Computer Science – Computational Geometry
Scientific paper
2011-12-20
Computer Science
Computational Geometry
16 pages, 11 figures
Scientific paper
We present a new circular-arc cartogram model in which countries are drawn with circular arcs instead of straight-line segments. Given a geographic map and values associated with each country in the map, the cartogram is a new map in which the areas of the countries represent the corresponding values. In the circular-arc cartogram model straight-line segments can be replaced with circular arcs in order to achieve the desired areas, while the corners of the polygons defining each country remain fixed. The countries in circular-arc cartograms have the aesthetically pleasing appearance of clouds or snowflakes, depending on whether their edges are bent outwards or inwards. This makes is easy to determine whether a country has grown or shrunk, just by its overall shape. We show that determining whether a given map and area-values can be realized with a circular-arc cartogram is an NP-hard problem. Next we describe a heuristic method for constructing circular-arc cartograms, which uses a max-flow computation on the dual of the map, along with a computation of the straight skeleton of the underlying polygonal decomposition. Our method is implemented and produces cartograms that, while not perfectly accurate, achieve the desired areas for many real-world examples.
Kämper Jan-Hinrich
Kobourov Stephen G.
Nöllenburg Martin
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