/// <summary>
/// Transforms a vector by a quaternion rotation.
/// </summary>
/// <param name="vec">The vector to transform.</param>
/// <param name="quat">The quaternion to rotate the vector by.</param>
/// <returns>The result of the operation.</returns>
public static GVector3 Transform(GVector3 vec, GQuaternion quat)
{
GVector3 result;
Transform(ref vec, ref quat, out result);
return(result);
}
/// <summary>
/// Transforms a vector by a quaternion rotation.
/// </summary>
/// <param name="vec">The vector to transform.</param>
/// <param name="quat">The quaternion to rotate the vector by.</param>
/// <param name="result">The result of the operation.</param>
public static void Transform(ref GVector3 vec, ref GQuaternion quat, out GVector3 result)
{
// Since vec.W == 0, we can optimize quat * vec * quat^-1 as follows:
// vec + 2.0 * cross(quat.xyz, cross(quat.xyz, vec) + quat.w * vec)
GVector3 xyz = quat.Xyz, temp, temp2;
GVector3.Cross(ref xyz, ref vec, out temp);
GVector3.Multiply(ref vec, quat.W, out temp2);
GVector3.Add(ref temp, ref temp2, out temp);
GVector3.Cross(ref xyz, ref temp, out temp);
GVector3.Multiply(ref temp, 2, out temp);
GVector3.Add(ref vec, ref temp, out result);
}