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On the Design of CGAL, the Computational Geometry Algorithms Library

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(1)On the Design of CGAL, the Computational Geometry Algorithms Library Andreas Fabri, Geert-Jan Giezeman, Lutz Kettner, Stefan Schirra, Sven Schönherr. To cite this version: Andreas Fabri, Geert-Jan Giezeman, Lutz Kettner, Stefan Schirra, Sven Schönherr. On the Design of CGAL, the Computational Geometry Algorithms Library. RR-3407, INRIA. 1998. �inria-00073283�. HAL Id: inria-00073283 https://hal.inria.fr/inria-00073283 Submitted on 24 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. On the Design of CGAL, the Computational Geometry Algorithms Library Andreas Fabri — Geert-Jan Giezeman — Lutz Kettner Stefan Schirra — Sven Schönherr. N˚ 3407 April 1998 THÈME 2. ISSN 0249-6399. apport de recherche.

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(28) »7·IÆ@¾¾ÇÁºÌĒ»6³²o½L–È. ž. Ó֎5†‚ƒÁ |̀M{6|„ˆ”~}†‚ŽŠMs‚Ðumonqs>ŽŠs(|„ˆ{¥€â—Bs,ŽŠÓÖs>ƒ ˆŠ€‚~}‡™ |̀M{ Š€ä nqsX—qŽŠsGƒ|„ˆb|}€‚{6—qŽŠ€M‹q~}s,r Ò@{q€eË { Û sGˆb—Bs>ƒ,|}†‚~Í~}‰7Ë |Ì n Žs>ˆŠ—ÑsGƒÁ × €–~}|͋qŽ5†’Ž|}s>ˆ>Ð)ŽŠ|}r.|Ì |ÍÔMs>ˆj‹¥†‚ˆŠs>˜+€M{ã|Ír.—qŽs>ƒ,|}ˆŠsLƒ€Mr.—q‡™ †’ Š|}€‚{¥ˆ†’ŽsDn¥†‚Ž˜Ã Š€zƒ€Mr$‹q|}{qsL†‚{¥˜z Šnqs>ŽŠs,Óր‚Žs ~}s>ˆˆ‡¥ˆŠsÓևq~o†‚ˆ$~Í|}‹qŽ5†’Ž‰âƒ,€‚r.—Ñ€M{qs,{N 5ˆ,Ð 4Ýq†‚ƒÁ ”ƒ€‚r.—q‡q †e |̀M{ |„ˆ—B€Mˆˆb|}‹q~}sÓր‚Žr.†‚{@‰äMs,€Mr”s, ŠŽ|}ƒ.—¥ŽŠ€M‹q~Ís>rˆ †’{јˆŠ†\ÔMs>ˆo nqs.ƒ€‚ŽŽs>ƒÁ {qs>ˆˆ —qŽ€@€’ӏ‚|}Ԃs>{TÓր‚Žz† nqs,€MŽŠs, Š|„ƒ,†’~r.€@˜qs,~€’ÓLƒ€Mr.—q‡™ †’ Š|}€‚{T €) nqs”†MƒÁ ‡¥†’~ƒ€™˜™s Û ‹q‡™ ”|Ì ”ˆb~}€eË[ˆ˜™€eË {ä Šn¥sƒ€Mr.—q‡™ †’ Š|}€‚{×Ð ®z¯×°j± †’~}~}€eË[ˆ+€‚{qs €^ƒ5nq€@€MˆŠs. Šn¥s)‡q{¥˜™s>ŽŠ~}‰@|Í{¥†’Ž|Ì nqr.s Š|„ƒ)†‚{¥˜ Šn¥s,Žs,‹@‰€’èRs,Ž5ˆãÒ@|}{¥˜ä€’Ó †( ŠŽ5†‚˜™s,Þå€‚è ‹Ñs, “ËÉs>s,{Úsß)ƒ|}s,{у‰â†‚{¥˜äŽŠ€M‹q‡¥ˆb Š{qsGˆŠˆ>Ð . . . éT†‚{N‰à˜™|ÍèBs>ŽŠs>{N ŒN‡¥†’~}|Ì |ÍsGˆƒ>†’{çƒ,€‚{N ŠŽ|͋¥‡™ ŠsT €7 Šn¥s^s>†Mˆbs,Þ倂ÓÅÞå‡ÑˆbsT€‚Óㆠ~Í|}‹qŽ5†’Ž‰ô†‚{¥˜ ˜™|ÍèBs>Ž(†Mƒ,ƒ€MŽ˜q|Í{qä € Šn¥ss,Ý@—Bs,Ž|}s,{¥ƒ,s€‚Ó ŠnqsX‡¥ˆŠs,ŽGÐumonqsX†’‹B€eԂs)r.s>{M |̀M{qs>˜æƒ€MŽŠŽs>ƒ Š{qsGˆŠˆ†’{¥˜7Ž€‚‹¥‡¥ˆ“ {qs>ˆˆ|}ˆˆb‡¥s>ˆ”†’Žs†’r.€M{q Šn¥s>ˆŠs”ŒN‡¥†‚~Í|Í Š|}s>ˆ>*Ð –ÓLMs,{qs>Ž†‚~j|}r.—Ñ€MŽb 5†’{¥ƒ,s$|„ˆ– nqs.~ÍsG†’Ž{q|}{q) |Ír.s.†’{¥˜^nq€eË Óf†‚ˆb à nqs.~Í|}‹qŽ5†’Ž‰Ms 5ˆÃ‡Ñˆbs,Óևq~IÐ  [{¥€’ Šn¥s,ŽT|„ˆŠˆŠ‡qsÚ|}ˆT Šnqs †‚r”€M‡q{N T€’Ó{¥s,˃€‚{уs,—q ˆT†’{ј s,ݙƒ,s,—™ |̀M{¥ˆX€’Ó Šnqs7Ms,{qs>Ž†‚~+ŽŠ‡q~}s>ˆ( n¥†e r‡¥ˆb ‹Bs~ÍsG†’Ž{qs>˜ô†’{ј掐s,r.s>r$‹Bs,Žs>˜h Ð L†‚ˆŠsÞ¹€’ÓÅÞ¹‡¥ˆbs( s,{¥˜qˆ Š€7‚s, )|Í{ ƒ,€‚{ Ü |„ƒÁ )Ë |Í Šn Ü sݙ|͋¥|Í~}|Ì “‰ Û ‹¥‡™ )|Í{ r†‚{N‰ ˆŠ|Ì ‡¥†e |̀M{¥ˆo†”ˆŠ€‚~}‡™ |̀M{ƒ,†‚{u‹BszÓր‚‡q{¥˜u Š€.—q~}s>†Mˆbsà Šn¥s,r!‹B€’ n×Ð DˆŠ—Bs>ƒ|„†’~}~}‰ Šnqs Ü s,ݙ|͋q|}~}|Ì “‰)€‚Ó ®z¯j°j± ˆbn¥€‚‡q~„˜ {q€‚ $˜™|}ˆb ŠŽ5†‚ƒ $†({q€eÔ@|}ƒ,s.Ó֎Š€Mr Šnqs)Õ¥Žˆb $ˆb Šs,—шãË |Ì n ®z¯×°j± Ð.  ð×ð © ì «™ª    jª ì Ã{qs–r.†’‘“€‚Ž—B€‚|}{N L€’ÓR Šn¥s–ˆb‡Ñƒ,ƒsGˆŠˆˆb Š€MŽŠ‰€’ÓÎ Ï@Ï Ëo†‚ˆ4|Í ˆÉ†’~}r”€Nˆ“ Lƒ,€‚r.—q~}s s ƒ €Mr.—¥†e |͋q|}~}|Ì “‰Ë |Í Šn6Î †’{¥˜â Šn¥s”—B€MˆˆŠ|͋q~}sˆbr.€@€’ n^ Ž†‚{¥ˆŠ|Ì |̀M{^Ó֎€‚rÎ Š€^Î Ï@Ï )Ó֎€‚r nqs{qs,˟ˆ“ “‰@~}s.€’Ó ƒ€Mr.r”s>{N ˆ Û Š€(r”s>r$‹Bs,Ž+Óևq{уÁ Š|}€‚{ш㆒{¥˜^|Í{qn¥s,Ž|Ì 5†’{¥ƒ,s Û ‡q—â Š€Óևq~}~D€‚‹™‘“sGƒÁ ŠÞå€MŽŠ|}s,{N ŠsG˜T—qŽ€‚MŽ†‚r”r.|}{q¥Ð D†Mƒ5n {qs>Ë ~͉(~ÍsG†’Ž{qs>˜(ÓÖsG†e ‡qŽŠsƒ€‚‡¥~}˜X‹Bs$—q‡q Ã|}{M €)—qŽ5†‚ƒ Š|„ƒs|}r.r”sG˜™|„†e Šs>~͉MÐ ®z¯j°j± ‡Ñˆbs>ŽˆÃ†’Žsˆb‡q—¥—Ñ€NˆbsG˜( Š€)n¥†\ÔMs †)‹Ñ†‚ˆŠsÒ@{q€eË ~ÍsG˜™‚s$€’Ó0Î0Ï@φ‚{¥˜X nqs  WoÐRmonqs$Žs>†M˜™s,ŽÃ€’ӏ Šn¥s$—¥†‚—Ñs>ŽzˆŠnq€‚‡¥~}˜T‹Bs†\Ëo†’Žs+ Šnцe z Šnqs>ŽŠs|„ˆz† ŠŽs,r.s>{¥˜™€‚‡Ñˆ”˜q|ÌèRs,Žs,{¥ƒ,s‹Bs “Ë0s,s>{ô˜qs,Ԃs>~̀M—q|}{qâ†â~Í|}‹qŽ5†’Ž‰ Û ˆŠ‡¥ƒ5næ†Mˆ ®z¯×°j±¥Û Ë nq|„ƒ5n6 nq|„ˆ.—¥†’—Bs,Ž.|„ˆ”†‚‹Ñ€M‡™ Û †’{ј nqs7‡¥ˆŠs7€’Ó.ˆb‡¥ƒ5n †ô~}|͋qŽ5†’Ž‰ Û Ë nq|„ƒ5nS|„ˆT‡¥ˆŠ‡¥†‚~Í~}‰çr$‡Ñƒ5n ˆŠ|}r”—¥~Ís>ŽX Š€ ‡q{¥˜qs,Ž5ˆ“ 5†’{¥˜hÐ(monq|„ˆXn¥†‚ˆT‹Bs,s>{ ˆŠ‡¥ƒ,ƒ,s>ˆˆ“Óևq~}~}‰âˆŠnq€eË {âË |Í Šn W YD[ °Û †‚{¥˜Úƒ,†’{7†‚~}ˆŠ€X‹Ñs)ˆŠs,s>{äË |Í ŠnÚ nqs   W Ð ®z¯j°j± |}ˆ(‹¥†MˆbsG˜ç|}{ r†’{@‰à—q~„†‚ƒ,s>ˆ(€‚{Sƒ€‚{уs,—q ˆ(Ò@{q€eË { Ó֎€‚r   W!€‚Ž Šnqsڀ‚ Šnqs>Ž(—ц’ŽŠ ˆ€’Ó nqs6Î0ÏNÏ N 5†’{¥˜q†‚Ž˜ ×|}‹qŽ5†’Ž‰‚Ð) [{ôsÝq†‚r”—¥~Ís(|}ˆ” nqsX‡¥ˆŠs€‚Ózˆb ŠŽs>†’rˆ”†’{¥˜æˆ“ ŽŠsG†’r €M—Ñs>Ž†’ Š€‚Ž5ˆ|Í{ ®z¯×°j± Р–{q€’ nqs,Ž sÝq†‚r”—¥~Ís|„ˆ+ Šn¥s‡¥ˆbs€‚Óoƒ,€‚{N †‚|Í{¥s,Žƒ~„†‚ˆˆŠs>ˆã†’{ј䆂~́M€‚Ž|Ì nqrˆÃÓ֎Š€Mr Šn¥s   WoÐ.

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