| public Rotate ( Vector3 &_Axis, double _Angle, Vector3 &_Out ) : void | ||
| _Axis | Vector3 | |
| _Angle | double | |
| _Out | Vector3 | |
| return | void | |
public static void std_coords_to_half_diff_coords(double _ThetaIn, double _PhiIn, double _ThetaOut, double _PhiOut,
out double _ThetaHalf, out double _PhiHalf, out double _ThetaDiff, out double _PhiDiff)
{
// compute in vector
double in_vec_z = Math.Cos(_ThetaIn);
double proj_in_vec = Math.Sin(_ThetaIn);
double in_vec_x = proj_in_vec * Math.Cos(_PhiIn);
double in_vec_y = proj_in_vec * Math.Sin(_PhiIn);
In.Set(in_vec_x, in_vec_y, in_vec_z);
// compute out vector
double out_vec_z = Math.Cos(_ThetaOut);
double proj_out_vec = Math.Sin(_ThetaOut);
double out_vec_x = proj_out_vec * Math.Cos(_PhiOut);
double out_vec_y = proj_out_vec * Math.Sin(_PhiOut);
Out.Set(out_vec_x, out_vec_y, out_vec_z);
// compute halfway vector
Half.Set(in_vec_x + out_vec_x, in_vec_y + out_vec_y, in_vec_z + out_vec_z);
Half.Normalize();
// compute _ThetaHalf, _PhiHalf
_ThetaHalf = Math.Acos(Half.z);
_PhiHalf = Math.Atan2(Half.y, Half.x);
// Compute diff vector
In.Rotate(ref Normal, -_PhiHalf, out Temp);
Temp.Rotate(ref BiTangent, -_ThetaHalf, out Diff);
// Compute _ThetaDiff, _PhiDiff
_ThetaDiff = Math.Acos(Math.Min(1.0, Diff.z));
_PhiDiff = Math.Atan2(Diff.y, Diff.x);
}
public static void half_diff_coords_to_std_coords(double _ThetaHalf, double _PhiHalf, double _ThetaDiff, double _PhiDiff,
out double _ThetaIn, out double _PhiIn, out double _ThetaOut, out double _PhiOut)
{
double SinTheta_half = Math.Sin(_ThetaHalf);
Half.Set(Math.Cos(_PhiHalf) * SinTheta_half, Math.Sin(_PhiHalf) * SinTheta_half, Math.Cos(_ThetaHalf));
// Build the 2 vectors representing the frame in which we can use the diff angles
Vector3 OrthoX;
Half.Cross(ref Normal, out OrthoX);
if (OrthoX.LengthSq() < 1e-6)
{
OrthoX.Set(1, 0, 0);
}
else
{
OrthoX.Normalize();
}
Vector3 OrthoY;
Half.Cross(ref OrthoX, out OrthoY);
// Rotate using diff angles to retrieve incoming direction
Half.Rotate(ref OrthoX, -_ThetaDiff, out Temp);
Temp.Rotate(ref Half, _PhiDiff, out In);
// We can get the outgoing vector either by rotating the incoming vector half a circle
// Temp.Rotate( ref Half, _PhiDiff + Math.PI, out Out );
// ...or by mirroring in "Half tangent space"
double MirrorX = -In.Dot(ref OrthoX);
double MirrorY = -In.Dot(ref OrthoY);
double z = In.Dot(ref Half);
Out.Set(
MirrorX * OrthoX.x + MirrorY * OrthoY.x + z * Half.x,
MirrorX * OrthoX.y + MirrorY * OrthoY.y + z * Half.y,
MirrorX * OrthoX.z + MirrorY * OrthoY.z + z * Half.z
);
// CHECK
// Vector3 CheckHalf = new Vector3() { x = In.x+Out.x, y = In.y+Out.y, z = In.z+Out.z };
// CheckHalf.Normalize(); // Is this Half ???
// CHECK
// Finally, we can retrieve the angles we came here to look for...
_ThetaIn = Math.Acos(In.z);
_PhiIn = Math.Atan2(In.y, In.x);
_ThetaOut = Math.Acos(Out.z);
_PhiOut = Math.Atan2(Out.y, Out.x);
}
