Parametrization of approximate algebraic surfaces by lines

In this paper we present an algorithm for parametrizing approximate algebraic surfaces by lines. The algorithm is applicable to -irreducible algebraic surfaces of degree d having an -singularity of multiplicity d - 1, and therefore it generalizes the existing approximate parametrization algorithms. In particular, given a tolerance > 0 and an -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(1/(2d)). 2004 Elsevier B.V. All rights reserved.

• Type: Journal
• Year: 2005
• Where: CAGD
• Authors: Sonia Pérez-Díaz, Juana Sendra, J. Rafael Sendra
• Keywords: Algebraic Surface, Algorithm, Approximate Parametrization Algorithms, CAGD 2005