Barry Kronenfeld, Eastern Illinois University
Automated algorithms are limited in their ability to produce aesthetically pleasing cartograms, while currently available methods for manual cartogram construction (i.e. block cartograms) do not define a continuous spatial transformation. I propose an alternative framework for cartogram construction using triangular lattice transformation. In the proposed framework, a regular lattice is transformed by repositioning vertices until vertex density approximates population density, forming a dot-density map. The original and transformed lattices define a continuous transformation from geographic space to cartogram space. The transformation is reusable and can be applied to any geographic dataset, acting as a type of map projection. Sample tools for constructing and applying cartograms are demonstrated, and the approach is illustrated with a population cartogram of Illinois, USA. By separating the task of defining a cartogram from the map design process, the proposed framework aims to facilitate more widespread application of cartograms to the analysis of population-dependent variables.