基于地形几何的智能布点,让采样点分布更均衡安全。
ToPos: Automated Optimal Positioning on Topographic Manifolds using Constrained Geodesic Voronoi Decomposition

- 用曲面测地距离替代平面距离,精准匹配真实地形
- 在非凸地形上实现74%的区域面积分布均衡提升
- 适合高海拔测绘、物流布点等需避障的场景
可靠自主测绘、环境采样、末端物流和基础设施部署依赖于空间参考点(SRS)在地表上的均衡分布。传统二维欧氏方法在高起伏环境中因忽略地形变化和物理障碍,导致平面畸变、空间聚集以及将目标设于不可达或遮蔽区域,影响数据完整性和作业安全。本文提出ToPos框架,实现基于地形的最优采样布局。将地形视为嵌入三维欧氏空间的离散二维流形,以测地距离替代标准平面距离,构建受约束的测地Voronoi分解优化模型,并采用黎曼Nesterov加速梯度求解器进行优化。通过限制目标点仅落在可通行的“安全区”内,考虑不可行坡度、植被覆盖与环境遮挡等因素。在非凸正弦地形上的评估表明,采用测地度量可有效缓解平面畸变,使Voronoi单元面积系数变异(CV)降低约74%,显著提升表面面积均衡性。该框架设计为地理信息系统(GIS)就绪的微服务,适用于上述应用。
原文摘要 · Abstract (English)
Reliable autonomous mapping, environmental sampling, last-mile logistics, and infrastructure deployment depend on the optimal surface area-balanced distribution of Spatial Reference Sites (SRS). Conventional 2D Euclidean methods often fail in high-relief environments by neglecting topographic variations and physical obstructions. This leads to significant planimetric distortion, spatial clustering, and the placement of targets in inaccessible or shadowed regions, compromising both data integrity and operational safety. This paper introduces ToPos, an automated framework for TOPography-aware Optimal Sampling on topographic manifolds. We treat the terrain as a discrete 2-dimensional manifold embedded in 3D Euclidean space and replace standard flat-map distances with non-Euclidean geodesic distances that follow the actual surface geometry. The point distribution is formulated as an optimization problem using a Constrained Geodesic Voronoi Decomposition, solved via a Riemannian Nesterov Accelerated Gradient (NAG) engine. Our approach restricts target locations to a feasible "safe zone," accounting for non-traversable slopes, vegetation, environmental occlusions, etc. Through evaluations on non-convex sinusoidal manifolds, we show that ToPos mitigates planimetric distortion by utilizing geodesic metrics. This approach results in a $\sim$74% improvement in optimal surface area-balanced distribution, as measured by the coefficient of variation (CV) of the Voronoi cell areas. The framework is architected as a Geographic Information System (GIS)-ready micro-service to bolster the mentioned applications. Index Terms: Topographic Manifolds, Geodesic Voronoi Decomposition, Infrastructure Deployment, 3D Mapping, Spatial Sampling, and Non-Euclidean Optimization.
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