Efficient spherical harmonic shading for separable BRDF

Spherical Harmonics (SH) are commonly and widely used in computer graphics in order to speed up the evaluation of the rendering equation. With separable BRDF, the diffuse and specular contributions are traditionally computed separately. Our first contribution is to demonstrate that there is a simple relationship between both computations, but one-way, i.e. from specular to diffuse. We show how to deduce the diffuse contribution from the specular contribution, using a single multiplication. This replaces the use of tens of multiplications for some cases up to complex rotations for other cases. Our second contribution is an efficient way to compute the SH product between an arbitrary function and a clamped cosine, much less expensive than the traditional SH triple product.