Mathematical Models and Monte Carlo Algorithms for Physically Based Rendering
Eric P. Lafortune · 1995
Algorithms for image synthesis render photo-realistic imagery, given the description of a scene. Physically based rendering specifically stresses the physical correctness of the algorithms and their results. The algorithms perform an accurate simulation of the behaviour of light, in order to faithfully render global illumination effects such as soft shadows, glossy reflections and indirect illumination. In this dissertation we investigate image-based Monte Carlo rendering algorithms. We pay special attention to their correctness, their versatility and their efficiency. First of all, we discuss theoretical frameworks that describe the global illumination problem. These formal mathematical models are the first step to ensure the correctness of the eventual results. Moreover, they allow to apply standard numerical techniques to compute a solution. We give an overview of existing models, which are based on the rendering equation and the potential equation. We then introduce a model based ...