Topology-Preserving Line Densification for Creating Contiguous Cartograms
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arXiv
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| Hauptverfasser: | , , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911383590797312 |
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| author | Miaji, Nihal Z. Singhania, Adi Goh, Matthias E. Le, Callista Tharatipyakul, Atima Gastner, Michael T. |
| author_facet | Miaji, Nihal Z. Singhania, Adi Goh, Matthias E. Le, Callista Tharatipyakul, Atima Gastner, Michael T. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08121 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topology-Preserving Line Densification for Creating Contiguous Cartograms Miaji, Nihal Z. Singhania, Adi Goh, Matthias E. Le, Callista Tharatipyakul, Atima Gastner, Michael T. Computational Geometry 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. |
| title | Topology-Preserving Line Densification for Creating Contiguous Cartograms |
| topic | Computational Geometry |
| url | https://arxiv.org/abs/2511.08121 |