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Spacetime Constraints

Andrew Witkin, Michael Kass

SIGGRAPHAcademic942 cites50 descendantsMotion Synthesis

Spacetime optimization formulation for physics-based character animation, optimizing motions over time to satisfy user-specified constraints.

Abstract

Spacetime constraints are a method for creating character animation in which the animator specifies what the character must do, how the motion should be performed, the character's physical structure, and the physical resources available to accomplish the motion. Together with Newton's laws these requirements form a constrained optimization problem whose solution is a physically valid motion that satisfies the constraints while optimizing the given criteria. The functions for position and force are discretized and solved over the entire time interval at once using a variant of Sequential Quadratic Programming with sparse matrix techniques, supported by an object-oriented symbolic algebra system that automates the difficult task of setting up the equations. The authors demonstrate the method with a Luxo lamp performing jumps and ski jumps, showing that traditional animation principles such as anticipation, squash-and-stretch, follow-through, and timing emerge automatically from minimal kinematic constraints.

How to read this

Category
Method: a spacetime optimization formulation for physics-based animation
Contributions
  • Spacetime constraints: posing animation as a constrained optimization over the whole time interval given goals, style, structure, and physical resources
  • A discretized position-and-force solve using sparse Sequential Quadratic Programming, with a symbolic algebra system to set up the equations
  • A demonstration (a Luxo lamp jumping and ski-jumping) showing anticipation, squash-and-stretch, follow-through, and timing emerge from minimal constraints
Context
Standalone foundational work (no prior context given) that links Newtonian physics and optimization, seeding later trajectory-optimization and physics-based motion synthesis.
Correctness
Solutions are physically valid motions that satisfy the constraints while optimizing a criterion; a reader should note the approach is computationally heavy, sensitive to the optimization setup, and shown on a simple character rather than full humanoids.
Clarity
Conceptually striking but technically demanding; a first pass conveys the idea, deeper passes are needed for the optimization and equation setup.
How to read it
Read for the elegant premise that animation principles fall out of optimization: focus on the constraint formulation and the Luxo result; budget a second/third pass for the SQP and symbolic-setup details if you do trajectory optimization.

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