Abstract
Let S be a rational projective surface given by means of a projective rational parametrization whose base locus satisfies a mild assumption. In this paper we present an algorithm that provides three rational maps f,g,h:A2⇢S⊂Pn such that the union of the three images covers S. As a consequence, we present a second algorithm that generates two rational maps f,g˜:A2⇢S, such that the union of its images covers the affine surface S∩An. In the affine case, the number of rational maps involved in the cover is in general optimal.
Funder
Junta de Extremadura
Ministerio de Ciencia, Innovación y Universidades
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference31 articles.
1. Handbook of Computer Aided Geometric Design,2002
2. Fundamentals of Computer Aided Geometric Design;Hoschek,1993
3. Computer Graphics and Geometric Modelling;Agoston,2005
4. Applied Geometry for Computer Graphics and CAD;Marsh,2005
5. Missing sets in rational parametrizations of surfaces of revolution
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. A note about rational surfaces as unions of affine planes;Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas;2023-02-18
2. On the existence of finite surjective parametrizations of affine surfaces;Journal of Algebra;2022-07