/// <summary>
/// Raise the quaternion to a given power.
/// </summary>
public Quaternion Pow(Quaternion power)
{
return power.Multiply(Ln()).Exp();
}
/// <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>
/// 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;
}
public Quaternion Subtract(Quaternion q)
{
return new Quaternion(qw - q.qw, qx - q.qx, qy - q.qy, qz - q.qz);
}
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);
}
public Quaternion Add(Quaternion q)
{
return new Quaternion(qw + q.qw, qx + q.qx, qy + q.qy, qz + q.qz);
}
/// <summary>
/// Subtract a quaternion from this quaternion.
/// </summary>
public Quaternion Subtract(Quaternion q)
{
return new Quaternion(
_w - q._w,
_x - q._x,
_y - q._y,
_z - q._z);
}
/// <summary>
/// Multiply a quaternion with this quaternion.
/// </summary>
public Quaternion Multiply(Quaternion q)
{
double ci = (+_x * q._w) + (_y * q._z) - (_z * q._y) + (_w * q._x);
double cj = (-_x * q._z) + (_y * q._w) + (_z * q._x) + (_w * q._y);
double ck = (+_x * q._y) - (_y * q._x) + (_z * q._w) + (_w * q._z);
double cr = (-_x * q._x) - (_y * q._y) - (_z * q._z) + (_w * q._w);
return new Quaternion(cr, ci, cj, ck);
}
/// <summary>
/// Add a quaternion to this quaternion.
/// </summary>
public Quaternion Add(Quaternion q)
{
return new Quaternion(
_w + q._w,
_x + q._x,
_y + q._y,
_z + q._z);
}
Distance(
Quaternion a,
Quaternion b
)
{
return a.Subtract(b).Abs;
}