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Airspace geofencing is a key capability for low-altitude Unmanned Aircraft System (UAS) Traffic Management (UTM). Geofenced airspace volumes can be allocated to safely contain compatible UAS flight operations within a fly-zone (keep-in geofence) and ensure the avoidance of no-fly zones (keep-out geofences). This paper presents the application of three-dimensional flight volumization algorithms to support airspace geofence management for UTM. Layered polygon geofence volumes enclose user-input waypoint-based 3-D flight trajectories, and a family of flight trajectory solutions designed to avoid keep-out geofence volumes is proposed using computational geometry. Geofencing and path planning solutions are analyzed in an accurately mapped urban environment. Urban map data processing algorithms are presented. Monte Carlo simulations statistically validate our algorithms, and runtime statistics are tabulated. Benchmark evaluation results in a Manhattan, New York City low-altitude environment compare our geofenced dynamic path planning solutions against a fixed airway corridor design. A case study with UAS route deconfliction is presented, illustrating how the proposed geofencing pipeline supports multi-vehicle deconfliction. This paper contributes to the nascent theory and the practice of dynamic airspace geofencing in support of UTM. 

Flat surfaces captured by 3D point clouds are often used for localization, mapping, and modeling. Dense point cloud processing has high computation and memory costs making low-dimensional representations of flat surfaces such as polygons desirable. We present Polylidar3D, a non-convex polygon extraction algorithm which takes as input unorganized 3D point clouds (e.g., LiDAR data), organized point clouds (e.g., range images), or user-provided meshes. Non-convex polygons represent flat surfaces in an environment with interior cutouts representing obstacles or holes. The Polylidar3D front-end transforms input data into a half-edge triangular mesh. This representation provides a common level of abstraction for subsequent back-end processing. The Polylidar3D back-end is composed of four core algorithms: mesh smoothing, dominant plane normal estimation, planar segment extraction, and finally polygon extraction. Polylidar3D is shown to be quite fast, making use of CPU multi-threading and GPU acceleration when available. We demonstrate Polylidar3D’s versatility and speed with real-world datasets including aerial LiDAR point clouds for rooftop mapping, autonomous driving LiDAR point clouds for road surface detection, and RGBD cameras for indoor floor/wall detection. We also evaluate Polylidar3D on a challenging planar segmentation benchmark dataset. Results consistently show excellent speed and accuracy.