Matrix-based implicit representations of rational algebraic curves and applications

Authors:
Laurent Busé;Thang Luu Ba
Affiliations:
INRIA, Galaad, 2004 route des Lucioles, 06902 Sophia Antipolis, France;INRIA, Galaad, 2004 route des Lucioles, 06902 Sophia Antipolis, France and Laboratoire J.A. Dieudonné, Université de Nice, Parc Valrose, 06108 Nice Cedex 02, France
Venue:
Computer Aided Geometric Design
Year:
2010

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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 calculation of the intersection between two rational curves.