Elastic beam algorithm for generating circular cartograms

ABSTRACT

The circular cartogram, also known as the Dorling map, is a widely used tool for visualizing statistical data. It represents regions as circles with their areas in proportion to the statistical values and requires circle displacement to avoid overlap and maintain spatial relationships. In this paper, we propose a new approach for circular cartogram production that utilizes the elastic beam displacement algorithm in cartographic generalization. First, the initial circles are generated with their areas in proportion to the statistical values. Second, an elastic beam structure is built as a proximity graph based on the spatial relations between the circles. Third, the circles violating the quality requirements are considered to have a force on the nodes of a beam. Fourth, the elastic beam algorithm is applied to assign forces for each node to determine the new positions of the circles. Steps two through four are repeated until a circular cartogram that meets the defined quality requirements is obtained. The experiments indicate that the proposed approach can successfully generate circular cartograms without overlaps while maintaining topology and relative relationships with higher quality than existing approaches. Project website: https://github.com/TrentonWei/DorlingMap

KEYWORDS:

• Cartogram
• Dorling map
• displacement
• population mapping
• energy minimization

Acknowledgments

The authors would like to thank Dr. Yuangang Liu, the editors and the anonymous reviewers for their helpful and constructive comments that greatly contributed to improve the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data and code availability statement and data deposition

The data and code that support the findings of this study are all openly available, website is: https://github.com/TrentonWei/DorlingMap.

Additional information

Funding

This work was supported by the The National Natural Science Foundation of China [grant agreement No 41871378] and The Youth Innovation Promotion Association Foundation of Chinese Academy of Sciences [grant agreement No Y9C0060].