Homeomorphic approximation of the intersection curve of two rational surfaces

Authors:
Li-Yong Shen;Jin-San Cheng;Xiaohong Jia
Affiliations:
School of Mathematical Sciences, Graduate University of CAS, Beijing, China;Key Laboratory of Mathematics Mechanization, AMSS, CAS, Beijing, China;Key Laboratory of Mathematics Mechanization, AMSS, CAS, Beijing, China
Venue:
Computer Aided Geometric Design
Year:
2012

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Abstract

We present an approach of computing the intersection curve C of two rational parametric surface S"1(u,s) and S"2(v,t), one being projectable and hence can easily be implicitized. Plugging the parametric surface to the implicit surface yields a plane algebraic curve G(v,t)=0. By analyzing the topology graph G of G(v,t)=0 and the singular points on the intersection curve C we associate a space topology graph to C, which is homeomorphic to C and therefore leads us to an approximation for C in a given precision.