## Linear Operators and Integral Equations in Global Illumination (1993)

Venue: | In SIGGRAPH '93 course notes(course 42 |

Citations: | 5 - 0 self |

### BibTeX

@INPROCEEDINGS{Arvo93linearoperators,

author = {James Arvo},

title = {Linear Operators and Integral Equations in Global Illumination},

booktitle = {In SIGGRAPH '93 course notes(course 42},

year = {1993}

}

### OpenURL

### Abstract

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 Nystrom 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. 1 Introduction The transfer of energy by radiation has a character fundamentally different from the processes of conduction and convection. One reason for this difference is that the radiant energy passing through a point in space cannot be completely described by a single scala...