Point label placement in 3D geographic scene via elastic beam algorithm

Labels are essential for conveying spatial information in maps, and their effective placement is critical for readability and clarity. In 3D geographical scenes, point labels are commonly displayed with leader lines to enhance visibility, providing flexibility in their positioning. Although the labels are rendered in 3D space, their placement optimization is often carried out in the 2D projected screen space, based on their screen coordinates. However, existing methods primarily rely on heuristic approaches or candidate position models to place the labels, leading to inefficient map space utilization and neglecting the relative relationships between labels. To address this issue, we propose a novel approach that conceptualizes leadered label positioning as a label displacement problem and applies the elastic beam displacement algorithm from cartographic generalization to solve it. In this approach, a triangulated graph is built as the elastic beam structure to delineate the spatial relationships among labels. Labels that violate label quality requirements are treated as applying forces on the beams’ nodes. Then the elastic beam algorithm is iteratively applied to assign forces to each node, determining the new positions of labels. Our experimental results demonstrate that this method effectively avoids label overlays while maintaining minimal directional deviation between adjacent labels.