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Closed-Form Expressions for Irradiance from Non-Uniform Lambertian Luminaires Part II: Polynomially-Varying Radiant Exitance

Chen, Min and Arvo, James (2000) Closed-Form Expressions for Irradiance from Non-Uniform Lambertian Luminaires Part II: Polynomially-Varying Radiant Exitance. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechCSTR:2000.cs-tr-00-04

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Abstract

We present new analytical techniques for computing illumination from non-uniform luminaires. The methods are based on new closed-form expressions derived by generalizing the concepts of irradiance tensor and angular moment to rational forms and an arbitrary number of directions, known as rational irradiance tensors and rational angular moments, respectively. The techniques apply to any emission, reflection or transmission distribution expressed as a polynomial over a polygonal surface, and provide a powerful mathematical tool to handle more complex BRDF's. We derive closed-form expressions for irradiance due to polygonal luminaires with polynomially varying radiant exitance, which satisfy a recurrence relation that subsumes Lambert's formula for uniform luminaires. Our formulas extend the class of available closed-form expressions for computing direct radiative transfer from planar surfaces to points, and can find many potential applications in simulating non-Lambertian illumination and scattering phenomena


Item Type:Report or Paper (Technical Report)
Additional Information:© 2000 California Institute of Technology. June 19, 2000. This work was supported by a Microsoft Research Fellowship and NSF Career Award CCR9876332.
Group:Computer Science Technical Reports
Funders:
Funding AgencyGrant Number
Microsoft ResearchUNSPECIFIED
NSFCCR-9876332
Subject Keywords:Illumination, Rendering, Radiosity, Irradiance Tensor, Angular Moment, Spatially Varying Luminaire
DOI:10.7907/Z9XG9P5B
Record Number:CaltechCSTR:2000.cs-tr-00-04
Persistent URL:http://resolver.caltech.edu/CaltechCSTR:2000.cs-tr-00-04
Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:26824
Collection:CaltechCSTR
Deposited By: Imported from CaltechCSTR
Deposited On:25 Apr 2001
Last Modified:07 Mar 2017 18:44

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