Manual construction of continuous cartograms through mesh transformation

A computer-assisted framework is proposed to support the manual construction of cartograms. The framework employs a joint triangulation, similar to that used in rubber-sheeting, to define a piecewise affine transformation between map space and cartogram space. This guarantees preservation of all topological relations within and among transformed datasets with insertion of a finite number of points. To support intuitive user control of cartogram appearance, methods are developed to translate generically defined user adjustments of the cartogram into mesh vertex positions on either the source map mesh or cartogram mesh. The framework is implemented in a working prototype application and used to create sample cartograms of the USA and China. Results are compared with cartograms produced using diffusion and carto3f algorithms in terms of accuracy, aesthetic appearance, and approximate construction time. Qualitative aspects of the manual construction process are also discussed.