Topology-Aware Algorithm for Constructing Cartograms from Density-Equalising Map Projections

Cartograms are maps in which the areas of enumeration units $\text{(}$e.g. administrative divisions$\text{)}$ are proportional to quantitative data $\text{(}$e.g. population$\text{)}$. Generating cartograms with density-equalising map projections guarantees that geographic neighbours remain neighbours in the cartograms if all boundaries are infinitely dense sequences of points. However, computers represent boundaries with only finitely many points, often causing invalid topologies in the cartogram. This talk shows how line densification and topology-aware simplification solve this problem.