Paul S. Heckbert and James M. Winget

EECS Department, University of California, Berkeley

Technical Report No. UCB/CSD-91-643

, 1991

http://www2.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. <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.

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BibTeX citation:

@techreport{Heckbert:CSD-91-643,
    Author= {Heckbert, Paul S. and Winget, James M.},
    Title= {Finite Element Methods for Global Illumination},
    Year= {1991},
    Month= {Jan},
    Url= {http://www2.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://www2.eecs.berkeley.edu/Pubs/TechRpts/1991/5415.html
%F Heckbert:CSD-91-643