Implementing global illumination using spherical harmonics lighting

In this recipe, we will learn about implementing simple global illumination using spherical harmonics. Spherical harmonics is a class of methods that enable approximation of functions as a product of a set of coefficients with a set of basis functions. Rather than calculating the lighting contribution by evaluating the bi-directional reflectance distribution function (BRDF), this method uses special HDR/RGBE images that store the lighting information. The only attribute required for this method is the per-vertex normal. These are multiplied with the spherical harmonics coefficients that are extracted from the HDR/RGBE images.

The RGBE image format was invented by Greg Ward. These images store three bytes for the RGB value (that is, the red, green, and blue channel) and an additional byte which stores a shared exponent. This enables these files to have an extended range and precision of floating point values. For details...