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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 (1965 - 2019), 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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Submitted on : Thursday, September 9, 2010 - 8:59:13 AM
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Laurent Busé, Thang Luu Ba. Matrix-based Implicit Representations of Rational Algebraic Curves and Applications. Computer Aided Geometric Design, 2010, 27 (9), pp.681-699. ⟨10.1016/j.cagd.2010.09.006⟩. ⟨inria-00468964v2⟩



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