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Motivated by the need of ATC systems for insideness, intrusion and collision detection, a number of efficient algorithms were designed and implemented. For the determination of the insideness of points in polygons, a simple generalization of the commonly used zero winding and even-odd rules is presented, and, building thereupon, a point-in-polygon algorithm based on the binary addressing of quad-tree nodes and prefix hashing. Subsequently, an octree-based high-performance algorithm for the intersection of rays with polygonal meshes is presented. For all of the presented methods, tests and performance analyses were conducted that confirm the low theoretical runtime complexity. The methods are in practical use in the PHOENIX radar data processing system.