Topology-Preserving Line Densification for Creating Contiguous Cartograms
Abstract
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.
Cite
@article{arxiv.2511.08121,
title = {Topology-Preserving Line Densification for Creating Contiguous Cartograms},
author = {Nihal Z. Miaji and Adi Singhania and Matthias E. Goh and Callista Le and Atima Tharatipyakul and Michael T. Gastner},
journal= {arXiv preprint arXiv:2511.08121},
year = {2026}
}
Comments
27 pages. 9 figures, and 5 tables in the main text. 1 supplementary figure and 6 supplementary tables. Accepted for publication in "Cartography and Geographic Information Science." This version includes higher-resolution figures, a publicly accessible Figshare link to the data, and updated funding information