Study on the Algorithm for Creating Projective Weighted Voronoi Diagrams and Competitive Triangles in GIS
GIS中投影加权Voronoi图及竞争三角形生成算法研究

Different from the former focus on the neighbor region analysis of spatial objects, the purpose of the study is to locate and analyze the competitive region of weighted objects in the Euclidian R 2 space. A new form of weighted Voronoi diagrams named projective weighted Voronoi diagram (PWVD) is introduced to resolve this problem. Based on the model of spatial tessellation of ordinary voronoi diagram and weighted Voronoi diagram, a projective spatial tessellate model is presented, which can produce competitive region in planar space. Thus the interspaces produced by the tessellation i.e. competitive triangles (CT), are examined. Next, three weighted methods: proportional, gravitational and Gaussian are applied to produce different CT respectively. The properties of the triangles and PWVD, such as the inclusion and overlap of CT and the intrusion, inter intrusion and neighbor region sharing of PWVD and CT are analyzed too. At last section, the creation algorithm of CT is discussed and the result of computer simulation shows that it is feasible to use the competitive triangles as the competitive region of the Euclidian R 2 space. From this study, it is concluded that the method might be widely used in future's GIS spatial analyses and practical applications.