Spacetime constraints

TLDR

Spacetime constraints are a new method for creating character animation. The method formulates animation as a constrained optimization problem, where the animator defines desired motion goals, performance criteria, and the character’s physical properties and resources, then solves for a physically valid trajectory using Newtonian dynamics. The resulting motions are physically valid, satisfy the specified constraints, and exhibit classic animation cues such as anticipation, squash‑and‑stretch, follow‑through, and timing.

Abstract

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.