Circular-arc cartograms

Jan Hinrich Kämper, Stephen G. Kobourov, Martin Nollenburg

Research output: Chapter in Book/Report/Conference proceedingConference contribution

16 Scopus citations


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.

Original languageEnglish (US)
Title of host publicationIEEE Symposium on Pacific Visualization 2013, PacificVis 2013 - Proceedings
Number of pages8
StatePublished - 2013
Event6th IEEE Symposium on Pacific Visualization, PacificVis 2013 - Sydney, NSW, Australia
Duration: Feb 26 2013Mar 1 2013

Publication series

NameIEEE Pacific Visualization Symposium
ISSN (Print)2165-8765
ISSN (Electronic)2165-8773


Other6th IEEE Symposium on Pacific Visualization, PacificVis 2013
CitySydney, NSW


  • I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Computer Vision and Pattern Recognition
  • Hardware and Architecture
  • Software


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