# Real time image based lighting for arbitrary BRDFs coordinate alignment

I was trying to understand how real-time illumination happens with image-based lighting.

I understood that importance of representing the Environment Map and BRDF in spherical harmonics. Because both of them orthonormal basis function so that the illumination integral becomes a matter of dot product of coefficients.

But before that,

Why is environment map in the global frame and BRDF in the local frame?

Edit 1: To help more this is the paper Fast, Arbitrary BRDF Shading