From river flow to spatial flow: flow map via river flow directions assignment algorithm

Flow maps are thematic maps that visualize object movements across space with a tree layout, in which the underlying tree structure is similar to a natural river system. In this paper, we present a novel and automated approach named RFDA-FM for flow maps from one origin to multiple destinations using a river extraction algorithm in digital elevation models (DEM). The RFDA-FM first models the mapping space as a flat surface by a DEM. A maze-solving algorithm (MSA) for river extraction is then adapted to calculate the flow path from one destination to the origin by constraining its searching directions, direction weights, and searching ranges according to the quality criteria of flow maps. All flow paths from the destinations to the origin are obtained iteratively based on the MSA according to their importance, which is defined by considering their length. Finally, these paths are smoothly rendered with varying widths according to their volume using B\'ezier curves. A comparison with existing approaches indicates that the flow maps generated by RFDA-FM can be better at keeping nodes away from edges without node overlaps and edge crosses. Two extension experiments demonstrate that RFDA-FM is applicable to heterogeneous mapping space or mapping space with obstacle areas. The parameter analysis shows that RFDA-FM can intuitively control the layouts of flow maps. Project website: https://github.com/TrentonWei/FlowMap