An Interactive Tour of Voronoi Diagrams on the GPU

Voronoi diagrams are fundamental geometric structures that have been both deeply and widely investigated since their inception in disguise by René Descartes for analyzing the gravitational influence of stars, in the 17 century. Voronoi diagrams find countless applications in science and engineering beyond graphics as attested by the long representative, and yet non-exhaustive, list of applications reported at the web portal www.voronoi.com (eg., collision detection, path planning, meshing and surface reconstruction, etc.). The Voronoi diagram of a finite set of points } ,...., { 1 n P P S = partitions the underlying space into elementary structures called Voronoi cells that define combinatorial proximity location information. The Voronoi cell of a site is defined as the locii of points closer