Medial-axis-based cartograms

Cartographers and geographers were making cartograms for centuries before digital computers and displays became available. In data visualization, an area cartogram distorts a map by resizing its regions according to some external geography-related parameter, such as population or epidemiological data. Cartograms are difficult to draw by hand because it's difficult to simultaneously optimize shape and area error while preserving the original map's topology. Automated methods for drawing cartograms have therefore received considerable interest. A method for generating cartograms that combines iterative relocation of a map's vertices with medial-axis-based transformations retains the input map's topology.