An E cient Symbolic Interface to Constraint Based

Symbolic methods have been used to provide a general user interface in optimization based animation systems. However, previous methods suuer 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 eecient interface to optimization based linked gure animation systems.