  We present an approach of computing the intersection curve $\mathcal{C}$ 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 $\mathcal{C}$ we associate a space topology graph to
$\mathcal{C}$, which is homeomorphic to $\mathcal{C}$ and therefore leads us to
an approximation for $\mathcal{C}$ in a given precision.
