We consider the segmentation of a trajectory into piece-wise polynomial parts, or possibly other forms. Segmentation is typically formulated as an optimization problem which trades off model fitting error versus the cost of introducing new segments. Heuristics such as split-and-merge are used to find the best segmentation. We show that for ordered data (eg., single curves or trajectories) the global optimum segmentation can be found by dynamic programming. The approach is easily extended to handle different segment types and top down information about segment boundaries, when available. We show segmentation results for video sequences of a basketball undergoing gravitional and non-gravitaional motion.