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PERIODIC CENTROIDAL VORONOI TESSELLATIONS
 INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
, 2012
"... Centroidal Voronoi tessellations (CVTs) are Voronoi tessellations whose generators coincide with the mass centroids of the respective Voronoi regions. CVTs have become useful tools in many application domains of arts, sciences and engineering. In this work, for the first time the concept of the pe ..."
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of the periodic centroidal Voronoi tessellations (PCVTs) CVTs that exhibit certain periodicity properties in the Euclidean space is introduced and given a rigorous treatment. We discuss the basic mathematical structures of the PCVTs and show how they are related to the socalled CVT clustering energy. We
Computing 2D periodic centroidal Voronoi tessellation
 In Proceedings of the 2011 International Symposium on Voronoi Diagrams in Science and Engineering
, 2011
"... Abstract—In this paper, we propose an efficient algorithm to compute the centroidal Voronoi tessellation in 2D periodic space. We first present a simple algorithm for constructing the periodic Voronoi diagram (PVD) from a Euclidean Voronoi diagram. The presented PVD algorithm considers only a small ..."
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Cited by 4 (0 self)
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Abstract—In this paper, we propose an efficient algorithm to compute the centroidal Voronoi tessellation in 2D periodic space. We first present a simple algorithm for constructing the periodic Voronoi diagram (PVD) from a Euclidean Voronoi diagram. The presented PVD algorithm considers only a small
Centroidal Voronoi tessellations: Applications and algorithms
 SIAM REV
, 1999
"... A centroidal Voronoi tessellation is a Voronoi tessellation whose generating points are the centroids (centers of mass) of the corresponding Voronoi regions. We give some applications of such tessellations to problems in image compression, quadrature, finite difference methods, distribution of res ..."
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Cited by 375 (39 self)
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A centroidal Voronoi tessellation is a Voronoi tessellation whose generating points are the centroids (centers of mass) of the corresponding Voronoi regions. We give some applications of such tessellations to problems in image compression, quadrature, finite difference methods, distribution
Constrained centroidal Voronoi tessellations for surfaces
 SIAM J. Sci. Comput
"... Abstract. Centroidal Voronoi tessellations are useful for subdividing a region in Euclidean space into Voronoi regions whose generators are also the centers of mass, with respect to a prescribed density function, of the regions. Their extensions to general spaces and sets are also available; for exa ..."
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Cited by 72 (25 self)
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Abstract. Centroidal Voronoi tessellations are useful for subdividing a region in Euclidean space into Voronoi regions whose generators are also the centers of mass, with respect to a prescribed density function, of the regions. Their extensions to general spaces and sets are also available
Hyperbolic Centroidal Voronoi Tessellation
"... The centroidal Voronoi tessellation (CVT) has found versatile applications in geometric modeling, computer graphics, and visualization. In this paper, we extend the concept of the CVT from Euclidean space to hyperbolic space. A novel hyperbolic CVT energy is defined, and the relationship between min ..."
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Cited by 1 (1 self)
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The centroidal Voronoi tessellation (CVT) has found versatile applications in geometric modeling, computer graphics, and visualization. In this paper, we extend the concept of the CVT from Euclidean space to hyperbolic space. A novel hyperbolic CVT energy is defined, and the relationship between
Anisotropic centroidal Voronoi tessellations and their applications
 SIAM J. SCI. COMPUT
, 2005
"... In this paper, we introduce a novel definition of the anisotropic centroidal Voronoi tessellation (ACVT) corresponding to a given Riemann metric tensor. A directional distance function is used in the definition to simplify the computation. We provide algorithms to approximate the ACVT using the Llo ..."
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Cited by 45 (7 self)
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In this paper, we introduce a novel definition of the anisotropic centroidal Voronoi tessellation (ACVT) corresponding to a given Riemann metric tensor. A directional distance function is used in the definition to simplify the computation. We provide algorithms to approximate the ACVT using
Convergence of the Lloyd algorithm for computing centroidal Voronoi tessellations
 SIAM Journal on Numerical Analysis
"... Abstract. Centroidal Voronoi tessellations (CVTs) are Voronoi tessellations of a bounded geometric domain such that the generating points of the tessellations are also the centroids (mass centers) of the corresponding Voronoi regions with respect to a given density function. Centroidal Voronoi tesse ..."
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Cited by 43 (4 self)
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Abstract. Centroidal Voronoi tessellations (CVTs) are Voronoi tessellations of a bounded geometric domain such that the generating points of the tessellations are also the centroids (mass centers) of the corresponding Voronoi regions with respect to a given density function. Centroidal Voronoi
On Centroidal Voronoi Tessellation  Energy Smoothness and Fast Computation
, 2008
"... Centroidal Voronoi tessellation (CVT) is a fundamental geometric structure that finds many applications in ..."
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Cited by 33 (15 self)
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Centroidal Voronoi tessellation (CVT) is a fundamental geometric structure that finds many applications in
Probabilistic methods for centroidal Voronoi
, 2001
"... tessellations and their parallel implementations ..."
Grid generation and optimization based on centroidal Voronoi tessellations
 Appl. Math. Comput
"... www.elsevier.com/locate/amc ..."
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