BRDF

analytic

::begin parameters
color Diffuse 1 0 0
color Specular 1 1 1
float DiffuseScale 0 1 0.5
float SpecularScale 0 1 .028
float Roughness 0.00005 2 0.2
float Roughness2 0.00005 2 0.2
float Retroreflective 0 1 0
bool FullFresnel 0 1 0
bool isotropic 1
::end parameters

::begin shader

//Thanks to Chris_F for starting ideas.
// Cook-Torrance, GGX distribution (bastardised with ashikhman shirley), Smith geometry, qualitative Oren-Nayar diffuse.

float saturate(float x) { return clamp(x,0,1); }

vec3 Fresnel(float CosTheta, vec3 Ks)
{
    CosTheta = min(CosTheta, 0.99999999999999999);
    vec3 n2 = (1.0 + sqrt(Ks)) / (1.0 - sqrt(Ks));
    vec3 SinTheta = vec3(sqrt(1 - CosTheta * CosTheta));

    vec3 SinThetaT = SinTheta / n2;
    vec3 CosThetaT = sqrt(1 - SinThetaT * SinThetaT);

    vec3 n2CosThetaT = n2 * CosThetaT;
    vec3 n2CosTheta = n2 * CosTheta;

    vec3 RsSqrt = (CosTheta - n2CosThetaT) / (CosTheta + n2CosThetaT);
    vec3 Rs = RsSqrt * RsSqrt;

    vec3 RpSqrt = (n2CosTheta - CosThetaT) / (n2CosTheta + CosThetaT);
    vec3 Rp = RpSqrt * RpSqrt;

    return (Rs + Rp) / 2;
}

vec3 BRDF( vec3 L, vec3 V, vec3 N, vec3 X, vec3 Y )
{
//vec3 temp = L; L = V; V = temp;
    float PI = 3.14159265358979323846;
    vec3 Kd = Diffuse * DiffuseScale;
    vec3 Ks = Specular * SpecularScale;

    vec3 H = normalize(L + V);
    float NdotL = clamp(dot(N, L), 0, 1);
    float NdotV = dot(N, V);
    float NdotH = dot(N, H);
    float LdotV = dot(L, V);
    float VdotH = dot(V, H);
    float LdotH = dot(L, H);
    float HdotX = dot(H,X);
    float HdotY = dot(H,Y);

    float m1 = 1/Roughness;
    float m2 = 1/Roughness2;
    float M = isotropic ? Roughness : (1-(NdotH*NdotH)) / ( m1*HdotX*HdotX + m2*HdotY*HdotY );
    float M_2 = isotropic ? M * M : M* min(Roughness, Roughness2);

    NdotH = mix( mix( NdotH, max(NdotH,LdotV), saturate(Retroreflective*2) ), LdotV, saturate(Retroreflective*2-1) );

    float NdotL_2 = NdotL * NdotL;
    float NdotV_2 = NdotV * NdotV;
    float NdotH_2 = NdotH * NdotH;
    float OneMinusNdotL_2 = 1.0 - NdotL_2;
    float OneMinusNdotV_2 = 1.0 - NdotV_2;

    vec3 Fd = 1.0 - Ks;

    float gamma = clamp(dot(V - N * NdotV, L - N * NdotL), 0, 1);
    float A = 1.0 - 0.5 * (M_2 / (M_2 + 0.33));
    float B = 0.45 * (M_2 / (M_2 + 0.09));
    float C = sqrt(OneMinusNdotL_2 * OneMinusNdotV_2) / max(NdotL, NdotV);

    vec3 Rd = Kd * Fd * (A + B * gamma * C) * 1/PI;

    float ggxDenom = NdotH_2 * (M_2 + (1-NdotH_2)/NdotH_2);
    float D = M/ggxDenom;
    D = D*D/PI;
    D *= isotropic ? 1 : min(m1,m2)/max(m1,m2);

    vec3 Fs;
    if( FullFresnel )
        Fs = Fresnel(NdotV, Ks);
    else
        Fs = Ks + Fd * pow(1-LdotH, 5);

    float G1_1 = 1.0 + sqrt(1.0 + M_2 * (OneMinusNdotL_2 / NdotL_2));
    float G1_2 = 1.0 + sqrt(1.0 + M_2 * (OneMinusNdotV_2 / NdotV_2));
    float G = ((2/G1_1) * (2/G1_2))/(4 * NdotV * NdotL);

    vec3 Rs = Fs * D * G;

    return vec3(Rd + Rs);
}

::end shader