/// <summary>
/// Multiplication operator.
/// </summary>
/// <param name="q1"> The lhs operand. </param>
/// <param name="q2"> The rhs operand. </param>
/// <returns> A new <see cref="Quaternion"/> that is the product of q1 and q2. </returns>
public static Quaternion operator*(Quaternion q1, Quaternion q2)
{
Quaternion ret = new Quaternion();
ret.Scalar = q1.Scalar * q2.Scalar - q1.Vector.Dot(q2.Vector);
ret.Vector = q2.Vector * q1.Scalar + q1.Vector * q2.Scalar + q1.Vector.Cross(q2.Vector);
return ret;
}
/// <summary>
/// Rotates the vector about the given axis with the given angle.
/// </summary>
/// <param name="axis"> Axis of rotation. </param>
/// <param name="angle"> Angle of rotation. </param>
public Vector Rotate(Vector axis, Angle angle)
{
// quaternion method
Quaternion R = new Quaternion();
R.Scalar = (angle/2.0).Cos();
R.Vector = axis.Normalize() * (angle/2.0).Sin();
Quaternion v = new Quaternion(0.0, this);
Quaternion res = R * v * R.T();
return res.Vector;
}