A New Construction Method for Circle Cartograms

An area cartogram is a transformed map on which areas of regions are proportional to statistical data values; it is considered to be a powerful tool for the visual representation of statistical data. A circle cartogram is a type of area cartograms, on which regions are represented by circles. Its first construction algorithm is proposed by Dorling in 1996, based on the following requirements to construct visually elegant cartograms: 1) maintain the similarity of configurations between circles and regions, 2) express the contiguity of regions on cartograms if possible, and 3) avoid overlap of circles. The algorithm is widely used for its easiness to use and its ability to express a spatial distribution of data; however, the relative positions of circles on cartograms sometimes greatly differ from the geographical maps, since the algorithm does not consider the first requirements explicitly. In this paper, it is first pointed out that the construction problem of circle cartograms resembles that of distance cartograms, and the only difference is the existence of third requirement. Then a new construction method for circle cartograms is proposed based on the distance cartogram construction method; the proposed method is formulated as non-linear minimization with inequality constraint conditions. Finally its applicability is confirmed using dataset, including the comparison with the result of previous algorithm.     

Manual construction of continuous cartograms through mesh transformation

A computer-assisted framework is proposed to support the manual construction of cartograms. The framework employs a joint triangulation, similar to that used in rubber-sheeting, to define a piecewise affine transformation between map space and cartogram space. This guarantees preservation of all topological relations within and among transformed datasets with insertion of a finite number of points. To support intuitive user control of cartogram appearance, methods are developed to translate generically defined user adjustments of the cartogram into mesh vertex positions on either the source map mesh or cartogram mesh. The framework is implemented in a working prototype application and used to create sample cartograms of the USA and China. Results are compared with cartograms produced using diffusion and carto3f algorithms in terms of accuracy, aesthetic appearance, and approximate construction time. Qualitative aspects of the manual construction process are also discussed.     

Effectiveness of Cartogram for the Representation of Spatial Data

Abstract

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Cartogram is a technique for visualisation of the geographical distribution of spatial data. It has two main types, i.e. distance cartogram and area cartogram. Area cartogram is a transformed map in which areas are resized in proportion to an attribute value. A number of techniques have been developed for the generation of area cartograms. Some researchers consider cartogram as a very effective technique for visualisation of spatial data, while others doubt about the effectiveness because of the possible distortion in shape and/or disconnectivity in topology. This study aims to evaluate the effectiveness of area cartogram for visualizing spatial data. In this study, two comparative experiments have been conducted. One is the comparison between thematic maps and cartograms, and the other is the comparison among different types of area cartogram. Two sets of data with different characteristics are used, i.e. 2005 China population data and 1996 US election data. Results show that cartogram is more effective in the representation of the 1996 US election data which provides a qualitative result (i.e. in binary form or nominal data), but thematic map is far more effective in the representation of 2005 China population data which provides a quantitative result (in classes or ordinal data). It is also found that among different types of area cartogram, pseudo-cartogram is the most preferred technique and Dorling cartogram is the least preferred one.     

Cartograms for Use in Forecasting Weather-Driven Natural Hazards

This paper evaluates the potential of using cartograms for visualizing and interpreting forecasts of weather-driven natural hazards in the context of global weather forecasting and early warning systems. The use of cartograms is intended to supplement traditional cartographic representations of the hazards in order to highlight the severity of an upcoming event. Cartogrammetric transformations are applied to forecasts of floods, heatwaves, windstorms and snowstorms taken from the European Centre for Medium-range Weather Forecasts (ECMWF) forecast archive. Key cartogram design principles in standard weather forecast visualization are tested. Optimal cartogram transformation is found to be dependent on geographical features (such as coastlines) and forecast features (such as snowstorm intensity). For highly spatially autocorrelated weather variables used in analysing several upcoming natural hazards such as 2m temperature anomaly, the visualization of the distortion provides a promising addition to standard forecast visualizations for highlighting upcoming weather-driven natural hazards.     

Communication Aspects of Value-by-Area Cartograms

The value-by-area cartogram is a form of mapping often used for its visual impact. The average reaction to cartogram area is potentially error free in that the components of a typical value-by-area cartogram are areal shapes. When not in map form, map readers generally respond to these areas in a linear fashion. Results of a testing program to measure this ability suggest that the accuracy of the average response depends upon whether shapes are amorphous or square and whether the anchor stimulus is relatively large or small. The accuracy of responses to the cartogram compare favorably with responses to a five-class Flannery circle map. Map reader attitudes point out that these cartograms are thought to be confusing and difficult to read. At the same time they appear interesting, generalized, innovative, unusual, and having—as opposed to lacking—style. Communication depends on how well the cartographer has maintained the overall shape quality of the original geographical units and the provision of an adequate stimulus anchor, a geographical-base inset map, and labeling on the statistical units.     

Value-by-alpha maps: An alternative technique to the cartogram

The cartogram, or value-by-area map, is a popular technique for cartographically representing social data. Such maps visually equalize a basemap prior to mapping a social variable by adjusting the size of each enumeration unit by a second, related variable. However, to scale the basemap units according to an equalizing variable, cartograms must distort the shape and/or topology of the original geography. Such compromises reduce the effectiveness of the visualization for elemental and general map-reading tasks. Here we describe a new kind of representation, termed a value-by-alpha map, which visually equalizes the basemap by adjusting the alpha channel, rather than the size, of each enumeration unit. Although not without its own limitations, the value-by-alpha map is able to circumvent the compromise inherent to the cartogram form, perfectly equalizing the basemap while preserving both shape and topology.     

Value-by-alpha Maps: An Alternative Technique to the Cartogram

Abstract

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The cartogram, or value-by-area map, is a popular technique for cartographically representing social data. Such maps visually equalize a basemap before mapping a social variable by adjusting the size of each enumeration unit by a second, related variable. However, to scale the basemap units according to an equalizing variable, cartograms must distort the shape and/or topology of the original geography. Such compromises reduce the effectiveness of the visualisation for elemental and general map-reading tasks. Here we describe a new kind of representation, termed a value-by-alpha map, which visually equalizes the basemap by adjusting the alpha channel, rather than the size, of each enumeration unit. Although not without its own limitations, the value-by-alpha map is able to circumvent the compromise inherent to the cartogram form, perfectly equalizing the basemap while preserving both shape and topology.     

关于Stokes公式的球面卷积和平面卷积的注记

讨论了Stokes公式球面卷积和平面卷积形式的近似性和严密性问题,分析了Stokes函数球面卷积形式和平面卷积形式的关系,推导了其间的差值表达式,估算了最大差值及其对计算大地水准面差距的误差影响。同时指出,将顾及Stokes函数全项的平面卷积公式称为严密公式的提法,仅仅是相对仅顾及Stokes函数首项的简单平面卷积公式而言,认为更合理的提法应该是"高精度Stokes平面近似卷积公式"。理论分析表明,球面卷积不可能严格转化为等效的平面卷积。     

面向双/多变量的连续面域拓扑图可视化方法

面域拓扑图是一种利用区域面积大小定量表达区域属性信息的可视化方法。由于其区域面积本身已经表示某一变量,因此这更有利于双/多变量的制图表达。针对目前基于面域拓扑图的双/多变量表达方法中存在的难以表达相邻区域之间基本状况和不利于不同地理现象的空间分布规律及差异表达的问题,本文提出一种面向双/多变量的连续面域拓扑图可视化方法。首先通过格网密度补偿和积分步长逐步试探的方法对基于扩散模型的连续面域拓扑图生成算法进行部分优化,完成基本变量的表达,然后分别通过空间内插和符号扩展完成第2和第3变量在连续面域拓扑图中的表达。最后以慕尼黑市人口密度和银行/ATM分布(双变量)数据以及奥格斯堡市人口密度数据、幼儿园分布以及规模数据(多变量)为试验数据进行可视化,并通过实证分析验证了该方法的有效性和优越性。     

基于O-QTM的球面VORONOI图的生成算法

提出了基于“Q－QTM”（Octahedral Quaternary Triangular Mesh）剖分的球面Voronoi图的格网生成算法；首先介绍了球面的QTM格网划发和编码方法，并根据地址码进行邻近球面三角形的探索；然后，参照数学形态学原理，重新定义了球面三角网的膨胀操作和膨胀算子，利用球面实体的递归膨胀来生成球面Voronoi图。应用VC^ 语言在OpenGL3维平台上开发了相应的实验程序，实验结果表明：利用此算法可生成球面上任意实体的Voronoi图，且生成点、弧和曲面Voronoi图的时间复杂度是一样的；而其误差受球面距离的影响较小，主要与球面实体的位置有关。最后给出了本文研究的结论及进一步的工作。     

球面四元三角网的基本拓扑关系描述和计算

球面四元三角网具有多分辨率和层次组织的特性,已成为目前研究球面问题的有效方法之一。本文在此基础上,利用引入集合多算子和对称差的欧拉数,给出描述和计算球面栅格拓扑关系的四元组模型。该模型利用两空间目标间的交(∩)、差(\)、被差(/)和对称差(Δ)的内容是否为空来初步区分相离/相接、交叉、相等、包含/覆盖、被包含/被覆盖这五对拓扑关系。然后通过引入对称差的欧拉数来进一步区分传统模型难以区分的相离/相接、包含/覆盖和被包含/被覆盖这三对拓扑关系。     

球面坐标系非连续变形分析折数学模型

从球面坐标系的弹性力学基础方程出发，推导出球面上块体的位移与6个位移不变量之间的数学关系，进一步建立了联立方程式的球面坐标形式，为大范围现代地壳运动的非连续形变形下了数学基础。     

一种尺度效应指数修正的格网数据示意地图制图算法

示意地图是统计数据可视化的一种新方法,但已有的面域示意地图制图算法不适用于局部数据差别大的应用。针对此问题,结合多尺度格网统计数据的尺度效应,修正了diffusionbasedmethod算法,并将该算法应用于北京市100m格网人口统计数据上,证明了算法的有效性。该算法可应用于格网统计数据示意地图制图。     

基于球面投影的单站地面激光点云直线段提取方法

由于激光点云离散分布于三维空间,导致特征计算困难,目前针对地面激光扫描点云的直线提取方法普遍存在计算量大、提取错误、或适应性不足等问题。本文提出了一种基于球面投影的单站地面激光点云直线段提取方法:首先将三维点云投影到球面上,球面投影后的三维点云保持了正确的邻接关系,同时也解决了三维数据计算量大的问题;然后,利用球面霍夫变换,正确提取球面投影后点云中的直线段特征;最后,利用稳健的直线拟合算法计算点云中的三维直线段参数。通过对室内室外场景数据的直线段提取试验及与商业软件Geomagic Studio等方法的对比试验,验证了本方法的正确性、适用性和准确性。     

地形改正与地形直接影响的转化关系

传统的第三边值问题的解算方法有Molodensky算法和Stokes-Helmert算法两种。在Molodensky算法中使用的地形改正和Stokes-Helmert算法中使用的直接影响均由大地水准面外地形产生,因而必然存在关系。本文通过推导给出了直接影响是地形改正、层间改正与压缩地形影响3项之和的结论。在此基础上,给出了直接影响的质量线平面积分算法、质量棱柱平面积分算法和地形改正的球面积分算法。此外本文还推导了布格球冠层间改正算法。通过实验得出,直接影响的质量线平面积分算法和质量棱柱平面积分算法与传统球面积分算法的差异分别为3.81和1.64 m Gal;地形改正球面积分算法与传统质量线、质量棱柱平面积分的差异分别为3.92和1.69 m Gal。该结果说明,本文推导的直接影响与地形改正的关系式是正确有效且实用的。     

一种顾及制图区域要素密度均衡的地图变换算法

制图区域要素密度分布不均衡会增加地图表达难度,常规地图表达方式无法解决视觉不平衡的问题。在Gastner-Newman地图变形算法的基础上,提出了一种顾及制图区域要素密度平衡和公众地图认知一致性的地图变换算法。首先,设计多种变形单元尺度以及配置制图要素密度权重组合;然后,代入线性扩散方程,构建变形格网并映射各离散控制点;最后,生成多种变形地图结果。开展了地图认知实验,获得56份问卷结果,针对中国广西南宁市青秀区行政区划图的形态控制,应控制S_周长 > 0.975、S_{周长面积比} > 0.961、S_形状比 > 0.966,能兼顾地图形变以及公众认知的一致性。为解决地图要素密度不均衡的问题提供了新的思路,变形后的地图达到视觉平衡,同时,通过调整形变权重参数实现了公众地图认知的一致性。     

Enabling geosimulations for global scale: Spherical geographic automata

Several complex dynamic spatial systems are operating on the global scale. Their representation with existing geosimulation models is limited to planar level and do not consider the curvature of the Earth's surface. Thus, the objective of this study is to propose and develop a spherical geographic automata (SGA) modeling approach to represent and simulate dynamic spatial processes at the global level. The proposed SGA model is implemented for three case studies including simulations of: (1) Game of Life as population dynamics; (2) urban land-use growth; and (3) deforestation all operating on the spherical Earth's surface. Simulation results indicate that the proposed SGA modeling approach can represent spatial processes such as expansion and shrinkage dynamics on the Earth's surface. The proposed approach has the potential to be adopted to represent different complex systems such as ecological, epidemiological, socioeconomic, and Earth systems processes to support environmental management and policymaking at the global level.     

多源重力数据球冠谐模型抗差融合法

提出了一种基于球冠谐模型的抗差岭估计数据融合算法,并通过数值计算对算法的有效性进行验证。结果表明融合后的球冠谐模型不仅能够抵抗系数阵的病态性,而且能够有效地消除观测粗差的影响。最后就观测噪声大小对融合结果的影响进行了探讨。     

基于压缩感知的SAR图像CFAR目标检测算法

在球不变随机向量的非高斯背景下,针对估计协方差矩阵可能奇异的情况,研究了距离扩展目标的自适应检测方法。首先,推导了非高斯背景下未知协方差矩阵和目标散射点幅度的修正最大似然(maximum likelihood,ML)估计;然后,基于纹理分量的近似ML估计,建立了自适应检测器(adaptively modified generalized likelihood ratio test,AMGLRT)。仿真结果表明,AMGLRT在目标散射点能量均匀分布时检测性能最佳,随着杂波尖峰的减小或阵元数的增加,AMGLRT的检测性能有所改善;且其对不同杂波相关性表现出很好的鲁棒性。另外,AMGLRT的检测性能优于已有的M/K检测器,且这种性能优势随着散射点个数的增加而增大。     

地面激光扫描球形标靶的球心误差研究

分析了球形标靶的特点,通过激光雷达方程描述了球心误差的产生过程和性质,研究统计了球心误差随激光入射方向的分布,采取多项式拟合和模拟球面的方法确定了球心位置和误差大小。实测数据验证了球心误差的系统性特点,并提出削弱球心误差的方法。