Topology-Preserving Line Densification for Creating Contiguous Cartograms

TL;DR

This paper introduces a topology-preserving line densification method that ensures cartogram regions remain connected and non-overlapping during density-equalizing map projections, improving accuracy and speed.

Contribution

The authors propose a novel densification technique combined with a flow-based generator to create strictly topology-preserving cartograms.

Findings

Produces more accurate cartograms

Faster than alternative methods

Maintains shape fidelity

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.