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Voronoi diagram

Type of plane partition / From Wikipedia, the free encyclopedia

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In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. It can be classified also as a tessellation. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). For each seed there is a corresponding region, called a Voronoi cell, consisting of all points of the plane closer to that seed than to any other. The Voronoi diagram of a set of points is dual to that set's Delaunay triangulation.

Euclidean_Voronoi_diagram.svg
20 points and their Voronoi cells (larger version below)

The Voronoi diagram is named after mathematician Georgy Voronoy, and is also called a Voronoi tessellation, a Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet). Voronoi cells are also known as Thiessen polygons, after Alfred H. Thiessen.[1][2][3] Voronoi diagrams have practical and theoretical applications in many fields, mainly in science and technology, but also in visual art.[4][5]

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