Topology-preserving line densification for creating contiguous cartograms

Cartograms depict geographic regions with areas proportional to quantitative data. However, when created using density-equalizing map projections, cartograms may exhibit invalid topologies if boundary polygons are drawn using only a finite set of vertices connected by straight lines. Here we introduce a method for topology-preserving line densification that guarantees that cartogram regions remain connected and non-overlapping when using density-equalizing map projections. By combining our densification technique with a flow-based cartogram generator, we present a robust framework for strictly topology-preserving cartogram construction. Quantitative evaluations demonstrate that the proposed algorithm produces cartograms with greater accuracy and speed than alternative methods while maintaining comparable shape fidelity.

Recommended citation: Miaji, Nihal Z., Adi Singhania, Matthias E. Goh, Callista Le, Atima Tharatipyakul, and Michael T. Gastner. "Topology-preserving line densification for creating contiguous cartograms." Cartography and Geographic Information Science, pp. 1-16. 2026.
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