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We propose a probabilistic generative model for extracting intended path shape qualities of an object moving under human control in real time. At each instant, we decide whether the object is moving in a straight, curved, or random path, or whether it has stopped moving. Our model incorporates sensor noise as well as human imperfections in the intended motion. As well as tracking the object's position, velocity, and motion direction, we compute the posterior probability of each shape quality hypothesis given all sensed-data in the horizon [t - N + 1,t]; the hypothesis maximizing this posterior is taken as the decision. The posterior is computed using the unscented Kalman filter (UKF), as our model is inherently nonlinear. The path-shape quality tracking is successfully embedded in a hybrid physical-digital interface where the position of an illuminated ball, sensed by a low-cost video camera array, triggers multimodal feedback in a mediated learning environment. We show successful results on a variety of real-world motion paths where the participant is given only verbal descriptions of how to move. Our generative model is further validated by user studies involving a simple color-based interaction, where participants discover shape quality controls as they interact.