Specular BRDF equation and the shader code

[Ulalinowykaj]

Hi,

I am trying to understand the specular BRDF equation and the code.

Most of the sources show this equation:

but when I looked into surface_shading_model_standard.fs, there's no 4 * NoV * NoL part.
Also, I cannot find it in other shader files.

Why is it skipped? Is this because of this part:

vec3 energyCompensation = 1.0 + f0 * (1.0 / dfg.y - 1.0);
// Scale the specular lobe to account for multiscattering
Fr *= pixel.energyCompensation;

?

[show50726]

You can refer to Normal distribution function (specular D).

Look at (10), we rewrite $G$ into a newly introduced visibility function $V$, which absorbs the $4(n\cdot v)(n\cdot l)$ term:

$$V(v,l,\alpha) = \frac{G(v, l, \alpha)}{4 (n\cdot v) (n\cdot l)} = V_1(l,\alpha) V_1(v,\alpha)$$

Then we can rewrite the original BRDF $f_r$ into

$$f_r(v,l) = D(h, \alpha) V(v, l, \alpha) F(v, h, f_0)$$

And after further taking the height of the microfacets into account, the formula will eventually become

$$V(v,l,\alpha) = \frac{0.5}{n \cdot l \sqrt{(n \cdot v)^2 (1 - \alpha^2) + \alpha^2} + n\cdot v \sqrt{(n \cdot l)^2 (1 - \alpha^2) + \alpha^2}}$$

You can refer to surface_brdf.fs for the implementation of this $V$ function, which will be called by the visibility function, and the visibility function is called by the functions in surface_shading_model_standard.fs.

[Ulalinowykaj]

Thanks