Numerical Reparametrization of Rational Parametric Plane Curves

Abstract

In this paper, we present an algorithm for reparametrizing algebraic plane curves from a numerical point of view. That is, we deal with mathematical objects that are assumed to be given approximately. More precisely, given a tolerance $\epsilon >0$ and a rational parametrization $\mathcal{P}$ with perturbed float coefficients of a plane curve $\mathcal{C}$, we present an algorithm that computes a parametrization $\mathcal{Q}$ of a new plane curve $\mathcal{D}$ such that $\mathcal{Q}$ is an {\it $\epsilon$--proper reparametrization} of $\mathcal{D}$. In addition, the error bound is carefully discussed and we present a formula that measures the "closeness" between the input curve $\mathcal{C}$ and the output curve $\mathcal{D}$.

31 pages, 23 figures

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