Simulation of Aircraft Flight Track by BéZier and B-spline Curve

To overcome the limitations of motion equation which can not control the curve shape of aircraft tracks, a method of track simulation by Bézier and B-spline curves was proposed since the civil aircrafts have regular flying rules and its motion follows the beacons in flight plan defined before flight. In this method, lengths of the Bézier and open uniform B-spline curves are approximated by sum of line segments subdivided from the curves; then, Bézier control points of the track curve are calculated with the beacon positions in flight plan and the real-time status such as flying speed, position, etc. of the aircraft. The B-spline method needs not to create new control points for generation of aircraft flight track curve because it can create a rational track curve using beacons. Furthermore, the position of the next point in flight track is calculated by the interpolation equation of Bézier or B-spline curve. The simulation result shows that the Bézier and B-spline track curve are basically the same as the real track curve. The proposed methods are superior to the method of motion equation, for it can create all kinds of track curves. Under the condition of 18 beacons, the calculating time of the Bézier method is 0.13 s and can satisfy the real-time requirement.