Journal
JOURNAL OF THE ACM
Volume 47, Issue 5, Pages 883-904Publisher
ASSOC COMPUTING MACHINERY
DOI: 10.1145/355483.355487
Keywords
algorithms; algorithms; computational geometry; mesh generation; mesh quality; slivers; tetrahedral meshes; (weighted) Delaunay triangulations
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A sliver is a tetrahedron whose four vertices lie close to a plane and whose orthogonal projection to that plane is a convex quadrilateral with no short edge. Slivers 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 triangulation contains no slivers. We also give an algorithm to compute such a weight assignment.
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