Rectangular cartograms

Abstract

Raisz [3] introduced rectangular cartograms in 1934 as a way of visualizing spatial information, such as population or economic strength, of a set of regions like countries or states. Rectangular cartograms represent geographic regions by rectangles; the positioning and adjacencies of the are chosen according to their geographic locations, while their areas are proportional to the numeric values being communicated by the cartogram. Rectangles have the advantage that the sizes (area) of the regions can be estimated easily. On the other hand the rectangular shape is less recognizable and imposes limitations on possible layouts of the cartogram. In recent years several algorithms [2, 4, 5] were developed to efficiently compute rectangular cartograms. This note describes a game that was inspired by these algorithmic results. The game was initially developed as part of the outreach effort of TU Eindhoven, and it has been used at TU Eindhoven’s Open Day. The goal of the Open Day is to popularize the research activities of the various departments; the audience are often families with children in the age 6–15, or parents of (prospective) students. The goal of our game was thus to show in an entertaining way the difficulties one faces when developing algorithms for automatic cartogram construction. The game was quite popular, especially with children. It is an applet and can be found at http://www.win.tue.nl/~speckman/demos/game/. Following [4, 5] the cartograms used in the game are each based on a rectangular layout: a subdivision of a rectangle into finitely many interior-disjoint rectangles. Each region of the input map corresponds to a rectangle of the layout, in addition the layout may contain additional sea rectangles that help to preserve the original outline of the regions. See, for example, Figure 1: the lower left corner shows a layout for the currently loaded map, in this case, the provinces of the Netherlands. The layout precisely specifies the required rectangle adjacencies of the final cartogram.