Very elegant algorithm, and nicely visualized, too. Closely related to the Voronoi Diagram is the Delaunay Triangulation: http://en.wikipedia.org/wiki/Delaunay_triangulation

"For modeling terrain or other objects given a set of sample points, the Delaunay triangulation gives a nice set of triangles to use as polygons in the model. In particular, the Delaunay triangulation avoids narrow triangles (as they have large circumcircles compared to their area)."