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
A condition guaranteeing the existence of higher-dimensional constrained Delaunay triangulations
Proceedings of the fourteenth annual symposium on Computational geometry
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
A new and simple algorithm for quality 2-dimensional mesh generation
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Dihedral bounds for mesh generation in high dimensions
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Smoothing and cleaning up slivers
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Delaunay refinement mesh generation
Delaunay refinement mesh generation
Sliver-free three dimensional delaunay mesh generation
Sliver-free three dimensional delaunay mesh generation
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A d-dimensional simplicial mesh is a Delaunay triangulation if the circumsphere of each of its simplices does not contain any vertices inside. A mesh is well-shaped if the maximum aspect ratio of all its simplices is bounded from above by a constant. It is a long-term open problem to generate well-shaped d-dimensional Delaunay meshes for a given polyhedral domain. In this paper, we present a refinement-based method that generates well-shaped d-dimensional Delaunay meshes for any PLC domain with no small input angles. Furthermore, we show that the generated well-shaped mesh has O(n) d-simplices, where n is the smallest number of d-simplices of any almost-good meshes for the same domain. A mesh is almost-good if each of its simplices has a bounded circumradius to the shortest edge length ratio.