On 10/3/2017 at 1:05 AM, MJP said:

With a metallic workflow the specular reflectance is fixed for dialectrics (constant IOR), or for metals the specular reflectance is equal to the base color.

If I understand Disney's presentation and code correctly, the used BRDF (diffuse and specular component) is something like this (after stripping it down a bit):

BRDF := F_diffuse  * BRDF_diffuse + F_specular * BRDF_specular

F_diffuse := (1-metallic) * lerp(1, FD90, Fresnel(n_dot_l)) * lerp(1, FD90, Fresnel(n_dot_v))

BRDF_diffuse := base_color/pi

F_specular := lerp(lerp(???, base_color, metallic), (1,1,1), Fresnel(n_dot_h))

BRDF_specular := (G * D) / (4 * n_dot_v * n_dot_l) // Fresnel(n_dot_h) moved to F_specular.

@Hodgman @MJP is the ??? factor the 0.3/0.4 you are talking about?

I am also still confused about their Fresnel calculation with Schlick's approximation: where is the reflectance gone? The Schlick approximation is defined as F(theta) := F0 + (1-F0)(1-cos(theta))^5. Disney uses (1-F(theta_l))*(1-F_theta_d) although they rather seem to use (1-F(theta_l))*(1-F_theta_v). If we expand the latter (while skipping the first F0 in Schlick's approximation???), we get: (1+(F0-1)(1-cos(theta_l))^5)(1+(F0-1)(1-cos(theta_v))^5). After replacing F0 with FD90, we get our F_diffuse above. My understanding is that they set 1 - lerp(a,b,m) to lerp(b,a,m) which is not correct? Or I am missing some approximations?

So instead of using the BRDF as available here.

I would rather use the following modified format:

float3 CookTorranceBRDFxCos(float3 n, float3 l, float3 v, 
    float3 base_color, float roughness, float metalness) {
    
    const float  alpha   = sqr(roughness);
    const float  n_dot_l = sat_dot(n, l);
    const float  n_dot_v = sat_dot(n, v);
    const float3 h       = HalfDirection(l, v);
    const float  n_dot_h = sat_dot(n, h);
    const float  v_dot_h = sat_dot(v, h);

    const float  Fd90    = F_D90(v_dot_h, roughness);
    const float  FL      = BRDF_F_COMPONENT(n_dot_l, Fd90);
    const float  FV      = BRDF_F_COMPONENT(n_dot_v, Fd90);
    const float  F_diff  = (1.0f - metalness) * (1.0f - FL) * (1.0f - FV);

    const float3 c_spec  = lerp(g_dielectric_F0, base_color, metalness);
    const float3 F_spec  = BRDF_F_COMPONENT(v_dot_h, c_spec);
    const float  D       = BRDF_D_COMPONENT(n_dot_h, alpha);
    const float  V       = BRDF_V_COMPONENT(n_dot_v, n_dot_l, n_dot_h, v_dot_h, alpha);

    const float3 Fd      = F_diff * base_color * g_inv_pi;
    const float3 Fs      = F_spec * 0.25f * D * V;

    return (Fd + Fs) * n_dot_l;
}

Note that instead of calculating the BRDF, I calculate the BRDF multiplied by the cosine factor. Furthermore, I do not use an explicit Geometry (G) component in the Microfacet model, but instead a Visibility (V) component. The V component is equal to the G component divided by the foreshortening terms (n_dot_l * n_dot_v). So the Microfacet model reduces to F * D * V / 4.

F_D90 is equal to (as mentioned in the course):

float F_D90(float v_dot_h, float roughness) {
    return 0.5f + 2.0f * roughness * sqr(v_dot_h);
}

Any thoughts?

On 10/2/2017 at 8:42 AM, Hodgman said:

Also, specular colour and specular reflection coefficient are usually the same thing.

Just wanted to say, they're not.

While they make similar results, coloured fresnel / IOR tends to lack colour at the borders, unlike specular colour. It's a subtle difference.

5 hours ago, Matias Goldberg said:

Just wanted to say, they're not.

While they make similar results, coloured fresnel / IOR tends to lack colour at the borders, unlike specular colour. It's a subtle difference.

Oh, I plug "specular color" into fresnel as F0 to get white borders, but I've seen other PBR shaders that multiply the result with a "reflection coefficient" to basically dull the entire specular results. I guess this is like a specular occlusion mask?

31 minutes ago, Hodgman said:

Oh, I plug "specular color" into fresnel as F0 to get white borders, but I've seen other PBR shaders that multiply the result with a "reflection coefficient" to basically dull the entire specular results. I guess this is like a specular occlusion mask?

Some BRDFs have both a diffuse and specular color. Some BRDFs seem to remove the specular color and just use a Fresnel component. Apparently, the specular color can be used to calculate this Fresnel component.

Actually I have seen Cook-Torrance with and without an explicit specular color.

Yeah now that you mention it, I remember reading a paper on trying to recreate real world measured data with cook-torrence, and their error numbers were smallest when they allowed coloured F0 and a coloured multiplier over the entire specular result (instead of just one or the other).

I've never actually seen this model used in games though

4 hours ago, Hodgman said:

Oh, I plug "specular color" into fresnel as F0 to get white borders, but I've seen other PBR shaders that multiply the result with a "reflection coefficient" to basically dull the entire specular results. I guess this is like a specular occlusion mask?

Yes.

This was discussed (but for some reason the blogpost was removed, likely in server migration) in Filmic Worlds' website. Fortunately Web Archive remembers.

Also twitter discussion: https://twitter.com/olanom/status/444116562430029825

19 hours ago, matt77hias said:

So instead of using the BRDF as available here.

I would rather use the following modified format:

float3 CookTorranceBRDFxCos(float3 n, float3 l, float3 v, 
    float3 base_color, float roughness, float metalness) {
    
    const float  alpha   = sqr(roughness);
    const float  n_dot_l = sat_dot(n, l);
    const float  n_dot_v = sat_dot(n, v);
    const float3 h       = HalfDirection(l, v);
    const float  n_dot_h = sat_dot(n, h);
    const float  v_dot_h = sat_dot(v, h);

    const float  Fd90    = F_D90(v_dot_h, roughness);
    const float  FL      = BRDF_F_COMPONENT(n_dot_l, Fd90);
    const float  FV      = BRDF_F_COMPONENT(n_dot_v, Fd90);
    const float  F_diff  = (1.0f - metalness) * (1.0f - FL) * (1.0f - FV);

    const float3 c_spec  = lerp(g_dielectric_F0, base_color, metalness);
    const float3 F_spec  = BRDF_F_COMPONENT(v_dot_h, c_spec);
    const float  D       = BRDF_D_COMPONENT(n_dot_h, alpha);
    const float  V       = BRDF_V_COMPONENT(n_dot_v, n_dot_l, n_dot_h, v_dot_h, alpha);

    const float3 Fd      = F_diff * base_color * g_inv_pi;
    const float3 Fs      = F_spec * 0.25f * D * V;

    return (Fd + Fs) * n_dot_l;
}

Note that instead of calculating the BRDF, I calculate the BRDF multiplied by the cosine factor. Furthermore, I do not use an explicit Geometry (G) component in the Microfacet model, but instead a Visibility (V) component. The V component is equal to the G component divided by the foreshortening terms (n_dot_l * n_dot_v). So the Microfacet model reduces to F * D * V / 4.

F_D90 is equal to (as mentioned in the course):

float F_D90(float v_dot_h, float roughness) {
    return 0.5f + 2.0f * roughness * sqr(v_dot_h);
}

Any thoughts?

I never check any of these dot products for equality with zero. I checked for NaNs or Infs by marking such pixels, but didn't found any in a couple of scenes.

The Fresnel effect at glancing angles feels sometimes a bit strange in for instance the Sponza scene. It seems like the walls are wet due to rain or so. (I use Disney's default roughness of 0.5f as my own default roughness if not specified).