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We present an approach of computing the intersection curve $\mathcal{C}$ oftwo rational parametric surface $\S_1(u,s)$ and $\S_2(v,t)$, one beingprojectable and hence can easily be implicitized. Plugging the parametricsurface to the implicit surface yields a plane algebraic curve $G(v,t)=0$. Byanalyzing the topology graph $\G$ of $G(v,t)=0$ and the singular points on theintersection curve $\mathcal{C}$ we associate a space topology graph to$\mathcal{C}$, which is homeomorphic to $\mathcal{C}$ and therefore leads us toan approximation for $\mathcal{C}$ in a given precision.

Homeomorphic approximation of the intersection curve of two rational surfaces