Quantitative analysis of tennis ball rotation and trajectory

In this study, tennis ball rotation and trajectory are analyzed quantitatively. Fourteen dots are marked on a tennis ball to detect the ball rotation, and the markers' x-y positions are detected from high-speed camera images. First, the 3-D positions of the markers are calculated. Then, the rotation matrix is calculated by using the 3-D marker positions of successive camera frames. The rotation parameters, roll, pitch, and yaw, are calculated from the rotation matrix. The 3-D trajectories of the ball center are calculated by the stereo method. The relation between ball rotation and trajectory is discussed.