Fresnel Implementation

Schlick Specular

This is an approximation by Schlick[1], and presented by [2], used and copied from [3].

x-visual shader

source:

lib/xutils/shaders/glx.glsl.js

vec3 fSchlick_specular( vec3 col, vec3 incident, vec3 viewDir, float rough) {
    incident = normalize(incident) ;
    float dotLH = clamp( dot( incident, normalize(viewDir) ), 0., 1. );

    float fresnel = exp2( ( -5.55473 * dotLH - 6.98316 ) * dotLH );
    vec3 Fr = max( vec3( 1.0 - rough ), col ) - col;

    return Fr * fresnel + col;
}

Schlick Fresnel

x-visual shader

source:

lib/xutils/shaders/glx.glsl.js

vec3 fSchlick( vec3 col, vec3 incident, vec3 viewDir, float rough) {
        incident = normalize(incident) ;
        vec3 halfDir = incident + normalize(viewDir);
        float dotLH = 1. - clamp( dot( incident, halfDir ), 0., 1. );

        float fresnel = exp2( ( -5.55473 * dotLH - 6.98316 ) * dotLH );
        vec3 Fo = max( vec3( 1.0 - rough ), col ) - col;

        return Fo * fresnel + col;
    }`,

Additional Info

where:

f1(x, t) = 0.7                        // normal color
f2(x, t) = 1 - f1(x, t)               // 1 - F0
f3(x, t) = cos((1 - x) * PI / 2)      // dot(V, H)
f4(x, t) = pow(2, ( -5.55473 * f3(x,t) - 6.98316 ) * f3(x,t))
f5(x, t) = (1 - f1(x,t)) * f4(x,t) + f1(x,t)

For Graphtoy, see [4].

References

[1] Schlick, Christophe, “An Inexpensive BRDF Model for Physically-based Rendering”, Computer Graphics Forum, vol. 13, no. 3, Sept. 1994, pp. 149–162. http://dept-info.labri.u-bordeaux.fr/~schlick/DOC/eur2.html

[2] Brian Karis, Epic Games, Real Shading in Unreal Engine 4 (Online PDF)

[3] Mrdoob, github.com, three.js/src/srcbsdf.glsl.js F_Schlick()

[4] Graphtoy v0.4 by Inigo Quilez, https://graphtoy.com