Circular cartograms via the elastic beam algorithm originated from cartographic generalization

The circular cartogram, also known as the Dorling map, is a widely used tool to visualize statistical data. The circular cartogram represents regions as circles with their sizes in proportion to the statistical values, and these circles are displaced with quality requirements such as no overlaps and contiguity maintenance satisfied. The displacement is a basic operation in cartographic generalization to fulfill map requirements, and many algorithms for map objects' displacements have been introduced. The circles in a circular cartogram can also be considered as map objects. Thus, we develop a new approach by using the elastic beam displacement algorithm in cartographic generalization to displace circles in circular cartogram production. First, the initial circles are generated with their sizes in proportion to the statistical values to avoid huge gaps or overlaps. Second, an elastic beam structure is built as a proximity graph by analyzing the spatial relationships between the circles. Third, the circles violating the quality requirements are considered to have a force on the node of a beam. Fourth, the elastic beam algorithm to achieve global optimization is applied to assign forces for each node to decide the new positions of the circles. Steps 2 to 4 are repeated until a circular cartogram that satisfies the defined quality requirements is obtained. The evaluation results indicate that the circular cartograms generated by the proposed approach have a higher quality for the maintenance of topology relations, contiguities, and relative relations with smaller displacement distances compared to the existing approaches.