Optimized 3D Point Labeling with Leaders Using the Beams Displacement Method

In three-dimensional geographical scenes, adding labels with leader lines to point features can significantly improve their visibility. To address the limitations of existing heuristic leader label configuration methods, which fail to effectively utilize the map space and struggle with the relative relationships between labels, we propose a Beams displacement method suitable for label configuration in 3D geographic scenes. First, the spatial relationships between labels are modeled using a triangular graph. Then, the forces on the labels are calculated based on their relative positions, and the new label positions are iteratively computed using the Beams displacement method. Finally, we explore a block-processing strategy to improve label configuration efficiency and analyze the impact of different proximity graph construction strategies on the configuration results. Experimental results show that in the self-constructed ship positioning and point of interest datasets, the proposed method resulted in zero label conflicts, with the relative direction deviations between adjacent labels reduced by 8.53° and 1.59°, respectively. Additionally, the method can adapt to the configuration needs of various types of leader annotations.