Geofence Boundary Violation Detection in 3D Using Triangle Weight Characterization with Adjacency

This paper introduces a computationally efficient geofence boundary violation detection method using the Triangle Weight Characterization with Adjacency (TWCA) algorithm. The geofence is defined as a maximum and a minimum altitude, and a horizontal boundary specified as a polygon that does not self-intersect. TWCA initialization divides the horizontal component and bounding box of each geofence into a finite set of triangles, then determines the triangle containing the vehicle. During flight, each position update is checked for containment within the vertical geofence boundaries using inequalities and the horizontal geofence boundaries using TWCA. TWCA searches for the triangle containing the vehicle position using breadth-first search of the adjacency graph. The root node of the search is the triangle occupied at the previous time step. This algorithm is applicable to three-dimensional geofences containing both keep-in (inclusion) geofences and keep-out (exclusion) geofences.