Near-Optimal Parameterization of the Intersection of Quadrics: II. A Classification of Pencils

Laurent Dupont; Daniel Lazard; Sylvain Lazard; Sylvain Petitjean

inria-00071228, version 1

Near-Optimal Parameterization of the Intersection of Quadrics: II. A Classification of Pencils

Laurent Dupont () ¹, Daniel Lazard ², Sylvain Lazard ¹, Sylvain Petitjean ¹

N° RR-5668 (2005)

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].

1: VEGAS (INRIA Lorraine - LORIA)
INRIA – CNRS : UMR7503 – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
2: Laboratoire d'Informatique de Paris 6 (LIP6)
CNRS : UMR7606 – Université Pierre et Marie Curie [UPMC] - Paris VI

inria-00071228, version 1
http://hal.inria.fr/inria-00071228
oai:hal.inria.fr:inria-00071228
From: Rapport De Recherche Inria <>
Submitted on: Tuesday, 23 May 2006 14:43:56
Updated on: Thursday, 29 June 2006 11:39:42

See detailed view

Associated documents

PS :

PDF :

Export

Bibtex EndNote TEI RefWorks

<?xml version="1.0" encoding="UTF-8"?>
<listBibl xmlns="http://www.tei-c.org/ns/1.0" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<listBibl type="report"><head>Research reports</head>
<biblStruct type="report" xml:id="inria-00071228"><monogr>
<author><persName><forename>Laurent</forename><surname>Dupont</surname></persName>
<affiliation>
<orgName type="laboratory">INRIA Lorraine - LORIA</orgName>
<orgName type="team">VEGAS</orgName>
<country>FR</country>
<orgName type="institution">INRIA</orgName>
<orgName type="institution">CNRS : UMR7503</orgName>
<orgName type="institution">Université Henri Poincaré - Nancy I</orgName>
<orgName type="institution">Université Nancy II</orgName>
<orgName type="institution">Institut National Polytechnique de Lorraine (INPL)</orgName>
</affiliation>
</author>
<author><persName><forename>Daniel</forename><surname>Lazard</surname></persName>
<affiliation>
<orgName type="laboratory">LIP6</orgName>
<orgName type="team">Laboratoire d'Informatique de Paris 6</orgName>
<country>FR</country>
<orgName type="institution">CNRS : UMR7606</orgName>
<orgName type="institution">Université Pierre et Marie Curie [UPMC] - Paris VI</orgName>
</affiliation>
</author>
<author><persName><forename>Sylvain</forename><surname>Lazard</surname></persName>
<affiliation>
<orgName type="laboratory">INRIA Lorraine - LORIA</orgName>
<orgName type="team">VEGAS</orgName>
<country>FR</country>
<orgName type="institution">INRIA</orgName>
<orgName type="institution">CNRS : UMR7503</orgName>
<orgName type="institution">Université Henri Poincaré - Nancy I</orgName>
<orgName type="institution">Université Nancy II</orgName>
<orgName type="institution">Institut National Polytechnique de Lorraine (INPL)</orgName>
</affiliation>
</author>
<author><persName><forename>Sylvain</forename><surname>Petitjean</surname></persName>
<affiliation>
<orgName type="laboratory">INRIA Lorraine - LORIA</orgName>
<orgName type="team">VEGAS</orgName>
<country>FR</country>
<orgName type="institution">INRIA</orgName>
<orgName type="institution">CNRS : UMR7503</orgName>
<orgName type="institution">Université Henri Poincaré - Nancy I</orgName>
<orgName type="institution">Université Nancy II</orgName>
<orgName type="institution">Institut National Polytechnique de Lorraine (INPL)</orgName>
</affiliation>
</author>
<title type="main" level="m">Near-Optimal Parameterization of the Intersection of Quadrics: II. A Classification of Pencils</title><title type="main" level="m">Near-Optimal Parameterization of the Intersection of Quadrics: II. A Classification of Pencils</title><imprint><biblScope type="publicationDate">2005-00-00</biblScope></imprint></monogr><idno type="HALid">http://hal.inria.fr/inria-00071228</idno><idno type="HALFile">http://hal.inria.fr/inria-00071228/PDF/RR-5668.pdf</idno></biblStruct>
</listBibl>
</listBibl>