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)

1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
2 SPIRAL - Systèmes Polynomiaux, Implantation, Résolution Algébrique

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].

Mots clés: INTERSECTION OF SURFACES; QUADRICS; PENCILS OF QUADRICS; CLASSIFICATION; CURVE PARAMETERIZATION

Domaines: Géométrie algorithmique [cs.CG]; Autre [cs.OH]

Laurent Dupont, Daniel Lazard, Sylvain Lazard, Sylvain Petitjean. Near-Optimal Parameterization of the Intersection of Quadrics: II. A Classification of Pencils. [Research Report] RR-5668, INRIA. 2005. ⟨inria-00071228⟩