Voronoi diagrams´ eccentricity measurement and application

Voronoi diagrams own very special characteristics and have been introduced into GIS field for spatial relation description, buffer analysis, spatial interpolation, spatial information visualization, measurement of spatial distribution. This paper proposes the concept of Voronoi diagrams´ eccentricity (VDE), i.e. VDE = d²/S, where the d is the distance from generator´s geometric center to the Voronoi polygon´s gravitational center, S is the area of the Voronoi polygon. Furthermore, the adjacent eccentricity direction (AED) is defined to sense VDE´s direction in different adjacent generator. VDEs and AEDs can reflect the spatial distribution´s uniform, density change and cluster outline feature. A preliminary experiment based on VDE and AED for extracting the outlines of clusters has been done and proves the method is feasible and meaningful.