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Generating Well-Shaped Delaunay Meshes in 3D (2001)
| Citations: | 31 - 0 self |
BibTeX
@MISC{Li01generatingwell-shaped,
author = {Xiang-Yang Li and Shang-Hua Teng},
title = {Generating Well-Shaped Delaunay Meshes in 3D},
year = {2001}
}
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Abstract
A triangular mesh in 3D is a decomposition of a given geometric domain into tetrahedra. The mesh is wellshaped if the aspect ratio of every of its tetrahedra is bounded from aboveby a constant. It is Delaunayifthe interior of the circum-sphere of each of its tetrahedra does not contain any other mesh vertices. Generating a well-shaped Delaunay mesh for any 3D domain has been a long term outstanding problem. In this paper, wepresent an efficient 3D Delaunay meshing algorithm that mathematically guarantees the well-shape quality of the mesh, if the domain does not have acute angles. The main ingredient of our algorithm is a novel refinement technique which systematically forbids the formation of slivers, a family of bad elements that none of the previous known algorithms can cleanly remove, especially near the domain boundary --- needless to say, that our algorithm ensure that there is no sliver near the boundary of the domain.
