Sampling and meshing a surface with guaranteed topology and geometry

This paper presents an algorithm for sampling and triangulating a generic C2 -smooth surface Σ ⊂ R3 that is input with an implicit equation. The output triangulation is guaranteed to be homeomorphic to Σ. We also prove that the triangulation has well-shaped triangles, large dihedral angles, and a small size. 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 Σ, computations of the critical points in a given direction, and computations of certain silhouette points.

• Type: Conference
• Year: 2004
• Where: COMPGEOM
• Authors: Siu-Wing Cheng, Tamal K. Dey, Edgar A. Ramos, Tathagata Ray
• Keywords: C2 -smooth Surface, COMPGEOM 2004, Computations, Large Dihedral Angles