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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

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.

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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From: Laurent Busé <>
Submitted on: Thursday, 9 September 2010 08:59:13
Updated on: Monday, 18 October 2010 09:25:35

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DOI: 10.1016/j.cagd.2010.09.006

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