Sampling plausible solutions to multi-body constraint problems

ABSTRACT

Traditional collision intensive multi-body simulations are difficult to control due to extreme sensitivity to initial conditions or model parameters. Furthermore, there may be multiple ways to achieve any one goal, and it may be difficult to codify a user's preferences before they have seen the available solutions. In this paper we extend simulation models to include plausible sources of uncertainty, and then use a Markov chain Monte Carlo algorithm to sample multiple animations that satisfy constraints. A user can choose the animation they prefer, or applications can take direct advantage of the multiple solutions. Our technique is applicable when a probability can be attached to each animation, with “good” animations having high probability, and for such cases we provide a definition of physical plausibility for animations. We demonstrate our approach with examples of multi-body rigid-body simulations that satisfy constraints of various kinds, for each case presenting animations that are true to a physical model, are significantly different from each other, and yet still satisfy the constraints.

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.7 Three-Dimensional Graphics and Realism
          Subjects: Animation

Additional Classification:
  G. Mathematics of Computing
  G.3 PROBABILITY AND STATISTICS
      Subjects: Probabilistic algorithms (including Monte Carlo)

  I. Computing Methodologies
  I.2 ARTIFICIAL INTELLIGENCE
        I.2.10 Vision and Scene Understanding
            Subjects: Modeling and recovery of physical attributes
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling
          Subjects: Physically based modeling
  I.6 SIMULATION AND MODELING
      I.6.5 Model Development
          Subjects: Modeling methodologies
      I.6.8 Types of Simulation
          Subjects: Monte Carlo

General Terms:
Design, Measurement, Performance, Theory

Keywords:
Markov chain Monte Carlo, motion synthesis, plausible motion, spacetime constraints