We present a new circular-arc cartogram model in which countries are drawn as
polygons with circular arcs instead of straight-line segments. Given a
political map and values associated with each country in the map, a cartogram
is a distorted map in which the areas of the countries are proportional to the
corresponding values. In the circular-arc cartogram model straight-line
segments can be replaced by circular arcs in order to modify the areas of the
polygons, while the corners of the polygons 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 it easy to determine whether a country has grown or shrunk, just by its
overall shape. We show that determining whether a given map and given
area-values can be realized as 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 graph 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 yet perfectly
accurate, achieve many of the desired areas in our real-world examples.Comment: 10 pages, 14 figures, extended version of proceedings paper in
PacificVis 201
