Intersecting Quadrics: An Efficient and Exact Implementation
Identifieur interne : 004A95 ( Hal/Checkpoint ); précédent : 004A94; suivant : 004A96Intersecting Quadrics: An Efficient and Exact Implementation
Auteurs : Sylvain Lazard [France] ; Luis Pe Aranda [France] ; Sylvain Petitjean [France]Source :
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Abstract
We present the first complete, exact and efficient C++ implementation of a method for parameterizing the intersection of two implicit quadrics with integer coefficients of arbitrary size. It is based on the near-optimal algorithm recently introduced by Dupont et al.~\cite{dupont03a}. Unlike existing implementations, it correctly identifies and parameterizes all the connected components of the intersection in all the possible cases, returning parameterizations with rational functions whenever such parameterizations exist. In addition, the coefficient field of the parameterizations is either minimal or involves one possibly unneeded square root.
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DOI: 10.1145/997817.997880
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type="indirect"><org type="institution" xml:id="struct-300293" status="OLD"><orgName>Institut National Polytechnique de Lorraine</orgName><orgName type="acronym">INPL</orgName><date type="end">2011-12-31</date><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-2496" type="direct"><org type="laboratory" xml:id="struct-2496" status="OLD"><orgName>INRIA Lorraine</orgName><desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/centre-de-recherche-inria/nancy-grand-est</ref></desc><listRelation><relation active="#struct-300009" type="direct"></relation></listRelation></org></tutelle></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Université Nancy 2</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Institut national polytechnique de Lorraine</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName></affiliation></author></analytic><idno type="DOI">10.1145/997817.997880</idno></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="mix" xml:lang="fr"><term>intersection de quadriques</term><term>quadric surface intersection</term><term>robustesse des calculs géométriques</term><term>robustness of geometric computation</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">We present the first complete, exact and efficient C++ implementation of a method for parameterizing the intersection of two implicit quadrics with integer coefficients of arbitrary size. It is based on the near-optimal algorithm recently introduced by Dupont et al.~\cite{dupont03a}. Unlike existing implementations, it correctly identifies and parameterizes all the connected components of the intersection in all the possible cases, returning parameterizations with rational functions whenever such parameterizations exist. In addition, the coefficient field of the parameterizations is either minimal or involves one possibly unneeded square root.</div></front></TEI><hal api="V3"><titleStmt><title xml:lang="en">Intersecting Quadrics: An Efficient and Exact Implementation</title><author role="aut"><persName><forename type="first">Sylvain</forename><surname>Lazard</surname></persName><email>sylvain.lazard@inria.fr</email><ptr type="url" target="http://www.loria.fr/~lazard/"></ptr><idno type="idhal">sylvain-lazard</idno><idno type="halauthor">661543</idno><affiliation ref="#struct-2350"></affiliation></author><author role="aut"><persName><forename type="first">Luis</forename><surname>Peñaranda</surname></persName><email>Luis.Penaranda@loria.fr</email><idno type="halauthor">135321</idno><orgName ref="#struct-300009"></orgName><affiliation ref="#struct-2350"></affiliation></author><author role="aut"><persName><forename type="first">Sylvain</forename><surname>Petitjean</surname></persName><email></email><idno type="halauthor">130242</idno><orgName ref="#struct-441569"></orgName><affiliation ref="#struct-2350"></affiliation></author><editor role="depositor"><persName><forename>Sylvain</forename><surname>Lazard</surname></persName><email>sylvain.lazard@inria.fr</email></editor></titleStmt><editionStmt><edition n="v1" type="current"><date type="whenSubmitted">2007-11-07 10:23:14</date><date type="whenWritten">2004</date><date type="whenModified">2016-05-19 01:09:10</date><date type="whenReleased">2007-11-07 16:21:35</date><date type="whenProduced">2004-06</date><date type="whenEndEmbargoed">2007-11-07</date><ref type="file" target="https://hal.inria.fr/inria-00104003/document"><date notBefore="2007-11-07"></date></ref><ref type="file" subtype="author" n="1" target="https://hal.inria.fr/inria-00104003/file/SoCG_final.pdf"><date notBefore="2007-11-07"></date></ref></edition><respStmt><resp>contributor</resp><name key="103314"><persName><forename>Sylvain</forename><surname>Lazard</surname></persName><email>sylvain.lazard@inria.fr</email></name></respStmt></editionStmt><publicationStmt><distributor>CCSD</distributor><idno type="halId">inria-00104003</idno><idno type="halUri">https://hal.inria.fr/inria-00104003</idno><idno type="halBibtex">lazard:inria-00104003</idno><idno type="halRefHtml">Symposium on Computational Geometry - SoCG'2004, Jun 2004, Brooklyn, NY, United States. ACM, pp.419 - 428, 2004, <10.1145/997817.997880></idno><idno type="halRef">Symposium on Computational Geometry - SoCG'2004, Jun 2004, Brooklyn, NY, United States. ACM, pp.419 - 428, 2004, <10.1145/997817.997880></idno></publicationStmt><seriesStmt><idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno><idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno><idno type="stamp" n="LORIA2">Publications du LORIA</idno><idno type="stamp" n="LORIA">LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications</idno><idno type="stamp" n="INRIA-NANCY-GRAND-EST">INRIA Nancy - Grand Est</idno><idno type="stamp" n="INRIA-LORRAINE">INRIA Nancy - Grand Est</idno><idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno><idno type="stamp" n="INPL">Institut National Polytechnique de Lorraine</idno><idno type="stamp" n="LABO-LORIA-SET" p="LORIA">LABO-LORIA-SET</idno></seriesStmt><notesStmt><note type="commentary">Colloque avec actes et comité de lecture. internationale.</note><note type="audience" n="2">International</note><note type="invited" n="0">No</note><note type="popular" n="0">No</note><note type="peer" n="1">Yes</note><note type="proceedings" n="1">Yes</note></notesStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Intersecting Quadrics: An Efficient and Exact Implementation</title><author role="aut"><persName><forename type="first">Sylvain</forename><surname>Lazard</surname></persName><email>sylvain.lazard@inria.fr</email><ptr type="url" target="http://www.loria.fr/~lazard/"></ptr><idno type="idHal">sylvain-lazard</idno><idno type="halAuthorId">661543</idno><affiliation ref="#struct-2350"></affiliation></author><author role="aut"><persName><forename type="first">Luis</forename><surname>Peñaranda</surname></persName><email>Luis.Penaranda@loria.fr</email><idno type="halAuthorId">135321</idno><orgName ref="#struct-300009"></orgName><affiliation ref="#struct-2350"></affiliation></author><author role="aut"><persName><forename type="first">Sylvain</forename><surname>Petitjean</surname></persName><idno type="halAuthorId">130242</idno><orgName ref="#struct-441569"></orgName><affiliation ref="#struct-2350"></affiliation></author></analytic><monogr><idno type="localRef">A04-R-021 || lazard04b</idno><meeting><title>Symposium on Computational Geometry - SoCG'2004</title><date type="start">2004-06</date><settlement>Brooklyn, NY</settlement><country key="US">United States</country></meeting><imprint><publisher>ACM</publisher><biblScope unit="pp">419 - 428</biblScope><date type="datePub">2004</date></imprint></monogr><idno type="doi">10.1145/997817.997880</idno></biblStruct></sourceDesc><profileDesc><langUsage><language ident="en">English</language></langUsage><textClass><keywords scheme="author"><term xml:lang="fr">robustesse des calculs géométriques</term><term xml:lang="fr">quadric surface intersection</term><term xml:lang="fr">intersection de quadriques</term><term xml:lang="fr">robustness of geometric computation</term></keywords><classCode scheme="halDomain" n="info.info-cg">Computer Science [cs]/Computational Geometry [cs.CG]</classCode><classCode scheme="halTypology" n="COMM">Conference papers</classCode></textClass><abstract xml:lang="en">We present the first complete, exact and efficient C++ implementation of a method for parameterizing the intersection of two implicit quadrics with integer coefficients of arbitrary size. It is based on the near-optimal algorithm recently introduced by Dupont et al.~\cite{dupont03a}. Unlike existing implementations, it correctly identifies and parameterizes all the connected components of the intersection in all the possible cases, returning parameterizations with rational functions whenever such parameterizations exist. In addition, the coefficient field of the parameterizations is either minimal or involves one possibly unneeded square root.</abstract></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
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