Sci. Form Vol. 3 (No. 2), pp. 103-111, 1988

Patterns of Weighted Voronoi Tessellation

Munekazu Sakamoto and Mikio Takagi

Center for Function-Oriented Electronics, Institute of Industrial Science, University of Tokyo, 7-22-1, Roppongi, Minato-ku, Tokyo 106, Japan

(Received September 20, 1988; Accepted December 25, 1988)

Keywords: Voronoi Tessellation, Weight, Ordered Incremental Construction, Filling

Abstract. Weighted Voronoi Tessellation (WVT) is a generalization of VT on the basis of weighted distance. An algorithm to draw a WV diagram is implemented in BASIC. It is based on filling and a "fundamental region," which is defined as the intersection of the dominance areas over all the given points having more weight than itself. Two sample applications are examined: service areas of radio stations in Japan and borders in Europe. In the latter case the weight is experimentally determined. These examples suggest how to determine the weight. Some possible applications are also mentioned.