Results 1  10
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51
Applications of Random Sampling in Computational Geometry, II
 Discrete Comput. Geom
, 1995
"... We use random sampling for several new geometric algorithms. The algorithms are "Las Vegas," and their expected bounds are with respect to the random behavior of the algorithms. These algorithms follow from new general results giving sharp bounds for the use of random subsets in geometric algorithms ..."
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Cited by 389 (12 self)
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We use random sampling for several new geometric algorithms. The algorithms are "Las Vegas," and their expected bounds are with respect to the random behavior of the algorithms. These algorithms follow from new general results giving sharp bounds for the use of random subsets in geometric algorithms. These bounds show that random subsets can be used optimally for divideandconquer, and also give bounds for a simple, general technique for building geometric structures incrementally. One new algorithm reports all the intersecting pairs of a set of line segments in the plane, and requires O(A + n log n) expected time, where A is the number of intersecting pairs reported. The algorithm requires O(n) space in the worst case. Another algorithm computes the convex hull of n points in E d in O(n log n) expected time for d = 3, and O(n bd=2c ) expected time for d ? 3. The algorithm also gives fast expected times for random input points. Another algorithm computes the diameter of a set of n...
Determining the Separation of Preprocessed Polyhedra  A Unified Approach
, 1990
"... We show how (now familiar) hierarchical representations of (convex) polyhedra can be used to answer various separation queries efficiently (in a number of cases, optimally). Our emphasis is i) the uniform treatment of polyhedra separation problems, ii) the use of hierarchical representations of prim ..."
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Cited by 106 (5 self)
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We show how (now familiar) hierarchical representations of (convex) polyhedra can be used to answer various separation queries efficiently (in a number of cases, optimally). Our emphasis is i) the uniform treatment of polyhedra separation problems, ii) the use of hierarchical representations of primitive objects to provide implicit representations of composite or transformed objects, and iii) applications to natural problems in graphics and robotics. Among the specific results is an O(log jP j 1 log jQj) algorithm for determining the sepa ration of polyhedra P and Q (which have been individually preprocessed in at most linear time).
Incremental algorithms for collision detection between solid models
 IEEE Transactions on Visualization and Computer Graphics
, 1995
"... solid models ..."
Merging Polyhedral Shapes with Scattered Features
, 2000
"... The paper presents a technique for merging two genus 0 polyhedra. Merging establishes correspondences between vertices of the models as a first step in a 3D morphing process. The technique allows for the specification of scattered features to be aligned. This is accomplished by performing the follow ..."
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Cited by 78 (5 self)
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The paper presents a technique for merging two genus 0 polyhedra. Merging establishes correspondences between vertices of the models as a first step in a 3D morphing process. The technique allows for the specification of scattered features to be aligned. This is accomplished by performing the following three steps: First, initial embeddings of the polyhedra on unit spheres are computed. Second, the embeddings are deformed such that user defined features (vertices) coincide on the spheres. Third, an overlay of the subdivisions is computed and the aligned vertices are fused in the merged model. Keywords. Polyhedra, Scattered Features, Morphing 1.
Rapid Collision Detection by Dynamically Aligned DOPTrees
 In Proc. of IEEE Virtual Reality Annual International Symposium; VRAIS ’98
, 1998
"... Based on a general hierarchical data structure, we present a fast algorithm for exact collision detection of arbitrary polygonal rigid objects. Objects consisting of hundreds of thousands of polygons can be checked for collision at interactive rates. ..."
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Cited by 62 (20 self)
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Based on a general hierarchical data structure, we present a fast algorithm for exact collision detection of arbitrary polygonal rigid objects. Objects consisting of hundreds of thousands of polygons can be checked for collision at interactive rates.
An optimal algorithm for intersecting threedimensional convex polyhedra
 SIAM J. Comput
, 1992
"... Abstract. This paper describes a lineartime algorithm for computing the intersection of two convex polyhedra in 3space. Applications of this result to computing intersections, convex hulls, and Voronoi diagrams are also given. Key words, computational geometry, convex polyhedra AMS(MOS) subject cl ..."
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Cited by 61 (4 self)
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Abstract. This paper describes a lineartime algorithm for computing the intersection of two convex polyhedra in 3space. Applications of this result to computing intersections, convex hulls, and Voronoi diagrams are also given. Key words, computational geometry, convex polyhedra AMS(MOS) subject classifications. 68Q25, 68H05 1. Introduction. Giventwo
Determining the Minimum Translational Distance between Two Convex Polyhedra
 Proceedings of International Conference on Robotics and Automation
, 1986
"... Given two objects we define the minimal translational distance (MTD) between them to be the length of the shortest relative translation that results in the objects being in contact. MTD is equivalent to the distance between two objects if the objects are not intersecting, but MTD is also defined for ..."
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Cited by 56 (4 self)
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Given two objects we define the minimal translational distance (MTD) between them to be the length of the shortest relative translation that results in the objects being in contact. MTD is equivalent to the distance between two objects if the objects are not intersecting, but MTD is also defined for intersecting objects and it then gives a measure of penetration. We show that the computation of MTD can be recast as a configuration space problem, and describe an algorithm for computing MTD for convex polyhedra.
Planar Separators and Parallel Polygon Triangulation
"... We show how to construct an O ( p n)separator decomposition of a planar graph G in O(n) time. Such a decomposition defines a binary tree where each node corresponds to a subgraph of G and stores an O ( p n)separator of that subgraph. We also show how to construct an O(n)way decomposition tree in ..."
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Cited by 52 (8 self)
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We show how to construct an O ( p n)separator decomposition of a planar graph G in O(n) time. Such a decomposition defines a binary tree where each node corresponds to a subgraph of G and stores an O ( p n)separator of that subgraph. We also show how to construct an O(n)way decomposition tree in parallel in O(log n) time so that each node corresponds to a subgraph of G and stores an O(n 1=2+)separator of that subgraph. We demonstrate the utility of such a separator decomposition by showing how it can be used in the design of a parallel algorithm for triangulating a simple polygon deterministically in O(log n) time using O(n = log n) processors on a CRCW PRAM.
Controlled Simplification of Genus for Polygonal Models
, 1997
"... Genusreducing simplifications are important in constructing multiresolution hierarchies for levelofdetailbased rendering, especially for datasets that have several relatively small holes, tunnels, and cavities. We present a genusreducing simplification approach that is complementary to the exis ..."
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Cited by 46 (1 self)
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Genusreducing simplifications are important in constructing multiresolution hierarchies for levelofdetailbased rendering, especially for datasets that have several relatively small holes, tunnels, and cavities. We present a genusreducing simplification approach that is complementary to the existing work on genuspreserving simplifications. We propose a simplification framework in which genusreducing and genuspreserving simplifications alternate to yield much better multiresolution hierarchies than would have been possible by using either one of them. In our approach we first identify the holes and the concavities by extending the concept of # hulls to polygonal meshes under the L1 distance metric and then generate valid triangulations to fill them. CR Categories and Subject Descriptors: I.3.3 [Computer Graphics]: Picture/Image Generation  Display algorithms; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling  Curve, surface, solid, and object represent...
Using Generic Programming for Designing a Data Structure for Polyhedral Surfaces
 Comput. Geom. Theory Appl
, 1999
"... Appeared in Computational Geometry  Theory and Applications 13, 1999, 6590. Software design solutions are presented for combinatorial data structures, such as polyhedral surfaces and planar maps, tailored for program libraries in computational geometry. Design issues considered are flexibility, ..."
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Cited by 46 (5 self)
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Appeared in Computational Geometry  Theory and Applications 13, 1999, 6590. Software design solutions are presented for combinatorial data structures, such as polyhedral surfaces and planar maps, tailored for program libraries in computational geometry. Design issues considered are flexibility, time and space efficiency, and easeofuse. We focus on topological aspects of polyhedral surfaces and evaluate edgebased representations with respect to our design goals. A design for polyhedral surfaces in a halfedge data structure is developed following the generic programming paradigm known from the Standard Template Library STL for C++. Connections are shown to planar maps and facebased structures. Key words: Library design; Generic programming; Combinatorial data structure; Polyhedral surface; Halfedge data structure 1 Introduction Combinatorial structures, such as planar maps, are fundamental in computational geometry. In order to be useful in practice, a solid library for compu...