Stochastic Rendering of Density Fields

Stochastic models are often economical to generate but problematic to render. Most previous algorithms rst generate a realization of the stochastic model and then render it. These algorithms become expensive when the realization of the stochastic model is complex, because a large number of primitives have to be rendered. In stochastic rendering we also model the intensity as a random eld, and the statistics of the intensity eld are related to the statistics of the stochastic model through an illumination model. Stochastic rendering algorithms then generate a realization of the intensity eld directly from these statistics. In other words, a random component is shifted from the modelling to the rendering. This paradigm is not entirely new in computer graphics, so related work will be discussed. The main contribution of this paper is a stochastic rendering algorithm of gaseous phenomena modelled as random density elds such as clouds, smoke and re. A simpliied version of the scattering equation is used to derive the statistics of the illumination eld. Our algorithm is therefore an improvement over similar algorithms both in terms of computational speed and generality. Le rendu de mod eles stochastiques est souvent probl ematique. La plupart des algorithmes existants g en erent d'abord une r ealization du mod ele stochas-tique avant le rendu. Ces algorithmes deviennent cou-teux dans le cas o u le mod ele est compliqu e a cause du grand nombre de primitives qui doivent ^ etre rendues. Dans la m ethode du rendu stochastique nous mod elisons l'intensit e comme un champs al eatoire, les statistiques du champs d'intensit e sont calcul ees a partir des statis-tiques du mod ele stochastique en utilisant un mod ele d'illumination. La m ethode du rendu stochastique g en ere une r ealization du champs d'intensit e directement a par-tir de ces statistiques. En d'autres termes la composante stochastique est translat ee du modellage au rendu. La contribution majeure de ce papier consiste en un algo-rithme pour le rendu de ph enom enes gazeux tels que les nuages, la fum ee et le feu.