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Summary: Proceedings of the Twelfth Eurographics Workshop on Rendering,
London, United Kingdom, June 2001.
Simulating Non-Lambertian Phenomena
Involving Linearly-Varying Luminaires
Min Chen James Arvo
California Institute of Technology, Pasadena, CA
{chen,arvo}@cs.caltech.edu
Abstract. We present a new technique for exactly computing glossy reflections
and transmissions of polygonal Lambertian luminaires with linearly-varying ra-
diant exitance. To derive the underlying closed-form expressions, we introduce
a rational generalization of irradiance tensors and an associated recurrence re-
lation. The generalized tensors allow us to integrate a useful class of rational
polynomials over regions of the sphere; this class of rational polynomials can
simultaneously account for the linear variation of radiant exitance across a pla-
nar luminaire and simple forms of non-Lambertian scattering. Applications in-
clude the computation of irradiance at a point, view-dependent reflections from
glossy surfaces, and transmissions through glossy surfaces, where the scattering
is limited to Phong distributions and the incident illumination is due to linearly-
varying luminaires. In polyhedral environments, the resulting expressions can
be exactly evaluated in quadratic time (in the Phong exponent) using dynamic
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