“Spherical Harmonic Gradients”

Spherical Harmonics (SH) are best suited for shading objects illuminated by infinitely-distant low-frequency environments. The main idea is to split the shading integral into two parts. Visibility (times diffuse BRDF) is precomputed at every vertex and projected into the SH basis resulting in the coefficient vector T. At run-time incident radiance is sampled at the object’s center and represented in SH as the coefficient vector L = (c0,c1,…) T . Objects can then be shaded in real-time by simply computing the dot-product L·T at every vertex.