Curve/surface intersection problem by means of matrix representations

Thang Luu Ba (1, 2) , Laurent Busé (2) , Bernard Mourrain (2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 GALAAD - Geometry, algebra, algorithms

In this paper, we introduce matrix representations of algebraic curves and surfaces for Computer Aided Geometric Design (CAGD). The idea of using matrix representations in CAGD is quite old. The novelty of our contribution is to enable non square matrices, extension which is motivated by recent research in this topic. We show how to manipulate these representations by proposing a dedicated algorithm to address the curve/surface intersection problem by means of numerical linear algebra techniques.

Domains: Symbolic Computation [cs.SC]

Thang Luu Ba, Laurent Busé, Bernard Mourrain. Curve/surface intersection problem by means of matrix representations. SNC, Aug 2009, Kyoto, Japan. pp.71-78, ⟨10.1145/1577190.1577205⟩. ⟨inria-00418403⟩