CartoDraw: a fast algorithm for generating contiguous cartograms.

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 study, we formally define a family of cartogram drawing problems. We show that even simple variants are unsolvable in the general case. Because the feasible variants are NP-complete, heuristics are needed to solve the problem. Previously proposed solutions suffer from problems with the quality of the generated drawings. For a cartogram to be recognizable, it is important to preserve the global shape or outline of the input map, a requirement that has been overlooked in the past. To address this, our objective function for cartogram drawing includes both global and local shape preservation. To measure the degree of shape preservation, we propose a shape similarity function, which is based on a Fourier transformation of the polygons' curvatures. Also, our application is visualization of dynamic data, for which we need an algorithm that recalculates a cartogram in a few seconds. None of the previous algorithms provides adequate performance with an acceptable level of quality for this application. In this paper, we therefore propose an efficient iterative scanline algorithm to reposition edges while preserving local and global shapes. Scanlines may be generated automatically or entered interactively to guide the optimization process more closely. We apply our algorithm to several example data sets and provide a detailed comparison of the two variants of our algorithm and previous approaches.