Fixed-wing unmanned aerial vehicles (UAVs) frequently encounter no-fly zones during mission execution, necessitating a route planning algorithm that effectively balances mission objectives with airspace constraints. This study models the UAV flight path as a combination of straight-line and arcs while representing no-fly zones as circular and polygonal regions. By leveraging geometric properties, the proposed algorithm efficiently detects intersections between the planned trajectory and restricted zones, thereby reducing computational overhead and improving accuracy. Experimental results on a general-purpose computer demonstrate the algorithm’s strong adaptability and high execution efficiency, making it well-suited for practical UAV applications.