Viewpoint planning is critical for efficient 3D data acquisition in applications such as 3D reconstruction, building life-cycle management, navigation, and interior decoration. However, existing methods often neglect key optimization objectives specific to static LiDAR systems, resulting in redundant or disconnected viewpoint networks. The viewpoint planning problem (VPP) extends the classical Art Gallery Problem (AGP) by requiring full coverage, strong registrability, and coherent network connectivity under constrained sensor capabilities. To address these challenges, we introduce a novel Visibility Field (VF) that accurately captures the directional and range-dependent visibility properties of static LiDAR scanners. We further observe that visibility information naturally converges onto a 1D skeleton embedded in the 2D space, enabling significant searching space reduction. Leveraging these insights, we develop a greedy optimization algorithm tailored to the VPP, which constructs a minimal yet fully connected Viewpoint Network (VPN) with low redundancy. Experimental evaluations across diverse indoor and outdoor scenarios confirm the scalability and robustness of our method. Compared to expert-designed VPNs and existing state-of-the-art approaches, our algorithm achieves comparable or fewer viewpoints while significantly enhancing connectivity. In particular, it reduces the weighted average path length by approximately 95%, demonstrating substantial improvements in compactness and structural efficiency. Code is available at https://github.com/xiongbiaostar/VFPlan.

翻译：暂无翻译