update: for a cool usage of Delaunay triangulation, see my isolining package for ActionScript 3
The Delaunay triangulation was invented in 1934 by Boris Delaunay. According to Paul Bourke,
The Delaunay triangulation is closely related geometrically to the Direchlet tesselation also known as the Voronoi or Theissen tesselations. These tesselations split the plane into a [...]