Abstract
Cartograms are a well-known technique for showing geography-related statistical information, such as population demographics and epidemiological data. The basic idea is to distort a map by resizing its regions according to a statistical parameter, but in a way that keeps the map recognizable. In this paper, we deal with the problem of making continuous cartograms that strictly retain the topology of the input mesh. We compare two algorithms that solve the continuous cartogram problem. The first one uses an iterative relocation of vertices based on scanlines. This algorithm explicitly accounts for induced shape error. The second one is based on the Gridfit technique, which uses pixel-based distortion based on a quadtree-like data structure. The basic idea is to insert pixels, the number of which corresponds to a statistical parameter, into the data structure and distort the pixels such that every pixel obtains a unique, nonoverlapping position. Relocation of vertices of the map are positioned using the same distortion. We discuss the results obtained from both methods, compare their shape and area trade-offs as well as their efficiency, and show results from different applications.
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