Cartogram Construction Research Articles

Point Location Conversion in Distance Cartogram Construction Based on Vector Field Analysis

Point Location Conversion in Distance Cartogram Construction Based on Vector Field Analysis

Development of a Point Location Conversion Approach for Distance Cartogram Construction

Development of a Point Location Conversion Approach for Distance Cartogram Construction

Improvement of moving least squares transformation in distance cartogram construction

Distance cartograms are deformed maps in which the distance of each of the preselected point pairs in the geographic map is changed in step with a specified value. They are constructed through two steps: locating the points included in the preselected pairs, and locating other points. A technique of moving least squares transformation is used in the second step. In this letter, the above technique is improved to maintain homeomorphism in the cartogram. The weight function used in the transformation is modified. Experimental results show the effectiveness of the proposed approach. © 2019 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Development of a Cartogram Construction Method for Visualizing Japanese Folk Dance Distribution

Development of a Cartogram Construction Method for Visualizing Japanese Folk Dance Distribution

Investigating biogeographical patterns using point‐based cartograms

AbstractAimVisualization is an important tool in the investigation of phylogenetic distributions of species. Several tools have been developed that allow a researcher to overlay species distributions and phylogenetic trees on a map. However, when samples span a large range but also have high density in some regions, it can be difficult to appreciate both the global and the local context of biodiversity in a single view.InnovationWe have developed an algorithm for cartogram construction that extends the Gastner–Newman approach to point‐based rather than region‐based data. Cartogram construction is controlled by parameters that impact the magnitude and extent of the distortion. We also introduce the geographically coupled phylogenetic distance (GCPD), a quantitative measure that combines phylogenetic diversity with geographical distance, as a criterion for distorting a map.Main conclusionsWe used our cartogram approach to develop enhanced geographical visualizations of datasets, including an outbreak of Vibrio cholerae in Haiti and the distribution of the salamander Aneides lugubris in California, U.S.A. In both examples, our cartogram approach allowed the concurrent visualization of local distributional patterns while preserving the broader context of the survey. Our implementation in the GenGIS software package allows joint visualization of cartogram, phylogenetic and other types of data.

Parallel construction of large circular cartograms using graphics processing units

Cartograms are a cartographic approach that is based on the geometric transformation of enumeration units to enhance spatial presentation of variables of interest. The automatic construction of cartograms within digital computing environments, as recognized in the literature, is impeded by the issue of computational efficiency. Parallel computing is a potential solution for tackling the computational issue of cartogram construction, and its importance is increasingly acknowledged with the wider spread and application of advanced cyberinfrastructure into geographic studies. The purpose of this article is to investigate the use of a state-of-the-art parallel computing approach, graphics processing units (GPUs), to accelerate the construction of large circular cartograms, a special form of area cartograms. GPUs, built on many-core computing architecture and thread parallelism, provide tremendous high-performance computing and even supercomputing support for general-purpose geocomputation. In this study, the construction of a circular cartogram is divided into a large number of fine-grained subtasks that can be efficiently and simultaneously computed on the underlying many-core GPUs. Simulated and real data were used in experiments to examine the computational performance of GPU-enabled construction of circular cartograms. Experimental results suggest that the GPU-enabled parallel computing approach offers significant acceleration performance for the construction of large circular cartograms, and thus sheds further light on the resolution of computationally intensive spatial and spatiotemporal problems using advanced cartographic and geovisualization approaches.

An Optimized Rubber-Sheet Algorithm for Continuous Area Cartograms*

This article optimizes a continuous area cartogram algorithm published in The Professional Geographer by Dougenik, Chrisman, and Niemeyer (DCN) in 1985. The DCN algorithm simulates a rubber sheet and is an iterative and approximate solution of cartogram construction. Although it remains popular because of its conceptual simplicity and cartographic quality, the DCN algorithm cannot completely preserve topology and its mathematical properties are inadequately explained. This article presents an optimization to the DCN algorithm, named Opti-DCN, with three improvements. First, it provides a mathematical condition for topology preservation. Second, new transformation equations that meet this condition are deduced from mathematics, which simultaneously optimize the global elasticity coefficient, a key parameter that greatly impacts the convergence rate of the rubber-sheet algorithm and the topological integrity of its generated cartograms. Last, the new algorithm simplifies the way of generating transforming forces in DCN and improves its efficiency of geometric transformation. Comparison shows that Opti-DCN is significantly faster to converge to equal-density cartograms and can mathematically and practically eliminate topological errors.

Voronoi distance based prospective space-time scans for point data sets: a dengue fever cluster analysis in a southeast Brazilian town

BackgroundThe Prospective Space-Time scan statistic (PST) is widely used for the evaluation of space-time clusters of point event data. Usually a window of cylindrical shape is employed, with a circular or elliptical base in the space domain. Recently, the concept of Minimum Spanning Tree (MST) was applied to specify the set of potential clusters, through the Density-Equalizing Euclidean MST (DEEMST) method, for the detection of arbitrarily shaped clusters. The original map is cartogram transformed, such that the control points are spread uniformly. That method is quite effective, but the cartogram construction is computationally expensive and complicated.ResultsA fast method for the detection and inference of point data set space-time disease clusters is presented, the Voronoi Based Scan (VBScan). A Voronoi diagram is built for points representing population individuals (cases and controls). The number of Voronoi cells boundaries intercepted by the line segment joining two cases points defines the Voronoi distance between those points. That distance is used to approximate the density of the heterogeneous population and build the Voronoi distance MST linking the cases. The successive removal of edges from the Voronoi distance MST generates sub-trees which are the potential space-time clusters. Finally, those clusters are evaluated through the scan statistic. Monte Carlo replications of the original data are used to evaluate the significance of the clusters. An application for dengue fever in a small Brazilian city is presented.ConclusionsThe ability to promptly detect space-time clusters of disease outbreaks, when the number of individuals is large, was shown to be feasible, due to the reduced computational load of VBScan. Instead of changing the map, VBScan modifies the metric used to define the distance between cases, without requiring the cartogram construction. Numerical simulations showed that VBScan has higher power of detection, sensitivity and positive predicted value than the Elliptic PST. Furthermore, as VBScan also incorporates topological information from the point neighborhood structure, in addition to the usual geometric information, it is more robust than purely geometric methods such as the elliptic scan. Those advantages were illustrated in a real setting for dengue fever space-time clusters.

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.

A new algorithm for distance cartogram construction

A distance cartogram is a diagram that visualizes the proximity indices between points in a network, such as time–distances between cities. The Euclidean distances between the points on the distance cartogram represent the given proximity indices. This is a useful visualization tool for the level of service of transport, e.g. difference in the level of service between regions or points in a network and its improvement in the course of time. The two previously proposed methods—multidimensional scaling (MDS) and network time–space mapping—have certain advantages and disadvantages. However, we observe that these methods are essentially the same, and the merits of both these methods can be combined to formulate a generalized solution. In this study, we first formulate the time–space mapping problem, which includes the key features of both of the above stated methods, and propose a generalized solution. We then apply this solution to the time–distances of Japan's railway networks to confirm its applicability.

Topological Coordinates: Numerically Encoding the Underlying Topological Structure of Plane Graphs

A new methodology is presented for the concise numerical encoding of a map's topological structure based on several surprising and beautifully intertwined graph decomposition results due to Walter Schnyder. Not only are Schnyder's methods used to determine new positions for a graph's vertices, a map's topological connectivity information is also simultaneously implicitly stored and recovered by folding information about the edge structure of its embedded line-segment graph into numerical topology-based barycentric coordinates chosen for the graph's vertices. Properties of the alternative geometric realization are explored and shown to permit cartogram construction by systematically altering the topological coordinates to modify the regions' relative areas.

Studies on New Cartogram Construction Algorithms and Their Applications

Cartograms are tools that show the spatial distribution of data by the transformation of map shapes, and they are considered as effective visualization tools for statistical data. In this paper, we focus on cartograms because they are capable of developing statistical GIS, and we propose cartogram construction algorithms. First, we establish the following principles for algorithm development I. Describe cartogram construction problems by the linear least squares method to simplify and elucidate algorithms. II. Regularize the problems through restrictions on the bearing changes of the edges in order to obtain visually clear cartograms in which the shapes of resultant regions resemble the corresponding shapes on geographical maps. Then, according to the principles, we propose construction algorithms for three types of cartograms and illustrate their applicability to the visualization of statistical data.

On rectangular cartograms

A rectangular cartogram is a type of map where every region is a rectangle. The size of the rectangles is chosen such that their areas represent a geographic variable (e.g., population). Good rectangular cartograms are hard to generate: The area specifications for each rectangle may make it impossible to realize correct adjacencies between the regions and so hamper the intuitive understanding of the map. We present the first algorithms for rectangular cartogram construction. Our algorithms depend on a precise formalization of region adjacencies and build upon existing VLSI layout algorithms. Furthermore, we characterize a non-trivial class of rectangular subdivisions for which exact cartograms can be computed efficiently. An implementation of our algorithms and various tests show that in practice, visually pleasing rectangular cartograms with small cartographic error can be generated effectively.

A New Algorithm for Continuous Area Cartogram Construction with Triangulation of Regions and Restriction on Bearing Changes of Edges

A continuous area cartogram is a transformed map in which regions are resized relative to their data. It is considered an effective visualization tool for statistical data, and many solutions have been proposed. However, most of these solutions are not mathematically clear or user friendly; further, they do not provide visually elegant area cartograms. An essential condition for the construction of a visually elegant area cartogram is that the resultant region shape should resemble the corresponding regions on geographical maps. Since it is impossible to determine the shape of a region based only on the information of size, area cartogram construction is an ill-posed problem that requires regularization. In this study, we propose a construction algorithm that involves triangulation of regions and regularization through restrictions on the bearing changes of the edges in order to obtain visually clear results. First, we formulate a construction using nonlinear least squares. Then, by linearizing, we derive a simple formula to create area cartograms. The application of our algorithm to the USA population datasets reveals that our algorithm has mathematical clarity and is user friendly.

A Note on the Importance of Shape in Cartogram Communication

Abstract Communicating with value-by-area cartograms is at best a difficult task. However, the mapmaker can render a cartogram more meaningful in communication by retaining the basic shapes of the statistical units. This idea was examined and several tests were administered to subjects to gain information about points along state shapes that are used as cues in map reading. It was determined that map readers mentally generalize geographic shapes into ones that are similar to the over-all shape quality of the originals. In cartogram construction, the mapmaker should provide at least those points along state outlines that are proven to be the cues for shape identification. Anything less will detract from its ability to communicate effectively and, in fact, if this is the case alternate mapping methods should be employed.