J.S. Mitchell, D.M. Mount, and C.H. Papdimitrou. The discrete geodesic problem. SIAM Journal of Computing, 16(4):647--668, 1987. Home/Search Document Not in Database Summary Related Articles Check |
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Approximation Algorithms for Minimum-Width Annuli and.. - Agarwal, Aronov.. (Correct)
....intersection points of with the edges of VorN (S) We can obviously compute VorN (S; in O(n log n) time by rst computing the entire VorN (S) and then intersecting with it. However, VorN (S; can be computed directly, in O(n log n) time, using a considerably simpler algorithm; see e.g. [29]. Next sentence: Why don t we drop it, if there are no objections is As an alternative, after having computed VorN (S) we can compute VorN (S; in O(n) time by tracing through VorN (S) We de ne Vor F (S; analogously; it can also be computed either directly in O(n log n) time or in ....
J. S. B. Mitchell, D. M. Mount, and C. H. Papadimitriou, The discrete geodesic problem, SIAM J. Comput., 16 (1987), 647-668.
Approximating Shortest Paths on Weighted Polyhedral Surfaces - Lanthier, Maheshwari, Sack (Correct)
....in the number of polyhedral objects as was shown by Sharir [36] For two polyhedral obstacles with a total of n vertices, Baltsan and Sharir [6] presented an O(n log n) time shortest path algorithm. The computation of Euclidean shortest paths on non convex polyhedra has been investigated by [8, 28, 30, 2]; currently, the best known algorithm is due to Chen and Han [8] and it runs in O(n ) time. For information regarding our GIS work see [39] iii Since most application models are approximations of reality and highquality paths are favored over optimal paths that are hard or expensive to ....
J.S.B. Mitchell, D.M. Mount and C.H. Papadimitriou, "The Discrete Geodesic Problem", SIAM Journal of Computing, 16, August 1987, pp. 647-668.
Robust Sculpting Using Boundary Represented Solids - Lee (Correct)
....u to v along some path F that lies entirely on S. The length of F depends on its trajectory. One way to specify this trajectory is to require F to be the shortest path between u and v. Finding a path that meets this requirement is non trivial as it involves solving the discrete geodesic problem [28]. A simpler approach is to constrain F to lie on a plane P that contains u, v, and an extra point us which is u translated by its unit normal vector (see Figure 4.2) Figure 4.2: Constraining a path to lie on a sphere S and a plane P Assuming that S and P intersect in a single closed loop, then ....
Mitchell, J.S.B., Mount, D.M., and Papadimitriou, C.H., "The Discrete Geodesic Problem", SIAM Journal of Computing, pp. 647-668 (1987).
Multivalued Distance Maps for Motion Planning on.. - Kimmel, Kiryati.. (1998) (9 citations) (Correct)
....propagation, level sets, moving obstacles, multivalued distance map, path planning. I. INTRODUCTION S EARCHING for shortest paths on surfaces with stationary obstacles is a classical problem in Robotic Navigation. Solutions to the problems are based on computational geometry methods [18], 23] 26] 29] differential geometry and hybrid techniques [2] 14] as well as graph search based algorithms, see e.g. Latombe book [17] as a good pointer for many classical techniques. The problem of finding the timeoptimal path of a robot in the presence of moving obstacles can be ....
J. S. B. Mitchell, D. M. Mount, and C. H. Papadimitriou, "The discrete geodesic problem," SIAM J. Comput., vol. 16, no. 4, pp. 647--668, 1987.
Normal Vector Voting: Crease Detection and Curvature.. - Page, Sun, Koschan.. (2002) (2 citations) (Correct)
....constraints. 6.1. Geodesic Neighborhood The first step in normal vector voting for both the first or the second pass is to find the triangles or vertices that are close in a geodesic sense to the vertex of interest. The geodesic neighborhood problem, which follows the discrete geodesic problem [29], is to find the m triangles that are within a user specified distance of the vertex. The key is that the distance is not the Euclidean distance but rather the shortest geodesic distance along the surface of the mesh. As noted in the literature this problem closely resembles the shortest path ....
J. S. B. Mitchell, D. M. Mount, and C. H. Papadimitriou, The discrete geodesic problem, SIAM J. Comput. 16, 1987, 647--668.
Facility Location on Terrains - Aronov, van Kreveld, van Oostrum.. (2001) (5 citations) (Correct)
....We do not know of any previous work on furthest site Voronoi diagrams on a polyhedron. The problem of computing the shortest path between two points along the surface of a polyhedron has received considerable attention; see the papers by Sharir and Schorr [12] Mitchell, Mount and Papadimitriou [8], and Chen and Han [2] The best known algorithms [2, 8] compute the shortest path between two given points, the source s and destination t, in roughly O(n ) time. In fact, these algorithms compute a data structure that allows one to compute the shortest path distance between the source s to ....
....Voronoi diagrams on a polyhedron. The problem of computing the shortest path between two points along the surface of a polyhedron has received considerable attention; see the papers by Sharir and Schorr [12] Mitchell, Mount and Papadimitriou [8] and Chen and Han [2] The best known algorithms [2, 8] compute the shortest path between two given points, the source s and destination t, in roughly O(n ) time. In fact, these algorithms compute a data structure that allows one to compute the shortest path distance between the source s to any query point p in O(logn) time. The algorithm of ....
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J. S. B. Mitchell, D. M. Mount, and C. H. Papadimitriou. The discrete geodesic problem. SIAM J. Comput., 16:647--668, 1987.
Parameterization of Manifold Triangulations - Floater, Hormann, Reimers (2002) (2 citations) (Correct)
....insert x j into by adding appropriate edges emanating from it, depending on whether x j lies on an edge of or is in the interior of some triangle of ; see Fig. 4. The problem of computing geodesics on polygonal surfaces is a classic one and has received considerable attention, see e.g. [2,12,14,17,18]. We have used Chen and Han s shortest path algorithm [2] see also [12] The method is exact and based on unfolding triangles. However, as the method is computationally quite expensive, we compute the geodesic #(x j , x k ) by restricting the search to a small subtriangulation jk of . The ....
Mitchell, J. S. B., D. M. Mount, and C. H. Papadimitriou, The discrete geodesic problem, SIAM J. Comput. 16 (1987), 647--668.
Piecewise Regular Meshes: Construction and Compression - Szymczak, Rossignac, King (2002) (2 citations) (Correct)
....a triangle to a relief based on the smallest angle between the triangle s normal vector and a defining vector tends to produce reliefs with jaggy boundaries and an unnecessary large number of connected components. Because of this, we developed a procedure which uses the geodesic distance function [19, 11, 16] and a variant of the farthest point Voronoi diagram [3] to obtain reliefs with smooth boundaries. We start by computing sets of triangles which will define the Voronoi cells. For a smoothing parameter # 0, each of the defining vectors v has a corresponding set Av , the union of all triangles ....
J.S.B.Mitchell, D.M.Mount and C.H.Papadimitriou, The discrete geodesic problem, SIAM J. Comput., 16:647--668, 1987.
Geometric Approximation Algorithms and Randomized Algorithms for .. - Har-Peled (1999) Self-citation (Mitchell) (Correct)
....of proportionality depend on ffi) The results of Section 3.2.1 appeared in [HP99a] Approximate geodesic diameter. We present in Section 3.3 an algorithm that computes, AAOS97] The results of Section 3.3 appeared in [HP99a] Approximate shortest path maps. The exact algorithms of [MMP87, SS86] receive as input a convex polytope or a polyhedral surface P, and a fixed source point s on P, and compute a map (i.e. a subdivision of P) of complexity Theta(n ) that can be used to answer (exact) shortest path queries from s to any point on P (along P) in O(log n) time (such a ....
....can use to answer approximate shortest path queries, for a source point s and approximation factor 0 fixed in advance. Using this technique, we solve two problems involving approximate shortest path maps in . Approximate shortest path maps on polyhedral surfaces. The exact algorithms of [MMP87, SS86] receive as input a convex polytope or a polyhedral surface P, and a fixed source point s on P, and compute a map (i.e. a subdivision of P) of complexity Theta(n ) that can be used to answer (exact) shortest path queries from s to any point on P (along P) in O(log n) time (such a ....
[Article contains additional citation context not shown here]
J.S.B. Mitchell, D. M. Mount, and C. H. Papadimitriou. The discrete geodesic problem. SIAM J. Comput., 16:647--668, 1987.
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J.S. Mitchell, D.M. Mount, and C.H. Papdimitrou. The discrete geodesic problem. SIAM Journal of Computing, 16(4):647--668, 1987.
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J.S. Mitchell, D.M. Mount, and C.H. Papadimitriou. The discrete geodesic problem. SIAM Journal of Computing, 16(4):647--668, 1987. ... AAA
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J.S. Mitchell, D.M. Mount, and C.H. Papadimitriou. The discrete geodesic problem. SIAM Journal of Computing, 16(4):647--668, 1987.
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J. S. B. Mitchell, D. M. Mount, and C. H. Papadimitriou. The discrete geodesic problem. SIAM Journal on Computing 16(4):647--668, August 1987.
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J. S. B. Mitchell, D. M. Mount and C. H. Papadimitriou, "The discrete geodesic problem", SIAM J. COMPUT. 16 (1987), pp.647-668.
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Mitchell, J.S.B., Mount, D.M., Papadimitriou, C.H. The discrete geodesic problem, SIAM J. Comput. 16 (1987), 647--668.
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. J. S. B. Mitchell, D. M. Mount, C. H. Papadimitriou. The discrete geodesic problem. SIAM J. Comput., Vol. 16, No. 4, 647-668(Aug. 1987).
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Joseph S. B. Mitchell, D. M. Mount, and C. H. Papadimitriou. The discrete geodesic problem. SIAM J. Comput., 16:647-668, 1987.
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J.S.B. Mitchell, D. M. Mount, and C. H. Papadimitriou. The discrete geodesic problem. SIAM J. Comput., 16:647--668, 1987. 17
Fast Voronoi Diagrams and Offsets on Triangulated Surfaces - Kimmel, Sethian (1999) (Correct)
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Mitchell, J. S. B., D. M. Mount, and C. H. Papadimitriou, The discrete geodesic problem, SIAM J. Comput. 16(4) (1987), 647--668.
Planar Graphs, Negative Weight Edges, Shortest Paths, and.. - Fakcharoenphol, Rao (Correct)
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Joseph S. B. Mitchell, David M. Mount, and Christos H. Papadimitriou. The discrete geodesic problem. SIAM Journal on Computing, 16(4):647--668, 1987.
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MITCHELL J., MOUNT D. M., PAPADIMITRIOU C. H.: The discrete geodesic problem. SIAM J. Comput. 16 (1987), 647--668.
Multiresolution Analysis of Arbitrary Meshes - Matthias Eck Tony (1995) (271 citations) (Correct)
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J.S. Mitchell, D.M. Mount, and C.H. Papadimitriou. The discrete geodesic problem. SIAM Journal of Computing, 16(4):647--668, 1987.
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J. S. B. Mitchell, D. M. Mount, and C. H. Papadimitriou. The discrete geodesic problem. SIAM Journal on Computing, 16(4):647--668, 1987.
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J. S. B. Mitchell, D. M. Mount, and C. H. Papadimitriou. The discrete geodesic problem. SIAM J. Comput., 16(4):647668, 1987.
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J. S. B. Mitchell, D. M. Mount, and C. H. Papadimitriou. The discrete geodesic problem. SIAM J. Comput. 16 (1987) 647--668.
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