A. Bowyer. Computing Dirichlet tessellations. The Computer Journal, 24:162-166, 1981.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....19] However, these algorithms have no guarantee of success. For example, the edge flip algorithm for constructing the Delaunay triangulation is easily modified to take anisotropy into account. Alternatively, George and Borouchaki [7] suggest an anisotropic version of the Bowyer Watson algorithm [6, 20] for inserting a site into a Delaunay triangulation. But is the final triangulation produced by either of these algorithms unique What are its properties Will the flip algorithm terminate or loop forever Here we describe an approach that puts anisotropic meshing on firm theoretical ground. In ....

Adrian Bowyer. Computing Dirichlet Tessellations. Computer Journal 24(2):162--166, 1981.

....by the insertion of additional vertices that split the segments into smaller segments, as described in Section 5. 4 Testing Edge Protection Testing whether a PLC X is edge protected is straightforward. Form the Delaunay tetrahedralization T of the vertices of X using any standard algorithm [1, 3, 28]. T covers the entire convex hull of X. If a segments is missing from T , thens is not strongly Delaunay. Ifs is an edge of T , thens is Delaunay but might not be strongly Delaunay. The recommended solution is to use the symbolic perturbation technique discussed in Section 9 while ....

....other segment at an angle of less than 90 # , let v i be the vertex where they meet. The algorithm inserts a new vertex at the points S i , as illustrated. Insert all the new vertices generated this way into the Delaunay tetrahedralization constructed in Section 4 (using the Bowyer Watson [1, 28] algorithm, so the mesh remains Delaunay) The protecting spheres cut off the ends of some segments. Each of these ends is guaranteed to be strongly Delaunay because no vertex lies on or inside its diametral sphere (the smallest sphere that contains the end) except its endpoints. Therefore, ....

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Adrian Bowyer. Computing Dirichlet Tessellations. Computer Journal 24(2):162--166, 1981.

....by the insertion of additional vertices that split the segments into smaller segments, as described in Section 5. 4 Testing Edge Protection Testing whether a PLC X is edge protected is straightforward. Form the Delaunay tetrahedralization T of the vertices of X using any standard algorithm [1, 3, 28]. T covers the entire convex hull of X. If a segment s is missing from T, then s is not strongly Delaunay. If s is an edge of T, then s is Delaunay but might not be strongly Delaunay. The recommended solution is to use the symbolic perturbation technique discussed in Section 9 while constructing ....

....meets some other segment at an angle of less than 90 , let vi be the vertex where they meet. The algorithm inserts a new vertex at the point s A Si, as illustrated. Insert all the new vertices generated this way into the Delaunay tetrahedralization constructed in Section 4 (using the Bowyer Watson [1, 28] algorithm, so the mesh remains Delaunay) The protecting spheres cut off the ends of some segments. Each of these ends is guaranteed to be strongly Delaunay because no vertex lies on or inside its diametral sphere (the smallest sphere that contains the end) except its endpoints. Therefore, ....

[Article contains additional citation context not shown here]

Adrian Bowyer. Computing Dirichlet Tessellations. Computer Journal 24(2): 16166, 1981.

....is wise to make B as small as possible. The central operation of Chew s and Ruppert s Delaunay refinement algorithms is the insertion of a vertex at the circumcenter of a triangle of poor quality. The Delaunay property is maintained, using Lawson s algorithm [19] or the Bowyer Watson algorithm [5, 32] for the incremental update of Delaunay triangulations. The poor quality triangle cannot survive, because its circumcircle is no longer empty. For brevity, I refer to the act of inserting a vertex at a triangle s circumcenter as splitting a triangle. The idea dates back at least to the engineering ....

Adrian Bowyer. Computing Dirichlet Tessellations. Computer Journal 24(2):162--166, 1981.

....of science. For relevant surveys and bibliographies consult [1, 16, 54] Various approaches for their con struction are described in the literature. Naturally, it was the planar case, which was solved first, but extensions to 3 and higher dimensions followed. Incremental methods (for example [4, 39]) compete with divide and conquer algorithms (for example [8,42] Newer research studies randomization [41] One approach uses a lifting map (see below) to transform the triangulation problem in R to the problem of constructing the convex hull in R . This idea goes back to [7] details on the ....

....a with p; E a for which search : p; a) is called. Since T is a Delaunay triangulation, the volume of A=0 a is strictly decreasing, for increasing . Thus, the function always terminates successfully. This simple idea of walking through the triangulation is not new, it was already mentioned in [4], with a reference to [39] where it was used for computing Delaunay triangulations in the plane. It is difficult to give a good estimate for the time complexity of search. In the worst case, it is quadratic in z, the number of points in 7 . A more realistic estimate is that the number of steps ....

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A Bowyer. Computing Dirichlet tessellations. The Computer Journal, 24(2):162 166, 1981.

....cliques (f) and triple site (g) and quadruple site (h) cliques. As the order of the neighborhood system increases, the number of cliques grow rapidly and so the involved computational expenses. # Algorithms for constructing a Delaunay triangulation in # # 2 dimensional space can be found in [18,133]. 11 Cliques for irregular sites do not have xed shapes as those for a regular lattice. Therefore, their types are essentially depicted bythenumber of involved sites. Consider the four sites # , #, # and # within the circle in Fig.3(a) in which # and # are supposed to be neighbors to each other ....

A. Bowyer. \Computing Dirichlet tessellations". Computer Journal, 24:162{ 166, 1981.

....coding algorithm simultaneously for each object region in the scene. This puzzle tree organization of regions can be more advantageous in reducing shape redundancy by coding the common boundaries only once. A second avenue of improvement could be the use of so called Voronoi or Dirichlet diagrams [1, 2, 19], which can eciently be utilized in the object tracking problem. A Voronoi diagram is a construct of image points each of which de nes a convex polygonal territory which is the region of the image plane nearer to it than to any other data point. Such a representation corresponds to a diagram of ....

A. Bowyer, \Computing Dirichlet Tessellations", The Computer Journal, Vol. 24, No. 2, 1981, pp. 162-166.

....element creation, where new triangles are built by connecting the new point with old points such that the resulting triangulation satis es certain geometric properties. This type of incremental construction of a Delaunay triangulation is sometimes referred to as the Bowyer Watson (BW) algorithm [43, 44]. In our parallel implementation of the BW algorithm, an initial Delaunay tetrahedralization, T 0 , of a set of points is overdecomposed into N P subdomains (or regions) where P is the number of processors. Regions are assigned to processors in a way that maximizes data locality, and each ....

Bowyer A, Computing Dirichlet Tessellations, The Computer Journal, 1981; 24(2):162-166.

.... John Rice suggested this taxonomy in late 80 s 3 For each submesh M i , rst, we index all the nodal degrees of freedom (dof) that correspond to the interior mesh points or edges of M, then we index all the dof on inner interfaces, and at the end we index all the dof on the outer interfaces [2]. Inner interface nodes for the domains D1 and D2 Outer interface nodes for the domains D1 and D2 D1 D2 Interior nodes for the domains D1 and D2. D3 n node A (n) x = n 1) x DOMAIN # DOMAIN # DOMAIN DOMAIN #4 INTERFACES LINK LINK LINK L N K I L N K I N K A A 2 ....

....incremental algorithms is due to: 1) di erent spatial point distribution methods for creating the points and (2) di erent local re connection techniques for creating the triangles or tetrahedra. The most popular local re connection methods are the ip edge face methods [20] and the BW kernel [2, 29]. The ip edge face methods are easier to implement on single CPU computers using simple and ecient data structures. However, the disadvantage of the ip methods is that the code complexity of the parallelization is increasing and performance is decreasing. In [22] we show that setbacks due to ....

A. Bowyer. Computing Dirichlet tessellations. The Computer Journal, 24(2):162-166, 1981.

....elements that violate the Delaunay property [16] Finally the fourth step, element creation builds new triangles by connecting the new point with old points such that the resulting triangulation satis es certain geometric properties. This kernel often is called the Bowyer Watson (BW) kernel [3, 19]. The parallel implementation of the BW algorithm, for 3D domains, begins with an initial Delaunay tetrahedralization of a set of points which is over decomposed into N P subdomains (or regions) where P is the number of processors. Regions are assigned to processors in a way that maximizes ....

A. Bowyer. Computing Dirichlet Tessellations. 1981.

....cliques (f) and triple site (g) and quadruple site (h) cliques. As the order of the neighborhood system increases, the number of cliques grow rapidly and so the involved computational expenses. 3 Algorithms for constructing a Delaunay triangulation in k 2 dimensional space can be found in [18,133]. 11 Cliques for irregular sites do not have xed shapes as those for a regular lattice. Therefore, their types are essentially depicted by the number of involved sites. Consider the four sites f , i, m and n within the circle in Fig.3(a) in which m and n are supposed to be neighbors to each ....

A. Bowyer. \Computing Dirichlet tessellations". Computer Journal, 24:162{ 166, 1981.

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A. Bowyer. Computing Dirichlet tessellations. The Computer Journal, 24:162-166, 1981.

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A. Bowyer. Computing Dirichlet tessellations. The Computer Journal, 24:162--166, 1981.

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A. Bowyer. Computing Dirichlet tessellations. The Computer Journal, 24(2):162-166, 1981.

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A. Bowyer. Computing Dirichlet tessellation. Computer Journal, 24:162--166, 1981.

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Adrian Bowyer. Computing Dirichlet Tessellations. Computer Journal 24(2):162--166, 1981.

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A. Bowyer. Computing dirichlet tessellations. The computer J., 24(2):162--166, 1981.

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Bowyer A. Computing Dirichlet tessellations. The Computer Journal 1981; 24:162--166.

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Bowyer A. Computing dirichlet tessellations. The Computer Journal 1981; 24(2):162--166.

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Bowyer, A. (1981) Computing Dirichlet tessellations. Comp. J., 24, 162--166.

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A. Bowyer. Computing Dirichlet tessellations. The Computer Journal, 24:162-166, 1981.

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Bowyer A. Computing Dirichlet tessellations. The Computer Journal 1981; 24:162 --166.

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A. Bowyer. Computing Dirichlet tessellations. The Computer Journal, 24(2):162--166, 1981.

No context found.

A. Bowyer. Computing Dirichlet tessellations. The Computer Journal, 24:162--166, 1981.

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Bowyer, A., "Computing Dirichlet Tessellations", The Computer Journal, Vol. 24, No. 2, 1981, pp. 162---166.

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