Weighted Voronoi diagram

[1] In the plane under the ordinary Euclidean distance, the multiplicatively weighted Voronoi diagram is also called circular Dirichlet tessellation[2][3] and its edges are circular arcs and straight line segments.

A Voronoi cell may be non-convex, disconnected and may have holes.

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.

In the plane under the ordinary Euclidean distance this diagram is also known as the hyperbolic Dirichlet tessellation and its edges are arcs of hyperbolas and straight line segments.

[1] The power diagram is defined when weights are subtracted from the squared Euclidean distance.