On the sizes of Delaunay meshes

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On the sizes of Delaunay meshes
Let P be a polyhedral domain occupying a convex volume. We prove that the size of a graded mesh of P with bounded vertex degree is within a factor O(H3 P ) of the size of any Delaunay mesh of P with bounded radius-edge ratio. The term HP depends on the geometry of P and it is likely a small constant when the boundaries of P are fine triangular meshes. There are several consequences. First, among all Delaunay meshes with bounded radius-edge ratio, those returned by Delaunay refinement algorithms have asymptotically optimal sizes. This is another advantage of meshing with Delaunay refinement algorithms. Second, if no input angle is acute, the minimum Delaunay mesh with bounded radius-edge ratio is not much smaller than any minimum mesh with aspect ratio bounded by a particular constant. Key words: mesh generation, Delaunay triangulation, radius-edge ratio, aspect ratio, gradedness
Siu-Wing Cheng
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Authors Siu-Wing Cheng
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