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Efficient Computation of Clipped Voronoi Diagram for Mesh Generation
"... The Voronoi diagram is a fundamental geometric structure widely used in various fields, especially in computer graphics and geometry computing. For a set of points in a compact domain (i.e. a bounded and closed 2D region or a 3D volume), some Voronoi cells of their Voronoi diagram are infinite or pa ..."
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or partially outside of the domain, but in practice only the parts of the cells inside the domain are needed, as when computing the centroidal Voronoi tessellation. Such a Voronoi diagram confined to a compact domain is called a clipped Voronoi diagram. We present an efficient algorithm to compute the clipped
Efficient computation of 3d clipped voronoi diagram
 In GMP conf. proc
, 2010
"... Abstract. The Voronoi diagram is a fundamental geometry structure widely used in various fields, especially in computer graphics and geometry computing. For a set of points in a compact 3D domain (i.e. a finite 3D volume), some Voronoi cells of their Voronoi diagram are infinite, but in practice onl ..."
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Cited by 6 (3 self)
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only the parts of the cells inside the domain are needed, as when computing the centroidal Voronoi tessellation. Such a Voronoi diagram confined to a compact domain is called a clipped Voronoi diagram. We present an efficient algorithm for computing the clipped Voronoi diagram for a set of sites
Fast Computation of Generalized Voronoi Diagrams Using Graphics Hardware
, 1999
"... We present a new approach for computing generalized 2D and 3D Voronoi diagrams using interpolationbased polygon rasterization hardware. We compute a discrete Voronoi diagram by rendering a three dimensional distance mesh for each Voronoi site. The polygonal mesh is a boundederror approximation of ..."
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Cited by 234 (26 self)
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We present a new approach for computing generalized 2D and 3D Voronoi diagrams using interpolationbased polygon rasterization hardware. We compute a discrete Voronoi diagram by rendering a three dimensional distance mesh for each Voronoi site. The polygonal mesh is a boundederror approximation
Efficient Computation of 3D . . . Diagram
, 2010
"... The Voronoi diagram is a fundamental geometry structure widely used in various fields, especially in computer graphics and geometry computing. For a set of points in a compact 3D domain (i.e. a finite 3D volume), some Voronoi cells of their Voronoi diagram are infinite, but in practice only the pa ..."
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the parts of the cells inside the domain are needed, as when computing the centroidal Voronoi tessellation. Such a Voronoi diagram confined to a compact domain is called a clipped Voronoi diagram. We present an efficient algorithm for computing the clipped Voronoi diagram for a set of sites with respect
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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in the Voronoi diagram. Given such a partition (P1,P2) of P, we present approximation algorithms to compute the minimum size separator realizing this partition. 1.
Hexahedral mesh generation using the embedded Voronoi graph
 In Proceedings of the 7th International Meshing Roundtable
, 1999
"... This work presents a new approach for automatic hexahedral meshing, based on the embedded Voronoi graph. The embedded Voronoi graph contains the full symbolic information of the Voronoi diagram and the medial axis of the object, and a geometric approximation to the real geometry. The embedded Vorono ..."
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Cited by 30 (0 self)
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volumes computed by the algorithm are guaranteed to be welldefined and disjoint. The size of the decomposition is relatively small since every subvolume contains a different Voronoi face. Mesh quality seems high since the decomposition avoids generation of sharp angles, and sweep and other basic methods are used
On the expected complexity of Voronoi diagrams on terrains
 In Proc. 28th Annu. ACM Sympos. Comput. Geom. (SoCG
, 2012
"... ar ..."
GPGPUAccelerated Construction of HighResolution Generalized Voronoi Diagrams and Navigation Meshes
"... Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of ..."
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Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and/or a fee.
Further results on the hyperbolic Voronoi diagrams
"... Abstract—In Euclidean geometry, it is wellknown that the korder Voronoi diagram in Rd can be computed from the vertical projection of the klevel of an arrangement of hyperplanes tangent to a convex potential function in Rd+1: the paraboloid. Similarly, we report for the Klein ball model of hyperb ..."
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Abstract—In Euclidean geometry, it is wellknown that the korder Voronoi diagram in Rd can be computed from the vertical projection of the klevel of an arrangement of hyperplanes tangent to a convex potential function in Rd+1: the paraboloid. Similarly, we report for the Klein ball model
Approximated Centroidal Voronoi Diagrams for Uniform Polygonal Mesh Coarsening
"... We present a novel clustering algorithm for polygonal meshes which approximates a Centroidal Voronoi Diagram construction. The clustering provides an efficient way to construct uniform tessellations, and therefore leads to uniform coarsening of polygonal meshes, when the output triangulation has man ..."
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Cited by 18 (1 self)
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We present a novel clustering algorithm for polygonal meshes which approximates a Centroidal Voronoi Diagram construction. The clustering provides an efficient way to construct uniform tessellations, and therefore leads to uniform coarsening of polygonal meshes, when the output triangulation has
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