Voronoi图的扩展、生成及其应用于界定城市空间影响范围

在总结国内外文献的基础上，提出了常规Voronoi图的两种扩展形式，即线的加权Voronoi图和面的加权Voronoi图，并在地理信息系统软件Are/Info的支持下，实现了基于栅格方法的若干类Voronoi图的自动构建，这种方法可以处理任意图形的线状和面状发生元情形。以界定河南省城市空间影响范围为例，尝试了发生元为离散点集的常规Voronoi图和国权Voronoi图应用于界定城市空间影响范围的试验研究。

The generalization and construction of Voronoi diagram and its application on delimitating city's affected coverage

Voronoi diagram is a method of partitioning a space, which has powerful potential in many fields. This paper presents two regular Voronoi diagrams: line weighted Voronoi diagram and area weighted Voronoi diagram. Owing to the difficulty of constructing regular Voronoi diagram based on vector method, it develops a raster based approach, which employs the Arc/Info, to compute a few regular Voronoi diagrams. Our programs can construct the following Voronoi diagrams: the ordinary Voronoi diagram, line Voronoi diagram, area Voronoi diagram, and the multiplicatively or additively or compoundly weighted Voronoi diagram generated by points or any figures(lines or polygons), in the plane. As there are a huge amount of grids, computing time in constructing line or polygon weighted Voronoi diagram is a bit more, and this problem is just the future research effort. Lastly, it makes an attempt to apply ordinary Voronoi diagram and weighted Voronoi diagram for delimitating city's affected coverage in Henan province whose experimental result shows that weighted Voronoi diagram is an efficient technique for delimitating economic object's affected coverage.