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Voronoi Diagrams of Lines in 3Space Under Polyhedral Convex Distance Functions
 J. Algorithms
"... The combinatorial complexity of the Voronoi diagram of n lines in three dimensions under a convex distance function induced by a polytope with a constant number of edges is shown to be O(n 2 ff(n) log n), where ff is a slowly growing inverse of the Ackermann function. There are arrangements of ..."
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Cited by 21 (5 self)
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The combinatorial complexity of the Voronoi diagram of n lines in three dimensions under a convex distance function induced by a polytope with a constant number of edges is shown to be O(n 2 ff(n) log n), where ff is a slowly growing inverse of the Ackermann function. There are arrangements
Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams
 ACM Tmns. Graph
, 1985
"... The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms ar ..."
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Cited by 543 (11 self)
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The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5350 (67 self)
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long time, ‘variational ’ problems have been identified mostly with the ‘calculus of variations’. In that venerable subject, built around the minimization of integral functionals, constraints were relatively simple and much of the focus was on infinitedimensional function spaces. A major theme
Surface Reconstruction by Voronoi Filtering
 Discrete and Computational Geometry
, 1998
"... We give a simple combinatorial algorithm that computes a piecewiselinear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled ..."
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Cited by 418 (15 self)
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We give a simple combinatorial algorithm that computes a piecewiselinear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled
A New VoronoiBased Surface Reconstruction Algorithm
, 2002
"... We describe our experience with a new algorithm for the reconstruction of surfaces from unorganized sample points in R³. The algorithm is the first for this problem with provable guarantees. Given a “good sample” from a smooth surface, the output is guaranteed to be topologically correct and converg ..."
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Cited by 422 (9 self)
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, rather than approximates, the input points. Our algorithm is based on the threedimensional Voronoi diagram. Given a good program for this fundamental subroutine, the algorithm is quite easy to implement.
Straight Skeletons by Means of Voronoi Diagrams Under Polyhedral Distance Functions
"... We consider the question under which circumstances the straight skeleton and the Voronoi diagram of a given input shape coincide. More precisely, we investigate convex distance functions that stem from centrally symmetric convex polyhedra as unit balls and derive sufficient and necessary conditio ..."
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We consider the question under which circumstances the straight skeleton and the Voronoi diagram of a given input shape coincide. More precisely, we investigate convex distance functions that stem from centrally symmetric convex polyhedra as unit balls and derive sufficient and necessary
Generalized Voronoi Diagrams on Polyhedral Terrains
, 2007
"... We present an algorithm for computing exact shortest paths, and consequently distances, from a generalized source (point, segment, polygonal chain or polygonal region) on a polyhedral terrain in which polygonal chain or polygon obstacles are allowed. We also present algorithms for computing discrete ..."
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discrete Voronoi diagrams of a set of generalized sites (points, segments, polygonal chains or polygons) on a polyhedral terrain with obstacles. To obtain the discrete Voronoi diagrams our algorithms, exploiting hardware graphics capabilities, compute shortest path distances defined by the sites.
The Extended Linear Complementarity Problem
, 1993
"... We consider an extension of the horizontal linear complementarity problem, which we call the extended linear complementarity problem (XLCP). With the aid of a natural bilinear program, we establish various properties of this extended complementarity problem; these include the convexity of the biline ..."
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Cited by 776 (28 self)
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of the bilinear objective function under a monotonicity assumption, the polyhedrality of the solution set of a monotone XLCP, and an error bound result for a nondegenerate XLCP. We also present a finite, sequential linear programming algorithm for solving the nonmonotone XLCP.
Results 1  10
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380,135