Abstract: This article presents a new motion model deformable motion models for human motion modeling and synthesis. Our key idea is to apply statistical analysis techniques to a set of precaptured human motion data and construct a low-dimensional deformable motion model of the form x = M($alpha $, $gamma $), where the deformable parameters $alpha $ and $gamma $ control the motion's geometric and timing variations, respectively. To generate a desired animation, we continuously adjust the deformable parameters' values to match various forms of user-specified constraints. Mathematically, we formulate the constraint-based motion synthesis problem in a Maximum A Posteriori (MAP) framework by estimating the most likely deformable parameters from the user's input. We demonstrate the power and flexibility of our approach by exploring two interactive and easy-to-use interfaces for human motion generation: direct manipulation interfaces and sketching interfaces.