Intersection and self-intersection of surfaces by means of Bezoutian matrices

Laurent Busé (1) , Mohamed Elkadi (1) , André Galligo (1)

1 GALAAD - Geometry, algebra, algorithms

The computation of intersection and self-intersection loci of parameterized surfaces is an important task in Computer Aided Geometric Design. Computer algebra tools need to be developed further for computing their implicit equations. We address these problems via four resultants with separated variables. Two of them are specializations of more general ones and the others are determinantal. We give a rigorous study in these cases and provide new and useful formulas via adapted computations of Bezoutians.

Domaines: Calcul formel [cs.SC]; Géométrie algébrique [math.AG]

Laurent Busé, Mohamed Elkadi, André Galligo. Intersection and self-intersection of surfaces by means of Bezoutian matrices. Computer Aided Geometric Design, 2008, 25 (2), pp.53-68. ⟨10.1016/j.cagd.2007.07.001⟩. ⟨inria-00096807v2⟩