Open source implementation of the Multiplicatively Weighted Voronoi Diagram as a TerraView plugin

Given a point set the Voronoi diagram associates to each point all the locations in a plane that are closer to it . This diagram is often used in spatial analysis to divide an area among points. In the ordinary Voronoi diagram the points are treated as equals and the division is done in a purely geometrical way. A weighted Voronoi diagram is defined as an extension of the original diagram. The weight given usually relates to some variable property of the phenomenon represented by each point. The weighted distance is then computed as a function that depends both on the weight and on the euclidean distance. This article describes a multiplicatively weighted Voronoi diagram implementation as an open source plugin for TerraView. The algorithm used computes an approximation of the diagram using multipolygons to represent each point’s area. This choice avoids the voids that might appear in most of the implementations that focus on finding the intersections and scales well in memory.