Siu-Wing Cheng
Associate Professor
Department of Computer Science
The Hong Kong University of Science and Technology
WEH 7220
2006-06-02 15:30
Sampling and Meshing a Surface with Guaranteed Topology and Geometry
This paper presents an algorithm for sampling and triangulating a smooth surface $\Sigma\subset \mathbb{R}3$. The only assumption we make is that the input surface representation is amenable to certain types of computations, namely computations of the intersection points of a line and $\Sigma$,computations of the {\em critical points} of some height functions defined on $\Sigma$ and its intersection with a plane, and computations of some {\em silhouette points}. The output triangulation is guaranteed to be homeomorphic to $\Sigma$. The algorithm also ensures bounded aspect ratio, size optimality, and smoothness of the output triangulation.
