# 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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A structure useful in capturing the proximity relationships among points distributed in two-dimensional space is the Voronoi diagram.
4 (with a different constant) for summands which depend, not on the [kappa] nearest neighbours, but on the the Voronoi cells of the Poisson points; see the arguments in Section 6.
Features include use of spherical and polyhedral objects of various shapes for particle approximation, random close packing modeling, Voronoi diagrams/Delaunay triangulations, flexible container geometry, and data import/export and compatibility with SIMAGIS image analysis software.
Then we describe the computation of spatial relationships, including qualitative topology and Voronoi diagrams.
Some of the existing optimization methods in this area rely on Voronoi partitioning.
Aiming for the shortest distance between the MCV's working place and the supply station, the idea of Voronoi [11] can be used here to allocate the working range of MCVs that belong to different supply stations, and realize the goal of reducing the power consumption of the moving period.
The random geometry of the particles, which is mostly provided by Voronoi tessellation, [8], helps to simulate crack patterns and their propagation.
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.
Belowground root biomass was evaluated using monoliths from Voronoi polygons, which is the space defined by the half distances between the sampled plant and its neighbours (Saint-Andre et al.
MoGraph Enhancements: Added workflow capabilities in Voronoi Fracturing and an all-new Sound Effector.
The new release includes the new ProRender that reportedly uses state-of-the-art graphics cards to create renderings; the improved Viewport, as per the company release, makes it possible to assess depth of field and object reflections in real-time; and the expanded Voronoi Fracture tool reportedly lets the user shatter objects even more precisely and realistically.
The borders of study areas were defined by Voronoi Diagrams within Euclidean distance, which defines a cluster of surveyed points (surveyed points within villages) to the surrounding non-surveyed points (Aurenhammer 1991).

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