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.     

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。     

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.     

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.     

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.     

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.     

Diffusion-based cartogram on spheres

A planar cartogram is a two-dimensional map, on which the area of each closed region is in direct proportion to a chosen extensive property. To date, various algorithms have been proposed to construct planar cartograms. This work extends the two-dimensional, diffusion-based, topologically invariant cartogram algorithm proposed by Gastner and Newman onto spheres. Unlike its planar counterpart, the spherical formulation does not require boundary conditions and is invariant to the rotation of input data on the sphere. An implementation of this spherical cartogram transformation is designed to generate readable topology-preserving cartograms on spheres. Lastly, the method is illustrated with applications to global data such as worldwide human population, gross domestic product (purchasing power parity), carbon dioxide emissions and regional data such as the Electoral College of the United States presidential election of 2016.     

TIN-based Tag Map Layout

With the widespread use of tag clouds, multiple map-based variations have been proposed. Like standard tag clouds (also called word clouds), these ‘tag maps’ all share the basic strategy of displaying words within a ‘geographic space’ and scaling the word size to depict frequency (or importance) of those words within some dataset. While some tag maps simply plot a standard tag cloud on top of a map, the subset of tag maps we focus on here are those in which the collection of words are displayed within bounded geographic regions (often of irregular shape) that the words are relevant for. For this form of tag map, map scale and polygon shape add constraints to word size and position that have not been considered in most prior approaches to tag map word layout. In this paper, we present a layout strategy for tag map generation that includes consideration of the shape and size of the geographical regions acting as containers for the tags. The method introduced here uses a triangulated irregular network (TIN) to subdivide the geographical region into many triangle subareas, with the centroid of each triangle being a potential location to centre a tag on. All the triangles are sorted by their area and all the tags are sorted by their weight value (e.g. frequency, importance or popularity). Positioning of tags is undertaken sequentially from most important (or frequent or popular) with potential locations being the TIN triangle centroids (tried from largest to smallest triangle). After each tag placement, the TIN is recalculated to integrate the tag centroid and bounding corners into the TIN creation. The limited whitespace in the geographical region, at any specific scale, is used fully by dynamically adjusting the font size along with the number and the direction of tags. The method can be applied to add tags within geographic polygons that are convex, concave and other more complex regions containing holes or islands.     

Groundwater Prospect Zoning Using Remote Sensing and Geographical Information System: A Case Study in Dala-Renukoot Area, Sonbhadra District, Uttar Pradesh

In the present study, ground water prospect zones in Dala-Renukoot area, in Sonebhadra district. Uttar Pradesh, India have been delineated, through integration of various thematic maps using ARC/INFO GIS. Thematic maps in respect of geology, geomorphology. slope, drainage, land-use/land cover, lineament and lineament intersection frequency were prepared on 1:50,000 scale using remote sensing and conventional methods. These maps were scanned and registered with reference to a basemap and are input as separate layers using ARC/INFO GIS. Each theme was assigned a weightage depending on its influence on the movement and storage of groundwater and each unit in every theme map is assigned a knowledge based ranking from 1 to 5 depending on its significance to groundwater occurrence. All the themes are overlaid, two at a time and the resultant composite coverage is classified into five groundwater prospect categories. This output map is correlated with the groundwater data collected in the field.     

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。     

基于空间信息网格的数字地图分幅(块)方法

针对传统地图分幅方法的缺陷,本文提出了一种既适合数字环境又充分考虑到地球空间的自然特征和社会属性特点的地图分幅新方法。它以不破坏地物和区域的完整性为划分原则,根据分辨率和区域内地理信息的数量决定图块大小,块内每个地理实体都有一个行政区划代码属性和标识码。这种数字地图分块方法将地理区按行政体系或自然区划划分为地理空间单元,对每个空间单元记录和存储各种基础地理要素,建立空间单元地理数据文件。这种地理空间的划分和空间数据的组织方法为空间索引提供了方便,更为空间统计提供了便利。它既是空间位置的划分方法,也是特定空间位置范围内自然、社会、经济属性的信息载体,同时也是适合时空坐标系变化的空间信息的一种新的表示方法,是为了更方便地在网格计算环境下实现对空间信息资源的整合、共享与利用。     

BinSq: visualizing geographic dot density patterns with gridded maps

ABSTRACT

Dot maps have become a popular way to visualize discrete geographic data. Yet, beyond showing how the data are spatially distributed, dot maps are often visually cluttered in terms of consistency, overlap, and representativeness. Existing clutter reduction techniques like jittering, refinement, distortion, and aggregation also address this issue, but do so by arbitrarily displacing dots from their exact location, removing dots from the map, changing the spatial reference of the map, or reducing its level of detail, respectively. We present BinSq, a novel visualization technique to compare variations in dot density patterns without visual clutter. Based on a careful synthesis of existing clutter reduction techniques, BinSq reduces the wide variety of dot density variations on the map to a representative subset of density intervals that are more distinguishable. The subset is derived from a nested binning operation that introduces order and regularity to the map. Thereafter, a dot prioritization operation improves the representativeness of the map by equalizing visible data values to correspond with the actual data. In this paper, we describe the algorithmic implementation of BinSq, explore its parametric design space, and discuss its capabilities in comparison to six existing clutter reduction techniques for dot maps.     

适宜空间认知结果表达的地图形式

心象地图是驻留在记忆中的关于地理世界空间特征认知结果的表达,具有如下特征:空间表达的非均一性、内容选取的主观性、空间定位的非确定性、度量特征上的非精确性.心象地图的可视化需要由特殊的图形形式来承担,经过分析提出了适宜这一表达特征的3种可视化技术,包括面向道路网认知表达的路网构架图、专题属性空间定位信息认知表达的面域拓扑图、虚拟网络空间导航认知的赛伯网络图.基于地图的定义,对这3种可视化形式度量特征进行了讨论,认为它们在有序量尺度上具有可度量特征.     

基于SVG的专题地图与Google地图混搭研究

Google地图开放API后,将Google地图作为地理底图,由用户定制专题要素成为专题地图制作的一种新形式。文中研究如何在Google地图上制作精美生动的网络专题地图。SVG用于表达网络专题要素有其独特的优势,文中结合SVG的优点探讨以Google地图为地理底图的网络专题地图的表达、设计与实现方法,尝试解决网络地理底图与专题要素的一致性表达问题。     

数字地图图像特征的形态学分析模型

本文在基本的数学形态学理论和运算的基础上，结合地图图像的连接性、形状、尺度、纹理、拓扑与几何等特征，系统地应用、扩展和提出了描述这些基本图像特征的各种形态学分析模型，构成了数字地图图像形态分析和处理的理论体系。     

导航电子地图多尺度显示与载负量的研究

导航电子地图的多尺度显示目的就是在导航终端有限的屏幕容量下．形成适宜载负量的地图。本文在对导航电子地图载负量指标进行研究的同时,将导航电子地图用于显示的道路形状数据、背景数据、地名数据,按照每一类要素的几何大小或重要程度再分为若干级别,利用分级显示技术,计算出导航电子地图各级显示尺度下的合理载负量,使导航电子地图在多尺度表达时显示要素载负量合理、分布均匀,尺度切换时鼐示要素过渡自然、流畅。     

Identification of priority watersheds for soil conservation in gomai,amravati and buray sub-catchments of ukai catchment

Sediment yields of different watersheds of three subcatchments have been worked out using the Musgrave and the Sediment Yield Predictive Equation. Data for the calculation were in the shape of a soil and land use map prepared by photo-interpretation with selective field check and such measurements as Relief Length Ratio, average slope percentages and particle size data for the surface 5 cm soil. Sediment yields by the Predictive Equation are markedly higher than those obtained by the Musgrave Equation. The Predtctive Equation values are also closer to the rate of sediment yields as measured at the Ukai dam site by the Inflow-outflow method; it thus appears to offer a satisfactory basis for the determination of priority subcatchments and watersheds. Based on sediment yields per unit drainage areainter se priorities have been worked out amongst the three subcatchments as well as for the watersheds within each of the subcatchments.     

Animated Maps of Aggregate Data: Conceptual and Practical Problems

Predictions of the 1960s about the computer's potential to change cartography are finally being fulfilled. Dynamic maps for vehicle navigation, interactive cartographic/statistical tools, and map animation are being investigated actively. As these new environments for mapping become available, we must reevaluate past questions about transformations from reality to data and data to map. In this paper, we consider these transformation questions in the context of statistical map animation. The issues discussed were raised in producing a “map movie” depicting the spread of acquired immune deficiency syndrome (AIDS) over time. Jenks' data model concept is used as the basis for a typology of data models representing phenomena typically depicted by enumeration unit data. The typology is then used to evaluate symbolization decisions for AIDS incidence maps. Implications for symbol selection imposed by dynamic rather than static maps are considered, as are technical issues involved in producing the animation on a microcomputer platform. A hybrid symbolization method that we have termed the “chorodot” is suggested as a way to meet the constraints on symbolization imposed by animation and to represent the appropriate data model for AIDS incidence.     

利用Snake移位模型构建中心型地图

中心型地图可表示空间各点到中心点的时间距离,能直观反映地理分布因交通系统影响而产生的相近性变化。其构建核心是依据控制点的位置移动确定非控制点的新位置,因此,将中心型地图的构建过程建模为地图目标的移位问题,以相对邻近图表示点之间的邻近关系,并基于控制点的位置移动计算点的初始受力,应用Snake移位方法迭代计算各点的新位置生成中心型地图,同时利用后处理解决潜在拓扑错误。利用所提方法和最小二乘方法可视化武汉市到其他各市的旅行时间,并定量、定性地进行对比分析。结果表明,所提方法能更好地避免拓扑错误,且局部形态保持更好。     

Choosing Geographic Units for Choropleth Rate Maps,with an Emphasis on Public Health Applications

Choropleth maps are the most widely used map type for mapping rates, such as those involving disease, crime, and socioeconomic indicators. The essential step of choosing a geographic unit to map is often made in an ad hoc manner. Among the desirable characteristics of choropleth mapping units are high degree of resolution, homogeneity of population size, homogeneity of land area, observation of minimum population thresholds and land area thresholds, temporal stability and currency, compactness of shape, audience familiarity, data availability, and the functional relevance of the unit to the phenomena mapped. Because of the uneven distribution of human populations, no single geographic unit can meet all of these characteristics in practice, and a well designed choropleth map necessarily involves some compromise. We present guidelines for choosing geographic units that take into account the above criteria, considering 12 geographic units ranging from census blocks to states. Even allowing for differences in scale and purpose, some units confer clear advantages over others.