Add coat darkening and saturation effects

portsmouth commented 5 months ago

This PR adds a detailed discussion to the spec of the coat darkening effect (incorporating the ideas discussed in https://github.com/AcademySoftwareFoundation/OpenPBR/issues/136 and https://github.com/AcademySoftwareFoundation/OpenPBR/issues/141), with:

introduction of a new coat_darkening parameter (defaulting to 1, the physically correct case).
a physical definition of how this parameter operates to reduce the darkening (via boosting of the base albedo)
a suggested practical implementation of the darkening factor for the base lobe, taking into account the IOR of the coat, and also the roughness of the base (based on the derivations and discussions linked elsewhere).
A suggested implementation of the darkening of colored coats at grazing angles due to longer path length in the absorbing medium.

I also include a placeholder for a discussion of how the coat roughness should affect the underlying lobes. (Probably to be done in a separate PR, and derivation of a reasonable physical approximation for this is WIP).

To make it easier to read, I broke the Coat section into sub-sections.

portsmouth commented 3 months ago

One aspect of the proposed formulas that I worry about is the effect of the base roughness on the darkening, i.e. Equation 61. This is designed so that a smooth base produces less darkening, basically blending between known formulas for the cases of a completely smooth and completely diffuse base. (See the discussion on Slack here, for background to that -- it is based on the Weta "The Path of Water" notes from SIGGRAPH 2023).

I assumed that if the base is dielectric, the roughness of the reflection from it is determined by the specular_roughness. However if the base has a scattering medium (i.e. as it does in the glossy-diffuse case, or if there is a transmission or subsurface volume) then the reflection is effectively roughened due to this scattering, apart from the initial Fresnel reflection. The proposed formula ignores this effect, so probably underestimates the darkening effect of the coat on a glossy-diffuse base or subsurface. We would need to do some proper investigation with Monte Carlo simulations to know.

Perhaps it's fine to still give these formulas merely as a convenient, reasonable approximation.

peterkutz commented 3 months ago

I assumed that if the base is dielectric, the roughness of the reflection from it is determined by the specular_roughness. However if the base has a scattering medium (i.e. as it does in the glossy-diffuse case, or if there is a transmission or subsurface volume) then the reflection is effectively roughened due to this scattering, apart from the initial Fresnel reflection. The proposed formula ignores this effect, so probably underestimates the darkening effect of the coat on a glossy-diffuse base or subsurface.

Is this not addressed by the formula below?

$r_d = \mathrm{lerp}(1, r, \xi_s F_s)$

I thought this was considering the diffuse component to have an effective roughness of $1$.

peterkutz commented 3 months ago

This is looking really good to me at a high level but I would need to do another pass to verify some of the formulas by looking more closely and by looking at the referenced equations and citations. A lot of my comments are questions and clarifications that I could potentially answer myself based on a more careful reading, however I figured I would post them anyway in case they raise any important points and in case the text can be clarified to prevent other readers from initially having the same questions.

portsmouth commented 3 months ago

Is this not addressed by the formula below?

rd=lerp(1,r,ξsFs)

I thought this was considering the diffuse component to have an effective roughness of 1.

I stated it incorrectly, I meant that if scattering medium is actually absent -- e.g. coat on clear glass (or glass with a volume with huge MFP, say), then it seems wrong to assume there is a diffuse component with a roughness of 1, that we should blend in according to the F0 of the glass.

Fixing that would involve the MFP somehow, but it would get a bit too elaborate probably.

portsmouth commented 3 months ago

This is looking really good to me at a high level but I would need to do another pass to verify some of the formulas by looking more closely and by looking at the referenced equations and citations. A lot of my comments are questions and clarifications that I could potentially answer myself based on a more careful reading, however I figured I would post them anyway in case they raise any important points and in case the text can be clarified to prevent other readers from initially having the same questions

Thanks, I appreciate the careful reading and discussion! :smiley:

portsmouth commented 3 months ago

Not sure it's helpful, but my implementation of this in the GLSL viewer might be a useful point of reference. It looks like this, where the darkening is applied to the weight of the "base substrate" lobe (which consists of the mix of metal and dielectric base lobes):

    // Compute base darkening factor due to presence of coat:
    vec3 base_darkening = vec3(1.0);
    if (coated && coat_darkening > 0.0)
    {
        float Kr = 1.0 - (1.0 - average_dielectric_fresnel(coat_ior))/sqr(coat_ior);
        float Ks = FresnelDielectricReflectance(abs(winputL.z), coat_ior);
        float Fr = clamp(specular_weight * fresnel_refl_normal_incidence(), 0.0, 1.0);
        float rd = mix(1.0, specular_roughness, Fr); // estimate of roughness of dielectric base
        float rm = specular_roughness;               // estimate of roughness of metallic base
        float rb = mix(rd, rm, M);  // thus estimated roughness of entire base
        float K = mix(Ks, Kr, rb);  // thus estimated internal diffuse reflection coeff.
        vec3 E_dielectric_base = mix(mix(albedos.m[ID_DIFF_BRDF], albedos.m[ID_SSSC_BTDF], S),
                                         albedos.m[ID_SPEC_BTDF], T);     // dielectric base albedo
        vec3 E_base = mix(E_dielectric_base, albedos.m[ID_META_BRDF], M); // entire base albedo
        vec3 Delta = (1.0 - K) / vec3(1.0 - E_base*K);                    // full darkening factor
        base_darkening = mix(vec3(1.0), Delta, C * coat_darkening);       // modulated darkening factor
    }
    vec3 w_base_substrate = w_coated_base * mix(vec3(1.0), base_darkening * coat_color * (vec3(1.0) - albedos.m[ID_COAT_BRDF]), C);

portsmouth commented 3 months ago

I'm not sure it's practical to implement this in the MaterialX graph. It would be very time consuming to construct all the math in XML without errors.

Also to implement this in the graph would require making various simplifications, as:

the view direction is not known in the graph (needed for $K_s$), so $K_s$ would have to be evaluated at normal incidence instead say
the dielectric Fresnel average integral would have to be coded up manually in the graph, which is a bit painful
the BSDF albedos are not possible to evaluate, so would need to make some approximation

I can try to do something minimal, but probably the relevant functions should instead be exposed as built-in utility nodes.

Conceptually, this is really just the physics of the BRDF obtained by layering a dielectric coat on a base slab. So ideally the layer operation should handle this (using the notion in MaterialX that the implementation of layering depends on the specific things being layered). Though then this would require MaterialX to explain the physics it thinks should be implemented, which it makes no attempt to do in the current spec except in a very loose, mathematics-free form.

jstone-lucasfilm commented 3 months ago

@portsmouth Would it be practical to implement this logic in vanilla OSL, using only the set of closures and functions that OSL natively provides? If so, then I could take the step of translating this back to a MaterialX graph that generates the vanilla OSL code.

portsmouth commented 3 months ago

@portsmouth Would it be practical to implement this logic in vanilla OSL, using only the set of closures and functions that OSL natively provides? If so, then I could take the step of translating this back to a MaterialX graph that generates the vanilla OSL code.

It would certainly be a lot easier than trying to write code in XML, yes.

If the native functions are the ones listed here, then it doesn't have them built in (i.e. the formula for dielectric Fresnel factor and its hemispherical albedo). It's also not possible I take it to compute the directional (or hemispherical) albedo of a BSDF closure in OSL (or the MaterialX graph), so those albedos will I assume just have to be be approximated ignoring the view direction.

jstone-lucasfilm commented 3 months ago

@portsmouth Yes, I believe that's the very latest specification for OSL, so that's the set of closures and functions that we would need to use here. Would you like to put together a proposal for a pure OSL definition of the behavior you'd like to see, and I can do the work of translating this to the equivalent MaterialX graph?

portsmouth commented 3 months ago

@jstone-lucasfilm

Here's a first pass at the OSL code, expressed in a self-contained form as a function for the coat darkening factor (which will be multiplied into the base closure combination in the graph -- that part not shown here), taking as input the relevant subset of the OpenPBR parameters:

// Hemispherical (average) albedo of dielectric Fresnel factor
float E_F(float eta)
{
    return log((10893.0*eta - 1438.2)/(-774.4*sqr(eta) + 10212.0*eta + 1.0)); // (NB, this is natural log)
}

float average_dielectric_fresnel(float eta)
{
    // Technically, this is only valid for IOR < 3, unless we use a more elaborate E_F approx.   
    if      (eta > 1.0) return E_F(eta);
    else if (eta < 1.0) return 1.0 - sqr(eta)*(1.0 - E_F(1.0/eta));
    else return 0.0;
}

float dielectric_F0(float eta)
{
   return sqr((eta - 1.0)/(eta + 1.0));
}

color coat_darkening_factor(color base_color, 
                            float base_metalness,
                            float specular_weight,
                            float specular_roughness,
                            float specular_ior,
                            float transmission_weight,
                            color subsurface_color,
                            float subsurface_weight,
                            float coat_ior,
                            float coat_weight,
                            float coat_darkening)
{ 
   // Compute estimate of roughness of base
   const float ambient_ior = 1.0;                                                // (Assume here no nested dielectrics, for simplicity)
   float coat_ior_average = mix(ambient_ior, coat_ior, coat_weight);             // (as described in Coat section of spec)
   float eta_s = specular_ior / coat_ior_average;                                // (as described in Coat section of spec)
   float Fr = clamp(specular_weight * dielectric_F0(eta_s), 0.0, 1.0);           // dielectric specular reflection F0, modulated by specular weight
   float rd = mix(1.0, specular_roughness, Fr);                                  // estimate of roughness of dielectric base
   float rm = specular_roughness;                                                // estimate of roughness of metallic base
   float rb = mix(rd, rm, base_metalness);                                       // thus estimated roughness of entire base
   // Compute "internal diffuse reflection coefficient", taking into account estimated base roughness
   float coat_eta = coat_ior / ambient_ior;
   float Kr = 1.0 - (1.0 - average_dielectric_fresnel(coat_eta))/sqr(coat_eta);  // internal diffuse reflection coefficient, rough case
   float Ks = dielectric_F0(coat_eta);                                           // internal diffuse reflection coefficient, smooth case
                                                                                 // (approx., since we don't have access to wi in the MaterialX graph)
   float K = mix(Ks, Kr, rb);                                                    // thus estimated internal diffuse reflection coeff.
   // Compute estimated total base albedo
   color diffuse_albedo      = color(Fr) + (1.0-Fr)*base_color;                  // approx. diffuse slab albedo
   color subsurface_albedo   = color(Fr) + (1.0-Fr)*subsurface_color;            // approx. subsurface slab albedo
   color transmission_albedo = Fr;                                               // approx. translucent slab albedo (ignore volume or tint, for simplicity)
   color metal_albedo        = specular_weight * base_color;                     // approx. metal slab albedo
   color albedo_opaque_dielectric = mix(diffuse_albedo,           subsurface_albedo,   subsurface_weight);
   color albedo_dielectric        = mix(albedo_opaque_dielectric, transmission_albedo, transmission_weight);
   color albedo_base              = mix(albedo_dielectric,        metal_albedo,        base_metalness);
   // Final darkening factor
   color Delta = color(1.0 - K) / (color(1.0) - albedo_base*K);
   return mix(color(1.0), Delta, coat_weight * coat_darkening);                  // modulate according to coat weight
}

(NB, this assumes the specular weight changes of https://github.com/AcademySoftwareFoundation/OpenPBR/pull/157 will be applied as well).

jstone-lucasfilm commented 3 months ago

Thanks @portsmouth, and that looks straightforward to implement in MaterialX as a collection of new subgraphs, which we can define in the same MaterialX document as the reference graph for OpenPBR. This will definitely add a significant amount of new code to generated shaders (e.g. GLSL, OSL, MDL), but it seems worthwhile to add this new logic and then evaluate the visual benefits versus the performance impact.

jstone-lucasfilm commented 3 months ago

Since this is dependent on PR #157, let's finalize and merge that one first, and then we can start on the MaterialX graph for this proposal.

jstone-lucasfilm commented 2 months ago

I've now merged #157, and the next step would be to resolve conflicts between these two pull requests, after which we can start on the MaterialX-side updates for this change.