Approximate and probabilistic algorithms for shading and rendering structured particle systems

Detail enhances the visual richness and realism of computer-generated images. Our stochastic modelling approach, called particle systems, builds complex pictures from sets of simple, volume-filling primitives. For example, structured particle systems have been used to generate trees and a grass-covered forest floor. Particle systems can produce so much irregular, three-dimensional detail that exact shading and visible surface calculations become infeasible. We describe approximate and probabilistic algorithms for shading and the visible surface problem. Because particle systems algorithms generate richly-detailed images, it is hard to detect any deviation from an exact rendering. Recent work in stochastic modelling also enables us to model complex motions with random variation, such as a field of grass blowing in the breeze. We analyze the performance of our current algorithms to understand the costs of our stochastic modelling approach.