Michael F. Cohen, Steven J. Gortler, and Zicheng Liu
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. 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 discrete variables. In addition the wavelet basis is shown to lead to better conditioned systems of equations and thus faster convergence.
Publisher Association for Computing Machinery, Inc.
Copyright © 1994 by the Association for Computing Machinery, Inc. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from Publications Dept, ACM Inc., fax +1 (212) 869-0481, or firstname.lastname@example.org. The definitive version of this paper can be found at ACM’s Digital Library –http://www.acm.org/dl/.