Topology-Preserving Line Densification for Creating Contiguous Cartograms
Density-equalizing map projections often suffer from topological failures—such as region disconnection or overlap—due to sparse boundary polygon vertices. To address this, we propose a conformal polyline densification method that, for the first time, rigorously guarantees regional connectivity and non-overlap in density-equalizing cartogram generation. Our approach integrates a flow-field-driven deformation framework, an adaptive boundary polyline subdivision strategy, and a geometry-topology co-verification mechanism, thereby preserving shape fidelity while enhancing structural consistency. Experimental evaluation demonstrates that our method outperforms state-of-the-art techniques in cartographic accuracy, computational efficiency, and topological robustness. It is particularly suitable for high-precision geographic data visualization, enabling reliable and interpretable spatial representations under significant density distortion.