Fresnel approximation: I have two different implementations, which one is "correct"?

Unity Engine
1

Consolidating various partially-redundant shader includes and noticed I used 2 different fresnel implementations:

First one from some PBS tutorials, can’t remember which:

const half fresTerm = pow(1.0 - dotHL, 5.0) * (1.0 - f0) + f0;

Second one from J. Hable:

const half expo = pow(1.0 - dotHL, 5.0);
const half fresTerm = expo + f0 * (1.0 - expo);

For specular, both look “fine” to the physically-based-untrained-eye and even to mine. I can’t tell visually which one is correct. But clearly both functions clearly give slightly different result floats as they do plain different things from their inputs.

2

what is wrong or right depends on your eye pleasure here, forexample i have 5 different fresnel calculations in my water shaders package for every case.

3

Yeah but I do everything reflective in a single deferred light pass so per-material fresnel is out :smile:

I found another one by Lagarde:

const half expo = pow(1.0 - dotHL, 5.0);
const half fresTerm = f0 + (1.0f - f0) * expo

Seems like there is no end to Fresnel approximations :smile:

4

I’ve always used Schlick’s approximation which is something like-

 fresnel = exponential + _Fresnel * (1.0 – exponential);

where exponential is: pow( 1 – dot(V,H), 5.0);

5

So what? Just pick the fastest one with the better visual.

6

Guess I could “try” that :smile: :smile:

7

It seems to me that both are pretty much the same. Just a different ordering of the variables with the same result.

a + (1 - a) * b = b + a * (1 - b)