3530 articles – 5253 Notices  [english version]

inria-00186090, version 1

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

Laurent Dupont () a, 1, Daniel Lazard b, 2, Sylvain Lazard () c, 1, Sylvain Petitjean c, 1

Journal of Symbolic Computation 43, 3 (2008) 192--215

Résumé : We present here the first classification of pencils of quadrics based on the type of their intersection in real projective space and we show how this classification can be used to compute efficiently the type of the real intersection. This classification is at the core of the design of the algorithms, presented in Part~III, for computing, in all cases of singular intersection, a near-optimal parameterization with polynomial functions, that is a parameterization in projective space whose coordinates functions are polynomial and such that the number of distinct square roots appearing in the coefficients is at most one away from the minimum.

  • a –  Université Nancy II
  • b –  Université Pierre et Marie Curie - Paris VI
  • c –  INRIA
  • 1 :  VEGAS (INRIA Lorraine - LORIA)
  • INRIA – CNRS : UMR7503 – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
  • 2 :  SALSA (INRIA Rocquencourt)
  • INRIA – CNRS : UMR7606 – Université Pierre et Marie Curie [UPMC] - Paris VI
  • Domaine : Informatique/Géométrie algorithmique
  • Mots-clés : Intersection of surfaces – pencils of quadrics – classification – curve parameterization
 
  • inria-00186090, version 1
  • http://hal.inria.fr/inria-00186090
  • oai:hal.inria.fr:inria-00186090
  • Contributeur : Sylvain Lazard <>
  • Soumis le : Mercredi 7 Novembre 2007, 20:13:57
  • Dernière modification le : Mardi 4 Novembre 2008, 10:53:05