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"Generating Sliver-Free Well-Shaped Three Dimensional Delaunay Meshes"

Shang-Hua Teng
Computer Science
Boston University
October 7, 2005
 
A mesh is cell-complex that decomposes a spatial domain for numerical simulation. Delaunay triangulations have many desirable properties for mesh generation. While there are several efficient methods for well-shaped 2D mesh generation, the generation of Delaunay meshes of well-shaped tetrahedra in 3D is considerably more difficult and has been an outstanding open problem for many years.
 
Most notably, slivers are notoriously common in three dimensional Delaunay meshes, where a sliver is a tetrahedron that has no short edge and whose four vertices lie closely to a great circle of its circum-sphere. In this talk, I will survey the algorithmic and geometric techniques using weighted Delaunay triangulations and perturbations, that are recently developed for sliver removal. In particular, I will present the first Delaunay refinement algorithm, developed by Li and Teng, that always generates sliver free well-shaped unstructured meshes in three dimensions. The main ingredient of this algorithm is a novel refinement technique, which systematically forbids the formation of slivers.
 
This talk contains collaborative works with Xiang-Yang Li, Siu-Wing Cheng, Tamal Dey, Herbert Edelsbrun
 

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