Lighting in most real scenes is complex, coming from a variety of sources including area lights and large continuous lighting distributions like skylight. But current graphics hardware only supports point or directional light sources. One reason is the lack of simple procedural formulas for general lighting distributions. Instead, an integration over the upper hemisphere must be done for each pixel.
We present such a simple formula for diffuse objects, i.e. for the irradiance. The key to our approach is the rapid computation of an analytic approximation to the irradiance environment map. For rendering, we demonstrate a simple procedural algorithm that runs at interactive frame rates, and is amenable to hardware implementation. No texture-mapping is required for the irradiance with our approach.
The main ingredient is the derivation of an analytic formula for the irradiance in terms of spherical harmonic coefficients of the lighting. For rendering, the key observation is that the Lambertian BRDF behaves sufficiently closely to a low-pass filter that we need consider only the first 2 orders of spherical harmonics, i.e. 9 parameters. The simple form of the first 9 spherical harmonics makes implementation straightforward.
