Computing intersection and self-intersection loci of parametrized surfaces using regular systems and Gröbner bases

Authors:
Yanli Huang;Dongming Wang
Affiliations:
LMIB - SKLSDE - School of Mathematics and Systems Science, Beihang University, Beijing 100191, China;Laboratoire dInformatique de Paris 6, Université Pierre et Marie Curie - CNRS, 4 place Jussieu - BP 169, 75252 Paris cedex 05, France
Venue:
Computer Aided Geometric Design
Year:
2011

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Abstract

This paper presents two general and efficient methods for determining intersection and self-intersection loci of rationally parametrized surfaces. One of the methods, based on regular systems, is capable of computing the exact parametric loci of intersection and self-intersection. The other, based on Grobner bases, can compute the minimal varieties passing through the exact parametric loci. The relation between the results computed by the two methods is established and algorithms for computing parametric loci of intersection and self-intersection are described. Experimental results and comparisons with some existing methods show that our algorithms have a good performance.