/// <summary>
/// Returns the Euler-Angles from the quatarnion.
/// </summary>
public V3d GetEulerAngles()
{
var test = W * Y - X * Z;
if (test > 0.49999) // singularity at north pole
{
return(new V3d(
-2 * Fun.Atan2(X, W),
Constant.PiHalf,
0));
}
if (test < -0.49999) // singularity at south pole
{
return(new V3d(
2 * Fun.Atan2(X, W),
-Constant.PiHalf,
0));
}
// From Wikipedia, conversion between quaternions and Euler angles.
return(new V3d(
Fun.Atan2(2 * (W * X + Y * Z),
1 - 2 * (X * X + Y * Y)),
Fun.AsinC(2 * test),
Fun.Atan2(2 * (W * Z + X * Y),
1 - 2 * (Y * Y + Z * Z))));
}