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

Flow map is an effective way to visualize object movements across space over time. It aims to model the paths from destinations to origins with quality constraints satisfied, which is similar to river system extraction in a digital elevation model (DEM). In this paper, we present a novel and automated approach called RFDA-FM for spatial flows from one origin to multiple destinations using a river flow directions assignment algorithm in DEM. The RFDA-FM first models the mapping space as a flat surface by DEM. An improved maze solving algorithm (MSA) is then introduced to assign the flow directions by constraining its searching directions, direction weights and searching range. The paths from the destinations to the origin are obtained iteratively based on the improved MSA according the path importance. Finally, these paths are rendered with varied widths and smoothed according to their volume using the B\'ezier curves. The evaluation results indicate that the flow maps generated by RFDA-FM can have a higher quality on uniform distribution of edge lengths and avoidance of self-intersections and acute angles by comparing to the existing approaches. The experiments demonstrate that RFDA-FM is also applicable for heterogeneous mapping space or mapping space with obstacle areas.