Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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.  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 beten 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.
['Yanli Huang', 'Dongming Wang']
I am writing a research paper on a idea Computing Self-intersection Loci of Parametrized Surfaces Using Regular Systems and Groebner Bases
[{"from": "human", "value": "I am writing a research paper on a idea Computing Self-intersection Loci of Parametrized Surfaces Using Regular Systems and Groebner Bases"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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.  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 beten 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."}]