منابع مشابه
Inverting Dirichlet Tessellations
Given a collection of points in the plane, one may draw a cell around each point in such a way that each point’s cell is the portion of the plane consisting of all locations closer to that point than to any of the other points. The resulting geometric figure is called a Dirichlet tessellation. An algorithm for obtaining the boundaries of the cells given the points was derived by Green and Sibso...
متن کاملAcceleration schemes for computing centroidal Voronoi tessellations
Centroidal Voronoi tessellations (CVT) have diverse applications in many areas of science and engineering. The development of e cient algorithms for their construction is a key to their success in practice. In this paper, we study some new algorithms for the numerical computation of the CVT, including the Lloyd–Newton iteration and the optimization based multilevel method. Both theoretical anal...
متن کاملFast Methods for Computing Centroidal Voronoi Tessellations
ACentroidalVoronoi tessellation (CVT) is aVoronoi tessellation inwhich the generators are the centroids for each Voronoi region. CVTs have many applications to computer graphics, image processing, data compression, mesh generation, and optimal quantization. Lloyd’s method, the most widely method used to generate CVTs, converges very slowly for larger scale problems. Recently quasi-Newton method...
متن کاملPlane-Sweep Incremental Algorithm: Computing Delaunay Tessellations of Large Datasets
We present the plane-sweep incremental algorithm, a hybrid approach for computing Delaunay tessellations of large point sets whose size exceeds the computer’s main memory. This approach unites the simplicity of the incremental algorithms with the comparatively low memory requirements of plane-sweep approaches. The procedure is to first sort the point set along the first principal component and ...
متن کاملConvergence of the Lloyd Algorithm for Computing Centroidal Voronoi Tessellations
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 tessellations may also be defined in more abstract and more general settings. Due to the natural optimization pr...
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ژورنال
عنوان ژورنال: The Computer Journal
سال: 1981
ISSN: 0010-4620,1460-2067
DOI: 10.1093/comjnl/24.2.162