Approaches to map anamorphosis

Map anamorphosis is the distortion of a map to show graphically the variation of some quantity from region to region. The process of anamorphosis modifies the original map regions, keeping the inter-region topology, to produce new regions whose areas are proportional to their respective values of the relevant quantity. A typical example would be a distorted map of the United States, where each state's area is proportional to its population, yet the states still fit together in the correct way. Such maps, called "cartograms", can provide a good visual sense of where a quantity such as population, is distributed. In this paper we look at five separate attempts to design a computer algorithm for generating cartograms, all of which use triangulation as a basis, and all of which, unfortunately, are unsuccessful. We also examine a working algorithm, in the literature that uses similar ideas in its initial approach. While this algorithm produces aesthetically displeasing results, it may indicate a way to solve the map anamorphosis problem robustly using triangulation.