Rendering interior-filled polygonal vector data in a virtual globe

Polygonal vector data are important for representing countries, lakes, residential settlements, and other polygonal features. The proper representation of polygonal vector data is the basis of efficient rendering and picking and quick access and display of the analysis results based on polygons (e.g., 3D overlaying and surface area measurement in mountainous areas) in a virtual globe. However, polygonal vector data are displayed using texture-based or boundary-based approaches in most existing virtual globes. The texture-based approach cannot easily support interactive operations (e.g., picking) and spatial analysis (e.g., adjacency analysis and spatial measurement). The boundary-based approach treats the holes as independent features; however, it is difficult to recognize which boundaries constitute a polygon. Further research is needed on how to better organize the polygons to support efficient rendering, picking, and analysis in a virtual globe. In this article, we propose two methods to drape interior filled 2D polygons onto a multi-resolution 3D terrain. Both proposed methods combine polygon clipping and polygon triangulation. The difference between the two methods is in the way holes are eliminated. Method 1 recursively subdivides a terrain triangle until the child-triangles contain no holes; every resulting clipped polygon, which is then triangulated, contains no holes. Method 2 directly clips a polygon against a terrain triangle and creates bridge edges to transform the resulting polygons with holes to degenerate polygons that are further triangulated. The experimental results demonstrate that both proposed methods can efficiently process polygons with holes resulting in appropriate numbers of triangles. The processed interior-filled polygons remain close to the terrain surface in a virtual globe. Both proposed methods support real-time rendering of polygonal vector data in a virtual globe.     

Topology revisited: representing spatial relations

Topology is a central, defining feature of geographical information systems (GIS). The advantages of topological data structures are that data storage for polygons is reduced because boundaries between adjacent polygons are not stored twice, explicit adjacency relations are maintained, and data entry and map production is improved by providing a rigorous, automated method to handle artifacts of digitizing. However, what explains the resurgence of non-topological data structures and why do contemporary desktop GIS packages support them? The historical development of geographical data structures is examined to provide a context for identifying the advantages and disadvantages of topological and non-topological data structures. Although explicit storage of adjacent features increases performance of adjacency analyses, it is not required to conduct these operations. Non-topological data structures can represent features that conform to planar graph theory (i.e. non-overlapping, space-filling polygons). A data structure that can represent proximal and directional spatial relations, in addition to topological relationships is described. This extension allows a broader set of functional relationships and connections between geographical features to be explicitly represented.     

Object-based spatial cluster analysis of urban landscape pattern using nighttime light satellite images: a case study of China

Previous studies have demonstrated urban built-up areas can be derived from nighttime light satellite (DMSP-OLS) images at the national or continent scale. This paper presents a novel object-based method for detecting and characterizing urban spatial clusters from nighttime light satellite images automatically. First, urban built-up areas, derived from the regionally adaptive thresholding of DMSP-OLS nighttime light data, are represented as discrete urban objects. These urban objects are treated as basic spatial units and quantified in terms of geometric and shape attributes and their spatial relationships. Next, a spatial cluster analysis is applied to these basic urban objects to form a higher level of spatial units – urban spatial clusters. The Minimum Spanning Tree (MST) is used to represent spatial proximity relationships among urban objects. An algorithm based on competing propagation of objects is proposed to construct the MST of urban objects. Unlike previous studies, the distance between urban objects (i.e., the boundaries of urban built-up areas) is adopted to quantify the edge weight in MST. A Gestalt Theory-based method is employed to partition the MST of urban objects into urban spatial clusters. The derived urban spatial clusters are geographically delineated through mathematical morphology operation and construction of minimum convex hull. A series of landscape ecologic and statistical attributes are defined and calculated to characterize these clusters. Our method has been successfully applied to the analysis of urban landscape of China at the national level, and a series of urban clusters have been delimited and quantified.     

中国土地利用空间格局刻画方法研究

土地利用空间格局研究是土地利用/覆盖变化（LUCC）理论和实践的基础,对土地利用空间格局进行有效刻画有利于国土资源空间优化,提升土地利用规划和管理水平。由于土地利用空间格局的研究范畴尚不明晰,目前土地利用空间格局的研究对形状、斑块分布和结构等方面关注较少,缺乏对不同土地利用类型间相互关系的研究;同时,格局指标繁多且存在较大的相关性,如何建立指标与土地利用空间格局的对应关系值得进一步研究。本文在深刻理解土地利用空间格局内涵的基础上,将面积、形状和斑块分布总结为土地利用几何特征,将结构和多样性总结为土地利用类型特征,建立了土地利用空间格局刻画指标体系,利用模糊C均值聚类分析,明确了指标与空间格局间的对应关系。结果表明,中国土地利用几何特征可以划分为简单大斑块型、复杂大斑块型、复杂小斑块型、简单小斑块型和散布型五种,不同的几何特征反映了不同土地利用类型的面积、形状和斑块分布的特点,体现了区域土地利用类型的组合关系。2010年中国土地利用共存在61种不同的结构,但主要的结构类型仅有14种,结构特征具有明显的空间聚集性,体现了不同土地利用类型的空间分异性。中国土地利用多样性以3~5类为主,占比达66.69%,其特征总体上呈现“东北、东南高,西北低”的态势。该研究丰富了土地利用空间格局研究的理论体系,填补了中国土地利用整体空间格局刻画的空白。     

Generalized Mathematical Morphological Method for 3D Shape Analysis of Geological Boundaries: Application in Identifying Mineralization-Associated Shape Features

The shapes of geological boundaries such as contacts and faults play a crucial role in the transportation, deposition and preservation of metals in magmatic and hydrothermal systems. Analyzing the shapes of geological boundaries, in particular those associated with mineralization, is an important step in 3D mineral prospectivity modeling. However, existing methods of shape analysis are limited in the adaptation of various shapes, scales and topologies of geological boundaries. This paper presents a general method of shape analysis based on mathematical morphology (MM), which is a generalization of the original MM method for shape analysis. The generalization extends the applicability of the original MM method from closed surfaces to general surfaces, while inheriting the real 3D and multi-scale analysis capabilities of the original method. This is achieved by regarding MM operations on 3D sphere structural elements as their equivalent operations, and redefining the operations to general surfaces. The generalized MM method enables us to handle complex 3D shapes such as overturned and/or recumbent geological boundaries as well as incomplete shapes due to weathering processes and data unavailability. The proposed method was applied to analyze the shape of an intrusive contact in the Fenghuangshan Cu ore field, Eastern China, whose shape was in the form of a non-closed surface. This analysis revealed a stronger spatial association between the large concave parts of the contact zone and the mineralization. Due to its enhanced adaptability to different shapes, the generalized MM method, compared with the original MM method, allows us to capture shape features that are more plausible for the geological setting.

     

Network-constrained bivariate clustering method for detecting urban black holes and volcanoes

ABSTRACT

Urban black holes and volcanoes are typical traffic anomalies that are useful for optimizing urban planning and maintaining public safety. It is still challenging to detect arbitrarily shaped urban black holes and volcanoes considering the network constraints with less prior knowledge. This study models urban black holes and volcanoes as bivariate spatial clusters and develops a network-constrained bivariate clustering method for detecting statistically significant urban black holes and volcanoes with irregular shapes. First, an edge-expansion strategy is proposed to construct the network-constrained neighborhoods without the time-consuming calculation of the network distance between each pair of objects. Then, a network-constrained spatial scan statistic is constructed to detect urban black holes and volcanoes, and a multidirectional optimization method is developed to identify arbitrarily shaped urban black holes and volcanoes. Finally, the statistical significance of multiscale urban black holes and volcanoes is evaluated using Monte Carlo simulation. The proposed method is compared with three state-of-the-art methods using both simulated data and Beijing taxicab spatial trajectory data. The comparison shows that the proposed method can detect urban black holes and volcanoes more accurately and completely and is useful for detecting spatiotemporal variations of traffic anomalies.     

Comparative tempo‐spatial pattern analysis: CTSPA

A new method is illustrated for describing the characteristics of urban pattern changes over different time periods. This method employs vector geometry, paired centroids, shared boundary lines, and overlain polygons. Three new statistics are proposed for characterizing local polygon feature changes in quantity, shape, and size. These statistics are standardized, based on conventional theories from urban geography such as directional concentric zones and user‐designated corridors to document both regional and global patterns of land‐use change. This method is used to analyse land‐use changes in metropolitan Detroit between 1990 and 2000. The Detroit case study indicates that the CTSPA statistics are effective in describing urban spatial pattern changes and in characterizing the evolution of discrete urban landscapes over selected periods.     

城市三维地理信息系统中三维模型的快速构建方法

大规模三维模型的快速构建一直是影响城市三维地理信息系统(3DUGIS)发展的一个重要因素.基于3DUGIS中景观模型的表达原则与分类,分别针对抽象的点、线、面状对象提出符号匹配和三角剖分的批量三维模型构建方法.这种建模方法方便、快捷、自动化程度高,可广泛应用于城市景观中地面、河流、道路、绿地、规则建筑物、地下管线等地物的三维建模.通过对上述三维模型快速构建方法的实现,验证了三维模型生成的效果和效率.     

Tagging-the-triangle algorithm for partitioning features with inconsistent boundaries

In spatial data sets, gaps or overlaps among features are frequently found in spatial tessellations due to the non-abutting edges with adjacent features. These non-abutting edges in loose tessellations are also called inconsistent boundaries or slivers; polygons containing at least one inconsistent boundary are called inconsistent polygons or sliver polygons. The existing algorithms to solve topological inconsistencies in sliver polygons suffer from one or more of three major issues, namely determination of tolerances, excessive CPU processing time for large data sets and loss of vertex history. In this article, we introduce a new algorithm that mitigates these three issues. Our algorithm efficiently searches the features with inconsistent polygons in a given spatial data set and logically partitions them among adjacent features. The proposed algorithm employs the constrained Delaunay triangulation technique to generate labelled triangles from which inconsistent polygons with gaps and overlaps are identified using label counts. These inconsistent polygons are then partitioned using the straight skeleton method. Moreover, each of these partitioned gaps or overlaps is distributed among the adjacent features to improve the topological consistency of the spatial data sets. We experimentally verified our algorithm using the real land cadastre data set. The comparison results show that the proposed algorithm is four times faster than the existing algorithm for data sets with 200,000 edges.     

土地空间分形结构的尺度转换特征

应用分形理论以及多元相关分析、灰色关联分析方法,分析浙江省慈溪市土地空间分形结构的尺度转换特征。结论为:①慈溪市、贵州省不同尺度分割区域的土地空间分形结构均客观存在,不因尺度不同而变化;②尺度转折点因尺度不同而出现,贵州省(省域尺度)土地利用存在尺度转折点,慈溪市(县域尺度)土地利用不存在尺度转折点;③不同尺度的慈溪市、贵州省土地空间结构的分维不仅主要受到土地类型本身几何属性的影响,而且其所受到的影响跨尺度存在;④尺度的差异造成不同影响因子的影响程度随尺度出现变化;平均图斑形状指数对慈溪市土地空间结构的分维影响最大,图斑数则对贵州省土地空间结构分维的影响最大。     

Quantifying the Shapes of U.S. Landfalling Tropical Cyclone Rain Shields*

Tropical cyclones (TCs) produce complex rainfall patterns that are difficult to predict due to atmospheric and land surface forcings. This study utilizes geographic information systems to spatially analyze radar returns and calculate several metrics that quantify the shapes of TC rain shields. Three stepwise discriminant analyses are performed to determine which of the shape metrics distinguish among TCs categorized by: intensity, distance traveled inland, and orientation of terrain encountered. Results confirm that TC rain shields often assume noncircular shapes. Utilizing shape indices to model rain shields could help produce TC rainfall forecasts that are more spatially accurate.     

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.     

Voronoi-based region approximation for geographical information retrieval with gazetteers

Gazeteers and geographical thesauri can be regarded as parsimonious spatial models that associate geographical location with place names and encode some semantic relations between the names. They are of particular value in processing information retrieval requests in which the user employs place names to specify geographical context. Typically the geometric locational data in a gazetteer are confined to a simple footprint in the form of a centroid or a minimum bounding rectangle, both of which can be used to link to a map but are of limited value in determining spatial relationships. Here we describe a Voronoi diagram method for generating approximate regional extents from sets of centroids that are respectively inside and external to a region. The resulting approximations provide measures of areal extent and can be used to assist in answering geographical queries by evaluating spatial relationships such as distance, direction and common boundary length. Preliminary experimental evaluations of the method have been performed in the context of a semantic modelling system that combines the centroid data with hierarchical and adjacency relations between the associated place names.     

线性抽样及分形理论在景观异质性研究中的应用

景观异质性是景观生态学研究的核心,对景观格局、动态和功能具有决定作用。将线性抽样与分形理论相结合的方法应用于景观空间异质性的表达中,相比于传统方法,可以定量表达景观类型在空间序列中的组合规律,而该组合规律可以作为指标来测度景观空间异质性的高低。景观类型在空间序列中的组合越复杂,则景观的空间异质性越高。该方法以景观类型空间序列的线形图像为基础,利用分形理论计算线形图像的分维,以分维数值的大小来表达景观空间异质性的高低。但样线的布设方法、分维计算方法以及景观分类系统的不同都会对分维数值产生影响。以妫水河流域为试验区,对该方法的适用性进行验证,结果表明,该方法可以有效表达景观空间异质性的高低。     

Quantification of spatial gradation of slope positions

Transition between slope positions (e.g., ridge, shoulder slope, back slope, foot slope, and valley) is often gradual. Quantification of spatial transitions or spatial gradations between slope positions can increase the accuracy of terrain parameterization for geographical or ecological modeling, especially for digital soil mapping at a fine scale. Current models for characterizing the spatial gradation of slope positions based on a gridded DEM either focus solely on the parameter space or depend on too many rules defined by topographic attributes, which makes such approaches impractical. The typical locations of a slope position contain the characteristics of the slope position in both parameter space and spatial context. Thus, the spatial gradation of slope positions can be quantified by comparing terrain characteristics (spatial and parametrical) of given locations to those at typical locations. Based on this idea, this paper proposes an approach to quantifying the spatial gradation of slope positions by using typical locations as prototypes. This approach includes two parts: the first is to extract the typical locations of each slope position and treat them as the prototypes of this position; and the second is to compute the similarity between a given location and the prototypes based on both local topographic attributes and spatial context. The new approach characterizes slope position gradation in both the attribute domain (i.e., parameter space) and the spatial domain (i.e., geographic space) in an easy and practicable way. Applications show that the new approach can quantitatively describe spatial gradations among a set of slope positions. Comparison of spatial gradation of A-horizon sand percentages with the quantified spatial gradation of slope positions indicates that the latter reflects slope processes, confirming the effectiveness of the approach. The comparison of a soil subgroup map of the study area with the maximum similarity map derived from the approach also suggests that the quantified spatial gradation of slope position can be used to aid geographical modeling such as digital soil mapping.     

Unique identification of vector geographic objects by location and geometry

This article presents a method to uniquely identify vector geographic objects based on their spatial position and geometric characteristics. The method comprises three steps. First, a grid-based spatial indexing (Quadtree grid) is automatically generated according to location, shape and size of the geographic objects. This allows for a simple Quadtree grid generation (the level, row and column number) for every geographic object by three grid parameters (origin, start and end size). Second, a set of algorithms have been developed for extracting geometric characteristics (e.g. representative points, outline and orientation) of geographic objects corresponding to the grid. Third, a strategy for the unique identification of geographic objects is proposed in order to integrate the Quadtree grid and the geometric information. The application of the proposed method is presented in a case study conducted in Jiangsu Province, China. The experiment indicates that this method is more efficient than existing methods at positioning, searching and querying. The unique identifier is also shown to be useful as a technical method to support geographic information systems analytical applications, such as the matching, conflating and sharing of spatial objects.     

降雨量地面观测数据空间探索与插值方法探讨

空间插值方法广泛应用于气象数据产品的制作,其精度与气象要素的空间变异特征、气象观测站分布和插值方法选择有关。选择美国得州599个地面观测站30年平均降雨量记录,设计了27个观测站样本方案,选择全年、1月和8月数据,利用空间统计、空间自相关、半变异函数等方法探索降雨量的空间变异特征,并采用5种常规方法进行空间插值,比较和解释插值结果,在此基础上讨论基于知识的气象要素空间插值方法。案例研究发现:①降雨量地面观测数据通常具有明显的空间趋势、较强的空间自相关特征和较稳定的空间变异规律,但针对不同时段或采样方案,其空间自相关强度和半变异函数模型会有一定的差异。②增加气象观测站数,空间插值误差有减小的趋势;但观测站数目达到一定数值后,增加观测站数,插值精度提高并不明显。③在观测站较少时,不同插值方法间的精度差异较大,而在观测站充足的情况下,其差异有减小的趋势。④探讨气象要素与地理环境要素之间的关系,获得定量化的先验知识,开发基于知识的空间插值模型,是高精度气象要素插值的关键;线性加权回归和地理加权回归方法的初步试验验证了这一思路的有效性。