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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
Voronoi diagrams in . . .
 STOC'07
, 2007
"... We reexamine fundamental problems from computational geometry in the word RAM model, where input coordinates are integers that fit in a machine word. We develop a new algorithm for offline point location, a twodimensional analog of sorting where one needs to order points with respect to segments. ..."
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. This result implies, for example, that the Voronoi diagram of n points in the plane can be constructed in (randomized) time n * 2O(plg lg n). Similar bounds hold for numerous other geometric problems, such as threedimensional convex hulls, planar Euclidean minimum spanning trees, line segment intersection
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 534 (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  a survey of a fundamental geometric data structure
 ACM COMPUTING SURVEYS
, 1991
"... This paper presents a survey of the Voronoi diagram, one of the most fundamental data structures in computational geometry. It demonstrates the importance and usefulness of the Voronoi diagram in a wide variety of fields inside and outside computer science and surveys the history of its development. ..."
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Cited by 743 (5 self)
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This paper presents a survey of the Voronoi diagram, one of the most fundamental data structures in computational geometry. It demonstrates the importance and usefulness of the Voronoi diagram in a wide variety of fields inside and outside computer science and surveys the history of its development
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
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