Curve/surface intersection problem by means of matrix representations

Thang Luu Ba 1, 2 Laurent Busé 2 Bernard Mourrain 2
2 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : 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.
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Conference papers
H. Kai and H. Sekigawa. SNC, Aug 2009, Kyoto, Japan. ACM Press, pp.71-78, 2009, Proceedings of the 2009 Conference on Symbolic Numeric Computation. 〈10.1145/1577190.1577205〉
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Thang Luu Ba, Laurent Busé, Bernard Mourrain. Curve/surface intersection problem by means of matrix representations. H. Kai and H. Sekigawa. SNC, Aug 2009, Kyoto, Japan. ACM Press, pp.71-78, 2009, Proceedings of the 2009 Conference on Symbolic Numeric Computation. 〈10.1145/1577190.1577205〉. 〈inria-00418403〉

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