An Efficient Symbolic Interface to Constraint Based Animation Systems
Symbolic methods have been used to provide a general user interface in optimization based animation systems. However, previous methods suffer from the exponential growth in the length of the symbolic expressions of the objectives, constraints and their derivatives. In this paper, we present a symbolic language which is general enough to represent common kinematic and dynamic quantities. The evaluation of these symbolic expressions and their gradients are as fast as numerical methods. In particular, the computational complexity is only a low degree polynomial compared to exponential growth of previous methods, and the optimum performance is achieved for computing the gradients of the generalized forces by extending Hollerbach’s technique of compuing inverse dynamics. Furthermore, in this new language the expressions are usually very small so that they can be easily typed in, therefore this method provides a general and efficient interface to optimization based linked figure animation systems.
KeywordsLocal Coordinate System Symbolic Expression Orientation Matrix Torque Variable Symbolic Language
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- 3.Michael Kass. Condor: Constraint-based dataflow. In Proceedings of SIGGRAPH’92 (Chicago, July 26–31, 1992), pages 321–330. ACM, July 1992.Google Scholar
- 4.Zicheng Liu and Michael F. Cohen. Keyframe motion opimization by relaxing speed and timing. In Proceedings of 6th EuroGraphics Workshop on Animation and Simulation, (Maastricht, The Netherlands, September2–3 1995 ).Google Scholar
- 5.Zicheng Liu, Steven Gortler, and Michael F. Cohen. Hierarchical spacetime control. Computer Graphics, pages 35–42, July 1994.Google Scholar