Recursive Algorithm for Determination of Proximal (Thiessen) Polygons in Any Metric Space

A new and recursive algorithm for determining proximal polygons is based on quadtree concepts. The algorithm can use any distance metric, and produces a quadtree of the image of the proximal polygons. This can be converted to vector form, or be incorporated directly into a quadtree-based geographic information system, in order to solve a number of closest-point problems. The algorithm can also produce the Delaunay triangulation, which is the dual of the proximal polygons. Empirically, the running time of the algorithm is proportional to the number of centers raised to the 1.6 power.