Parametrization of approximate algebraic surfaces by lines

摘要

In this paper we present an algorithm for parametrizing approximate algebraic surfaces by lines. The algorithm is applicable to epsilon-irreducible algebraic surfaces of degree d having an epsilon-singularity of multiplicity d - 1, and therefore it generalizes the existing approximate parametrization algorithms. In particular, given a tolerance epsilon > 0 and an epsilon-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) over bar. In addition, in the error analysis we show that the output surface (V) over bar and the input surface V are close. More precisely, we prove that (V) over bar lies in the offset region of V at distance, at most, O(epsilon(1/(2d))). (C) 2004 Elsevier B.V. All rights reserved.