面向雷利法则的加权Voronoi图生成方法  

A Generating Method for Weighted Voronoi Diagram Based on Reilly's Law

作　　者：康顺[1] 瞿珊珊 KANG Shun1, QU Shanshan2(1. College of Geoscience and Surveying Engineerlng,China University of Mining and Technology （Beijing） ,Beijing 100083,China; 2. School of Geosciences and Info-physics, Central South University, Changsha 410083, China)

机构地区：[1]中国矿业大学(北京)地球科学与测绘工程学院,北京100083 [2]中南大学地球科学与信息物理学院,湖南长沙410083

出　　处：《测绘通报》2018年第3期55-59,70,共6页Bulletin of Surveying and Mapping

基　　金：国家自然科学基金(41161061)

摘　　要：Voronoi图及其生成是计算几何的重要内容。针对传统栅格加权Voronoi图的权重界定局限性,以及栅格数据下Voronoi图生成的计算效率问题,本文研究了基于雷利法则的生长元规模权重和栅格欧氏距离变换权重作为综合权重条件下,规避单图幅背景栅格与每一生长元之间的距离计算,根据生长元各自距离变换图幅构建栅格加权Voronoi图,即雷利Voronoi图(Reilly Voronoi diagram,RVD)的地图代数生成方法。经试验验证,该方法生成的Voronoi图不仅完善了传统的权重因素,而且避免了因背景栅格与生长元的距离运算、判断而产生的大量计算,证明了该方法的切实可行性。Voronoi diagram and its generation are quite important in computational geometry.As to the limitation of weight defined and the generating efficiency for raster-based Voronoi diagram, taking the comprehensive conditions of generating grid scale weight and raster distance transformation weight into consideration, from multi-distance map angle, a raster-based weighted Voronoi diagram, i. e. Reilly Voronoi diagram （RVD） is proposed by map algebra method based on Reilly＇s law of retail gravitation, by which it avoids the multicomputing between background grids and generating grids in single map. Through experiment verification, it has been proved to be a feasible way for generating raster-based Voronoi diagram meanwhile improve and perfect the traditional weight factor and need not multicomputing between background grids and generating cell to generate spatial Voronoi tessellations.

关 键 词：VORONOI 雷利法则 规模权重 距离变换权重 地图代数 

分 类 号：P208[天文地球—地图制图学与地理信息工程]