inline double magnitudeSquared () const
    {
        return X * X + Y * Y + Z * Z;
    }

    inline  double magnitude () const
    {
        return sqrt(magnitudeSquared());
    }

    inline  void normalize (double mag = 1.0)
    {
        const double by = mag / magnitude();

        X *= by;
        Y *= by;
        Z *= by;
    }