Constructing topology‐constrained distance cartograms with application on spatial interaction data

Abstract

A distance cartogram is a deformed map where the distance between points conforms to a specific proximity indicator. Its readability is crucial, requiring a similar spatial arrangement of points between the original map and cartogram. Previous studies mainly incorporated angle changes of point pairs into the optimization objective. However, this soft constraint fails to provide high readability for spatial interaction data with numerous points and links. This study emphasizes the significance of maintaining Delaunay triangulation during deformation. To achieve this, topology‐constrained particle swarm optimization (TC‐PSO) is proposed, in which triangle intersections and flipping are prevented during optimization. Additionally, a topology error is introduced to evaluate the difference in triangulation between the original and deformed maps. TC‐PSO outperforms previous approaches by exhibiting the smallest topology error and producing more readable cartograms in simulation experiments and Baidu index data. These show TC‐PSO's advantage as a cartographic tool.