The Role of Functional Analysis in Global Illumination

Abstract: The problem of global illumination is virtually synonymouswith solving the rendering equation. Although a great deal of research has been directed toward Monte Carlo and finite element methods for solving the rendering equation, little is knownabout the continuousequationbeyondthe existenceanduniqueness of its solution. The continuous problem may be posed in terms of linear operators acting on infinite-dimensional function spaces. Such operators are fundamentally different from their finite-dimensional counterparts, and are properly studied using the methods of functional analysis. This paper summarizes some of the basic concepts of functional analysis and shows how these concepts may be applied to a linear operator formulation of the rendering equation. In particular, operator norms are obtained from thermodynamic principles, and a number of common function spaces are shown to be closed under global illumination. Finally, several fundamental operators that arise in global...

• Type: Conference
• Year: 1995
• Where: RT
• Authors: James Arvo
• Keywords: Computer Graphics, Global Illumination, Operators, Rendering Equation, RT 1995