一种构建任意发生元Voronoi图的实用算法

针对GIS中线状、面状等复杂形态地理要素,提出一种构建任意发生元Voronoi图的实用算法.主要步骤包括:将复杂发生元离散为点集;对点集采用扫描线算法构建Voronoi图,构建过程中对所生成的Voronoi多边形以其发生点所在要素的序号赋属性值;根据拟定的规则进行Voronoi多边形的合并,得到面向复杂发生元的广义Voronoi多边形,每个复杂发生元有且仅有一个Voronoi多边形与之对应.论述了算法实现的关键过程,并结合实例验证了该方法的可行性,算法的执行效率相对较高.     

等级Voronoi图及加权Voronoi图的ArcGIS矢量生成算法

等级Voronoi图及加权Voronoi图是以树状形式表达事物层次关系的方法,可作为一种空间数据模型应用于城镇等级体系、组织结构关系表达等地学领域。该文首次提出一种等级Voronoi图及加权Voronoi图的ArcGIS矢量生成算法,以ArcGIS Engine为开发工具,利用增量法思想,通过区域分割和合并方法实现了对空间的多级划分,为研究和发展GIS空间数据模型提供了重要的方法手段。     

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.     

顾及障碍物的一般图形Voronoi图及其加权图的ArcGIS栅格实现

Voronoi图作为计算几何的重要分支,广泛应用于地学领域。一般图形Voronoi图是对普通Voronoi图的扩充,经普通Voronoi图生成元扩展为点、线、面而成。当前算法均难以嵌入主流GIS软件,限制了其在地学领域的应用。该文结合C#和ArcEngine,以栅格结晶方式生成了顾及障碍物的一般图形Voronoi图及其加权图。算法实现灵活,实验效果良好,为研究和发展GIS空间数据结构和空间模型提供了重要方法。     

基于逆向加权Voronoi图的面状地理景观特征化研究

基于逆向加权Voronoi图的方法,采用角度、线宽、线长和方向四参数对面状地理景观进行特征化研究。实例表明,该方法既具备在保持曲线弯曲特征转折点精确性方面的优点,还在曲线化简时重点顾及了目标的形态维护,并在不损耗面状地理景观的方向、凹凸性及数量等关键信息的基础上,明显减少了数据存储量,还可实现面状目标的跨时段、跨地区比较,是一种记录、描述和可视化比较研究面状地理景观时空演化特征的有效方法,可实现特征信息保留与结果简化间的平衡。     

基于Voronoi图的物流配送中心服务范围研究

配送中心服务范围的合理划分是物流配送中心决策的重要前提之一。针对目前按照行政区域界定物流配送中心服务范围的不科学性,引入了Voronoi图并介绍了其基本原理,并分析了在配送中心服务范围划分问题上应用的可行性,然后基于MapInfo软件的Voronoi图生成功能,给出了实际案例,进行了相关的研究和分析。结果表明:Voronoi图在配送中心服务范围划分问题上具有较好的效果,应用Voronoi图可以合理划分物流配送中心的服务范围,比传统的按照行政区域界定物流配送中心服务范围的方法更加符合物流市场的客观情况。     

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Voronoi图的新疆塔里木盆地城镇影响范围分析

确定塔里木盆地城镇影响范围,是新疆城镇体系规划、城市经济区划的一项基本工作,具有现实意义.建立城镇综合实力指标体系,运用Voronoi图在空间分割和地图制图应用中的诸多特性,提供一种新的城镇空间影响范围的划分方法,来实现对塔里木盆地城镇空间影响范围的生成和界定.结果表明:综合实力指数较高的城镇的影响范围一般会超过其所在市县的行政范围,较低的则小于其行政范围;盆地北部、西北部城镇密度较大的区域,城镇的辐射半径较小,影响范围绝对面积不大,南部、东南部城镇密度较小的区域,城镇的辐射半径大,影响范围绝对面积较大.此外,塔里木盆地南部县域的中心城镇的辐射范围呈现为竖向的条块状,并与其行政区划基本吻合,反映出塔里木盆地南部绿洲经济相对的独立性和完整性.     

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。     

Voronoi生成的Clifford代数实现方法

引入具有维度融合、坐标无关等特性的Clifford几何代数,构建不同维度统一Voronoi生成框架及算法流程。定义了可支撑不同维度、不同对象间距离、相交及对偶关系的几何、拓扑运算,基于多重向量设计了可支撑不同维度地理对象的统一存储结构及关系表达机制,实现了基于Clifford代数的多维统一Voronoi生成算法。以中国城市气象数据为例进行了算法验证,并分析了算法复杂度。结果表明,该算法可根据输入数据维度自适应地实现相应维度的Voronoi分析,可为以维度统一为特征的GIS分析算法实现提供借鉴。     

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。     

Voronoi tessellation on the ellipsoidal earth for vector data

Voronoi tessellation, and its dual the Delaunay triangulation, provide a cohesive framework for the study and interpretation of phenomena of geographical space in two and three dimensions. The planar and spherical solutions introduce errors in the positional accuracy of both Voronoi vertices and Voronoi edges due to errors in distance computations and the path connecting two locations with planar lines or great circle arcs instead of geodesics. For most geospatial applications the introduction of the above errors is insignificant or tolerable. However, for applications where the accuracy is of utmost importance, the ellipsoidal model of the Earth must be used. Characteristically, the introduction of any positional error in the delimitation of maritime zones and boundaries results in increased maritime space for one state at the expense of another. This is a situation that may, among others, have a serious impact on the financial activities and the relations of the states concerned. In the context of previous work on maritime delimitation we show that the Voronoi diagram constitutes the ideal solution for the development of an automated methodology addressing the problem in its entirety. Due to lack of a vector methodology for the generation of Voronoi diagram on the ellipsoid, the aforementioned solution was constrained by the accuracy of existing approaches. In order to fill this gap, in this paper we deal with the inherent attributes of the ellipsoidal model of the Earth, e.g. the fact that geodesics are open lines, and we elaborate on a methodology for the generation of the Voronoi diagram on the ellipsoid for a set of points in vector format. The resulting Voronoi diagram consists of vertices with positional accuracy that is only bounded by the user needs and edges that are comprised of geodesics densified with vertices equidistant to their generators. Finally, we present the implementation of the proposed algorithm in the Python programming language and the results of two case studies, one on the formation of closest service areas and one on maritime boundaries delimitation, with the positional accuracy set to 1 cm.     

GIS-based stochastic modeling of physical accessibility using GPS-based floating car data and Monte Carlo simulation

The term physical accessibility has long been used by geographers, economists, and urban planners and reflects the relative ease of access to/from several urban/rural services by considering the traveling costs. Numerous accessibility measures, ranging from simple to sophisticated, can be observed in the geographical information systems (GIS)-based accessibility modeling literature. However, these measures are generally calculated from a constant catchment boundary (a most likely or average catchment boundary) based on constant deterministic transportation costs. This is one of the fundamental shortcomings of the current GIS-based accessibility modeling and creates uncertainty about the accuracy and reliability of the accessibility measures, especially when highly variable speeds in road segments are considered. The development of a new stochastic approach by using global positioning system (GPS)-based floating car data and Monte Carlo simulation (MCS) technique could enable handling the variations in transportation costs in a probabilistic manner and help to consider all possible catchment boundaries, instead of one average catchment boundary, in accessibility modeling process. Therefore, this article proposes a stochastic methodology for GIS-based accessibility modeling by using GPS-based floating car data and MCS technique. The proposed methodology is illustrated with a case study on medical emergency service accessibility in Eskisehir, Turkey. Moreover, deterministic and stochastic accessibility models are compared to demonstrate the differences between the models. The proposed model could provide better decision support for the decision-makers who are supposed to deal with accessibility, location/allocation, and service/catchment area related issues.     

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。     

A scale-explicit model for checking directional consistency in multi-resolution spatial data

Multi-resolution spatial data always contain the inconsistencies of topological, directional, and metric relations due to measurement methods, data acquisition approaches, and map generalization algorithms. Therefore, checking these inconsistencies is critical for maintaining the integrity of multi-resolution or multi-source spatial data. To date, research has focused on the topological consistency, while the directional consistency at different resolutions has been largely overlooked. In this study we developed computation methods to derive the direction relations between coarse spatial objects from the relations between detailed objects. Then, the consistency of direction relations at different resolutions can be evaluated by checking whether the derived relations are compatible with the relations computed from the coarse objects in multi-resolution spatial data. The methods in this study modeled explicitly the scale effects of direction relations induced by the map generalization operator – merging, thus they are efficient for evaluating consistency. The directional consistency is an essential complement to topological and object-based consistencies.