8
To my knowledge, there is no easy and analytic way of recovering the energy lost in single-scattering models. The previous techniques precompute the energy loss and reinject it in the BRDF as a diffuse-like component:
http://sirkan.iit.bme.hu/~szirmay/scook.pdf
http://www.cs.cornell.edu/projects/layered-sg14/layered.pdf
What they propose is energy ...
6
The goal of Heitz et al.'s model is pretty much the opposite of subsurface scattering: They only consider surface scattering, i.e. the ray can never enter the material.
Because microfacets are statistical in nature, they can recast their problem in such a way that it can be solved by microflakes, which allows them to compute properties such as the mean free ...
5
TL;DR: Your $G1$ formula is wrong.
Just to avoid confusion, I am assuming the isotropic version of the BRDF, the Smith microfacet model (as opposed to the V-cavity model), and the GGX microfacet distribution.
According to Heitz 2014, the masking/shadowing term $G1$ is
$$
\chi^{+}\left(\omega_{v}\cdot\omega_{m}\right)
\frac{2}{1+\sqrt{1+\alpha_{o}^{2}\tan^...
3
Most normal distribution functions (NDFs) are parametrized by some variable (tipically $m$ or $\alpha$) that determines the "roughness" or "spikiness" of the NDF (this is often meant to be the rms slope of the surface).
Here is an example of how a roughness parameter effects an NDF: https://www.desmos.com/calculator/kcevxp3wm0
we can think of the NDF as a ...
3
Dielectric materials (which is what you get when metalness is 0) don't exhibit a mirror-like effect. Think of a sheet of smooth, non-transparent plastic. Real-life mirrors are panes of glass or transparent plastic covered with a thin layer of metal. Try a white base colour (1,1,1) and full metalness (1) instead.
As Hubble pointed out in his comment, Unity ...
2
If this was correct, $\frac{D(H)G(L,V,H)}{4|N⋅V|}$ should be a dirac delta function. But I don't think so.
Actually, you're close to your answer - you just are trying to find out, what the assumption was in the very beginning - if you're talking about a specular BRDF. The term $F\frac{DG}{4|N⋅V||N⋅L|}$ only works, if you start with the precondition, that ...
2
In microfacet BRDFs, the half-vector is the same as the microfacet normal. The half-vector is exactly the required normal for a microfacet to reflect light from the incident ray to the outgoing ray, by the law of reflection. So, for given incident and outgoing directions, only those microfacets whose normals are aligned with the half-vector are "active".
...
2
for each point $p$ in theory we have a 3D function that tells us the orientation in a given direction
You have missunderstood this. $D$ is a Normal Distribution Function (or short NDF), so it doesn't really give you a single normal, but a distribution. In a (specular) BRDF you are always using the normal that is the half vector between the incoming and ...
2
Initially and still I'm not so sure how to get the color of the object behind the glass into the formulas.
Normal, this was written with path / ray tracers in mind where that part is easy. Your idea of a cube map might be ok for some use cases (eg. reasonably rough surface for the distance to the surrounding objects). It is not a general solution however. ...
1
In truth, there is no mathematical maximum value for $\alpha$. As you noted, microfacet slope is unbounded, so in principle you could have arbitrarily large slope values and hence arbitrarily large $\alpha$. There's nothing wrong with that—the mathematics of the microfacet model keeps working fine.
As a practical matter, beyond a certain point you don't ...
1
It turns out that the ring was happening from a negative divided by a negative, so adding nom = max(nom, 0.0); fixed the problem. The new highlight, amplified:
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