GIS中投影加权Voronoi图及竞争三角形生成算法研究

Study on the Algorithm for Creating Projective Weighted Voronoi Diagrams and Competitive Triangles in GIS

在 GIS空间分析中 ,为了定位和分析空间区域中含权对象的竞争区域 ,提出了加权 Voronoi图的新形式——投影加权 Voronoi图 ,该图是从常规 Voronoi图和一般加权 Voronoi图的平面剖分模型出发 ,首先引入了能够产生空间竞争区域的空间投影剖分模型 ,然后由此形成空间中的三角形空隙 ,即竞争三角形 ,同时归纳了形成竞争三角形的 3种加权方式 ,并分析了其生成算法和特性 ,计算机的模拟结果显示 ,将竞争三角形作为空间的竞争区域是可行的 ,最后论述了它在 GIS空间分析中广泛的应用前景。

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.