van Dijk, van Goethem, Haunert, Meulemans and Speckmann – AN AUTOMATED METHOD FOR CIRCULAR-ARC METRO MAPS 2014

Description

The paper presents an automated method to schematize metro maps using circular arcs. Starting from a geographic transit network, the algorithm first deforms the map with minimum-distortion focus maps to even out network density and improve readability. It then partitions the network into strokes—simple paths and cycles—by aggregating adjacent connections that share lines and by grouping branches based on minimal angular change, further merging segments by angular deviation. Schematization proceeds iteratively by replacing pairs of arcs with a single candidate arc chosen to approximate the deformed geometry via the Fréchet distance, continuing until a user-set arc count is reached. Special handling for high-degree interchange vertices allows replacements to cross interchanges: degree-3 vertices extend the remaining connection, while higher-degree vertices constrain replacement arcs to stay near original locations, represented as minimum-enclosing disks. Examples (Vienna, Karlsruhe, London) illustrate results at varying arc budgets. Future work includes enforcing inter-station and inter-line distances and balancing continuity at different-degree vertices.