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Fixed-wing Unmanned Aerial Vehicle (UAV) rendezvous is necessary for reduced fuel consumption during leader-follower formation flight. We propose a heuristic direct search algorithm that plans a time-optimal path for a follower UAV to rendezvous with a leader whose future path is known and unchanging. The kinematic constraints of the UAV are considered and discontinuities inherent to the minimum-length paths are dealt with. Experiments using quadrotors to emulate fixed-wings, demonstrate the algorithm planning and replanning optimal paths to rendezvous in real-time.