/// <summary>
/// SUbtract a quaternion from this quaternion.
/// </summary>
public Quaternion Subtract(
Quaternion q
)
{
return new Quaternion(
qw - q.qw,
qx - q.qx,
qy - q.qy,
qz - q.qz
);
}
/// <summary>
/// Raise the quaternion to a given power.
/// </summary>
public Quaternion Pow(
Quaternion power
)
{
return power.Multiply(Ln()).Exp();
}
/// <summary>
/// Multiply a quaternion with this quaternion.
/// </summary>
public Quaternion Multiply(
Quaternion q
)
{
double ci = +qx * q.qw + qy * q.qz - qz * q.qy + qw * q.qx;
double cj = -qx * q.qz + qy * q.qw + qz * q.qx + qw * q.qy;
double ck = +qx * q.qy - qy * q.qx + qz * q.qw + qw * q.qz;
double cr = -qx * q.qx - qy * q.qy - qz * q.qz + qw * q.qw;
return new Quaternion(cr, ci, cj, ck);
}
/// <summary>
/// Multiplies a Quaternion with the inverse of another
/// Quaternion (q*q<sup>-1</sup>). Note that for Quaternions
/// q*q<sup>-1</sup> is not the same then q<sup>-1</sup>*q,
/// because this will lead to a rotation in the other direction.
/// </summary>
public Quaternion Divide(
Quaternion q
)
{
return Multiply(q.Inverse());
}
/// <summary>
/// Add a quaternion to this quaternion.
/// </summary>
public Quaternion Add(
Quaternion q
)
{
return new Quaternion(
qw + q.qw,
qx + q.qx,
qy + q.qy,
qz + q.qz
);
}
/// <summary>
/// Returns the distance |a-b| of two quaternions, forming a metric space.
/// </summary>
public static double Distance(
Quaternion a,
Quaternion b
)
{
return a.Subtract(b).Abs;
}