Near-Optimal Parameterization of the Intersection of Quadrics: II. A Classification of Pencils
Identifieur interne : 006812 ( Main/Merge ); précédent : 006811; suivant : 006813Near-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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Paris 6</orgName><orgName type="acronym">UPMC</orgName><desc><address><addrLine>4 place Jussieu - 75005 Paris</addrLine><country key="FR"></country></address><ref type="url">http://www.upmc.fr/</ref></desc></org></tutelle><tutelle name="UMR7606" active="#struct-441569" type="direct"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno><idno type="IdRef">02636817X</idno><orgName>Centre National de la Recherche Scientifique</orgName><orgName type="acronym">CNRS</orgName><date type="start">1939-10-19</date><desc><address><country key="FR"></country></address><ref type="url">http://www.cnrs.fr/</ref></desc></org></tutelle></tutelles></hal:affiliation><country>France</country></affiliation></author><author><name sortKey="Lazard, Sylvain" sort="Lazard, Sylvain" uniqKey="Lazard S" first="Sylvain" last="Lazard">Sylvain Lazard</name><affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-2573" status="OLD"><idno type="RNSR">200518305E</idno><orgName>Effective Geometric Algorithms for Surfaces and Visibility</orgName><orgName type="acronym">VEGAS</orgName><desc><address><country key="FR"></country></address><ref type="url">http://www.inria.fr/equipes/vegas</ref></desc><listRelation><relation active="#struct-160" type="direct"></relation><relation name="UMR7503" active="#struct-441569" type="indirect"></relation><relation active="#struct-300009" type="indirect"></relation><relation active="#struct-300291" type="indirect"></relation><relation active="#struct-300292" type="indirect"></relation><relation active="#struct-300293" type="indirect"></relation><relation active="#struct-2496" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-160" type="direct"><org type="laboratory" xml:id="struct-160" status="OLD"><orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName><orgName type="acronym">LORIA</orgName><desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.loria.fr</ref></desc><listRelation><relation name="UMR7503" active="#struct-441569" type="direct"></relation><relation active="#struct-300009" type="direct"></relation><relation active="#struct-300291" type="direct"></relation><relation active="#struct-300292" type="direct"></relation><relation active="#struct-300293" type="direct"></relation></listRelation></org></tutelle><tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno><idno type="IdRef">02636817X</idno><orgName>Centre National de la Recherche Scientifique</orgName><orgName type="acronym">CNRS</orgName><date type="start">1939-10-19</date><desc><address><country key="FR"></country></address><ref type="url">http://www.cnrs.fr/</ref></desc></org></tutelle><tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName><orgName type="acronym">Inria</orgName><desc><address><addrLine>Domaine de VoluceauRocquencourt - 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BP 10578153 Le Chesnay Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/en/</ref></desc></org></tutelle><tutelle active="#struct-300291" type="indirect"><org type="institution" xml:id="struct-300291" status="OLD"><orgName>Université Henri Poincaré - Nancy 1</orgName><orgName type="acronym">UHP</orgName><date type="end">2011-12-31</date><desc><address><addrLine>24-30 rue Lionnois, BP 60120, 54 003 NANCY cedex, France</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300292" type="indirect"><org type="institution" xml:id="struct-300292" status="OLD"><orgName>Université Nancy 2</orgName><date type="end">2011-12-31</date><desc><address><addrLine>91 avenue de la Libération, BP 454, 54001 Nancy cedex</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300293" 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></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term>CLASSIFICATION</term><term>CURVE PARAMETERIZATION</term><term>INTERSECTION OF SURFACES</term><term>PENCILS OF QUADRICS</term><term>QUADRICS</term></keywords></textClass></profileDesc></teiHeader><front><div type="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].</div></front></TEI></record>Pour manipuler ce document sous Unix (Dilib)
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