基于GIS的任意发生元Voronoi图逼近方法

许多地理问题的空间分析中需要采用Voronoi图，但是目前我们尚缺乏一些简单的易于实现的构建任意发生元Voronoi图的方法，也缺乏一个能直接生成任意发生元Voronoi图的软件，为此我们提出了一种基于GIS的构建任意发生元的未加权Voronoi图的逼近方法。首先用有限点来逼近原始发生元，然后构建这些点发生元Voronoi图，最后消除那些属于同一发生元的顶点和边，即得到原始发生元的逼近的Voronoi图。在该算法的具体实现过程中，充分利用了现有GIS软件可以生成点发生元Voronoi图的特性和处理空间数据的能力。试验结果表明，这种方法可以生成未加权的任意形状发生元的逼近Voronoi图，能满足地理问题空间分析的需要。如地理客体可以是点状地理客体(城市、县城、交通枢纽、商业中心和金融中心等)、线状地理客体(交通运输线、经济地带和河系等)、面状地理客体(经济区、公园和绿地等)或者它们的组合，它们的空间影响范围或空间服务范围都可以采用Voronoi图来界定。

GIS-based Approximation Algorithm for Constructing Voronoi Diagrams with General Generators

Voronoi diagram is a very useful tool for spatial analysis of many geographical problems. However, we now still lack a simple approach or a software to construct Voronoi diagram with general generators (such as curves and areas), and so this paper presents a GIS-based Approximation Algorithms for Constructing Voronoi Diagrams with general generators. We first replace each generators with a finite number of points that approximate the original generators, then the Voronoi diagrams for these points are constructed, and superfluous Voronoi edges and superfluous Voronoi vertices are finally removed. Thus we can get the approximation of Voronoi diagram with original generators. In practical implementation, we fully employed the module of ARCGIS software with a fast and robust algorithm to construct the ordinary Voronoi diagrams, and also some other modules of it. The result of experiment shows that it is an efficient and effective method for constructing Voronoi diagram with generators of any form figures, and it is a promising approach for the need of geographical research issues. For example, Voronoi diagrams by this approach can be represented as he spatial effect area for a variety of geographical objects with the different forms, such as points (cities, towns, transport junctions, trade centers), and lines (transport lines, industrial belts, river system), and areas (economic regions, parks and green lands), and so forth.