Homeomorphic approximation of the intersection curve of two rational surfaces

We present an approach of computing the intersection curve CC of two rational parametric surface S1(u,s)S1(u,s) and S2(v,t)S2(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)=0G(v,t)=0. By analyzing the topology graph GG of G(v,t)=0G(v,t)=0 and the singular points on the intersection curve CC we associate a space topology graph to CC, which is homeomorphic to CC and therefore leads us to an approximation for CC in a given precision.

► The problem to approximate intersection two rational surfaces is well known but not well solved, we enhance some techniques of a typical process.
► A simpler implicitization method is applied for projectable surfaces and an improved method is introduced for planar topology determination.
► The planar topology is refined such that the topology and more geometric features of the intersection curve are preserved.
► The numerical approximation is designed and proved to be homeomorphic to the intersection curve.