I have been trying to implement the GGX shader in my path tracer based on this paper: Microfacet Models for Refraction through Rough Surfaces It's pretty clear how the importance sampling works, but I would also like to do next event estimation (direct lighting) for when the object is more rough and acts close to a diffuse shader.
The part that is really confusing to me is equation  and :
I don't understand why in  they use the microsurface normal, but in  they use the macrosurface normal. The transmission term I don't need because I'm just working on the reflectance, but I still don't get why it's m on  and n on . Is it possible to use any incident direction and outgoing direction and get back a proper BRDF? Or does the scatter direction "o" have to match where the microsurface normal makes it bounce to? In direct lighting the directions would need to be independent of each other for it to work since you're grabbing a from the hit point to the light, and from the hit point to the camera.