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float calculateRoughness( in vec3 N, in float roughnessU, in float roughnessV, in vec3 tangentU )
{
float roughness = roughnessU;
if ( abs(roughnessU - roughnessV) > 0.00001)
{
// determine major and minor radii a and b, and the vector along the major axis
float a = roughnessU;
float b = roughnessV;
// we need the angle between the major axis and the projection of viewDir on the tangential plane
// the major axis is the orthonormalization of tangentU with respect to N
// the projection of viewDir is the orthonormalization of viewDir with respect to N
// as both vectors would be calculated by orthonormalize, we can as well leave the second cross
// product in those calculations away, as they don't change the angular relation.
vec3 minorAxis = normalize( cross( tangentU, N ) ); // crossing this with N would give the major axis
// which is equivalent to orthonormalizing tangentU with respect to N
if ( roughnessU < roughnessV )
{
a = roughnessV;
b = roughnessU;
minorAxis = cross( N, minorAxis );
}
vec3 po = normalize( cross( viewDir, N ) );
float cosPhi = dot( po, minorAxis );
// determine the polar coordinate of viewDir, take that radius as the roughness
float excentricitySquare = 1.0f - square( b / a );
roughness = b / sqrt( 1.0f - excentricitySquare * square( cosPhi ) );
}
return( roughness );
}
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