Dirichlet tessellation

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A tessellation that divides a region into n subregions, one for each measurement point, with the jth subregion consisting of all points in the region that are nearer to the jth measurement point than to any other. The Dirichlet tessellation has been rediscovered many times. Other names include Voronoi polygons and Thiessen polygons. Every edge of a Dirichlet subregion separates two of the original measurement points. Joining each such pair produces a new tessellation in which the subregions are Delaunay triangles.

Dirichlet tessellation. The tessellation is defined by the locations of 22 rain-gauges in the Bolton area, England.

Subjects: Probability and Statistics.

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