# Finite Element Methods for Global Illumination

### Paul S. Heckbert and James M. Winget

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/CSD-91-643

January 1991

### http://www.eecs.berkeley.edu/Pubs/TechRpts/1991/CSD-91-643.pdf

The interreflection of light between surfaces is governed by an integral equation. Existing radiosity algorithms approximate the solution of this integral equation by transforming it into a system of linear equations. It is shown that such algorithms are simple applications of the finite element method.

Techniques are presented for applying more advanced finite element techniques to the global illumination problem in order to yield more accurate results. First, piecewise-linear, piecewise-quadratic, and higher order elements are discussed as a superior alternative to current piecewise-constant radiosity assumptions. Second, Galerkin techniques are a more robust alternative to current point collocation (point sampling) techniques. Finally, occlusions in a scene give rise to discontinuities such as shadow edges in the solution function. Discontinuity meshing is introduced as a technique for resolving these discontinuities by adaptive placement of element boundaries. Illustrations, algorithms, and results are given for two-dimensional radiosity in flatland problems.

BibTeX citation:

@techreport{Heckbert:CSD-91-643, Author = {Heckbert, Paul S. and Winget, James M.}, Title = {Finite Element Methods for Global Illumination}, Institution = {EECS Department, University of California, Berkeley}, Year = {1991}, Month = {Jan}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1991/5415.html}, Number = {UCB/CSD-91-643}, Abstract = {The interreflection of light between surfaces is governed by an integral equation. Existing radiosity algorithms approximate the solution of this integral equation by transforming it into a system of linear equations. It is shown that such algorithms are simple applications of the finite element method. <p>Techniques are presented for applying more advanced finite element techniques to the global illumination problem in order to yield more accurate results. First, piecewise-linear, piecewise-quadratic, and higher order elements are discussed as a superior alternative to current piecewise-constant radiosity assumptions. Second, Galerkin techniques are a more robust alternative to current point collocation (point sampling) techniques. Finally, occlusions in a scene give rise to discontinuities such as shadow edges in the solution function. Discontinuity meshing is introduced as a technique for resolving these discontinuities by adaptive placement of element boundaries. Illustrations, algorithms, and results are given for two-dimensional radiosity in flatland problems.} }

EndNote citation:

%0 Report %A Heckbert, Paul S. %A Winget, James M. %T Finite Element Methods for Global Illumination %I EECS Department, University of California, Berkeley %D 1991 %@ UCB/CSD-91-643 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/1991/5415.html %F Heckbert:CSD-91-643