Homeomorphic approximation of the intersection curve of two rational surfaces

Details Homeomorphic approximation of the intersection curve of two rational surfaces Homeomorphic approximation of the intersection curve of two rational surfaces

2012-03-02

arxiv.org/abs/1203.0442v1

Computer Science

Computational Geometry

18 pages,15 figures

Scientific paper

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.

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