Xiang-Yang Li and Shang-Hua Teng. Generating Well-Shaped Delaunay Meshes in 3D. Proceedings of the Twelfth Annual Symposium on Discrete Algorithms (Washington, D.C.), pages 28--37. Association for Computing Machinery, January 2001.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....uncluttered nor easilycovered polyhedra are necessarily local. We discuss the connection between locality and clutter in more detail in Section 5. We can also compare 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 shortest edge of that simplex. Well shaped triangulations have bounded local scale factor #, but they are not necessarily local, since the global scale factor # could be ....

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.

....tetrahedra in the mesh. An important challenge in mesh generation is to construct a mesh with good quality. Our contribution is a simple Delaunay refinement algorithm that produces tetrahedra with provably good edge lengths and radius edge ratio. Our algorithm is distinguished from previous ones [2, 5, 8, 11, 13, 14] by its ability to handle input angles less than =2 and its theoretical guarantees. Our input domain is a bounded volume in 3D whose boundary is specified by a piecewise linear complex P . The elements of P are vertices, edges and facets that intersect properly. That is, the intersection of two ....

....ratio is bounded, almost all tetrahedra have bounded aspect ratio except for a class known as slivers. Nevertheless, bounded radius edge ratio works well in some applications [9] Recently, methods have been discovered to eliminate slivers when every input angle is at least =2. Li and Teng [8] improved Delaunay refinement with a random point placement strategy in line of Chew [4] Cheng et al. 3] introduced sliver exudation to eliminate slivers from a Delaunay mesh of a periodic point set with bounded radius edge ratio. Cheng and Dey [2] introduced weighted Delaunay refinement which ....

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X.-Y. Li and S.-H. Teng. Generating well-shaped Delaunay meshes in 3D. Proc. 12th ACM-SIAM Sympos. Discrete Alg., 2001, 28--37.

....inability to remove slivers, which are rather at tetrahedra with relatively small circumspheres. The persistent presence of slivers in large Delaunay triangulations has been observed experimentally at least as early as 1985 [1] but e ective methods dealing with them have been found only recently [2, 3, 6, 9]. This paper implements the sliver exudation algorithm of Cheng et al. and studies its e ectiveness in practice. The question in focus is how large a minimum dihedral angle this method can achieve. The positive lower bound proved in [2] is conservative and exceedingly small, and this paper con ....

....makes the sliver exudation algorithm a viable method in practice. Our experimental results are, however, inconclusive for tetrahedra near the mesh boundary. The reason is a fundamental weakness of the sliver exudation method. Boundary treatment methods such as the one described by Li and Teng [9] will have to be added in the fu ture to get software that guarantees good mesh quality throughout the domain. Outline. Section 2 reviews background material on Delaunay triangulations and mesh quality. Section 3 describes weighted Delaunay triangulations and the sliver exudation algorithm. ....

X.-Y. Li and S.-H. Teng. Generating well-shaped Delaunay meshes in 3D. In \Proc. 12th Ann. ACM-SIAM Sympos. Discrete Alg.", 2001, 28-37.

....could not handle boundaries and was applied to periodic point sets. In a recent work Edelsbrunner and Guoy [11] experimented with the sliver exudation method which reveals that the technique is very effective to eliminate slivers though boundary handling remains a challenge. Recently, Li and Teng [12] showed for the first time that it is possible to construct a sliver free Delaunay mesh, in the presence of boundaries, with a randomized point placement strategy in line of Chew [6] The analysis of this algorithm is a nice example of the confluence of the results developed over the years by Chew ....

....We show that this technique achieves graded meshing and also close to optimal size. Our work can be viewed as another milestone to the line of research initiated by Chew and Ruppert [4, 16] advanced by Dey et al. 8] Shewchuk [17] Cheng et al. 7] Edelsbrunner et al. 10] and Li and Teng [12]. 2 Definitions. We need the following definitions most of which have been introduced in earlier works. Piecewise linear complex. The input we consider is a piecewise linear complex (PLC) with no input angle less than as in previous works [17, 12] A collection of vertices, edges ....

[Article contains additional citation context not shown here]

X.-Y. Li and S.-H. Teng. Generating well-shaped Delaunay meshes in 3D. Proc. 12th. Annu. ACM-SIAM Sympos. Discrete. Alg., (2001), 28--37.

....could not handle boundaries and was applied to periodic point sets. In a recent work Edelsbrunner and Guoy [11] experimented with the sliver exudation method which reveals that the technique is very effective to eliminate slivers though boundary handling remains a challenge. Recently, Li and Teng [12] showed for the first time that it is possible to construct a sliver free Delaunay mesh, in the presence of boundaries, with a randomized point placement strategy in line of Chew [6] The analysis of this algorithm is a nice example of the confluence of the results developed over the years by Chew ....

....We show that this technique achieves graded meshing and also close to optimal size. Our work can be viewed as another milestone to the line of research initiated by Chew and Ruppert [4, 16] advanced by Dey et al. 8] Shewchuk [17] Cheng et al. 7] Edelsbrunner et al. 10] and Li and Teng [12]. 2 Definitions. We need the following definitions most of which have been introduced in earlier works. Piecewise linear complex. The input we consider is a piecewise linear complex (PLC) with no input angle less than =2 as in previous works [17, 12] A collection P of vertices, edges and ....

[Article contains additional citation context not shown here]

X.-Y. Li and S.-H. Teng. Generating well-shaped Delaunay meshes in 3D. Proc. 12th. Annu. ACM-SIAM Sympos. Discrete. Alg., (2001), 28--37.

....(n ) whose n vertices have spread . 1 Introduction Delaunay triangulations and Voronoi diagrams are one of the most thoroughly studies objects in computational geometry, with applications to nearest neighbor searching [3, 21, 25, 43] clustering [1, 46, 48, 54] niteelement mesh generation [20, 32, 49, 56], deformable surface modeling [19] and surface reconstruction [4, 5, 6, 7, 12, 45] Many algorithms in these application domains begin by constructing the Delaunay triangulation or Voronoi diagram of a set of points in IR 3 . Since three dimensional Delaunay triangulations can have complexity ....

....investigation of practical geometric constraints that imply low complexity Delaunay triangulations. Previous works in this direction have studied random point sets under various distributions [28, 27, 35, 38] well spaced point sets, which are lowdiscrepancy samples of Lipschitz density functions [20, 49, 51, 52]; and surface samples with various density Portions of this work were done while the author was visiting The Ohio State University. This research was partially supported by a Sloan Fellowship and by NSF CAREER grant CCR 0093348. See http: www.cs.uiuc.edu je e pubs screw.html for the most ....

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.

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Xiang-Yang Li and Shang-Hua Teng. Generating Well-Shaped Delaunay Meshes in 3D. Proceedings of the Twelfth Annual Symposium on Discrete Algorithms (Washington, D.C.), pages 28--37. Association for Computing Machinery, January 2001.

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X.-Y. Li and S.-H. Teng. Generating well-shaped Delaunay meshes in 3D. Proc. 12th. Annu. ACMSIAM Sympos. Discrete. Alg., (2001), 28--37.

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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.

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X.-Y. Li and S.-H. Teng. Generating well-shaped Delaunay meshes in 3D. Proc. 12th ACM-SIAM Sympos. Discrete Alg., 2001, 28--37.

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