Le contrôle de l'erreur dans la méthode de radiosité hiérarchique. (Error Control in Hierarchical Radiosity)

We introduce several improvements to the hierarchical radiosity method. First, a complete analysis of a specific implementation of the hierarchical radiosity method allows to point out its bottlenecks. Based on this analysis, we suggest two simple improvements: a lazy evaluation of top-level interactions, and a new refinement criterion, that greatly reduces the number of interactions, without loss of precision. A brief introduction to the properties of functions of several variables and their derivatives follows, which allows a rewriting of the expression of radiosity, and hence a better numerical approximation. Methods for the estimation of the error produced during the radiosity computations are analysed. We then introduce the concavity properties of the radiosity function that, combined with an exact computationof the radiosityderivatives, allow a complete control of the error on the interactions between patches, and hence a precise minoration and majoration of the radiosity on all the patches. We introduce a new refinement criterion based on this modelling of interactions, and a complete hierarchical radiosity algorithm using this refinement criterion. The last part of the thesis is devoted to practical computations of the radiosity derivatives (gradient and Hessian), first for a constant emitter with total visibility, then for a constant emitter with partial visibility and for an emitter with linear radiosity.