This paper discusses a Three Dimensional (3D; 2D in space and 1D in time) trajectory synthesis algorithms for future air traffic control automation. The control automation aims to generate computational advisories that help controllers to produce a safe, efficient and expeditious flow of traffic over the extended terminal area. Trajectories are generated from initial aircraft positions to the fixed way-point or outer marker, depending on the particular route condition of an airport. Time optimal flight path is constructed in the horizontal path. Trajectories are synthesized from straight lines and left turn or right turn arcs with the constant maximum angle of bank by combining twelve types of trajectory depending on the initial position and the initial orientation. Synthesis of the simultaneous plural trajectories with constant speed is discussed aiming to substitute for human controller who plans simultaneously 3D trajectories of eight aircraft at most.