Sampling and Meshing a Surface with Guaranteed Topology and Geometry

  • Authors:
  • Siu-Wing Cheng;Tamal K. Dey;Edgar A. Ramos;Tathagata Ray

  • Affiliations:
  • -;-;-;-

  • Venue:
  • SIAM Journal on Computing
  • Year:
  • 2007

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Abstract

This paper presents an algorithm for sampling and triangulating a generic $C^2$-smooth surface $\Sigma\subset \mathbb{R}^3$ that is input with an implicit equation. The output triangulation is guaranteed to be homeomorphic to $\Sigma$. 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 $\Sigma$, computations of the critical points in a given direction, and computations of certain silhouette points.