Cartogram Algorithms
Force-based algorithms for contiguous cartograms
Cartogram Algorithms
Abstract from my recent cartogram algorithm publication
“Automatic production of contiguous area cartograms has become practical with computer algorithms, particularly applying forces to rubber-sheets and simulating diffusion processes. Reformulating the existing force-based and rubber-sheet methods, this article presents a fast and flexible force-based computational framework for general space transformation with solid physical and mathematical foundations. When being applied to cartogram production, this framework guarantees topological integrity, allows flexible force generation, achieves fast convergence, and avoids extreme shape deformation. Benchmarked against the recently published fast flow-based diffusion method using five datasets of various volume, compactness, and complexity, this force-based framework is faster, reduces more shape deformation, and can produce cartograms with distinctive slim or inflated styles. Additionally, the force-based framework is robust and can handle complicated datasets, whereas the flow-based method produces errors from them. Although the flow-based diffusion method often reduces cartogram size error more than the force-based (typical weighted mean error is below 0.1% versus 1%), both are outstanding with such low levels of error and their cartograms generally register little visual differences. Overall, the force-based transformation framework provides a fast, flexible, and robust alternative to the diffusion method for cartogram production.”
References
Sun, S. (2020). Applying forces to generate cartograms: a fast and flexible transformation framework. Cartography and Geographic Information Science, 1-19. https://doi.org/10.1080/15230406.2020.1745092
Sun, S. (2013). A Fast Free-Form Rubber-Sheet Algorithm for Contiguous Area Cartograms. International Journal of Geographic Information Science, 27(3), 567-593. https://doi.org/10.1080/13658816.2012.709247
Sun, S. (2013). An Optimized Rubber-Sheet Algorithm for Continuous Area Cartograms. The Professional Geographer, 65(1), 16-30. https://doi.org/10.1080/00330124.2011.639613