Modeling stochastic dynamical systems for interactive simulation

We present techniques for constructing approximate stochastic models of complicated dynamical systems for applications in interactive computer graphics. The models are designed to produce realistic interaction at low cost. We describe two kinds of stochastic models: continuous state (ARX) models and discrete state (Markov chains) models. System identification techniques are used for learning the input-output dynamics automatically, from either measurements of a real system or from an accurate simulation. The synthesis of behavior in this manner is several orders of magnitude faster than physical simulation. We demonstrate the techniques with two examples: (1) the dynamics of candle flame in the wind, modeled using data from a real candle and (2) the motion of a falling leaf, modeled using data from a complex simulation. We have implemented an interactive Java program which demonstrates real-time interaction with a realistically behaving simulation of a cartoon candle flame. The user makes the flame animation flicker by blowing into a microphone.