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Approximating Voronoi Diagrams with Voronoi Diagrams
"... The tremendous usefulness of Voronoi diagrams is tempered by their worstcase O(n ⌈d/2 ⌉ ) size blowup. This makes them an obvious target for approximation, and indeed, several methods have been proposed ..."
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Cited by 1 (1 self)
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The tremendous usefulness of Voronoi diagrams is tempered by their worstcase O(n ⌈d/2 ⌉ ) size blowup. This makes them an obvious target for approximation, and indeed, several methods have been proposed
The Voronoi Diagram
"... We present a graphics hardware implementation of the tangentplane algorithm for computing the kthorder Voronoi diagram of a set of point sites in image space. Correct and efficient implementation of this algorithm using graphics hardware is possible only with the use of an appropriate shader progr ..."
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We present a graphics hardware implementation of the tangentplane algorithm for computing the kthorder Voronoi diagram of a set of point sites in image space. Correct and efficient implementation of this algorithm using graphics hardware is possible only with the use of an appropriate shader
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
Voronoi Diagrams on the Sphere
, 2001
"... Given a set of compact sites on a sphere, we show that their spherical Voronoi diagram can be computed by computing two planar Voronoi diagrams of suitably transformed sites in the plane. We also show that a planar furthestsite Voronoi diagram can always be obtained as a portion of a nearestsit ..."
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Cited by 16 (0 self)
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Given a set of compact sites on a sphere, we show that their spherical Voronoi diagram can be computed by computing two planar Voronoi diagrams of suitably transformed sites in the plane. We also show that a planar furthestsite Voronoi diagram can always be obtained as a portion of a nearest
On Bregman Voronoi Diagrams
 in "Proc. 18th ACMSIAM Sympos. Discrete Algorithms
, 2007
"... The Voronoi diagram of a point set is a fundamental geometric structure that partitions the space into elementary regions of influence defining a discrete proximity graph and dually a wellshaped Delaunay triangulation. In this paper, we investigate a framework for defining and building the Voronoi ..."
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Cited by 60 (27 self)
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The Voronoi diagram of a point set is a fundamental geometric structure that partitions the space into elementary regions of influence defining a discrete proximity graph and dually a wellshaped Delaunay triangulation. In this paper, we investigate a framework for defining and building the Voronoi
Results 1  10
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15,817