Decomposition of Linked Figure Motion: Diving

We present simplied techniques to simulate and control complex motions. The spacetime constraint paradigm has proven successful for providing animators with control of motion without burdening them with explicit denition of the motion trajectories. Unfortunately, this method suers from undue computational complexity as the creatures or motions approach those one wouldlike to animate. Some of these problems have recently been addressed, but it is worth taking a closer look to see if simplications of the problem statement itself can be made. This extended abstract presents some experiments in decomposing the spacetime constraint formulation into smaller and simpler subproblems. Each subproblem can then be solved with an appropriate numerical methodology or perhaps through an analytic formulation. The key to this is a close examination of the physical principles in an attempt to nd assumptions which do not unduly restrict the motion, yet provide quick and simple solution methodologies. In particular, physical relationships such as angular momentum conservation laws are pulled out of the nonlinear optimization problem so that the original problem leads to a much simpler optimization problem (without the conservation equation) and two point boundary problems. By, in addition, approximating the energy minimization objective fair sized problems can be solved in real time. A human-like diving motion is used to illustrate these concepts. Experimental results are shown. Some thoughts on how to generalize this approach are given.