Spacetime constraints

Spacetime constraints are a new method for creating character animation. The animator specifies what the character has to do, for instance, "jump from here to there, clearing a hurdle in between;" how the motion should be performed, for instance "don't waste energy," or "come down hard enough to splatter whatever you land on;" the character's physical structure ---the geometry, mass, connectivity, etc. of the parts; and the physical resources' available to the character to accomplish the motion, for instance the character's muscles, a floor to push off from, etc. The requirements contained in this description, together with Newton's laws, comprise a problem of constrained optimization. The solution to this problem is a physically valid motion satisfying the "what" constraints and optimizing the "how" criteria. We present as examples a Luxo lamp performing a variety of coordinated motions. These realistic motions conform to such principles of traditional animation as anticipation, squash-and-stretch, follow-through, and timing.