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Summary: JOURNAL OF INTEGRAL EQUATIONS
AND APPLICATIONS
Volume 10, Number 3, Fall 1998
THE COLLOCATION METHOD FOR SOLVING
THE RADIOSITY EQUATION FOR
UNOCCLUDED SURFACES
KENDALL ATKINSON AND GRAEME CHANDLER
This is dedicated to Professor Phil Anselone, a valued friend and colleague.
ABSTRACT. The radiosity equation occurs in computer
graphics, and its solution leads to more realistic illumination
for the display of surfaces. We consider the behavior of the
radiosity integral operator, for smooth and piecewise smooth
surfaces. A collocation method for solving the radiosity equa-
tion is proposed and analyzed. The method uses piecewise
linear interpolation; and for one particular choice of such lin-
ear interpolation, it is shown that superconvergence results
are obtained when solving on a smooth surface. Numerical
results conclude the paper.
1. Introduction. The radiosity equation is a mathematical model
for the brightness of a collection of one or more surfaces when their
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