Summary: Proceedings of the Eleventh Eurographics Workshop on Rendering,
Brno, Czech Republic, June 2000, pages 137­148.
A Closed­Form Solution for the Irradiance due
to Linearly­Varying Luminaires
Min Chen James Arvo
California Institute of Technology, Pasadena, CA
{chen,arvo}@cs.caltech.edu
Abstract. We present a closed­form expression for the irradiance at a point on a
surface due to an arbitrary polygonal Lambertian luminaire with linearly­varying
radiant exitance. The solution consists of elementary functions and a single well­
behaved special function that can be either approximated directly or computed
exactly in terms of classical special functions such as Clausen's integral or the
closely related dilogarithm. We first provide a general boundary integral that
applies to all planar luminaires and then derive the closed­form expression that
applies to arbitrary polygons, which is the result most relevant for global illumi­
nation. Our approach is to express the problem as an integral of a simple class
of rational functions over regions of the sphere, and to convert the surface inte­
gral to a boundary integral using a generalization of irradiance tensors. The result
extends the class of available closed­form expressions for computing direct radia­
tive transfer from finite areas to differential areas. We provide an outline of the

Source: Arvo, Jim - Departments of Information and Computer Science & Electrical and Computer Engineering, University of California, Irvine

Collections: Computer Technologies and Information Sciences