Matrix-based Implicit Representations of Rational Algebraic Curves and Applications
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.
Domains
Symbolic Computation [cs.SC]
Origin : Files produced by the author(s)
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