D. Muller and F. Preparata. Finding the intersection of two convex polyhedra. Theoretical Computer Science, 7:217-236, 1978.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....which when repeated gives FVD(R 0 0 ) FVD(S) See Section 4.4 for details. During the construction of FVD(S) we create closest and furthest site Voronoi diagrams of subsets of S as intermediate structures. We maintain FVD(S) and these intermediate structures as doubly connected edge lists [3, 10], to be able to efficiently determine and preserve topological relations between Voronoi regions, edges, and vertices. 4.1 Edge tracing Several stages of the algorithm for constructing FVD(S) involve the computation of new Voronoi cells of FVD(S # ) for S # S, or the modification of existing ....

D. E. Muller and F. P. Preparata. Finding the intersection of two convex polyhedra. Theoret. Comput. Sci., 7:217--236, 1978.

.... not well formed objects: there might be gaps between polygons belonging to the same object, polygons could overlap, it might even be unclear which polygons belong to which object The basic algorithm presented in this section is so trivial that it is not even worth a literature reference [MP78b] It goes as follows. Check every edge of polyhedron P if it intersects any of the polygons of polyhedron Q, and vice versa. It is not sufficient to check only the edges of P against polygons of Q; besides, it is not sufficient to check whether there are some vertices inside the other polyhedron ....

D. E. Muller and F. P. Preparata. Finding the intersection of two convex polyhedra. Theoret. Comput. Sci., 7:217--236, 1978.

....its orientation location may be assumed to be in some special position without loss of generality. Furthermore, almost all algorithms consider only convex polyhedra. Construction algorithms The first to present an algorithm which has an asymptotical complexity below the trivial O(n ) were [MP78a] Like many linear programming algorithms, the algorithm consists of two phases: the first one searches for a point in the intersection of the two polyhedra, the second phase then constructs the actual intersection (if any) by taking the dual of the two polyhedra, forming the union of these ....

D. E. Muller and F. P. Preparata. Finding the intersection of two convex polyhedra. Theoret. Comput. Sci., 7:217--236, 1978.

....the edges triangles incident to a triangle edge and the vertices incident to an edge can be accessed in constant time. We assume also that the edges incident to a vertex are stored in a doubly linked list providing access to edges both in clockwise and in counterclockwise order, see for example [12]. The enumeration algorithm accomplishes the depth first traversal of the triangulation tree T . We store all flips of the triangulation T in a balanced search tree T 1 according to their lexicographical order. The edges of T max are stored in a static search tree T 2 which allows to detect if an ....

D. E. Muller and F. P. Preparata. Finding the intersection of two convex polyhedra. Theoret. Comput. Sci., 7:217--236, 1978.

....the correct order of intersections. The algorithm consists of two main parts: First, finding all intersections, and second, constructing a representation for the merged model. In both cases a sophisticated data structure is needed to represent the models. We use the doubly connected edge list [15]. This data structure contains information about each face, each directed edge, and each vertex. The following information is stored for the different types: The face record contains a pointer to an arbitrary half edge on its boundary. The edge record contains pointer to: The vertex it is ....

D.E. Muller and F.P. Preparata. Finding the intersections of two convex polyhedra. Theor. Comp. Sc., 7, 212-236, 1978

....conclusions and describes future directions for research on hierarchical collision detection. 2 Related work Interference and collision detection problem have been extensively studied in the literature. Computational geometry first focused on the construction of the intersection of two polyhedra [18, 17] and later on the detection problem [5, 20] The algorithms are very efficient in the asymptotical worst case. However, most of them are restricted to static environments and many of them have not been implemented. Configuration space has been used to detect collisions for path planning in ....

D. E. Muller and F. P. Preparata. Finding the intersection of two convex polyhedra. Theoret. Comput. Sci., 7:217--236, 1978.

....modeling and animation had a special need for exact collision detection. Despite its comparatively long history, real time exact collision detection has not been tackled except for the past few years. Computational geometry first focused on the construction of the intersection of two polyhedra (Muller and Preparata, 1978; Mehlhorn and Simon, 1985) Later, researchers realized that the detection problem is interesting by itself and can be solved more efficiently than the construction problem (Dobkin and Kirkpatrick, 1985; Reichling, 1988) The algorithms are very efficient in the asymptotical worst case, however, ....

Muller, D. E. and Preparata, F. P. (1978). Finding the intersection of two convex polyhedra. Theoret. Comput. Sci., 7:217--236.

....modeling and animation had a special need for exact collision detection. Despite its comparatively long history, real time exact collision detection has not been tackled except for the past few years. Computational geometry first focused on the construction of the intersection of two polyhedra [22, 20]. Later, researchers realized that the detection problem is interesting by itself and can be solved more efficiently than the construction problem [7, 6, 27] In the field of robotics, a completely different approach has been pursued: collisions are detected in configuration space (see [8] for ....

D. E. Muller and F. P. Preparata. Finding the intersection of two convex polyhedra. Theoret. Comput. Sci., 7:217--236, 1978.

....graph to the polygons in Gamma. There are a number of ways one can represent the polygon arrangement, e.g. by generalizing the winged edge structure of Baumgart [2] the quad edge structure 5 of Guibas and Stolfi [14] or the doubly connected edge list structure of Muller and Preparata [20, 25]. In any case, the polygon arrangement would be stored as a collection of cross referenced adjacency lists and arrays. In order to be specific in how one can implement the various aspects of our algorithms we give an implementation of the polygon arrangement here. The implementation we choose ....

D.E. Muller and F.P. Preparata, "Finding the Intersection of Two Convex Polyhedra, " Theoretical Computer Science, Vol. 7, No. 2, October 1978, 217--236.

....embedded planar graph. The methods from this interface are inherited by the PlanarSubdivision interface and are used in the preprocessing of the case study. There exist several possible representations for an embedded planar graph, such as the DCEL representation, originally presented in Ref. [64] and later refined (see, e.g. Ref. 21] the quad edge representation [44] and the dynamic representations described in Refs. 29, 30, 81] Each representation presents advantages and disadvantages, and some may be more suitable than others for a specific application. For instance, in ....

D. E. Muller and F. P. Preparata. Finding the intersection of two convex polyhedra. Theoret. Comput. Sci., 7(2):217--236, 1978.

....that the edges triangles incident to a triangle edge and the vertices incident to an edge can be accessed in constant time. We assume also that the edges incident to a vertex are stored in doubly linked list providing access to edges in clockwise and in counterclockwise order, see for example [9]. The enumeration algorithm accomplishes the depth first traversal of the triangulation tree T . We store all flips of the triangulation T in a balanced search tree T 1 according to their lexicographical order. The edges of Tmax are stored in a tree T 2 which allows to detect if an edge is in Tmax ....

D. E. Muller and F. P. Preparata. Finding the intersection of two convex polyhedra. Theoret. Comput. Sci., 7:217--236, 1978.

....general polygonal scenes. One of the applications of ray shooting presented in this paper is for computing the intersection of two polyhedra in 3 space. The intersection of two convex polyhedra in R 3 of total complexity n is computed in time O(n log n) by an algorithm of Muller and Preparata [MP78] Chazelle [Cha89] gives a worst case optimal O(n) algorithm. The case when only one of the two polyhedra in convex is treated in [MS85, Sha88] When the two polyhedra are terrains with the same vertical direction Chazelle et al..t. CEGS89] give an O(n 1:5 ffl k log 2 n) time algorithm for ....

D.E. Muller and F.P. Preparata. Finding the intersection of two convex polyhedra. Theoret. Comput. Sci., 7:217--236, 1978.

....if loops or multi edges are allowed all four edge pointers must remain. Otherwise the traversal around a vertex or around a facet is no longer uniquely defined [35] The winged edge data structure where the wings PCCW and NCCW are omitted has been called Doubly Connected Edge List (DCEL) by [23], though this name is now more commonly used for the halfedge data structure [6] 3 3 In order to avoid confusion we will not use the name DCEL since it turned out to be ambiguous. In fact, the name is misleading when denoting halfedges and the possible variants of single linking. 6 opposite ....

D. E. Muller and F. P. Preparata. Finding the Intersection of two Convex Polyhedra. Theoretical Computer Science, 7:217--236, 1978.

....e in direction vu. Finally, rev(e) returns a pointer to the edge (v; u) See Figure 1 for an illustration of these functions. This functionality is available in or can be simulated by the most commonly used data structures for storing planar subdivisions including the doublyconnected edge list [11, 14], the quad edge structure [8] the fully topological network structure [1] the ARC INFO structure [12] and the DIME le [13] Our algorithm also requires the use of some geometric operations. Let dist(a; b) be the distance between two points a and b. Let ab be the direction of the ray ....

D. E. Muller and F. P. Preparata. Finding the intersection of two convex polyhedra. Theoretical Computer Science, 7(2):217-236, 1978.

....are described which abstract some of the properties of Dobkin and Kirkpatrick s hierarchical representations. The properties of such cell complexes are described for arbitrary dimensions, although their use is restricted to three dimensions in this thesis. As shown by Muller and Preparata[7], the problem of computing the intersection of two convex polytopes can be linearly reduced to that of computing a description of the intersection of their boundaries. Intuitively, such a description provides a pattern for sewing together facets of the two polyhedra to form their intersection. ....

....facial graph is available for each polytope in the sequence, with each face being represented explicitly. For polytopes of three or less dimensions, this graph will be planar and hence can be represented in linear space using the doubly connected edge list representation of Muller and Preparata[7]. In this representation, edges are oriented and represented explicitly by data structures containing the names of the two vertices which terminate them, the two facets which they separate, and pointers to the next edges encountered when proceeding clockwise around their terminating vertices. We ....

D. E. Muller and F. P. Preparata. Finding the intersection of two convex polyhedra. Theoretical Computer Science, 7:217--236, 1978.

....intersect only if the sum of their affine hulls is the entire space. The intersection of two regular polyhedra in general position is again regular. The standard data structures for three dimensional polyhedra, e.g. the quad edge structure of [GS85, EM85] the doubly connected edge list of [MP78, PS85], and the half edge structure of [Man88] cannot represent all polyhedra. This implies that the class of representable (in any one of these data structures) polyhedra is not closed under the basic boolean operations intersection, union, and complement. For instance, Figure 2 shows that the ....

....The details are given in section 2. Apart from the algorithm given by Mehlhorn Simon [MS85] mentioned above, all efficient algorithm for intersecting two polyhedra in space apply only to convex polyhedra. The first efficient algorithm for solving this problem was given by Muller and Preparata [MP78]. This algorithm takes, for two convex polyhedra C 1 and C 2 , time O( jC 1 j jC 2 j) log(jC 1 j jC 2 j) Alternative algorithms were proposed by Hertel et al. HMMN84] and by Dobkin and Kirkpatrick [DK83] The former is based on the space sweep technique and the latter uses the hierarchical ....

D. E. Muller and F. P. Preparata. Finding the intersection of two convex polyhedra. Theoret. Comput. Sci., 7:217--236, 1978.

....simply the union of n convex polyhedra. The union of n convex polyhedra can be computed from their pairwise intersections. Intersection of two convex polyhedra with p and q vertices can be accomplished in optimal time O#p q# [4] A simpler algorithm to implement takes time O(#p q# log#p q#)[30]. With our approach one could, in principle, compute the union of # prisms over the entire polygonal object (and not just along the boundary of the region of interest as shown in Figure 4) This will result in automatic identification of the region abcde as being partially inaccessible to the L1 ....

D. E. Muller and F. P. Preparata. Finding the intersection of two convex polyhedra. Theoret. Comput. Sci., 7:217--236, 1978.

....simply the union of n convex polyhedra. The union of n convex polyhedra can be computed from their pairwise intersections. Intersection of two convex polyhedra with p and q vertices can be accomplished in optimal time O#p q# [30] A simpler algorithm to implement takes time O(#p q# log#p q#) [31]. With our approach one could, in principle, compute the union of # prisms over the entire polygonal object (and not just along the boundary of the region of interest as shown in Fig. 3) This will result in automatic identification of the region abcde as being partially inaccessible to the L1 ....

D. E. Muller and F. P. Preparata, "Finding the intersection of two convex polyhedra," Theoret. Comput. Sci., vol. 7, pp. 217--236, 1978.

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D. Muller and F. Preparata. Finding the intersection of two convex polyhedra. Theoretical Computer Science, 7:217-236, 1978.

No context found.

D. Muller and F. Preparata. Finding the intersection of two convex polyhedra. Theoretical Computer Science, 7:217--236, 1978.

No context found.

D. E. Muller, and F. P. Preparata. Finding the intersection of two convex polyhedra. Theoret. Comput. Sci., 7:217--236, 1978.

No context found.

D.E. Muller and F.P. Preparata, Finding the intersection of two convex polyhedra, Theoret. Comput. Sci. 7 (1978), 217--236.

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D. E. Muller and F. P. Preparata. Finding the intersection of two convex polyhedra. Theoret. Comput. Sci., 7(2):217--236, 1978.

No context found.

D.E. Muller and F.P. Preparata, "Finding the Intersection of Two Convex Polyhedra," Theoretical Computer Science, vol. 7, no. 2, pp. 217-236, 1978.

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D.E. Muller and F.P. Preparata, "Finding the Intersection of Two Convex Polyhedra," Theoretical Computer Science, Vol. 7, 1978, 217--236.

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