A Delaunay refinement algorithm for quality 2-dimensional mesh generation
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
A Delaunay based numerical method for three dimensions: generation, formulation, and partition
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Guaranteed-quality Delaunay meshing in 3D (short version)
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Tetrahedral mesh generation by Delaunay refinement
Proceedings of the fourteenth annual symposium on Computational geometry
On the Radius-Edge Condition in the Control Volume Method
SIAM Journal on Numerical Analysis
Quality Mesh Generation in Higher Dimensions
SIAM Journal on Computing
Journal of the ACM (JACM)
Generating well-shaped Delaunay meshed in 3D
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Geometry and topology for mesh generation
Geometry and topology for mesh generation
Graded conforming Delaunay tetrahedralization with bounded radius-edge ratio
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Quality Meshing with Weighted Delaunay Refinement
SIAM Journal on Computing
Quality meshing for polyhedra with small angles
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
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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(HP3) 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.