Computing Self-intersection Loci of Parametrized Surfaces Using Regular Systems and Groebner Bases

The computation of self-intersection loci of parametrized surfaces is needed for constructing trimmed parametrizations and describing the topology of the considered surfaces in real settings. This paper presents two general and efficient methods for determining self-intersection loci of rationally parametrized surfaces. One of the methods, based on regular systems, is capable of computing the exact parametric locus of self-intersection of a given surface and the other, based on Groebner bases, can compute the minimal variety passing through the exact parametric locus. The relation between the results computed by the two methods is established and two algorithms for computing parametric loci of self-intersection are described. Experimental results and comparisons with some existing methods show that our algorithms have a good performance for parametrized surfaces.