Silver exudation

  • Authors:
  • Siu-Wing Cheng;Tamal K. Dey;Herbert Edelsbrunner;Michael A. Facello;Shang-Hua Teng

  • Affiliations:
  • Hong Kong Univ. of Science and Technology, Hong Kong, China;Ohio State Univ., Columbus;Duke Univ., Durham, NC;Raindrop Geomagic, Research Triangle Park, NC;Univ. of Illinois at Urbana-Champaign, Urbanna

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 2000

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Abstract

A silver is a tetrahedon whose four vertices lie close to a plane and whose orthogonal projection to that plane is a convex quadrilateral with no short edge. Silvers are notoriously common in 3-dimensional Delaunay triangulations even for well-spaced point sets. We show that, if the Delaunay triangulation has the ratio property introduced in Miller et al. [1995], then there is an assignment of weights so the weighted Delaunay traingulation contains no silvers. We also give an algorithm to compute such a weight assignment.