Population landscape: a geometric approach to studying spatial patterns of the US urban hierarchy

We present a geometric and graphic approach to studying spatial patterns of urban hierarchy in the US. The multiplicatively weighted Voronoi diagram is found to be effective for visualizing theoretical regions delineated by socio‐economic variables. The population landscape of the continental US demonstrates overall and stepwise patterns reflecting population, neighborhood and distance, with overwhelming influence from huge metropolitan areas. Stepwise exploration and cluster analysis of the spatial pattern reveal an urban hierarchy. Attributes and arrangement are the two important factors of urban hierarchy, with attribute having a stronger local influence and arrangement having a stronger global influence. The study also presents a variation of Zipf's law to visualize the rank‐size distribution from tabular and statistical space to map space.     

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。     

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.     

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.     

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。     

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。     

春运人口流动透视的转型期中国城市网络结构

基于春运人口流动大数据,选取对外联系度、优势流、城市位序-规模分析等方法对转型期中国城市网络特征进行分析。结果显示：① 城市网络层级结构中蕴藏着位序-规模规律,但与理想的帕累托分布有所区别,城市规模彼此差异相对较小;② 空间距离与城市等级在城市网络联系中发挥支配性作用,保证了城市网络的层级性与有序性;③ 中国城市网络核心联系呈现“两横三纵”特征,该特征与铁路大动脉的空间分布高度吻合;④ 东部地区城市网络联系更加密切,而西北、西南地区则相对稀疏,基本上以“胡焕庸线”为界,而“兰新线”是突破这一限制的潜在力量;⑤ 中国东北地区未形成明显的区域性中心,城市联系形成带状网络;⑥ 华北与华南地区的“灯下黑”现象值得警惕,缓解这一问题的可行办法是核心城市功能的对外疏散,加强核心城市与周边城市之间的联系;⑦ 带状区域发展或许将成为未来中国区域经济发展的流行模式和中坚力量。总体上看,针对于揭示转型期中国城市网络结构特征,春运人口流动数据具有一定的研究价值,是城市与人口研究领域一个值得深入挖掘的重要数据源。     

基于Voronoi图剖分的区域旅游中心城市体系——以苏浙沪地区为例

在区域范围的城市旅游体系中,引入"中心地的中心性"概念,可以在这种旅游性的空间网络中考察城市地位的相对重要性,划分出城市的等级层次,判断出不同级别的中心城市,更可以进一步得到区域空间的城市旅游构成关系.Voronoi图在地理学中是一种利用中心地的中心性广泛用于空间分割、空间邻域查找的空间剖分方法.引入这种方法,以苏浙沪地区为例,在25个地级以上城市中,利用Voronoi图的空间分割原理,找出不仅具有规模性,而且具有空间组织功能的旅游中心城市.     

1947年中国南海断续线精准划定的地形依据

基于1947年中国政府内政部印制的1:400万《南海诸岛位置图》,采用地理信息系统及数字化仿射变换精准测量出11段断续线的地理坐标,同时利用4.4万多个实测水深点数据建立南海海底三维地形模型,通过叠加分析获得了1947年南海断续线所在位置的海底地形特征。结果显示：断续线东长西短,间距东西大、南北小,其走向、形态与下伏地形特征相符合,主要分布在大陆坡和大陆架上;并基于断续线下伏海底地形分析,推断出当时断续线划定时可能遵循如下依据：① 在浅海盆地、海峡处采用“等距离中间线”原则进行划分;② 在具有明显地形变化处沿海槽坡麓或海槽槽沟中线进行划分;③ 在西南部陆坡陆架区,结合岸线走向及下伏地形特征进行划分。     

Voronoi Diagrams and Spatial Analysis of Crime

A range of spatial analyses are used in the field of crime mapping, such as kernel density estimation, Ripley's K-function, and spatial autocorrelation, but there is limited use of Voronoi diagrams (VDs). The goal of this article is to contribute to the spatial analysis of crime through the use of VDs. We use four years of commercial robbery data from Campinas, Brazil, and employ several VD techniques: (1) We analyze crime concentrations through the properties of VDs—area and number of vertices—and coverage curve; (2) we introduce a new crime geovisualization with VD in three dimensions; and (3) we apply a network VD technique to crime analysis. The results demonstrate associations between these VD techniques and the ability of the researcher to recognize crime patterns associated with crime concentration, crime along pathways, and the highly regularized distribution of crime in limited areas spatially.     

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。     

沈阳城市应急避难场所的识别、空间格局与服务功能

以沈阳市为例,运用高分辨率遥感影像识别城市应急避难场所,采用空间插值、波段集统计等方法刻画应急避难场所空间分布及其与人口的空间匹配性,通过栅格成本分析和加权Voronoi图等方法测算空间可达性并划分其服务区范围。研究表明:(1)沈阳市应急避难场所分布呈现出"小集聚、大分散"的基本格局,与人口分布的空间匹配性差;(2)应急避难场所可达性表现出空间异质性,大型用地对整体格局起到主要塑造作用;(3)研究区域可划分为14个较为明确的应急避难场所服务区,不同服务范围在空间上存在大小、数量和构成上的差异。最后,从城市安全视角对沈阳市应急避难场所的空间布局提出优化建议,为政府部门决策提供科学依据与政策参考。     

行为网络视角下区域空间结构研究进展

论文系统综述了区域空间结构研究的多种视角与分析方法及其发展脉络,认为行为视角下区域空间结构的研究经历了从行为汇总到行为交互、地方属性到网络联系的转变过程。早期的空间结构研究多通过行为汇总与地方属性的分析,聚焦于区域内空间单元的属性相关性,具体包括社会区、同质区与空间邻域等视角与方法。近期研究则逐步发生了“关系转向”与“网络转向”,更多从行为交互与网络联系出发,分析区域的网络结构和空间格局,包括传统的功能区分析、社群结构分析、核心—边缘结构研究等。通过比较不同分析视角,论文最后提出未来城市与区域空间结构研究应加深对行为交互与网络联系的理解,加强对行为空间网络的中观尺度结构分析,在方法应用上需要避免“方法决定论”,并探索适用于多尺度、多要素的多层网络分析视角与方法。     

Polygon Characterization With the Multiplicatively Weighted Voronoi Diagram*

Many landscape features are represented as polygons in GIS. This paper characterizes polygon shapes with the multiplicatively weighted Voronoi (MW‐Voronoi) diagram and improves its understanding. The MW‐Voronoi diagram's composition is implemented with topological overlay, growth simulation, and vertex calculation methods. The decomposition is done by reversing a polygon to MW‐Voronoi point pairs by segment. It is a new approach to record, characterize, and compare polygons with form and process. The implementation also serves as a geographic education and visualization tool. Applications of the methods are presented with precipitation, fire polygon, and population change data.     

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.     

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.     

公路客流视域下中国城市网络的空间集聚、层级体系与演化模式

借助公路客流大数据,研究中国公路客运交通网络的空间分布格局与集聚机理,以系统解析区域城市网络“多中心、多层级、多节点”的层级体系与演化模式。研究显示,中国公路客运交通网络总体上呈现出区域性中心集聚分布格局,公路客运联系的距离衰减和地理邻近分布特征很好体现了地理学的空间相关性,公路客运联系的区域性空间集聚和层级叠套现象则是地理学空间异质性分布规律的表征。对中国公路客运交通网络进行省域尺度社区探测,出现类似省级行政区划的社区划分,更大区域尺度的社区探测则出现类似全国七大地理分区的空间划分,反映出公路客运交通联系的集聚特性是以各级中心城市为核心的区域性空间集聚分布。随着区域发展阶段和经济发展水平的提升,中国城市网络由西向东明显呈现出单中心到多中心、弱层级到多层级、少节点到多节点的渐进式空间演化过程。西北、东北、湖北、山西、江西、广西和云南等社区为“单中心、弱层级、少节点”的网络体系,广东、成渝和山东社区呈现“双中心、多层级、多节点”的网络结构,沪苏皖社区则发育出最为成熟的“多中心、多层级、多节点”城市网络体系。研究以空间换时间,将区域系统的城市网络演化过程划分为节点城市发育、地方中心增长、省...     

湖南茶陵县域生态空间网络稳定性识别与重构策略

县域是国土空间规划与管理的基本单元,针对县域生态空间网络的识别与重构是空间优化的重要途径,对生态保护红线划定具有积极作用,但现有空间网络分析的方法论明显滞后。以典型丘陵山区县湖南茶陵县生态空间网络构建和识别为基础,运用鲁棒性分析法表达生态系统受特定干扰后的变化特征,进行节点重要度评价和网络稳定性分析。结果表明：节点重要度和数量是判定网络稳定性的关键因子,该类节点数量占5%左右且多位于茶陵县域罗霄山片区,对应景观类型多为林地,其次为水域和草地、园地等生态用地;生态空间网络稳定性变化值均表现出与节点数量的高度一致,网络节点失效比率高于92%时将完全瘫痪,低于20%可恢复稳定;以人类活动干扰为主的蓄意破坏情景中连通鲁棒性变化更为敏感,对网络连通性影响较大;依据重要节点分布及稳定性判断结果,结合生态保护红线划定方案,提出区域生态保护的差异化管理和生态空间网络重构建议。研究既为县域生态空间规划和生态保护红线管控提供有效支撑,也为类似区域生态空间网络研究提供了案例借鉴。