Hello guys, these past weeks I've been trying to implement a PBR shader and OMG there are so many little details. First I started reading this article: https://learnopengl.com/PBR/Theory

because it had a lot of good explanations and sample code, and did A LOT of googling for the stuff that wasn't clear enough. Right now I am very confused about why the fresnel term uses the dot product between de halfway vector and the view vector. From theory I thought that the fresnel computes the amount of light that should reflect off a surface depending on the viewing angle and the surface normal, and there are a lot of articles explaining it like that:

- https://learnopengl.com/PBR/Theory
- https://docs.unrealengine.com/en-US/Engine/Rendering/Materials/HowTo/Fresnel/index.html
- https://en.wikipedia.org/wiki/Schlick's_approximation (in the first paragraphs)

And I was happy with that knowledge until I started to discover a lot of articles (and even that wiki one in the last sentence) that actually tell you to use the dot product between the halfway vector and light direction.

- http://filmicworlds.com/blog/everything-has-fresnel/ (this one just says that it got the formula from the gpu gems article https://developer.nvidia.com/gpugems/GPUGems3/gpugems3_ch14.html which unfortunately doesn't give details about that)
- http://www.codinglabs.net/article_physically_based_rendering_cook_torrance.aspx
- https://computergraphics.stackexchange.com/questions/2494/in-a-physically-based-brdf-what-vector-should-be-used-to-compute-the-fresnel-co (there are really good answers here but I couldn't wrap my head around)

I tried to read the original schlick's paper but I'm the kind of person that can't really follow all that math without visual examples...

In the first image I'm using the dot(N,V) and visually it makes sense. In the second image I'm using the suggested dot(H,L) while having a point light behind the sphere, and I'm just confused, I can't understand what I'm looking at, and why is the normal not needed at all.

I have the feeling I may be mistunderstanding or mixing concepts, so I decided to come here and create a thread so maybe someone could explain it with more....simple words?

Also here is a code snippet of what I'm currently doing, but just for illustrative purposes ( I'm not looking for code, just some theory explanations):

void frag()
{
  float NDF = DistributionGGX(N,H,roughness);
  float G = GeometrySmith(N, V, L,roughness);
  float3 F = SchlickFresnel(saturate(dot(V,H)??), F0);
  
  float3 radiance = lightColor*attenuation*dot(N,L); // only have a single point light
  
  float3 numerator    = NDF * G * F;
  float denominator = 4.0 * saturate(dot(N, V)) * saturate(dot(N, L));
  float3 specular     = numerator/ max(denominator, 0.001);  //avoid division by 0
  float3 kd = float3(1,1,1) - F; // if I understood correctly, ks is not needed as it is included in the F term
  
  float3 diffuse = albedo/PI;

  float3 irradiance = (kd * diffuse + specular) * radiance * NdotL;
}

I know there are a lot of posts talking about this, and I spent a lot of time reading those, but it wasn't entirely clear...so apologies for making another thread asking basically the same thing. Thanks for your time...cheers!

3 hours ago, ramirofages said:

From theory I thought that the fresnel computes the amount of light that should reflect off a surface depending on the viewing angle and the surface normal

You are (almost) correct, just only one thing you may not catch up with so well, that in microfacet theory, we always give the "surface" 2 normal, the macro-normal n, and the micro-normal m.

SIGGRAPH 2013 Course: Physically Based Shading in Theory and Practice - Background: Physics and Math of Shading

I suggest you read "Surface Reflectance (Specular Term)" from pg.12 thoroughly and I hope you could understand the reason why it's VdotH, that we would use halfway-vector h as the assumption of the micro surface's normal.

Quote

For microfacet BRDFs, the usual simplifying assumption is that individual microfacets are perfect specular reflectors. Then, given the LL and VV at which to evaluate, the only microfacets that can contribute are those that are aligned along H=normalize(L+V)H=normalize(L+V), because that's the only way they can reflect light from the incoming to the outgoing ray.

The second answer in https://computergraphics.stackexchange.com/questions/2494/in-a-physically-based-brdf-what-vector-should-be-used-to-compute-the-fresnel-co explained as above, it's crystal clear ?

The reason we don't need kS is not "as it is included in the F term", rather it's because F term is kS, it's all about the nature of specular reflectance.

3 hours ago, ramirofages said:

visually it makes sense

When you split each term and try to visualize them, you could only expect that the visual result is depending on the parameters of the term's formula, rather than the complete visual appearance. When you put a point light behind the sphere, you could only count on the macro Visibility term (or macro Geometry term) to occlude the light, which in microfacet theory the macro V term is made up by micro D and G term. F term did nothing here.