Sequential-goal constraints for computer animation

The dynamic constraints technique has been proposed for building geometrical models composed of rigid bodies, which are made to act naturally, according to Newtonian laws, by specifying constraints on their states. In computer animation, the dynamic constraints technique alleviates the work-load of animators who formerly had to plan animated sequences in detail by intuition alone. Nevertheless, for some real-world applications, it is desirable to have a mechanism that makes physically-based elements move according to a given scenario by providing some control states. The control states can be represented by transient constraints that are to be met and then released immediately. In this paper, a technique called the sequential-goal constraints technique is proposed to provide such a mechanism. With the sequential-goal constraints technique, it is easy to specify transient constraints according to a given scenario and derive proper forces and torques to drive an element to meet each transient constraint exactly at a specified time so that the whole motion of the element is continuous and integral.