Cartogram

Abstract: The notion of a cartogram is reviewed. Then, based on a presentation from the 1960s, a direct and simple introduction is given to the design of a computer algorithm for the construction of contiguous value-by-area cartograms. As an example, a table of latitude/longitude to rectangular plane coordinates is included for a cartogram of the United States, along with Tissot's measures for this map projection. This is followed by a short review of the subsequent history of the subject and includes citation of algorithms proposed by others. In contrast to the usual geographic map, the most common use of cartograms is solely for the display and emphasis of a geographic distribution. A second use is in analysis, as a nomograph or problem-solving device similar in use to Mercator's projection, or in the transform-solve-invert paradigm. Recent innovations by computer scientists modify the objective and suggest variation similar to Airy's (1861) “balance of errors” idea for map projections.

Abstract: 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.

Abstract: In many application domains, data is collected and referenced by its geospatial location. Nowadays, different kinds of maps are used to emphasize the spatial distribution of one or more geospatial attributes. The nature of geospatial statistical data is the highly nonuniform distribution in the real world data sets. This has several impacts on the resulting map visualizations. Classical area maps tend to highlight patterns in large areas, which may, however, be of low importance. Cartographers and geographers used cartograms or value-by-area maps to address this problem long before computers were available. Although many automatic techniques have been developed, most of the value-by-area cartograms are generated manually via human interaction. In this paper, we propose a novel visualization technique for geospatial data sets called RecMap. Our technique approximates a rectangular partition of the (rectangular) display area into a number of map regions preserving important geospatial constraints. It is a fully automatic technique with explicit user control over all exploration constraints within the exploration process. Experiments show that our technique produces visualizations of geospatial data sets, which enhance the discovery of global and local correlations, and demonstrate its performance in a variety of applications

Abstract: Area cartograms are used for visualizing geographically distributed data by attaching measurements to regions of a map and scaling the regions such that their areas are proportional to the measured quantities. A continuous area cartogram is a cartogram that is constructed without changing the underlying map topology. We present a new algorithm for the construction of continuous area cartograms that was developed by viewing their construction as a constrained optimization problem. The algorithm uses a relaxation method that exploits hierarchical resolution, constrained dynamics, and a scheme that alternates goals of achieving correct region areas and adjusting region shapes. It is compared favorably to existing methods in its ability to preserve region shape recognition cues, while still achieving high accuracy.