Confused with PBR implementations I'm discovering the wonderful world of math and I'm hitting a huge wall with PBR and naming so I have a few questions:
As far as I understand BRDF describe how a material react to light (incoming direct light and reflections). But in "Cook-Torrance" I don't see anything about reflections I don't understand how I integrate it so I only get diffuse light and reflections.

I've read a lot about different "diffuse term" like "Oren-Nayar" is it a part of Cook-Torrance like a different "D" in the DFG nominator ? does it replace it without specular calculations ?

I've read a lot about "GGX" from my blender artist background I thought it was something that make a blurry reflection but It seems I was wrong and now I find this GGX term in a lot of different situations like in micro-facet normal distribution in this tutorial

So in short the question is: how "Oren-Nayar" and "GGX" and "Cook-Torrance" are related to each other (if they are) and how do I integrate "vec3 reflection" in those algorithm ?

As I said before I'm a newbie in math so If your answer is "math heavy" please write a glsl/hlsl version of your equations it's much easier to understand for me so an equivalence will help me a lot

PS: I understand my question is blurry but it is also as blurry as my understanding of the subject.
DFG pops up in the family of microfacet based BRDFs. It is simply the product of three terms:


D : The microfacet distribution.
F : The fresnel coefficient.
G : The geometric attenuation between microfacets.


When someone says Cook-Torrance, they usually mean a microfacet BRDF where the distribution (D) is Beckmann, which I think is what the original Cook-Torrance paper was about.

GGX is really just a different distribution (D term). GTR is another one. The names are often used as a shortcut to mean a BRDF using that distribution.

Now all of these assume specular reflection (or refraction) on the microfacets, hence the fresnel term. If you take a similar idea but use diffuse (lambertian) microfacets, you get the Oren-Nayar BRDF. I think that one is based on a gaussian distribution of the microfacets but I'm not familiar with the details.