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A general mathematical model is developed as an idealization of the problem of determining cloud motions from satellite pictures. The model consists of superimposed planes of rigid moving polygons. The problem is to determine from a sequence of scenes the linear and angular velocities of the figures, and to decompose the scene into its component figures. Study of the model reveals a number of fundamental relations that form the basis for an analysis program. In particular, a systematic anaylsis is given of the topological changes that can occur when overlapping figures move together or apart. A computer program based on these results is described, and experimental results are presented.