Abstract
Cartograms are tools that show the spatial distribution of data by the transformation of map shapes, and they are considered as effective visualization tools for statistical data. In this paper, we focus on cartograms because they are capable of developing statistical GIS, and we propose cartogram construction algorithms. First, we establish the following principles for algorithm development I. Describe cartogram construction problems by the linear least squares method to simplify and elucidate algorithms. II. Regularize the problems through restrictions on the bearing changes of the edges in order to obtain visually clear cartograms in which the shapes of resultant regions resemble the corresponding shapes on geographical maps. Then, according to the principles, we propose construction algorithms for three types of cartograms and illustrate their applicability to the visualization of statistical data.
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