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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
Separating a Voronoi Diagram∗
, 2014
"... Given a set P of n points in IRd, we show how to insert a set X of O n1−1/d additional points, such that P can be broken into two sets P1 and P2, of roughly equal size, such that in the Voronoi diagram V(P ∪ X), the cells of P1 do not touch the cells of P2; that is, X separates P1 from P2 in the Vor ..."
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Given a set P of n points in IRd, we show how to insert a set X of O n1−1/d additional points, such that P can be broken into two sets P1 and P2, of roughly equal size, such that in the Voronoi diagram V(P ∪ X), the cells of P1 do not touch the cells of P2; that is, X separates P1 from P2
Queries with Segments in Voronoi Diagrams
, 1999
"... In this paper we consider proximity problems in which the queries are line segments in the plane. We build a query structure that for a set of n points P can determine the closest point in P to a query segment outside the convex hull of P in O(log n) time. With this we solve the problem of computing ..."
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office problem preprocess a set of points, or sites, in the plane to quickly report the nearest to a query pointand Shamos and Hoey [17] suggested Voronoi diagrams as a solution, there have been a number of proximity problems in the plane whose solution is to build some type of Voronoi diagram
Rounding Voronoi diagram
, 1998
"... Computational geometry classically assumes realnumber arithmetic which does not exist in actual computers. A solution consists in using integer coordinates for data and exact arithmetic for computations. This approach implies that if the results of an algorithm are the input of another, these resul ..."
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Computational geometry classically assumes realnumber arithmetic which does not exist in actual computers. A solution consists in using integer coordinates for data and exact arithmetic for computations. This approach implies that if the results of an algorithm are the input of another
Riemannian Computational Geometry  Voronoi Diagram . . .
, 1998
"... One of most famous theorems in computational geometry is the duality between Voronoi diagram and Delaunay triangulation in Euclidean space. This paper proposes an extension of that theorem to the Voronoi diagram and Delaunaytype triangulation in dually flat space. In that space, the Voronoi diagram ..."
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diagram and the triangulation can be computed efficiently by using potential functions. We also propose higherorder Voronoi diagrams and prove that Delaunaytype triangulation is as good in dually flat space as it is in Euclidean space.
FarthestPolygon Voronoi Diagrams
, 2007
"... Given a family of k disjoint connected polygonal sites of total complexity n, we consider the farthestsite Voronoi diagram of these sites, where the distance to a site is the distance to a closest point on it. We show that the complexity of this diagram is O(n), and give an O(n log 3 n) time algori ..."
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Cited by 3 (0 self)
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algorithm to compute it. We also prove a number of structural properties of this diagram. In particular, a Voronoi region may consist of k − 1 connected components, but if one component is bounded, then it is equal to the entire region.
Indexing network voronoi diagrams
 in DASFAA 2012
, 2012
"... Abstract. The Network Voronoi diagram and its variants have been extensively used in the context of numerous applications in road networks, particularly to efficiently evaluate various spatial proximity queries such as k nearest neighbor (kNN), reverse kNN, and closest pair. Although the existing ap ..."
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Abstract. The Network Voronoi diagram and its variants have been extensively used in the context of numerous applications in road networks, particularly to efficiently evaluate various spatial proximity queries such as k nearest neighbor (kNN), reverse kNN, and closest pair. Although the existing
TimeBased Voronoi Diagram
"... We consider a variation of Voronoi diagram, or timebased Voronoi diagram, for a set S of points in the presence of transportation lines or highways in the plane. A shortest timedistance path from a query point to any given point in S is a path that takes the least travelling time. The travelling s ..."
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speeds and hence travelling times of the subpaths along the highways and in the plane are different. M. Abellanas et al. [1] gave a simple algorithm that runs in O(n log n) time, for computing the timebased Voronoi diagram for a set of n points in the presence of one highway in the plane. We consider a
Voronoi Diagrams for Oriented Spheres
"... We consider finite sets of oriented spheres in R k−1 and, by interpreting such spheres as points in R k, study the Voronoi diagrams they induce for several variants of distance between spheres. We give bounds on the combinatorial complexity of these diagrams in R² and R³ and derive properties useful ..."
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We consider finite sets of oriented spheres in R k−1 and, by interpreting such spheres as points in R k, study the Voronoi diagrams they induce for several variants of distance between spheres. We give bounds on the combinatorial complexity of these diagrams in R² and R³ and derive properties
A Theoretical Study of Parallel Voronoi Diagram
, 2006
"... In this paper, we concentrate on the problem of computing a Voronoi diagram using Hypercube model of computation. The main contribution of this work is the O(log³ n) parallel algorithm for computing Voronoi diagram on the Euclidean plane. Our technique parallelizes the wellknown seemingly inherent ..."
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In this paper, we concentrate on the problem of computing a Voronoi diagram using Hypercube model of computation. The main contribution of this work is the O(log³ n) parallel algorithm for computing Voronoi diagram on the Euclidean plane. Our technique parallelizes the wellknown seemingly inherent
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