  In this paper, we present a new mathematical foundation for image-based
lighting. Using a simple manipulation of the local coordinate system, we derive
a closed-form solution to the light integral equation under distant environment
illumination. We derive our solution for different BRDF's such as lambertian
and Phong-like. The method is free of noise, and provides the possibility of
using the full spectrum of frequencies captured by images taken from the
environment. This allows for the color of the rendered object to be toned
according to the color of the light in the environment. Experimental results
also show that one can gain an order of magnitude or higher in rendering time
compared to Monte Carlo quadrature methods and spherical harmonics.
