Vector-Based Realization of Area-Weight Proportional Multiplicatively Weighted Voronoi Diagrams With the ArcGIS Engine

In the geographical field, the studies have been on service areas using the Voronoi diagram and its derived models is extensive, but there is a lack of effective methods to achieve a good area-weight proportionality between generators and their exclusive regions. As a famous visualizing method, adaptive multiplicatively weighted Voronoi diagrams are able to achieve it, but are limited to displaying non-spatial data. The approach of the area-weight proportional multiplicatively weighted Voronoi diagram is proposed to solve these problems by allowing for spatial division with a point-fixed iteration approach and a vector-based multiplicatively weighted Voronoi diagram construction method from point features with spatial coordinates and references in GIS environments. It enables one to create a set of regions that is proportional to the weights of the generators. The method is successfully tested on a series of cases. The approach aims to establish a kind of spatial data model to represent demand and supply situations in real life.