Voronoi Diagrams

The Voronoi diagram (also called a Dirichlet tessellation or a set of Thiessen polygons) is a partition of a metric space such that we associate all locations in that space with the closest object in that space, based on the specified metric. Thus, each object is the generator of a cell or tile, and the set of tiles covers the space or map.

In the simplest case, we are given a set of points S in the Euclidean plane, which are the Voronoi generators. Each generator, s, has a Voronoi cell, V(s), consisting of all points closer to s than to any other generator. The cell boundaries of the Voronoi diagram are all the points in the plane that are equidistant to two generators, and the ...