Matrix-based Implicit Representations of Rational Algebraic Curves and Applications

Laurent Busé 1 Thang Luu Ba 1, 2
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : 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.
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Laurent Busé, Thang Luu Ba. Matrix-based Implicit Representations of Rational Algebraic Curves and Applications. Computer Aided Geometric Design, Elsevier, 2010, 27 (9), pp.681-699. 〈10.1016/j.cagd.2010.09.006〉. 〈inria-00468964v2〉

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