Hierarchical spacetime control

New features to the spacetime constraints paradigm are described, which provide a means to automatically add detailed motion only where it is required, thus minimizing the number of discrete variables and leading to better conditioned systems of equations and thus faster convergence.

Abstract

Specifying the motion of an animated linked figure such that it achieves given tasks (e.g., throwing a ball into a basket) and performs 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 suffers from computational complexity growth as creatures and tasks approach those one would like to animate. The complexity is shown to be, in part, due to the choice of finite basis with which to represent the trajectories of the generalized degrees of freedom. This paper describes new features to the spacetime constraints paradigm to address this problem.