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A fast procedure for computing the distance between complex objects in three space
 in Proc. IEEE Int. Conf. on Robotics and Automation
, 1987
"... AbstractAn efficient and reliable algorithm for computing the Euclidean distance between a pair of convex sets in Rm is described. Extensive numerical experience with a broad family of polytopes in R3 shows that the computational cost is approximately linear in the total number of vertices specifyi ..."
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Cited by 348 (9 self)
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AbstractAn efficient and reliable algorithm for computing the Euclidean distance between a pair of convex sets in Rm is described. Extensive numerical experience with a broad family of polytopes in R3 shows that the computational cost is approximately linear in the total number of vertices specifying the two polytopes. The algorithm has special features which makes its application in a variety of robotics problems attractive. These are discussed and an example of collision detection is given. I.
Dynamic Trees and Dynamic Point Location
 In Proc. 23rd Annu. ACM Sympos. Theory Comput
, 1991
"... This paper describes new methods for maintaining a pointlocation data structure for a dynamicallychanging monotone subdivision S. The main approach is based on the maintenance of two interlaced spanning trees, one for S and one for the graphtheoretic planar dual of S. Queries are answered by using ..."
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Cited by 46 (9 self)
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This paper describes new methods for maintaining a pointlocation data structure for a dynamicallychanging monotone subdivision S. The main approach is based on the maintenance of two interlaced spanning trees, one for S and one for the graphtheoretic planar dual of S. Queries are answered by using a centroid decomposition of the dual tree to drive searches in the primal tree. These trees are maintained via the linkcut trees structure of Sleator and Tarjan, leading to a scheme that achieves vertex insertion/deletion in O(log n) time, insertion/deletion of kedge monotone chains in O(log n + k) time, and answers queries in O(log 2 n) time, with O(n) space, where n is the current size of subdivision S. The techniques described also allow for the dual operations expand and contract to be implemented in O(log n) time, leading to an improved method for spatial pointlocation in a 3dimensional convex subdivision. In addition, the interlacedtree approach is applied to online pointlo...
Geometric Learning Algorithms
, 1990
"... Emergent computation in the form of geometric learning is central to the development of motor and perceptual systems in biological organisms and promises to have a similar impact on emerging technologies including robotics, vision, speech, and graphics. This paper examines some of the tradeoffs inv ..."
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Cited by 20 (5 self)
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Emergent computation in the form of geometric learning is central to the development of motor and perceptual systems in biological organisms and promises to have a similar impact on emerging technologies including robotics, vision, speech, and graphics. This paper examines some of the tradeoffs involved in different implementation strategies, focussing on the tasks of learning discrete classifications and smooth nonlinear mappings. The tradeoffs between local and global representations are discussed, a spectrum of distributed network implementations are examined, and an important source of computational inefficiency is identified. Efficient algorithms based on kd trees and the Delaunay triangulation are presented and the relevance to biological networks is discussed. Finally, extensions of both the tasks and the implementations are given. Keywords: learning algorithms, neural networks, computational geometry, emergent computation, robotics. 1. Introduction Intelligent systems must...
Parallel techniques for computational geometry
 Proc. IEEE, 80:1435– 1448
, 1992
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Voronoi ProjectionBased Fast NearestNeighbor Search Algorithms: BoxSearch and Mapping TableBased Search Techniques
, 1997
"... In this paper we consider fast nearestneighbor search techniques based on the projections of Voronoi regions. The Voronoi diagram of a given set of points provides an implicit geometric interpretation of nearestneighbor search and serves as an important basis for several proximity search algorithm ..."
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In this paper we consider fast nearestneighbor search techniques based on the projections of Voronoi regions. The Voronoi diagram of a given set of points provides an implicit geometric interpretation of nearestneighbor search and serves as an important basis for several proximity search algorithms in computational geometry and in developing structurebased fast vector quantization techniques. The Voronoi projections provide an approximate characterization of the Voronoi regions with respect to their locus property of localizing the search to a small subset of codevectors. This can be viewed as a simplified and practically viable equivalent of point location using the Voronoi diagram while circumventing the complexity of the full Voronoi diagram. In this paper, we provide a comprehensive study of two fast search techniques using the Voronoi projections, namely, the boxsearch and mapping tablebased search in the context of vector quantization encoding. We also propose and study the effect and advantage of using the principal component axes for data with high degree of correlation across their components, in reducing the complexity of the search based on Voronoi projections.
Discrete Comput Geom 1:201217 (1986) © 1986 Spr~ngerVedag New York Inc, y Generalized Delaunay Triangulation for Planar Graphs*
"... Abstract. We introduce the notion of generalized Delaunay triangulation of a planar straightline graph G = (V, E) in the Euclidean plane and present some characterizations of the triangulation. It is shown that the generalized Delaunay triangulation has the property that the minimum angle of the tr ..."
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Abstract. We introduce the notion of generalized Delaunay triangulation of a planar straightline graph G = (V, E) in the Euclidean plane and present some characterizations of the triangulation. It is shown that the generalized Delaunay triangulation has the property that the minimum angle of the triangles in the triangulation is maximum among all possible triangulations ofthe graph. A general algorithm that runs in O(I VI 2) time for computing the generalized Delaunay triangulation is presented. When the underlying raph is a simple polygon, a divideandconquer algorithm based on the polygon cutting theorem of Chazelle is given that runs in O ( I V I logl VI) time. 1.
Sweep Methods for Parallel Computational Geometry
, 1996
"... In this paper we give efficient parallel algorithms for a number of problems from computational geometry by using versions of parallel plane sweeping. We illustrate our approach with a number of applications, which include: 9 General hiddensurface elimination (even if the overlap relation contain ..."
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In this paper we give efficient parallel algorithms for a number of problems from computational geometry by using versions of parallel plane sweeping. We illustrate our approach with a number of applications, which include: 9 General hiddensurface elimination (even if the overlap relation contains cycles). 9 CSG boundary evaluation. 9 Computing the contour of a collection of rectangles. 9 Hiddensurface elimination for rectangles. There are interesting subproblems that we solve as a part of each parallelization. For example, we give an optimal parallel method for building a data structure for linestabbing queries (which, incidentally, improves the sequential complexity of this problem). Our algorithms are for the CREW PRAM, unless otherwise noted.
Communications Robot Navigation in Unknown Terrains Using Learned specialized computer architectures, algorithms for concurrent com Visibility Graphs. Part I: The Disjoint Convex
"... putations, path planning and navigation, and coordinated manipulation. Path planning and navigation is one of the most important aspects ..."
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putations, path planning and navigation, and coordinated manipulation. Path planning and navigation is one of the most important aspects
unknown title
, 1986
"... Graham [6] proposed an O(n log n) algorithm for determining the convex hull of a finite set of points in the plane. Variations of this method have been described in [14,915]. However, five of ..."
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Graham [6] proposed an O(n log n) algorithm for determining the convex hull of a finite set of points in the plane. Variations of this method have been described in [14,915]. However, five of