An algorithm for accurate and simple-looking metaphorical maps
Eleni Katsanou, Tamara Mchedlidze, Antonios Symvonis, Thanos Tolias

TL;DR
This paper extends a force-based algorithm for creating metaphorical maps of vertex-weighted graphs, significantly improving area accuracy while maintaining visual simplicity, and generalizing to non-triangulated graphs.
Contribution
It introduces region stiffness variation, a weight coefficient for narrow passages, and handles non-triangulated graphs, enhancing accuracy, simplicity, and generality of metaphorical maps.
Findings
Maps achieve nearly perfect area accuracy
Minimal sacrifice in map simplicity
Effective for non-triangulated graphs
Abstract
"Metaphorical maps" or "contact representations" are visual representations of vertex-weighted graphs that rely on the geographic map metaphor. The vertices are represented by countries, the weights by the areas of the countries, and the edges by contacts/ boundaries among them. The accuracy with which the weights are mapped to areas and the simplicity of the polygons representing the countries are the two classical optimization goals for metaphorical maps. Mchedlidze and Schnorr [Metaphoric Maps for Dynamic Vertex-weighted Graphs, EuroVis 2022] presented a force-based algorithm that creates metaphorical maps that balance between these two optimization goals. Their maps look visually simple, but the accuracy of the maps is far from optimal - the countries' areas can vary up to 30% compared to required. In this paper, we provide a multi-fold extension of the algorithm in [Metaphoric Maps…
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