Viewpoint planning is crucial for 3D data collection and autonomous navigation, yet existing methods often miss key optimization objectives for static LiDAR, resulting in suboptimal network designs. The Viewpoint Planning Problem (VPP), which builds upon the Art Gallery Problem (AGP), requires not only full coverage but also robust registrability and connectivity under limited sensor views. We introduce a greedy optimization algorithm that tackles these VPP and AGP challenges through a novel Visibility Field (VF) approach. The VF captures visibility characteristics unique to static LiDAR, enabling a reduction from 2D to 1D by focusing on medial axis and joints. This leads to a minimal, fully connected viewpoint network with comprehensive coverage and minimal redundancy. Experiments across diverse environments show that our method achieves high efficiency and scalability, matching or surpassing expert designs. Compared to state-of-the-art methods, our approach achieves comparable viewpoint counts (VC) while reducing Weighted Average Path Length (WAPL) by approximately 95\%, indicating a much more compact and connected network. Dataset and source code will be released upon acceptance.

翻译：视点规划对于三维数据采集与自主导航至关重要，但现有方法常忽略针对静态激光雷达的关键优化目标，导致网络设计欠佳。基于美术馆问题构建的视点规划问题不仅要求全覆盖，还需在有限传感器视角下实现鲁棒的配准能力与连接性。本文提出一种贪婪优化算法，通过新颖的可见性场方法解决上述VPP与AGP挑战。该VF能够捕捉静态激光雷达特有的可见性特征，通过聚焦中轴与关节实现从二维到一维的降维处理，从而构建出具备全覆盖性、最小冗余度的极简全连接视点网络。多环境实验表明，本方法在保持高效率和可扩展性的同时，达到或超越了专家设计水平。与前沿方法相比，本方案在获得可比拟视点数量的同时，将加权平均路径长度降低约95%，表明网络结构更为紧凑且连通性更优。数据集与源代码将在论文录用后公开。