Numerical proper reparametrization of parametric plane curves

•We introduce the problem of numerical improper parametrization of plane curves.•The approximate improper index is firstly defined in this paper.•A numerical algorithm is designed to find the approximate proper reparametrization.•The relationship between the numerical curve and its reparametrization is well studied.

We present an algorithm for reparametrizing algebraic plane curves from a numerical point of view. More precisely, given a tolerance ϵ>0ϵ>0 and a rational parametrization PP of a plane curve CC with perturbed float coefficients, we present an algorithm that computes a parametrization QQ of a new plane curve DD such that QQ is an ϵϵ–proper reparametrization   of DD. In addition, the error bound is carefully discussed and we present a formula that measures the “closeness” between the input curve CC and the output curve DD.