Physical models are an important source of simulations for training and animations. However, physical models are notoriously difficult to direct. A training simulation may require that all objects are consistent with physics in their behavior, and that a particular object fall and land in a particular way. In typical physical models these requirements are mutually exclusive, because surface geometry and properties are exactly specified.

The problem largely disappears if various geometric and physical properties of objects are modeled as random variables. Attention can now be confined to samples of these random variables that nearly meet the constraints specified by the director, using a device we call a masking distribution. Such samples can be drawn using the Markov chain Monte Carlo algorithm.

This approach is simple, general and effective. It is particularly attractive because it generates many animations, all of which are close to satisfying the constraints and consistent with the physics of the world; furthermore, the distribution of these animations is consistent with the distribution of paths satisfying the constraints in the world, an important consideration for training simulations. The approach is illustrated by many examples where collision based physical systems, including a thrown die, are directed using this method.