295 research outputs found
The State of the Art in Cartograms
Cartograms combine statistical and geographical information in thematic maps,
where areas of geographical regions (e.g., countries, states) are scaled in
proportion to some statistic (e.g., population, income). Cartograms make it
possible to gain insight into patterns and trends in the world around us and
have been very popular visualizations for geo-referenced data for over a
century. This work surveys cartogram research in visualization, cartography and
geometry, covering a broad spectrum of different cartogram types: from the
traditional rectangular and table cartograms, to Dorling and diffusion
cartograms. A particular focus is the study of the major cartogram dimensions:
statistical accuracy, geographical accuracy, and topological accuracy. We
review the history of cartograms, describe the algorithms for generating them,
and consider task taxonomies. We also review quantitative and qualitative
evaluations, and we use these to arrive at design guidelines and research
challenges
Diffusion-based method for producing density equalizing maps
Map makers have long searched for a way to construct cartograms -- maps in
which the sizes of geographic regions such as countries or provinces appear in
proportion to their population or some other analogous property. Such maps are
invaluable for the representation of census results, election returns, disease
incidence, and many other kinds of human data. Unfortunately, in order to scale
regions and still have them fit together, one is normally forced to distort the
regions' shapes, potentially resulting in maps that are difficult to read. Many
methods for making cartograms have been proposed, some of them extremely
complex, but all suffer either from this lack of readability or from other
pathologies, like overlapping regions or strong dependence on the choice of
coordinate axes. Here we present a new technique based on ideas borrowed from
elementary physics that suffers none of these drawbacks. Our method is
conceptually simple and produces useful, elegant, and easily readable maps. We
illustrate the method with applications to the results of the 2000 US
presidential election, lung cancer cases in the State of New York, and the
geographical distribution of stories appearing in the news.Comment: 12 pages, 3 figure
Evaluating Cartogram Effectiveness
Cartograms are maps in which areas of geographic regions (countries, states)
appear in proportion to some variable of interest (population, income).
Cartograms are popular visualizations for geo-referenced data that have been
used for over a century and that make it possible to gain insight into patterns
and trends in the world around us. Despite the popularity of cartograms and the
large number of cartogram types, there are few studies evaluating the
effectiveness of cartograms in conveying information. Based on a recent task
taxonomy for cartograms, we evaluate four major different types of cartograms:
contiguous, non-contiguous, rectangular, and Dorling cartograms. Specifically,
we evaluate the effectiveness of these cartograms by quantitative performance
analysis, as well as by subjective preferences. We analyze the results of our
study in the context of some prevailing assumptions in the literature of
cartography and cognitive science. Finally, we make recommendations for the use
of different types of cartograms for different tasks and settings
Density-equalizing maps for simply-connected open surfaces
In this paper, we are concerned with the problem of creating flattening maps
of simply-connected open surfaces in . Using a natural principle
of density diffusion in physics, we propose an effective algorithm for
computing density-equalizing flattening maps with any prescribed density
distribution. By varying the initial density distribution, a large variety of
mappings with different properties can be achieved. For instance,
area-preserving parameterizations of simply-connected open surfaces can be
easily computed. Experimental results are presented to demonstrate the
effectiveness of our proposed method. Applications to data visualization and
surface remeshing are explored
Optimization-Based Construction of Quadrilateral Table Cartograms
A quadrilateral table cartogram is a rectangle-shaped figure that visualizes table-form data; quadrilateral cells in a table cartogram are transformed to express the magnitude of positive weights by their areas, while maintaining the adjacency of cells in the original table. However, the previous construction method is difficult to implement because it consists of multiple operations that do not have a unique solution and require complex settings to obtain the desired outputs. In this article, we propose a new construction for quadrilateral table cartograms by recasting the construction as an optimization problem. The proposed method is formulated as a simple minimization problem to achieve mathematical clarity. It can generate quadrilateral table cartograms with smaller deformation of rows and columns, thereby aiding readers to recognize the correspondence between table cartograms and original tables. In addition, we also propose a means of sorting rows and/or columns prior to the construction of table cartograms to reduce excess shape deformation. Applications of the proposed method confirm its capability to output table cartograms that clearly visualize the characteristics of datasets
The use of cartograms for BGS data and information representation
Cartograms are shown to be superior to both choropleth maps and bar charts, as they are
designed to deliver geospatial statistics effectively and efficiently. This report presents the results
of research in establishing the potential for the use of area cartograms for science information
delivery. The research involved establishing an overview of all the types of cartogram used;
noting the types of data used in their creation and identifying similar sources of data that may
prove appropriate for use in cartograms. Test examples were created and presented along with an
evaluation as to their effectiveness and efficiency in communicating spatially orientated datasets.
The work was carried out as part of the Data Representation and Presentation project for the
Geospatial Capture and Solutions team. This forms part of a wider research project investigating
new ways in which BGS can display science and information more effectively to a broad range
of audiences
Computing Fast and Scalable Table Cartograms for Large Tables
Given an m x n table T of positive weights and a rectangle R with an area equal to the sum of the weights, a table cartogram computes a partition of R into m x n convex quadrilateral faces such that each face has the same adjacencies as its corresponding cell in T, and has an area equal to the cell's weight. In this thesis, we explored different table cartogram algorithms for a large table with thousands of cells and investigated the potential applications of large table cartograms. We implemented Evans et al.'s table cartogram algorithm that guarantees zero area error and adapted a diffusion-based cartographic transformation approach, FastFlow, to produce large table cartograms. We introduced a constraint optimization-based table cartogram generation technique, TCarto, leveraging the concept of force-directed layout. We implemented TCarto with column-based and quadtree-based parallelization to compute table cartograms for table with thousands of cells. We presented several potential applications of large table cartograms to create the diagrammatic representations in various real-life scenarios, e.g., for analyzing spatial correlations between geospatial variables, understanding clusters and densities in scatterplots, and creating visual effects in images (i.e., expanding illumination, mosaic art effect). We presented an empirical comparison among these three table cartogram techniques with two different real-life datasets: a meteorological weather dataset and a US State-to-State migration flow dataset. FastFlow and TCarto both performed well on the weather data table. However, for US State-to-State migration flow data, where the table contained many local optima with high value differences among adjacent cells, FastFlow generated concave quadrilateral faces. We also investigated some potential relationships among different measurement metrics such as cartographic error (accuracy), the average aspect ratio (the readability of the visualization), computational speed, and the grid size of the table. Furthermore, we augmented our proposed TCarto with angle constraint to enhance the readability of the visualization, conceding some cartographic error, and also inspected the potential relationship of the restricted angles with the accuracy and the readability of the visualization. In the output of the angle constrained TCarto algorithm on US State-to-State migration dataset, it was difficult to identify the rows and columns for a cell upto 20 degree angle constraint, but appeared to be identifiable for more than 40 degree angle constraint
- …