Parametrization of aproximate algebraic surfaces by lines

Abstract

In this paper we present an algorithm for parametrizing approximate algebraic surfaces by lines. The algorithm is applicable to ²-irreducible algebraic surfaces of degree d having an ²–singularity of multiplicity d−1, and therefore it generalizes the existing approximate parametrization algorithms. In particular, given a tolerance ² > 0 and an ²-irreducible algebraic surface V of degree d, the algorithm computes a new algebraic surface V , that is rational, as well as a rational parametrization of V . In addition, in the error analysis we show that the output surface V and the input surface V are close. More precisely, we prove that V lies in the offset region of V at distance, at most, O(² 1 2d ).