基于四叉树索引构建TIN的高效合成算法

不规则三角网(TIN)可以逼真的模拟地形表面,因此被广泛应用于地学领域。Delaunay三角剖分算法是构建TIN网的最优算法,该文对传统Delaunay三角网构建算法进行分析,提出了一种针对大规模离散数据点生成TIN的高效合成算法。该算法首先根据离散点的分布位置和密度对其进行四叉树区域划分;然后以每个叶子节点的边界四边形为凸包,采用逐点插入法构建三角网;最后采用顶点合并法自底向上合并具有相同父节点的4个子节点,生成Delaunay三角网。实验结果表明,该算法时间复杂度较低,有效提高了TIN网的构建效率。     

Comparison of existing triangulation methods for regularly and irregularly spaced height fields

Over the last two decades, the Delaunay triangulation has been the only choice for most geographical information system (GIS) users and researchers to build triangulated irregular networks (TINs). The classical Delaunay triangulation for creating TINs only considers the 2D distribution of data points. Recent research efforts have been devoted to generating data-dependent triangulation which incorporate information on both distribution and values of input data in the triangulation process. This paper compares the traditional Delaunay triangulations with several variant data-dependent triangulations based on Lawson's local optimization procedure (LOP). Two USGS digital elevation models (DEMs) are used in the comparison. It is clear from the experiments that the quality of TINs not only depends on the vertex placement but also on the vertex connection. Traditonal two step processes for TIN construction, which separate point selection from the triangulation, generate far worse results than the methods which iteratively select points during the triangulation process. A pure data-dependent triangulation contains a large amount of slivers and steep triangles, which greatly affect the quality of TINs constructed. Among the triangulation methods tested, the classical Delaunay triangulation is still the most successful technique for constructing TINs for approximating natural terrain surfaces.     

Characterisation and generalisation of cartographic lines using Delaunay triangulation

A method is presented for generalising cartographic lines using an approach based on determination of their structure. Constrained Delaunay triangulation is used to construct a skeleton of the space surrounding the lines and hence represent line features in terms of skeleton branches. Several statistical measures are used to characterise the triangulation branches. The measures enable selective generalisation of different types of line feature, leading to the possibility of user-specification of the style of generalisation. In our implementation of the approach, the triangulation is updated dynamically to allow both sides of multiple lines to be processed, while guaranteeing topological consistency between the resulting generalised lines.     

自适应的IDW插值方法及其在气温场中的应用

反距离权重(Inverse Distance Weighting,IDW)插值通常采用距离搜索策略选择插值参考点,当采样点集分布不均匀时,距离搜索策略使得参考点聚集一侧影响插值精度。自然邻近关系具有良好的自适应分布特性,可有效地解决参考点分布不均匀问题。结合自然邻近关系,提出自适应的反距离权重(Adaptive-IDW,AIDW)插值方法。首先对采样数据构建初始Delaunay三角网,然后采用逐点插入法,将待插值点插入初始Delaunay三角网中,局部调整得到新的Delaunay三角网,以待插值点的一阶邻近点作为IDW插值的参考点,使参考点自适应均匀地分布在待插值点周围,再进行IDW插值计算。利用AIDW插值方法对Franke函数、全国气温观测数据进行插值实验,结果表明此方法具有较高的精度,且减少了“牛眼”现象。     

A density-based approach for detecting network-constrained clusters in spatial point events

Existing spatial clustering methods primarily focus on points distributed in planar space. However, occurrence locations and background processes of most human mobility events within cities are constrained by the road network space. Here we describe a density-based clustering approach for objectively detecting clusters in network-constrained point events. First, the network-constrained Delaunay triangulation is constructed to facilitate the measurement of network distances between points. Then, a combination of network kernel density estimation and potential entropy is executed to determine the optimal neighbourhood size. Furthermore, all network-constrained events are tested under a null hypothesis to statistically identify core points with significantly high densities. Finally, spatial clusters can be formed by expanding from the identified core points. Experimental comparisons performed on the origin and destination points of taxis in Beijing demonstrate that the proposed method can ascertain network-constrained clusters precisely and significantly. The resulting time-dependent patterns of clusters will be informative for taxi route selections in the future.     

多边形主骨架线提取算法的设计与实现

在Delaunay三角网的基础上对骨架线节点进行了分类,通过确定主骨架线的两个端点,运用回溯法提取了多边形的主骨架线,同时给出了详细的算法步骤,并在Visual C++2003环境下实现了该算法。较之其他算法,该算法思路简捷,易于编程,生成的主骨架线形态优良,较好地反映了多边形的主体形状特征和主延伸方向。     

A TIN compression method using Delaunay triangulation

This study introduces a new Triangulated Irregular Network(TIN) compression method and a progressive visualization technique using Delaunay triangulation. The compression strategy is based on the assumption that most triangulated 2.5-dimensional terrains are very similar to their Delaunay triangulation. Therefore, the compression algorithm only needs to maintain a few edges that are not included in the Delaunay edges. An efficient encoding method is presented for the set of edges by using vertex reordering and a general bracketing method. In experiments, the compression method examined several sets of TIN data with various resolutions, which were generated by five typical terrain simplification algorithms. By exploiting the results, the connecting structures of common terrain data are compressed to 0.17 bits per vertex on average, which is superior to the results of previous methods. The results are shown by a progressive visualization method for web-based GIS.     

An efficient incremental algorithm for generating the characteristic shape of a dynamic set of points in the plane

Several algorithms have been proposed to generate a polygonal ‘footprint’ to characterize the shape of a set of points in the plane. One widely used type of footprint is the χ-shape. Based on the Delaunay triangulation (DT), χ-shapes guaranteed to be simple (Jordan) polygons. This paper presents for the first time an incremental χ-shape algorithm, capable of processing point data streams. Our incremental χ-shape algorithm allows both insertion and deletion operations, and can handle streaming individual points and multiple point sets. The experimental results demonstrated that the incremental algorithm is significantly more efficient than the existing, batch χ-shape algorithm for processing a wide variety of point data streams.     

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.     

Spatially ordered networks and topographic reconstructions

Abstract

A technique is discussed for obtaining a contour tree efficiently as a byproduct of an operational contouring system. This tree may then be used to obtain contour symbolism or interval statistics as well as for further geomorphological study. Alternatively, the tree may be obtained without the computational expense of detailed contour interpolation. The contouring system proceeds by assuming a Voronoi neighbourhood or domain about each data point and generating a dual-graph Delaunay triangulation accordingly. Since a triangulation may be traversed in a tree order, individual triangles may be processed in a guaranteed top-to-bottom sequence on the map. At the active edge of the map under construction a linked list is maintained of the contour ‘stubs’ available to be updated by the next triangle processed. Any new contour segment may extend an existing stub, open two new stubs or close (connect) two previous stubs. Extending this list of edge links backwards into the existing map permits storage of contour segments within main memory until a dump (either to plotter or disc) is required by memory overflow, contour closure, contour labelling or job completion. Maintenance of an appropriate status link permits the immediate distinction of local closure (where the newly-connected segments are themselves not connected) from global closure (where a contour loop is completed and no longer required in memory). The resulting contour map may be represented as a tree, the root node being the bounding contour of the map. The nature of the triangle-ordering procedure ensures that inner contours are closed before enclosing ones, and hence a preliminary contour tree may be generated as conventional contour generation occurs. A final scan through the resulting tree eliminates any inconsistencies.     

二维Delaunay三角网的任意点删除算法研究

针对目前基于影响域多边形剖分的点删除算法缺陷,提出一种二维Delaunay三角网点删除算法。首先利用具有拓扑关系的三角网搜索影响多边形,并以三角形矢量面积为工具三角剖分影响域多边形,最后通过镶嵌优化后的剖分三角网完成点的删除,且满足Delaunay法则。通过测试证明了算法的可靠性和高效性。     

Natural trees—neighbourhood-location in a nutshell

Abstract

We present the notion of a natural tree as an efficient method for storing spatial information for quick access. A natural tree is a representation of spatial adjacency, organised to allow efficient addition of new data, access to existing data, or deletions. The nodes of a natural tree are compound elements obtained by a particular Delaunay triangulation algorithm. Improvements to that algorithm allow both the construction of the triangulation and subsequent access to neighbourhood information to be O(N log N). Applications include geographical information systems, contouring, and dynamical systems reconstruction.     

DEM格网与畸变遥感影像的一体化显示研究

遥感影像可以极大地增强DEM的表达效果,然而由于各种因素的影响,通常需对其进行预处理,传统方法是通过同名控制点进行校正。该文提出一种新的自动匹配算法,即提取DEM和遥感影像对应的特征线,利用Douglas-Peucker算法提取对应的特征点,以DEM特征点为离散点进行Delaunay三角剖分,并基于TIN完成纹理映射。实验结果表明,该算法显示效果较好,可有效改善畸变图像引起的错误显示。     

Assessing the implications of the recent community opening policy on the street centrality in China: A GIS-based method and case study

Recently, the Chinese government raised an urban planning policy which suggests communities open their private roads for public transport and establish street networks with high spatial density in cities. In this context, the purpose of this study is to analyze the potential changes to street network accessibility using GIS techniques and to provide spatial information that may influence the decision making of urban managers. In addition to the existing street network data in the case study city, Shenzhen, intra-community roads are extracted from building footprints in GIS topographic database and used to construct a potential street network with respect to the community opening policy. An automatic GIS-based method is proposed here to analyze the location advantage information in the simulated urban environment, by combining Delaunay triangulation model and graph theory concepts. Specifically, we establish a two-step framework based on the spatial relationships between roads and buildings. Firstly, intra-community roads between neighboring building footprints are generated using a Delaunay triangulation skeleton model, and with the existing inter-community roads they form the simulated network. Secondly, street centrality indices of the current and simulated networks are compared in terms of closeness, betweenness and straightness. Results indicate that after applying the policy the global accessibility in the city would be increased at some places and decreased at others, and places' directness among others would be generally improved. In addition, the skeleton of central routes for through traffic would not change much. The presented method can also be applied to other cities.     

约束Delaunay三角网点删除的一体化凸耳消元法(IEE)

对Delaunay三角网(CD—TIN)点删除算法——凸耳消元法(EE)进行剖析,提出约束Delaunay三角网的点删除算法——体化凸耳消元法(IEE)。该算法将CD-TIN的点删除转化为点的影响域重构,并保证重构后的CD—TIN满足CD—TIN的可视性与空圆法则,确保了CD—TIN的拓扑完备性,实现了CD—TIN中约束点与非约束点删除的一体化操作和局部更新,并得到实验验证。     

Quality assessment of linear data

This paper presents methods to evaluate the geometric quality of spatial data. Firstly, a point‐based method is presented, adapting conventional assessment methods whereby common points between datasets are compared. In our approach, initial matches are established automatically and refined further through interactive editing. Second, a line‐based method which uses correspondences between line segments is proposed. Here, the geometry of line segments in vector is transformed into a set of rasterized values so that their combination at each pixel can restore their original vector geometry. Matching is performed on rasterized line segments and their matching lengths and displacements are measured. Experimental results show that the line‐based approach proposed is efficient to evaluate the geometric quality of spatial data without requirements of topological relationships among line features.     

Computing least air pollution exposure routes

Personalized routing counts on traveler’s preferences which are usually based on different criteria, such as shortest, fastest, least traffic, or less expensive (e.g., less fuel cost, toll free). However, people are increasingly becoming concerned about the adverse health effects of exposure to air pollution in chosen routes. Exposures to elevated air pollution concentrations particularly endanger children, pregnant women, elderly people, and people with asthma and other respiratory conditions. Choosing routes with least air pollution exposure (APE) is seen as one approach to minimize the level of pollution exposed, which is a major public health issue. Routing algorithms use weights on segments of road networks to find optimum routes. While existing weights are commonly distance and time, among a few others, there is currently no weight based on APE to compute least APE routes. In this paper, we present a weight function that computes weight based on APE. Two different approaches, geostatistical and non-geostatistical, were used to compute APE weight. Each approach was evaluated, and the results indicate that the APE weight is suitable for computing least APE routes.