Rectangular cartograms
Sander Florisson, Marc J. van Kreveld, Bettina Speckmann · 2005
Cartograms, which are also referred to as value-by-area maps, are a useful and intuitive way to visualize statistical data about a set of regions like countries, states or provinces. The size of a region in a cartogram corresponds to a particular geographic variable [1]. Since the sizes of the regions are not their true sizes they generally cannot keep both their shape and their adjacencies. A good cartogram, however, preserves the recognizability in some way. Globally speaking, there are three types of cartogram. The standard type (the contiguous area cartogram) has deformed regions so that the desired sizes can be obtained and the adjacencies kept. Algorithms for such cartograms are described in [2, 3, 6, 9]. The second type of cartogram is the non-contiguous area cartogram [7]. The regions have the true shape, but are scaled down and generally do not touch anymore. The third type of cartogram is the rectangular cartogram, introduced by Raisz in 1934 [8], where each region is represented by a rectangle. This has the advantage that the sizes (area) of the regions can be estimated much better than with the first two types. Tobler states in a recent survey, “Thirty-five years of computer cartograms” [10], that none of the existing cartogram algorithms are capable of generating rectangular cartograms. However, even more recently the last two authors of this abstract presented the first algorithms for rectangular cartogram construction [11].