Stochastic approaches are very effective for modelling natural phenomena. This paper presents a motion model based on a stochastic process as well as physics, and proposes motion synthesis techniques for stochastic motion—motion under the influence of wind.
The motion synthesis process is modelled by a cascade system of three components: wind model, dynamic model, and deformation model. Wind models produce spatio-temporal wind velocity fields using the power spectrum and auto-correlation of wind, just like fractal geometry. Dynamic models describe the dynamic response of the systems, using equation systems or response functions. Deformation models produce deformed shapes of objects according to the geometric models of the objects and the results of the dynamic systems.
The biggest advantage of the model is its generality and consistency. The model is applicable to most of the existing trees and grass models, including structural models, particle systems, impressionist models, and 3D texture. It is demonstrated that the coupling of stochastic approaches and physically-based approaches can synthesize realistic motion of trees, grass and snow with modest computational cost.