Calculating an Approximate Voronoi Diagram using QuadTrees and Triangles

Calculating Voronoi diagrams quickly is useful across a range of fields and application areas. However, existing divide-and-conquer methods decompose into squares while boundaries between Voronoi diagram regions are often not perfectly horizontal or vertical. In this paper we introduce a novel method of dividing Approximate Voronoi Diagram spaces into triangles stored by quadtree data structures. While our implementation stores the resulting Voronoi diagram in a data structure, rather than setting each approximated point to its closest region, we provide a comparison of the decomposition time alone.