D.T. Lee and B.J. Schachter. Two algorithms for constructing a Delaunay triangulation. Int. J. Comput. Inform. Sci., Vol. 9, pp. 219-242, 1980.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....found the median line between sub domains by convex hull algorithm, then triangulated sub domain by the divide and conquer algorithm. Its parallel efficiency of 128k points is 48 90 on IBM SP2 with 8 nodes. Details of the divide and conquer Delaunay algorithm are reported in reference [3, 2]. This algorithm divides the original point set into small data sets of two or three points, then recursively merge the triangulation of small data sets to form the whole Delaunay triangulation. The main complexity of this algorithm lies in the merge phase. Since the boundary of Delaunay ....

D. T. LEE AND B. J. SCHACHTER, Two algorithms for constructing the Delaunay Triangulation, International Journal of Computer and Information Sciences, 9(1980), pp. 219--242.

....[4] because it has been shown to be the fastest algorithm and it is very robust [12, 13] Dwyer s algorithm is described as follows. First, it sorts points into m Theta m buckets (m = p n= log n, n the number of points) Then it triangulates each bucket with Lee s divide conquer algorithm [9]. Finally, it merges triangulations from all buckets. The major parts of Lee s divide conquer algorithm are the convex hull generating phase and the merging phase. In the convex hull phase, the first active edge are formed by the nearest points on the boundaries of two triangulations, then the ....

....edge to the top. The new Delaunay edge is constructed if the neighboring edge passes the in circle test, that is, if the far point of the neighbor is not in the circumcircle of the new and base edge. For the edge that does not pass the test, it is deleted. Interested readers are referred to [9] for more details of this algorithm. To construct a Delaunay triangulation of a point set, we first bisect the point set recursively into partitions each of two or three points. We then recursively merge the triangulated partitions until we have a triangulation of the entire point set. ....

D. T. Lee and B. J. Schachter, Two algorithms for constructing the Delaunay triangulation, Int. J. Comput. Inf. Sci., 9 (1980), pp. 219--242.

....The act of inserting a vertex to improve poor quality triangles in one part of a mesh will not unnecessarily perturb a distant part of the mesh that has no bad triangles. Furthermore, Delaunay triangulations have been extensively studied, and good algorithms for their construction are available [21, 17, 15, 7]. The greatest advantage of Delaunay triangulations is less obvious. The central question of any Delaunay refinement algorithm is, Where should the next vertex be inserted As Section 2 will demonstrate, a reasonable answer is, As far from other vertices as possible. If a new vertex is ....

Der-Tsai Lee and Bruce J. Schachter. Two Algorithms for Constructing a Delaunay Triangulation. International Journal of Computer and Information Sciences 9(3):219--242, 1980.

....du site supprimer. L algorithme a t effectivement programm et des rsultats exprimentaux sont fournis. 1 Introduction The Delaunay triangulation and its dual, the Vorono diagram, are subjects of major interest in Computational Geometry. A lot of algorithms compute it in optimal fl(tzlogtz) time [23,14,13,10,20]. But these algorithms are rather complicated and difficult to implement effectively, so the sub optimal algorithm [11] is often preferred. Furthermore, this algorithm is on line and does not impose to compute again the whole triangulation at each insertion. In the last few years some simpler ....

D.T. Lee and B.J. Schachter. Two algorithms for constructing a Delaunay triangulation. International Journal of Computer' and Lnformation Sciences, 9(3), 1980.

.... the points in the E a space and then compute the convex hull of the transformed points; the DT is obtained by simply projecting the convex hull back in E a [2] Divide g: Conquer (D C) algorithms have been proven to be optimal in the E 2 space in both mean and worst case time complexity [17]. These methods are based on recursive partitioning and local triangulation of the pointset, and then on a merging phase where the resulting triangulations are joined. D C algorithms presented in the literature manage E 2 pointsets only. This, because specification of the merge phase is simple in ....

....and the overall overhead of the solution. 3 The DeWall triangulation algorithm An algorithm for DT of a pointset P in E d is presented in this section. The algorithm, described in detail in [5] is based on the divide conquer paradigm applied differently from the usual D C Delaunay algorithms [17] [9] In our problem the pointset P can easily be split, using a cutting plane a, in two subsets P and P of comparable cardinality. In DXcC triangulation algorithms the problem is the logical complexity of the merge phase, i.e. the union of the two triangulations S and S built on P and P . It ....

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D.T Lee and B.J. Schachter. Two algorithms for constructing a Delaunay triangulation. Int. d. of Computer and Information Science, 9(3):219 242, 1980.

....applications of computer graphics (e.g. in GIS systems and architecturalCAD) it is necessary to transform a closed and possibly unconnected polyline into the plane polygon it is boundary of. This transformation is often accomplished by computing a (possiblyconstrained) Delaunay s triangulation [2, 4, 3]. Boolean operations over BSP trees strongly resemble to CSG trees, so that the Naylor s approach to Booleans [5] can certainly be considered a mixed BSP CSG. So, the transformation discussed here can also be considered a boundary to CSG mapping. In [7, 8] Shapiro and Vossler discusses several ....

Lee, D. T., Schachter, B. Two algorithms for constructing Delaunay triangulations. International Journal of Computers and Information Science, 9(3) 219-242, 1980

....not be collected at a common set of spatial locations. Therefore, it is necessary to apply an interpolation procedure to the data to change data resolution and to compute values for a common set of locations. Deterministic interpolation techniques such as inverse distance [19] and triangulation [20] can be used but they do not take into account a model of the spatial process, or variograms. Interpolation techniques appropriate for spatial data such as kriging [19] and interpolation using the minimum curvature method [21] are often preferable and are provided in the software system in ....

Lee, D. T., Schachter, B. J., "Two algorithms for constructing a Delaunay Triangulation," International Journal of Computer and Information Sciences, Vol. 9, No. 3, pp. 219-242, 1980.

....in Two Triangulation Programs To evaluate the effectiveness of the adaptive tests in applications, I tested them in two of my Delaunay triangulation codes. Triangle [23] is a 2D Delaunay triangulator and mesh generator, publicly available from Netlib, that uses a divide and conquer algorithm [16, 12]. Pyramid is a 3D Delaunay tetrahedralizer that uses an incremental algorithm [25] For both 2D and 3D, three types of inputs were tested: uniform random points, points lying (approximately) on the boundary of a circle or sphere, and a square or cubic grid of lattice points, tilted so as not to be ....

Der-Tsai Lee and Bruce J. Schachter. Two Algorithms for Constructing a Delaunay Triangulation. International Journal of Computer and Information Sciences 9(3):219--242, 1980.

....grid edges of arbitrary orientation and position. A Delaunay triangulation D of a set of points V is a triangular tessellation of the plane in which the circumcircle of every triangle (v i ; v j ; v k ) where v i ; v j ; v k 2 V , does not contain in its interior any other point v l 2 V , [11] for example. The tessellation grid is adjusted to the semantics of the image data by combining two basic, complementary information cues similarity and difference: if a global similarity criterion defined on a connected region is not satisfied, pixels of the heterogeneous region lying on image ....

Lee, D. L. and Schachter, B. J., Two Algorithms for Constructing a Delaunay Triangulation , Int. J. of Comput. and Inf. Sc., Vol. 9, No. 3, pp. 219-424, 1980.

....locations and orientations are unknown. The classical correspondence problem is a fundamental and difficult problem in computer vision, as evidenced by more than 30 years of research. Notable approaches include feature based parameter estimation [18, 23] interpolation of feature correspondences [4, 11, 20], optical flow [1, 3] layered motion [2, 9, 22] and correspondence along conjugate epipolar lines [5, 6, 10, 12, 21] While in some applications, an unstructured optical flow field may be an adequate representation of correspondence between an image pair, there are many practical situations in ....

D.T. Lee and B.J. Schachter. Two algorithms for constructing a Delaunay triangulation. Int. J. Comput. Inform. Sci., Vol. 9, pp. 219-242, 1980.

....maximizes the minimum angles over all triangulations. Sites Voronoi Cell Voronoi Edge Delaunay Edge Figure 2: Voronoi diagram (dotted lines) and Delaunay triangulation (filled lines) 14 . Several algorithms are available to efficiently compute the Delaunay triangulation [29] [39]. Hence, the Delaunay triangulation generates an efficient representation of the cross sections, affords an angle maximal surface tessellation, and has a worst case time complexity of O(n 2 ) with an expected time that increases linearly. A detailed explanation of a reconstruction algorithm ....

D. Lee and B. Schachter, "Two Algorithms for Constructing a Delaunay Triangulation," International Journal of Computer and Information Sciences, Vol. 9, No. 3, 1980.

....and builds an adjacency between two curves if the edge checked connects the two curves. The result is a D graph. A run of the algorithm is given in Fig. 3. The algorithm has a time complexity of O(M log(M ) where M is the total number of points. A Delaunay triangulation takes O(M log(M) time (Lee Shachter 1980), and the relation aggregation step takes only O(M) time since there are O(M) edges in a Delaunay neighborhood graph, which is a planar graph. A D graph is connected and has the same node set as its corresponding T graph. Next we show that when the points in each curve are dense enough, a D graph ....

Lee, and Shachter. 1980. Two algorithms for constructing delaunay triangulations. Int'l J. Comput. and Info. Sci. 18.

....sites. The algorithm has been effectively coded and experimental results are given. 1 Introduction The Delaunay triangulation and its dual, the Voronoi diagram, are subjects of major interest in Computational Geometry. A lot of algorithms compute it in optimal Omega Gamma n log n) time [24, 15, 14, 11, 21]. But these algorithms are rather complicated and difficult to implement effectively, so the sub optimal algorithm [12] is often preferred. Furthermore, this algorithm is on line and does not impose to compute again the whole triangulation at each insertion. In the last few years some simpler ....

D.T. Lee and B.J. Schachter. Two algorithms for constructing a Delaunay triangulation. International Journal of Computer and Information Sciences, 9(3), 1980.

....[1] computer vision [2] and mesh generation [3] Its property of producing triangulations with well shaped triangles makes it particularly appropriate for subsequent analysis techniques such as finite element methods. Many algorithms for computing Delaunay triangulations are known, including [4, 5, 6, 7]. Some of these construct a supertriangle surrounding the points to be triangulated [5, 7] insert the points incrementally into the triangulation, then remove the supertriangle and all edges from it. Sloan and Houlsby note that boundary of the triangulation produced may be locally concave [8] ....

....very large local concavities to occur with supertriangle methods, giving a (tight) upper bound on their size. The second presents a fast algorithm to restore the convex boundary. Definitions Only two dimensional problems will be considered. The Delaunay triangulation may be defined as follows [6]. Let V be a set of n 3 points in the Euclidean plane, 1 which are not all colinear, and let E be the set of edges joining pairs of points in V . A triangulation of V is is a graph T (V; E T ) where E T is a maximal subset of E such that no two edges of E T intersect except at a common vertex. A ....

D. T. Lee and B. J. Shachter. Two algorithms for constructing a Delaunay triangulation. Int. Journ. Computer and Inf. Sciences, 9(3):219--242, 1980.

.... no points in P [21] The eciency of naive implementation is low (O(n 3 ) in the worst case in E 3 ) but e ective acceleration techniques can be devised [7] 14] Divide conquer (D C) algorithms have been proven to be optimal in the E 2 space in both mean and worst case time complexities [20]. These methods are based on recursive partitioning and local triangulation of the pointset, and then on a merging phase where the resulting triangulations are joined. A new D C solution working in any space has been proposed in [7] 2.1 Parallel Delaunay Triangulation: previous works The ....

D.T Lee and B.J. Schachter. Two algorithms for constructing a Delaunay triangulation. Int. J. of Computer and Information Science, 9(3):219-242, 1980.

....Sun Yat Sen University, Kaohsiung, Taiwan, March 2000. mesh generation becomes a critical component both for sequential and parallel execution of large solvers. There exist many sequential algorithms for constructing Delaunay triangulation, for example, sweep line [7] divide and conquer [8, 10], incremental construction [6, 3] and point insertion [5] just to name a few. Work on parallelization of mesh generation has also been reported in literature [4, 11, 12] In this paper, we aim to study the parallelization of Delaunay triangulation with High Performance Fortran. In particular, we ....

.... conquer, and incremental construction. Divide and Conquer (D C) This method recursively partitions and constructs the local triangulations of the point set, and then the DT is obtained by merging all the triangulations. Details of this method are described in Section 3.1. These algorithms [8, 10] gave an O(n log n) DT which is asymptotically optimal; Incremental Construction (I C) With an initial Delaunay triangle, the generic DT can be constructed by successively building simplices next to the previous simplex, and the circumcircles of new simplices contain no point in P . The details ....

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D. T. Lee and B. J. Schachter, Two algorithms for constructing a Delaunay triangulation, International Journal of Computer and Information Sciences, 9 (1980), pp. 219--242.

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D.T. Lee and B.J. Schachter. Two algorithms for constructing a Delaunay triangulation. Int. J. Comput. Inform. Sci., Vol. 9, pp. 219-242, 1980.

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Der-Tsai Lee and Bruce J. Schachter. Two Algorithms for Constructing a Delaunay Triangulation. International Journal of Computer and Information Sciences 9(3):219--242, 1980.

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Lee, D. L. and Schachter, B. J., Two Algorithms for Constructing a Delaunay Triangulation , International Journal of Comput. and Inf. Sciences, Vol. 9, No. 3, pp. 219-424, 1980.

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D. T. Lee, B, Schachter, Two algorithms for constructing a Delaunay triangulation, Int. J. Comp. Inform. Sci. 9 (1980) pp 219-242

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D. Lee and B. Schachter. Two algorithms for constructing a Delaunay triangulation. Int. J. Comput. Inform. Sci., 9:219-- 242, 1980.

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D. T. Lee and B. J. Schachter. Two algorithms for constructing a Delaunay triangulation. International Journal of Computer and Information Sciences, 9(3):219--242, 1980.

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D. T. Lee and B. J. Schachter. Two algorithms for constructing a Delaunay triangulation. International Journal of Computer & Information Sciences, 9(3):219--242, June 1980.

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D.T. Lee and B.J. Schachter. Two algorithms for constructing a Delaunay triangulation. Int. J. of Computer and Information Sciences 9 (1980), 219--242.

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Lee, D.-T. and Schachter, B. J. (1980). Two algorithms for constructing the Delaunay triangulation. International Journal of Computer and Information Sciences, 9 (3): 219-242.

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