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

翻译：流地图是一种以树状布局可视化物体在空间中移动的专题地图，其底层树状结构与自然河流系统相似。本文提出一种名为RFDA-FM的全新自动化方法，利用数字高程模型（DEM）中的河流提取算法生成单源多目的流地图。RFDA-FM首先将映射空间建模为DEM的平坦表面，随后改编一种用于河流提取的迷宫求解算法（MSA），通过根据流地图质量准则约束其搜索方向、方向权重及搜索范围，计算从单一目的地到源点的流路径。所有目的地到源点的流路径基于MSA按重要性（由路径长度定义）迭代获取，最后利用贝塞尔曲线根据流量以渐变宽度平滑渲染这些路径。与现有方法的对比表明，RFDA-FM生成的流地图在避免节点重叠与边交叉方面更优，且能保持节点远离边缘。两项扩展实验证明，RFDA-FM适用于异质映射空间或含障碍区域的映射空间。参数分析显示，RFDA-FM可直观控制流地图布局。项目网站：https://github.com/TrentonWei/FlowMap