Voronoi diagram

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Voronoi diagram

(mathematics, graphics)
(After G. Voronoi) For a set S of points in the Euclidean plane, the partition Vor(S) of the plane into the voronoi polygons associated with the members of S. Vor(S) is the dual of the Delaunay triangulation of S.
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In [18], a first-order Voronoi tessellation was used in conjunction with the Lagrange multiplier method to perform localization in a WSN.
A Voronoi tessellation of randomly distributed points on a plane is used as a template.
In order to assess the spatial uniformity of the particles, we propose in this study to process the TRISO particles in a 3-dimensional (3D) coordinate system and assess the uniformity of the TRISO particle distribution using the geometric metrics extracted from the Voronoi tessellation and Delaunay triangulation.
Thirdly, laboratory-scale microflexible rolling experiments are carried out to further verify and validate this novel model which produces more accurate predictions than the multilinear isotropic hardening model and the Voronoi tessellation based model.
Voronoi tessellation is a simple but effective geometric representation for charactering the microstructures of the composite.
AREPO [16], the code behind the simulation, uses an unstructured Voronoi tessellation of the simulation volume, where the mesh-generating points of this tessellation are moved with the gas flow.
The random geometry of the particles, which is mostly provided by Voronoi tessellation, [8], helps to simulate crack patterns and their propagation.
Emphasis is given in the inadequacy of classical spatial Voronoi tessellation for coverage purposes, compared to the proposed space partitioning technique, which takes into account this heterogeneity.
A centroidal Voronoi tessellation has been found.Since Voronoi diagram construction algorithms can be highly non-trivial, especially for inputs of dimension higher than two, the steps of calculating this diagram and finding the centroids of its cells may be approximated by a suitable discretization in which, for each cell of a fine grid, the closest site is determined, after which the centroid for a site's cell is approximated by averaging the centers of the grid cells assigned to it.
To further explain the structural features of SOZs at different deformation stages of ZrCu metallic glass, the Voronoi tessellation method was used [30].
Therefore, the Voronoi tessellation may be used alternatively to the Delaunay triangulation.
3 are defined as follows: Consider the Voronoi tessellation of the unit sphere [S.sup.2] with respect to the point field {[[theta].sub.1], ..., [[theta].sub.m], -[[theta].sub.1], ..., -[[theta].sub.m]}.