Roughening improvements #261
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I think we need to think a bit about what the effect of the fuzz tint color should be. With the roughening heuristic above, I get the following results when the fuzz color is varied from light to dark.
When the fuzz is dark, our heuristic reduces the roughening, so we see a sharp highlight. I find that a bit unconvincing as if the fuzz is same density in the left and right image, you would expect the highlight to be much more dimmed on the right. In reality, more absorbing dust should reduce the transmittance as well as the reflection. It may be inherent in the Zeltner model though, that this more realistic volumetric absorption isn't really captured. |
| The effect of the coat roughening can then be modeled as the convolution of these Gaussian NDFs, which corresponds to adding the variances (double counting the coat variance since the reflection passes through the coat boundary twice). The IOR ratio of the coat and ambient medium $\eta_\mathrm{ca}$ also needs to be accounted for, since as $\eta_\mathrm{ca} \rightarrow 1$ the roughening due to the coat goes to zero. | ||
| This leads to the following suggested approximate formula for the modified roughness $r'_\mathrm{B}$ of the base due to the coat: | ||
| \begin{equation} \label{coat_roughening_heuristic} | ||
| r'_\mathrm{B} = \mathrm{min} \bigl(1, r^4_\mathrm{B} + 2 x_C r^4_\mathrm{C} \bigr)^\frac{1}{4} \quad \textrm{with } x_C = 1 - \mathrm{min}(\eta_\mathrm{ca}, 1/\eta_\mathrm{ca}) |
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Does "x" mean something or is it just an arbitrary available variable name?
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Just a variable name. It accounts for the IOR, so not sure what symbol to use. Putting the min inside the brackets looked worse.
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Regarding the effect of dark fuzz in the images, I think the
True. The Zeltner model is based on non-absorbing microflakes and it doesn't make a distinction between scattered and unscattered transmission. So some of the transmitted light is actually scattered light that should be eliminated if the single-scattering albedo of the microflakes is zero. So I agree that the dark fuzz should technically darken the base surface more. That said, in your renders it's hard to see how much the dark fuzz is actually darkening the base because the specular highlight is overexposed and the background is black. |
| \mu_i \, f_\mathrm{fuzz}(\omega_i, \omega_o) = \mathbf{F} \, E_\mathrm{fuzz}(\mu_o, r_F) \, D(\mu_i | \mu_o, r_F) | ||
| \end{equation} | ||
| where $\mathbf{F}$ = **`fuzz_color`**, $E_\mathrm{fuzz}(\mu_o, \alpha)$ (termed $R$ in [#Zeltner2022]) is the reflectance at angle cosine $\mu_o$ given roughness $\alpha$ = **`fuzz_roughness`** $\in [0,1]$, and $D(\mu_i | \mu_o, \alpha)$ is a lobe defined by linear transformations of a cosine lobe (LTCs), where the transformation matrices (and $E_\mathrm{fuzz}$) are tabulated in a grid in the $(\mu_o, \alpha)$ plane, with values fitted to a simulation of the scattering in the volumetric fuzz microflake layer. Since the LTC lobe $D$ is a normalized PDF over the hemisphere, the resulting albedo of $f_\mathrm{fuzz}$ is $\mathbf{F} \, E_\mathrm{fuzz}(\mu_o, \alpha)$. | ||
| where $\mathbf{F}$ = **`fuzz_color`**, $E_\mathrm{fuzz}(\mu_o, r_F)$ (termed $R$ in [#Zeltner2022]) is the reflectance at angle cosine $\mu_o$ given roughness $r_F$ = **`fuzz_roughness`** $\in [0,1]$ (termed $\alpha$ in [#Zeltner2022]), and $D(\mu_i | \mu_o, r_F)$ is a lobe defined by linear transformations of a cosine lobe (LTCs), where the transformation matrices (and $E_\mathrm{fuzz}$) are tabulated in a grid in the $(\mu_o, r_F)$ plane, with values fitted to a simulation of the scattering in the volumetric fuzz microflake layer. Since the LTC lobe $D$ is a normalized PDF over the hemisphere, the resulting albedo of $f_\mathrm{fuzz}$ is $\mathbf{F} \, E_\mathrm{fuzz}(\mu_o, r_F)$. |
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I assume you're using different variables than the Zeltner paper to be consistent with other formulas in the OpenPBR spec. Is that right?
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Yes, since
| The scattering within the fuzz layer will have the effect of roughening the appearance of the substrate beneath it. | ||
| A simple suggested approximation for this can be adapted from the formula used to model the coat roughening, in equation [coat_roughening_heuristic]. If we consider the fuzz layer to generate roughening by scattering, we can approximate its effective roughness as being proportional to the albedo of the layer, as well as to the tint color (since darker fuzz will physically scatter less and absorb more). This leads to the following heuristic for the modified roughness $r'_\mathrm{B}$ of the substrate lobe: | ||
| \begin{equation} \label{fuzz_roughening_heuristic} | ||
| r'_\mathrm{B} = \mathrm{min} \bigl(1, r^4_\mathrm{B} + 2 R^4_\mathrm{F} \bigr)^\frac{1}{4} \quad \textrm{with $R_F = \mathrm{lum}(\mathbf{F} E_\mathrm{fuzz})$} |
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The inclusion of E_fuzz here means that the roughening will be more intense at grazing angles where the optical density is higher, correct?
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The fuzz doesn't use a GGX distribution like the coat, so I wonder whether these fourth powers are still justifiable.
Based on my own empirical testing, I had to tone down the fuzz roughening quite a bit (compared to coat roughening) to get it to look plausible.
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Also, the E_fuzz functions almost like a coverage weight, since it's essentially the opacity of the fuzz layer, so intuitively it seems like the blending based on E_fuzz (and maybe the color F too) should be a simple lerp on the final roughness (unaffected by the powers and roots).
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The inclusion of E_fuzz here means that the roughening will be more intense at grazing angles where the optical density is higher, correct?
Yes true.
The fuzz doesn't use a GGX distribution like the coat, so I wonder whether these fourth powers are still justifiable.
The
So I am just loosely assuming that this albedo can be a sort of proxy of the "amount of scattering", and thus the amount of roughening captured in a roughness scalar
If the roughening is some (angular) Gaussian blurring with the angular blur varying with
We'll need to do some simulations to check how it compares to reality, and fix it up accordingly.
E_fuzz functions almost like a coverage weight, since it's essentially the opacity of the fuzz layer
Not sure I agree, since as noted it's really the albedo (varying with input direction). The coverage (and opacity) is constant in the Zeltner model, i.e. unit optical depth of fuzz.
Obviously we also have the fuzz weight, functioning as an actual coverage weight, which should affect the roughening.
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Great to have the IOR officially included in the spec's coat roughening formula and a mention of fuzz roughening. Conceptually, the form of the fuzz roughening is questionable compared to coat roughening. The coat has a refractive interface, so all light passing through it is scattered. But the fuzz is effectively a volume without an interface, so only some of the transmitted light is scattered. The fuzz should ideally produce a mixture of roughened and un-roughened base lobes. Plus the scattering distribution should ideally be different due to the anisotropic scattering of the fuzz. So, I wonder if a stochastic selection of roughened and un-roughened base roughness (based on a rough estimate of the scattered/unscattered transmission of the fuzz) would produce better results. (The proposed specular haze could potentially be leveraged to roughen only a fraction of the light, but the haze might already be in use.) |
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Totally agree that we need to do more work on both of these formulas to produce the best approximation we can offer. For this we are going to need a combination of theory and simulation. I’m hoping we can work on this in the coming weeks as part of the preparation for the siggraph presentation. Even if it doesn’t make it into the presentation, we probably have enough time (say till the end of the year) to come up with a more physically based model for the 1.2 release. |
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According to the discussion in #239 (and on Slack), we need to provide a less obviously wrong suggestion for the coat roughening effect.
I wrote up the formula for the IOR dependence suggested by @peterkutz (with my simplification applied):
According to the discussion in #226, we also need to provide some suggested approximation for the roughening effect of fuzz.
I wrote up the formula I proposed, based on feedback from @peterkutz and @virtualzavie.
In my Arnold test implementation, I also had$R_F$ multiplied by the
fuzz_roughnessparameter, but on reflection that seems unjustified, since the reasoning is supposed to be that the roughening is being approximated/proxied by the reflection albedo (times tint), which is a function of thefuzz_roughness(so no need for an extra factor offuzz_roughness). Intuitively, iffuzz_roughnessis low, the microflakes are thin fibres which scatter very little so light normally incident travels more-or-less straight through undeflected, except near grazing where a forest of fibres is visible so the resulting albedo is significant, so such lowfuzz_roughnessfuzz will roughen the base only when viewed near grazing.I will re-do my renders of the effect to check what visible difference this makes.
I'll note these formulas (particularly the one for fuzz) are obviously just generated purely out of (educated) guesswork. Possibly we should add some caveat noting that, though we do say they are just approximations. The use of the luminance of the tint to get a scalar roughening seems particularly flaky. It still seems worth suggesting them, as without them implementations have no guidance, and the resulting look will be less plausible.
Ideally we would have a better sense of how bad the approximations are, by comparing to some data/simulations, and develop more principled fits. We're working on that. (And if we do develop better approximations, we should eventually move them into our tech report, rather than provide the details in the spec itself).