High Quality Content by WIKIPEDIA articles! In mathematics, a weighted Voronoi diagram in n dimensions is a Voronoi diagram for which the Voronoi cells are defined in terms of a distance defined by some common metrics modified by weights assigned to generator points. The multiplicatively weighted Voronoi diagram is defined when the distance between points is multiplied by positive weights. In the plane under the ordinary Euclidean distance, the multiplicatively weighted Voronoi diagram is also called circular Dirichlet tessellation and its edges are circular arc and straight line segments. A Voronoi cell may be non-convex, disconnected and may have holes. This diagram arises, e.g., as a model of crystal growth, where crystals from different points may grow with different speed. Since crystals may grow in empty space only and are continuous objects, a natural variation is the crystal Voronoi diagram, in which the cells are defined somewhat differently.

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