Weight-proportional Space Partitioning Using Adaptive Voronoi Diagrams - Reitsma,Reindert; Trubin,S; Mortensen,E. (Geoinformatica, 2007)
Traditional application of Voronoi diagrams for space partitioning results in Voronoi regions, each with a specific area determined by the generators’ relative locations and weights. Particularly in the area of information space (re)construction, however, there is a need for inverse solutions; i.e., finding weights that result in regions with predefined area ratios. In this paper, we formulate an adaptive Voronoi solution and propose a raster-based optimization method for finding the associated weight set. The solution consists of a combination of simple, fixed-point iteration with an optional spatial resolution refinement along the regions’ boundaries using quadtree decomposition. We present the corresponding algorithm and its complexity analysis. The method is successfully tested on a series of ideal”typical cases and the interactions between the adaptive technique and boundary resolution refinement are explored and assessed.
Keywords: BIS