Homeomorphic approximation of the intersection curve of two rational surfaces

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.