Specifying the motion of an animated linked fi\fgure such that it achieves given tasks (e.g., throwing a ball into a basket) and performing the tasks in a realistic fashion (e.g., gracefully, and following physical laws such as gravity) has been an elusive goal for computer animators. The spacetime constraints paradigm has been shown to be a valuable approach to this problem, but it suff\u000bers from the computational complexity growth as creatures and tasks approach those one would like to animate. There are two sources which contribute to the complexity problem: one is the symbolic processing of the animator’s constraints and the objective functions derived from the physical models and the second lies in the numerical optimization phase. This thesis reports on work to enhance the spacetime constraints techniques both symbolically and numerically to signifi\fcantly speed up computations. Our \ffirst contribution is to develop a new symbolic interface with a recursive evaluation scheme so that the time required for gradient computation which is needed by the numerical optimization is reduced from exponential growth to the optimal quadratic growth. Furthermore, with the new symbolic method, a language developed for the symbolic expressions can be easily input, thus it provides a more convenient interface. Secondly, we develop a keyframe optimization system which allows the user to specify a few key frames while letting the computer determine the speed and timing, parameters which may be less intuitive for the animator, by using optimization methods. The novelty of this approach is that the user-specifi\fed key frames are used both to provide control over the motion and to reduce the complexity of the optimization problem. This method has the advantage of providing much of the user control of the iv traditional animation system while providing the physical realism of the optimization based system. Due to the reduced complexity of the optimization problem, the computation time is nearly interactive for complex fi\fgures. Finally we develop a hierarchical scheme to solve the nonlinear variational problem arising in the spacetime constraints formulation by using wavelets. In this scheme, the functions through time of the generalized degrees of freedom are reformulated in a hierarchical wavelet representation. This provides a means to automatically add detailed motion only where it is required, thus minimizing the number of unknowns. In addition, the optimization problem is better conditioned so that the convergence is faster.<\/p>\n","protected":false},"excerpt":{"rendered":"
Specifying the motion of an animated linked fi\fgure such that it achieves given tasks (e.g., throwing a ball into a basket) and performing the tasks in a realistic fashion (e.g., gracefully, and following physical laws such as gravity) has been an elusive goal for computer animators. 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