Michael F. Cohen and Zicheng Liu
We present simplified 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 definition of the motion trajectories. Unfortunately, this method suffers from undue computational complexity as the creatures or motions approach those one would like to animate. Some of these problems have recently been addressed, but it is worth taking a closer look to see if simplifications 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 find assumptions which do not unduly restrict the motion, yet provide quick and simple solution methodologies. In particular, physical relationships such as angular momentum conversation 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.