Left: 10 randomly selected points in the square (the filled circles), the associated Voronoi cells (the polygons), and the centers of mass of the Voronoi cells with respect to a constant density (the open circles); note that the generating points and centroids do not coincide. Right: a 10 point centroidal Voronoi tessellation (CVT) of the square; note that open circles are both the generating points of the Voronoi tessellation and the centroids of the Voronoi cells.

Left: the Voronoi tessellation of 256 uniformly distributed randomly selected points in the square. Right: a 256-point CVT of the square corresponding to a uniform density.

Left: the Voronoi tessellation of 256 nonuniformly distributed randomly selected points in the square. Right: a 256-point CVT of the square corresponding to a nonuniform density.