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A REVIEW OF PROPERTIES AND VARIATIONS OF VORONOI DIAGRAMS
"... This paper is a review of Voronoi diagrams, Delaunay triangulations, and many properties of specialized Voronoi diagrams. We will also look at various algorithms for computing these diagrams. The ..."
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This paper is a review of Voronoi diagrams, Delaunay triangulations, and many properties of specialized Voronoi diagrams. We will also look at various algorithms for computing these diagrams. The
Dirichlet–Voronoi Diagrams and Delaunay Triangulations
"... In this chapter we present very briefly the concepts of a Voronoi diagram and of a Delaunay triangulation. These are important tools in computational geometry, and Delaunay triangulations are important in problems where it is necessary to fit 3D data using surface splines. It is usually useful to co ..."
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In this chapter we present very briefly the concepts of a Voronoi diagram and of a Delaunay triangulation. These are important tools in computational geometry, and Delaunay triangulations are important in problems where it is necessary to fit 3D data using surface splines. It is usually useful
Visualizing the Connection Among Convex Hull, Voronoi Diagram and Delaunay Triangulation
"... The convex hull, Voronoi diagram and Delaunay triangulation are all essential concepts in computational geometry. Algorithms for solving the convex hull problem are commonly taught in an algorithms course, but the important relationship between convex hulls and the Voronoi diagram/Delaunay triangula ..."
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Cited by 2 (0 self)
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The convex hull, Voronoi diagram and Delaunay triangulation are all essential concepts in computational geometry. Algorithms for solving the convex hull problem are commonly taught in an algorithms course, but the important relationship between convex hulls and the Voronoi diagram/Delaunay
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 532 (11 self)
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are given, one that constructs the Voronoi diagram in O(n log n) time, and another that inserts a new site in O(n) time. Both are based on the use of the Voronoi dual, or Delaunay triangulation, and are simple enough to be of practical value. The simplicity of both algorithms can be attributed
Computing Delaunay Triangulations in Manhattan and Maximum Metric
, 1995
"... We modify the incremental algorithm for computing Voronoi diagrams in the Euclidean metric proposed by Ohya, Iri and Murota [6] in order to obtain an algorithm for computing Voronoi diagrams (resp. Delaunay triangulations) in Manhattan and Maximum metric, that is rather simply to implement. We gener ..."
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Cited by 3 (0 self)
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We modify the incremental algorithm for computing Voronoi diagrams in the Euclidean metric proposed by Ohya, Iri and Murota [6] in order to obtain an algorithm for computing Voronoi diagrams (resp. Delaunay triangulations) in Manhattan and Maximum metric, that is rather simply to implement. We
Delaunay triangulations and Voronoi diagrams for Riemannian manifolds
 ACM SYMPOSIUM ON COMPUTATIONAL GEOMETRY
, 2000
"... For a sufficiently dense set of points in any closed Riemannian manifold, we prove that a unique Delaunay triangulation exists. This triangulation has the same properties as in Euclidean space. Algorithms for constructing these triangulations will also be described. ..."
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Cited by 72 (1 self)
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For a sufficiently dense set of points in any closed Riemannian manifold, we prove that a unique Delaunay triangulation exists. This triangulation has the same properties as in Euclidean space. Algorithms for constructing these triangulations will also be described.
Chapter 8 Dirichlet–Voronoi Diagrams and
"... In this chapter we present the concepts of a Voronoi diagram and of a Delaunay triangulation. These are important tools in computational geometry and Delaunay triangulations are important in problems where it is necessary to fit 3D data using surface splines. It is usually useful to compute a good m ..."
Abstract
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In this chapter we present the concepts of a Voronoi diagram and of a Delaunay triangulation. These are important tools in computational geometry and Delaunay triangulations are important in problems where it is necessary to fit 3D data using surface splines. It is usually useful to compute a good
Vector Weighted Voronoi Diagrams and Delaunay Triangulations
 CCCG
, 2007
"... We introduce a weighting scheme for Voronoi diagrams that has preferred directions. This generalizes the concept of weighted Delaunay triangulations and overcomes some of the difficulties of using multiplicative anisotropic weight systems. We discuss properties that make these weighting schemes attr ..."
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We introduce a weighting scheme for Voronoi diagrams that has preferred directions. This generalizes the concept of weighted Delaunay triangulations and overcomes some of the difficulties of using multiplicative anisotropic weight systems. We discuss properties that make these weighting schemes
The Delaunay triangulation, its dual Voronoi Diagram
"... AbstractA new method for detecting Delaunay edge by modifying the links in the star of a vertex is proposed. This is based on selecting vertex points of the input triangulation in such a way that the star formed from the selected point should belong to the given input set S. That star should not hav ..."
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AbstractA new method for detecting Delaunay edge by modifying the links in the star of a vertex is proposed. This is based on selecting vertex points of the input triangulation in such a way that the star formed from the selected point should belong to the given input set S. That star should
Results 1  10
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