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inria-00468964, version 2

Matrix-based Implicit Representations of Rational Algebraic Curves and Applications

Laurent Busé () ¹, Thang Luu Ba () ^1, 2

Computer Aided Geometric Design 27, 9 (2010) 681-699

Résumé : Given a parameterization of an algebraic rational curve in a projective space of arbitrary dimension, we introduce and study a new implicit representation of this curve which consists in the locus where the rank of a single matrix drops. Then, we illustrate the advantages of this representation by addressing several important problems of Computer Aided Geometric Design: The point-on-curve and inversion problems, the computation of singularities and the intersection problem between two rational curves.

1 : GALAAD (INRIA Sophia Antipolis)
INRIA – CNRS : UMR6621 – Université de Nice Sophia Antipolis (UNS)
2 : Laboratoire Jean Alexandre Dieudonné (JAD)
CNRS : UMR6621 – Université de Nice Sophia Antipolis (UNS)

inria-00468964, version 2
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Contributeur : Laurent Busé <>
Soumis le : Jeudi 9 Septembre 2010, 08:59:13
Dernière modification le : Lundi 18 Octobre 2010, 09:25:35

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DOI : 10.1016/j.cagd.2010.09.006

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