Ebook: Linear Operators and Integral Equations in Global Illumination

Paper, 25 p, Program of Computer Graphics Cornell University, 1993.
These notes introduce the basic concepts of integral equations and their application in global illumination. Much of the discussion is expressed in the language of linear operators to simplify the notation and to emphasize the algebraic properties of the integral equations. We start by reviewing some facts about linear operators and examining some of the operators that occur in global illumination. Six general methods of solving operator and integral equations are then discussed the Neumann series successive approximations the Nystr om method collocation least squares and the Galerkin method. Finally we look at some of the steps involved in applying these techniques in the context of global illumination.