Define the glossy-diffuse albedo to explicitly correct for darkening #165
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…penPBR into glossy_diffuse_darkening_compensation
…b.com/portsmouth/OpenPBR into glossy_diffuse_darkening_compensation
…tch subsurface discussion.
to make it clear that we do not define the albedo of the Oren-Nayar lobe directly, we instead define the specified "observed base color at normal incidence" C according to an equation, which would then constrain the albedo of the lobe to satisfy that. In albedo-scaling approx., it just reduces to requiring albedo=C.
…b.com/portsmouth/OpenPBR into glossy_diffuse_darkening_compensation
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| The resulting BRDF of the glossy-diffuse slab is the combination of a "glossy" specular lobe provided by reflection from the dielectric interface, and a diffuse lobe provided by bounces off the substrate. This models for example the reflection from shiny, totally opaque surfaces such as dense plastic, rock, and concrete. This form of BRDF model is classic in computer graphics and typically termed the Ashikhmin-Shirley or Kelemen model ([#Ashikhmin2000], [#Kelemen2001], [#Kulla2017], [#Kutz2021]). | ||
| Physically there will be darkening and saturation of the observed color due to multiple inter-reflections (scattering) within the gloss layer, as described in the coat darkening section. However in this case, we wish to automatically compensate for this effect by adjusting the albedo of $f_\mathrm{diffuse}$ in order to make the observed color match the input color $\mathbf{C} =$ **`base_weight`** * **`base_color`** (in a similar spirit to the albedo remapping described in the Subsurface section). |
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I'm assuming the "coat darkening section" is not something that can be linked to? (No link is produced for this section reference.)
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It will be linked to eventually, just it's still in review. The method we use to define the coloring of:
- coat
- glossy-diffuse
- subsurface
are all using the same basic formulation, so we should make sure to connect the discussions.
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Makes sense and sounds good.
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| Glossy-diffuse params | Label | Type | Range | Default | Description | ||
| ----------------------|-----------|----------|:----------------:|:-------------------:|---------------------------------------------- | ||
| **`base_weight`** | Weight | `float` | $ [0, 1] $ | $ 1 $ | Scalar multiplier to **`base_color`** | ||
| **`base_color`** | Color | `color3` | $ [0, 1]^3 $ | $ (0.8, 0.8, 0.8) $ | Reflection albedo color of $f_\mathrm{diffuse}$ | ||
| **`base_color`** | Color | `color3` | $ [0, 1]^3 $ | $ (0.8, 0.8, 0.8) $ | Base reflection albedo color according to equation [glossy_diffuse_albedo_constraint]. | ||
| **`base_roughness`** | Roughness | `float` | $ [0, 1] $ | $ 0 $ | Roughness of the diffuse lobe $f_\mathrm{diffuse}$ |
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Tangential, but I feel like the behavior would clearer if "base roughness" were instead called "diffuse roughness".
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Jamie suggested base_diffuse_roughness on Slack, which would eliminate the ambiguity while keeping the "base" concept intact.
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We can raise this at the meeting, if we have time. In any case, that change would be for a different PR.
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| \begin{eqnarray} \label{glossy_diffuse_albedo_constraint} | ||
| \mathbf{E}_\textrm{diffuse} = \bigl( 1 - \mathbf{E}_\textrm{spec} \bigr) \mathbf{C} \ . | ||
| \end{eqnarray} | ||
| In other words, the selected color $\mathbf{C}$ parametrizes the fraction of the energy transmitted into the dielectric layer that is subsequently transmitted back out due to reflection from the base interface. Thus since $0 \le \mathbf{C} \le 1$, $\mathbf{E}_\textrm{glossy-diffuse} \le 1$ so energy is always conserved, and if $\mathbf{C}=1$ then $\mathbf{E}_\textrm{glossy-diffuse}=1$ which guarantees that a white $\mathbf{C}$ passes the furnace test. According to this definition, $\mathbf{C}$ is the observed reflection color (viewed at normal incidence under uniform illumination) in areas where the Fresnel reflection is negligible, and otherwise the observed color is a blend of $\mathbf{C}$ with the gray Fresnel reflection that conserves total reflected energy. |
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Just to clarify, in this version of the text, the base color behaves similarly to the subsurface color in that it represents the observed color. However, as discussed on Slack, we would like to modify this such that the base color instead represents the single-scattering microfacet albedo, implying that the observed diffuse color will be darker / more saturated than the specified color (when it's not white). This will be consistent with our current description of the metal component.
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I don't think that scheme (i.e. saying we "only take single-scattering into account" in
The way we set this up we demanded that if the selected/desired color
I think the right way to say it is to say that the formulas define what the Oren-Nayar albedo has to be in the zero roughness case (i.e. assuming a Lambertian base). Assuming albedo-scaling, this simply implies that the Oren-Nayar albedo equals
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I think it makes sense to add this change for now, even though it doesn't seem to affect anything
(189e2f8):
This will be more important though in a subsequent PR where I give the specific form of the Oren-Nayar lobe, including the energy compensation, which exhibits the darkening/saturation due to roughening. Then it will be more obvious that this form of the definition is required.
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Makes sense. That looks like a good clarification for future proofing.
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Ready to merge. |
jstone-lucasfilm
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jstone-lucasfilm
merged commit 10695cc
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AcademySoftwareFoundation:main
Addresses issue #141.
We need to explain that, although physically the glossy-diffuse slab (as described) should exhibit darkening/saturation due to the same physics as the coat darkening (i.e. multiple bounces inside the gloss layer losing energy as they hit the colored base), we want to prevent this so that the user sees -- to the extent possible -- the base color she selected.
But she can't see the exact base color she selected, because the Fresnel of the gloss is superimposed on the diffuse base lobe. So we make the required color be a blend of the Fresnel and unsaturated base color (i.e. essentially the albedo-scaling formula). This is the same mechanism we used to define how the coat "un-darkening" works. Thus albedo-scaling automatically does the right thing (but if the implementation does something different, e.g. more physically correct, it is still well-defined what the goal albedo needs to be so the appearance won't break).
Note this won't make any difference to implementations that already use the albedo-scaling approximation (e.g. Arnold, MaterialX).
This will need to be tweaked once we get the coat darkening PR #162 in, as it should reference that discussion.