' a copy of R. - - -File: 3DLDF.info, Node: Returning Points for Rectangles, Next: Querying Rectangles, Prev: Rectangle Operators, Up: Rectangle Reference - -Returning Points -================ - - - Function: Point corner (unsigned short C) - Returns the corner `Point' indicated by the argument C, which must - be between 0 and 3. - - - `const' function: Point mid_point (unsigned short M) - Returns the mid-point of one of the sides. The argument C must be - between 0 and 3. - - -File: 3DLDF.info, Node: Querying Rectangles, Next: Ellipses for Rectangles, Prev: Returning Points for Rectangles, Up: Rectangle Reference - -Querying -======== - - - `const' functions: real get_axis_h (void) - - : real get_axis_v (void) - These functions return `axis_h' and `axis_v', respectively. - - Please note, that `axis_h' and `axis_v' are currently not - recalculated, when a `Rectangle' is transformed. I plan to do - something about this soon. - - - `const' function: bool is_rectangular (void) - Returns `true', if the `Rectangle' is rectangular, otherwise - `false'. Transformations, such as shearing, can cause - `Rectangles' to become non-rectangular. - - -File: 3DLDF.info, Node: Ellipses for Rectangles, Prev: Querying Rectangles, Up: Rectangle Reference - -Ellipses -======== - - - `const' function: Ellipse out_ellipse (`void') - Returns the smallest `Ellipse' that surrounds the `Rectangle'. - - Point P(-1, -1, 3); - Rectangle r(P, 3, 4, 60, 30, 15); - Ellipse e = r.out_ellipse(); - e.filldraw(black, gray); - r.unfilldraw(black); - - - - `const' function: Ellipse in_ellipse (`void') - Returns the `Ellipse' enclosed by the `Rectangle'. - - Point P(-1, -1, 3); - Rectangle r(P, 3, 4, 60, 30, 15); - Ellipse e = r.in_ellipse(); - r.filldraw(black, gray); - e.unfilldraw(black); - - - - `const' function: Ellipse draw_out_ellipse ([const Color& - ddraw_color = `*Colors::default_color', [string ddashed = "", - [string ppen = "", [Picture& picture = `current_picture']]]]) - Draws the smallest `Ellipse' that surrounds the `Rectangle'. The - arguments are like those of `Path::draw()' (*note Path Reference; - Drawing and Filling: Drawing and Filling Paths.). The return - value is the surrounding `Ellipse'. - - - `const' function: Ellipse draw_in_ellipse ([const Color& ddraw_color - = `*Colors::default_color', [string ddashed = "", [string - ppen = "", [Picture& picture = `current_picture']]]]) - Draws the `Ellipse' enclosed by the `Rectangle'. The arguments - are like those of `Path::draw()' (*note Path Reference; Drawing - and Filling: Drawing and Filling Paths.). The return value is the - enclosed `Ellipse'. - - -File: 3DLDF.info, Node: Regular Closed Plane Curve Reference, Next: Ellipse Reference, Prev: Rectangle Reference, Up: Top - -Regular Closed Plane Curve Reference -************************************ - - Class `Reg_Cl_Plane_Curve' is defined in `curves.web'. It is -derived from `Path' using `public' derivation. - - `Reg_Cl_Plane_Curve' is not called "`Regular_Closed_Plane_Curve'" -because the longer name causes too many "Overfull boxes"(1) in the -CWEAVE output of the program code. *Note CWEB Documentation::. - - `Reg_Cl_Plane_Curve' is meant to be used as a base class; no -objects should be declared of type `Reg_Cl_Plane_Curve'. Currently, -`class Ellipses' is derived from `Reg_Cl_Plane_Curve' and `class -Circle' is derived from `Ellipse'. - - At present, I have no fixed definition of what constitutes -"regularity" as far as `Reg_Cl_Plane_Curves' are concerned. Ellipses -and circles are "regular" in the sense that they have axes of symmetry. -There must be an equation for a `Reg_Cl_Plane_Curve', such as x^2 + -y^2 = r^2 for a circle. A derived class should have a `solve()' -function that uses this equation. -`Reg_Cl_Plane_Curve::intersection_points()' in turn uses `solve()' to -find the intersection points of a line with the `Reg_Cl_Plane_Curve'. -This way, the derived classes don't need their own functions for -finding their intersections with a line. However, such functions can -be added, if desired. - - It is assumed that classes derived from `Reg_Cl_Plane_Curve' are -fillable, which implies that they must be closed `Paths'. -`Reg_Cl_Plane_Curves' inherit their drawing and filling functions from -`Path'. - - The constructors and setting functions of classes derived from -`Reg_Cl_Plane_Curve' must ensure that the resulting geometric figures -are planar, convex, and that the number of `Points' they contain is a -multiple of 4. The latter assumption is of importance in -`intersection_points()', `segment()', `half()', and `quarter()'. *Note -Regular Closed Plane Curve Reference; Intersections: Regular Closed -Plane Curve Intersections, and *Note Regular Closed Plane Curve -Reference; Segments: Regular Closed Plane Curve Segments. - -* Menu: - -* Regular Closed Plane Curve Data Members:: -* Querying Regular Closed Plane Curves:: -* Regular Closed Plane Curve Intersections:: -* Regular Closed Plane Curve Segments:: - - ---------- Footnotes ---------- - - (1) If you don't know what "overfull boxes" are, don't worry about -it. It has to do with TeX's line and page breaking algorithms. If you -want to know more, see Knuth, Donald E., `The TeXbook'. - - -File: 3DLDF.info, Node: Regular Closed Plane Curve Data Members, Next: Querying Regular Closed Plane Curves, Prev: Regular Closed Plane Curve Reference, Up: Regular Closed Plane Curve Reference - -Data Members -============ - - - Protected variable: Point center - The center of the `Reg_Cl_Plane_Curve', if it has one. - - - Protected variable: unsigned short number_of_points - The number of `Points' on `points' in a `Reg_Cl_Plane_Curve'. - - -File: 3DLDF.info, Node: Querying Regular Closed Plane Curves, Next: Regular Closed Plane Curve Intersections, Prev: Regular Closed Plane Curve Data Members, Up: Regular Closed Plane Curve Reference - -Querying -======== - - - `const' inline virtual functions: bool is_quadratic (void) - - : bool is_cubic (void) - - : bool is_quartic (void) - These functions all return `false'. They are intended to be - overloaded by member functions of derived classes. - - - `const' inline virtual function: real_triple get_coefficients (real - SLOPE, real V_INTERCEPT) - Returns a `real_triple' with all three values == `INVALID_REAL'. - Intended to be overloaded by member functions of derived classes. - - - `const' inline virtual function: pair solve (char - AXIS_UNKNOWN, real KNOWN) - Returns a `pair' with `first' = `second' = - `INVALID_REAL'. Intended to be overloaded by member functions of - derived classes. - - - `const' virtual function: signed short location (Point REF_PT, Point - P) - Returns a `signed short' indicating the location of P with respect - to the `Reg_Cl_Plane_Curve', which must be planar. The - `Reg_Cl_Plane_Curve' constructors should ensure that - `Reg_Cl_Plane_Curves' are, but there is no guarantee that they will - not have been manipulated into a non-planar state, by shearing, for - example. - - The argument REF_PT is used within the function for shifting a - copy of the `Reg_Cl_Plane_Curve' to a convenient position. It - need not be the |center| of the `Reg_Cl_Plane_Curve', however, - classes derived from `Reg_Cl_Plane_Curve' will probably have their - own versions of `location()', which will pass `center' as the - REF_PT argument to this function. `Reg_Cl_Plane_Curves' need not - have a meaningful |center|. - - `location()' returns the following values: - -1 - P and `*this' are coplanar, and P lies outside the perimeter - of `*this'. - - 0 - P and `*this' are coplanar, and P lies on the perimeter of - `*this'. - - 1 - P and `*this' are coplanar, and P lies inside the perimeter - of `*this'. - - -2 - P and `*this' are not coplanar. - - -3 - Something has gone terribly wrong. - - -4 - The normal to `*this' has 0 magnitude, i.e., the |Points| on - `*this' are colinear. - - -5 - An error occurred in putting `*this' in one of the major - planes. - - - Virtual function: Point angle_point (real ANGLE) - Returns `INVALID_POINT'. Intended to be overloaded by member - functions of derived classes. - - -File: 3DLDF.info, Node: Regular Closed Plane Curve Intersections, Next: Regular Closed Plane Curve Segments, Prev: Querying Regular Closed Plane Curves, Up: Regular Closed Plane Curve Reference - -Intersections -============= - - - `const' function: bool_point_pair intersection_points (Point REF_PT, - Point P0, Point P1) - - `const' function: bool_point_pair intersection_points (const Point& - REF_PT, const Path& P) - The version of this function taking `Point' arguments finds the - intersection points, if any, of the `Reg_Cl_Plane_Curve' and the - line p that passes through the `Points' p_0 and p_1. In the other - version, the `Path' argument must be a linear `Path', and its - first and last `Points' are passed to the first version of this - function as P0 and P1, respectively. - - Let C be the `Reg_Cl_Plane_Curve'. C and p can intersect at at - most two intersection points i_1 and i_2. Let `bpp' be the return - value of this function. The intersection points need not be on - the _line segment_ between `pt0' and `pt1'. `bpp.first.pt' will - be set to the first intersection point if it exists, or - `INVALID_POINT' if it doesn't. If the first intersection point - exists and is on the line segment between `pt0' and `pt1' - - In [next figure] , the line AB is normal to the `Ellipse' e, or, - to put it another way, AB is perpendicular to the plane of e. - The intersection point i_0 lies within the perimeter of e. - - The line DE is skew to the plane of e, and intersects e at i_1, - on the perimeter of e. - - Point p0(2, 2, 3); - Ellipse e(p0, 3, 4, 30, -60, -5.2); - Point p1 = p0.mediate(e.get_point(11), .5); - Point A = e.get_normal(); - A *= 2.5; - A.shift(p1); - Point B = A.mediate(p1, 2); - bool_point_pair bpp = e.intersection_points(A, B); - Point C(0, 2, 0); - Point D(0, -3.5, 0); - C *= D.rotate(2, 0, -5); - C *= D.shift(e.get_point(4)); - bpp = e.intersection_points(C, D); - - In [next figure] , q and e are coplanar. In this case, only the - intersections of q with the perimeter of e are returned by - `intersection_points()'. - - A = p0.mediate(e.get_point(3), 1.5); - B = p0.mediate(e.get_point(11), 1.5); - Path q(A, B); - bpp = e.intersection_points(q); - - - -File: 3DLDF.info, Node: Regular Closed Plane Curve Segments, Prev: Regular Closed Plane Curve Intersections, Up: Regular Closed Plane Curve Reference - -Segments -======== - - - `const' function: Path segment (unsigned int FACTOR, [real ANGLE = - 0, [bool CLOSED = `true']]) - Returns a `Path' representing a segment of the - `Reg_Cl_Plane_Curve'. FACTOR must be >1 and <= - `number_of_points'. If it is not, an error message is issued and - an empty `Path' is returned. - - If ANGLE is non-zero, the segment `Path' is rotated by ANGLE about - a line from `center' in the direction of the normal to the plane - of the `Reg_Cl_Plane_Curve'. Please note, that a - `Reg_Cl_Plane_Curve' must have a meaningful `center', in order for - rotation to work. If the absolute value of ANGLE >360, a warning - is issued, and `fmod(ANGLE, 360)' is used. - - If CLOSED is `true', the `Path' will be a cycle, with the ends of - the curved segment joined using the connector `--'. The curved - segment is joined to the line using `&' on each side. - - Circle c(origin, 4, 30, 30, 30); - Path p = c.segment(3, 130); - p.show("p:"); - -| p: - points.size() == 8 - connectors.size() == 8(-0.00662541, -0.888379, -1.79185) .. - (0.741088, -0.673392, -1.73128) .. - (1.37598, -0.355887, -1.40714) .. - (1.80139, 0.0157987, -0.868767) .. - (1.95255, 0.385079, -0.198137) .. (1.80646, 0.695735, 0.502658) & - (1.80646, 0.695735, 0.502658) -- - (-0.00662541, -0.888379, -1.79185) & cycle; - - - - `const' inline function: Path half ([real ANGLE = 0, [bool CLOSED = - true]]) - Returns a `Path' using half of the `Points' on the - `Reg_Cl_Plane_Curve'. The effect of the arguments ANGLE and - CLOSED is similar to that in `segment()', above. - - Ellipse e(origin, 3, 5, 20, 15, 12.5); - Path p = e.half(0, false); - - - - `const' inline function: Path quarter ([real ANGLE = 0, [bool CLOSED - = `true']]) - Returns a `Path' using a quarter of the `Points' on the - `Reg_Cl_Plane_Curve'. The effect of the arguments ANGLE and - CLOSED is similar to that in `segment()', above. - - Ellipse e(origin, 3, 5, 60, 5, 2.5); - Path p = e.quarter(180, false); - - - -File: 3DLDF.info, Node: Ellipse Reference, Next: Circle Reference, Prev: Regular Closed Plane Curve Reference, Up: Top - -Ellipse Reference -***************** - - Class `Ellipse' is defined in `ellipses.web'. It is derived from -`Reg_Cl_Plane_Curve' using public derivation. - -* Menu: - -* Ellipse Data Members:: -* Ellipse Constructors and Setting Functions:: -* Performing Transformations on Ellipses:: -* Ellipse Operators:: -* Labeling Ellipses:: -* Affine Transformations for Ellipses:: -* Querying Ellipses:: -* Returning Elements and Information for Ellipses:: -* Ellipse Intersections:: -* Solving Ellipses:: -* Rectangles for Ellipses:: - - -File: 3DLDF.info, Node: Ellipse Data Members, Next: Ellipse Constructors and Setting Functions, Prev: Ellipse Reference, Up: Ellipse Reference - -Data Members -============ - - - Protected variables: Point focus0 - - : Point focus1 - The foci of the `Ellipse'. They are located on the major axis of - the `Ellipse' at a distance of `linear_eccentricity' from - `center', on opposite sides of the minor axis. - - - Protected variable: real linear_eccentricity - The linear eccentricity of the `Ellipse' e, such that e = \sqrta^2 - - b^2, where a and b are half the lengths of the major and minor - axes, respectively. Let h stand for `axis_h' and v for `axis_v'. - If h>v, then a = h/2 and b = v/2. If v>h, then a =v/2 and b = - h/2. If h = v, then the `Ellipse' is circular (but not an object - of type `Circle'!), and a = b = v/2 = h/2. - - The linear eccentricity is the distance along the major axis of the - `Ellipse' from `center' to `focus0' and `focus1'. - - - Protected variable: real numerical_eccentricity - The numerical eccentricity \epsilon of the `Ellipse', such that - \epsilon = e/a < 1, where e is the linear eccentricity of the - `Ellipse', and a is half the length of the major axis of the - `Ellipse'. - - - Protected variables: real axis_h - - : real axis_v - The horizontal and vertical axes, respectively, of the `Ellipse'. - - Actually, they are only or vertical horizontal by convention, - since there are no restrictions on the orientation of an `Ellipse'. - - - Protected static variable: unsigned short DEFAULT_NUMBER_OF_POINTS - The number of `Points' on an `Ellipse', unless another number is - specified when an `Ellipse' constructor is invoked. - - -File: 3DLDF.info, Node: Ellipse Constructors and Setting Functions, Next: Performing Transformations on Ellipses, Prev: Ellipse Data Members, Up: Ellipse Reference - -Constructors and Setting Functions -================================== - - - Default constructor: void Ellipse (void) - Creates an empty `Ellipse'. - - - Constructor: void Ellipse (const Point& CCENTER, const real AAXIS_H, - const real AAXIS_V, [const real ANGLE_X = 0, [const real - ANGLE_Y = 0, [const real ANGLE_Z = 0, [const unsigned short - NNUMBER_OF_POINTS = DEFAULT_NUMBER_OF_POINTS]]]]) - Creates an `Ellipse' in the x-z plane, centered at the origin, with - its horizontal axis == AAXIS_H and its vertical axis == AAXIS_V. - If any of the arguments ANGLE_X, ANGLE_Y, or ANGLE_Z is non-zero, - the `Ellipse' is rotated about the x, y, and z-axis in that order, - by the amounts indicated by the corresponding arguments. Finally, - the `Ellipse' is shifted such that its center comes to lie at - CCENTER. - - Ellipse e(origin, 6, 4); - e.draw(); - - Point P(1, 1, 1); - Ellipse e(P, 6, 4, 15, 12, 11); - e.draw(); - - - - Setting function: void set (const Point& CCENTER, const real - AAXIS_H, const real AAXIS_V, [const real ANGLE_X = 0, [const - real ANGLE_Y = 0, [const real ANGLE_Z = 0, [const unsigned - short NNUMBER_OF_POINTS = DEFAULT_NUMBER_OF_POINTS]]]]) - Corresponds to the constructor above. - - - Static function: Ellipse* create_new_ellipse ([const Ellipse* E = 0]) - - Static function: Ellipse* create_new_ellipse (const Ellipse& E) - Pseudo-constructors for dynamic allocation. - - In the first version, E is an optional pointer argument. If E is - non-zero, the new `Ellipse' will be a copy of *E. Otherwise, it - will be empty. - - In the second version, E is a required reference argument, and the - new `Ellipse' will be a copy of E. - - -File: 3DLDF.info, Node: Performing Transformations on Ellipses, Next: Ellipse Operators, Prev: Ellipse Constructors and Setting Functions, Up: Ellipse Reference - -Performing Transformations -========================== - - - Virtual function: Transform do_transform (const Transform& T, [bool - CHECK = `false']) - Performs a transformation on an `Ellipse'. The `Points' on the - `Ellipse' are multiplied by T. Then, if CHECK is `true', - `is_elliptical()' is called on the `Ellipse'. If the - transformation has caused it to become non-elliptical, `axis_h' - and `axis_v' are set to `INVALID_REAL', and a warning is issued to - `stderr'. `center', `focus0', and `focus1' are not set to - `INVALID_POINT'. They may may no longer really be the center and - foci of the (non-elliptical) `Ellipse', but they may have some use - for the programmer and/or user. - - If CHECK is `true', and the transformation does not cause `*this' - to become non-elliptical, `axis_h', `axis_v', - `linear_eccentricity', `numerical_eccentricity', `focus0', and - `focus1' are recalculated. - - - -File: 3DLDF.info, Node: Ellipse Operators, Next: Labeling Ellipses, Prev: Performing Transformations on Ellipses, Up: Ellipse Reference - -Operators -========= - - - Assignment operator: Ellipse& operator= (const Ellipse& E) - Makes the `Ellipse' a copy of E. - - - Virtual function: Transform operator*= (const Transform& T) - Calls `do_transform(t, true)', and returns the latter's return - value. *Note Ellipse Reference; Performing Transformations: - Performing Transformations on Ellipses. diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-9 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-9 --- 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.info-9 2003-12-10 18:44:55.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.info-9 2004-01-16 19:03:28.000000000 +0100 @@ -1,11 +1,11 @@ This is 3DLDF.info, produced by makeinfo version 4.5 from 3DLDF.texi. -This is the 3DLDF User and Reference Manual, edition 1.1.4 for 3DLDF -1.1.4. This manual was last updated on 10 December 2003. 3DLDF is a +This is the 3DLDF User and Reference Manual, edition 1.1.5.1 for 3DLDF +1.1.5.1. This manual was last updated on 16 January 2004. 3DLDF is a GNU package for three-dimensional drawing with MetaPost output. The author is Laurence D. Finston. - Copyright (C) 2003 Laurence D. Finston. + Copyright (C) 2003, 2004 Laurence D. Finston. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, @@ -20,6 +20,618 @@ END-INFO-DIR-ENTRY  +File: 3DLDF.info, Node: Rectangle Reference, Next: Regular Closed Plane Curve Reference, Prev: Regular Polygon Reference, Up: Top + +Rectangle Reference +******************* + + Class `Rectangle' is defined in `rectangs.web', and is derived from +`Polygon', using public derivation. + + As noted above in *Note Polygon Reference; Affine Transformations: +Affine Transformations for Polygons, `class Rectangle', like `class +Reg_Polygon', currently inherits its transformation functions and +`operator*=(const Transform&)' from `Polygon'. Consequently, the data +members of a `Rectangle', except for `center', are not recalculated +when it's transformed. I plan to change this soon! It will also be +necessary to add the function `Rectangle::is_rectangular()', in order +to test whether a `Rectangle' is still rectangular. + +* Menu: + +* Rectangle Data Members:: +* Rectangle Constructors and Setting Functions:: +* Rectangle Operators:: +* Returning Points for Rectangles:: +* Querying Rectangles:: +* Ellipses for Rectangles:: + + +File: 3DLDF.info, Node: Rectangle Data Members, Next: Rectangle Constructors and Setting Functions, Prev: Rectangle Reference, Up: Rectangle Reference + +Data Members +============ + + - Private variables: real axis_h + - : real axis_v + The lengths of the horizontal and vertical axes, respectively, of + the `Rectangle'. Actually, they are merely the horizontal and + vertical axes by convention, since there are no restrictions on + the orientation of an `Rectangle'. + + Please note that `axis_h' and `axis_v' are currently not + recalculated, when a `Rectangle' is transformed. I plan to do + something about this soon. + + - Private variable: bool on_free_store + `true', if the `Rectangle' was dynamically allocated on the free + store, otherwise `false'. Dynamic allocation of `Rectangles' + should only be performed by `create_new()', which sets + `on_free_store' to `true'. + + +File: 3DLDF.info, Node: Rectangle Constructors and Setting Functions, Next: Rectangle Operators, Prev: Rectangle Data Members, Up: Rectangle Reference + +Constructors and Setting Functions +================================== + + - Default constructor: void Rectangle (void) + Creates an empty `Rectangle'. + + - Constructor: void Rectangle (const Point& CCENTER, const real + AAXIS_H, const real AAXIS_V, [const real ANGLE_X = 0, [const + real ANGLE_Y = 0, [const real ANGLE_Z = 0]]]) + Creates a `Rectangle' in the x-z plane, centered at the origin, + with width == AAXIS_H (in the + or - x direction), and height == + AAXIS_V (in the + or - z direction). If one or more of the + arguments ANGLE_X, ANGLE_Y, or ANGLE_Z are used, it is rotated by + those amounts around the appropriate axes. Finally, the + `Rectangle' is shifted such that its center lies at CCENTER. + + Point C(-1, -1, 1); + Rectangle r(C, 3, 4, 30, 30, 30); + + [Figure 151 not displayed.] + + + - Setting function: void set (const Point& CCENTER, const real + AAXIS_H, const real AAXIS_V, [const real ANGLE_X = 0, [const + real ANGLE_Y = 0, [const real ANGLE_Z = 0]]]) + Corresponds to the constructor described above. + + - Constructor: void Rectangle (const Point& P0, const Point& P1, const + Point& P2, const Point& P3) + Creates `Rectangle' using four `Point' arguments. The order of + the arguments must correspond with a path around the `Rectangle'. + + This function does not currently check that the arguments yield a + valid `Rectangle', therefore all code using it must ensure that + they do. + + - Setting function: void set (const Point& PT0, const Point& PT1, + const Point& PT2, const Point& PT3) + Corresponds to the constructor above. + + - Template specializations: Rectangle* create_new (const + Rectangle* R) + - : Rectangle* create_new (const Rectangle& R) + Pseudo-constructors for dynamic allocation of `Rectangles'. They + create a `Rectangle' on the free store and allocate memory for it + using `new(Rectangle)'. They return a pointer to the new + `Rectangle'. + + If R is a non-zero pointer or a reference, the new `Rectangle' + will be a copy of R. If the new object is not meant to be a copy + of an existing one, `0' must be passed to + `create_new()' as its argument. *Note Dynamic + Allocation of Shapes::, for more information. + + +File: 3DLDF.info, Node: Rectangle Operators, Next: Returning Points for Rectangles, Prev: Rectangle Constructors and Setting Functions, Up: Rectangle Reference + +Operators +========= + + - Assignment Operator: const Rectangle& operator= (const Rectangle& R) + Makes the `Rectangle' a copy of R. + + +File: 3DLDF.info, Node: Returning Points for Rectangles, Next: Querying Rectangles, Prev: Rectangle Operators, Up: Rectangle Reference + +Returning Points +================ + + - Function: Point corner (unsigned short C) + Returns the corner `Point' indicated by the argument C, which must + be between 0 and 3. + + - `const' function: Point mid_point (unsigned short M) + Returns the mid-point of one of the sides. The argument C must be + between 0 and 3. + + +File: 3DLDF.info, Node: Querying Rectangles, Next: Ellipses for Rectangles, Prev: Returning Points for Rectangles, Up: Rectangle Reference + +Querying +======== + + - `const' functions: real get_axis_h (void) + - : real get_axis_v (void) + These functions return `axis_h' and `axis_v', respectively. + + Please note, that `axis_h' and `axis_v' are currently not + recalculated, when a `Rectangle' is transformed. I plan to do + something about this soon. + + - `const' function: bool is_rectangular (void) + Returns `true', if the `Rectangle' is rectangular, otherwise + `false'. Transformations, such as shearing, can cause + `Rectangles' to become non-rectangular. + + +File: 3DLDF.info, Node: Ellipses for Rectangles, Prev: Querying Rectangles, Up: Rectangle Reference + +Ellipses +======== + + - `const' function: Ellipse out_ellipse (`void') + Returns the smallest `Ellipse' that surrounds the `Rectangle'. + + Point P(-1, -1, 3); + Rectangle r(P, 3, 4, 60, 30, 15); + Ellipse e = r.out_ellipse(); + e.filldraw(black, gray); + r.unfilldraw(black); + + [Figure 152 not displayed.] + + + - `const' function: Ellipse in_ellipse (`void') + Returns the `Ellipse' enclosed by the `Rectangle'. + + Point P(-1, -1, 3); + Rectangle r(P, 3, 4, 60, 30, 15); + Ellipse e = r.in_ellipse(); + r.filldraw(black, gray); + e.unfilldraw(black); + + [Figure 153 not displayed.] + + + - `const' function: Ellipse draw_out_ellipse ([const Color& + ddraw_color = `*Colors::default_color', [string ddashed = "", + [string ppen = "", [Picture& picture = `current_picture']]]]) + Draws the smallest `Ellipse' that surrounds the `Rectangle'. The + arguments are like those of `Path::draw()' (*note Path Reference; + Drawing and Filling: Drawing and Filling Paths.). The return + value is the surrounding `Ellipse'. + + - `const' function: Ellipse draw_in_ellipse ([const Color& ddraw_color + = `*Colors::default_color', [string ddashed = "", [string + ppen = "", [Picture& picture = `current_picture']]]]) + Draws the `Ellipse' enclosed by the `Rectangle'. The arguments + are like those of `Path::draw()' (*note Path Reference; Drawing + and Filling: Drawing and Filling Paths.). The return value is the + enclosed `Ellipse'. + + +File: 3DLDF.info, Node: Regular Closed Plane Curve Reference, Next: Ellipse Reference, Prev: Rectangle Reference, Up: Top + +Regular Closed Plane Curve Reference +************************************ + + Class `Reg_Cl_Plane_Curve' is defined in `curves.web'. It is +derived from `Path' using `public' derivation. + + `Reg_Cl_Plane_Curve' is not called "`Regular_Closed_Plane_Curve'" +because the longer name causes too many "Overfull boxes"(1) in the +CWEAVE output of the program code. *Note CWEB Documentation::. + + `Reg_Cl_Plane_Curve' is meant to be used as a base class; no +objects should be declared of type `Reg_Cl_Plane_Curve'. Currently, +`class Ellipses' is derived from `Reg_Cl_Plane_Curve' and `class +Circle' is derived from `Ellipse'. + + At present, I have no fixed definition of what constitutes +"regularity" as far as `Reg_Cl_Plane_Curves' are concerned. Ellipses +and circles are "regular" in the sense that they have axes of symmetry. +There must be an equation for a `Reg_Cl_Plane_Curve', such as x^2 + +y^2 = r^2 for a circle. A derived class should have a `solve()' +function that uses this equation. +`Reg_Cl_Plane_Curve::intersection_points()' in turn uses `solve()' to +find the intersection points of a line with the `Reg_Cl_Plane_Curve'. +This way, the derived classes don't need their own functions for +finding their intersections with a line. However, such functions can +be added, if desired. + + It is assumed that classes derived from `Reg_Cl_Plane_Curve' are +fillable, which implies that they must be closed `Paths'. +`Reg_Cl_Plane_Curves' inherit their drawing and filling functions from +`Path'. + + The constructors and setting functions of classes derived from +`Reg_Cl_Plane_Curve' must ensure that the resulting geometric figures +are planar, convex, and that the number of `Points' they contain is a +multiple of 4. The latter assumption is of importance in +`intersection_points()', `segment()', `half()', and `quarter()'. *Note +Regular Closed Plane Curve Reference; Intersections: Regular Closed +Plane Curve Intersections, and *Note Regular Closed Plane Curve +Reference; Segments: Regular Closed Plane Curve Segments. + +* Menu: + +* Regular Closed Plane Curve Data Members:: +* Querying Regular Closed Plane Curves:: +* Regular Closed Plane Curve Intersections:: +* Regular Closed Plane Curve Segments:: + + ---------- Footnotes ---------- + + (1) If you don't know what "overfull boxes" are, don't worry about +it. It has to do with TeX's line and page breaking algorithms. If you +want to know more, see Knuth, Donald E., `The TeXbook'. + + +File: 3DLDF.info, Node: Regular Closed Plane Curve Data Members, Next: Querying Regular Closed Plane Curves, Prev: Regular Closed Plane Curve Reference, Up: Regular Closed Plane Curve Reference + +Data Members +============ + + - Protected variable: Point center + The center of the `Reg_Cl_Plane_Curve', if it has one. + + - Protected variable: unsigned short number_of_points + The number of `Points' on `points' in a `Reg_Cl_Plane_Curve'. + + +File: 3DLDF.info, Node: Querying Regular Closed Plane Curves, Next: Regular Closed Plane Curve Intersections, Prev: Regular Closed Plane Curve Data Members, Up: Regular Closed Plane Curve Reference + +Querying +======== + + - `const' inline virtual functions: bool is_quadratic (void) + - : bool is_cubic (void) + - : bool is_quartic (void) + These functions all return `false'. They are intended to be + overloaded by member functions of derived classes. + + - `const' inline virtual function: real_triple get_coefficients (real + SLOPE, real V_INTERCEPT) + Returns a `real_triple' with all three values == `INVALID_REAL'. + Intended to be overloaded by member functions of derived classes. + + - `const' inline virtual function: pair solve (char + AXIS_UNKNOWN, real KNOWN) + Returns a `pair' with `first' = `second' = + `INVALID_REAL'. Intended to be overloaded by member functions of + derived classes. + + - `const' virtual function: signed short location (Point REF_PT, Point + P) + Returns a `signed short' indicating the location of P with respect + to the `Reg_Cl_Plane_Curve', which must be planar. The + `Reg_Cl_Plane_Curve' constructors should ensure that + `Reg_Cl_Plane_Curves' are, but there is no guarantee that they will + not have been manipulated into a non-planar state, by shearing, for + example. + + The argument REF_PT is used within the function for shifting a + copy of the `Reg_Cl_Plane_Curve' to a convenient position. It + need not be the |center| of the `Reg_Cl_Plane_Curve', however, + classes derived from `Reg_Cl_Plane_Curve' will probably have their + own versions of `location()', which will pass `center' as the + REF_PT argument to this function. `Reg_Cl_Plane_Curves' need not + have a meaningful |center|. + + `location()' returns the following values: + -1 + P and `*this' are coplanar, and P lies outside the perimeter + of `*this'. + + 0 + P and `*this' are coplanar, and P lies on the perimeter of + `*this'. + + 1 + P and `*this' are coplanar, and P lies inside the perimeter + of `*this'. + + -2 + P and `*this' are not coplanar. + + -3 + Something has gone terribly wrong. + + -4 + The normal to `*this' has 0 magnitude, i.e., the |Points| on + `*this' are colinear. + + -5 + An error occurred in putting `*this' in one of the major + planes. + + - Virtual function: Point angle_point (real ANGLE) + Returns `INVALID_POINT'. Intended to be overloaded by member + functions of derived classes. + + +File: 3DLDF.info, Node: Regular Closed Plane Curve Intersections, Next: Regular Closed Plane Curve Segments, Prev: Querying Regular Closed Plane Curves, Up: Regular Closed Plane Curve Reference + +Intersections +============= + + - `const' function: bool_point_pair intersection_points (Point REF_PT, + Point P0, Point P1) + - `const' function: bool_point_pair intersection_points (const Point& + REF_PT, const Path& P) + The version of this function taking `Point' arguments finds the + intersection points, if any, of the `Reg_Cl_Plane_Curve' and the + line p that passes through the `Points' p_0 and p_1. In the other + version, the `Path' argument must be a linear `Path', and its + first and last `Points' are passed to the first version of this + function as P0 and P1, respectively. + + Let C be the `Reg_Cl_Plane_Curve'. C and p can intersect at at + most two intersection points i_1 and i_2. Let `bpp' be the return + value of this function. The intersection points need not be on + the _line segment_ between `pt0' and `pt1'. `bpp.first.pt' will + be set to the first intersection point if it exists, or + `INVALID_POINT' if it doesn't. If the first intersection point + exists and is on the line segment between `pt0' and `pt1' + + In [next figure] , the line AB is normal to the `Ellipse' e, or, + to put it another way, AB is perpendicular to the plane of e. + The intersection point i_0 lies within the perimeter of e. + + The line DE is skew to the plane of e, and intersects e at i_1, + on the perimeter of e. + + Point p0(2, 2, 3); + Ellipse e(p0, 3, 4, 30, -60, -5.2); + Point p1 = p0.mediate(e.get_point(11), .5); + Point A = e.get_normal(); + A *= 2.5; + A.shift(p1); + Point B = A.mediate(p1, 2); + bool_point_pair bpp = e.intersection_points(A, B); + Point C(0, 2, 0); + Point D(0, -3.5, 0); + C *= D.rotate(2, 0, -5); + C *= D.shift(e.get_point(4)); + bpp = e.intersection_points(C, D); + + [Figure 154 not displayed.] + + In [next figure] , q and e are coplanar. In this case, only the + intersections of q with the perimeter of e are returned by + `intersection_points()'. + + A = p0.mediate(e.get_point(3), 1.5); + B = p0.mediate(e.get_point(11), 1.5); + Path q(A, B); + bpp = e.intersection_points(q); + + [Figure 155 not displayed.] + + + +File: 3DLDF.info, Node: Regular Closed Plane Curve Segments, Prev: Regular Closed Plane Curve Intersections, Up: Regular Closed Plane Curve Reference + +Segments +======== + + - `const' function: Path segment (unsigned int FACTOR, [real ANGLE = + 0, [bool CLOSED = `true']]) + Returns a `Path' representing a segment of the + `Reg_Cl_Plane_Curve'. FACTOR must be >1 and <= + `number_of_points'. If it is not, an error message is issued and + an empty `Path' is returned. + + If ANGLE is non-zero, the segment `Path' is rotated by ANGLE about + a line from `center' in the direction of the normal to the plane + of the `Reg_Cl_Plane_Curve'. Please note, that a + `Reg_Cl_Plane_Curve' must have a meaningful `center', in order for + rotation to work. If the absolute value of ANGLE >360, a warning + is issued, and `fmod(ANGLE, 360)' is used. + + If CLOSED is `true', the `Path' will be a cycle, with the ends of + the curved segment joined using the connector `--'. The curved + segment is joined to the line using `&' on each side. + + Circle c(origin, 4, 30, 30, 30); + Path p = c.segment(3, 130); + p.show("p:"); + -| p: + points.size() == 8 + connectors.size() == 8(-0.00662541, -0.888379, -1.79185) .. + (0.741088, -0.673392, -1.73128) .. + (1.37598, -0.355887, -1.40714) .. + (1.80139, 0.0157987, -0.868767) .. + (1.95255, 0.385079, -0.198137) .. (1.80646, 0.695735, 0.502658) & + (1.80646, 0.695735, 0.502658) -- + (-0.00662541, -0.888379, -1.79185) & cycle; + + [Figure 156 not displayed.] + + + - `const' inline function: Path half ([real ANGLE = 0, [bool CLOSED = + true]]) + Returns a `Path' using half of the `Points' on the + `Reg_Cl_Plane_Curve'. The effect of the arguments ANGLE and + CLOSED is similar to that in `segment()', above. + + Ellipse e(origin, 3, 5, 20, 15, 12.5); + Path p = e.half(0, false); + + [Figure 157 not displayed.] + + + - `const' inline function: Path quarter ([real ANGLE = 0, [bool CLOSED + = `true']]) + Returns a `Path' using a quarter of the `Points' on the + `Reg_Cl_Plane_Curve'. The effect of the arguments ANGLE and + CLOSED is similar to that in `segment()', above. + + Ellipse e(origin, 3, 5, 60, 5, 2.5); + Path p = e.quarter(180, false); + + [Figure 158 not displayed.] + + + +File: 3DLDF.info, Node: Ellipse Reference, Next: Circle Reference, Prev: Regular Closed Plane Curve Reference, Up: Top + +Ellipse Reference +***************** + + Class `Ellipse' is defined in `ellipses.web'. It is derived from +`Reg_Cl_Plane_Curve' using public derivation. + +* Menu: + +* Ellipse Data Members:: +* Ellipse Constructors and Setting Functions:: +* Performing Transformations on Ellipses:: +* Ellipse Operators:: +* Labeling Ellipses:: +* Affine Transformations for Ellipses:: +* Querying Ellipses:: +* Returning Elements and Information for Ellipses:: +* Ellipse Intersections:: +* Solving Ellipses:: +* Rectangles for Ellipses:: + + +File: 3DLDF.info, Node: Ellipse Data Members, Next: Ellipse Constructors and Setting Functions, Prev: Ellipse Reference, Up: Ellipse Reference + +Data Members +============ + + - Protected variables: Point focus0 + - : Point focus1 + The foci of the `Ellipse'. They are located on the major axis of + the `Ellipse' at a distance of `linear_eccentricity' from + `center', on opposite sides of the minor axis. + + - Protected variable: real linear_eccentricity + The linear eccentricity of the `Ellipse' e, such that e = \sqrta^2 + - b^2, where a and b are half the lengths of the major and minor + axes, respectively. Let h stand for `axis_h' and v for `axis_v'. + If h>v, then a = h/2 and b = v/2. If v>h, then a =v/2 and b = + h/2. If h = v, then the `Ellipse' is circular (but not an object + of type `Circle'!), and a = b = v/2 = h/2. + + The linear eccentricity is the distance along the major axis of the + `Ellipse' from `center' to `focus0' and `focus1'. + + - Protected variable: real numerical_eccentricity + The numerical eccentricity \epsilon of the `Ellipse', such that + \epsilon = e/a < 1, where e is the linear eccentricity of the + `Ellipse', and a is half the length of the major axis of the + `Ellipse'. + + - Protected variables: real axis_h + - : real axis_v + The horizontal and vertical axes, respectively, of the `Ellipse'. + + Actually, they are only or vertical horizontal by convention, + since there are no restrictions on the orientation of an `Ellipse'. + + - Protected static variable: unsigned short DEFAULT_NUMBER_OF_POINTS + The number of `Points' on an `Ellipse', unless another number is + specified when an `Ellipse' constructor is invoked. + + +File: 3DLDF.info, Node: Ellipse Constructors and Setting Functions, Next: Performing Transformations on Ellipses, Prev: Ellipse Data Members, Up: Ellipse Reference + +Constructors and Setting Functions +================================== + + - Default constructor: void Ellipse (void) + Creates an empty `Ellipse'. + + - Constructor: void Ellipse (const Point& CCENTER, const real AAXIS_H, + const real AAXIS_V, [const real ANGLE_X = 0, [const real + ANGLE_Y = 0, [const real ANGLE_Z = 0, [const unsigned short + NNUMBER_OF_POINTS = DEFAULT_NUMBER_OF_POINTS]]]]) + Creates an `Ellipse' in the x-z plane, centered at the origin, with + its horizontal axis == AAXIS_H and its vertical axis == AAXIS_V. + If any of the arguments ANGLE_X, ANGLE_Y, or ANGLE_Z is non-zero, + the `Ellipse' is rotated about the x, y, and z-axis in that order, + by the amounts indicated by the corresponding arguments. Finally, + the `Ellipse' is shifted such that its center comes to lie at + CCENTER. + + Ellipse e(origin, 6, 4); + e.draw(); + + [Figure 159 not displayed.] + + Point P(1, 1, 1); + Ellipse e(P, 6, 4, 15, 12, 11); + e.draw(); + + [Figure 160 not displayed.] + + + - Setting function: void set (const Point& CCENTER, const real + AAXIS_H, const real AAXIS_V, [const real ANGLE_X = 0, [const + real ANGLE_Y = 0, [const real ANGLE_Z = 0, [const unsigned + short NNUMBER_OF_POINTS = DEFAULT_NUMBER_OF_POINTS]]]]) + Corresponds to the constructor above. + + - Template specializations: Ellipse* create_new (const + Ellipse* E) + - : Ellipse* create_new (const Ellipse& E) + Pseudo-constructors for dynamic allocation of `Ellipses'. They + create a `Ellipse' on the free store and allocate memory for it + using `new(Ellipse)'. They return a pointer to the new `Ellipse'. + + If E is a non-zero pointer or a reference, the new `Ellipse' will + be a copy of E. If the new object is not meant to be a copy of an + existing one, `0' must be passed to `create_new()' as its + argument. *Note Dynamic Allocation of Shapes::, for more + information. + + +File: 3DLDF.info, Node: Performing Transformations on Ellipses, Next: Ellipse Operators, Prev: Ellipse Constructors and Setting Functions, Up: Ellipse Reference + +Performing Transformations +========================== + + - Virtual function: Transform do_transform (const Transform& T, [bool + CHECK = `false']) + Performs a transformation on an `Ellipse'. The `Points' on the + `Ellipse' are multiplied by T. Then, if CHECK is `true', + `is_elliptical()' is called on the `Ellipse'. If the + transformation has caused it to become non-elliptical, `axis_h' + and `axis_v' are set to `INVALID_REAL', and a warning is issued to + `stderr'. `center', `focus0', and `focus1' are not set to + `INVALID_POINT'. They may may no longer really be the center and + foci of the (non-elliptical) `Ellipse', but they may have some use + for the programmer and/or user. + + If CHECK is `true', and the transformation does not cause `*this' + to become non-elliptical, `axis_h', `axis_v', + `linear_eccentricity', `numerical_eccentricity', `focus0', and + `focus1' are recalculated. + + + +File: 3DLDF.info, Node: Ellipse Operators, Next: Labeling Ellipses, Prev: Performing Transformations on Ellipses, Up: Ellipse Reference + +Operators +========= + + - Assignment operator: Ellipse& operator= (const Ellipse& E) + Makes the `Ellipse' a copy of E. + + - Virtual function: Transform operator*= (const Transform& T) + Calls `do_transform(t, true)', and returns the latter's return + value. *Note Ellipse Reference; Performing Transformations: + Performing Transformations on Ellipses. + + File: 3DLDF.info, Node: Labeling Ellipses, Next: Affine Transformations for Ellipses, Prev: Ellipse Operators, Up: Ellipse Reference Labeling @@ -35,6 +647,8 @@ e.draw(); e.label(); + [Figure 161 not displayed.] + - Inline `const' function: void dotlabel ([string POS = "top", [Picture& PICTURE = `current_picture']]) @@ -44,6 +658,8 @@ e.draw(); e.dotlabel(); + [Figure 162 not displayed.] +  File: 3DLDF.info, Node: Affine Transformations for Ellipses, Next: Querying Ellipses, Prev: Labeling Ellipses, Up: Ellipse Reference @@ -116,6 +732,8 @@ / (e.get_axis_v()/2 * e.get_axis_v()/2)); -| 1 + [Figure 163 not displayed.] + - `const' virtual functions: bool is_cubic (`void') - : bool is_quartic (`void') @@ -218,6 +836,8 @@ ERROR! In Ellipse::location(): Ellipse is non-elliptical. Returning -3. + [Figure 164 not displayed.] + - `const' function: Point angle_point (real ANGLE) Returns a point on the `Ellipse' given an angle. A `Point' P is @@ -231,6 +851,8 @@ Point P = e.angle_point(135); current_picture.output(Projections::PARALLEL_X_Z); + [Figure 165 not displayed.] + [next figure] demonstrates, that the rotation is unfortunately not always in the direction one would prefer. I don't have a solution to this problem yet. @@ -239,6 +861,8 @@ Point P = e.angle_point(135); Point Q = e.angle_point(-135); + [Figure 166 not displayed.] +  File: 3DLDF.info, Node: Ellipse Intersections, Next: Solving Ellipses, Prev: Returning Elements and Information for Ellipses, Up: Ellipse Reference @@ -278,9 +902,11 @@ bpp.first.pt.dotlabel("$i_1$", "llft"); bpp.second.pt.dotlabel("$i_2$", "ulft"); + [Figure 167 not displayed.] + - `const' virtual function: bool_point_quadruple intersection_points - (Ellipse E, [const bool VERBOSE = false]) + (Ellipse E, [const real STEP = 3, [bool VERBOSE = `false']]) Returns the intersection points of two `Ellipses'. Two `Ellipses' can intersect at at most four points. @@ -291,6 +917,16 @@ `INVALID_POINT'. If a `Point' is found, the `b' element of the `bool_point' will be `true', otherwise `false'. + The STEP argument is used when the `Ellipses' are coplanar and + either have different centers or the vertical axis of one + `Ellipse' is colinear with the horizontal axis of the other (and + vice versa). In these cases, the intersection points must be + found by an iterative routine. A `Point' p travels around the + perimeter of `*this', and its location with respect to E is + tested. STEP is the angle of rotation used for stepping around + the perimeter of `*this'. The default value, 3, should be + adequate, unless the `Ellipses' differ greatly in size. + If the VERBOSE argument is `true', `intersection_points()' will print information about the intersection points to standard output. @@ -305,6 +941,8 @@ bpq.third.pt.dotlabel(3, "ulft"); bpq.fourth.pt.dotlabel(4, "lrt"); + [Figure 168 not displayed.] + In [next figure] , e and f are coplanar, but don't lie in a major plane, have different centers, and only intersect at two points. @@ -319,6 +957,8 @@ bpq.first.pt.dotlabel(1, "urt"); bpq.second.pt.dotlabel(2, "ulft"); + [Figure 169 not displayed.] + If the planes of the `Ellipses' are parallel, there are, of course, no intersection points. If the `Ellipses' are non-coplanar, and their planes are not parallel to each other, @@ -353,6 +993,8 @@ Fourth point lies inside *this. Fourth point lies on the perimeter of e. + [Figure 170 not displayed.] + In [next figure] , the two `Ellipses' lie in skew planes. The plane of f intersects with e at the `Points' labelled "1" and "2". The plane of e does not intersect with f, so `bpq.third.pt' and @@ -371,6 +1013,8 @@ Third intersection point is INVALID_POINT. Fourth intersection point is INVALID_POINT. + [Figure 171 not displayed.] +  File: 3DLDF.info, Node: Solving Ellipses, Next: Rectangles for Ellipses, Prev: Ellipse Intersections, Up: Ellipse Reference @@ -438,6 +1082,8 @@ r.filldraw(black, gray); e.unfilldraw(black); + [Figure 172 not displayed.] + - `const' function: Rectangle in_rectangle (`void') Returns the `Rectangle' enclosed within the `Ellipse'. @@ -446,6 +1092,8 @@ e.filldraw(black, gray); r.unfilldraw(black); + [Figure 173 not displayed.] + - `const' function: Rectangle draw_out_rectangle ([const Color& DDRAW_COLOR = `*Colors::default_color', [string DDASHED = "", @@ -459,6 +1107,8 @@ e.shift(-1, 1, 1); e.draw_out_rectangle(black, "evenly", "pencircle scaled .3mm"); + [Figure 174 not displayed.] + - `const' function: Rectangle draw_in_rectangle ([const Color& DDRAW_COLOR = `*Colors::default_color', [string DDASHED = "", @@ -472,6 +1122,8 @@ e.shift(-1, 1, 1); e.draw_in_rectangle(black, "evenly", "pencircle scaled .3mm"); + [Figure 175 not displayed.] +  File: 3DLDF.info, Node: Circle Reference, Next: Pattern Reference, Prev: Ellipse Reference, Up: Top @@ -533,12 +1185,18 @@ [const real ANGLE_Z = 0]]]) Corresponds to the constructor above. - - Static functions: Circle* create_new_circle ([const Circle* P = 0]) - - : Circle* create_new_circle (const Circle& P) - Pseudo-constructors for dynamic allocation. In the first version, - if P is a pointer to a `Circle', the new `Circle' will be a copy - of *P. In the second version, the new `Circle' will be a copy of - P. + - Template specializations: Circle* create_new (const Circle* + C) + - : Circle* create_new (const Circle& C) + Pseudo-constructors for dynamic allocation of `Circles'. They + create a `Circle' on the free store and allocate memory for it + using `new(Circle)'. They return a pointer to the new `Circle'. + + If C is a non-zero pointer or a reference, the new `Circle' will + be a copy of C. If the new object is not meant to be a copy of an + existing one, `0' must be passed to `create_new()' as its + argument. *Note Dynamic Allocation of Shapes::, for more + information.  File: 3DLDF.info, Node: Circle Operators, Next: Querying Circles, Prev: Circle Constructors and Setting Functions, Up: Circle Reference @@ -578,6 +1236,8 @@ cout << d.is_circular(); -| 0 + [Figure 176 not displayed.] + - Inline function: real get_radius (`void') Returns `radius'. @@ -613,6 +1273,8 @@ bpq.first.pt.dotlabel("$f$"); bpq.second.pt.dotlabel("$s$"); + [Figure 177 not displayed.] +  File: 3DLDF.info, Node: Pattern Reference, Next: Solid Reference, Prev: Circle Reference, Up: Top @@ -629,610 +1291,3 @@ * Plane Tesselations:: * Roulettes and Involutes:: - -File: 3DLDF.info, Node: Plane Tesselations, Next: Roulettes and Involutes, Prev: Pattern Reference, Up: Pattern Reference - -Plane Tesselations -================== - - 3DLDF can be used to make perspective projections of plane -tesselations and other two-dimensional patterns. These can be used for -drawing tiled floors and other architectural items, among other things. -While patterns can be generated by using the basic facilities of C++ -and 3DLDF without any specially defined functions, it can be useful to -define such functions. - - 3DLDF currently contains only one function for drawing patterns -based on a plane tessellation. I plan to add more soon. - - - Function: unsigned int hex_pattern_1 ([real DIAMETER_OUTER = 5, - [real DIAMETER_MIDDLE = 0, [real DIAMETER_INNER = 0, - [unsigned short FIRST_ROW = 5, [unsigned short DOUBLE_ROWS = - 10, [unsigned short ROW_SHIFT = 2, [Color DRAW_COLOR_OUTER = - `*Colors::default_color', [Color FILL_COLOR_OUTER = - `*Colors::background_color', [Color DRAW_COLOR_MIDDLE = - `*Colors::default_color', [Color FILL_COLOR_MIDDLE = - `*Colors::background_color', [Color DRAW_COLOR_INNER = - `*Colors::default_color', [Color FILL_COLOR_INNER = - `*Colors::background_color', [string PEN_OUTER = "pencircle - scaled .5mm", [string PEN_MIDDLE = "pencircle scaled .3mm", - [string PEN_INNER = "pencircle scaled .3mm", [Picture& - PICTURE = `current_picture', [unsigned int MAX_HEXAGONS = - 1000]]]]]]]]]]]]]]]]]) - Draws a pattern consisting of hexagons forming a tesselation of - the x-z plane, with additional hexagons within them. - - The arguments: - `real' DIAMETER_OUTER - Default: 5. The diameter of the outer hexagon in each set - of three hexagons. The outer hexagons form a tessellation of - the plane. - - `real' DIAMETER_MIDDLE - Default: 0. The diameter of the middle hexagon in a set of - three hexagons. - - `real' DIAMETER_INNER - Default: 0. The diameter of the inner hexagon in a set of - three hexagons. - - `unsigned short' FIRST_ROW - Default: 5. The number of sets of hexagons in the first - single row. The second single row will have FIRST_ROW + 1 - sets of hexagons. - - `unsigned short' DOUBLE_ROWS - Default: 10. The number of double rows drawn. - - `unsigned short' ROW_SHIFT - Default: 2. For ROW_SHIFT != 0, the number of sets of - hexagons in each (single) row is increased by 2 every - ROW_SHIFT rows. If ROW_SHIFT == 0, the number sets of - hexagons remains constant. The rows remain centered around - the z-axis. - - `Color' DRAW_COLOR_OUTER - Default: `*Colors::default_color'. The `Color' used for - drawing the outer hexagons. - - `Color' FILL_COLOR_OUTER - Default: `*Colors::background_color'. The `Color' used for - filling the outer hexagons. - - `Color' DRAW_COLOR_MIDDLE - Default: `*Colors::default_color'. The `Color' used for - drawing the middle hexagon. - - `Color' fill_color_middle - Default: `*Colors::background_color'. The `Color' used for - filling the middle hexagons. - - `Color' DRAW_COLOR_INNER - Default: `*Colors::default_color'. The `Color' used for - drawing the inner hexagons. - - `Color' FILL_COLOR_INNER - Default: `*Colors::background_color'. The `Color' used for - filling the inner hexagons. - - `string' PEN_OUTER - Default: `"pencircle scaled .5mm"'. The pen used for drawing - the outer hexagons. - - `string' PEN_MIDDLE - Default: `"pencircle scaled .3mm"'. The pen used for - drawing the middle hexagons. - - `string' pen_inner - Default: `"pencircle scaled .3mm"'. The pen used for - drawing the inner hexagons. - - `Picture&' PICTURE - Default: `current_picture'. The `Picture' onto which the - pattern is put. - - `unsigned int' MAX_HEXAGONS - Default: 1000. The maximum number of hexagons that will be - drawn. - - - Draws a pattern in the x-z plane consisting of hexagons. The outer - hexagons form a tessellation. The middle and inner hexagons fit - within the outer hexagons. The hexagons are drawn in double rows. - The tessellation can be repeated by copying a double row and - shifting the copy to lie directly behind the first double row. If - the `Picture' with the pattern is projected with the `Focus' in - front of the pattern, looking in the direction of the back of the - pattern, the first row of hexagons will appear larger than the rows - behind it. Therefore, in order for the perspective projection of - the pattern to fill a rectangular area on the plane of projection, - it will generally be necessary to increase the number of sets of - hexagons in each double row. On the other hand, if the same - number of sets of hexagons were used in the front double row, as - will be needed for the back double row, many of them would - probably be unprojectable. - - The return value of this function is the number of hexagons drawn. - - default_focus.set(0, 10, -10, 0, 10, 25, 10); - hex_pattern_1(1, 0, 0, 5, 5); - - default_focus.set(-5, 5, -10, 0, 10, 25, 10); - hex_pattern_1(2, 1.5, 1, 2, 5, 2, black, gray, black, - light_gray, black); - - - -File: 3DLDF.info, Node: Roulettes and Involutes, Prev: Plane Tesselations, Up: Pattern Reference - -Roulettes and Involutes -======================= - - "A "roulette" is the curve generated by a point which is carried by - a curve which rolls on a fixed curve. [...] The locus of a point - carried by a circle rolling on a straight line is a "trochoid". If - the point is inside the circle the trochoid has inflexions; if it - is outside the circle, but rigidly attached to it, the trochoid - has loops. [...] In the particular case when the point is on the - circumference of the rolling circle the roulette is a "cycloid". - When the circle rolls on the outside of another circle the - corresponding curves are the "epitrochoids" and "epicycloids"; if - it rolls on the inside, they are the "hypotrochoids" and - "hypocycloids"." - H. Martyn Cundy and A. P. Rollett, _Mathematical Models_, p. 46. - -* Menu: - -* Epicycloids:: - - -File: 3DLDF.info, Node: Epicycloids, Prev: Roulettes and Involutes, Up: Roulettes and Involutes - -Epicycloids ------------ - - - Function: unsigned int epicycloid_pattern_1 (real DIAMETER_INNER, - real DIAMETER_OUTER_START, real DIAMETER_OUTER_END, real - STEP, int ARC_DIVISIONS, unsigned int OFFSETS, [vector COLORS = `Colors::default_color_vector']) - Draws a pattern consisting of epicycloids. The outer circle rolls - around the circumference of the inner circle and a `Point' on the - outer circle traces an epicycloid. - - If OFFSETS is greater than 1, the outer circle is rotated OFFSET - times around the center of the inner circle by 360 / offsets - (starting from the outer circle's original position). From each - of these new positions, an epicycloid is drawn. - - While DIAMETER_OUTER_START is greater than or equal to - DIAMETER_OUTER_END, the diameter of the outer circle is reduced by - STEP, and another set of epicycloids is traced, as described - above. Each time the diameter of the outer circle is reduced, a - new `Color' is taken from COLORS for the drawing commands. If - there are more iterations than `Colors', the last `Color' on - COLORS is used for the remaining iterations. - - The arguments: - `real' DIAMETER_INNER - The diameter of the inner circle. - - `real' DIAMETER_OUTER_START - The diameter of the outer circle for the first iteration. It - must be greater than or equal to DIAMETER_OUTER_END. - - `real' DIAMETER_OUTER_END - The diameter of the outer circle for the last iteration. It - must be less than or equal to DIAMETER_OUTER_START. - - `real' STEP - The amount by which the diameter of the outer circle is - _reduced_ upon each iteration. - - `int' ARC_DIVISIONS - The number of divisions of the circle used for calculating - `Points' on the epicycloid. For instance, if ARC_DIVISIONS - is 90, then the `Path' for each epicycloid will only have 4 - `Points', since 360 / 90 = 4. - - `unsigned int' OFFSETS - The number of epicycloids drawn upon each iteration. Each - one is rotated by 360 / OFFSETS around the center of the - inner circle. OFFSETS must be greater than or equal to 1. - - `vector' COLORS - Default: `Colors::default_color_vector'. The `Colors' pointed - to by the pointers on this vector are used for drawing the - epicycloids. One `Color' is used for each iteration. - - - Example: - epicycloid_pattern_1(5, 3, 3, 1, 72); - current_picture.output(Projections::PARALLEL_X_Z); - - Example: - default_focus.set(2, 5, -10, 2, 5, 10, 10); - epicycloid_pattern_1(5, 3, 3, 1, 36); - current_picture.output(); - - - -File: 3DLDF.info, Node: Solid Reference, Next: Faced Solid Reference, Prev: Pattern Reference, Up: Top - -Solid Reference -*************** - - Class `Solid' is defined in `solids.web'. It's derived from `Shape' -using public derivation. It is intended to be used as a base class for -more specialized classes representing solid figures, e.g., cuboids, -polyhedra, solids of rotation, etc. - -* Menu: - -* Solid Data Members:: -* Solid Constructors and Setting Functions:: -* Solid Destructor:: -* Solid Operators:: -* Copying Solids:: -* Setting Solid Members:: -* Querying Solids:: -* Returning Elements and Information Solids:: -* Showing Solids:: -* Affine Transformations for Solids:: -* Applying Transformations to Solids:: -* Outputting Solids:: -* Drawing and Filling Solids:: -* Clearing Solids:: - - -File: 3DLDF.info, Node: Solid Data Members, Next: Solid Constructors and Setting Functions, Prev: Solid Reference, Up: Solid Reference - -Data Members -============ - - - Protected variable: bool on_free_store - `true', if the `Solid' was dynamically allocated on the free - store, otherwise `false'. `Solids' should only be allocated on - the free store by `create_new_solid()' (*note Solid Reference; - Constructors and Setting Functions: Solid Constructors and Setting - Functions.), or analogous functions for derived classes. - - - Protected variable: Point center - The center of the `Solid'. An object of a type derived from - `Solid' need not have a meaningful `center'. However, many do, so - it's convenient to be able to access it using the member functions - of `Solid'. - - - Protected variable: bool do_output - Set to `false' in `Picture::output()', if the `Solid' cannot be - projected using the arguments of that particular invocation of - `output()'. Reset to `true' at the end of `Picture::output()', so - that the `Solid' will be tested for projectability again, if - `output()' is called on the `Picture' again. - - - Protected variables: vector paths - - : vector circles - - : vector ellipses - - : vector reg_polygons - - : vector rectangles - Vectors of pointers to the `Paths', `Circles', `Ellipses', - `Reg_Polygons', and `Rectangles', respectively, belonging to the - `Solid', if any exist. - - - Protected variable: valarray projective_extremes - The maximum and minimum values for the x, y, and z-coordinates of - the `Points' belonging to the `Solid'. Used in - `Picture::output()' for testing whether a `Solid' is projectable - using a particular set of arguments. - - - Public static `const' variables: unsigned short CIRCLE - - : unsigned short ELLIPSE - - : unsigned short PATH - - : unsigned short RECTANGLE - - : unsigned short REG_POLYGON - Used as arguments in the functions `get_shape_ptr()' and - `get_shape_center()' (*note Returning Elements and Information: - Returning Elements and Information Solids.). - - -File: 3DLDF.info, Node: Solid Constructors and Setting Functions, Next: Solid Destructor, Prev: Solid Data Members, Up: Solid Reference - -Constructors and Setting Functions -================================== - - - Default constructor: `void' Solid (`void') - Creates an empty `Solid'. - - - Copy constructor: `void' Solid (const Solid& S) - Creates a new `Solid' and makes it a copy of S. - - - Static function: Solid* create_new_solid (`void') - Pseudo-constructor for dynamic allocation. - - -File: 3DLDF.info, Node: Solid Destructor, Next: Solid Operators, Prev: Solid Constructors and Setting Functions, Up: Solid Reference - -Destructor -========== - - - `virtual' Destructor: void ~Solid (`void') - This function currently has an empty definition, but its existence - prevents GCC 3.3 from issuing the following warning: "`class - Solid' has virtual functions but non-virtual destructor". - - -File: 3DLDF.info, Node: Solid Operators, Next: Copying Solids, Prev: Solid Destructor, Up: Solid Reference - -Operators -========= - - - Virtual function: const Solid& operator= (const Solid& S) - Assignment operator. Makes `*this' a copy of S, discarding the - old contents of `*this'. - - - Virtual function: Transform operator*= (const Transform& T) - Multiplication by a `Transform'. All of the `Shapes' that make up - the `Solid' are transformed by T. - - -File: 3DLDF.info, Node: Copying Solids, Next: Setting Solid Members, Prev: Solid Operators, Up: Solid Reference - -Copying -======= - - - `const' virtual function: Shape* get_copy (`void') - Dynamically allocates a new `Solid' on the free store, using - `create_new_solid()', and makes it a copy of `*this'. Then, a - pointer to `Shape' is pointed at the copy and returned. Used for - putting `Solids' onto `Picture::shapes' in the drawing and filling - functions for `Solid'. *Note Solid Reference; Drawing and - Filling: Drawing and Filling Solids. - - -File: 3DLDF.info, Node: Setting Solid Members, Next: Querying Solids, Prev: Copying Solids, Up: Solid Reference - -Setting Members -=============== - - - Inline virtual function: bool set_on_free_store ([bool B = `true']) - Sets `on_free_store' to B. This function is currently never used. - It was intended for use in a "`create_new()'" template function, - which I haven't been able to get to work. - - -File: 3DLDF.info, Node: Querying Solids, Next: Returning Elements and Information Solids, Prev: Setting Solid Members, Up: Solid Reference - -Querying -======== - - - `const' virtual function: bool is_on_free_store (`void') - Returns the value of `on_free_store'; `true', if the `Solid' was - dynamically allocated on the free store, otherwise `false'. - - -File: 3DLDF.info, Node: Returning Elements and Information Solids, Next: Showing Solids, Prev: Querying Solids, Up: Solid Reference - -Returning Elements and Information -================================== - - - `const' virtual function: const Point& get_center (void) - Returns `center'. If the `Solid' doesn't have a meaningful - center, the return value will probably be `INVALID_POINT'. - -* Menu: - -* Getting Shape Centers Solids:: -* Getting Shapes Solids:: - - -File: 3DLDF.info, Node: Getting Shape Centers Solids, Next: Getting Shapes Solids, Prev: Returning Elements and Information Solids, Up: Returning Elements and Information Solids - -Getting Shape Centers ---------------------- - - - `const' virtual function: const Point& get_shape_center (const - unsigned short SHAPE_TYPE, const unsigned short S) - Returns the `center' of a `Shape' belonging to the `Solid'. - Currently, the object can be a `Circle', `Ellipse', `Rectangle', - or `Reg_Polygon', and it is accessed through a pointer on one of - the following vectors of pointers to `Shape': `circles', - `ellipses', `rectangles', or `reg_polygons'. The type of object - is specified using the SHAPE_TYPE argument. The following `public - static const' data members of `Solid' can (and probably should) be - passed as the SHAPE_TYPE argument: `CIRCLE', `ELLIPSE', - `RECTANGLE', and `REG_POLYGON'. - - The argument S is used to index the vector. - - This function is called within the more specialized functions in - this section, namely: `get_circle_center()', - `get_ellipse_center()', ``get_rectangle_center()'', and - `get_reg_polygon_center()'. I don't expect it to be needed in user - code very often. - - Dodecahedron d(origin, 3); - d.filldraw(); - Point C = d.get_shape_center(Solid::REG_POLYGON, 1); - C.dotlabel("C"); - - Note that this function will have to be changed, if new vectors of - `Shape' pointers are added to `class Solid'! - - - `const' virtual functions: const Point& get_circle_center (const - unsigned short S) - - : const Point& get_ellipse_center (const unsigned short S) - - : const Point& get_rectangle_center (const unsigned short S) - - : const Point& get_reg_polygon_center (const unsigned short S) - These functions all return the center of the `Shape' pointed to by - a pointer on one of the vectors of `Shapes' belonging to the - `Solid'. The argument S indicates which element on the vector is - to be accessed. For example, `get_rectangle_center(2)' returns - the center of the `Rectangle' pointed to by `rectangles[2]'. - - Cuboid c(origin, 3, 4, 5, 0, 30); - c.draw(); - for (int i = 0; i < 6; ++i) - c.get_rectangle_center(i).label(i, ""); - - - -File: 3DLDF.info, Node: Getting Shapes Solids, Prev: Getting Shape Centers Solids, Up: Returning Elements and Information Solids - -Getting Shapes --------------- - - The functions in this section all return `const' pointers to -`Shape', or one of its derived classes. Therefore, they must be invoked -in such a way, that the `const' qualifier is not discarded. See the -description of `get_reg_polygon_ptr()' below, for an example. - - - `const' virtual function: Shape* get_shape_ptr (const unsigned short - shape_type, const unsigned short s) - Copies one of the objects belonging to the `Solid', and returns a - pointer to `Shape' that points to the copy. The object is found - by dereferencing one of the pointers on one of the vectors of - pointers belonging to the `Solid'. Currently, these vectors are - `circles', `ellipses', `paths', `rectangles', and `reg_polygons'. - The argument SHAPE_TYPE specifies the vector, and the argument S - specifies which element of the vector should be accessed. The - following `public static const' data members of `Solid' can (and - probably should) be passed as the SHAPE_TYPE argument: `CIRCLE', - `ELLIPSE', `PATH', `RECTANGLE', and `REG_POLYGON'. - - This function was originally intended to be called within the more - specialized functions in this section, namely: `get_circle_ptr()', - `get_ellipse_ptr()', `get_path_ptr()', `get_rectangle_ptr', and - `get_reg_polygon_ptr'. However, these functions no longer use - `get_shape_ptr()', so this function is probably no longer needed. - - Icosahedron I(origin, 3); - I.filldraw(); - Reg_Polygon* t = - static_cast(I.get_shape_ptr(Solid::REG_POLYGON, 9)); - t->fill(gray); - - - - `const' virtual functions: const Reg_Polygon* get_circle_ptr (const - unsigned short S) - - : const Reg_Polygon* get_ellipse_ptr (const unsigned short S) - - : const Reg_Polygon* get_path_ptr (const unsigned short S) - - : const Reg_Polygon* get_rectangle_ptr (const unsigned short S) - - : const Reg_Polygon* get_reg_polygon_ptr (const unsigned short S) - Each of these functions returns a pointer from one of the vectors - of `Shape' pointers belonging to the `Solid'. The argument S - specifies which element of the appropriate vector should be - returned. For example, `get_reg_polygon_ptr(2)' returns the - `Reg_Polygon*' in `reg_polygons[2]'. - - Since these functions return `const' pointers, they must be invoked - in such a way, that the `const' qualifier is not discarded, as - noted at the beginning of this section. The following example - demonstrates two ways of invoking `get_reg_polygon_ptr()': - - Dodecahedron d(origin, 3); - d.draw(); - const Reg_Polygon* ptr = d.get_reg_polygon_ptr(0); - ptr->draw(black, "evenly scaled 4", "pencircle scaled 1mm"); - Reg_Polygon A = *d.get_reg_polygon_ptr(5); - A.fill(gray); - - - -File: 3DLDF.info, Node: Showing Solids, Next: Affine Transformations for Solids, Prev: Returning Elements and Information Solids, Up: Solid Reference - -Showing -======= - - - `const' virtual function: `void' show ([string TEXT = "", [char - COORDS = 'w', [const bool DO_PERSP = `true', [const bool - DO_APPLY = `true', [Focus* f = 0, [const unsigned short PROJ - = `Projections::PERSP', [const real FACTOR = 1]]]]]]]) - Prints TEXT and the value of `on_free_store' to the standard - output (`stdout'), and then calls `show()' on the objects pointed - to by the pointers on `paths', `circles', `ellipses', - `reg_polygons', and `rectangles', unless the vectors are empty. - The arguments are passed to `Path::show()', `Ellipse::show()', - etc. If a vector is empty, a message to this effect is printed to - the standard output. - - -File: 3DLDF.info, Node: Affine Transformations for Solids, Next: Applying Transformations to Solids, Prev: Showing Solids, Up: Solid Reference - -Affine Transformations -====================== - - - Virtual functions: Transform scale (real X, [real Y = 0, [real Z = - 0]]) - `Solid'. - - - : Transform shear (real XY, [real XZ = 0, [real YX = 0, [real YZ = - 0, [real ZX = 0, [real ZY = 0]]]]]) - - : Transform shift (real X, [real Y = 0, [real Z = 0]]) - - : Transform shift (const Point& PT) - - : Transform rotate (const real X, [const real Y = 0, [const real Z = - 0]]) - - : Transform rotate (const Point& P0, const Point& P1, [const real - ANGLE = 180]) - These functions perform the corresponding transformations on all - of the `Shapes' belonging to the `Solid'. *Note Transform - Reference; Affine Transformations: Affine Transformations for - Transforms. - - -File: 3DLDF.info, Node: Applying Transformations to Solids, Next: Outputting Solids, Prev: Affine Transformations for Solids, Up: Solid Reference - -Applying Transformations -======================== - - - Virtual function: void apply_transform (`void') - Calls `apply_transform()' on all of the `Shapes' belonging to the - `Solid'. - - -File: 3DLDF.info, Node: Outputting Solids, Next: Drawing and Filling Solids, Prev: Applying Transformations to Solids, Up: Solid Reference - -Outputting -========== - - The functions in this section are are called, directly or -indirectly, by `Picture::output()'. *Note Picture Reference; -Outputting: Outputting Pictures. - - - Virtual function: void output (`void') - Writes the MetaPost code for drawing, filling, filldrawing, - undrawing, unfilling, or unfilldrawing the `Solid' to `out_stream'. - - - Virtual function: void suppress_output (`void') - Used in `Picture::output()'. Sets `do_output' to `false', if the - `Solid' cannot be projected using a particular set of arguments to - `Picture::output()'. - - - Virtual function: void unsuppress_output (`void') - Used in `Picture::output()'. Resets `do_output' to `true', so - that the `Solid' will be tested for projectability again, if the - `Picture' it's on is output again. - - - Virtual function: vector extract (const Focus& F, const - unsigned short PROJ, real FACTOR) - Tests whether all of the `Shapes' belonging to the `Solid' are - projectable, using the arguments passed to `output()'. If it is, - this function returns a vector of pointers to `Shape' containing a - single pointer to the `Solid'. If not, an empty vector is - returned. - - - Virtual function: bool set_extremes (`void') - Sets `projective_extremes' to contain the maximum and minimum - values for the x, y, and z-coordinates of the `Points' on the - `Shape'. Used for determining projectability of a `Solid' using a - particular set of arguments. - - - `const' inline virtual function: const valarray get_extremes - (`void') - Returns `projective_extremes'. - - - `const' virtual functions: real get_minimum_z (`void') - - : real get_maximum_z (`void') - - : real get_mean_z (`void') - Returns the minimum, maximum, or mean z-value, respectively, of the - `Points' belonging to the `Solid'. Used for surface hiding. - *Note Surface Hiding::. - diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.pdf 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.pdf --- 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.pdf 1970-01-01 01:00:00.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.pdf 2004-01-16 18:17:42.000000000 +0100 @@ -0,0 +1,15932 @@ +%PDF-1.2 +%Çì¢ +6 0 obj +<> +stream +xœ•SËnÛ0ì™_ÁczКK._WÇ ê"Ò@m΂%§*j¹ÖEÿ¾$%* ‚ +"4CqgfW.¹ˆkÙ'va›GâÏ»pLTÞ'¾-^¥£æå‘Íß!÷‚D°ÄË»R»»ÝíÇòs +H£ +GÊš]}š>¢šÀ£[Àª«#FÎh¹€Í±é›îÐD +…)ôBÝW]:¯Áxmpª~Fð¦ä_‚pRrÖ\Ç÷à7ÂZ0.šÜîÙfÏÇ~jØæ‰#Û|ŠíÃuØö;þÝìÓMÿˆ@¼ðø:%$âÚKæR EÝžšnhÏݬÏ8ðÖe“u_%{ˆlÎèwÛ=GTjðÞ¼ ã÷„Xo(GÑŒÕC„‚r:ÃçaL÷Zpds±ó4þšFˆD!‚@äJðæuª2nÕ²¤Š”\/jêv †RYÒ)³0ʬÄñœºŽ¬Y¯YGDyФsw¿EȆ=b.ع‚AÒïëJy÷ÆÑçÙÑ\õÅQÿgIõš®‚":k8íddìlA¡ÍÂQœ£0‚.¾«¦u2…2 Ú¥tel¿ÎâoÛngõï†3üF”‡µŽ¥þc8ãú e¹ÙŠendstream +endobj +7 0 obj +472 +endobj +20 0 obj +<> +stream +xœ¥WÛnÛF}×W}Jk½÷ òÔÄuÑÂ)RGé“_h‰²ØH¤MRuü÷îÎ^|Ib ðƒ€ÙåîÌ9gάï*JXEç?ü]w‹»ŠùXüYªw«Åé%!Ž:V­¶‹ð«­¸¤DÈjuX¼YíÚñçÕ? ®ˆZÂŽÕfñ&Ä#FXŽ±i×ø #Š›ggçsx>Ѫøýç±ðTç´ÀhÝm|—O¸l¶ÍÐtk¸‚S(³¸ô¡îp?µ&r¬÷'>Ê SéèfÓNmï· 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(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)55 -b FF(213)150 4633 y(30)97 b(Circle)34 b(Reference)42 +b FF(222)150 4915 y(32)97 b(Circle)34 b(Reference)42 b FD(.)19 b(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h (.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)73 -b FF(229)150 4774 y(31)97 b(P)m(attern)33 b(Reference)j +b FF(238)150 5056 y(33)97 b(P)m(attern)33 b(Reference)j FD(.)20 b(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f (.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)67 -b FF(232)150 4915 y(32)97 b(Solid)33 b(Reference)d FD(.)19 +b FF(242)150 5197 y(34)97 b(Solid)33 b(Reference)d FD(.)19 b(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g (.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)60 -b FF(238)150 5056 y(33)97 b(F)-8 b(aced)33 b(Solid)g(Reference)14 +b FF(248)150 5338 y(35)97 b(F)-8 b(aced)33 b(Solid)g(Reference)14 b FD(.)21 b(.)e(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f -(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)46 b FF(247)150 -5197 y(34)97 b(Cub)s(oid)33 b(Reference)42 b FD(.)20 -b(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f -(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)73 b FF(248)150 -5338 y(35)97 b(P)m(olyhedron)34 b(Reference)17 b FD(.)k(.)f(.)f(.)g(.)h -(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.) -h(.)f(.)g(.)h(.)49 b FF(250)p eop end +(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)46 b FF(257)p +eop end %%Page: -2 4 TeXDict begin -2 3 bop 3696 -116 a FF(ii)150 83 y(36)97 -b(Utilit)m(y)34 b(F)-8 b(unctions)24 b FD(.)c(.)f(.)h(.)f(.)g(.)h(.)f -(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.) -f(.)h(.)f(.)g(.)h(.)56 b FF(261)150 224 y(37)97 b(Adding)33 -b(a)f(File)g FD(.)19 b(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f -(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.) -h(.)63 b FF(263)150 365 y(38)97 b(F)-8 b(uture)33 b(Plans)18 +b(Cub)s(oid)33 b(Reference)42 b FD(.)20 b(.)f(.)g(.)h(.)f(.)h(.)f(.)h +(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.) +g(.)h(.)f(.)73 b FF(258)150 224 y(37)97 b(P)m(olyhedron)34 +b(Reference)17 b FD(.)k(.)f(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f +(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)49 +b FF(260)150 365 y(38)97 b(Utilit)m(y)34 b(F)-8 b(unctions)24 +b FD(.)c(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.) +h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)56 +b FF(271)150 506 y(39)97 b(Adding)33 b(a)f(File)g FD(.)19 +b(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f +(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)63 +b FF(273)150 648 y(40)97 b(F)-8 b(uture)33 b(Plans)18 b FD(.)i(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.) h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)50 -b FF(265)150 506 y(39)97 b(Changes)20 b FD(.)h(.)e(.)h(.)f(.)h(.)f(.)g +b FF(275)150 789 y(41)97 b(Changes)20 b FD(.)h(.)e(.)h(.)f(.)h(.)f(.)g (.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.) -f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)52 b FF(266)150 -648 y(Bibliograph)m(y)24 b FD(.)c(.)g(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f +f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)52 b FF(278)150 +930 y(Bibliograph)m(y)24 b FD(.)c(.)g(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f (.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.) -h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)56 b FF(267)150 789 y(A)122 -b(GNU)32 b(F)-8 b(ree)33 b(Do)s(cumen)m(tation)g(License)d +h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)56 b FF(280)150 1071 +y(A)122 b(GNU)32 b(F)-8 b(ree)33 b(Do)s(cumen)m(tation)g(License)d FD(.)20 b(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f -(.)g(.)61 b FF(269)150 930 y(Data)32 b(T)m(yp)s(e)i(and)e(V)-8 +(.)g(.)61 b FF(282)150 1212 y(Data)32 b(T)m(yp)s(e)i(and)e(V)-8 b(ariable)33 b(Index)18 b FD(.)j(.)e(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.) 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b(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f -(.)h(.)f(.)g(.)h(.)f(.)h(.)82 b FH(84)449 4410 y FI(15.1)92 -b(Global)32 b(V)-8 b(ariables)27 b FC(.)15 b(.)g(.)g(.)g(.)g(.)g(.)g(.) +g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)56 b FI(89)449 +4790 y(16.4)92 b(Mo)s(difying)23 b FC(.)15 b(.)h(.)f(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g -(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)54 -b FI(84)449 4520 y(15.2)92 b(I/O)31 b(F)-8 b(unctions)29 -b FC(.)15 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g -(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) -g(.)g(.)g(.)g(.)g(.)g(.)58 b FI(84)p eop end +(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.) +g(.)52 b FI(89)449 4899 y(16.5)92 b(Sho)m(wing)17 b FC(.)e(.)g(.)g(.)g +(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) +g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g +(.)g(.)g(.)g(.)g(.)g(.)g(.)46 b FI(90)449 5009 y(16.6)92 +b(Querying)20 b FC(.)15 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g +(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) +g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)50 +b FI(90)449 5118 y(16.7)92 b(De\014ning)31 b(and)f(Initializing)i +(Colors)9 b FC(.)15 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g +(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)38 b FI(90)449 +5228 y(16.8)92 b(Namespace)32 b(Colors.)22 b FC(.)15 +b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g +(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) +51 b FI(90)p eop end %%Page: -5 7 -TeXDict begin -5 6 bop 3702 -116 a FI(v)150 83 y FH(16)135 -b(Shap)t(e)44 b(Reference)18 b FD(.)j(.)e(.)h(.)f(.)g(.)h(.)f(.)h(.)f -(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)62 -b FH(85)449 220 y FI(16.1)92 b(Data)32 b(Mem)m(b)s(ers)17 +TeXDict begin -5 6 bop 3702 -116 a FI(v)150 83 y FH(17)135 +b(Input)44 b(and)h(Output)37 b FD(.)20 b(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.) +f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)82 +b FH(92)449 220 y FI(17.1)92 b(Global)32 b(V)-8 b(ariables)27 +b FC(.)15 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g +(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) +h(.)f(.)g(.)g(.)54 b FI(92)449 330 y(17.2)92 b(I/O)31 +b(F)-8 b(unctions)29 b FC(.)15 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) +g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g +(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)58 b FI(92)150 +572 y FH(18)135 b(Shap)t(e)44 b(Reference)18 b FD(.)j(.)e(.)h(.)f(.)g +(.)h(.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.) +f(.)h(.)62 b FH(93)449 709 y FI(18.1)92 b(Data)32 b(Mem)m(b)s(ers)17 b FC(.)e(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g -(.)g(.)h(.)f(.)g(.)g(.)46 b FI(85)449 330 y(16.2)92 b(Op)s(erators)26 +(.)g(.)h(.)f(.)g(.)g(.)46 b FI(93)449 819 y(18.2)92 b(Op)s(erators)26 b FC(.)15 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) -g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)56 b FI(85)449 -439 y(16.3)92 b(Cop)m(ying)18 b FC(.)e(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g +g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)56 b FI(93)449 +928 y(18.3)92 b(Cop)m(ying)18 b FC(.)e(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g -(.)g(.)47 b FI(85)449 549 y(16.4)92 b(Mo)s(difying)23 +(.)g(.)47 b FI(93)449 1038 y(18.4)92 b(Mo)s(difying)23 b FC(.)15 b(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) -g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)52 b FI(85)449 -658 y(16.5)92 b(A\016ne)31 b(T)-8 b(ransformations)26 +g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)52 b FI(93)449 +1147 y(18.5)92 b(A\016ne)31 b(T)-8 b(ransformations)26 b FC(.)15 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)56 -b FI(86)449 768 y(16.6)92 b(Applying)30 b(T)-8 b(ransformations)27 +b FI(94)449 1257 y(18.6)92 b(Applying)30 b(T)-8 b(ransformations)27 b FC(.)15 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)56 -b FI(86)449 878 y(16.7)92 b(Clearing)15 b FC(.)h(.)f(.)g(.)g(.)g(.)g(.) -g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g -(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) -g(.)g(.)h(.)f(.)44 b FI(86)449 987 y(16.8)92 b(Querying)20 +b FI(94)449 1367 y(18.7)92 b(Clearing)15 b FC(.)h(.)f(.)g(.)g(.)g(.)g +(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) 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-FH(17)135 b(T)-11 b(ransform)45 b(Reference)17 b FD(.)j(.)g(.)f(.)g(.)h +g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)50 b FI(94)150 1938 y +FH(19)135 b(T)-11 b(ransform)45 b(Reference)17 b FD(.)j(.)g(.)f(.)g(.)h (.)f(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)62 -b FH(88)449 1586 y FI(17.1)92 b(Data)32 b(Mem)m(b)s(ers)17 +b FH(96)449 2075 y FI(19.1)92 b(Data)32 b(Mem)m(b)s(ers)17 b FC(.)e(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g -(.)g(.)h(.)f(.)g(.)g(.)46 b FI(88)449 1695 y(17.2)92 +(.)g(.)h(.)f(.)g(.)g(.)46 b FI(96)449 2184 y(19.2)92 b(Global)32 b(V)-8 b(ariables)32 b(and)d(Constan)m(ts)c FC(.)15 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g -(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)53 b FI(88)449 1805 y(17.3)92 +(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)53 b FI(96)449 2294 y(19.3)92 b(Constructors)12 b FC(.)j(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)42 b -FI(88)449 1914 y(17.4)92 b(Op)s(erators)26 b FC(.)15 +FI(96)449 2403 y(19.4)92 b(Op)s(erators)26 b FC(.)15 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) -g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)56 b FI(88)449 2024 y(17.5)92 +g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)56 b FI(96)449 2513 y(19.5)92 b(Matrix)32 b(In)m(v)m(ersion)23 b FC(.)15 b(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)52 -b FI(91)449 2134 y(17.6)92 b(Setting)32 b(V)-8 b(alues)26 +b FI(99)449 2623 y(19.6)92 b(Setting)32 b(V)-8 b(alues)26 b FC(.)15 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) -g(.)g(.)g(.)g(.)g(.)g(.)55 b FI(91)449 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-(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) -g(.)g(.)g(.)g(.)g(.)g(.)59 b FI(145)449 4047 y(22.3)92 -b(Constructors)11 b FC(.)k(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g -(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) -g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)41 b FI(145)449 -4157 y(22.4)92 b(Op)s(erators)25 b FC(.)15 b(.)g(.)g(.)g(.)g(.)g(.)g(.) -g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g -(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) -55 b FI(146)449 4266 y(22.5)92 b(Get)32 b(P)m(ath)18 -b FC(.)e(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) -g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g -(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)48 b FI(146)449 -4376 y(22.6)92 b(Sho)m(wing)15 b FC(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g -(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) -g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g -(.)45 b FI(146)p eop end +(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)45 b FI(153)p +eop end %%Page: -7 9 -TeXDict begin -7 8 bop 3652 -116 a FI(vii)150 83 y FH(23)135 -b(Plane)46 b(Reference)27 b FD(.)20 b(.)g(.)f(.)h(.)f(.)h(.)f(.)g(.)h -(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)71 -b FH(148)449 220 y FI(23.1)92 b(Data)32 b(Mem)m(b)s(ers)16 +TeXDict begin -7 8 bop 3652 -116 a FI(vii)150 83 y FH(24)135 +b(Line)45 b(Reference)36 b FD(.)19 b(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.) +h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)78 +b FH(154)449 220 y FI(24.1)92 b(Data)32 b(Mem)m(b)s(ers)16 b FC(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g -(.)g(.)g(.)g(.)g(.)46 b FI(148)449 330 y(23.2)92 b(Global)32 +(.)g(.)g(.)g(.)g(.)46 b FI(154)449 330 y(24.2)92 b(Global)32 b(Constan)m(ts)d FC(.)15 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b(Rectangles)10 +(.)g(.)g(.)g(.)43 b FI(235)449 3769 y(31.11)93 b(Rectangles)10 b FC(.)17 b(.)e(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) -g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)39 b FI(227)150 3194 -y FH(30)135 b(Circle)46 b(Reference)18 b FD(.)j(.)e(.)h(.)f(.)h(.)f(.)h +g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)39 b FI(236)150 4012 +y FH(32)135 b(Circle)46 b(Reference)18 b FD(.)j(.)e(.)h(.)f(.)h(.)f(.)h (.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)63 -b FH(229)449 3331 y FI(30.1)92 b(Data)32 b(Mem)m(b)s(ers)16 +b FH(238)449 4149 y FI(32.1)92 b(Data)32 b(Mem)m(b)s(ers)16 b FC(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g -(.)g(.)g(.)g(.)g(.)46 b FI(229)449 3440 y(30.2)92 b(Constructors)30 +(.)g(.)g(.)g(.)g(.)46 b FI(238)449 4258 y(32.2)92 b(Constructors)30 b(and)g(Setting)h(F)-8 b(unctions)10 b FC(.)16 b(.)f(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)40 -b FI(229)449 3550 y(30.3)92 b(Op)s(erators)25 b FC(.)15 +b FI(238)449 4368 y(32.3)92 b(Op)s(erators)25 b FC(.)15 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h (.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) -g(.)g(.)g(.)g(.)g(.)g(.)g(.)55 b FI(229)449 3660 y(30.4)92 +g(.)g(.)g(.)g(.)g(.)g(.)g(.)55 b FI(238)449 4477 y(32.4)92 b(Querying)19 b FC(.)c(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)49 -b FI(230)449 3769 y(30.5)92 b(In)m(tersections)16 b FC(.)h(.)e(.)g(.)g +b FI(239)449 4587 y(32.5)92 b(In)m(tersections)16 b FC(.)h(.)e(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.) f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g -(.)g(.)46 b FI(231)150 4012 y FH(31)135 b(P)l(attern)46 +(.)g(.)46 b FI(240)150 4829 y FH(33)135 b(P)l(attern)46 b(Reference)32 b FD(.)19 b(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h -(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)74 b FH(232)449 -4149 y FI(31.1)92 b(Plane)31 b(T)-8 b(esselations)11 +(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)74 b FH(242)449 +4966 y FI(33.1)92 b(Plane)31 b(T)-8 b(esselations)11 b FC(.)17 b(.)e(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.) -g(.)g(.)40 b FI(232)449 4258 y(31.2)92 b(Roulettes)32 +g(.)g(.)40 b FI(242)449 5076 y(33.2)92 b(Roulettes)32 b(and)e(In)m(v)m(olutes)11 b FC(.)16 b(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)h (.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) -g(.)g(.)g(.)g(.)41 b FI(234)748 4368 y(31.2.1)93 b(Epicycloids)8 +g(.)g(.)g(.)g(.)41 b FI(244)748 5186 y(33.2.1)93 b(Epicycloids)8 b FC(.)16 b(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h (.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) -38 b FI(235)p eop end +38 b FI(245)p eop end %%Page: -9 11 -TeXDict begin -9 10 bop 3677 -116 a FI(ix)150 83 y FH(32)135 +TeXDict begin -9 10 bop 3677 -116 a FI(ix)150 83 y FH(34)135 b(Solid)45 b(Reference)16 b FD(.)21 b(.)e(.)g(.)h(.)f(.)h(.)f(.)h(.)f (.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)60 -b FH(238)449 220 y FI(32.1)92 b(Data)32 b(Mem)m(b)s(ers)16 +b FH(248)449 220 y FI(34.1)92 b(Data)32 b(Mem)m(b)s(ers)16 b FC(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g -(.)g(.)g(.)g(.)g(.)46 b FI(238)449 330 y(32.2)92 b(Constructors)30 +(.)g(.)g(.)g(.)g(.)46 b FI(248)449 330 y(34.2)92 b(Constructors)30 b(and)g(Setting)h(F)-8 b(unctions)10 b FC(.)16 b(.)f(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)40 -b FI(238)449 439 y(32.3)92 b(Destructor)12 b FC(.)k(.)f(.)g(.)g(.)g(.)g +b FI(248)449 439 y(34.3)92 b(Destructor)12 b FC(.)k(.)f(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g -(.)g(.)42 b FI(239)449 549 y(32.4)92 b(Op)s(erators)25 +(.)g(.)42 b FI(249)449 549 y(34.4)92 b(Op)s(erators)25 b FC(.)15 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g (.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) -g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)55 b FI(239)449 658 -y(32.5)92 b(Cop)m(ying)17 b FC(.)e(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g +g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)55 b FI(249)449 658 +y(34.5)92 b(Cop)m(ying)17 b FC(.)e(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)46 -b FI(239)449 768 y(32.6)92 b(Setting)32 b(Mem)m(b)s(ers)15 +b FI(249)449 768 y(34.6)92 b(Setting)32 b(Mem)m(b)s(ers)15 b FC(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g -(.)g(.)g(.)45 b FI(239)449 878 y(32.7)92 b(Querying)19 +(.)g(.)g(.)45 b FI(249)449 878 y(34.7)92 b(Querying)19 b FC(.)c(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g -(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)49 b FI(239)449 -987 y(32.8)92 b(Returning)30 b(Elemen)m(ts)h(and)f(Information)c +(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)49 b FI(250)449 +987 y(34.8)92 b(Returning)30 b(Elemen)m(ts)h(and)f(Information)c FC(.)15 b(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g -(.)g(.)56 b FI(240)748 1097 y(Getting)32 b(Shap)s(e)d(Cen)m(ters)f +(.)g(.)56 b FI(250)748 1097 y(Getting)32 b(Shap)s(e)d(Cen)m(ters)f FC(.)15 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)57 -b FI(240)748 1206 y(Getting)32 b(Shap)s(es)23 b FC(.)15 +b FI(250)748 1206 y(Getting)32 b(Shap)s(es)23 b FC(.)15 b(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) -g(.)55 b FI(241)449 1316 y(32.9)92 b(Sho)m(wing)15 b +g(.)55 b FI(251)449 1316 y(34.9)92 b(Sho)m(wing)15 b FC(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.) -g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)45 b FI(243)449 -1425 y(32.10)93 b(A\016ne)30 b(T)-8 b(ransformations)24 +g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)45 b FI(253)449 +1425 y(34.10)93 b(A\016ne)30 b(T)-8 b(ransformations)24 b FC(.)15 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)54 -b FI(243)449 1535 y(32.11)93 b(Applying)30 b(T)-8 b(ransformations)24 +b FI(253)449 1535 y(34.11)93 b(Applying)30 b(T)-8 b(ransformations)24 b FC(.)15 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g -(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)54 b FI(243)449 -1645 y(32.12)93 b(Outputting)19 b FC(.)c(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) +(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)54 b FI(254)449 +1645 y(34.12)93 b(Outputting)19 b FC(.)c(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h (.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)49 -b FI(243)449 1754 y(32.13)93 b(Dra)m(wing)31 b(and)f(Filling)17 +b FI(254)449 1754 y(34.13)93 b(Dra)m(wing)31 b(and)f(Filling)17 b FC(.)f(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)47 -b FI(244)449 1864 y(32.14)93 b(Clearing)13 b FC(.)i(.)g(.)g(.)g(.)g(.)g +b FI(255)449 1864 y(34.14)93 b(Clearing)13 b FC(.)i(.)g(.)g(.)g(.)g(.)g (.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g -(.)g(.)h(.)42 b FI(246)150 2106 y FH(33)135 b(F)-11 b(aced)44 +(.)g(.)h(.)42 b FI(256)150 2106 y FH(35)135 b(F)-11 b(aced)44 b(Solid)i(Reference)13 b FD(.)21 b(.)e(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g -(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)57 b FH(247)449 2243 -y FI(33.1)92 b(Data)32 b(Mem)m(b)s(ers)16 b FC(.)f(.)g(.)g(.)g(.)g(.)g +(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)57 b FH(257)449 2243 +y FI(35.1)92 b(Data)32 b(Mem)m(b)s(ers)16 b FC(.)f(.)g(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)46 -b FI(247)150 2486 y FH(34)135 b(Cub)t(oid)44 b(Reference)e +b FI(257)150 2486 y FH(36)135 b(Cub)t(oid)44 b(Reference)e FD(.)19 b(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.)h -(.)f(.)h(.)f(.)g(.)h(.)84 b FH(248)449 2623 y FI(34.1)92 +(.)f(.)h(.)f(.)g(.)h(.)84 b FH(258)449 2623 y FI(36.1)92 b(Data)32 b(Mem)m(b)s(ers)16 b 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b(Data)32 b(Mem)m(b)s(ers)16 b FC(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) -g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)46 b FI(250)449 3331 -y(35.2)92 b(Regular)31 b(Platonic)h(P)m(olyhedra)18 b +g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)46 b FI(260)449 3331 +y(37.2)92 b(Regular)31 b(Platonic)h(P)m(olyhedra)18 b FC(.)e(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g -(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)48 b FI(250)748 -3440 y(35.2.1)93 b(T)-8 b(etrahedron)10 b FC(.)15 b(.)g(.)g(.)g(.)g(.)g +(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)48 b FI(260)748 +3440 y(37.2.1)93 b(T)-8 b(etrahedron)10 b FC(.)15 b(.)g(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) -g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)40 b FI(250)1047 -3550 y(35.2.1.1)94 b(Data)32 b(Mem)m(b)s(ers)12 b FC(.)j(.)g(.)g(.)g(.) +g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)40 b FI(260)1047 +3550 y(37.2.1.1)94 b(Data)32 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FC(.)j(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) -g(.)g(.)g(.)g(.)g(.)42 b FI(254)1047 4098 y(35.2.2.2)94 +g(.)g(.)g(.)g(.)g(.)42 b FI(264)1047 4098 y(37.2.2.2)94 b(Constructors)29 b(and)h(Setting)h(F)-8 b(unctions)29 -b FC(.)15 b(.)57 b FI(254)1047 4208 y(35.2.2.3)94 b(Net)19 +b FC(.)15 b(.)57 b FI(264)1047 4208 y(37.2.2.3)94 b(Net)19 b FC(.)c(.)h(.)f(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)49 -b FI(255)748 4317 y(35.2.3)93 b(Icosahedron)18 b FC(.)d(.)g(.)g(.)g(.)g +b FI(265)748 4317 y(37.2.3)93 b(Icosahedron)18 b FC(.)d(.)g(.)g(.)g(.)g (.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.) -g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)47 b FI(256)1047 -4427 y(35.2.3.1)94 b(Data)32 b(Mem)m(b)s(ers)12 b FC(.)j(.)g(.)g(.)g(.) +g(.)g(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)47 b FI(266)1047 +4427 y(37.2.3.1)94 b(Data)32 b(Mem)m(b)s(ers)12 b FC(.)j(.)g(.)g(.)g(.) 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Fo(.)j(.)f(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.) g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)36 -b Fr(53)2025 2927 y FH(P)2025 3045 y Fr(pain)n(ter's)26 +b Fr(54)2025 4870 y FH(P)2025 4987 y Fr(pain)n(ter's)26 b(algorithm)8 b Fo(.)13 b(.)g(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f (.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)33 -b Fr(67)2025 3133 y(P)n(ath)25 b(connectors)c Fo(.)13 -b(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f -(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)46 b Fr(72)2025 -3221 y(P)n(ath)25 b(in)n(tersections)7 b Fo(.)14 b(.)e(.)g(.)h(.)f(.)g +b Fr(68)2025 5076 y(patc)n(hes)19 b Fo(.)13 b(.)f(.)g(.)g(.)h(.)f(.)g (.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.) -g(.)h(.)f(.)g(.)33 b Fr(72)2025 3310 y(paths)17 b Fo(.)12 -b(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h -(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.) -g(.)h(.)f(.)43 b Fr(27)2025 3398 y(p)r(en)25 b(expression)8 -b Fo(.)k(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.) -h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)34 -b Fr(135)2025 3486 y(p)r(ens)15 b Fo(.)d(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.) -h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f -(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)41 -b Fr(23)2025 3574 y Fs(Points)p Fr(,)27 b(connecting)7 -b Fo(.)13 b(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g -(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)32 b Fr(23)2025 -3829 y FH(R)2025 3947 y Fr(ra)n(w)26 b(MetaP)n(ost)h(co)r(de)c -Fo(.)12 b(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f -(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)48 b Fr(57)2025 -4035 y(R)n(GB)25 b(\(red-green-blue\))15 b Fo(.)d(.)g(.)h(.)f(.)g(.)h -(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.) -41 b Fr(80)2025 4294 y FH(S)2025 4412 y Fr(surface)27 -b(hiding)20 b Fo(.)12 b(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g -(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.) -46 b Fr(67)2025 4500 y(sym)n(b)r(ols)13 b Fo(.)f(.)h(.)f(.)g(.)h(.)f(.) -g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h -(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)39 -b Fr(4)2025 4588 y(system)25 b(dep)r(endencies)17 b Fo(.)c(.)f(.)g(.)h +g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)46 b Fr(276)2025 +5164 y(P)n(ath)25 b(connectors)c Fo(.)13 b(.)f(.)g(.)g(.)h(.)f(.)g(.)h +(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.) +h(.)f(.)g(.)46 b Fr(73)2025 5252 y(P)n(ath)25 b(in)n(tersections)7 +b Fo(.)14 b(.)e(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h +(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)33 b Fr(73)2025 +5340 y(paths)17 b Fo(.)12 b(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h +(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.) +h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)43 b Fr(28)p eop +end +%%Page: 296 308 +TeXDict begin 296 307 bop 150 -116 a FI(Concept)31 b(Index)2882 +b(296)150 299 y Fr(p)r(en)25 b(expression)8 b Fo(.)13 +b(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f +(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)33 b Fr(144)150 +389 y(p)r(ens)15 b Fo(.)d(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h (.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.) -h(.)f(.)g(.)43 b Fr(78)2025 4843 y FH(T)2025 4961 y Fr(tension)8 +h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)40 b Fr(24)150 +480 y(PNG)26 b(\(P)n(ortable)g(Net)n(w)n(ork)g(Graphics\))9 +b Fo(.)j(.)35 b Fr(4,)27 b(77,)f(79,)h(278)150 570 y +Fs(Points)p Fr(,)g(connecting)7 b Fo(.)13 b(.)f(.)g(.)h(.)f(.)g(.)h(.)f +(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.) +h(.)32 b Fr(24)150 661 y(P)n(ortable)27 b(Net)n(w)n(ork)e(Graphics)h +(\(PNG\))9 b Fo(.)j(.)35 b Fr(4,)27 b(77,)f(79,)h(278)150 +751 y(P)n(ostScript)f(\(PS\))12 b Fo(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.) +h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)38 +b Fr(4,)27 b(77,)f(79)150 842 y(P)n(ostScript,)g(structured)21 +b Fo(.)12 b(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f +(.)g(.)g(.)h(.)47 b Fr(77,)26 b(79)150 932 y(pro)t(jectiv)n(e)g(in)n(v) +l(ariance)15 b Fo(.)f(.)e(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g +(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)41 b Fr(276)150 +1023 y(PS)26 b(\(P)n(ostScript\))12 b Fo(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.) +g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)38 +b Fr(4,)27 b(77,)f(79)150 1293 y FH(R)150 1416 y Fr(ra)n(w)g(MetaP)n +(ost)h(co)r(de)c Fo(.)13 b(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f +(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)48 +b Fr(58)150 1507 y(re\015ections)12 b Fo(.)h(.)f(.)h(.)f(.)g(.)h(.)f(.) +g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h +(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)38 b Fr(276)150 1597 +y(R)n(GB)26 b(\(red-green-blue\))15 b Fo(.)c(.)i(.)f(.)g(.)g(.)h(.)f(.) +g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)41 +b Fr(88)150 1868 y FH(S)150 1991 y Fr(shading)16 b Fo(.)d(.)f(.)h(.)f +(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.) +h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)42 +b Fr(276)2025 299 y(shado)n(ws)6 b Fo(.)14 b(.)e(.)g(.)g(.)h(.)f(.)g(.) +h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g +(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)33 b Fr(276)2025 +386 y(spline)26 b(curv)n(es)21 b Fo(.)12 b(.)g(.)h(.)f(.)g(.)h(.)f(.)g +(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.) +g(.)h(.)f(.)g(.)h(.)47 b Fr(276)2025 473 y(splines)15 +b Fo(.)e(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.) +f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g +(.)h(.)f(.)41 b Fr(276)2025 561 y(structured)25 b(P)n(ostScript)14 +b Fo(.)e(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.) +f(.)g(.)h(.)f(.)39 b Fr(77,)27 b(79)2025 648 y(surface)g(hiding)20 +b Fo(.)12 b(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g +(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)46 +b Fr(68)2025 735 y(surface)27 b(patc)n(hes)17 b Fo(.)12 +b(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h +(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)43 b Fr(276)2025 +822 y(sym)n(b)r(ols)13 b Fo(.)f(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h +(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.) +g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)39 b Fr(4)2025 910 +y(system)25 b(dep)r(endencies)17 b Fo(.)c(.)f(.)g(.)h(.)f(.)g(.)h(.)f +(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)43 +b Fr(82)2025 1159 y FH(T)2025 1276 y Fr(template)26 b(functions)14 +b Fo(.)f(.)f(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.) +f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)40 b Fr(74)2025 +1363 y(templates)20 b Fo(.)12 b(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g +(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.) +g(.)h(.)f(.)g(.)h(.)f(.)45 b Fr(74)2025 1450 y(tension)8 b Fo(.)k(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.) g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h -(.)f(.)g(.)h(.)33 b Fr(27)2025 5049 y(theory)25 b(of)h(in)n(tersection) +(.)f(.)g(.)h(.)33 b Fr(28)2025 1537 y(theory)25 b(of)h(in)n(tersection) f Fo(.)12 b(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g -(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)50 b Fr(72)2025 5137 y(TO)26 +(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)50 b Fr(73)2025 1625 y(TO)26 b(DO)8 b Fo(.)k(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g (.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.) -f(.)34 b Fr(57,)27 b(79)2025 5392 y FH(U)2025 5510 y +f(.)34 b Fr(58,)27 b(83)2025 1874 y FH(U)2025 1991 y Fr(units)e(of)i(measuremen)n(t)20 b Fo(.)13 b(.)f(.)g(.)h(.)f(.)g(.)h (.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)h(.)f(.)g(.)g(.)h(.)46 b Fr(10)p eop end diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.texi 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.texi --- 3DLDF-1.1.4/DOC/TEXINFO/3DLDF.texi 2003-12-10 18:05:14.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.texi 2004-01-16 18:09:46.000000000 +0100 @@ -1,11 +1,11 @@ %%%% 3DLDF.texi - + %% This file is part of the 3DLDF User and Reference Manual. -%% Copyright (C) 2003 Laurence D. Finston +%% Copyright (C) 2003, 2004 Laurence D. Finston %% See the section "GNU Free Documentation License" in the file %% fdl.texi for copying conditions. -%%%% $Id: 3DLDF.texi,v 1.9 2003/12/10 17:05:14 lfinsto1 Exp $ +%%%% $Id: 3DLDF.texi,v 1.18 2004/01/16 17:09:21 lfinsto1 Exp lfinsto1 $ %%%% LDF 2002.11.16. I hope doing this before I load texinfo.tex doesn't cause a problem. @@ -245,16 +245,7 @@ \vskip\parskip \vbox{\centerline{\epsffile{% %% -%% Uncomment the line for the directory you want, -%% depending on which version you're using, unless the EPS files are in -%% the same directory as this file, in which they should all be -%% commented-out. -%% -%../LINUX_GCC_2_95/% -%../LINUX_GCC_3_3/% -%../DEC/% -%../BSD/% -./EPS/% +./graphics/eps/% 3DLDFmp.\the\figcnt}}\nobreak \centerline{Figure \the\figcnt.}}% %% @@ -333,10 +324,10 @@ @c %**end of header -@set EDITION 1.1.4 -@set VERSION 1.1.4 -@set UPDATED 10 December 2003 -@set UPDATE-MONTH December 2003 +@set EDITION 1.1.5.1 +@set VERSION 1.1.5.1 +@set UPDATED 16 January 2004 +@set UPDATE-MONTH January 2004 @c ********************* @@ -349,7 +340,7 @@ output. The author is Laurence D. Finston. -Copyright @copyright{} 2003 Laurence D. Finston. +Copyright @copyright{} 2003, 2004 Laurence D. Finston. @quotation Permission is granted to copy, distribute and/or modify this document @@ -412,12 +403,10 @@ @ifnottex @insertcopying -Please note that the figures cannot be shown in the Info or HTML output -formats! +Please note that the figures cannot be shown in the Info output +format. @end ifnottex - - @menu * Introduction:: * Contributing to 3DLDF:: @@ -434,6 +423,8 @@ * Installing and Running 3DLDF:: * Typedefs and Utility Structures:: * Global Constants and Variables:: +* Dynamic Allocation of Shapes:: +* System Information:: * Color Reference:: * Input and Output:: * Shape Reference:: @@ -466,8 +457,7 @@ * Function Index:: * Concept Index:: -@detailmenu ---- The Detailed Node Listing --- +@detailmenu --- The Detailed Node Listing --- Introduction @@ -488,15 +478,83 @@ * Accuracy:: * No Input Routine:: +Points + +* Declaring and Initializing Points:: +* Setting and Assigning to Points:: +* Shifting Points:: +* Scaling Points:: +* Shearing Points:: +* Rotating Points:: + +Transforms + +* Applying Transforms to Points Intro:: +* Inverting Transforms:: + +Drawing and Labeling Points + +* Drawing Points Intro:: +* Labeling Points Intro:: + +Paths + +* Declaring and Initializing Paths:: +* Drawing and Filling Paths Intro:: + +Plane Figures + +* Regular Polygons Getstart:: +* Rectangles Getstart:: +* Ellipses Getstart:: +* Circles Getstart:: + +Solid Figures + +* Cuboid Getstart:: +* Polyhedron Getstart:: + +Polyhedron + +* Tetrahedron Getstart:: +* Dodecahedron Getstart:: +* Icosahedron Getstart:: + +Pictures + +* Projections:: +* Focuses Getstart:: +* Surface Hiding:: + +Projections + +* Parallel Projections:: +* The Perspective Projection:: + Installing and Running 3DLDF * Installing 3DLDF:: * Running 3DLDF:: +Installing 3DLDF + +* Template Functions:: + Running 3DLDF +* Converting EPS Files:: * Command Line Arguments:: +Converting EPS Files + +* Converting EPS Files ELISP:: + +System Information + +* Endianness:: +* Register Width:: +* Get Second Largest Real:: + Color Reference * Color Data Members:: @@ -684,6 +742,7 @@ * Affine Transformations for Ellipses:: * Querying Ellipses:: * Returning Elements and Information for Ellipses:: +* Ellipse Intersections:: * Solving Ellipses:: * Rectangles for Ellipses:: @@ -768,21 +827,37 @@ Semi-Regular Archimedean Polyhedra -* Truncated Octahedron:: +* Truncated Octahedron:: -Truncated Octahedron +Truncated Octahedron * Truncated Octahedron Data Members:: -* Truncated Octahedron Net:: +* Truncated Octahedron Constructors and Setting Functions:: +* Truncated Octahedron Net:: Utility Functions * Perspective Functions:: +Future Plans + +* Geometry:: +* Curves and Surfaces:: +* Shadows:: +* Multi-Threading:: + +Changes + +* Changes in 3DLDF 1.1.5.1:: +* Changes in 3DLDF 1.1.5:: +* Changes in 3DLDF 1.1.4.2:: +* Changes in 3DLDF 1.1.4.1:: +* Changes in 3DLDF 1.1.4:: +* Initial version:: + @end detailmenu @end menu - @macro bibskip {} @iftex @tex @@ -843,14 +918,20 @@ @c UBAR is only used in code written to examples.web. There's no need @c for versions for it for Info or HTML. LDF 2003.12.07. @c -@macro UBAR {} +@c +@c @iftex @tex -$@noexpand@@underline{@noexpand@@hbox to 1ex{@noexpand@@hfil}}$ +\gdef\UBAR{$\noexpand\\underline{\noexpand\\hbox to 1ex% + {\noexpand\\hfil}}$} @end tex @end iftex +@ifnottex +@macro UBAR {} +_@c @end macro - +@end ifnottex + @macro NEXTFIG {} @iftex @tex @@ -1028,6 +1109,8 @@ @include intro.texi + + @include contrib.texi @c @c Got rid of getstart.texi, because it confuses Emacs and makeinfo @@ -1073,6 +1156,10 @@ @include glbcnvar.texi +@include creatnew.texi + +@include system.texi + @include color.texi @include io.texi @@ -1110,7 +1197,7 @@ @include pattern.texi @include solid.texi - + @include solfaced.texi @include cuboid.texi @@ -1126,7 +1213,7 @@ @include changes.texi @include biblio.texi - + @iftex @tex \ifdoepsf diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/ChangeLog 3DLDF-1.1.5.1/DOC/TEXINFO/ChangeLog --- 3DLDF-1.1.4/DOC/TEXINFO/ChangeLog 2003-12-10 18:34:38.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/ChangeLog 2004-01-16 18:57:28.000000000 +0100 @@ -1,3 +1,185 @@ +2004-01-16 Laurence Finston + + * Makefile.am: LDF 2004.01.16. + Added `3DLDF.pdf' to `EXTRA_DIST'. + + * 3DLDF.texi: LDF 2004.01.16. + Changed `EDITION' and `VERSION' to 1.1.5.1. Changed `UPDATED' to today's date. + + * Makefile.am: LDF 2004.01.16. + Changed release number to 1.1.5.1. + + * Makefile.am: LDF 2004.01.16. + Changed names of PNG files. This was necessary, because I couldn't write + some of the files with the old names to a CD-R, namely the ones with more than one + digit in the numerical part of their names. + + Changed the order of the `.texi' files in `3dldf_TEXINFOS'. They are now no longer + ordered alphabetically. Instead, they are in the order of their inclusion in + `3DLDF.texi'. + + Added missing `.texi' files to `3dldf_TEXINFOS'. + + * instlrun.texi: LDF 2004.01.16. + Updated copyright date. + Changed names of included PNG files. This was necessary, because I couldn't + some of the files with the old names to a CD-R, namely the ones with more than one + digit in the numerical part of their names. + + * gstransf.texi, gspoint.texi, gsplane.texi, gspaths.texi: + LDF 2004.01.16. + Updated copyright date. Deleted unneeded comment. + + * getstart.texi: LDF 2004.01.16. + No longer using this file. + +2004-01-14 Laurence Finston + + * future.texi: LDF 2004.01.14. + Added text about rendering. + + * changes.texi: LDF 2004.01.14. + Added items for release 1.1.5. + + * 3DLDF.texi: LDF 2004.01.14. + Release 1.1.5. + + * ellipse.texi: LDF 2004.01.14. + Changed the description of |intersection_points()| with an |Ellipse| argument. + Documented the new |step| argument. Corrected an error: |verbose| was erroneously + said to be |const|. + + * Makefile.am: LDF 2004.01.14. + Added the variables `3dldf_EPS' and `3dldf_PNG'. They contain the + EPS and PNG files for the illustrations in the Texinfo documentation. + The variables are used in `EXTRA_DIST'. + + Added phony `show' target. + +2004-01-12 Laurence Finston + + * Makefile.am: LDF 2004.01.12. + Changed version number from `1.1.4' to `1.1.5'. + + Changed copyright date from ``2003'' to ``2003, 2004''. + + * varidx.texi, utility.texi, using.texi, typeglb.texi, transfor.texi, system.texi, solid.texi, solfaced.texi, shape.texi, regpolyg.texi, rectang.texi, rcpcurve.texi, polyhed.texi, polygon.texi, point.texi, plane.texi, picture.texi, pattern.texi, path.texi, line.texi, label.texi, io.texi, intro.texi, intersct.texi, instlrun.texi, gstransf.texi, gstranpt.texi, gssolfig.texi, gspoint.texi, gsplane.texi, gspict.texi, gspaths.texi, gsdlpt.texi, glbcnvar.texi, getstart.texi, future.texi, funcidx.texi, focus.texi, ellipse.texi, ellipint.texi, cuboid.texi, creatnew.texi, contrib.texi, color.texi, circle.texi, changes.texi, biblio.texi, addfile.texi, 3DLDF.texi: + LDF 2004.01.12. + Edition 1.1.5 for 3DLDF Release 1.1.5. + +2004-01-02 Laurence Finston + + * creatnew.texi: LDF 2004.1.2. + Initial version. + This file contains the description of + |template C* create_new()|. + + * system.texi, creatnew.texi: New file. + +2003-12-23 Laurence Finston + + * 3DLDF.texi: LDF 2003.12.23. + Minor correction. + +2003-12-19 Laurence Finston + + * changes.texi: LDF 2003.12.19. + Added text for changes in editions 1.1.4.1 and 1.1.4.2. + + * intro.texi: LDF 2003.12.19. + Changed `@url' to `@uref' in one place. + + * 3DLDF.texi: LDF 2003.12.19. + Changed the edition number to 1.1.4.2. + + * intro.texi: LDF 2003.12.19. + Changed what I said about this manual being designed for printing + only. It now works to generate Info and HTML output. + + * 3DLDF.texi: LDF 2003.12.19. + Changed what I said about the illustrations not being available in + the HTML output format. They are now. + +2003-12-16 Laurence Finston + + * 3DLDF.texi: LDF 2003.12.16. + Changed `UPDATED'. + + * 3DLDF.texi: LDF 2003.12.16. + Changed `EDITION' to `1.1.4.1'. + The difference is, that I've added `@ifhtml' and `@ifinfo' code for the + illustrations. + + PNG files are included in the HTML output. They are of the correct size and + use the same fonts as in the TeX output, i.e., Computer Modern. It wasn't + easy to get this to work! + + Graphics are not displayed in Info output. Instead, text indicates that + ``Fig. X'' is not displayed. + + + I've put the figure numbers for HTML and Info output into the Texinfo files + explicitly using Emacs-Lisp. These numbers are also used to identify the PNG + files. This isn't necessary in the TeX output, because I can use `\figcnt'. + The HTML and Info formats currently don't support incrementing numerical + variables. + + * add_figure_code.el: New file. + + * regpolyg.texi, utility.texi, polyhed.texi: LDF 2003.12.16. + Added `@ifhtml' and `@ififno' code for the figures. + + * cuboid.texi: LDF 2003.12.16. + Added `@ifhtml' and `@ififno' code for the figures. + + Put the TeX code for the figure in an `@iftex' environment. I missed this file, + when I did it for the others. + + * solid.texi, pattern.texi, circle.texi, ellipse.texi, rcpcurve.texi, rectang.texi, polygon.texi, path.texi, plane.texi, line.texi: + LDF 2003.12.16. + Added `@ifhtml' and `@ififno' code for the figures. + + * gspict.texi: LDF 2003.12.16. + Removed a `\smallskip' from after `\PEX', so that it doesn't interfere with the + Emacs-Lisp routine I'm using to insert the figure numbers for HTML and Info + output. + + * point.texi, picture.texi, label.texi, transfor.texi, instlrun.texi, gspaths.texi, gsplane.texi, gssolfig.texi, gspict.texi, gsdlpt.texi, gstranpt.texi: + LDF 2003.12.16. + Added `@ifhtml' and `@ififno' code for the figures. + +2003-12-15 Laurence Finston + + * using.texi: New file. + + * point.texi: LDF 2003.12.15. + Changed a call to `@UBAR', which I've redefined in `3DLDF.texi'. + + * picture.texi: LDF 2003.12.15. + Changed two calls to `@UBAR', which I've redefined in `3DLDF.texi'. + + * 3DLDF.texi: LDF 2003.12.15. + Redefined `@UBAR'. The old version caused errors. It's not usually + used, because it only occurs in code written to `examples.web'. + It used to work; it probably works with a different version of + Texinfo. I don't care enough to try to find out, though. + +2003-12-14 Laurence Finston + + * examples.complete.web: LDF 2003.12.14. + This file contains all of the examples generated by running + `tex 3DLDF.texi'. + + This version is for 3DLDF 1.1.4, and Edition 1.1.4 of the _3DLDF User + and Reference Manual_. + + * examples.complete.web: New file. + + * gstranpt.texi: LDF 2003.12.14. + First revision following release of Edition 1.1.4. + + Corrected a typo. + 2003-12-10 Laurence Finston * changes.texi: LDF 2003.12.10. @@ -501,7 +683,7 @@ * intro.texi: LDF 2003.11.28. Minor changes to comments at beginning of file. - * intro.texi, intro.bak, intersct.texi, instlrun.texi, gstransf.texi, gstranpt.texi, gssolfig.texi, gspoint.texi, gsplane.texi, gspict.texi, gspaths.texi, gsdlpt.texi, getstart.texi, future.texi, funcidx.texi, focus.texi: + * intro.texi, intersct.texi, instlrun.texi, gstransf.texi, gstranpt.texi, gssolfig.texi, gspoint.texi, gsplane.texi, gspict.texi, gspaths.texi, gsdlpt.texi, getstart.texi, future.texi, funcidx.texi, focus.texi: New file. * ellipse.texi: diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/Makefile.am 3DLDF-1.1.5.1/DOC/TEXINFO/Makefile.am --- 3DLDF-1.1.4/DOC/TEXINFO/Makefile.am 2003-12-10 18:03:26.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/Makefile.am 2004-01-16 19:17:17.000000000 +0100 @@ -1,9 +1,9 @@ -## 3DLDF-1.1.4/DOC/TEXINFO/Makefile.am +## 3DLDF-1.1.5.1/DOC/TEXINFO/Makefile.am ## Makefile for the DOC/TEXINFO subdirectory of the 3DLDF package. # This file is part of 3DLDF, a package for three-dimensional drawing. -# Copyright (C) 2003 Laurence D. Finston. +# Copyright (C) 2003, 2004 Laurence D. Finston. # 3DLDF is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by @@ -31,25 +31,65 @@ -# $Id: Makefile.am,v 1.8 2003/12/10 17:03:26 lfinsto1 Exp $ +# $Id: Makefile.am,v 1.13 2004/01/16 17:56:59 lfinsto1 Exp $ ## Process this file with automake to produce Makefile.in. info_TEXINFOS = 3DLDF.texi -3dldf_TEXINFOS = addfile.texi biblio.texi changes.texi circle.texi color.texi \ - concidx.texi contrib.texi cuboid.texi dataidx.texi \ - ellipse.texi fdl.texi focus.texi funcidx.texi future.texi \ - glbcnvar.texi \ - gsdlpt.texi gspaths.texi gspict.texi gsplane.texi gspoint.texi \ - gssolfig.texi gstranpt.texi gstransf.texi instlrun.texi \ - intersct.texi intro.texi io.texi label.texi line.texi path.texi \ - pattern.texi picture.texi plane.texi point.texi polygon.texi \ - polyhed.texi rcpcurve.texi rectang.texi regpolyg.texi shape.texi solfaced.texi \ - solid.texi transfor.texi typeglb.texi utility.texi varidx.texi - +3dldf_TEXINFOS = intro.texi contrib.texi using.texi gspoint.texi gstranpt.texi \ + gstransf.texi gsdlpt.texi gspaths.texi gsplane.texi gssolfig.texi \ + gspict.texi intersct.texi instlrun.texi typeglb.texi glbcnvar.texi \ + creatnew.texi system.texi color.texi io.texi shape.texi transfor.texi \ + label.texi picture.texi point.texi focus.texi line.texi plane.texi \ + path.texi polygon.texi regpolyg.texi rectang.texi rcpcurve.texi \ + ellipse.texi circle.texi pattern.texi solid.texi solfaced.texi \ + cuboid.texi polyhed.texi utility.texi addfile.texi future.texi \ + changes.texi biblio.texi fdl.texi varidx.texi funcidx.texi \ + concidx.texi + +3dldf_EPS = $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.1 \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.2 \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.3 \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.4 \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.5 \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.6 \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.7 \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.8 \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.9 \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.1? \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.2? \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.3? \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.4? \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.5? \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.6? \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.7? \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.8? \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.9? \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.1?? + +3dldf_PNG = $(GRAPHICSDIR)/$(PNGDIR)/3DLDF1.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF2.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF3.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF4.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF5.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF6.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF7.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF8.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF9.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF1?.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF2?.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF3?.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF4?.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF5?.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF6?.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF7?.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF8?.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF9?.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF1??.png EXTRA_DIST = .rcsfreeze.log .rcsfreeze.log.dev 3DLDF.ps \ - ChangeLog.dev $(3dldf_TEXINFOS) EPS/* + ChangeLog.dev $(3dldf_TEXINFOS) \ + $(3dldf_EPS) $(3dldf_PNG) 3DLDF.pdf .PHONY : dummy dummy: @@ -88,6 +128,18 @@ etags $(info_TEXINFOS) $(3dldf_TEXINFOS) +.PHONY : show +show: + @echo "GRAPHICSDIR: $(GRAPHICSDIR)" + @echo "EPSDIR: $(EPSDIR)" + @echo "PNGDIR: $(PNGDIR)" + @echo "CURDIR: $(CURDIR)" + @echo "3dldf_PNG: $(3dldf_PNG)" + @echo "3dldf_EPS: $(3dldf_EPS)" + + + + ## Local Variables: ## mode:Makefile ## End: diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/Makefile.in 3DLDF-1.1.5.1/DOC/TEXINFO/Makefile.in --- 3DLDF-1.1.4/DOC/TEXINFO/Makefile.in 2003-12-10 18:41:53.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/Makefile.in 2004-01-16 19:18:52.000000000 +0100 @@ -15,7 +15,7 @@ @SET_MAKE@ # This file is part of 3DLDF, a package for three-dimensional drawing. -# Copyright (C) 2003 Laurence D. Finston. +# Copyright (C) 2003, 2004 Laurence D. Finston. # 3DLDF is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by @@ -41,7 +41,7 @@ # lfinsto1@gwdg.de # s246794@stud.uni-goettingen.de -# $Id: Makefile.am,v 1.8 2003/12/10 17:03:26 lfinsto1 Exp $ +# $Id: Makefile.am,v 1.13 2004/01/16 17:56:59 lfinsto1 Exp $ srcdir = @srcdir@ top_srcdir = @top_srcdir@ @@ -139,20 +139,63 @@ target_alias = @target_alias@ info_TEXINFOS = 3DLDF.texi -3dldf_TEXINFOS = addfile.texi biblio.texi changes.texi circle.texi color.texi \ - concidx.texi contrib.texi cuboid.texi dataidx.texi \ - ellipse.texi fdl.texi focus.texi funcidx.texi future.texi \ - glbcnvar.texi \ - gsdlpt.texi gspaths.texi gspict.texi gsplane.texi gspoint.texi \ - gssolfig.texi gstranpt.texi gstransf.texi instlrun.texi \ - intersct.texi intro.texi io.texi label.texi line.texi path.texi \ - pattern.texi picture.texi plane.texi point.texi polygon.texi \ - polyhed.texi rcpcurve.texi rectang.texi regpolyg.texi shape.texi solfaced.texi \ - solid.texi transfor.texi typeglb.texi utility.texi varidx.texi +3dldf_TEXINFOS = intro.texi contrib.texi using.texi gspoint.texi gstranpt.texi \ + gstransf.texi gsdlpt.texi gspaths.texi gsplane.texi gssolfig.texi \ + gspict.texi intersct.texi instlrun.texi typeglb.texi glbcnvar.texi \ + creatnew.texi system.texi color.texi io.texi shape.texi transfor.texi \ + label.texi picture.texi point.texi focus.texi line.texi plane.texi \ + path.texi polygon.texi regpolyg.texi rectang.texi rcpcurve.texi \ + ellipse.texi circle.texi pattern.texi solid.texi solfaced.texi \ + cuboid.texi polyhed.texi utility.texi addfile.texi future.texi \ + changes.texi biblio.texi fdl.texi varidx.texi funcidx.texi \ + concidx.texi + + +3dldf_EPS = $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.1 \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.2 \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.3 \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.4 \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.5 \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.6 \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.7 \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.8 \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.9 \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.1? \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.2? \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.3? \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.4? \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.5? \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.6? \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.7? \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.8? \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.9? \ + $(GRAPHICSDIR)/$(EPSDIR)/3DLDFmp.1?? + + +3dldf_PNG = $(GRAPHICSDIR)/$(PNGDIR)/3DLDF1.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF2.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF3.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF4.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF5.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF6.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF7.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF8.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF9.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF1?.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF2?.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF3?.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF4?.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF5?.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF6?.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF7?.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF8?.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF9?.png \ + $(GRAPHICSDIR)/$(PNGDIR)/3DLDF1??.png EXTRA_DIST = .rcsfreeze.log .rcsfreeze.log.dev 3DLDF.ps \ - ChangeLog.dev $(3dldf_TEXINFOS) EPS/* + ChangeLog.dev $(3dldf_TEXINFOS) \ + $(3dldf_EPS) $(3dldf_PNG) 3DLDF.pdf subdir = DOC/TEXINFO mkinstalldirs = $(SHELL) $(top_srcdir)/mkinstalldirs @@ -256,7 +299,7 @@ distdir = $(top_distdir)/$(PACKAGE)-$(VERSION) distdir: $(DISTFILES) - $(mkinstalldirs) $(distdir)/EPS + $(mkinstalldirs) $(distdir)/$(GRAPHICSDIR)/$(EPSDIR) $(distdir)/$(GRAPHICSDIR)/$(PNGDIR) @srcdirstrip=`echo "$(srcdir)" | sed 's|.|.|g'`; \ topsrcdirstrip=`echo "$(top_srcdir)" | sed 's|.|.|g'`; \ list='$(DISTFILES)'; for file in $$list; do \ @@ -431,6 +474,15 @@ TAGS : $(info_TEXINFOS) $(3dldf_TEXINFOS) @echo "Regenerating the tags table for the TEXINFO files." etags $(info_TEXINFOS) $(3dldf_TEXINFOS) + +.PHONY : show +show: + @echo "GRAPHICSDIR: $(GRAPHICSDIR)" + @echo "EPSDIR: $(EPSDIR)" + @echo "PNGDIR: $(PNGDIR)" + @echo "CURDIR: $(CURDIR)" + @echo "3dldf_PNG: $(3dldf_PNG)" + @echo "3dldf_EPS: $(3dldf_EPS)" # Tell versions [3.59,3.63) of GNU make to not export all variables. # Otherwise a system limit (for SysV at least) may be exceeded. .NOEXPORT: diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/addfile.texi 3DLDF-1.1.5.1/DOC/TEXINFO/addfile.texi --- 3DLDF-1.1.4/DOC/TEXINFO/addfile.texi 2003-12-03 20:32:35.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/addfile.texi 2004-01-16 17:40:16.000000000 +0100 @@ -1,12 +1,12 @@ @c addfile.texi - + @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: addfile.texi,v 1.3 2003/12/03 19:32:35 lfinsto1 Exp $ +@c $Id: addfile.texi,v 1.4 2004/01/12 18:32:23 lfinsto1 Exp lfinsto1 $ @node Adding a File, Future Plans, Utility Functions, Top @chapter Adding a File diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/biblio.texi 3DLDF-1.1.5.1/DOC/TEXINFO/biblio.texi --- 3DLDF-1.1.4/DOC/TEXINFO/biblio.texi 2003-12-08 20:02:41.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/biblio.texi 2004-01-16 17:40:16.000000000 +0100 @@ -1,11 +1,11 @@ @c biblio.texi - + @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: biblio.texi,v 1.4 2003/12/08 19:02:41 lfinsto1 Exp $ +@c $Id: biblio.texi,v 1.5 2004/01/12 18:32:44 lfinsto1 Exp lfinsto1 $ @node Bibliography, GNU Free Documentation License, Changes, Top @unnumbered Bibliography @@ -52,6 +52,23 @@ @bibskip @noindent +Harbison, Samuel P., and Guy L. Steele Jr. +@i{C, A Reference Manual}. +Prentice Hall. +Englewood Cliffs, New Jersey 1995. +@w{ISBN 0-13-326232-4 @OCB{}Case@CCB{}.} +@w{ISBN~0-13-326224-3 @OCB{}Paperback@CCB{}.} +@bibskip + +@noindent +Hobby, John D. +@i{Smooth, Easy to Compute Interpolating Splines}. +Discrete and Computational Geometery 1(2). +Springer-Verlag. +New York 1986. +@bibskip + +@noindent Hobby, John D. @i{A User's Manual for MetaPost}. AT & T Bell Laboratories. @@ -103,6 +120,14 @@ @bibskip @noindent +Rokicki, Tomas. +@i{Dvips: A DVI-to-PostScript Translator} +for version 5.66a. +February 1997. +@uref{http://dante.ctan.org/CTAN/dviware/dvips/} +@bibskip + +@noindent Salomon, David. @i{Computer Graphics and Geometric Modeling}. Berlin 1999. @@ -120,6 +145,14 @@ @bibskip @noindent +Stallman, Richard M. +@i{Using and Porting the GNU Compiler Collection}. +For GCC Version 3.3.2. +Boston 2003. +Free Software Foundation, Inc. +@bibskip + +@noindent Stroustrup, Bjarne. @i{The @cpp{} Programming Language}. Special Edition. diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/changes.texi 3DLDF-1.1.5.1/DOC/TEXINFO/changes.texi --- 3DLDF-1.1.4/DOC/TEXINFO/changes.texi 2003-12-10 18:23:44.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/changes.texi 2004-01-16 17:40:16.000000000 +0100 @@ -1,11 +1,11 @@ @c changes.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: changes.texi,v 1.4 2003/12/10 17:23:44 lfinsto1 Exp $ +@c $Id: changes.texi,v 1.7 2004/01/14 20:54:43 lfinsto1 Exp lfinsto1 $ @node Changes, Bibliography, Future Plans, Top @chapter Changes @@ -13,8 +13,127 @@ @noindent Updated @value{UPDATED}. -Changes in 3DLDF 1.1.4: +@menu +* Changes in 3DLDF 1.1.5.1:: +* Changes in 3DLDF 1.1.5:: +* Changes in 3DLDF 1.1.4.2:: +* Changes in 3DLDF 1.1.4.1:: +* Changes in 3DLDF 1.1.4:: +* Initial version:: +@end menu + +@node Changes in 3DLDF 1.1.5.1, Changes in 3DLDF 1.1.5, Changes, Changes +@section 3DLDF 1.1.5.1 + +@itemize @bullet + +@item +Added missing Texinfo files to the @code{3dldf_TEXINFOS} variable in +@file{3DLDF-1.1.5.1/DOC/TEXINFO/Makefile.am}, and reordered the +filenames. + +@item +@cindex PNG (Portable Network Graphics) +@cindex Portable Network Graphics (PNG) @c +Changed the names of the PNG (Portable Network Graphics) files +included in the HTML version of this manual. +Changed the names in the commands for including these +files in the Texinfo files. I wasn't able to write some of the +files with the old names to a CD-R (Compact Disk, Recordable). +@end itemize + +@node Changes in 3DLDF 1.1.5, Changes in 3DLDF 1.1.4.2, Changes in 3DLDF 1.1.5.1, Changes +@section 3DLDF 1.1.5 + +In release 1.1.5, I've tied up some loose ends. I wanted to do this +before starting on the input routine. + +@itemize @bullet + +@item +Added @code{const real} @var{step} argument to the version of +@code{Ellipse::intersection_points()} that takes an @code{Ellipse} +argument. +@xref{Ellipse Intersections, , Ellipse Reference; Intersections}. + +@item +It is now possible to ``typedef'' @code{real} to either @code{float} +or @code{double}. This means that @code{real} can now be made a synonym +for either @code{float} or @code{double} by using a @code{typedef} +declaration. @code{real} is typedeffed to @code{float} by default. + +@item +Added @code{const bool ldf_real_float} and +@code{extern const bool ldf_real_double} +for use in non-conditionally compiled code. +They are set according to the values +of @code{LDF_REAL_FLOAT} and @code{LDF_REAL_DOUBLE}. + +@item +@code{Transform::epsilon()} and @code{Point::epsilon()} now return +different values, depending on the values of the preprocessor macros +@code{LDF_REAL_FLOAT} and @code{LDF_REAL_DOUBLE}. I have not yet tested +whether good values are returned when @code{real} is @code{double}. + +@item +@code{MAX_REAL} and @code{MAX_REAL_SQRT} are no longer constants. +Their values are set at the beginning of @code{main()}. However, +users should not change their values. @code{MAX_REAL} is the +second-largest @code{float} or @code{double} on a given machine. This +now works for all common architectures. + +@item +Added @code{namespace System} containing the following functions: +@code{get_endianness()}, @code{is_big_endian()}, +@code{is_little_endian()}, @code{get_register_width()}, +@code{is_32_bit()}, @code{is_64_bit()}, and the template function +@code{get_second_largest()}. + +@code{namespace System} and its functions are documented in +@file{system.texi}, which is new in edition @value{EDITION}. + +@item +Replaced the various @code{create_new_}<@i{type}>@code{()} functions with the +template function @code{create_new()}. The latter is documented in +@file{creatnew.texi}, which is new in edition @value{EDITION}. + +@item +Added the file @file{3DLDF-@value{VERSION}/CWEB/cnepspng.el} to +the distribution. It contains the definitions of the Emacs-Lisp +functions @command{convert-eps} and @command{convert-eps-loop}. +@xref{Converting EPS Files ELISP,, +Running 3DLDF; Converting EPS Files; Emacs-Lisp Functions}. + +@item +Added the files +@file{3DLDF-@value{VERSION}/CWEB/exampman.web} and +@file{3DLDF-@value{VERSION}/CWEB/examples.mp} to the +distribution. They contain the @cpp{} and MetaPost code, +respectively, for generating the illustrations in this manual. + +@end itemize + +@node Changes in 3DLDF 1.1.4.2, Changes in 3DLDF 1.1.4.1, Changes in 3DLDF 1.1.5, Changes +@section 3DLDF 1.1.4.2 + +@itemize @bullet +@item +The illustrations in the HTML output are now scaled to +@code{magstep3}. +@end itemize + +@node Changes in 3DLDF 1.1.4.1, Changes in 3DLDF 1.1.4, Changes in 3DLDF 1.1.4.2, Changes +@section 3DLDF 1.1.4.1 + +@itemize @bullet +@item +The HTML output now includes illustrations. +@end itemize + +@node Changes in 3DLDF 1.1.4, Initial version, Changes in 3DLDF 1.1.4.1, Changes +@section 3DLDF 1.1.4 + @itemize @bullet @item @code{MAX_REAL} is now the second largest float value. However, the @@ -37,6 +156,10 @@ formats. @end itemize + +@node Initial version, , Changes in 3DLDF 1.1.4, Changes +@section 3DLDF 1.1.1 + 3DLDF 1.1.1 was the first version of 3DLDF since it became a GNU package (the current version is @value{VERSION}). It is now conformant to the GNU Coding Standards, except that diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/circle.texi 3DLDF-1.1.5.1/DOC/TEXINFO/circle.texi --- 3DLDF-1.1.4/DOC/TEXINFO/circle.texi 2003-12-08 14:34:28.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/circle.texi 2004-01-16 17:40:16.000000000 +0100 @@ -1,11 +1,11 @@ @c circle.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: circle.texi,v 1.5 2003/12/08 13:34:28 lfinsto1 Exp $ +@c $Id: circle.texi,v 1.7 2004/01/12 18:33:05 lfinsto1 Exp lfinsto1 $ @node Circle Reference, Pattern Reference, Ellipse Reference, Top @chapter Circle Reference @@ -30,7 +30,7 @@ * Querying Circles:: * Circle Intersections:: @end menu - + @node Circle Data Members, Circle Constructors and Setting Functions, Circle Reference, Circle Reference @section Data Members @@ -72,14 +72,25 @@ Corresponds to the constructor above. @end deftypefn -@deftypefn {Static functions} Circle* create_new_circle ([{const Circle*} @var{p} = 0]) -@deftypefnx {} Circle* create_new_circle ({const Circle&} @var{p}) -Pseudo-constructors for dynamic allocation. In the first version, if -@var{p} is a pointer to a @code{Circle}, the new @code{Circle} will be a -copy of @var{*p}. In the second version, the new @code{Circle} will be a copy of -@var{p}. + + +@deftypefn {Template specializations} Circle* create_new ({const Circle*} @var{c}) +@c +@deftypefnx {} Circle* create_new ({const Circle&} @var{c}) +@c +Pseudo-constructors for dynamic allocation of @code{Circles}. +They create a @code{Circle} on the free store and allocate memory for it using +@code{new(Circle)}. They return a pointer to the new @code{Circle}. + +If @var{c} is a non-zero pointer or a reference, +the new @code{Circle} will be a copy of +@var{c}. If the new object is not meant to be a +copy of an existing one, @samp{0} must be passed to +@code{create_new()} as its argument. +@xref{Dynamic Allocation of Shapes}, for more information. @end deftypefn + @node Circle Operators, Querying Circles, Circle Constructors and Setting Functions, Circle Reference @section Operators @@ -138,6 +149,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 176. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 176 not displayed.] +@end ifinfo + @c @end deftypefn @@ -208,9 +239,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 177. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 177 not displayed.] +@end ifinfo + @c @end deftypefn diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/color.texi 3DLDF-1.1.5.1/DOC/TEXINFO/color.texi --- 3DLDF-1.1.4/DOC/TEXINFO/color.texi 2003-12-07 18:56:47.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/color.texi 2004-01-16 17:40:17.000000000 +0100 @@ -1,13 +1,13 @@ @c color.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: color.texi,v 1.3 2003/12/07 17:56:47 lfinsto1 Exp $ +@c $Id: color.texi,v 1.4 2004/01/12 18:33:22 lfinsto1 Exp lfinsto1 $ -@node Color Reference, Input and Output, Global Constants and Variables, Top +@node Color Reference, Input and Output, System Information, Top @chapter Color Reference @tindex Color @@ -23,7 +23,7 @@ * Defining and Initializing Colors:: * Namespace Colors:: @end menu - + @node Color Data Members, Color Constructors and Setting Functions, Color Reference, Color Reference @section Data Members @@ -40,11 +40,12 @@ @deftypevar bool on_free_store @code{true}, if the @code{Color} has been created by -@code{create_new_color()}, which allocates memory for the +@code{create_new()}, which allocates memory for the @code{Color} on the free store. Otherwise @code{false}. @code{Colors} should only ever be dynamically allocated by using -@code{create_new_color()} -(@pxref{Color Constructors and Setting Functions,,Color Reference;;Constructors and Setting Functions}). +@code{create_new()}. +@xref{Color Constructors and Setting Functions,, +Color Reference;;Constructors and Setting Functions}. @end deftypevar @deftypevar real red_part @@ -103,10 +104,20 @@ Corresponds to the constructor above. @end deftypefn -@deftypefn {Inline static function} Color* create_new_color (void) -Pseudo-constructor for dynamic allocation of @code{Colors}. -It creates a @code{Color} on the free store and allocate memory for it using -@code{new(Color)}. It returns a pointer to the new @code{Color}. +@deftypefn {Template specializations} Color* create_new ({const Color*} @var{c}) +@c +@deftypefnx {} Color* create_new ({const Color&} @var{c}) +@c +Pseudo-constructors for dynamic allocation of @code{Colors}. +They create a @code{Color} on the free store and allocate memory for it using +@code{new(Color)}. They return a pointer to the new @code{Color}. + +If @var{c} is a non-zero pointer or a reference, +the new @code{Color} will be a copy of +@var{c}. If the new object is not meant to be a +copy of an existing one, @samp{0} must be passed to +@code{create_new()} as its argument. +@xref{Dynamic Allocation of Shapes}, for more information. @c !! TO DO: This function is used in the drawing and filling functions for @@ -206,11 +217,11 @@ @node Querying Colors, Defining and Initializing Colors, Showing Colors, Color Reference @section Querying -@deftypefn {Inline @code{const} function} bool is_on_free_store (void) +@deftypefn {@code{const} function} bool is_on_free_store (void) Returns @code{on_free_store}. This will only be true, if the -@code{Color} was created by @code{create_new_color()} -(@pxref{Color Constructors and Setting Functions,,Color Reference; -Constructors and Setting Functions}). +@code{Color} was created by @code{create_new()}. +@xref{Color Constructors and Setting Functions,,Color Reference; +Constructors and Setting Functions}. @end deftypefn @deftypefn {Inline @code{const} function} real get_red_part ([bool @var{decimal} = @code{false}]) diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/concidx.texi 3DLDF-1.1.5.1/DOC/TEXINFO/concidx.texi --- 3DLDF-1.1.4/DOC/TEXINFO/concidx.texi 2003-12-03 20:38:13.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/concidx.texi 2004-01-16 17:40:15.000000000 +0100 @@ -1,11 +1,11 @@ @c concidx.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: concidx.texi,v 1.1 2003/11/28 14:16:42 lfinsto1 Exp $ +@c $Id: concidx.texi,v 1.1 2003/11/28 14:16:42 lfinsto1 Exp lfinsto1 $ @node Concept Index, , Function Index, Top diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/contrib.texi 3DLDF-1.1.5.1/DOC/TEXINFO/contrib.texi --- 3DLDF-1.1.4/DOC/TEXINFO/contrib.texi 2003-12-03 20:38:41.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/contrib.texi 2004-01-16 17:40:17.000000000 +0100 @@ -1,11 +1,11 @@ @c contrib.texi - + @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: contrib.texi,v 1.1 2003/11/28 14:16:57 lfinsto1 Exp $ +@c $Id: contrib.texi,v 1.2 2004/01/12 18:33:54 lfinsto1 Exp lfinsto1 $ @node Contributing to 3DLDF, Using 3DLDF, Introduction, Top @section Contributing to 3DLDF diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/creatnew.texi 3DLDF-1.1.5.1/DOC/TEXINFO/creatnew.texi --- 3DLDF-1.1.4/DOC/TEXINFO/creatnew.texi 1970-01-01 01:00:00.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/creatnew.texi 2004-01-16 17:40:17.000000000 +0100 @@ -0,0 +1,74 @@ +@c creatnew.texi + +@c This file is part of the 3DLDF User and Reference Manual. +@c Copyright (C) 2003, 2004 Laurence D. Finston +@c See the section "GNU Free Documentation License" in the file +@c fdl.texi for copying conditions. + +@c $Id: creatnew.texi,v 1.3 2004/01/12 18:34:14 lfinsto1 Exp lfinsto1 $ + +@node Dynamic Allocation of Shapes, System Information, Global Constants and Variables, Top +@chapter Dynamic Allocation of Shapes + +@deftypefn {Template function} {@code{template C*}} create_new ({const C*} @var{arg}) +@deftypefnx {Template function} {@code{template C*}} create_new ({const C&} @var{arg}) +@c +These functions dynamically allocate an object derived from +@code{Shape} on the free store, +returning a pointer to the type of the @code{Shape} and setting +@code{on_free_store} to @code{true}. + +If a non-zero pointer or a reference is passed to @code{create_new()}, +the new object will be a copy of @var{arg}. + +It is not possible to instantiate more than one specialization of +@code{create_new()} that takes no argument, because calls to these +functions would be ambiguous. If the new object is not meant to be a +copy of an existing one, @samp{0} must be passed to @code{create_new()} +as its argument. + +@code{create_new} is called like this: + +@example +Point* p = create_new(0); +p->show("*p:"); +@print{} *p: (0, 0, 0) + +Color c(.3, .5, .25); +Color* d = create_new(c); +d->show("*d:"); +@print{} +*d: +name == +use_name == 0 +red_part == 0.3 +green_part == 0.5 +blue_part == 0.25 + + +Point a0(3, 2.5, 6); +Point a1(10, 11, 14); +Path q(a0, a1); +Path* r = create_new(&q); +r->show("*r:"); +@print{} +*r: +points.size() == 2 +connectors.size() == 1 +(3, 2.5, 6) -- (10, 11, 14); +@end example + + + +Specializations of this template function are currently declared for +@code{Color}, @code{Point}, @code{Path}, @code{Reg_Polygon}, +@code{Rectangle}, @code{Ellipse}, @code{Circle}, @code{Solid}, and +@code{Cuboid}. +@end deftypefn + + + + + + + diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/cuboid.texi 3DLDF-1.1.5.1/DOC/TEXINFO/cuboid.texi --- 3DLDF-1.1.4/DOC/TEXINFO/cuboid.texi 2003-12-03 20:39:03.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/cuboid.texi 2004-01-16 17:40:16.000000000 +0100 @@ -1,11 +1,11 @@ @c cuboid.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: cuboid.texi,v 1.2 2003/12/03 19:39:03 lfinsto1 Exp $ +@c $Id: cuboid.texi,v 1.4 2004/01/12 18:34:46 lfinsto1 Exp lfinsto1 $ @node Cuboid Reference, Polyhedron Reference, Faced Solid Reference, Top @chapter Cuboid Reference @@ -19,7 +19,7 @@ * Cuboid Constructors and Setting Functions:: * Cuboid Operators:: @end menu - + @node Cuboid Data Members, Cuboid Constructors and Setting Functions, Cuboid Reference, Cuboid Reference @section Data Members @@ -59,6 +59,7 @@ Cuboid c(P, 3, 5, 2.93, 35, 10, 60); @end example +@iftex @tex \ifmakeexamples \BEX @@ -73,16 +74,46 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex - +@end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 186. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 186 not displayed.] +@end ifinfo @end deftypefn -@deftypefn {Static function} Cuboid* create_new_cuboid ([{const Cuboid*} @var{c} = 0]) -Dynamically allocates a new @code{Cuboid} on the free store and returns -a pointer to it. If a non-zero argument @var{c} is used, -the new @code{Cuboid} will be a copy of @var{*c}. + +@deftypefn {Template specializations} Cuboid* create_new ({const Cuboid*} @var{c}) +@c +@deftypefnx {} Cuboid* create_new ({const Cuboid&} @var{c}) +@c +Pseudo-constructors for dynamic allocation of @code{Cuboids}. +They create a @code{Cuboid} on the free store and allocate memory for it using +@code{new(Cuboid)}. They return a pointer to the new @code{Cuboid}. + +If @var{c} is a non-zero pointer or a reference, +the new @code{Cuboid} will be a copy of +@var{c}. If the new object is not meant to be a +copy of an existing one, @samp{0} must be passed to +@code{create_new()} as its argument. +@xref{Dynamic Allocation of Shapes}, for more information. @end deftypefn @deftypefn {Destructor} {void} {~Cuboid} (@code{void}) diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/dataidx.texi 3DLDF-1.1.5.1/DOC/TEXINFO/dataidx.texi --- 3DLDF-1.1.4/DOC/TEXINFO/dataidx.texi 2003-12-03 20:39:20.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/dataidx.texi 1970-01-01 01:00:00.000000000 +0100 @@ -1,13 +0,0 @@ -@c dataidx.texi - -@c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston -@c See the section "GNU Free Documentation License" in the file -@c fdl.texi for copying conditions. - -@c $Id: dataidx.texi,v 1.1 2003/11/28 14:17:03 lfinsto1 Exp $ - -@node Data Type Index -@unnumbered Data Type Index -@printindex tp - diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/ellipse.texi 3DLDF-1.1.5.1/DOC/TEXINFO/ellipse.texi --- 3DLDF-1.1.4/DOC/TEXINFO/ellipse.texi 2003-12-09 19:58:57.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/ellipse.texi 2004-01-16 17:40:16.000000000 +0100 @@ -1,11 +1,11 @@ @c ellipse.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: ellipse.texi,v 1.6 2003/12/09 18:58:56 lfinsto1 Exp $ +@c $Id: ellipse.texi,v 1.9 2004/01/14 18:09:36 lfinsto1 Exp lfinsto1 $ @node Ellipse Reference, Circle Reference, Regular Closed Plane Curve Reference, Top @chapter Ellipse Reference @@ -27,7 +27,7 @@ * Solving Ellipses:: * Rectangles for Ellipses:: @end menu - + @node Ellipse Data Members, Ellipse Constructors and Setting Functions, Ellipse Reference, Ellipse Reference @section Data Members @@ -124,6 +124,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 159. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 159 not displayed.] +@end ifinfo + @example Point P(1, 1, 1); Ellipse e(P, 6, 4, 15, 12, 11); @@ -147,6 +166,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 160. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 160 not displayed.] +@end ifinfo + @c @end deftypefn @@ -157,18 +196,20 @@ Corresponds to the constructor above. @end deftypefn -@deftypefn {Static function} Ellipse* create_new_ellipse ([{const Ellipse*} @var{e} = 0]) +@deftypefn {Template specializations} Ellipse* create_new ({const Ellipse*} @var{e}) @c -@deftypefnx {Static function} Ellipse* create_new_ellipse ({const Ellipse&} @var{e}) -Pseudo-constructors for dynamic allocation. - -In the first version, @var{e} is an optional pointer argument. If -@var{e} is non-zero, the new @code{Ellipse} will be a copy of -@var{*e}. Otherwise, it will be empty. - -In the second version, -@var{e} is a required reference argument, and the new @code{Ellipse} -will be a copy of @var{e}. +@deftypefnx {} Ellipse* create_new ({const Ellipse&} @var{e}) +@c +Pseudo-constructors for dynamic allocation of @code{Ellipses}. +They create a @code{Ellipse} on the free store and allocate memory for it using +@code{new(Ellipse)}. They return a pointer to the new @code{Ellipse}. + +If @var{e} is a non-zero pointer or a reference, +the new @code{Ellipse} will be a copy of +@var{e}. If the new object is not meant to be a +copy of an existing one, @samp{0} must be passed to +@code{create_new()} as its argument. +@xref{Dynamic Allocation of Shapes}, for more information. @end deftypefn @node Performing Transformations on Ellipses, Ellipse Operators, Ellipse Constructors and Setting Functions, Ellipse Reference @@ -242,6 +283,24 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 161. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 161 not displayed.] +@end ifinfo @end deftypefn @@ -271,6 +330,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 162. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 162 not displayed.] +@end ifinfo + @end deftypefn @node Affine Transformations for Ellipses, Querying Ellipses, Labeling Ellipses, Ellipse Reference @@ -371,6 +449,24 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 163. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 163 not displayed.] +@end ifinfo @end deftypefn @@ -524,6 +620,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 164. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 164 not displayed.] +@end ifinfo + @end deftypefn @deftypefn {@code{const} function} Point angle_point (real @var{angle}) @@ -568,6 +683,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 165. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 165 not displayed.] +@end ifinfo + @NEXTFIG{} demonstrates, that the rotation is unfortunately not always in the direction one would prefer. I don't have a solution to this problem yet. @@ -613,6 +747,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 166. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 166 not displayed.] +@end ifinfo + @end deftypefn @node Ellipse Intersections, Solving Ellipses, Returning Elements and Information for Ellipses, Ellipse Reference @@ -692,9 +845,29 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 167. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 167 not displayed.] +@end ifinfo + @end deftypefn -@deftypefn {@code{const} virtual function} bool_point_quadruple intersection_points (Ellipse @var{e}, [{const bool} @var{verbose} = false]) +@deftypefn {@code{const} virtual function} bool_point_quadruple intersection_points (Ellipse @var{e}, [{const real} @var{step} = 3, [bool @var{verbose} = @code{false}]]) Returns the intersection points of two @code{Ellipses}. Two @code{Ellipses} can intersect at at most four points. @@ -706,6 +879,16 @@ @code{b} element of the @code{bool_point} will be @code{true}, otherwise @code{false}. +The @var{step} argument is used when the @code{Ellipses} are coplanar +and either have different centers or the vertical axis of one @code{Ellipse} is +colinear with the horizontal axis of the other (and vice versa). In +these cases, the intersection points must be found by an iterative +routine. A @code{Point} @math{p} travels around the perimeter of @code{*this}, +and its location with respect to @var{e} is tested. @var{step} is the +angle of rotation used for stepping around the perimeter of +@code{*this}. The default value, 3, should be adequate, unless the +@code{Ellipses} differ greatly in size. + If the @var{verbose} argument is @code{true}, @code{intersection_points()} will print information about the intersection points to standard output. @@ -752,6 +935,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 168. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 168 not displayed.] +@end ifinfo + In @NEXTFIG{}, @math{e} and @math{f} are coplanar, but don't lie in a major plane, have different centers, and only intersect at two points. @@ -797,6 +999,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 169. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 169 not displayed.] +@end ifinfo + If the planes of the @code{Ellipses} are parallel, there are, of course, no intersection points. If the @code{Ellipses} are non-coplanar, and their planes are not parallel to each other, @@ -863,6 +1084,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 170. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 170 not displayed.] +@end ifinfo + In @NEXTFIG{}, the two @code{Ellipses} lie in skew planes. The plane of @math{f} intersects with @math{e} at the @code{Points} labelled ``1'' and ``2''. The plane of @math{e} does not intersect with @math{f}, so @code{bpq.third.pt} @@ -907,6 +1147,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 171. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 171 not displayed.] +@end ifinfo + @end deftypefn @node Solving Ellipses, Rectangles for Ellipses, Ellipse Intersections, Ellipse Reference @@ -1046,6 +1306,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 172. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 172 not displayed.] +@end ifinfo + @end deftypefn @deftypefn {@code{const} function} Rectangle in_rectangle (@code{void}) @@ -1077,6 +1356,24 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 173. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 173 not displayed.] +@end ifinfo @end deftypefn @@ -1112,6 +1409,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 174. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 174 not displayed.] +@end ifinfo + @end deftypefn @deftypefn {@code{const} function} Rectangle draw_in_rectangle ([{const Color&} @var{ddraw_color} = @code{*Colors::default_color}, [string @var{ddashed} = "", [string @var{ppen} = "", [Picture& @var{picture} = @code{current_picture}]]]]) @@ -1143,11 +1460,28 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex - +@ifhtml +@html +

+
+ +
+
+Fig. 175. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 175 not displayed.] +@end ifinfo @end deftypefn diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/focus.texi 3DLDF-1.1.5.1/DOC/TEXINFO/focus.texi --- 3DLDF-1.1.4/DOC/TEXINFO/focus.texi 2003-12-08 13:51:19.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/focus.texi 2004-01-16 17:40:16.000000000 +0100 @@ -1,11 +1,11 @@ @c focus.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: focus.texi,v 1.3 2003/12/08 12:51:19 lfinsto1 Exp $ +@c $Id: focus.texi,v 1.4 2004/01/12 18:35:47 lfinsto1 Exp lfinsto1 $ @node Focus Reference, Line Reference, Point Reference, Top @chapter Focus Reference @@ -25,7 +25,7 @@ * Querying Focuses:: * Showing Focuses:: @end menu - + @node Focus Data Members, Focus Global Variables, Focus Reference, Focus Reference @section Data Members diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/funcidx.texi 3DLDF-1.1.5.1/DOC/TEXINFO/funcidx.texi --- 3DLDF-1.1.4/DOC/TEXINFO/funcidx.texi 2003-12-03 20:42:56.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/funcidx.texi 2004-01-16 17:40:15.000000000 +0100 @@ -1,11 +1,11 @@ @c funcidx.texi - + @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: funcidx.texi,v 1.1 2003/11/28 14:18:27 lfinsto1 Exp $ +@c $Id: funcidx.texi,v 1.2 2004/01/12 18:35:58 lfinsto1 Exp lfinsto1 $ @node Function Index, Concept Index, Data Type and Variable Index, Top diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/future.texi 3DLDF-1.1.5.1/DOC/TEXINFO/future.texi --- 3DLDF-1.1.4/DOC/TEXINFO/future.texi 2003-12-03 20:43:18.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/future.texi 2004-01-16 17:40:16.000000000 +0100 @@ -1,80 +1,260 @@ @c This is ~/metafont/metapost/perspective/DOCUMENTATION/future.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: future.texi,v 1.1 2003/11/28 14:18:30 lfinsto1 Exp $ +@c $Id: future.texi,v 1.3 2004/01/14 20:55:05 lfinsto1 Exp lfinsto1 $ @node Future Plans, Changes, Adding a File, Top @chapter Future Plans 3DLDF is a work-in-progress. In fact, it can never be -finished, because the supply of interesting geometric constructions is -inexhaustible. However, presently 3DLDF still has a number of major +finished, because the supply of interesting geometric constructions +is inexhaustible. However, presently 3DLDF still has a number of major gaps. -The following is a list of matters that I plan to address sooner -rather than later: + +If you're interesting in contributing to 3DLDF, with respect to one of +the topics below and in the following sections, or if you have ideas +of your own, see @ref{Contributing to 3DLDF}. @itemize @bullet -@item -Program an input routine. The lack of one is the most significant +@item Input routine. +The lack of one is the most significant defect in 3DLDF, as mentioned in @ref{No Input Routine}. -@item -Port to other platforms. +@item Port to other platforms. +@xref{Ports}. +@end itemize + +@menu +* Geometry:: +* Curves and Surfaces:: +* Shadows:: +* Multi-Threading:: +@end menu + +@node Geometry, Curves and Surfaces, Future Plans, Future Plans +@section Geometry + +3DLDF currently provides a set of basic plane and solid geometrical +figures. However, some important ones are still missing. +There are many useful geometrical data types and functions whose +implementation would require no more than elementary geometry. + +@itemize @bullet @item -Add @code{class Octahedron} to complete the set of regular Platonic -polyhedra. +Add constructors with a normal vector argument rather than angles of +rotation about the main axes. @item -Improve the polyhedra, by storing the vertices as @code{Points}, rather -than @code{Reg_Polygons}. Find a better way of generating them, if -possible, without using rotations. +I have started defining @code{class Triangle}, which can be used for +calculating triangle solutions. @item -Add classes for the Kepler-Poinsot polyhedra, the semi-regular -Archimedean polyhedra, the dual solids, the stellated Archimedean -polyhedra, and the regular compounds.@c +@cindex multiple inheritance +@cindex derived classes +@cindex derivation @c -@footnote{Cundy and Rollet, @cite{Mathematical Models}, Chapter 3, -``Polyhedra'', pp.@: 76--160.} +Add a class @code{Conic_Section} and derive @code{Ellipse} +from it. This will be the first case of +@dfn{multiple inheritance}@c +@c +@footnote{Stroustrup, @cite{The @cpp{} Programming Language}, +@c +@iftex +@tex +\S 15.2 +@end tex +@end iftex +@ifhtml +§15.2 +@end ifhtml +@ifinfo +section 15.2 +@end ifinfo +@c +``Multiple Inheritance'', pp.@w{ }390--92.} +@c +in 3DLDF, since @code{Ellipse} is already +derived from @code{Path}. @xref{Ellipse Reference}. +Add the classes @code{Parabola} and @code{Hyperbola}. @item Add more functions for finding the intersections of objects of various -types, starting with the plane figures. In particular, I believe I've -found an algebraic solution for +types, starting with the plane figures. +In particular, I believe I've found an algebraic solution for the intersection of an @code{Ellipse} and a @code{Circle} in a plane, but I haven't had a chance to try implementing it yet. -@item -Add constructors with a normal vector argument rather than angles of -rotation about the main axes. +If this works, I think it will make it possible to find the intersection +of two coplanar ellipses algebraically, because it will be possible to +transform them both such that one of them becomes circular. -@item -Add the classes @code{Sphere} and @code{Ellipsoid}. + +@item Class @code{Octahedron} will complete the set of regular Platonic +polyhedra. @item -Provide a means for calculating triangle solutions, perhaps using a -@code{class Triangle}. +Add classes for the Kepler-Poinsot polyhedra, the semi-regular +Archimedean polyhedra, the dual solids, the stellated Archimedean +polyhedra, and the regular compounds.@c +@c +@footnote{Cundy and Rollet, @cite{Mathematical Models}, Chapter 3, +``Polyhedra'', pp.@: 76--160.} @item -Provide a means of producing shadows and reflections. +Add class @code{Ellipsoid} and a derived class @code{Sphere}. @item -Improve the indexes in the manual. +Improve the specification of @code{Solid} and +@code{Solid_Faced}. +In particular, it would help to store the vertices of +@code{Polyhedra} as individual @code{Points}, rather +than using @code{Reg_Polygons}. I'd also +like to find a better way of generating @code{Solids}, without using +rotations, if possible. + @end itemize +@node Curves and Surfaces, Shadows, Geometry, Future Plans +@section Curves and Surfaces + +@cindex splines +@cindex spline curves +@cindex B@'ezier curves +@cindex B-splines +@cindex NURBS (non-uniform rational B-splines) +@cindex non-uniform rational B-splines (NURBS) +@cindex patches +@cindex surface patches +@c +3D modelling software usually supports the creation and manipulation of +various kinds of @dfn{spline curves}: @dfn{B@'ezier curves}, +@dfn{B-splines}, and @dfn{non-uniform rational B-splines} or +@dfn{NURBS}. These curves can be used for generating surfaces.@c +@c +@footnote{Huw Jones, +@i{Computer Graphics through Key Mathematics}, and +David Salomon, +@i{Computer Graphics and Geometric Modeling}, are my main sources of +information about spline curves.} + +@cindex projective invariance +@cindex invariance, projective +@c +@code{paths} in Metafont and MetaPost are B@'ezier curves. +It would be possible to implement three-dimensional B@'ezier curves in +3DLDF, but unfortunately they are not @dfn{projectively invariant}: + +Let @math{c_0} represent a B@'ezier curve in three dimensions, +@math{P} the control points of @math{c_0}, and +@math{t} a projection transformation. +Further, let @math{Q} represent the points generated from applying +@math{t} to @math{P}, and @math{c_1} the curve generated from @math{Q}. +Finally, let @math{R} represent the points generated from applying +@math{t} to all of the points on @math{c_0}, and + @math{c_2} the curve through @math{R}: +@math{c_1 \not\equiv c_2}. + +@cindex NURBS (non-uniform rational B-splines) +@cindex non-uniform rational B-splines (NURBS) +@cindex projective invariance +@cindex invariance, projective +@c +NURBS, on the other hand, are projectively invariant,@c +@c +@footnote{Jones, Huw. +@i{Computer Graphics through Key Mathematics}, p.@w{ }282.} +@c +so I will probably +concentrate on implementing them. On the other hand, it would be nice +to be able to implement Metafont's way of specifying @code{paths} +using `@code{curl}', `@code{tension}', and `@code{dir}' in 3DLDF. +This may prove to be difficult or impossible. I do not yet know +whether Metafont's @code{path} creation algorithm can be generalized to +three dimensions.@c +@c +@footnote{Knuth, Donald Ervin. +@i{The METAFONTbook}, p.@w{ }130, and +Hobby, John D. +@i{Smooth, Easy to Compute Interpolating Splines}. +Discrete and Computational Geometery 1(2).} +Curves and surfaces are advanced topics, so it may be a while +before I implement them in 3DLDF. +@node Shadows, Multi-Threading, Curves and Surfaces, Future Plans +@section Shadows, Reflections, and Rendering -If you're interesting in contributing to 3DLDF, with respect to one of -these ideas, or if you have others of your own, see -@ref{Contributing to 3DLDF}. +@cindex shadows +@cindex reflections +@c +Shadows and reflections are closely related to transformations and +projections. +A shadow is the projection of the outline of an object onto a surface or +surfaces, and reflection in a plane is an affine transformation. +@cindex shading +@c +3D rendering software generally implements shadows, or more generally, +@dfn{shading}, reflections, and certain other effects using methods +involving the calculation of individual pixel values. +Surface hiding is also often implemented at the pixel level. +3DLDF does no scan converting ((@pxref{Accuracy}), and hence +no calculation of pixel values at all, so these methods cannot be +used in 3DLDF at present. + +However, it is possible to define functions for generating +shadows and reflections within 3DLDF by other means. + +I have defined the function @code{Point::reflect()} for reflecting a +@code{Point} in a @code{Plane}, and have begun definining versions for +other classes. + +However, in order for reflections to work, I must define functions for +breaking up objects into smaller units. This is also necessary for +surface hiding to work properly. + +For MetaPost output, I will have to implement shadows, reflections, and +surface hiding in this way. However, 3DLDF could be made to produce +output in other formats. There are two possibilities: implementing +rendering functionality within 3DLDF, or interfacing to +existing rendering software. If I decide to do the latter, there are +again two possibilities: having 3DLDF write output in a format that a +renderer can input, or linking to a library supplied by a rendering +package. + +I haven't yet decided which course to pursue. However, in the long run, +I'd like it to be possible to use 3DLDF for fancier graphics than is +currently possible using MetaPost and PostScript alone. +@node Multi-Threading, , Shadows, Future Plans +@section Multi-Threading + +@cindex multi-threading +@c +When 3DLDF is run, there is only one thread of execution. +However, it could benefit from the use of multiple threads. +In particular, it may be faster and more efficient to have +@code{Picture::output()} run in its own thread. +In this case, it will no longer be possible to share +@code{current_picture} among figures. + +It may also be +worthwhile to execute the code for ``figures'', i.e., the code +between @samp{beginfig()} and @samp{endfig()}, inclusive, +in their own threads. This will require some changes in the way data +are handled. For example, if non-constant objects are shared +among figures, there may be no advantage to multi-threading because of +the need to coordinate the access of the threads to the objects. +If threads are used, then non-constant objects should be +declared locally within the figure. They may be locally declared +copies of global objects. Alternatively, @code{beginfig()} could be +changed so that objects could be passed to it as arguments, perhaps as +a @code{vector} and/or a @code{vector}. @c Local Variables: @c eval:(outline-minor-mode) diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/glbcnvar.texi 3DLDF-1.1.5.1/DOC/TEXINFO/glbcnvar.texi --- 3DLDF-1.1.4/DOC/TEXINFO/glbcnvar.texi 2003-12-09 19:07:41.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/glbcnvar.texi 2004-01-16 17:40:17.000000000 +0100 @@ -1,20 +1,36 @@ @c glbcnvar.texi - + @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: glbcnvar.texi,v 1.4 2003/12/09 18:07:41 lfinsto1 Exp $ +@c $Id: glbcnvar.texi,v 1.5 2004/01/12 18:36:30 lfinsto1 Exp lfinsto1 $ -@node Global Constants and Variables, Color Reference, Typedefs and Utility Structures, Top +@node Global Constants and Variables, Dynamic Allocation of Shapes, Typedefs and Utility Structures, Top @chapter Global Constants and Variables The global constants and variables described in this chapter are found in @file{pspglb.web}. Others, of types defined in 3DLDF, are described in subsequent chapters. + +@deftypevr {Constants} bool ldf_real_float +@deftypevrx {} bool ldf_real_double +@c +Set to 0 or 1 to match the values of the preprocessor macros +@code{LDF_REAL_FLOAT} and @code{LDF_REAL_DOUBLE}. The latter are used +for conditional compilation and determine whether @code{real} is +``typedeffed'' to @code{float} or @code{double}, i.e., whether +@code{real} is made to be a synonym of @code{float} or @code{double} +using @code{typedef}. + +@code{ldf_real_float} and @code{ldf_real_double} can be used to control +conditional expressions in non-conditionally compiled code. +@end deftypevr + + @deftypevr {Constant} real PI @c The value of @code{PI} @@ -63,26 +79,37 @@ @code{first} is @code{INVALID_REAL} and @code{second} is 0. @end deftypevr -@deftypevr Constant real MAX_REAL +@deftypevar real MAX_REAL @c @cindex system dependencies @c -The largest @code{real} value permitted in 3DLDF. It -is the second largest @code{real} value (i.e., @code{float} or -@code{double}) on a given machine (@code{INVALID_REAL} is the largest). - -However, the way it's calculated -depends on the system's floating point representation and the size of -certain data types. Currently, @code{MAX_REAL} can only be calculated -correctly for 32-bit, little-endian architectures. I plan to fix this soon, -so that it will work on other architectures soon. When I have, I will -supply a patch. -@xref{Ports}. +The largest @code{real} value permitted in the the elements of +@code{Transforms} and the coordinates of +@code{Points}. It is the second largest @code{real} value (i.e., +@code{float} or @code{double}) on a given machine (@code{INVALID_REAL} +is the largest). + +@code{MAX_REAL} is a variable, but it should be used like a constant. +In other words, users should never reset its value. It can't be +declared @code{const} because its value must be calculated using +function calls, which can't be done before the entry point of the +program, i.e., @code{main()}. Therefore, the value of @code{MAX_REAL} +is calculated at the beginning of @code{main()}. +@end deftypevar -@end deftypevr +@deftypevar real MAX_REAL_SQRT +The square root of @code{MAX_REAL}. + +@code{MAX_REAL_SQRT} is a variable, but it should be used like a +constant. In other words, users should never reset its value. It can't +be declared @code{const} because its value is calculated using the +@code{sqrt()} function, +which can't be done before the entry point of the +program, i.e., @code{main()}. Therefore, the value of +@code{MAX_REAL_SQRT} is set after @code{MAX_REAL} is calculated, at the +beginning of @code{main()}. -@deftypevr Constant real MAX_REAL_SQRT -The square root of @code{MAX_REAL}. Used in @code{Point::magnitude()} +@code{MAX_REAL_SQRT} is used in @code{Point::magnitude()} (@pxref{Vector Operations}). The magnitude of a @code{Point} is found by using the formula @iftex @@ -101,6 +128,9 @@ will all be less than or equal to @code{MAX_REAL} before trying to calculate them. + + + @c !! TO DO. Metafont implements an operation called @dfn{Pythagorean addition}, notated as ``@code{++}''which @@ -159,4 +189,4 @@ @cindex TO DO @c list of ``things to do''. -@end deftypevr +@end deftypevar diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/graphics/eps/3DLDFmp.1 3DLDF-1.1.5.1/DOC/TEXINFO/graphics/eps/3DLDFmp.1 --- 3DLDF-1.1.4/DOC/TEXINFO/graphics/eps/3DLDFmp.1 1970-01-01 01:00:00.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/graphics/eps/3DLDFmp.1 2003-11-12 20:54:56.000000000 +0100 @@ -0,0 +1,114 @@ +%!PS +%%BoundingBox: -100 -34 264 120 +%%Creator: MetaPost +%%CreationDate: 2003.02.25:1619 +%%Pages: 1 +%*Font: cmmi10 9.96265 9.96265 50:c00000006 +%*Font: cmr7 6.97385 6.97385 30:f +%*Font: cmr10 9.96265 9.96265 28:ca9d04 +%%EndProlog +%%Page: 1 1 + 0 0.5 dtransform truncate idtransform setlinewidth pop [] 0 setdash + 1 setlinejoin 10 setmiterlimit +newpath 0 0 moveto +85.03935 0 lineto +85.03935 85.03935 lineto +0 85.03935 lineto + closepath stroke + [3 3 ] 0 setdash 1 setlinecap +newpath 0 0 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n0Ÿ89è´´ƒ¿ú·¿ZB´£ ݼ¤˜4$VC;–n]‰½;[&†vÂ^§Ÿ…˜.y]íìé÷`÷“28Q7»ä•ÄwNHש™èu‚ù:“BtšÙ¥NÿŒ;¹I}6½ìÒ鸡ã:õ²K§[£ÓØŽ_{VŒN_»9ÿ踶v:öåúcŽ‚”I™vºì^'_2)Ñ®:=íÓÙ–£ÂtZÚø@›øC΂”IivüêÿËXôNƒôfx:-íüö“gœûOi´âtØÕÒn8õl£¿ZÎFOB]'X2)µõ;ã¿þ: +ÆžN[»§ý¯FO§­Ýæ®sÔÙƒNW» ãñÓ§ÏZû-°«©]Ë`—í@­M¬©Ýã§ûÓif%8»Û¿ eR¢]ßÀ.èŤLJ³ŸžOJ¸±Žvå¤LÈnŸRÉ_*ÙáK%;|©d‡/•ì𥒾T²Ã—JvøRÉ_*ÙáK%;|©d‡/•ì𥒾T²Ã—JvøRÉ_*ÙáK%;|©d‡/•ì𥒾T²Ã—JvøRÉ_*ÙáK%;|©d‡/•ì𥒾T²Ã—JvøRÉ_*ÙáK%;|©d‡/•ìð¥JfçîÿuE:;…Bvø>d‡ÙáCvø>d‡ÙáCvø>d‡ÙáCvø>d‡ÙáCvø>d‡ÙáCvø>d‡ÙáCvø>d‡ÙáCvø>d‡ÙáCvø>d‡ÏÚε)¨ôWÿÌ­(¦¸>Xì +
+ +
+
+Fig. 3. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 3 not displayed.] +@end ifinfo + In @code{drawdot()}, a @code{Color} argument precedes the @code{string} argument for the pen, so ``@code{Colors::black}'' must be specified as a placeholder in the call to @@ -118,6 +137,24 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 4. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 4 not displayed.] +@end ifinfo @noindent For complete descriptions of @code{drawdot()} and @code{undrawdot()}, @@ -159,6 +196,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 5. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 5 not displayed.] +@end ifinfo + @noindent @code{p0.draw(p1)} is equivalent in its effect to @code{p1.draw(p0)}. @@ -200,10 +256,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 6. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 6 not displayed.] +@end ifinfo + The function @code{Point::undraw()} takes a required @code{Point&} argument and optional @code{string} arguments for the dash pattern and the @@ -235,10 +310,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 7. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 7 not displayed.] +@end ifinfo + For complete descriptions of @code{draw()} and @code{undraw()}, see @ref{Point Drawing Functions,,Point Reference; Drawing}. @@ -321,6 +415,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 8. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 8 not displayed.] +@end ifinfo + For complete descriptions of @code{Point::label()} and @code{Point::dotlabel()}, see @ref{Labelling Points,,Points; Labelling}. diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/gspaths.texi 3DLDF-1.1.5.1/DOC/TEXINFO/gspaths.texi --- 3DLDF-1.1.4/DOC/TEXINFO/gspaths.texi 2003-12-09 19:59:58.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/gspaths.texi 2004-01-16 17:40:17.000000000 +0100 @@ -1,16 +1,12 @@ @c gspaths.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: gspaths.texi,v 1.4 2003/12/09 18:59:58 lfinsto1 Exp $ - -@c @ifinfo -@c @include 3DLDFmac.texi -@c @end ifinfo - +@c $Id: gspaths.texi,v 1.7 2004/01/16 13:45:00 lfinsto1 Exp lfinsto1 $ + @node Paths, Plane Figures, Drawing and Labeling Points, Top @chapter Paths @@ -77,7 +73,7 @@ * Declaring and Initializing Paths:: * Drawing and Filling Paths Intro:: @end menu - + @node Declaring and Initializing Paths, Drawing and Filling Paths Intro, Paths, Paths @section Declaring and Initializing Paths @@ -112,7 +108,24 @@ @end tex @end iftex - +@ifhtml +@html +

+
+ +
+
+Fig. 9. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 9 not displayed.] +@end ifinfo @code{Paths} created in this way are important, because they are guaranteed to be linear, as long as no operations are performed on them @@ -168,6 +181,24 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 10. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 10 not displayed.] +@end ifinfo Another constructor must be used for @code{Paths} with more than one connector and an arbitrary number of @code{Points}. @@ -233,6 +264,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 11. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 11 not displayed.] +@end ifinfo + As mentioned above (@pxref{Accuracy}), specifying connectors is problematic for three-dimensional @code{Paths}, because MetaPost ultimately calculates the ``most pleasing curve'' @@ -299,6 +349,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 12. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 12 not displayed.] +@end ifinfo + Since @code{pa} is closed, it can be filled as well as drawn. The following example uses @code{fill()} with a @code{Color} argument, in order to avoid having a large splotch of black on the page. @@ -321,6 +390,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 13. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 13 not displayed.] +@end ifinfo + Closed @code{Paths} can be filled and drawn, using the function @code{filldraw()}. This function draws the @code{Path} using the pen specified, or MetaPost's @code{currentpen} by default. A @code{Color} @@ -360,6 +448,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 14. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 14 not displayed.] +@end ifinfo + The following example uses arguments for the @code{Colors} used for drawing and filling, and the pen. The empty string argument before the pen argument is a placeholder for the dash pattern argument. @@ -382,6 +489,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 15. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 15 not displayed.] +@end ifinfo + @code{Paths} can also be ``undrawn'', ``unfilled'', and ``unfilldrawn'', using the corresponding functions: @@ -401,10 +527,29 @@ \OEX{Projections::PARALLEL_X_Y} \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 16. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 16 not displayed.] +@end ifinfo + @example pa.fill(gray); Path q; @@ -425,10 +570,29 @@ \OEX{Projections::PARALLEL_X_Y} \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 17. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 17 not displayed.] +@end ifinfo + The function @code{unfilldraw()} takes a @code{Color} argument for drawing the @code{Path}, which is @code{*Colors::background_color} by default. This makes it possible to unfill the @code{Path} while drawing @@ -451,10 +615,29 @@ \OEX{Projections::PARALLEL_X_Y} \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 18. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 18 not displayed.] +@end ifinfo + The following example demonstrates the use of @code{unfilldraw()} with @code{black} as its @code{Color} argument. Unfortunately, it also demonstrates one of the limitations of the surface hiding algorith: The @@ -498,10 +681,30 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 19. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 19 not displayed.] +@end ifinfo + @xref{Drawing and Filling Paths,,Paths; Drawing and Filling}, for more information, and complete descriptions of the functions. + diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/gspict.texi 3DLDF-1.1.5.1/DOC/TEXINFO/gspict.texi --- 3DLDF-1.1.4/DOC/TEXINFO/gspict.texi 2003-12-09 20:00:19.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/gspict.texi 2004-01-16 17:40:17.000000000 +0100 @@ -1,11 +1,11 @@ @c gspict.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: gspict.texi,v 1.5 2003/12/09 19:00:19 lfinsto1 Exp $ +@c $Id: gspict.texi,v 1.8 2004/01/12 18:37:07 lfinsto1 Exp lfinsto1 $ @node Pictures, Intersections, Solid Figures, Top @chapter Pictures @@ -80,6 +80,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 50. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 50 not displayed.] +@end ifinfo + The @cpp{} code for @PREFIG{} starts with the command @code{beginfig(1)} and ends with the command @code{endfig(1)}. @@ -153,6 +172,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 51. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 51 not displayed.] +@end ifinfo + Multiple objects, or complex objects made up of sub-objects, can be stored in a @code{Picture}, so that operations can be applied to them as a group: @@ -251,6 +289,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 52. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 52 not displayed.] +@end ifinfo + Let's say the complex object in @PREFIG{} represents a furnace. From the point of view of 3DLDF, however, it's not an object at all, and the drawing consists of a collection of unrelated @@ -368,7 +425,7 @@ * Parallel Projections:: * The Perspective Projection:: @end menu - + @node Parallel Projections, The Perspective Projection, Projections, Projections @subsection Parallel Projections @@ -411,6 +468,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 53. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 53 not displayed.] +@end ifinfo + If the objects do not lie in the x-y plane, or a plane parallel to the x-y plane, then the projection will be distorted: @@ -436,6 +512,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 54. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 54 not displayed.] +@end ifinfo + @code{Picture::output()} can be called with an additional @code{real} argument @var{factor} for magnifying or shrinking the @code{Picture}. @@ -480,10 +575,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 55. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 55 not displayed.] +@end ifinfo + Parallel projection onto the x-z and z-y planes are completely analogous to parallel projection onto the x-y plane. @@ -554,10 +668,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 56. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 56 not displayed.] +@end ifinfo + While it's possible to use 3DLDF to make a perspective construction in the traditional way, as @PREFIG{} shows, the code for @NEXTFIG{} achieves the same result more efficiently: @@ -593,6 +726,24 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 57. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 57 not displayed.] +@end ifinfo In @TWOPREFIG{}, it was convenient to start with the corner point @math{r_0}; @@ -726,10 +877,29 @@ \EGRP \SEEX{.25cm}{.5cm}{0cm}{0cm} \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 58. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 58 not displayed.] +@end ifinfo + In @PREFIG{}, the @DEG{0.5} vanishing point is nearly @iftex @tex @@ -807,6 +977,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 59. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 59 not displayed.] +@end ifinfo + @node Focuses Getstart, Surface Hiding, Projections, Pictures @section Focuses @@ -920,6 +1109,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 60. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 60 not displayed.] +@end ifinfo + The ``up'' direction is calculated by the @code{Focus} constructor automatically. An optional argument can be used to specify the angle by which to rotate the @code{Focus} about @@ -965,6 +1173,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 61. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 61 not displayed.] +@end ifinfo + Alternatively, a @code{Focus} can be declared using three @code{real} arguments each for the x, y, and z-coordinates of @code{position} and @code{direction}, respectively, followed by the @code{real} arguments @@ -997,6 +1224,24 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 62. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 62 not displayed.] +@end ifinfo @code{Focuses} contain two @code{Transforms}, @code{transform} and @code{persp}. A @code{Focus} can be located anywhere in 3DLDF's coordinate system. @@ -1073,6 +1318,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 63. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 63 not displayed.] +@end ifinfo + In @PREFIG{}, @code{current_picture} is output 5 times within a single MetaPost figure. Since the file passed to MetaPost is called @file{persp.mp}, the file of Encapsulated PostScript (EPS) code @@ -1152,6 +1416,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 64. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 64 not displayed.] +@end ifinfo + If instead, @var{c} is filled or filldrawn, only the parts of @var{r} that are not covered by @var{c} should be visible: @@ -1176,6 +1459,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 65. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 65 not displayed.] +@end ifinfo + What parts of @code{r} are covered depend on the point of view, i.e., the position and direction of the @code{Focus} used for outputting the @code{Picture}: @@ -1201,6 +1503,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 66. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 66 not displayed.] +@end ifinfo + @cindex surface hiding @cindex hidden surface algorithm @c @@ -1333,6 +1654,24 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 67. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 67 not displayed.] +@end ifinfo In @PREFIG{}, the @code{Rectangles} @math{r_0} and @math{r_1} intersect along the x-axis. The z-values of the @code{world_coordinates} of @math{r_0} are @@ -1391,6 +1730,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 68. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 68 not displayed.] +@end ifinfo + In @NEXTFIG{}, the @code{Shapes} on @code{current_picture} are sorted according to the minimum z-values of the @code{projective_coordinates} of the @code{Points} belonging to the @code{Shapes}. @code{r1} is drawn @@ -1426,6 +1784,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 69. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 69 not displayed.] +@end ifinfo + Neither sorting by the mean z-value in the @code{projective_coordinates}, nor suppressing sorting does any good. In each case, one @code{Rectangle} is always drawn and filled last, @@ -1462,6 +1839,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 70. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 70 not displayed.] +@end ifinfo + Even where objects don't intersect, their projections may. In order to handle these cases properly, it is necessary to break up the @code{Shapes} on a @code{Picture} into smaller @code{Shapes}, until @@ -1548,6 +1944,34 @@ \EEX 0 \fi \PEX +@end tex +@end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 71. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 71 not displayed.] +@end ifinfo + +@c I've put this here, so that it doesn't interfere with the Emacs-Lisp +@c routine I'm using to insert the figure numbers for HTML and Info +@c output. LDF 2003.12.16. +@c +@iftex +@tex \smallskip @end tex @end iftex diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/gsplane.texi 3DLDF-1.1.5.1/DOC/TEXINFO/gsplane.texi --- 3DLDF-1.1.4/DOC/TEXINFO/gsplane.texi 2003-12-08 19:37:44.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/gsplane.texi 2004-01-16 17:40:17.000000000 +0100 @@ -1,22 +1,15 @@ @c gsplane.texi - + @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: gsplane.texi,v 1.3 2003/12/08 18:37:44 lfinsto1 Exp $ - -@c @ifinfo -@c @include 3DLDFmac.texi -@c @end ifinfo +@c $Id: gsplane.texi,v 1.6 2004/01/16 13:45:28 lfinsto1 Exp lfinsto1 $ @node Plane Figures, Solid Figures, Paths, Top @chapter Plane Figures - - - @tindex Circle @tindex Ellipse @tindex Polygon @@ -55,6 +48,8 @@ * Circles Getstart:: @end menu + + @node Regular Polygons Getstart, Rectangles Getstart, Plane Figures, Plane Figures @section Regular Polygons @@ -82,10 +77,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 20. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 20 not displayed.] +@end ifinfo + Three additional arguments cause the pentagon to be rotated about the x, y, and z axes by the amount indicated. In this example, it's rotated @DEG{90} @@ -110,10 +124,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 21. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 21 not displayed.] +@end ifinfo + In this example, it's rotated @DEG{36} about the y-axis, so that it appears to point in the opposite @@ -138,10 +171,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 22. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 22 not displayed.] +@end ifinfo + In this example, it's rotated @DEG{90} about the z-axis, so that it lies in the z-y plane: @@ -167,10 +219,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 23. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 23 not displayed.] +@end ifinfo + In this example, it's rotated @DEG{45} about the x, y, and z-axes in that order: @@ -195,10 +266,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 24. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 24 not displayed.] +@end ifinfo + @code{Reg_Polygons} need not be centered about the @code{origin}. If another @code{Point} @var{pt} is used as the first argument, the @code{Reg_Polygon} is first created with its center at the origin, then the specified @@ -227,10 +317,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 25. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 25 not displayed.] +@end ifinfo + In the following example, the @code{Reg_Polygon} @code{polygon} is first declared using the default constructor, which creates an empty @code{Reg_Polygon}. Then, the @code{polygon} is repeatedly changed using @@ -273,6 +382,24 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 26. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 26 not displayed.] +@end ifinfo @node Rectangles Getstart, Ellipses Getstart, Regular Polygons Getstart, Plane Figures @section Rectangles @@ -303,6 +430,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 27. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 27 not displayed.] +@end ifinfo + Three additional arguments can be used to specify rotation about the x, y, and z-axes respectively: @@ -325,10 +471,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 28. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 28 not displayed.] +@end ifinfo + If a @code{Point} @var{p} other than the origin is specified as the center of the @code{Rectangle}, the latter is first created in the x-z plane, centered about the origin, as above. Then, any rotations specified are @@ -364,6 +529,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 29. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 29 not displayed.] +@end ifinfo + This constructor has a corresponding setting function: @example @@ -396,6 +580,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 30. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 30 not displayed.] +@end ifinfo + @code{Rectangles} can also be specified using four @code{Points} as arguments, whereby they must be ordered so that they are contiguous in the resulting @code{Rectangle}: @@ -439,6 +642,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 31. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 31 not displayed.] +@end ifinfo + This constructor checks whether the @code{Point} arguments are coplanar, however, it does not check whether they are really the corners of a valid rectangle; the user, or the code that calls this function, must @@ -483,6 +705,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 32. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 32 not displayed.] +@end ifinfo + This constructor is not really intended to be used directly, but should mostly be called from within other functions, that should ensure that the arguments produce a rectangular @code{Rectangle}. There is also no @@ -534,6 +775,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 33. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 33 not displayed.] +@end ifinfo + As you may expect, this constructor has a corresponding setting function: @@ -588,6 +848,24 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 34. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 34 not displayed.] +@end ifinfo @node Circles Getstart, , Ellipses Getstart, Plane Figures @section Circles @@ -622,6 +900,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 35. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 35 not displayed.] +@end ifinfo + This constructor, too, has a corresponding setting function: @example @@ -653,10 +950,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 36. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 36 not displayed.] +@end ifinfo + In the preceding example, the last argument to @code{set()}, namely ``64'', is for the number of @code{Points} used for constructing the perimeter of the @code{Circle}. The default value is 16, however, if it is used, diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/gspoint.texi 3DLDF-1.1.5.1/DOC/TEXINFO/gspoint.texi --- 3DLDF-1.1.4/DOC/TEXINFO/gspoint.texi 2003-12-03 21:08:20.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/gspoint.texi 2004-01-16 17:40:17.000000000 +0100 @@ -1,15 +1,11 @@ @c gspoint.texi - + @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: gspoint.texi,v 1.2 2003/12/03 20:08:19 lfinsto1 Exp $ - -@c @ifinfo -@c @include 3DLDFmac.texi -@c @end ifinfo +@c $Id: gspoint.texi,v 1.4 2004/01/16 13:45:57 lfinsto1 Exp lfinsto1 $ @node Points, Transforming Points, Using 3DLDF, Top @chapter Points @@ -18,7 +14,7 @@ * Declaring and Initializing Points:: * Setting and Assigning to Points:: @end menu - + @node Declaring and Initializing Points, Setting and Assigning to Points, Points, Points @section Declaring and Initializing Points diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/gssolfig.texi 3DLDF-1.1.5.1/DOC/TEXINFO/gssolfig.texi --- 3DLDF-1.1.4/DOC/TEXINFO/gssolfig.texi 2003-12-08 19:38:59.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/gssolfig.texi 2004-01-16 17:40:17.000000000 +0100 @@ -1,11 +1,11 @@ @c gssolfig.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: gssolfig.texi,v 1.3 2003/12/08 18:38:59 lfinsto1 Exp $ +@c $Id: gssolfig.texi,v 1.5 2004/01/12 18:37:48 lfinsto1 Exp lfinsto1 $ @node Solid Figures, Pictures, Plane Figures, Top @chapter Solid Figures @@ -53,10 +53,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 37. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 37 not displayed.] +@end ifinfo + In the following example, the @code{Cuboid} is ``filldrawn'', so that the lines dilineating the hidden surfaces of the @code{Cuboid} are covered. @@ -77,10 +96,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 38. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 38 not displayed.] +@end ifinfo + @node Polyhedron Getstart, , Cuboid Getstart, Solid Figures @section Polyhedron @@ -110,7 +148,7 @@ * Dodecahedron Getstart:: * Icosahedron Getstart:: @end menu - + @node Tetrahedron Getstart, Dodecahedron Getstart, Polyhedron Getstart, Polyhedron Getstart @subsection Tetrahedron @@ -138,10 +176,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 39. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 39 not displayed.] +@end ifinfo + @node Dodecahedron Getstart, Icosahedron Getstart, Tetrahedron Getstart, Polyhedron Getstart @subsection Dodecahedron @@ -168,10 +225,29 @@ \OEX{PARALLEL_X_Y} \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 40. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 40 not displayed.] +@end ifinfo + @c ***************************** @iftex @@ -184,10 +260,29 @@ \OEX{PARALLEL_X_Z} \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 41. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 41 not displayed.] +@end ifinfo + @c ***************************** Please note that the @code{Dodecahedron} in @NEXTFIG{} is drawn, and not @@ -203,10 +298,29 @@ \OEX{PARALLEL_Z_Y} \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 42. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 42 not displayed.] +@end ifinfo + @c ***************************** @iftex @@ -219,10 +333,29 @@ \OEX{} \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 43. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 43 not displayed.] +@end ifinfo + @c ********************************** In @NEXTFIG{}, @code{d} is filldrawn. In this case, @@ -239,10 +372,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 44. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 44 not displayed.] +@end ifinfo + @node Icosahedron Getstart, , Dodecahedron Getstart, Polyhedron Getstart @subsection Icosahedron @@ -269,10 +421,29 @@ \OEX{PARALLEL_X_Y} \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 45. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 45 not displayed.] +@end ifinfo + @c *************** @iftex @@ -285,10 +456,29 @@ \OEX{PARALLEL_X_Z} \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 46. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 46 not displayed.] +@end ifinfo + @c *************** @iftex @@ -301,10 +491,29 @@ \OEX{PARALLEL_Z_Y} \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 47. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 47 not displayed.] +@end ifinfo + @c *************** @iftex @@ -318,10 +527,29 @@ \OEX{} \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 48. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 48 not displayed.] +@end ifinfo + @c *************** In @NEXTFIG{}, @code{i} is filldrawn. In this case, @@ -338,9 +566,26 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex - +@ifhtml +@html +

+
+ +
+
+Fig. 49. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 49 not displayed.] +@end ifinfo diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/gstranpt.texi 3DLDF-1.1.5.1/DOC/TEXINFO/gstranpt.texi --- 3DLDF-1.1.4/DOC/TEXINFO/gstranpt.texi 2003-12-08 19:41:17.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/gstranpt.texi 2004-01-16 17:40:17.000000000 +0100 @@ -1,11 +1,11 @@ @c gstranpt.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: gstranpt.texi,v 1.3 2003/12/08 18:41:17 lfinsto1 Exp $ +@c $Id: gstranpt.texi,v 1.6 2004/01/12 18:38:48 lfinsto1 Exp lfinsto1 $ @node Transforming Points, Transforms, Points, Top @chapter Transforming Points @@ -74,10 +74,8 @@ @node Shifting Points, Scaling Points, Transforming Points, Transforming Points @section Shifting - - The function -@c @code{shift()} +@code{shift()} adds its arguments to the corresponding @code{world_coordinates} of a @code{Point}. In the following example, the function @code{show()} is used to print the @code{world_coordinates} @@ -241,6 +239,24 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 1. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 1 not displayed.] +@end ifinfo @node Rotating Points, , Shearing Points, Transforming Points @section Rotating @@ -366,6 +382,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 2. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 2 not displayed.] +@end ifinfo + @cindex bugs I have sometimes gotten erroneous results using @code{rotate()} for rotation about two @code{Points}. It's usually worked to reverse the diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/gstransf.texi 3DLDF-1.1.5.1/DOC/TEXINFO/gstransf.texi --- 3DLDF-1.1.4/DOC/TEXINFO/gstransf.texi 2003-12-08 19:59:14.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/gstransf.texi 2004-01-16 17:40:17.000000000 +0100 @@ -1,15 +1,11 @@ @c gstransf.texi - + @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: gstransf.texi,v 1.3 2003/12/08 18:59:14 lfinsto1 Exp $ - -@c @ifinfo -@c @include 3DLDFmac.texi -@c @end ifinfo +@c $Id: gstransf.texi,v 1.5 2004/01/16 13:46:25 lfinsto1 Exp lfinsto1 $ @node Transforms, Drawing and Labeling Points, Transforming Points, Top @chapter Transforms @@ -247,7 +243,7 @@ 0 0 0 1 @end example - + @menu * Applying Transforms to Points Intro:: diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/instlrun.texi 3DLDF-1.1.5.1/DOC/TEXINFO/instlrun.texi --- 3DLDF-1.1.4/DOC/TEXINFO/instlrun.texi 2003-12-09 18:50:17.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/instlrun.texi 2004-01-16 17:40:17.000000000 +0100 @@ -1,11 +1,11 @@ @c instlrun.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: instlrun.texi,v 1.4 2003/12/09 17:50:14 lfinsto1 Exp $ +@c $Id: instlrun.texi,v 1.7 2004/01/16 14:41:12 lfinsto1 Exp lfinsto1 $ @node Installing and Running 3DLDF, Typedefs and Utility Structures, Intersections, Top @@ -62,6 +62,67 @@ See the files @file{README} and @file{INSTALL} in the 3DLDF distribution for more information. +@menu +* Template Functions:: +@end menu + +@node Template Functions, , Installing 3DLDF, Installing 3DLDF +@subsection Template Functions + +@cindex templates +@cindex template functions +@cindex function templates +@c +3DLDF 1.1.5 is the first release that contains @dfn{template functions}, +namely +@code{template C* create_new()}, which is defined in +@file{creatnew.web}, and +@code{template Real get_second_largest()}, which is defined +in @code{gsltmplt.web}. +@xref{Dynamic Allocation of Shapes}, and +@ref{Get Second Largest Real}. + +In order for template functions to be instantiated correctly, their +@emph{definitions} must be available in each compilation unit where +specializations are declared or used. For non-template functions, it +suffices for their @emph{declarations} to be available, and their +definitions are found at link-time. For this reason, the +definitions of @code{create_new()} and @code{get_second_largest()} are +in their own CWEB files, and are written to their own header files. The +latter are included in the other CWEB files that need them. + +In addition, @samp{AM_CXXFLAGS = -frepo} has been added to the file +@file{Makefile.am} in @file{3DLDF-1.1.5/CWEB/}, so that the @cpp{} +compiler is called using the @samp{-frepo} option. +The manual @cite{Using and Porting the GNU Compiler +Collection} explains this as follows: + +@quotation +``Compile your template-using code with @samp{-frepo}. The compiler will +generate files with the extension @file{.rpo} listing all of the template +instantiations used in the corresponding object files which could be +instantiated there; the link wrapper, @samp{collect2}, will then update the +@file{.rpo} files to tell the compiler where to place those instantiations and +rebuild any affected object files. The link-time overhead is negligible +after the first pass, as the compiler will continue to place the +instantiations in the same files.''@c +@c +@footnote{Stallman, Richard M. @cite{Using and Porting the GNU Compiler +Collection}, p.@w{ }285.} +@c +@end quotation + +The first time the executable @file{3dldf} is built, the files that use +the template functions are recompiled one or more times, and the linker +is also called several times. This doesn't happen anymore, once the +@file{.rpo} files exist. + +Template instantiation differs from compiler to compiler, so using +template functions will tend to make 3DLDF less portable. I am no +longer able to compile it on the DECalpha Personal Workstation I had +been using with the DEC @cpp{} compiler. +@xref{Ports}, for more information. + @node Running 3DLDF, , Installing 3DLDF, Installing and Running 3DLDF @section Running 3DLDF @@ -151,6 +212,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 72. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 72 not displayed.] +@end ifinfo + @enumerate @item Save @file{main.web}, and any other CWEB files you've changed. @@ -221,7 +301,6 @@ @code{ps2pdf}, or to some other format using the appropriate program. @end enumerate - I sincerely hope that it worked. If it didn't, ask your local computer wizard for help. @@ -242,10 +321,214 @@ document correctly. @menu +* Converting EPS Files:: * Command Line Arguments:: @end menu -@node Command Line Arguments, , Running 3DLDF, Running 3DLDF + +@node Converting EPS Files, Command Line Arguments, Running 3DLDF, Running 3DLDF +@subsection Converting EPS Files + +@cindex ImageMagick +@cindex ImageMagick convert +@cindex convert (ImageMagick) +@cindex PNG (Portable Network Graphics) +@cindex Portable Network Graphics (PNG) +@cindex PS (PostScript) +@cindex PostScript (PS) +@cindex structured PostScript +@cindex PostScript, structured +@cindex EPS (Encapsulated PostScript) +@cindex Encapsulated PostScript (EPS) +@c +@uref{http://www.imagemagick.org, ImageMagick} is a +``collection of tools and libraries'' for image manipulation. +It provides a `@t{convert}' utility which can convert images from one +format to another. It can convert structured PostScript (PS) to +to @uref{http://www.libpng.org/pub/png/index.html, +Portable Network Graphics (PNG)}, but @emph{not} +EPS (Encapsulated PostScript) to PNG. Nor can it convert EPS to +structured PostScript. + +It is possible to have MetaPost generate structured PostScript directly +by including the command @samp{prologues:=1;} at the beginning of the +MetaPost input. +However, this ``generally doesn't work when you use @TeX{} +fonts.''@c +@footnote{Hobby, @cite{A User's Manual for MetaPost}, pp.@w{ }21--22.} +@c +This is a significant problem if your labels contain math mode +material, and you haven't already taken steps to ensure that appropriate +fonts will be used in the PS output. + +In the following, I describe the @emph{only way} I've found to convert +an EPS image to PNG format while still using @TeX{} fonts. There may be +other and better ways of doing this, but I haven't found them. + + +@enumerate +@item +Assume the EPS image is in the file @file{3DLDFmp.1} +Include the EPS image in a @TeX{} file +which looks like this: + +@example +\advance\voffset by -1in +\advance\hoffset by -1in +\nopagenumbers +\input epsf +\epsfverbosetrue +\def\epsfsize#1#2@OCB{}#1@CCB{} +\setbox0=\vbox@OCB{}\epsffile@OCB{}3DLDFmp.1@CCB{}@CCB{} +\vsize=\ht0 +\hsize=\wd0 +\special@OCB{}papersize=\the\wd0,\the\ht0@CCB{} +\box0 +\bye +@end example + +@b{Do not} name this file @file{3DLDFmp.1.tex}! +While this worked fine for me on a DECalpha Personal Workstation +running under Tru64 Unix 5.1, with @TeX{}, Version 3.1415 +(C version 6.1), and @b{dvipsk} 5.58f, +it failed on a PC Pentium II XEON under Linux 2.4, +with @TeX{}, Version 3.14159 (Web2C 7.4.5), and +@b{dvips(k)} 5.92b, kpathsea version 3.4.5, +with the following error message: +@display +``No BoundingBox comment found in file examples.1; using defaults'' +@end display + +@noindent +The resulting PS image had the wrong size and the +the graphic was positioned improperly. + +Apparently, it confuses the EPSF macros when the name of an +included image is the same as @samp{\jobname}. +So, for this example, let's call it @file{3DLDFmp.1_.tex}. + +You don't really need to call the macro @samp{\epsfverbosetrue}. If you +do, it will print the measurements of the bounding box and other information +to standard output.@c +@c +@footnote{Rokicki, @cite{Dvips: A DVI-to-PostScript Translator}, p.@w{ }24.} + +@item +Run @samp{tex 3DLDFmp.1_.tex}. + +@item +Run @samp{dvips -o 3DLDF.1.ps 3DLDFmp.1_.dvi}. + +@item +Run @samp{convert 3DLDF.1.ps 3DLDFmp.1.png}. +@end enumerate + +@cindex ImageMagick +@cindex ImageMagick display +@cindex display (ImageMagick) +@c +@uref{http://www.imagemagick.org, ,ImageMagick} +supplies a `@command{display}' utility, which can be used to display the +PNG image: + +@example +display 3DLDFmp.1.png +@end example + +It can be included in an HTML document as follows: + +@example +[Fig. 1]..png} to a CD-R (Compact +Disk, Recordable), when `@i{number}' had more than one digit. + +@menu +* Converting EPS Files ELISP:: +@end menu + +@node Converting EPS Files ELISP, , Converting EPS Files, Converting EPS Files +@subsubsection Emacs-Lisp Functions + + +@cindex PNG (Portable Network Graphics) +@cindex Portable Network Graphics (PNG) +@cindex PS (PostScript) +@cindex PostScript (PS) +@cindex structured PostScript +@cindex PostScript, structured +@cindex EPS (Encapsulated PostScript) +@cindex Encapsulated PostScript (EPS) +@c +@cindex Emacs-Lisp +The file @file{3DLDF-@value{VERSION}/CWEB/cnepspng.el} contains +definitions of two Emacs-Lisp functions that can be used to +convert Encapsulated PostScript (EPS) files to structured PostScript +(PS) and Portable Network Graphics (PNG) files. + +@deffn {Emacs-Lisp function} convert-eps filename do-not-delete-files +@c +Converts an EPS image file to the PS and PNG formats. + +If called interactively, @command{convert-eps} prompts for the +filename, including the extension, of an +EPS image file. It follows the procedure described above in +@ref{Converting EPS Files}, to create +@file{@var{filename}.ps} and @file{@var{filename}.png}. + +If @var{do-not-delete-files} is @code{nil}, +the @file{.tex}, @file{.dvi}, and @file{.log} files will be deleted. +This is the case when @command{convert-eps} is called interactively +with no prefix argument. +If @command{convert-eps} is called interactively with a prefix +argument, or non-interactively with a non-@code{nil} +@var{do-not-delete-files} argument, these files will not be deleted. +@end deffn + +@deffn {Emacs-Lisp function} convert-eps-loop arg start end +@c +Converts a set of EPS image files to the PS and PNG formats. +The files +must all have the same filename, and the extensions must form a range of +positive integers. For example, @command{convert-eps-loop} can be +used to convert the files @file{3DLDFmp.1}, @file{3DLDFmp.2}, and +@file{3DLDFmp.3} to @file{3DLDFmp.1.ps}, @file{3DLDFmp.2.ps}, and +@file{3DLDFmp.3.ps} on the one hand, and +@file{3DLDFmp.1.png}, @file{3DLDFmp.2.png}, +@file{3DLDFmp.3.png} on the other. + +If @command{convert-eps-loop} is called interactively, +it prompts for @var{filename} @emph{with no extension} +and the starting and ending numbers of the range. + +For all @math{i \in \INT} and @var{start} @math{\le i \le} @var{end}, +@command{convert-eps-loop} checks whether a file named +@file{@var{filename.@math{i}}} exists. If it does, +it calls @command{convert-eps}, passing +@file{@var{filename.@math{i}}} as the latter's @var{filename} argument. + + +@var{do-not-delete-files} is also passed to @command{convert-eps}. If +it's @code{nil}, +the @file{.tex}, @file{.dvi}, and @file{.log} files will be deleted. +This is the case when @command{convert-eps-loop} is called interactively +with no prefix argument. +If @command{convert-eps-loop} is called interactively with a prefix +argument, or non-interactively with a non-@code{nil} +@var{do-not-delete-files} argument, these files will not be deleted. +@end deffn + + +@node Command Line Arguments, , Converting EPS Files, Running 3DLDF @subsection Command Line Arguments @command{3dldf} can be called with the following @dfn{command line arguments}. diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/intersct.texi 3DLDF-1.1.5.1/DOC/TEXINFO/intersct.texi --- 3DLDF-1.1.4/DOC/TEXINFO/intersct.texi 2003-12-03 20:54:15.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/intersct.texi 2004-01-16 17:40:17.000000000 +0100 @@ -1,11 +1,11 @@ @c intersct.texi - + @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: intersct.texi,v 1.2 2003/12/03 19:54:14 lfinsto1 Exp $ +@c $Id: intersct.texi,v 1.3 2004/01/12 18:39:16 lfinsto1 Exp lfinsto1 $ @node Intersections, Installing and Running 3DLDF, Pictures, Top @chapter Intersections diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/intro.texi 3DLDF-1.1.5.1/DOC/TEXINFO/intro.texi --- 3DLDF-1.1.4/DOC/TEXINFO/intro.texi 2003-12-09 19:22:06.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/intro.texi 2004-01-16 17:40:17.000000000 +0100 @@ -1,11 +1,11 @@ @c intro.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: intro.texi,v 1.8 2003/12/09 18:22:05 lfinsto1 Exp $ +@c $Id: intro.texi,v 1.11 2004/01/12 18:39:23 lfinsto1 Exp lfinsto1 $ @comment node-name, next, previous, up @node Introduction, Contributing to 3DLDF, Top, Top @@ -142,6 +142,9 @@ This manual has been created using Texinfo, a documentation system which is part of the GNU Project, whose main sponsor is the Free Software Foundation. +Texinfo can be used to generate online and printed documentation from +the same input files. + For more information about Texinfo, see: @@ -155,14 +158,6 @@ For more information about the GNU Project and the Free Software Foundation, see the following web site: @uref{http://www.gnu.org}. -Texinfo can be used to generate online and printed documentation from -the same input files. This manual is currently designed for printing -@emph{only}. It contains a large amount of @TeX{} text, including the -illustrations, which would be lost if the input files were used to -generate an online version of this manual in its current form. I plan -to make the changes necessary in order to make it possible to generate -online documentation in the not-too-distant future. - The edition of this manual is @value{EDITION} and it documents version @value{VERSION} of 3DLDF. The edition number of the manual and the version number of the program @@ -389,9 +384,30 @@ possible to make use of the latter's facility for writing ASCII text to files using @TeX{}'s @code{\write} command. -@cindex figures -Please note that the figures cannot be shown in the Info or HTML output -formats! +The file @file{3DLDF-@value{VERSION}/CWEB/exampman.web} contains the +@cpp{} code, and the file @file{3DLDF-@value{VERSION}/CWEB/examples.mp} +contains the MetaPost code for generating the illustrations. +3DLDF was built using GCC 2.95 when the illustrations were generated. +For some reason, GCC 3.3 has difficulty with them. It works to generate +them in batches of about 50 with GCC 3.3. + + +@cindex PNG (Portable Network Graphics) +@cindex Portable Network Graphics (PNG) +@cindex PS (PostScript) +@cindex PostScript (PS) +@cindex EPS (Encapsulated PostScript) +@cindex Encapsulated PostScript (EPS) +@c +MetaPost outputs Encapsulated PostScript files. These can be included +in @TeX{} files, as explained below. However, in order to display the +illustrations in the HTML version of this manual, I had to convert them +to @uref{http://www.libpng.org/pub/png/index.html, +PNG (``Portable Network Graphics'') format}. +@xref{Converting EPS Files}, for instructions on how to do this. + +Please note that the illustrations cannot be shown in the Info output +format! If you have problems including the illustrations in the printed version, for example, if your @@ -498,7 +514,10 @@ The version of @file{examples.web} in @file{3DLDF-@value{VERSION}/CWEB} merely includes the files @file{subex1.web} and @file{subex2.web}. If you rename @file{3DLDF-@value{VERSION}/CWEB/exampman.web} to @file{examples.web}, -you can generate the illustrations. +you can generate the illustrations. + + + @node CWEB Documentation, Metafont and MetaPost, About This Manual, Introduction @section CWEB Documentation @@ -672,7 +691,7 @@ @node Caveats, Ports, Metafont and MetaPost, Introduction @section Caveats - + @menu * Accuracy:: * No Input Routine:: @@ -751,7 +770,7 @@ @c @footnote{Flex is a program for generating text scanners and Bison is a parser generator. They are available from -@url{http://www.gnu.org}.} +@uref{http://www.gnu.org}.} @c The syntax of the input code should be as close as possible to that of MetaPost, while taking account of the @@ -768,8 +787,10 @@ @section Ports I originally developed 3DLDF on a DECalpha Personal Workstation with two -processors, under Tru64 Unix 5.1, using the DEC @cpp {} compiler. -I then ported it to a PC Pentium 4 under Linux 2.4, using +processors running under the operating system Tru64 Unix 5.1, using the +DEC @cpp {} compiler. +I then ported it to a PC Pentium 4 running under Linux 2.4, using +the GNU @cpp{} compiler GCC 2.95.3, and a PC Pentium II XEON under Linux 2.4, using GCC 3.3. I am currently only maintaining the last version. I do not believe that it's worthwhile to maintain a version for GCC 2.95. While I would like @@ -778,19 +799,6 @@ This is something where I would be grateful for help from other programmers. -The global constant @code{MAX_REAL}, defined in -@file{pspglb.web}, is initialized using system dependent code. -@xref{Global Constants and Variables}. Currently, 3DLDF can only be -built correctly on a 32-bit little-endian architecture. You don't -necessarily need to know what this means; If @code{MAX_REAL} cannot be -set correctly, 3DLDF will exit with an error message when you try to run -it. Intel and VAX are little-endian, while Motorola and -SPARC are big-endian, as is the DECalpha mentioned -above. If your computer is big-endian, you will need to fix the way @code{MAX_REAL} is -initialized, or get somebody to do it for you. I plan to fix this soon, -so that it will work on other architectures soon. When I have, I will -supply a patch. - Although I am no longer supporting ports to other systems, I have left some conditionally compiled code for managing platform dependencies in the CWEB sources of 3DLDF. This may @@ -818,9 +826,19 @@ handling code for the case that a file can't be included. I hope to improve the way 3DLDF works together with Autoconf and Automake in the near future. - - +3DLDF 1.1.5 is the first release that contains template functions. +Template instantiation differs from compiler to compiler, so using +template functions will tend to make 3DLDF less portable. +@xref{Template Functions}, for more information. +I am no longer able to build 3DLDF on the DECalpha Personal Workstation. +I'm fairly sure that it would be possible to port it, but +I don't plan to do this, since Tru64 Unix 5.1 and the DEC @cpp {} +compiler are non-free software. +@c Local Variables: +@c mode:Texinfo +@c eval:(outline-minor-mode) +@c End: diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/io.texi 3DLDF-1.1.5.1/DOC/TEXINFO/io.texi --- 3DLDF-1.1.4/DOC/TEXINFO/io.texi 2003-12-03 20:54:54.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/io.texi 2004-01-16 17:40:17.000000000 +0100 @@ -1,11 +1,11 @@ @c io.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: io.texi,v 1.2 2003/12/03 19:54:54 lfinsto1 Exp $ +@c $Id: io.texi,v 1.3 2004/01/12 18:39:33 lfinsto1 Exp lfinsto1 $ @node Input and Output, Shape Reference, Color Reference, Top @chapter Input and Output @@ -14,7 +14,7 @@ * I/O Global Variables:: * I/O Functions:: @end menu - + @node I/O Global Variables, I/O Functions, Input and Output, Input and Output @section Global Variables diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/label.texi 3DLDF-1.1.5.1/DOC/TEXINFO/label.texi --- 3DLDF-1.1.4/DOC/TEXINFO/label.texi 2003-12-08 20:11:39.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/label.texi 2004-01-16 17:40:17.000000000 +0100 @@ -1,11 +1,11 @@ @c label.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: label.texi,v 1.3 2003/12/08 19:11:39 lfinsto1 Exp $ +@c $Id: label.texi,v 1.5 2004/01/12 18:39:42 lfinsto1 Exp lfinsto1 $ @node Label Reference, Picture Reference, Transform Reference, Top @chapter Label Reference @@ -42,7 +42,7 @@ * Copying Labels:: * Outputting Labels:: @end menu - + @node Label Data Members, Copying Labels, Label Reference, Label Reference @section Data Members @@ -91,9 +91,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 76. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 76 not displayed.] +@end ifinfo + @end deftypevr diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/line.texi 3DLDF-1.1.5.1/DOC/TEXINFO/line.texi --- 3DLDF-1.1.4/DOC/TEXINFO/line.texi 2003-12-08 20:11:59.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/line.texi 2004-01-16 17:40:16.000000000 +0100 @@ -1,11 +1,11 @@ @c line.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: line.texi,v 1.3 2003/12/08 19:11:59 lfinsto1 Exp $ +@c $Id: line.texi,v 1.5 2004/01/12 18:39:49 lfinsto1 Exp lfinsto1 $ @node Line Reference, Plane Reference, Focus Reference, Top @chapter Line Reference @@ -31,7 +31,7 @@ * Get Path:: * Showing:: @end menu - + @node Line Data Members, Line Global Constants, Line Reference, Line Reference @section Data Members @@ -96,10 +96,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 104. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 104 not displayed.] +@end ifinfo + @end deftypefn @deftypefn {Copy constructor} void Line ({const Line&} @var{l}) diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/path.texi 3DLDF-1.1.5.1/DOC/TEXINFO/path.texi --- 3DLDF-1.1.4/DOC/TEXINFO/path.texi 2003-12-09 20:01:30.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/path.texi 2004-01-16 17:40:16.000000000 +0100 @@ -1,11 +1,11 @@ @c path.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: path.texi,v 1.4 2003/12/09 19:01:30 lfinsto1 Exp $ +@c $Id: path.texi,v 1.6 2004/01/12 18:39:57 lfinsto1 Exp lfinsto1 $ @node Path Reference, Polygon Reference, Plane Reference, Top @chapter Path Reference @@ -33,7 +33,7 @@ * Outputting Paths:: * Path Intersections:: @end menu - + @node Path Data Members, Path Constructors and Setting Functions, Path Reference, Path Reference @section Data Members @@ -92,6 +92,24 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 109. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 109 not displayed.] +@end ifinfo @cindex linear @code{Paths} Some @code{Path} functions only work on @emph{linear @code{Paths}}, @@ -110,7 +128,7 @@ @deftypevr {Protected variable} bool on_free_store @code{true} if the @code{Path} was dynamically allocated on the free store. Otherwise @code{false}. Set to @code{true} only in -@code{create_new_path()}, which should be the only way @code{Paths} are +@code{create_new()}, which should be the only way @code{Paths} are ever dynamically allocated. @xref{Path Constructors and Setting Functions, Path Reference; Constructors and Setting Functions}. @@ -272,6 +290,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 110. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 110 not displayed.] +@end ifinfo + @end deftypefn @@ -368,6 +405,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 111. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 111 not displayed.] +@end ifinfo + @end deftypefn @deftypefn {Setting function} void set (string @var{connector}, bool @var{cycle}, Point* @var{p}, [@dots{}], 0) @@ -411,6 +467,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 112. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 112 not displayed.] +@end ifinfo + @end deftypefn @deftypefn {Constructor} void Path (Point* @var{first_point_ptr}, char* @var{s}, Point* @var{p}, [@dots{}], 0) @@ -465,6 +540,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 113. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 113 not displayed.] +@end ifinfo + @end deftypefn @deftypefn {Setting function} void set (Point @var{*first_point_ptr}, string @var{s}, Point @var{*p}, [@dots{}], 0) @@ -476,30 +570,37 @@ @end deftypefn -@deftypefn {Static function} {Path*} create_new_path ([{const Path*} @var{p} = 0]) -@deftypefnx {Static function} {Path*} create_new_path ({const Path&} @var{p}) +@deftypefn {Template specializations} Path* create_new ({const Path*} @var{p}) +@c +@deftypefnx {} Path* create_new ({const Path&} @var{p}) +@c Pseudo-constructors for dynamic allocation of @code{Paths}. -@code{Paths} should never be dynamically allocated, except by means of -@code{create_new_path()}. -Sets @code{on_free_store} to @code{true}. -@xref{Path Data Members,,Path Reference; Data Members}. +They create a @code{Path} on the free store and allocate memory for it using +@code{new(Path)}. They return a pointer to the new @code{Path}. -In the first version, if @var{p} is 0, the new @code{Path} will be -empty. Otherwise, it will be a copy of @var{*p}. -In the second version, the new @code{Path} will be a -copy of @var{p}. +If @var{p} is a non-zero pointer or a reference, +the new @code{Path} will be a copy of +@var{p}. If the new object is not meant to be a +copy of an existing one, @samp{0} must be passed to +@code{create_new()} as its argument. +@xref{Dynamic Allocation of Shapes}, for more information. -@code{create_new_path()} is used in the drawing and filling functions + +@code{create_new()} is used in the drawing and filling functions for copying a @code{Path} and putting the copy onto a @code{Picture}. @xref{Drawing and Filling Paths, , Path Reference; Drawing and Filling}. @end deftypefn + + + + @node Path Destructor, Path Operators, Path Constructors and Setting Functions, Path Reference @section Destructor @deftypefn {@code{virtual} Destructor} void {~Path} (@code{void}) All of the @code{Points} on a @code{Path} are created by -@code{create_new_point()}, which allocates them dynamically on +@code{create_new()}, which allocates them dynamically on the free store. Therefore, the destructor calls @code{delete()} on all of the pointers on @code{points}. Following this, it calls @code{points.clear()} and @code{connectors.clear()}. @@ -632,6 +733,24 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 114. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 114 not displayed.] +@end ifinfo @end deftypefun @@ -639,7 +758,7 @@ @section Copying @deftypefn {@code{const} virtual function} {Shape*} get_copy (void) -Creates a copy of the @code{Path} using @code{create_new_path()}, which +Creates a copy of the @code{Path} using @code{create_new()}, which returns a pointer to @code{Path}. @code{get_copy()} then casts this pointer to a pointer to @code{Shape} and returns it. @@ -669,12 +788,11 @@ @node Modifying Paths , Affine Transformations for Paths, Clearing Paths , Path Reference @section Modifying -@deftypefn {Inline virtual function} bool set_on_free_store ([bool @var{b} = @code{true}]) -Sets @code{on_free_store} to @var{b}. This function is never used, but -it's a pure virtual function in @code{class Shape}, so every class -derived from @code{Shape} must have one. It was intended for use in the -template function @code{create_new()}, but I haven't been able to get -the latter to work. +@deftypefn {Virtual function} bool set_on_free_store ([bool @var{b} = @code{true}]) +Sets @code{on_free_store} to @var{b}. This is used in the +template function @code{create_new()}. +@xref{Path Constructors and Setting Functions,, +Path Reference; Constructors and Setting Functions}. @end deftypefn @deftypefn {Virtual function} void set_fill_draw_value ({const signed short} @var{s}) @@ -789,10 +907,28 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 115. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 115 not displayed.] +@end ifinfo @end deftypefun @@ -844,10 +980,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 116. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 116 not displayed.] +@end ifinfo + @end deftypefun @deftypefun Transform shift (real @var{x}, [real @var{y} = 0, [real @var{z} = 0]]) @@ -901,10 +1056,28 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 117. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 117 not displayed.] +@end ifinfo @end deftypefun @@ -962,9 +1135,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 118. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 118 not displayed.] +@end ifinfo + @end deftypefun @deftypefn {Virtual function} void shift_times (real @var{x}, [real @var{y} = 1, [real @var{z} = 1]]) @@ -1116,6 +1309,24 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 119. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 119 not displayed.] +@end ifinfo @end deftypefn @@ -1182,6 +1393,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 120. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 120 not displayed.] +@end ifinfo + The arguments: @table @var @@ -1225,6 +1455,24 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 121. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 121 not displayed.] +@end ifinfo @item ddashed A @code{string} representing a ``dash pattern'', as defined in @@ -1256,6 +1504,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 122. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 122 not displayed.] +@end ifinfo + @item ppen A @code{string} representing a ``pen'', as defined in Metafont and MetaPost@c @@ -1297,6 +1564,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 123. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 123 not displayed.] +@end ifinfo + @item picture Indicates the @code{Picture} on which the @code{Path} should be drawn. @@ -1345,6 +1631,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 124. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 124 not displayed.] +@end ifinfo + @end table @end deftypefn @@ -1396,6 +1701,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 125. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 125 not displayed.] +@end ifinfo + @end deftypefn @deftypefn {Non-member function} void draw_axes ([real @var{dist} = 2.5, [string @var{pos_x} = "bot", [string @var{pos_y} = "lft", [string @var{pos_z} = "bot", [{const Color&} @var{ddraw_color} = @code{*Colors::default_color}, [{const string} @var{ddashed} = "", [{const string} @var{ppen} = "", [{const Point&} @var{shift_x} = @code{origin}, [{const Point&} @var{shift_y} = @code{origin}, [{const Point&} @var{shift_z} = @code{origin}, [Picture& @var{picture} = @code{current_picture}]]]]]]]]]]]) @@ -1467,6 +1791,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 126. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 126 not displayed.] +@end ifinfo + In addition, the arguments @var{shift_x}, @var{shift_y}, and @var{shift_z} can be used to adjust the positions of the labels further (see below). @@ -1500,10 +1843,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 127. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 127 not displayed.] +@end ifinfo + In @NEXTFIG{}, the @code{Point P} is used to shift the labels. Please note that placeholders must be used for the first arguments. @@ -1523,10 +1885,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 128. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 128 not displayed.] +@end ifinfo + Please note that the @code{Points} used for placing the labels are three-dimensional @code{Points}, whether the @var{shift_x}, @var{shift_y}, and/or @var{shift_z} arguments are used or not. @@ -1576,7 +1957,24 @@ @end tex @end iftex - +@ifhtml +@html +

+
+ +
+
+Fig. 129. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 129 not displayed.] +@end ifinfo @end deftypefn @@ -1627,6 +2025,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 130. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 130 not displayed.] +@end ifinfo + It can often be useful to draw the outline of a @code{Path}, but to have it hide objects that lie behind it. This is why the default for @var{ffill_color} is @code{*Colors::background_color}. @@ -1694,7 +2111,24 @@ @end tex @end iftex - +@ifhtml +@html +

+
+ +
+
+Fig. 131. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 131 not displayed.] +@end ifinfo @end deftypefn @@ -1750,6 +2184,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 132. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 132 not displayed.] +@end ifinfo + @end deftypefun @deftypefun void unfill ([Picture& @var{picture} = @code{current_picture}]) @@ -1792,10 +2245,28 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 133. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 133 not displayed.] +@end ifinfo @end deftypefun @@ -1865,6 +2336,24 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 134. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 134 not displayed.] +@end ifinfo @end deftypefun @@ -2005,6 +2494,24 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 135. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 135 not displayed.] +@end ifinfo @end deftypefn @@ -2020,9 +2527,7 @@ @c !! ADD EXAMPLES to the function descriptions in this section. @c LDF 2003.07.16. - - -@deftypefn {@code{const} inline function} bool is_on_free_store (void) +@deftypefn {@code{const} function} bool is_on_free_store (void) Returns @code{true}, if the @code{Path} was dynamically allocated on the free store, otherwise @code{false}. @end deftypefn @@ -2144,6 +2649,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 136. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 136 not displayed.] +@end ifinfo + In 3DLDF, plane figures generally have constructors taking a |Point| argument for the center, a variable number of |real| arguments for the dimensions, and three |real| arguments for the rotation about the major @@ -2201,6 +2725,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 137. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 137 not displayed.] +@end ifinfo + @end deftypefn @deftypefun void set_cycle ([{const bool} @var{c} = @code{true}]) @@ -2353,5 +2897,23 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 138. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 138 not displayed.] +@end ifinfo @end deftypefun diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/pattern.texi 3DLDF-1.1.5.1/DOC/TEXINFO/pattern.texi --- 3DLDF-1.1.4/DOC/TEXINFO/pattern.texi 2003-12-08 20:18:37.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/pattern.texi 2004-01-16 17:40:16.000000000 +0100 @@ -1,11 +1,11 @@ @c pattern.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: pattern.texi,v 1.2 2003/12/08 19:18:37 lfinsto1 Exp $ +@c $Id: pattern.texi,v 1.4 2004/01/12 18:40:03 lfinsto1 Exp lfinsto1 $ @node Pattern Reference, Solid Reference, Circle Reference, Top @chapter Pattern Reference @@ -164,6 +164,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 178. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 178 not displayed.] +@end ifinfo + @example default_focus.set(-5, 5, -10, 0, 10, 25, 10); hex_pattern_1(2, 1.5, 1, 2, 5, 2, black, gray, black, @@ -185,6 +204,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 179. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 179 not displayed.] +@end ifinfo + @end deftypefun @node Roulettes and Involutes, , Plane Tesselations, Pattern Reference @@ -209,7 +247,7 @@ @menu * Epicycloids:: @end menu - + @node Epicycloids, , Roulettes and Involutes, Roulettes and Involutes @subsection Epicycloids @@ -308,6 +346,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 180. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 180 not displayed.] +@end ifinfo + Example: @example default_focus.set(2, 5, -10, 2, 5, 10, 10); @@ -326,9 +383,27 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 181. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 181 not displayed.] +@end ifinfo @end deftypefun diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/picture.texi 3DLDF-1.1.5.1/DOC/TEXINFO/picture.texi --- 3DLDF-1.1.4/DOC/TEXINFO/picture.texi 2003-12-08 20:30:49.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/picture.texi 2004-01-16 17:40:17.000000000 +0100 @@ -1,11 +1,11 @@ @c picture.texi - + @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: picture.texi,v 1.3 2003/12/08 19:30:47 lfinsto1 Exp $ +@c $Id: picture.texi,v 1.6 2004/01/12 18:40:10 lfinsto1 Exp lfinsto1 $ @node Picture Reference, Point Reference, Label Reference, Top @chapter Picture Reference @@ -114,14 +114,14 @@ \immediate\write\examples{Point p1(c.get_point(8));} \immediate\write\examples{Point p0(p1);} \immediate\write\examples{p0.shift(-1);} -\immediate\write\examples{p0.dotlabel("current\UBAR picture", "ulft");} +\immediate\write\examples{p0.dotlabel("current@UBAR picture", "ulft");} \immediate\write\examples{p0.drawarrow(p1);} \immediate\write\examples{Point p2(c.get_point(0));} \immediate\write\examples{p2.shift(2);} %% This shift must be the same as the %% shift applied to new_picture above! \immediate\write\examples{Point p3(p2); p3.shift(1);} \immediate\write\examples{p3.drawarrow(p2);} -\immediate\write\examples{p3.dotlabel("new\UBAR picture", "urt");} +\immediate\write\examples{p3.dotlabel("new@UBAR picture", "urt");} \OEX{Projections::PARALLEL_X_Z} \EEX 1 \fi @@ -129,6 +129,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 77. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 77 not displayed.] +@end ifinfo + @end deftypefn @node Picture Operators, Affine Transformations for Pictures, Picture Constructors, Picture Reference @@ -195,6 +214,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 78. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 78 not displayed.] +@end ifinfo + @end deftypefn @@ -312,7 +351,7 @@ * Namespace Projections:: * Namespace Sorting:: @end menu - + @node Namespace Projections, Namespace Sorting, Picture Output Namespaces, Picture Output Namespaces @subsubsection Namespace Projections @@ -550,9 +589,29 @@ \immediate\write\examples{current_picture.unsuppress_labels();} \EEX 1 \fi -\PEX +\PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 79. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 79 not displayed.] +@end ifinfo + @end deftypefun @deftypefn {Inline function} void unsuppress_labels (void) diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/plane.texi 3DLDF-1.1.5.1/DOC/TEXINFO/plane.texi --- 3DLDF-1.1.4/DOC/TEXINFO/plane.texi 2003-12-09 20:01:58.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/plane.texi 2004-01-16 17:40:16.000000000 +0100 @@ -2,11 +2,11 @@ @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: plane.texi,v 1.4 2003/12/09 19:01:57 lfinsto1 Exp $ +@c $Id: plane.texi,v 1.6 2004/01/12 18:40:18 lfinsto1 Exp lfinsto1 $ @node Plane Reference, Path Reference, Line Reference, Top @chapter Plane Reference @@ -36,7 +36,7 @@ * Plane Intersections:: * Planes Showing:: @end menu - + @node Planes Data Members, Planes Global Constants, Plane Reference, Plane Reference @section Data Members @@ -180,6 +180,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 105. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 105 not displayed.] +@end ifinfo + @c @end deftypefn @@ -344,6 +364,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 106. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 106 not displayed.] +@end ifinfo + @c @@ -441,6 +481,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 107. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 107 not displayed.] +@end ifinfo + @c @@ -536,9 +596,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 108. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 108 not displayed.] +@end ifinfo + @c @end deftypefn diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/point.texi 3DLDF-1.1.5.1/DOC/TEXINFO/point.texi --- 3DLDF-1.1.4/DOC/TEXINFO/point.texi 2003-12-09 19:56:49.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/point.texi 2004-01-16 17:40:16.000000000 +0100 @@ -1,11 +1,11 @@ @c point.texi - + @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: point.texi,v 1.4 2003/12/09 18:56:49 lfinsto1 Exp $ +@c $Id: point.texi,v 1.7 2004/01/12 18:40:24 lfinsto1 Exp lfinsto1 $ @node Point Reference, Focus Reference, Picture Reference, Top @chapter Point Reference @@ -92,10 +92,15 @@ @end deftypevr @deftypevr {Private variable} bool on_free_store -Indicates whether a @code{Point} has been dynamically allocated on the -free store or not. @code{Points} should only ever be dynamically -allocated by @code{create_new_point()}, which sets @code{on_free_store} +Returns @code{on_free_store}. This should only be @code{true} if +the @code{Point} was dynamically allocated on the +free store. @code{Points} should only ever be dynamically +allocated by @code{create_new()}, which +uses @code{set_on_free_store()} to set @code{on_free_store} to @code{true}. +@xref{Point Constructors and Setting Functions,, +Point Reference; Constructors and Setting Functions}, and +@ref{Modifying Points,,Point Reference; Modifying}. @end deftypevr @deftypevr {Private variable} {signed short} drawdot_value @@ -340,15 +345,23 @@ same function. @end deftypefn -@deftypefn {Static function} {Point*} create_new_point ([{const Point*} @var{p} = 0]) +@deftypefn {Template specializations} Point* create_new ({const Point*} @var{p}) +@c +@deftypefnx {} Point* create_new ({const Point&} @var{p}) +@c +Pseudo-constructors for dynamic allocation of @code{Points}. +They create a @code{Point} on the free store and allocate memory for it using +@code{new(Point)}. They return a pointer to the new @code{Point}. -@deftypefnx {Static function} {Point*} create_new_point ({const Point&} @var{p}) +If @var{p} is a non-zero pointer or a reference, +the new @code{Point} will be a copy of +@var{p}. If the new object is not meant to be a +copy of an existing one, @samp{0} must be passed to +@code{create_new()} as its argument. +@xref{Dynamic Allocation of Shapes}, for more information. -@deftypefnx {Static function} {Point*} create_new_point ({const real} @var{x}, [{const real} @var{y} = 0, [{const real} @var{z} = 0]]) -Pseudo-constructors for dynamic allocation of @code{Points}. -These functions create a @code{Point} on the free store and allocate -memory for it using @code{new(Point)}. They return a pointer to the new -@code{Point}. One use is in the constructors for @code{classes} of +One use for @code{create_new} is in the constructors for +@code{classes} of objects that can contain a variable number of @code{Points}, such as @code{Path} and @code{Polygon}. Another use is in the drawing and filling functions, where objects are copied and the copies put onto a @@ -356,22 +369,7 @@ Programmers who dynamically allocate @code{Points} must ensure that they are deallocated properly using @code{delete}! - -In the first version, the optional argument @var{p} can be a pointer to -@code{Point}. If an argument is present, the x, y, and -z-coordinates of the new @code{Point} are copied from @code{*p} (after -they've been updated, if necessary). Otherwise, they are all set to 0. - -In the second version, @var{p} is a reference to a @code{Point}, and the -x, y, and z-coordinates of the new @code{Point} are copied from @var{p}. - -In the third version, at least one @code{real} value is passed as an -argument. The coordinates of the new @code{Point} are set using the -values of the arguments @var{x}, @var{y}, and @var{z}. Please note, -that if @var{z} or -@var{y} and @var{z} are not specified, the corresponding coordinates are -set to 0, not @code{CURR_Y} or @code{CURR_Z}. -@end deftypefn +@end deftypefn @node Point Destructor, Point Operators, Point Constructors and Setting Functions, Point Reference @section Destructor @@ -542,7 +540,7 @@ @deftypefn {@code{const} function} Shape* get_copy (void) Creates a copy of the @code{Point}, and allocates memory for it on the -free store using @code{create_new_point()}. +free store using @code{create_new()}. It returns a pointer to @code{Shape} that points to the new @code{Point}. This function is used in the drawing commands for putting @code{Points} onto @code{Pictures}. @@ -560,11 +558,13 @@ Returns @code{transform}. @end deftypefn -@deftypefn {@code{const} inline function} bool is_on_free_store (void) +@deftypefn {@code{const} function} bool is_on_free_store (void) Returns @code{true} if memory for the @code{Point} has been dynamically allocated on the free store, i.e., if the @code{Point} has been created using -@code{create_new_point()}. +@code{create_new()}. +@xref{Point Constructors and Setting Functions,, +Point Reference; Constructors and Setting Functions}. @end deftypefn @@ -627,6 +627,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 80. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 80 not displayed.] +@end ifinfo + @end deftypefn @deftypefn {@code{const} function} bool is_in_triangle ({const Point&} @var{p0}, {const Point&} @var{p1}, {const Point&} @var{p2}, [bool @var{verbose} = @code{false}, [bool @var{test_points} = @code{true}]]) @@ -752,30 +772,73 @@ @node Returning Information for Points, Modifying Points, Returning Coordinates, Point Reference @section Returning Information -@deftypefn {Inline static function} real epsilon (void) -Returns the absolute value of the @code{real} number of smallest magnitude -that should be used as a coordinate value in a @code{Point}. -This value is also used for testing the equality of @code{Points}: +@deftypefn {Static function} real epsilon (void) +Returns the positive @code{real} value of smallest magnitude +@math{\epsilon} that should be used as a coordinate value in a +@code{Point}. +A coordinate of a @code{Point} may also contain +@math{-\epsilon}. + +The value @math{\epsilon} is used for testing the equality of +@code{Points} in @code{Point::operator==()} +(@pxref{Point Operators, ,Point Reference; Operators}): -Let @math{e} be the value returned by @code{epsilon()}, @math{P} and @math{Q} be +Let @math{\epsilon} be the value returned by @code{epsilon()}, +@math{P} and @math{Q} be @code{Points}, and @math{P_x}, @math{Q_x}, @math{P_y}, @math{Q_y}, @math{P_z}, and @math{Q_z} the updated x, y, and z-coordinates of @math{P} and @math{Q}, respectively. If and only if -@math{||P_x| - |Q_x|| < e$, $||P_y| - |Q_y|| < e}, +@math{||P_x| - |Q_x|| < \epsilon, ||P_y| - |Q_y|| < \epsilon}, and -@math{||P_z| - |Q_z|| < e}, then -@math{P @equiv{} Q}. -@end deftypefn +@math{||P_z| - |Q_z|| < \epsilon}, then +@math{P = Q}. +@code{epsilon()} returns different values, depending on whether +@code{real} is @code{float} or @code{double}: +If @code{real} is @code{float} (the default), @code{epsilon()} +returns 0.00001. +If @code{real} is @code{double}, it returns 0.000000001. + +@b{Please note}: I haven't tested whether 0.000000001 is a good +value yet, so users should be aware of this if they set @code{real} to +@code{double}!@c +@c +@footnote{For that matter, I haven't really tested whether 0.00001 is a +good value when @code{real} is @code{float}.} +@c +The way to test this is to start with two @code{Points} +@math{P} and @math{Q} at different locations. +Then they should be transformed using different rotations in such a way +that they should end up at the same location. +Let @math{\epsilon} stand for the value returned by @code{epsilon()}, +and let @math{x}, @math{y}, and @math{y} stand for +the @code{world_coordinates} of the @code{Points} after +@code{apply_transform()} has been called on them. +If @math{x_P = x_Q}, @math{y_P = y_Q}, and +@math{z_P = z_Q}, +@math{\epsilon} is a good value. + +Rotation causes a significant loss of precision to due to the use of the +@code{sin()} and @code{cos()} functions. Therefore, neither +@code{Point::epsilon()} nor @code{Transform::epsilon()} +(@pxref{Returning Information for Transforms,, +Tranform Reference; Returning Information}) +can be as small as I'd like them to be. If they are two +small, operations that test for equality of @code{Transforms} and +@code{Points} will return @code{false} for objects that should be +equal. +@end deftypefn + @node Modifying Points, Affine Transformations for Points, Returning Information for Points, Point Reference @section Modifying -@deftypefn {@code{inline} virtual function} bool set_on_free_store ([bool @var{b} = true]) -This function was intended to be used in the template function -@code{create_new()}, which I -haven't been able to get to work yet. Otherwise, there is currently no -need for it. +@deftypefn {Virtual function} bool set_on_free_store ([bool @var{b} = true]) +This function is used in the template function +@code{create_new()}. It sets @code{on_free_store} to @code{true}. +@xref{Point Data Members,,Point Reference; Data Members}, and +@ref{Point Constructors and Setting Functions,, +Point Reference; Constructors and Setting Functions}. @end deftypefn @deftypefun void clear (void) @@ -853,6 +916,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 81. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 81 not displayed.] +@end ifinfo + Please note that rotations are not commutative operations. Nor are they commutative with other transformations. So, if you want to rotate a @code{Point} about the x, y and z-axes in @@ -917,6 +999,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 82. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 82 not displayed.] +@end ifinfo + @c @end deftypefun @@ -969,6 +1071,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 83. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 83 not displayed.] +@end ifinfo + @c @end deftypefun @@ -1041,6 +1163,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 84. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 84 not displayed.] +@end ifinfo + @end deftypefun @deftypefun Transform shift (real @var{x}, [real @var{y} = 0, [real @var{z} = 0]]) @@ -1127,6 +1268,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 85. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 85 not displayed.] +@end ifinfo + @end deftypefun @node Applying Transformations to Points, Projecting Points, Affine Transformations for Points, Point Reference @@ -1267,6 +1427,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 86. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 86 not displayed.] +@end ifinfo + If the angle @math{\theta} between two vectors @math{P} and @math{Q} is @DEG{90}, then @math{\cos(\theta)} is 0, so @@ -1327,6 +1506,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 87. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 87 not displayed.] +@end ifinfo + @end deftypefn @deftypefn {@code{const} function} Point cross_product (Point @var{p}) @@ -1427,6 +1626,25 @@ @end tex @end iftex +@ifhtml +@html +

+
+ +
+
+Fig. 88. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 88 not displayed.] +@end ifinfo + If @iftex @tex @@ -1480,7 +1698,26 @@ \PEX @end tex @end iftex - + +@ifhtml +@html +

+
+ +
+
+Fig. 89. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 89 not displayed.] +@end ifinfo + @end deftypefn @deftypefn {@code{const} function} real magnitude (void) @@ -1558,6 +1795,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 90. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 90 not displayed.] +@end ifinfo + @c @end deftypefn @@ -1705,6 +1962,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 91. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 91 not displayed.] +@end ifinfo + @c @@ -1810,7 +2087,7 @@ \immediate\write\examples{Point F(D);} \immediate\write\examples{F.shift(-1, 1);} \immediate\write\examples{F.dotlabel("$F$"); } -\immediate\write\examples{F.label("$r@DBKS{equiv}$ @OCB@DBKS{tt} INVALID@UBAR{}REAL@CCB", "llft");} +\immediate\write\examples{F.label("$r@DBKS{equiv}$ @OCB@DBKS{tt} INVALID@UBAR REAL@CCB", "llft");} \OEX{Projections::PARALLEL_X_Y} \EGRP \EEX 1 @@ -1818,6 +2095,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 92. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 92 not displayed.] +@end ifinfo + @c @end deftypefn @@ -1865,6 +2162,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 93. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 93 not displayed.] +@end ifinfo + @c @end deftypefn @@ -1927,6 +2244,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 94. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 94 not displayed.] +@end ifinfo + @c @example @@ -1967,6 +2304,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 95. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 95 not displayed.] +@end ifinfo + @c @end deftypefn @@ -2021,6 +2378,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 96. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 96 not displayed.] +@end ifinfo + @c @end deftypefn @@ -2054,6 +2431,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 97. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 97 not displayed.] +@end ifinfo + @c @end deftypefun @@ -2092,6 +2489,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 98. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 98 not displayed.] +@end ifinfo + @c @end deftypefun @@ -2132,6 +2549,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 99. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 99 not displayed.] +@end ifinfo + @c @end deftypefun @@ -2182,6 +2619,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 100. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 100 not displayed.] +@end ifinfo + @c @end deftypefun @@ -2234,6 +2691,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 101. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 101 not displayed.] +@end ifinfo + @c If backslashes are needed in the text of the label, then @@ -2267,6 +2744,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 102. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 102 not displayed.] +@end ifinfo + @c The @var{position} argument indicates where the text of the label should @@ -2307,9 +2804,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 103. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 103 not displayed.] +@end ifinfo + @c @end deftypefn diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/polygon.texi 3DLDF-1.1.5.1/DOC/TEXINFO/polygon.texi --- 3DLDF-1.1.4/DOC/TEXINFO/polygon.texi 2003-12-09 20:02:42.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/polygon.texi 2004-01-16 17:40:16.000000000 +0100 @@ -1,11 +1,11 @@ @c polygon.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: polygon.texi,v 1.4 2003/12/09 19:02:42 lfinsto1 Exp $ +@c $Id: polygon.texi,v 1.6 2004/01/12 18:40:29 lfinsto1 Exp lfinsto1 $ @node Polygon Reference, Regular Polygon Reference, Path Reference, Top @chapter Polygon Reference @@ -26,7 +26,7 @@ * Affine Transformations for Polygons:: * Polygon Intersections:: @end menu - + @node Polygon Data Members, Polygon Operators, Polygon Reference, Polygon Reference @section Data Members @@ -168,6 +168,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 139. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 139 not displayed.] +@end ifinfo + @c @@ -230,6 +250,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 140. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 140 not displayed.] +@end ifinfo + @c @@ -275,6 +315,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 141. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 141 not displayed.] +@end ifinfo + @c @@ -324,6 +384,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 142. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 142 not displayed.] +@end ifinfo + @c If the @code{Polygons} lie in parallel planes, there can be no @@ -380,6 +460,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 143. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 143 not displayed.] +@end ifinfo + @c In @NEXTFIG{}, the @code{Rectangle} @math{r} and the @code{Reg_Polygon} @math{p} @@ -425,9 +525,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 144. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 144 not displayed.] +@end ifinfo + @c diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/polyhed.texi 3DLDF-1.1.5.1/DOC/TEXINFO/polyhed.texi --- 3DLDF-1.1.4/DOC/TEXINFO/polyhed.texi 2003-12-09 17:30:53.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/polyhed.texi 2004-01-16 17:40:16.000000000 +0100 @@ -1,11 +1,11 @@ @c polyhed.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: polyhed.texi,v 1.4 2003/12/09 16:30:52 lfinsto1 Exp $ +@c $Id: polyhed.texi,v 1.6 2004/01/12 18:40:35 lfinsto1 Exp lfinsto1 $ @node Polyhedron Reference, Utility Functions, Cuboid Reference, Top @chapter Polyhedron Reference @@ -143,9 +143,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 187. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 187 not displayed.] +@end ifinfo + @c @example @@ -170,9 +190,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 188. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 188 not displayed.] +@end ifinfo + @c @end deftypefn @@ -229,6 +269,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 189. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 189 not displayed.] +@end ifinfo + @c This function is used in the non-default constructor. @@ -282,6 +342,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 190. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 190 not displayed.] +@end ifinfo + @c The net is drawn in the x-y plane, because it currently doesn't work to @@ -364,6 +444,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 191. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 191 not displayed.] +@end ifinfo + @c @example @@ -384,6 +484,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 192. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 192 not displayed.] +@end ifinfo + @c @end deftypefn @@ -427,6 +547,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 193. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 193 not displayed.] +@end ifinfo + @c @end deftypefn @@ -464,6 +604,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 194. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 194 not displayed.] +@end ifinfo + @c @end deftypefn @@ -538,6 +698,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 195. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 195 not displayed.] +@end ifinfo + @c @example @@ -557,6 +737,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 196. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 196 not displayed.] +@end ifinfo + @c @end deftypefn @@ -600,6 +800,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 197. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 197 not displayed.] +@end ifinfo + @c @end deftypefn @@ -634,9 +854,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 198. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 198 not displayed.] +@end ifinfo + @c @end deftypefn @@ -650,12 +890,12 @@ for the semi-regular Archimedean polyhedra. @menu -* Truncated Octahedron:: +* Truncated Octahedron:: @end menu @comment node-name, next, previous, up -@node Truncated Octahedron, Truncated Octahedron Data Members, Semi-Regular Archimedean Polyhedra, Semi-Regular Archimedean Polyhedra +@node Truncated Octahedron, , Semi-Regular Archimedean Polyhedra, Semi-Regular Archimedean Polyhedra @subsection Truncated Octahedron @tindex Trunc_Octahedron @@ -668,10 +908,10 @@ @menu * Truncated Octahedron Data Members:: -* Truncated Octahedron Net:: -* Truncated Octahedron Constructors and Setting Functions:: +* Truncated Octahedron Constructors and Setting Functions:: +* Truncated Octahedron Net:: @end menu - + @comment node-name, next, previous, up @node Truncated Octahedron Data Members, Truncated Octahedron Constructors and Setting Functions, Truncated Octahedron, Truncated Octahedron diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/rcpcurve.texi 3DLDF-1.1.5.1/DOC/TEXINFO/rcpcurve.texi --- 3DLDF-1.1.4/DOC/TEXINFO/rcpcurve.texi 2003-12-09 20:03:06.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/rcpcurve.texi 2004-01-16 17:40:16.000000000 +0100 @@ -1,11 +1,11 @@ @c rcpcurve.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: rcpcurve.texi,v 1.4 2003/12/09 19:03:06 lfinsto1 Exp $ +@c $Id: rcpcurve.texi,v 1.6 2004/01/12 18:40:41 lfinsto1 Exp lfinsto1 $ @node Regular Closed Plane Curve Reference, Ellipse Reference, Rectangle Reference, Top @chapter Regular Closed Plane Curve Reference @@ -68,7 +68,7 @@ * Regular Closed Plane Curve Intersections:: * Regular Closed Plane Curve Segments:: @end menu - + @node Regular Closed Plane Curve Data Members, Querying Regular Closed Plane Curves, Regular Closed Plane Curve Reference, Regular Closed Plane Curve Reference @section Data Members @@ -250,6 +250,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 154. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 154 not displayed.] +@end ifinfo + @c In @NEXTFIG{}, @math{q} and @math{e} are coplanar. In this case, @@ -288,6 +308,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 155. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 155 not displayed.] +@end ifinfo + @c @end deftypefn @@ -350,6 +390,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 156. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 156 not displayed.] +@end ifinfo + @c @end deftypefn @@ -384,6 +444,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 157. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 157 not displayed.] +@end ifinfo + @c @end deftypefn @@ -416,9 +496,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 158. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 158 not displayed.] +@end ifinfo + @c @end deftypefn diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/rectang.texi 3DLDF-1.1.5.1/DOC/TEXINFO/rectang.texi --- 3DLDF-1.1.4/DOC/TEXINFO/rectang.texi 2003-12-09 20:50:51.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/rectang.texi 2004-01-16 17:40:16.000000000 +0100 @@ -1,11 +1,11 @@ @c rectang.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: rectang.texi,v 1.4 2003/12/09 19:50:51 lfinsto1 Exp $ +@c $Id: rectang.texi,v 1.6 2004/01/12 18:40:49 lfinsto1 Exp lfinsto1 $ @node Rectangle Reference, Regular Closed Plane Curve Reference, Regular Polygon Reference, Top @chapter Rectangle Reference @@ -24,7 +24,7 @@ will also be necessary to add the function @code{Rectangle::is_rectangular()}, in order to test whether a @code{Rectangle} is still rectangular. - + @menu * Rectangle Data Members:: * Rectangle Constructors and Setting Functions:: @@ -53,7 +53,7 @@ @code{true}, if the @code{Rectangle} was dynamically allocated on the free store, otherwise @code{false}. Dynamic allocation of @code{Rectangles} should only be -performed by @code{create_new_rectangle()}, which sets +performed by @code{create_new()}, which sets @code{on_free_store} to @code{true}. @end deftypevr @@ -101,6 +101,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 151. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 151 not displayed.] +@end ifinfo + @c @end deftypefn @@ -126,18 +146,20 @@ Corresponds to the constructor above. @end deftypefn -@deftypefn {Static functions} Rectangle* create_new_rectangle ([{const Rectangle* @var{r}} = 0]) +@deftypefn {Template specializations} Rectangle* create_new ({const Rectangle*} @var{r}) @c -@deftypefnx {} Rectangle* create_new_rectangle ({const Rectangle&} @var{r}) -Pseudo-constructors for dynamic allocation. - -In the first version, @var{r} is an optional pointer argument. If -@var{r} is non-zero, the new @code{Rectangle} will be a copy of -@var{*r}. Otherwise, it will be empty. - -In the second version, -@var{r} is a required reference argument, and the new @code{Rectangle} -will be a copy of @var{r}. +@deftypefnx {} Rectangle* create_new ({const Rectangle&} @var{r}) +@c +Pseudo-constructors for dynamic allocation of @code{Rectangles}. +They create a @code{Rectangle} on the free store and allocate memory for it using +@code{new(Rectangle)}. They return a pointer to the new @code{Rectangle}. + +If @var{r} is a non-zero pointer or a reference, +the new @code{Rectangle} will be a copy of +@var{r}. If the new object is not meant to be a +copy of an existing one, @samp{0} must be passed to +@code{create_new()} as its argument. +@xref{Dynamic Allocation of Shapes}, for more information. @end deftypefn @node Rectangle Operators, Returning Points for Rectangles, Rectangle Constructors and Setting Functions, Rectangle Reference @@ -221,6 +243,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 152. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 152 not displayed.] +@end ifinfo + @c @end deftypefn @@ -254,9 +296,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 153. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 153 not displayed.] +@end ifinfo + @c @end deftypefn diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/regpolyg.texi 3DLDF-1.1.5.1/DOC/TEXINFO/regpolyg.texi --- 3DLDF-1.1.4/DOC/TEXINFO/regpolyg.texi 2003-12-09 20:03:32.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/regpolyg.texi 2004-01-16 17:40:16.000000000 +0100 @@ -1,11 +1,11 @@ @c regpolyg.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: regpolyg.texi,v 1.4 2003/12/09 19:03:31 lfinsto1 Exp $ +@c $Id: regpolyg.texi,v 1.6 2004/01/12 18:40:55 lfinsto1 Exp lfinsto1 $ @node Regular Polygon Reference, Rectangle Reference, Polygon Reference, Top @@ -26,7 +26,7 @@ @code{Reg_Polygon::is_reg_polygonal()}, in order to test whether a @code{Reg_Polygon} is still regular and polygonal. - + @menu * Regular Polygon Data Members:: * Regular Polygon Constructors and Setting Functions:: @@ -60,7 +60,7 @@ @code{true}, if the @code{Reg_Polygon} was dynamically allocated on the free store, otherwise @code{false}. Dynamic allocation of @code{Reg_Polygons} should only be -performed by @code{create_new_reg_polygon()}, which sets +performed by @code{create_new()}, which sets @code{on_free_store} to @code{true}. @end deftypevr @@ -106,6 +106,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 145. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 145 not displayed.] +@end ifinfo + @c @end deftypefn @@ -151,20 +171,42 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 146. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 146 not displayed.] +@end ifinfo + @c @end deftypefn - -@deftypefn {Static function} {Reg_Polygon*} create_new_reg_polygon ([const Reg_Polygon* @var{r} = 0]) -@deftypefnx {Static function} {Reg_Polygon*} create_new_reg_polygon (const Reg_Polygon& @var{r}) -Pseudo-constructors for dynamic allocation. -In the first version, @var{r} is an optional pointer argument. If -@var{r} is non-zero, the new @code{Reg_Polygon} will be a copy of -@var{*r}. Otherwise, it will be empty. - -In the second version, -@var{r} is a required reference argument, and the new @code{Reg_Polygon} -will be a copy of @var{r}. +@deftypefn {Template specializations} Reg_Polygon* create_new ({const Reg_Polygon*} @var{r}) +@c +@deftypefnx {} Reg_Polygon* create_new ({const Reg_Polygon&} @var{r}) +@c +Pseudo-constructors for dynamic allocation of @code{Reg_Polygons}. +They create a @code{Reg_Polygon} on the free store and allocate memory for it using +@code{new(Reg_Polygon)}. They return a pointer to the new @code{Reg_Polygon}. +If @var{r} is a non-zero pointer or a reference, +the new @code{Reg_Polygon} will be a copy of +@var{r}. If the new object is not meant to be a +copy of an existing one, @samp{0} must be passed to +@code{create_new()} as its argument. +@xref{Dynamic Allocation of Shapes}, for more information. @end deftypefn @node Regular Polygon Operators, Querying Regular Polygons, Regular Polygon Constructors and Setting Functions, Regular Polygon Reference @@ -220,6 +262,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 147. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 147 not displayed.] +@end ifinfo + @c @end deftypefn @@ -257,6 +319,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 148. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 148 not displayed.] +@end ifinfo + @c @@ -295,6 +377,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 149. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 149 not displayed.] +@end ifinfo + @c @end deftypefn @@ -332,6 +434,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 150. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 150 not displayed.] +@end ifinfo + @c @end deftypefn diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/shape.texi 3DLDF-1.1.5.1/DOC/TEXINFO/shape.texi --- 3DLDF-1.1.4/DOC/TEXINFO/shape.texi 2003-12-03 21:13:35.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/shape.texi 2004-01-16 17:40:17.000000000 +0100 @@ -1,11 +1,11 @@ @c shape.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: shape.texi,v 1.2 2003/12/03 20:13:35 lfinsto1 Exp $ +@c $Id: shape.texi,v 1.3 2004/01/12 18:41:01 lfinsto1 Exp lfinsto1 $ @node Shape Reference, Transform Reference, Input and Output, Top @@ -40,7 +40,7 @@ * Showing Shapes:: * Outputting Shapes:: @end menu - + @node Shape Data Members, Shape Operators, Shape Reference, Shape Reference @section Data Members @@ -87,16 +87,10 @@ derived from @code{Shape} must therefore also have a data member @code{on_free_store}. -This function was intended for use with a @code{create_new<@i{type}>} -template function, however, I was unable to get it to work. I -@emph{was} able to get a template function to work when a program was -generated from a single compilation unit, so I suspect the problem has -something to do with linkage when there are several compilation units. -However, I haven't bothered to try to solve this problem yet. -Therefore, each class that needs one has a function for creating a new -object of that class, and allocating memory for it on the free store, -e.g., @code{Point::create_new_point()}, @code{Path::create_new_path()}, -etc. +This function is used in the template function +@code{create_new<@i{type}>}. +@xref{Dynamic Allocation of Shapes}, for more information. + @end deftypefn @node Affine Transformations for Shapes, Applying Transformations to Shapes, Modifying Shapes, Shape Reference diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/solfaced.texi 3DLDF-1.1.5.1/DOC/TEXINFO/solfaced.texi --- 3DLDF-1.1.4/DOC/TEXINFO/solfaced.texi 2003-12-03 21:13:49.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/solfaced.texi 2004-01-16 17:40:16.000000000 +0100 @@ -1,11 +1,11 @@ @c solfaced.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: solfaced.texi,v 1.2 2003/12/03 20:13:49 lfinsto1 Exp $ +@c $Id: solfaced.texi,v 1.3 2004/01/12 18:41:05 lfinsto1 Exp lfinsto1 $ @node Faced Solid Reference, Cuboid Reference, Solid Reference, Top @chapter Faced Solid Reference @@ -22,7 +22,7 @@ @menu * Solid_Faced Data Members:: @end menu - + @node Solid_Faced Data Members, , Faced Solid Reference, Faced Solid Reference @section Data Members diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/solid.texi 3DLDF-1.1.5.1/DOC/TEXINFO/solid.texi --- 3DLDF-1.1.4/DOC/TEXINFO/solid.texi 2003-12-09 17:56:01.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/solid.texi 2004-01-16 17:40:16.000000000 +0100 @@ -1,11 +1,11 @@ @c solid.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: solid.texi,v 1.3 2003/12/09 16:56:00 lfinsto1 Exp $ +@c $Id: solid.texi,v 1.5 2004/01/12 18:41:30 lfinsto1 Exp lfinsto1 $ @node Solid Reference, Faced Solid Reference, Pattern Reference, Top @chapter Solid Reference @@ -40,10 +40,10 @@ @deftypevr {Protected variable} bool on_free_store @code{true}, if the @code{Solid} was dynamically allocated on the free store, otherwise @code{false}. @code{Solids} should only be allocated -on the free store by @code{create_new_solid()} -(@pxref{Solid Constructors and Setting Functions,,Solid Reference; -Constructors and Setting Functions}), or analogous functions +on the free store by @code{create_new()}, or analogous functions for derived classes. +@xref{Solid Constructors and Setting Functions,,Solid Reference; +Constructors and Setting Functions}. @end deftypevr @deftypevr {Protected variable} Point center @@ -101,11 +101,22 @@ Creates a new @code{Solid} and makes it a copy of @var{s}. @end deftypefn -@deftypefn {Static function} Solid* create_new_solid (@code{void}) -Pseudo-constructor for dynamic allocation. +@deftypefn {Template specializations} Solid* create_new ({const Solid*} @var{s}) +@c +@deftypefnx {} Solid* create_new ({const Solid&} @var{s}) +@c +Pseudo-constructors for dynamic allocation of @code{Solids}. +They create a @code{Solid} on the free store and allocate memory for it using +@code{new(Solid)}. They return a pointer to the new @code{Solid}. + +If @var{s} is a non-zero pointer or a reference, +the new @code{Solid} will be a copy of +@var{s}. If the new object is not meant to be a +copy of an existing one, @samp{0} must be passed to +@code{create_new()} as its argument. +@xref{Dynamic Allocation of Shapes}, for more information. @end deftypefn - @node Solid Destructor, Solid Operators, Solid Constructors and Setting Functions, Solid Reference @section Destructor @@ -140,7 +151,7 @@ @deftypefn {@code{const} virtual function} Shape* get_copy (@code{void}) Dynamically allocates a new @code{Solid} on the free store, using -@code{create_new_solid()}, and makes it a copy of @code{*this}. Then, a +@code{create_new()}, and makes it a copy of @code{*this}. Then, a pointer to @code{Shape} is pointed at the copy and returned. Used for putting @code{Solids} onto @code{Picture::shapes} in the drawing and filling functions for @code{Solid}. @@ -151,11 +162,12 @@ @node Setting Solid Members, Querying Solids, Copying Solids, Solid Reference @section Setting Members -@deftypefn {Inline virtual function} bool set_on_free_store ([bool @var{b} = @code{true}]) +@deftypefn {Virtual function} bool set_on_free_store ([bool @var{b} = @code{true}]) Sets @code{on_free_store} to @var{b}. This function is -currently never used. It was intended for use in a -``@code{create_new()}'' template function, which I haven't been able to -get to work. +called in the template function +@code{create_new()}. +@xref{Solid Constructors and Setting Functions,, +Solid Reference; Constructors and Setting Functions}. @end deftypefn @node Querying Solids, Returning Elements and Information Solids, Setting Solid Members, Solid Reference @@ -165,6 +177,11 @@ Returns the value of @code{on_free_store}; @code{true}, if the @code{Solid} was dynamically allocated on the free store, otherwise @code{false}. +@code{Solids}, and objects of classes derived from @code{Solid}, +should only ever be allocated on the free store by +a specialization of the template function @code{create_new()}. +@xref{Solid Constructors and Setting Functions,, +Solid Reference; Constructors and Setting Functions}. @end deftypefn @node Returning Elements and Information Solids, Showing Solids, Querying Solids, Solid Reference @@ -181,7 +198,7 @@ * Getting Shape Centers Solids:: * Getting Shapes Solids:: @end menu - + @node Getting Shape Centers Solids, Getting Shapes Solids, Returning Elements and Information Solids, Returning Elements and Information Solids @unnumberedsubsec Getting Shape Centers @@ -230,9 +247,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 182. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 182 not displayed.] +@end ifinfo + @c @c !! NOTE. LDF 2003.08.15. @@ -275,6 +312,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 183. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 183 not displayed.] +@end ifinfo + @c @end deftypefn @@ -333,9 +390,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 184. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 184 not displayed.] +@end ifinfo + @c @end deftypefn @@ -382,9 +459,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 185. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 185 not displayed.] +@end ifinfo + @c @end deftypefn diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/system.texi 3DLDF-1.1.5.1/DOC/TEXINFO/system.texi --- 3DLDF-1.1.4/DOC/TEXINFO/system.texi 1970-01-01 01:00:00.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/system.texi 2004-01-16 17:40:17.000000000 +0100 @@ -0,0 +1,209 @@ +@c system.texi + +@c This file is part of the 3DLDF User and Reference Manual. +@c Copyright (C) 2003, 2004 Laurence D. Finston +@c See the section "GNU Free Documentation License" in the file +@c fdl.texi for copying conditions. + +@c $Id: system.texi,v 1.2 2004/01/12 18:41:44 lfinsto1 Exp lfinsto1 $ + +@node System Information, Color Reference, Dynamic Allocation of Shapes, Top +@chapter System Information + +The functions described in this chapter are all declared in the +@code{namespace System}. They are for finding out information +about the system on which 3DLDF is being run. They are declared and +defined in @file{pspglb.web}, except for the template function +@code{get_second_largest()}, which is declared and defined in +@file{gsltmplt.web}. + +There are two reasons for this. The first is that template definitions +must be available +in the compilation units where specializations are instantiated. +I therefore write the template definition of @code{get_second_largest()} +to @file{gsltmplt.h}, so it can be included by the CWEB files that need +it, currently @file{main.web} only. If I +wrote it to @file{pspglb.h}, it would be included by all of the CWEB +files except for @file{loader.web}, causing unnecessarily bloated object +code. + +The other reason is because of the way way 3DLDF is built using Automake +and @t{make}. I originally tried to define @code{get_second_largest()} +in @file{pspglb.web} and wrote the definition to @file{gsltmplt.cc}, +which is no problem with CWEB. However, I was unable to express the +dependencies among the CWEB, @cpp{}, and object files in such a way that +3DLDF was built properly. + +Therefore all template functions will be put into files either by +themselves, or in small groups. + + +@menu +* Endianness:: +* Register Width:: +* Get Second Largest Real:: +@end menu + +@node Endianness, Register Width, System Information, System Information +@section Endianness + +@deftypefun {signed short} get_endianness ([{const bool} @var{verbose} = @code{false}]) +@c +Returns the following values: + +@table @asis + +@item 0 +if the processor is little-endian. + +@item 1 +if the processor is big-endian. + +@item -1 +if the endianness cannot be determined. + +@end table + +It is called by @code{is_little_endian()} and +@code{is_big_endian()}. + +If @var{verbose} is @code{true}, messages are printed to standard +output. + +This function has been adapted from +Harbison, Samuel@w{ }P., and Guy@w{ }L. Steele Jr. +@cite{C, A Reference Manual}, pp.@w{ }163--164. +This book has the clearest explanation of endianness that I've found so +far. + +This is the @cpp{} code: + +@example +signed short +System::get_endianness(const bool verbose) +@OCB{} + union @OCB{} + long Long; + char Char[sizeof(long)]; + @CCB{} u; + u.Long = 1; + if (u.Char[0] == 1) + @OCB{} + if (verbose) + cout << "Processor is little-endian." + << endl << endl << flush; + return 0; + @CCB{} + else if (u.Char[sizeof(long) - 1] == 1) + @OCB{} + if (verbose) + cout << "Processor is big-endian." + << endl << endl << flush; + return 1; + @CCB{} + else + @OCB{} + cerr << "ERROR! In System::get_endianness():\n" + << "Can't determine endianness. Returning -1" + << endl << endl << flush; + return -1; + @CCB{} +@CCB{} +@end example +@end deftypefun + +@deftypefun bool is_big_endian ([{const bool} @var{verbose} = @code{false}]) +@c +Returns @code{true} if the processor is big-endian, otherwise @code{false}. +If @var{verbose} is @code{true}, messages are printed to standard +output. +@end deftypefun + +@deftypefun bool is_little_endian ([{const bool} @var{verbose} = @code{false}]) +@c +Returns @code{true} if the processor is little-endian, otherwise @code{false}. +If @var{verbose} is @code{true}, messages are printed to standard +output. +@end deftypefun + + +@node Register Width, Get Second Largest Real, Endianness, System Information +@section Register Width + + +@deftypefun {unsigned short} get_register_width (void) +@c +Returns the register width of the CPU of the system on which 3DLDF is +being run. This will normally be either 32 or 64 bits. + +This is the @cpp{} code: + +@example +return (sizeof(void*) * CHAR_BIT); +@end example + +This assumes that an address will be the same size as the processor's +registers, and that @code{CHAR_BIT} will be the number of bits in a +byte. These are reasonable assumptions that apply to all architectures +I know about. + +This function is called by @code{is_32_bit()} and @code{is_64_bit()}. +@end deftypefun + + +@deftypefun bool is_32_bit (void) +Returns @code{true} if the CPU of the system on which 3DLDF is being run +has a register width of 32 bits, otherwise @code{false}. +@end deftypefun + +@deftypefun bool is_64_bit (void) +Returns @code{true} if the CPU of the system on which 3DLDF is being run +has a register width of 64 bits, otherwise @code{false}. +@end deftypefun + +@node Get Second Largest Real, , Register Width, System Information +@section Get Second Largest Real + +@deftypefn {Template function} {template Real} get_second_largest (Real @var{MAX_VAL}, [bool @var{verbose} = @code{false}]) +@c +@deftypefnx {Template specialization} float get_second_largest (float, bool) +@c +@deftypefnx {Template specialization} double get_second_largest (double, bool) +@c +@code{get_second_largest} returns the second largest floating point +number of the type specified the template paramater @var{Real}. +If @var{verbose} is @code{true}, messages are printed to standard +output. + +This function is used for setting the value of @code{MAX_REAL}. +@xref{Global Constants and Variables}. + +@code{get_second_largest} depends on there +being an unsigned integer type with the same length as @var{Real}. +This should always be the case for @code{float} and @code{double}, but +may not be @code{long double}. + +@var{MAX_VAL} should be the largest number of type @var{Real} on a given +architecture. The GNU @cpp{} compiler GCC 3.3 does not currently supply +the @code{numeric_limits} template, so it is necessary to pass +one of the macros @code{FLT_MAX} or @code{DBL_MAX} explicitly, depending +on which specialization you use@c +@c +@footnote{If your system supplies an unsigned integer type with the same +length as @code{long double}, then you can instantiate +@code{get_second_largest()} and call +@samp{get_second_largest(LDBL_MAX)}. However, I doubt +that this amount of precision would be worthwhile. If it ever were +required, 3DLDF would have to be changed in other ways, too. In +particular, it would have to use more precise trigonometric functions +for rotations. @xref{Accuracy}.}. +@c +When and if GCC supplies the @code{numeric_limits} template, I will +eliminate the @var{MAX_REAL} argument. +@end deftypefn + + + + + + diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/transfor.texi 3DLDF-1.1.5.1/DOC/TEXINFO/transfor.texi --- 3DLDF-1.1.4/DOC/TEXINFO/transfor.texi 2003-12-09 18:34:01.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/transfor.texi 2004-01-16 17:40:17.000000000 +0100 @@ -1,11 +1,11 @@ f@c transfor.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: transfor.texi,v 1.3 2003/12/09 17:34:01 lfinsto1 Exp $ +@c $Id: transfor.texi,v 1.5 2004/01/12 18:43:23 lfinsto1 Exp lfinsto1 $ @node Transform Reference, Label Reference, Shape Reference, Top @chapter Transform Reference @@ -478,31 +478,56 @@ @print{} 0.224 @end example @end deftypefn - + @node Returning Information for Transforms, Showing Transforms, Querying Transforms, Transform Reference @section Returning Information -@deftypefn {Inline function} real epsilon (void) -Returns the smallest @code{real} value which a @code{Transform} should -contain. This value is used for comparing @code{Transforms} and in the -function @code{clean()} (@pxref{Cleaning Transforms,,Transform -Reference; Cleaning}). It is currently 0.00001. +@deftypefn {Static function} real epsilon (void) +Returns the positive @code{real} value of smallest magnitude +@math{\epsilon} which an element of a @code{Transform} should +contain. An element of a @code{Transform} may also contain +@math{-\epsilon}. -The value of @code{epsilon()} should be smaller when @code{real} is -@code{double} than when @code{real} is @code{float}. Currently, it -doesn't work to have @code{real} be @code{double}. +The value @math{\epsilon} is used for in the +function @code{clean()} (@pxref{Cleaning Transforms,,Transform +Reference; Cleaning}). +It will also be used for comparing @code{Transforms}, when I've added +the equality operator @code{Transform::operator==()}. + +@code{epsilon()} returns different values, depending on whether +@code{real} is @code{float} or @code{double}: +If @code{real} is @code{float} (the default), @code{epsilon()} +returns 0.00001. +If @code{real} is @code{double}, it returns 0.000000001. + +@b{Please note}: I haven't tested whether 0.000000001 is a good +value yet, so users should be aware of this if they set @code{real} to +@code{double}!@c +@c +@footnote{For that matter, I haven't really tested whether 0.00001 is a +good value when @code{real} is @code{float}.} +@c +The way to test this is to transform two different +@code{Transforms} +@math{t_1} and @math{t_2} +using different rotations in such a way that the end +result should be the same for both @code{Transforms}. +Let @math{\epsilon} stand for the value returned by @code{epsilon()}. +If for all sets of +corresponding elements @math{E_1} and @math{E_2} of @math{t_1} and +@math{t_2}, @math{||E_1| - |E_2|| \le \epsilon}, then +@math{\epsilon} is a good value. +@c !! TO DO: +It will be easier to test this when I've added +@code{Transform::operator==()}. Rotation causes a significant loss of precision to due to the use of the @code{sin()} and @code{cos()} functions. Therefore, neither @code{Transform::epsilon()} nor @code{Point::epsilon()} (@pxref{Returning Information for Points,,Point Reference; Returning Information}) can be as small as I'd like them to be. If they are two -small, the operations that test for equality of @code{Transforms} and +small, operations that test for equality of @code{Transforms} and @code{Points} will return @code{false} for objects that should be equal. - -Another problem is how to determine what value @code{epsilon()} should -return. A good value on one computer may not be good on another, -especially if one has a 32-bit, and the other a 64-bit processor. @end deftypefn @node Showing Transforms, Affine Transformations for Transforms, Returning Information for Transforms, Transform Reference @@ -848,6 +873,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 73. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 73 not displayed.] +@end ifinfo + @c @example @@ -905,6 +950,26 @@ \PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 74. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 74 not displayed.] +@end ifinfo + @c @end deftypefun @@ -1020,9 +1085,29 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 75. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 75 not displayed.] +@end ifinfo + @c diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/typeglb.texi 3DLDF-1.1.5.1/DOC/TEXINFO/typeglb.texi --- 3DLDF-1.1.4/DOC/TEXINFO/typeglb.texi 2003-12-09 18:35:04.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/typeglb.texi 2004-01-16 17:40:17.000000000 +0100 @@ -1,11 +1,11 @@ @c typeglb.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: typeglb.texi,v 1.3 2003/12/09 17:35:04 lfinsto1 Exp $ +@c $Id: typeglb.texi,v 1.4 2004/01/12 18:43:34 lfinsto1 Exp lfinsto1 $ @comment node-name, next, previous, up @node Typedefs and Utility Structures, Global Constants and Variables, Installing and Running 3DLDF, Top @@ -26,12 +26,11 @@ @code{LDF_REAL_DOUBLE}. The meaning of @code{real} is determined by means of conditional compilation. If @code{real} is @code{float}, 3DLDF will require less memory than if @code{real} is @code{double}, but its -calculations will be less precise. - -Please note that it currently does not work to define @code{real} to be -@code{double}! +calculations will be less precise. @code{real} is ``typedeffed'' to +@code{float} by default. @end deftp + @deftp typedef real_pair first second Synonymous with @code{pair}. @end deftp @@ -73,3 +72,4 @@ + diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/using.texi 3DLDF-1.1.5.1/DOC/TEXINFO/using.texi --- 3DLDF-1.1.4/DOC/TEXINFO/using.texi 1970-01-01 01:00:00.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/using.texi 2004-01-16 17:40:17.000000000 +0100 @@ -0,0 +1,10 @@ +@node Using 3DLDF, Points, Contributing to 3DLDF, Top +@chapheading Using 3DLDF + +Since 3DLDF does not yet have an input routine, user code must be +written in @cpp{} (in @file{main.web}, or some other file) and compiled. +Then, 3DLDF must be relinked, together with the new file of object +code resulting from the compilation. +For now, the important point is that the text of +the examples in this manual represent @cpp{} code. +@xref{Installing and Running 3DLDF}, for more information. diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/utility.texi 3DLDF-1.1.5.1/DOC/TEXINFO/utility.texi --- 3DLDF-1.1.4/DOC/TEXINFO/utility.texi 2003-12-09 18:41:57.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/utility.texi 2004-01-16 17:40:16.000000000 +0100 @@ -1,11 +1,11 @@ @c utility.texi @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: utility.texi,v 1.4 2003/12/09 17:41:57 lfinsto1 Exp $ +@c $Id: utility.texi,v 1.6 2004/01/12 18:43:50 lfinsto1 Exp lfinsto1 $ @node Utility Functions, Adding a File, Polyhedron Reference, Top @chapter Utility Functions @@ -67,7 +67,7 @@ @result{} r.second @equiv{} INVALID_REAL @end example - + @end deftypefun @menu @@ -144,8 +144,28 @@ \EGRP \EEX 1 \fi -\PEX +\PEX @end tex @end iftex + +@ifhtml +@html +

+
+ +
+
+Fig. 199. +
+

+@end html +@end ifhtml + +@ifinfo +[Figure 199 not displayed.] +@end ifinfo + @c @end deftypefun diff -Naur 3DLDF-1.1.4/DOC/TEXINFO/varidx.texi 3DLDF-1.1.5.1/DOC/TEXINFO/varidx.texi --- 3DLDF-1.1.4/DOC/TEXINFO/varidx.texi 2003-12-03 21:14:48.000000000 +0100 +++ 3DLDF-1.1.5.1/DOC/TEXINFO/varidx.texi 2004-01-16 17:40:15.000000000 +0100 @@ -1,11 +1,11 @@ @c varidx.texi - + @c This file is part of the 3DLDF User and Reference Manual. -@c Copyright (C) 2003 Laurence D. Finston +@c Copyright (C) 2003, 2004 Laurence D. Finston @c See the section "GNU Free Documentation License" in the file @c fdl.texi for copying conditions. -@c $Id: varidx.texi,v 1.1 2003/11/28 14:21:32 lfinsto1 Exp $ +@c $Id: varidx.texi,v 1.2 2004/01/12 18:43:56 lfinsto1 Exp lfinsto1 $ @node Data Type and Variable Index, Function Index, GNU Free Documentation License, Top @unnumbered Data Type and Variable Index diff -Naur 3DLDF-1.1.4/INSTALL 3DLDF-1.1.5.1/INSTALL --- 3DLDF-1.1.4/INSTALL 2003-12-09 21:18:58.000000000 +0100 +++ 3DLDF-1.1.5.1/INSTALL 2004-01-16 17:12:09.000000000 +0100 @@ -1,9 +1,9 @@ INSTALL This file is part of 3DLDF, a package for three-dimensional drawing. -Copyright (C) 2003 Laurence D. Finston. +Copyright (C) 2003, 2004 Laurence D. Finston. -$Id: INSTALL,v 1.5 2003/12/09 20:18:58 lfinsto1 Exp $ +$Id: INSTALL,v 1.7 2004/01/16 16:12:09 lfinsto1 Exp $ 3DLDF is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by @@ -49,24 +49,24 @@ s246794@stud.uni-goettingen.de -To install 3DLDF, decompress 3DLDF-1.1.4.tar.gz using gzip, or a +To install 3DLDF, decompress 3DLDF-1.1.5.1.tar.gz using gzip, or a compatible program, e.g., -`gunzip 3DLDF-1.1.4.tar.gz'. -Then, expand 3DLDF-1.1.4.tar using the tar command, typically: -`tar xvpf 3DLDF-1.1.4.tar' +`gunzip 3DLDF-1.1.5.1.tar.gz'. +Then, expand 3DLDF-1.1.5.1.tar using the tar command, typically: +`tar xvpf 3DLDF-1.1.5.1.tar' The exact syntax of the tar command may differ, depending on what system you're using. -3DLDF unpacks into the directory /3DLDF-1.1.4/. +3DLDF unpacks into the directory /3DLDF-1.1.5.1/. -Change your working directory to /3DLDF-1.1.4/ and run -`configure --prefix=/3DLDF-1.1.4/' -to generate the Makefiles. There is one each in /3DLDF-1.1.4/, -/3DLDF-1.1.4/CWEB, /3DLDF-1.1.4/DOC, and /3DLDF-1.1.4/DOC/TEXINFO. +Change your working directory to /3DLDF-1.1.5.1/ and run +`configure --prefix=/3DLDF-1.1.5.1/' +to generate the Makefiles. There is one each in /3DLDF-1.1.5.1/, +/3DLDF-1.1.5.1/CWEB, /3DLDF-1.1.5.1/DOC, and /3DLDF-1.1.5.1/DOC/TEXINFO. `' must be the absolute path of the directory where you -want to put the /3DLDF-1.1.4/ subdirectory. For example, if you want +want to put the /3DLDF-1.1.5.1/ subdirectory. For example, if you want to put 3DLDF into /usr/local/mydirectory/, enter - `configure --prefix=/usr/local/mydirectory/3DLDF-1.1.4/' + `configure --prefix=/usr/local/mydirectory/3DLDF-1.1.5.1/' Since 3DLDF currently does not have an input routine, the executable 3dldf will need to be regenerated each time the user code changes. @@ -76,11 +76,13 @@ `configure' can be called with a different `prefix' argument, or the default (/usr/local/bin/) can be used. -Change the working directory to /3DLDF-1.1.4/ and +Change the working directory to /3DLDF-1.1.5.1/ and call `make install' from the command line of a shell. This creates the executable file `3dldf'. For information on running 3dldf, see the README file in this directory, and the _3DLDF User and Reference Manual_, which is included in this -distribution as the PostScript file /3DLDF-1.1.4/DOC/TEXINFO/3DLDF.ps. +distribution as the PostScript file /3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.ps. + +End of INSTALL diff -Naur 3DLDF-1.1.4/Makefile.am 3DLDF-1.1.5.1/Makefile.am --- 3DLDF-1.1.4/Makefile.am 2003-12-09 21:09:25.000000000 +0100 +++ 3DLDF-1.1.5.1/Makefile.am 2004-01-16 17:25:11.000000000 +0100 @@ -1,10 +1,10 @@ -## 3DLDF-/Makefile.am +## 3DLDF-1.1.5.1/Makefile.am # Created by Laurence Finston. -# $Id: Makefile.am,v 1.7 2003/12/09 20:09:24 lfinsto1 Exp $ +# $Id: Makefile.am,v 1.9 2004/01/16 16:25:11 lfinsto1 Exp $ # This file is part of 3DLDF, a package for three-dimensional drawing. -# Copyright (C) 2003 Laurence D. Finston. +# Copyright (C) 2003, 2004 Laurence D. Finston. # 3DLDF is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by @@ -35,9 +35,16 @@ CWEBDIR := CWEB DOCDIR := DOC TEXINFODIR := TEXINFO -EPSDIR := EPS - - +GRAPHICSDIR := graphics +EPSDIR := eps +PNGDIR := png + +export CWEBDIR +export DOCDIR +export TEXINFODIR +export GRAPHICSDIR +export EPSDIR +export PNGDIR vpath %.web $(CWEBDIR) vpath %.h $(CWEBDIR) @@ -93,6 +100,12 @@ $(MAKE) TAGS -C $(CWEBDIR) $(MAKE) TAGS -C $(DOCDIR) +.PHONY : show +show: + $(MAKE) show -C $(CWEBDIR) + $(MAKE) show -C $(DOCDIR) + + ## Local Variables: ## mode:Makefile ## End: diff -Naur 3DLDF-1.1.4/Makefile.in 3DLDF-1.1.5.1/Makefile.in --- 3DLDF-1.1.4/Makefile.in 2003-12-10 18:42:51.000000000 +0100 +++ 3DLDF-1.1.5.1/Makefile.in 2004-01-16 19:18:52.000000000 +0100 @@ -16,10 +16,10 @@ # Created by Laurence Finston. -# $Id: Makefile.am,v 1.7 2003/12/09 20:09:24 lfinsto1 Exp $ +# $Id: Makefile.am,v 1.9 2004/01/16 16:25:11 lfinsto1 Exp $ # This file is part of 3DLDF, a package for three-dimensional drawing. -# Copyright (C) 2003 Laurence D. Finston. +# Copyright (C) 2003, 2004 Laurence D. Finston. # 3DLDF is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by @@ -143,7 +143,9 @@ CWEBDIR := CWEB DOCDIR := DOC TEXINFODIR := TEXINFO -EPSDIR := EPS +GRAPHICSDIR := graphics +EPSDIR := eps +PNGDIR := png SUBDIRS = $(CWEBDIR) $(DOCDIR) @@ -503,6 +505,13 @@ uninstall-info-recursive uninstall-recursive +export CWEBDIR +export DOCDIR +export TEXINFODIR +export GRAPHICSDIR +export EPSDIR +export PNGDIR + vpath %.web $(CWEBDIR) vpath %.h $(CWEBDIR) vpath %.c $(CWEBDIR) @@ -547,6 +556,11 @@ TAGS : $(MAKE) TAGS -C $(CWEBDIR) $(MAKE) TAGS -C $(DOCDIR) + +.PHONY : show +show: + $(MAKE) show -C $(CWEBDIR) + $(MAKE) show -C $(DOCDIR) # Tell versions [3.59,3.63) of GNU make to not export all variables. # Otherwise a system limit (for SysV at least) may be exceeded. .NOEXPORT: diff -Naur 3DLDF-1.1.4/NEWS 3DLDF-1.1.5.1/NEWS --- 3DLDF-1.1.4/NEWS 2003-12-10 18:19:43.000000000 +0100 +++ 3DLDF-1.1.5.1/NEWS 2004-01-16 17:26:27.000000000 +0100 @@ -1,7 +1,7 @@ 3DLDF NEWS -- history of user-visible changes. 2003-11-12 This file is part of 3DLDF, a package for three-dimensional drawing. -Copyright (C) 2003 Laurence D. Finston. +Copyright (C) 2003, 2004 Laurence D. Finston. 3DLDF is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by @@ -29,9 +29,90 @@ -$Id: NEWS,v 1.4 2003/12/10 17:19:42 lfinsto1 Exp $ +$Id: NEWS,v 1.7 2004/01/16 16:26:26 lfinsto1 Exp $ -Version 1.1.4 +Release 1.1.5.1 + +* Added missing Texinfo files to the `3dldf_TEXINFOS' variable in + `3DLDF-1.1.5.1/DOC/TEXINFO/Makefile.am', and reordered the filenames. + +* Changed the names of the PNG (Portable Network Graphics) files + included in the HTML version of the _3DLDF User and Reference + Manual_. Changed the names in the commands for including these + files in the Texinfo files. I wasn't able to write some of the + files with the old names to a CD-R (Compact Disk, Recordable). + +Release 1.1.5 + +* In release 1.1.5, I've tied up some loose ends. I wanted to do this + before starting on the input routine. + +* Added `const real step' argument to the version of + Ellipse::intersection_points() that takes an Ellipse + argument. + +* BUG FIX: Added `touch 3DLDFmp.mp' to the `3DLDFmp.mp' target in + 3DLDF-1.1.5/CWEB/Makefile.am. This ensures that + TeX and dvips will be run if MetaPost is run on `3DLDFmp.mp'. This happens if + `3DLDFput.mp' is newer than `3DLDFmp.mp', but the latter isn't changed, so TeX and dvips + weren't being run. I'm surprized nobody's complained about this. + Not yet documented in the _3DLDF User and Reference Manual_. + +* Added `PHONY' targets as synonyms for certain targets: + `cpl' for `3dldf'. For compiling and linking `3dldf'. + `mp' for `3DLDFmp.mp'. For running MetaPost on `3DLDFmp.mp'. + `ldf' for `3DLDFput.mp'. For running `3dldf'. + Not yet documented in the _3DLDF User and Reference Manual_. + +* It is now possible to ``typedef'' `real' to either `float' + or `double'. This means that `real' can now be made a synonym + for either `float' or `double' by using a `typedef' + declaration. `real' is typedeffed to `float' by default. + +* Added `const bool ldf_real_float' and + `extern const bool ldf_real_double' + for use in non-conditionally compiled code. + They are set according to the values + of `LDF_REAL_FLOAT' and `LDF_REAL_DOUBLE'. + +* `Transform::epsilon()' and `Point::epsilon()' now return + different values, depending on the values of the preprocessor macros + `LDF_REAL_FLOAT' and `LDF_REAL_DOUBLE'. I have not yet tested + whether good values are returned when `real' is `double'. + +* `MAX_REAL' and `MAX_REAL_SQRT' are no longer constants. + Their values are set at the beginning of `main()'. However, + users should not change their values. `MAX_REAL' is the + second-largest `float' or `double' on a given machine. This + now works for all common architectures. + +* Added `namespace System' containing the following functions: + `get_endianness()', `is_big_endian()', + `is_little_endian()', `get_register_width()', + `is_32_bit()', `is_64_bit()', and the template function + `get_second_largest()'. + + `namespace System' and its functions are documented in + `system.texi', which is new in edition 1.1.5 of the + _3DLDF User and Reference Manual_. + +* Replaced the various `create_new_()' functions with the + template function `create_new()'. The latter is documented in + `creatnew.texi', which is new in edition 1.1.5 of the + _3DLDF User and Reference Manual_. + +* Added the file `3DLDF-1.1.5/CWEB/cnepspng.el' to + the distribution. It contains the definitions of the Emacs-Lisp + functions `convert-eps' and `convert-eps-loop'. + +* Added the files + 3DLDF-1.1.5/CWEB/exampman.web and + 3DLDF-1.1.5/CWEB/examples.mp to the + distribution. They contain the C++ and MetaPost code, + respectively, for generating the illustrations in the + _3DLDF User and Reference Manual_. + +Release 1.1.4 * MAX_REAL is now the second largest float value. However, the calculation is system dependent, and will only work on 32-bit little-endian architectures. I will start working on porting this @@ -47,22 +128,22 @@ * It is now possible to generate the Texinfo manual in the Info and HTML formats. -Version 1.1.3 +Release 1.1.3 * Bug fixes to /3DLDF-1.1.3/CWEB/Makefile.am and /3DLDF-1.1.3/CWEB/tsthdweb. Retangling, reCompilation, and relinking should now work properly. This was tricky to fix, though, so problems may crop up. -Version 1.1.2 +Release 1.1.2 * Minor changes. -Version 1.1.1 +Release 1.1.1 * Autoconf and Automake are now used. * Made changes to the documentation. -Version 1.0 -* Initial version. +Release 1.0 +* Initial release. Local variables: diff -Naur 3DLDF-1.1.4/README 3DLDF-1.1.5.1/README --- 3DLDF-1.1.4/README 2003-12-10 18:32:29.000000000 +0100 +++ 3DLDF-1.1.5.1/README 2004-01-16 17:24:27.000000000 +0100 @@ -1,7 +1,11 @@ README - + This file is part of 3DLDF, a package for three-dimensional drawing. -Copyright (C) 2003 Laurence D. Finston. +Copyright (C) 2003, 2004 Laurence D. Finston. + +$Id: README,v 1.10 2004/01/16 16:24:27 lfinsto1 Exp $ + +* Top 3DLDF is a GNU package. It is part of the GNU Project of the Free Software Foundation. See the website http://www.gnu.org for more @@ -28,30 +32,7 @@ See the website http://www.gnu.org for more information. - -3DLDF is available for downloading from -http://ftp.gnu.org/gnu/3dldf -It is also available from -http://www.dante.de/software/ctan/, the Dante www-server -and from http://wwwuser.gwgd.de/~lfinsto1, -the author's website. - -Please send bug reports to bug-3DLDF@gnu.org -The mailing list help-3DLDF@gnu.org is available for people to -ask other users for help. -The mailing list info-3DLDF@gnu.org is for sending -announcements to users. To subscribe to these mailing lists, send an -email with ``subscribe '' as the subject. - - -The official 3DLDF website will be -http://www.gnu.org/software/3dldf. This site may not yet be -available. -I hope it will be soon. See also the author's website, -http://wwwuser.gwdg.de/~lfinsto1, which will contain news about 3DLDF, -and a section ``Errata and -Addenda'', which may be helpful, if a user has problems. - +* Contact The author can be contacted at: Laurence D. Finston @@ -61,55 +42,83 @@ lfinsto1@gwdg.de s246794@stud.uni-goettingen.de + +* Downloading + +3DLDF is available for downloading from the following servers using +the protocols indicated (i.e., `ftp', `http', and `rsync'): + +Free Software Foundation/GNU Project server: + +ftp://ftp.gnu.org/gnu/3dldf +http://ftp.gnu.org/gnu/3dldf + +GWDG (Gesellschaft fuer wissenschaftliche Datenverarbeitung) server: + +http://ftp.gwdg.de/pub/gnu2/3dldf/ +ftp://ftp.gwdg.de/pub/gnu2/3dldf/ +rsync://ftp.gwdg.de/pub/gnu2/3dldf/ + +DANTE's CTAN server (DANTE = Deutschsprachige Anwendervereinigung TeX e.V., + CTAN = Comprehensive TeX Archive Network) + +http://dante.ctan.org/CTAN/graphics/3DLDF/ -$Id: README,v 1.7 2003/12/10 17:00:37 lfinsto1 Exp lfinsto1 $ +and from the author's website: +http://wwwuser.gwgd.de/~lfinsto1 + +* Mailing lists + +The following mailing lists are planned, but not yet available: +bug-3dldf@gnu.org --- For bug reports. +help-3dldf@gnu.org --- For users to ask one another for help. +info-3DLDF@gnu.org --- For sending announcements to users. + +To subscribe to these mailing lists, +once they are available, send an +email with ``subscribe'' as the subject. + +Until they are, users can send an email with +``subscribe 3dldf'' in the subject line to me at +lfinsto1@gwdg.de + + +* Web sites +The official 3DLDF website will be +http://www.gnu.org/software/3dldf. This site is not yet +available. +I hope it will be soon. See also the author's website, +http://wwwuser.gwdg.de/~lfinsto1, which contains news about 3DLDF, +and a section ``Errata and +Addenda'', which may be helpful, if a user has problems. + + +* Description of 3DLDF 3DLDF is a package for three-dimensional drawing with MetaPost output. It currently does not possess an input routine, so that user code must be written in C++, compiled, and linked with the rest of the program. This file, and the _User and Reference Manual_ -(/3DLDF-1.1.4/DOC/TEXINFO/3DLDF.ps) contain instructions on how to do +(/3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.ps) contain instructions on how to do this. 3DLDF is intended, among other things, to provide a fairly convenient way of making 3D drawings that can be included in TeX documents. -See the file INSTALL for instructions on installing 3DLDF. - -Please send bug reports to bug-3DLDF@gnu.org. (Not yet available!) - -The mailing list help-3DLDF@gnu.org is available for people to ask -other users for help. (Not yet available!) -The mailing list info-3DLDF@gnu.org is for sending announcements to -users. (Not yet available!) - -To subscribe to these mailing lists (once they are available), send an -email with `subscribe ' as the subject. - is optional; if it's -missing, I will use the `Reply-To' address of the email you sent. -Until they are made available, please contact the author at: -lfinsto1@gwdg.de +* Documentation -If you send a mail with `subscribe 3DLDF ' to me, I -will put you on my 3DLDF mailing list, and subscribe you to -info-3DLDF@gnu.org, when it becomes available. is -optional, as above. - - -Documentation - -The files /3DLDF-1.1.4/CWEB/3DLDFprg.ps and -/3DLDF-1.1.4/DOC/TEXINFO/3DLDF.ps contain respectively the documents +The files /3DLDF-1.1.5.1/CWEB/3DLDFprg.ps and +/3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.ps contain respectively the documents _3DLDF: The Program_ and the _3DLDF User and Reference Manual_ in PostScript format. In addition, -/3DLDF-1.1.4/CWEB/3DLDFprg.dvi contains _3DLDF: The Program_ in DVI +/3DLDF-1.1.5.1/CWEB/3DLDFprg.dvi contains _3DLDF: The Program_ in DVI format. If you need to regenerate the documentation for some reason, type `make ps' at the -command line from the directory /3DLDF-1.1.4/. +command line from the directory /3DLDF-1.1.5.1/. Please note, that if you decide to run cweave on 3DLDFprg.web by hand, be sure to use the version of the file cwebmacs.tex -in /3DLDF-1.1.4/CWEB/, since I've made a number of additions and changes +in /3DLDF-1.1.5.1/CWEB/, since I've made a number of additions and changes to the original. Ordinarily, it will be used automatically, so most users won't need to worry about this. @@ -119,58 +128,149 @@ `makeinfo --html 3DLDF.texi'. I apologize for the number of typos and other errors in the -documentation. I hope they don't detract from their usefulness. I -would have liked to have proofread and corrected them again before -publication, but for reasons external to 3DLDF, it is necessary -for me to publish now. -I plan to set up an errata list on the website: -http://www.gnu.org/software/3DLDF +documentation. I hope they don't detract from their usefulness. +Please see the section ``Errata and Addenda'' on my website: +http://wwwuser.gwdg.de/~lfinsto1/index.html + +* Installing + +See the file INSTALL for instructions on installing 3DLDF. + + +* Patch instructions + +Since 3DLDF 1.1.5.1 is being released so soon after 3DLDF 1.1.5, I'm +supplying two patch files: `3DLDF-1.1.4-1.1.5.1.diff.gz' and +`3DLDF-1.1.5-1.1.5.1.diff.gz'. + +The following instructions explain how to use +`3DLDF-1.1.4-1.1.5.1.diff.gz' to update 3DLDF 1.1.4. They apply +equally to 3DLDF 1.1.5, except where noted, as long as the names of +the files and diretories are changed appropriately. + +The best way to apply the patch `3DLDF-1.1.4-1.1.5.1.diff.gz' is to +put the distribution of 3DLDF 1.1.4 in a new directory, e.g., +`3DLDF-1.1.4'. +You may want you create a distribution by calling `make dist' from a +shell in the working directory `3DLDF-1.1.4/'. +Then you will have to uncompress and expand `3DLDF-1.1.4.tar.gz': + + gunzip 3DLDF-1.1.4.tar.gz + tar pxvf 3DLDF-1.1.4.tar + +If you choose to use your existing `3DLDF-1.1.4' directory instead, +you should save any files you don't want changed in a safe place. + + +Delete the directory `3DLDF-1.1.4/DOC/TEXINFO/EPS' (not if you're +patching 3DLDF 1.1.5!): + + rm -rf 3DLDF-1.1.4/DOC/TEXINFO/EPS + +This directory doesn't exist in 3DLDF 1.1.5 and 3DLDF 1.1.5.1. +Instead, the illustrations for the Texinfo manual are in +`3DLDF-1.1.5.1/DOC/TEXINFO/graphics/eps' (for the PostScript version) +and `3DLDF-1.1.5.1/DOC/TEXINFO/graphics/png' (for the HTML version). + +Please note that the HTML version of the Texinfo manual is not part of +the distribution. It is, however, downloadable separately from +my website and the GWDG server, so there should be no need to +generate it yourself. See `* Downloading', above, for the +URLs (Uniform Resource Locators). + +Rename `3DLDF-1.1.4' `3DLDF-1.1.5.1' + + mv 3DLDF-1.1.4 3DLDF-1.1.5.1 + +Now, put `3DLDF-1.1.4-1.1.5.1.diff.gz' in `3DLDF-1.1.5.1'. +Change the working directory to `3DLDF-1.1.5.1' and unpack +`3DLDF-1.1.4-1.1.5.1.diff.gz': + + mv 3DLDF-1.1.4-1.1.5.1.diff.gz 3DLDF-1.1.5.1/ + cd 3DLDF-1.1.5.1 + gunzip 3DLDF-1.1.4-1.1.5.1.diff.gz + +Apply the patch: + + patch -p1 -i 3DLDF-1.1.4-1.1.5.1.diff + +* Running 3DLDF Once 3DLDF is installed, put the code for your drawings in -/3DLDF-1.1.4/main.web, and call `make run' from the command -line in the directory /3DLDF-1.1.4/ to run 3dldf (the executable +/3DLDF-1.1.5.1/main.web, and call `make run' from the command +line in the directory /3DLDF-1.1.5.1/ to run 3dldf (the executable program), MetaPost, TeX, and dvips, to generate a PostScript file containing your drawings. -As a convenience, /3DLDF-1.1.4/ and /3DLDF-1.1.4/CWEB/ both contain an +As a convenience, 3DLDF-1.1.5.1/ and 3DLDF-1.1.5.1/CWEB/ both contain an identical shell script called `ldfr', which simply calls 'make run', so that 3DLDF can be used conveniently from either directory. - -make Targets +* make Targets + +BUG FIX: I've added `touch 3DLDFmp.mp' to the `3DLDFmp.mp' target in +3DLDF-1.1.5.1/CWEB/Makefile.am. This ensures that +TeX and dvips will be run if MetaPost is run on `3DLDFmp.mp'. This +happens if `3DLDFput.mp' is newer than `3DLDFmp.mp', but the latter +isn't changed, so TeX and dvips weren't being run. I'm surprized +nobody's complained about this. Not yet documented in the +_3DLDF User and Reference Manual_. + +3DLDF-1.1.5.1/CWEB/Makefile.am contains several +`PHONY' targets as synonyms for several targets. + +These are targets that users may want to call often: + +`cpl' for `3dldf': For compiling and linking `3dldf'. + +`mp' for `3DLDFmp.mp': For running MetaPost on `3DLDFmp.mp'. + +`ldf' for `3DLDFput.mp': For running `3dldf'. + +Most users should never need to call `make ps' or `make pdf', +unless they are making changes to 3DLDF. + +`ps' for generating `3DLDFprg.ps'. + +`pdf' for generating `3DLDFprg.pdf'. It uses `ps2pdf'. Automake +doesn't generate a `pdf' target in 3DLDF-1.1.5.1/CWEB/ automatically, +but it does in 3DLDF-1.1.5.1/DOC/TEXINFO/. However, it requires +`pdftex', which is not installed on the computer I'm using. It may be +on yours, however, so I didn't want to override the default `pdf' target. + +If you want to generate `3DLDF.pdf' for some reason, and `make pdf' +doesn't work on your computer either, try `ps2pdf 3DLDF.ps'. However, +please note that `3DLDF.pdf' is included in the distribution and +available separately from my website and other download sites (see +"Downloading" above), along with `3DLDF.ps'. +The HTML version is also available from my website, +http://ftp.gwdg.de/pub/gnu2/3dldf/ +ftp://ftp.gwdg.de/pub/gnu2/3dldf/ +and +rsync://ftp.gwdg.de/pub/gnu2/3dldf/ + +These targets are new in 3DLDF 1.1.5.1, and are not yet documented in +the _3DLDF User and Reference Manual_ (/3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.ps). To get rid of the files that 3DLDF generates, without deleting any important ones, call `make purge'. For further information, see the _3DLDF User and -Reference Manual_ (/3DLDF-1.1.4/DOC/TEXINFO/3DLDF.ps). +Reference Manual_ (/3DLDF-1.1.5.1/DOC/TEXINFO/3DLDF.ps). Users should avoid the use of the following extensions in -/3DLDF-1.1.4/CWEB/: .hbk, .tim, and .tmw. +/3DLDF-1.1.5.1/CWEB/: .rpo, .h, .hbk, .tim, and .tmw. Each CWEB file has corresponding files with the same name and -these extensions. They are used for controlling retangling, -recompilation, and relinking. - - -System dependencies: +these extensions. -In 3DLDF 1.1.4, the constant float MAX_REAL is now really the second -largest float value, but only on 32-bit little-endian architectures. -On big-endian and 64-bit little-endian architectures, this will fail, -and 3dldf will exit with an error message. - -I plan to fix this so it will work on other architectures soon. If -you have this problem, and can't fix it yourself, please contact me. - - -Information on building: +* Information on building: If only TeX text, comments, or whitespace in the CWEB file are changed, then no recompilation or relinking takes place, and the CWEB file isn't retangled the next time `make 3dldf' is called. Unfortunately, whitespace in literal strings that are part of the C++ code are also ignored, contrary to what I wrote in -3DLDF-1.1.4/CWEB/ChangeLog. It's not likely that this will cause any +3DLDF-1.1.5.1/CWEB/ChangeLog. It's not likely that this will cause any problems in actual use, though. If only the C++ code has changed, the .cxx file is recompiled, and 3dldf is @@ -179,10 +279,8 @@ If the header file has changed, all of the C++ files that depend on it are recompiled, and 3dldf is relinked. -Previously, a ``timer'' file was used for keeping track of whether -.h had changed. Now, a second ``timer'' is used for keeping -track of whether .cxx has changed. (Insert pun about -``two-timing'' here, when I've thought of one.) +Two ``timer'' files are used for keeping track of whether +.h and/or .cxx has changed. The procedure seems to work when multiple files are changed in various ways. However, one unpleasant consequence is that the CWEB file must @@ -191,40 +289,47 @@ has changed (but only in this case!). This means that the file has changed on disk, so that the buffer must be reverted, if the user is currently working on it, -which is likely. This shell script prints a message to this effect to -standard output. This is annoying, but I haven't thought of a way +which is likely. The shell script `tsthdweb' prints a message to this +effect to standard output. It's annoying to have to revert the +buffer, but I haven't thought of a way around this problem. It's a consequence of using the timestamps of files to decide whether they need to be reprocessed. The best solution may be to return to using an auxilliary program for controlling recompilation. However, this will mean maintaining two different methods of rebuilding, because Automake requires valid build rules. +** Reverting buffers + If you're using Emacs, you can set a key to revert the buffer without -querying by putting the following sexp (s-expression, but I've -forgotten what ``s'' stands for) into your .emacs file: +querying by putting the following sexp (s-expression, but I don't know +what ``s'' stands for) into your `.emacs' file: + (global-set-key [f5] '(lambda () (interactive) (revert-buffer t t))) Or, if you're using, for example, foo mode, you can put the following sexp into your foo-mode-hook declaration: + (local-set-key foo-mode-map [f5] '(lambda () (interactive) (revert-buffer t t))) For example, (setq lisp-mode-hook '(lambda () (local-set-key [f5] '(lambda () (interactive) - (revert-buffer t t))) -) + (revert-buffer t t))))) Or, if you've defined a foo mode yourself, you can put the key assignment into foo-mode-map: + (if foo-mode-map () (setq foo-mode-map (nconc (make-sparse-keymap) c-mode-map)) (define-key foo-mode-map [f5] '(lambda () (interactive) (revert-buffer t t)))) -Information about Changes -For information about changes to 3DLDF, see ChangeLog, ./CWEB/ChangeLog, +*Information about Changes + +For information about changes to 3DLDF, see +NEWS, ChangeLog, ./CWEB/ChangeLog, ./DOC/ChangeLog, ./DOC/TEXINFO/ChangeLog, ./RCSFREEZE.log ./CWEB/RCSFREEZE.log, ./DOC/RCSFREEZE.log, and ./DOC/TEXINFO/RCSFREEZE.log. @@ -239,9 +344,8 @@ - - - %% Local Variables: %% mode:TeX +%% outline-minor-mode:t +%% outline-regexp:"^\\*+" %% End: diff -Naur 3DLDF-1.1.4/configure 3DLDF-1.1.5.1/configure --- 3DLDF-1.1.4/configure 2003-12-10 18:42:52.000000000 +0100 +++ 3DLDF-1.1.5.1/configure 2004-01-16 19:18:46.000000000 +0100 @@ -1537,7 +1537,7 @@ # Define the identity of the package. PACKAGE=3DLDF - VERSION=1.1.4 + VERSION=1.1.5.1 # Some tools Automake needs. @@ -1659,8 +1659,6 @@ ac_config_headers="$ac_config_headers CWEB/config.h" - - # Checks for programs. ac_ext=cc ac_cpp='$CXXCPP $CPPFLAGS' diff -Naur 3DLDF-1.1.4/configure.ac 3DLDF-1.1.5.1/configure.ac --- 3DLDF-1.1.4/configure.ac 2003-12-09 21:12:59.000000000 +0100 +++ 3DLDF-1.1.5.1/configure.ac 2004-01-16 19:05:24.000000000 +0100 @@ -1,10 +1,10 @@ # configure.ac. # Created by Laurence Finston 2003.11.11. - -# $Id: configure.ac,v 1.5 2003/12/09 20:12:58 lfinsto1 Exp $ + +# $Id: configure.ac,v 1.7 2004/01/16 18:05:24 lfinsto1 Exp $ # This file is part of 3DLDF, a package for three-dimensional drawing. -# Copyright (C) 2003 Laurence D. Finston. +# Copyright (C) 2003, 2004 Laurence D. Finston. # 3DLDF is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by @@ -35,13 +35,11 @@ AC_INIT(CWEB/main.web) -AM_INIT_AUTOMAKE(3DLDF, 1.1.4, lfinsto1@gwdg.de) +AM_INIT_AUTOMAKE(3DLDF, 1.1.5.1, lfinsto1@gwdg.de) AC_CONFIG_SRCDIR([CWEB/main.web]) AM_CONFIG_HEADER(CWEB/config.h) - - # Checks for programs. AC_PROG_CXX AC_PROG_CC