gistfile1.txt

// construct SunDir from cosine of an angle between the vector and zenith (MuS)
SunDir.x = 0.0;
SunDir.y = MuS;
SunDir.z = sqrt(1.0 - MuS * MuS);

// construct EyeDir from cosine of an angle between the vector and zenith (Mu)
EyeDir.x = 0.0;
EyeDir.y = Mu;
EyeDir.z = sqrt(1.0 - Mu * Mu);

Theta => angular difference of projection SunDir and some vector EyeDirRot onto XZ-plane

          [ CosTheta 0 SinTheta]
RotYMat = [    0     1     0   ]
          [-SinTheta 0 CosTheta]


// construct EyeDirRot from EyeDir and RotYMat
EyeDirRot.x = SinTheta * sqrt(1.0 - Mu * Mu);
EyeDirRot.y = Mu
EyeDirRot.z = CosTheta * sqrt(1.0 - Mu * Mu);

// compute dot-product SunDir and EyeDirRot
Nu = dot(SunDir, EyeDirRot) = Mu * MuS + CosTheta * SinFromMu * SinFromMuS;

// Express EyeDirRot.z in terms of original parameters
EyeDirRot.z = (Mu * MuS - Nu) / SunDir.z;