What I don't understand yet is what this is supposed to accomplish ?
Short answer, more accurate physical light calculations. (with respect to some light surface interaction characteristics).
Why not evaluate everything with the diffuse BRDF the normal way?
Unfortunately the problem lies within the definition of the normal way. The "normal" phong reflection model has been embraced long time ago by the real time rendering community from the beginning and has been the de facto standard because of it's simplicity that makes it appropriate for the use of real time rendering.
The problem though, real life light/material interaction is so complicated that it cannot be actually modeled by a single BRDF.
BRDFs are an abstraction of how the actual light interaction is supposed to happen. phong is just one many other, that has the advantage of simplicity.
But what are the actual advantages ?
In computer graphics there are different BRDFs that fall into two main categories:
- Based on physical theory.
- Designed to fit specific a class of surface type and are usually used in real time rendering.
Talking about the second category each BRDF tries to accomplish certain characteristics with light surface interaction. The simplest possible BRDF is Lambertian which tries to model subsurface scattering and are often used in computer graphics, The constant reflectance value of a Lambertian BRDF is commonly refered to as the diffuse color.
In real time computer graphics usually BRDFs are manually selected and their
parameters set to achieve a desired look (e.g. using Phong with certain values to model a plastic or a chrome surface).
On the other hand, sometimes BRDFs are measured directly from the desired surface (and are not represented by a math equation). This gives us much more physically accurate data about the surface that are otherwise hard to accomplish analytaclly.
One method to fit those captured data is to select an analytical BRDF and fit these data into it. Spherical Harmonics is just a technique used to represent those measured quantities, and fit them into an analytical BRDF model.
The best resource for BRDF theory can be found in real time rendering
- 7.5 BRDF Theory.
- On spherical harmonics revise 7.7.2 Representations for Measured