A faster algorithm for weighted distance tiles

Dirichlet tesselation is commonly used in the biological sciences to model competition between individuals. A recognized weakness of this approach, however, is the lack of ability to consider individual attributes such as size or height. The concept of weighted distance tiles, which would address this weakness, was initially developed by F. Aurenhammer et al. (1984) and an algorithm using inversive geometry described. The authors develop an algorithm which is simpler and more effective at determining these complex tessellations and is organized to make maximum use of the graphics concept of early rejection. A sequence of improving approximations to the final tile is obtained. Three diagrams were produced by an implementation of this algorithm and depict (1) vertices whose weights are all equal, (2) some vertices with equal weights and some vertices with unequal weights, and (3) vertices with unequal weights