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Generating Well-Shaped Delaunay Meshes in 3D (2001)  (Make Corrections)  (10 citations)
Xiang-Yang Li, Shang-Hua Teng



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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... (Update)

Context of citations to this paper:   More

...our model to quality metrics used for simplicial finite element mesh generation. For example, Miller, Talmor, Teng, and others [21, 23, 33, 38, 40] define a triangulation to be well shaped if the circumradius of each simplex is only a constant factor longer than the...

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General-Dimensional Constrained Delaunay and Constrained Regular .. - Shewchuk (2004)   (Correct)
Quality Meshing with Weighted Delaunay Refinement - Siu-Wing Cheng Tamal (2002)   (Correct)
Local Polyhedra and Geometric Graphs - Erickson (2003)   (Correct)

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BibTeX entry:   (Update)

X.-Y. Li and S.-H. Teng. Generating well-shaped Delaunay meshes in 3D. Proc. 12th Annu. ACM-SIAM Sympos. Discrete Algorithms, 28-37, 2001. http://citeseer.ist.psu.edu/li01generating.html   More

@inproceedings{ ligenerating,
    author = "{Xiang-Yang} Li and {Shang-Hua} Teng",
    title = "Generating {Well-Shaped} Delaunay Meshes in {3D}",
    pages = "28--37",
    url = "citeseer.ist.psu.edu/li01generating.html" }
Citations (may not include all citations):
86   Constrained Delaunay triangulations (context) - Chew - 1989
64   Qualitymesh generation in three dimensions - Mitchell, Vavasis - 1992
58   Incremental topological flipping works for regular triangula.. (context) - Edelsbrunner, Shah - 1996
42   A delaunay based numerical method for three dimensions: gene.. - Miller, Talmor et al. - 1995
38   A new and simple algorithm for quality 2-dimensional mesh ge.. (context) - Ruppert - 1992
26   Tetrahedral mesh generation by delaunay refinement - Shewchuk - 1998
25   Control volume meshes using sphere packing: generation - Miller, Talmor et al. - 1996
22   An approach to automatic three-dimensional finite element me.. (context) - Cavendish, Field et al. - 1985
22   Well-Spaced Points for Numerical Methods (context) - Talmor - 1997
15   Guaranteed-quality delaunay meshing in 3d (context) - Chew - 1997
13   Biting: advancing front meets sphere packing - Li, Teng et al. - 2000
7   Smoothing and cleaning up slivers - Edelsbrunner, Li et al. - 2000
5   Sliver-free Three Dimensional Delaunay Mesh Generation (context) - Li - 2000
5   Silver exudation (context) - Cheng, Dey et al. - 1999
2   AnAnalysis of the Finite Element Method (context) - Strang, Fix - 1973
2   Functional delaunay refinement - Li - 2000



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