 
Summary: The Irradiance Jacobian for Partially Occluded
Polyhedral Sources
James Arvo
Program of Computer Graphics \Lambda
Cornell University
Abstract
The irradiance at a point on a surface due to a polyhedral source
of uniform brightness is given by a wellknown analytic formula.
In this paper we derive the corresponding analytic expression for
the irradiance Jacobian, the derivative of the vector representation
of irradiance. Although the result is elementary for unoccluded
sources, within penumbrae the irradiance Jacobianmust incorporate
more information about blockers than either the irradiance or vector
irradiance. The expression presented here holds for any number of
polyhedral blockers and requires only a minor extension of standard
polygon clipping to evaluate. To illustrate its use, three related
applications are briefly described: direct computation of isolux
contours, finding local irradiance extrema, and isomeshing. Isolux
contours are curves of constant irradiance across asurface that can be
followed using a predictorcorrector method based on the irradiance
