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。     

基于钻孔点集Voronoi 图的矿产储量新算法

该文在分析平面点集Voronoi图特性及其生成算法的基础上,针对传统矿产储量计算方法的不足,提出了一种新的方法。该法以钻孔平面点集的Voronoi图为基础,利用Voronoi多边形的势力范围特性,实现了任意区域内矿床体积与矿产储量的计算。并给出了以Delphi编程实现的系统界面与计算实例,讨论了基于钻孔三维点集的Voronoi体进行矿产品位与经济可采性分析的前景。     

Accuracy of quantized Voronoi diagrams

Quantization of spatial objects, which usually means vector‐to‐raster conversion in GIS and remote sensing, is a basic operation used for handling spatial data from data creation to visualization. Since quantization is an approximation of spatial objects, it inevitably yields errors in measuring their properties such as area, perimeter, diameter, and so forth. This paper discusses the accuracy of a quantized Voronoi diagram, a spatial tessellation generated from a set of points. A measure is proposed to evaluate the accuracy of the area of Voronoi regions calculated after quantization. In one‐dimensional space the measure is expressed as an explicit function of the expected number of generators in a cell. In two‐dimensional space, on the other hand, the measure is defined by an implicit function, whose approximation is derived in an explicit form. These functions permit us to evaluate the accuracy of quantization in relation to the size of lattice cells and the density of Voronoi generators. This leads to an appropriate choice of a lattice to keep the quality of a quantized Voronoi diagram at a desirable level.     

基于道路网络的商业网点市场域分析

社会经济活动中人们的空间行为往往是基于道路网络来实现的。但是,目前多数研究都假设地理空间是一个均质空间,采用基于平面欧氏距离的空间分析方法,这是有局限的。本文阐述了基于网络距离的网络Voronoi图基本概念和实现方法,以武汉市商业零售连锁企业为例,分别采用基于欧氏距离的普通Voronoi图方法和基于网络距离的网络Voronoi图方法来确定商业零售网点的市场域,结果表明武汉市主城区商业网点市场域较小、主城区外围市场域较大。市场域大小与城市路网密度呈现一定相关关系,路网密度高、市场域小,路网密度低、市场域大。两种方法的计算结果存在一定差异,差异大小与路网密度有关,路网密度大、差异小,路网密度小、差异大。这表明在路网密度大的情况下,可以采用普通Voronoi图粗略地模拟商业网点的市场域。     

A comparison of neighbourhood relations based on ordinary Delaunay diagrams and area Delaunay diagrams: an application to define the neighbourhood relations of buildings

ABSTRACT

The aim of this article is to describe a convenient but robust method for defining neighbourhood relations among buildings based on ordinary Delaunay diagrams (ODDs) and area Delaunay diagrams (ADDs). ODDs and ADDs are defined as a set of edges connecting the generators of adjacent ordinary Voronoi cells (points representing centroids of building polygons) and a set of edges connecting two centroids of building polygons, which are the generators of adjacent area Voronoi cells, respectively. Although ADDs are more robust than ODDs, computation time of ODDs is shorter than that of ADDs (the order of their computation time complexity is O(nlogn)). If ODDs can approximate ADDs with a certain degree of accuracy, the former can be used as an alternative. Therefore, we computed the ratio of the number of ADD edges to that of ODD edges overlapping ADDs at building and regional scales. The results indicate that: (1) for approximately 60% of all buildings, ODDs can exactly overlap ADDs with extra ODD edges; (2) at a regional scale, ODDs can overlap approximately 90% of ADDs with 10% extra ODD edges; and (3) focusing on judging errors, although ADDs are more accurate than ODDs, the difference is only approximately 1%.     

Combining spatial data with survey data improves predictions of boundaries between settlements

Studies of land-use change often require the combination of socioeconomic survey data with spatially continuous maps of land-cover change. One approach is to define maps of land ownership, assuming that all land-use change can be attributed to the owners or managers of each parcel of land. Unfortunately, records of administrative boundaries between towns and villages are commonly unavailable in developing countries and prohibitively costly or time consuming to map for individual projects. However, point locations of the settlements themselves can be obtained easily from existing maps or remotely-sensed imagery. In this paper we compare three methods – circular buffers, unweighted Voronoi polygons (sometimes referred to as Thiessen polygons) and multiplicatively weighted Voronoi polygons – for estimating boundaries between villages in an agricultural landscape in West Africa. The benefits and limitations of each approach are discussed, and their accuracy assessed using 98 independently collected GPS coordinates of village boundaries. We present a novel method for generating and optimising weights for multiplicatively weighted Voronoi polygons using survey data of village sizes from a subset of villages. By using both spatial information and survey data from villages, we show that multiplicatively weighted Voronoi polygons outperform other methods of predicting village boundaries, and increase the correlation coefficient between surveyed village area and mapped areas from 0.18 to 0.68 compared with more commonly used unweighted Voronoi polygons. Our method of weighting Voronoi polygons can be implemented with data and software commonly available to researchers and non-governmental organisations.     

一种用于界定经济客体空间影响范围的方法——Voronoi图

经济客体的空间影响范围界定十分复杂,但在区域规划和城市规划中有着重要的理论和实际意义。该文提出可采用Voronoi图方法用于经济客体的空间影响范围界定,介绍了Voronoi图的基本原理和其若干扩展,编写了生成Voronoi图的程序,最后以城市为例探讨了Voronoi图在经济客体空间影响范围界定中的应用。     

Calculating on a round planet

Despite incontrovertible scientific evidence to support a round Earth, GIS software implementation typically models the Earth with flat map projections. This choice has consequences that vary from mild to severe. This paper explores solutions that range from moderate measures to correct for map projection errors to radical revisions of standard practice that place all calculations on the ellipsoid. On examination, the best practice requires a distinct projection choice for each geometric operation. Multiple reasons, from the technical to ethical, justify revised practices and increased vigilance for the errors induced by inappropriate projections.     

Error assessment of grid-based flow routing algorithms used in hydrological models

This paper reports an investigation on the accuracy of grid-based routing algorithms used in hydrological models. A quantitative methodology has been developed for objective and data-independent assessment of errors generated from the algorithms that extract hydrological parameters from gridded DEM. The generic approach is to use artificial surfaces that can be described by a mathematical model, thus the ‘true’ output value can be pre-determined to avoid uncertainty caused by uncontrollable data errors. Four mathematical surfaces based on an ellipsoid (representing convex slopes), an inverse ellipsoid (representing concave slopes), saddle and plane were generated and the theoretical ‘true’ value of the Specific Catchment Area (SCA) at any given point on the surfaces could be computed using mathematical inference. Based on these models, tests were made on a number of algorithms for SCA computation. The actual output values from these algorithms on the convex, concave, saddle and plane surfaces were compared with the theoretical ‘true’ values, and the errors were then analysed statistically. The strengths and weaknesses of the selected algorithms are also discussed.     

A discrete square global grid system based on the parallels plane projection

We developed a direct partitioning method to construct a seamless discrete global grid system (DGGS) with any resolution based on a two‐dimensional projected plane and the earth ellipsoid. This DGGS is composed of congruent square grids over the projected plane and irregular ellipsoidal quadrilaterals on the ellipsoidal surface. A new equal area projection named the parallels plane (PP) projection derived from the expansion of the central meridian and parallels has been employed to perform the transformation between the planar squares and the corresponding ellipsoidal grids. The horizontal sides of the grids are parts of the parallel circles and the vertical sides are complex ellipsoidal curves, which can be obtained by the inverse expression of the PP projection. The partition strategies, transformation equations, geometric characteristics and distortions for this DGGS have been discussed. Our analysis proves that the DGGS is area‐preserving while length distortions only occur on the vertical sides off the central meridian. Angular and length distortions positively correlate to the increase in latitudes and the spanning of longitudes away from a chosen central meridian. This direct partition only generates a small number of broken grids that can be treated individually.     

基于互联网信息的城市商业游憩网点空间竞争域划分研究

提出了一种基于互联网信息的空间竞争域划分方法。在Voronoi图的模型中尝试以网络平台数据作加权因子,使空间竞争域体现互联网中的消费者偏好差异,通过对加权Voronoi图的类型划分和地理学解释,描述竞争环境的空间特征。以北京市健身俱乐部为例,选择大众点评网、爱帮等网络平台信息作为权重因子,构建样本网点的传统Voronoi、互联网信息加权Voronoi计算模型并对比边界线、面积等空间特征分析的结果表明:互联网信息对城市商业游憩网点的空间竞争力产生着不同的影响强度,对Voronoi图空间特征的分类和地理解释可以指示商业网点跨越距离阻碍的消费吸引力及竞争差异,弥补传统加权方法未考虑消费者偏好和购物习惯而对竞争域划分表达不足的缺点。     

Zone design of specific sizes using adaptive additively weighted Voronoi diagrams

Territory or zone design processes entail partitioning a geographic space, organized as a set of areal units, into different regions or zones according to a specific set of criteria that are dependent on the application context. In most cases, the aim is to create zones of approximately equal sizes (zones with equal numbers of inhabitants, same average sales, etc.). However, some of the new applications that have emerged, particularly in the context of sustainable development policies, are aimed at defining zones of a predetermined, though not necessarily similar, size. In addition, the zones should be built around a given set of seeds. This type of partitioning has not been sufficiently researched; therefore, there are no known approaches for automated zone delimitation. This study proposes a new method based on a discrete version of the adaptive additively weighted Voronoi diagram that makes it possible to partition a two-dimensional space into zones of specific sizes, taking both the position and the weight of each seed into account. The method consists of repeatedly solving a traditional additively weighted Voronoi diagram, so that each seed's weight is updated at every iteration. The zones are geographically connected using a metric based on the shortest path. Tests conducted on the extensive farming system of three municipalities in Castile-La Mancha (Spain) have established that the proposed heuristic procedure is valid for solving this type of partitioning problem. Nevertheless, these tests confirmed that the given seed position determines the spatial configuration the method must solve and this may have a great impact on the resulting partition.     

Revisiting John Snow's map: network-based spatial demarcation of cholera area

Dr. John Snow's cholera map is known as one of the pioneering examples of an epidemiology map, illustrating the spatial distribution of the victims from the cholera outbreak. This article revisits his map and expands on his attempt at visualizing the distribution of the victims by focusing on spatial demarcation using the sphere of influence along the street network by applying two analytical methods that are designed for analysis of network space. First, the article generates a network-based Voronoi diagram of the water pumps in the map that encompasses Snow's original version of the equidistance line that was drawn around a single pump. The article then presents a new, revised equidistance line that better reflects the circumstances around the time of the outbreak. This is followed by the construction of another set of boundaries derived by the application of a network-based clumping method. Comparing the demarcation lines produced with the two methods shows a sphere of influence which was unclear when using the network Voronoi diagram alone. Results from the analysis using the clumping method also confirm some of Snow's observations on the spatial distribution of the victims.     

非均质栅格Voronoi图生成方法研究

提出一个非均质栅格Voronoi图的生成方法.假定在Voronoi领域扩张中,经过每个栅格的距离权值不相等.由于非均质栅格Voronoi图生成复杂,提出了一种基于A*启发式空间搜索确定每个栅格的归属来产生Voronoi区域的方法.讨论了非均质栅格Voronoi图的基本定义、启发式函数确定、具体生成方法等.利用C#语言实现了所提出的方法,并分析了该方法的时间复杂度.但该方法仅适合于简单点发生元情况,在面向复杂发生元的情况下,需进一步研究更有效的方法.     

Quantifying positional error induced by line simplification

This study examines the effects of line simplification on the positional accuracy of linear features. The goal is to quantify the relation between the level of simplification and the degree of positional error, so that users can choose appropriate levels of simplification that will yield results meeting specific accuracy criteria. The study focuses on the Douglas-Peucker line simplification algorithm and examines both natural and anthropogenic features (streams and roads) derived from United States Geological Survey Digital Line Graphs. Results show that error can be modelled at an aggregate level using cumulative frequency curves and their confidence limits. This makes it possible to identify the level of simplification that eliminates the largest number of vertices while still attaining a specific positional accuracy standard. A simple implementation strategy is described in which an optimal level of simplification is identified and simplification is applied selectively for different lines. The study shows that management of simplification induced error is possible using simple tools well within the reach of GIS users.     

New method for positional quality control in cartography based on lines. A comparative study of methodologies

This article describes a set of new metrics for evaluating the positional accuracy of lines to apply a positional control to cartographic databases. In the same way as traditional points-based studies, control based on lines compares the positions between the lines (one from a given database to be controlled and the other from a more accurate independent control database). The proposed method is based on vertex displacements and their influence on adjacent segments. The new methodology which applies these metrics is called ‘vertex influence method’. It also includes an analysis for detection of systematic displacements and a variability value of displacements based on the accuracy of the lines. All the proposed metrics are applied to a real case made up of more than 180 km of roads from the two databases. By means of this study we also compare the results obtained from the main traditional methodologies. This study has revealed the viability of the use of this method to obtain an accuracy value of positional cartographic products.     

基于网络加权Voronoi图分析的南京市商业中心辐射域研究

道路网络在城市社会和经济活动中发挥重要作用.它是联系商业中心与需求间的桥梁.道路系统的更新与变化必然会对它们的关联产生影响Voronoi图足划分势力空间的有效工具,基于道路网络分析构建的加权Voronoi图可以模拟城市商业中心功能辐射的实际情形.本文给出了基于道路网络分析的Voronoi图和加权Voronoi图构建方法.通过对各种Voronoi图的比较分析,认为基于网络路径时间分析构建的加权Voronoi面域图在商业中心辐射域模拟中最为有效.将空间相互作用和断裂点理论与网络加权Voronoi面域图相结合.模拟不同交通条件下南京市商业中心辐射域空间格局及其需求覆盖变化,并提取了辐射域的覆盖面积、覆盖人口、最远辐射路径距离和平均辐射路径距离等信息.对商业中心的地铁邻近度与其辐射域的扩张面积进行相关分析.采用域邻接矩阵描述空间划分平衡与不平衡之间的相互转变过程,可分析道路系统变更后商业中心之间空间竞争的变化趋势.分析结果表明商业中心的地铁邻近度与辐射域的扩张具有较大的相关性,快速轨道交通在商业中心空间竞争中发挥关键作用.     

基于局部聚类的网络Voronoi图生成方法研究

提出一种将网络约束下的Voronoi和空间聚类相结合的方法,通过构造局部的聚类分析方法对网络边进行加权,根据实际的点过程性质可以把权重定义为加权或者乘权,进行标准化后与道路段本身长度融合进行计算,依此生成网络Voronoi图,以期理解城市街道的空间特性。以武汉市江汉区为例,对城市网格管理系统产生的城市事件进行算法验证,结果表明,该方法提供了一种灵活的网络约束下的服务区域划分工具,可用于基于网络空间点过程影响下的服务区划分,也可用于系统性地定量刻画城市管理的动态特性。     

Automated building generalization based on urban morphology and Gestalt theory

Building generalization is a difficult operation due to the complexity of the spatial distribution of buildings and for reasons of spatial recognition. In this study, building generalization is decomposed into two steps, i.e. building grouping and generalization execution. The neighbourhood model in urban morphology provides global constraints for guiding the global partitioning of building sets on the whole map by means of roads and rivers, by which enclaves, blocks, superblocks or neighbourhoods are formed; whereas the local constraints from Gestalt principles provide criteria for the further grouping of enclaves, blocks, superblocks and/or neighbourhoods. In the grouping process, graph theory, Delaunay triangulation and the Voronoi diagram are employed as supporting techniques. After grouping, some useful information, such as the sum of the building's area, the mean separation and the standard deviation of the separation of buildings, is attached to each group. By means of the attached information, an appropriate operation is selected to generalize the corresponding groups. Indeed, the methodology described brings together a number of well-developed theories/techniques, including graph theory, Delaunay triangulation, the Voronoi diagram, urban morphology and Gestalt theory, in such a way that multiscale products can be derived.