Near-Optimal Parameterization of the Intersection of Quadrics: II. A Classification of Pencils
Identifieur interne : 004901 ( Hal/Checkpoint ); précédent : 004900; suivant : 004902Near-Optimal Parameterization of the Intersection of Quadrics: II. A Classification of Pencils
Auteurs : Laurent Dupont [France] ; Daniel Lazard [France] ; Sylvain Lazard [France] ; Sylvain Petitjean [France]Source :
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Abstract
While Part I [2] of this paper was devoted mainly to quadrics intersecting in a smooth quartic, we now focus on singular intersections. To produce optimal or near-optimal parameterizations in all cases, we first determine the the real type of the intersection before computing the actual parameterization. In this second part, we present the first classification of pencils of quadrics based on the type of the real intersection and we show how this classification can be used to compute efficiently the type of the real intersection. The near-optimal parameterization algorithms in all singular cases will be given in Part III [3].
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To produce optimal or near-optimal parameterizations in all cases, we first determine the the real type of the intersection before computing the actual parameterization. In this second part, we present the first classification of pencils of quadrics based on the type of the real intersection and we show how this classification can be used to compute efficiently the type of the real intersection. The near-optimal parameterization algorithms in all singular cases will be given in Part III [3].</div></front></TEI><hal api="V3"><titleStmt><title xml:lang="en">Near-Optimal Parameterization of the Intersection of Quadrics: II. A Classification of Pencils</title><author role="aut"><persName><forename type="first">Laurent</forename><surname>Dupont</surname></persName><email>laurent.dupont@loria.fr</email><idno type="idhal">laurent-dupont</idno><idno type="halauthor">99077</idno><affiliation ref="#struct-2573"></affiliation></author><author role="aut"><persName><forename type="first">Daniel</forename><surname>Lazard</surname></persName><email></email><idno type="halauthor">97856</idno><affiliation ref="#struct-233"></affiliation></author><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-2573"></affiliation></author><author role="aut"><persName><forename type="first">Sylvain</forename><surname>Petitjean</surname></persName><email></email><idno type="halauthor">60838</idno><affiliation ref="#struct-2573"></affiliation></author><editor role="depositor"><persName><forename>Rapport De Recherche</forename><surname>Inria</surname></persName><email>rrrt-editeurs@inria.fr</email></editor></titleStmt><editionStmt><edition n="v1" type="current"><date type="whenSubmitted">2006-05-23 14:43:56</date><date type="whenWritten">2005-09</date><date type="whenModified">2016-05-18 08:56:59</date><date type="whenReleased">2006-05-31 14:24:25</date><date type="whenProduced">2005</date><date type="whenEndEmbargoed">2006-05-23</date><ref type="file" target="https://hal.inria.fr/inria-00071228/document"><date notBefore="2006-05-23"></date></ref><ref type="file" n="1" target="https://hal.inria.fr/inria-00071228/file/RR-5668.pdf"><date notBefore="2006-05-23"></date></ref></edition><respStmt><resp>contributor</resp><name key="111068"><persName><forename>Rapport De Recherche</forename><surname>Inria</surname></persName><email>rrrt-editeurs@inria.fr</email></name></respStmt></editionStmt><publicationStmt><distributor>CCSD</distributor><idno type="halId">inria-00071228</idno><idno type="halUri">https://hal.inria.fr/inria-00071228</idno><idno type="halBibtex">dupont:inria-00071228</idno><idno type="halRefHtml">[Research Report] RR-5668, INRIA. 2005</idno><idno type="halRef">[Research Report] RR-5668, INRIA. 2005</idno></publicationStmt><seriesStmt><idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno><idno type="stamp" n="INRIA-RRRT">Rapports de recherche et Technique de l'Inria</idno><idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno><idno type="stamp" n="INPL">Institut National Polytechnique de Lorraine</idno><idno type="stamp" n="LORIA2">Publications du LORIA</idno><idno type="stamp" n="INRIA-NANCY-GRAND-EST">INRIA Nancy - Grand Est</idno><idno type="stamp" n="LORIA">LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications</idno><idno type="stamp" n="LORIA-ACGI" p="LORIA">Algorithmique, calcul, image et géométrie</idno><idno type="stamp" n="LIP6" p="UPMC">Laboratoire d'Informatique de Paris 6</idno><idno type="stamp" n="UPMC">Université Pierre et Marie Curie</idno><idno type="stamp" n="INRIA2">INRIA 2</idno><idno type="stamp" n="INRIA-LORRAINE">INRIA Nancy - Grand Est</idno><idno type="stamp" n="LABO-LORIA-SET" p="LORIA">LABO-LORIA-SET</idno><idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno></seriesStmt><notesStmt><note type="audience" n="0">Not set</note><note type="report" n="6">Research Report</note></notesStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Near-Optimal Parameterization of the Intersection of Quadrics: II. A Classification of Pencils</title><author role="aut"><persName><forename type="first">Laurent</forename><surname>Dupont</surname></persName><email>laurent.dupont@loria.fr</email><idno type="idHal">laurent-dupont</idno><idno type="halAuthorId">99077</idno><affiliation ref="#struct-2573"></affiliation></author><author role="aut"><persName><forename type="first">Daniel</forename><surname>Lazard</surname></persName><idno type="halAuthorId">97856</idno><affiliation ref="#struct-233"></affiliation></author><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-2573"></affiliation></author><author role="aut"><persName><forename type="first">Sylvain</forename><surname>Petitjean</surname></persName><idno type="halAuthorId">60838</idno><affiliation ref="#struct-2573"></affiliation></author></analytic><monogr><idno type="reportNumber">RR-5668</idno><imprint><date type="datePub">2005</date></imprint><authority type="institution">INRIA</authority></monogr></biblStruct></sourceDesc><profileDesc><langUsage><language ident="en">English</language></langUsage><textClass><keywords scheme="author"><term xml:lang="en">PENCILS OF QUADRICS</term><term xml:lang="en">CLASSIFICATION</term><term xml:lang="en">CURVE PARAMETERIZATION</term><term xml:lang="en">INTERSECTION OF SURFACES</term><term xml:lang="en">QUADRICS</term></keywords><classCode scheme="halDomain" n="info.info-cg">Computer Science [cs]/Computational Geometry [cs.CG]</classCode><classCode scheme="halDomain" n="info.info-oh">Computer Science [cs]/Other [cs.OH]</classCode><classCode scheme="halTypology" n="REPORT">Reports</classCode></textClass><abstract xml:lang="en">While Part I [2] of this paper was devoted mainly to quadrics intersecting in a smooth quartic, we now focus on singular intersections. To produce optimal or near-optimal parameterizations in all cases, we first determine the the real type of the intersection before computing the actual parameterization. In this second part, we present the first classification of pencils of quadrics based on the type of the real intersection and we show how this classification can be used to compute efficiently the type of the real intersection. The near-optimal parameterization algorithms in all singular cases will be given in Part III [3].</abstract></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
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