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Oren-Nayar Lighting Model

We used a lookup texture for optimization for a while
( http://content.gpwiki.org/index.php/D3DBook:(Lighting)_Oren-Nayar )

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half computeOrenNayarLighting_TextureLookup( half3 N, half3 L, half3 V, half roughness )
{
half LdotN = dot( L, N );
half result = saturate(LdotN);
if ( roughness > 0 )
{
// compute the other aliases
half VdotN = dot( V, N );
half gamma = dot( V - N * VdotN, L - N * LdotN );
half rough_sq = roughness * roughness;
half A = 1.0 - 0.5 * (rough_sq / (rough_sq + 0.33));
half B = 0.45 * (rough_sq / (rough_sq + 0.09));
// The two dot-products will be in the range of
// 0.0 to 1.0 which is perfect for a texture lookup:
half2 tex_coord = half2( VdotN, LdotN ) * 0.5 + 0.5;
half C = tex2D(gOrenNayarSampler, tex_coord).x;
result *= (A + B * max(0.0, gamma) * C);
}
return result;
}

Oren-Nayar Lighting Model

But we made it even faster with an approximation

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Practically, we didn’t notice any badness from this

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half ComputeOrenNayarLighting_Fakey( half3 N, half3 L, half3 V, half roughness )

{

// Through brute force iteration I found this approximation. Time to test it out.

half LdotN = dot( L, N );

half VdotN = dot( V, N );

half result = saturate(LdotN);

half soft_rim = saturate(1-VdotN/2); //soft view dependant rim

half fakey = pow(1-result*soft_rim,2);//modulate lambertian by rim lighting

half fakey_magic = 0.62;

//(1-fakey)*fakey_magic to invert and scale down the lighting

fakey = fakey_magic - fakey*fakey_magic;

return lerp( result, fakey, roughness );

}