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A weighted Voronoi diagram is the one in which the function of a pair of points to define a Voronoi cell is a distance function modified by multiplicative or additive weights assigned to generator points.
This diagram arises, e.g., as a model of crystal growth, where crystals from different points may grow with different speed. Since crystals may grow in empty space only and are continuous objects, a natural variation is the crystal Voronoi diagram, in which the cells are defined somewhat differently. In an additively weighted Voronoi diagram ...
As Fortune describes in ref., [1] a modified version of the sweep line algorithm can be used to construct an additively weighted Voronoi diagram, in which the distance to each site is offset by the weight of the site; this may equivalently be viewed as a Voronoi diagram of a set of disks, centered at the sites with radius equal to the weight of the site. the algorithm is found to have ...
Voronoi diagram; Metadata. This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.
Worley noise, also called Voronoi noise and cellular noise, is a noise function introduced by Steven Worley in 1996. Worley noise is an extension of the Voronoi diagram that outputs a real value at a given coordinate that corresponds to the Distance of the nth nearest seed (usually n=1) and the seeds are distributed evenly through the region.
Voronyi introduced the concept of what we today call Voronoi diagrams or tessellations. They are used in many areas of science, such as the analysis of spatially distributed data, having become an important topic in geophysics, meteorology, condensed matter physics, and Lie groups.
The general mathematical concept embodied in a Wigner–Seitz cell is more commonly called a Voronoi cell, and the partition of the plane into these cells for a given set of point sites is known as a Voronoi diagram. The construction process for the Wigner–Seitz cell of a hexagonal lattice. The cell may be chosen by first picking a lattice ...
Centroidal Voronoi tessellations are useful in data compression, optimal quadrature, optimal quantization, clustering, and optimal mesh generation. [3]A weighted centroidal Voronoi diagrams is a CVT in which each centroid is weighted according to a certain function.
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