$$\left[\begin{array}{cccc}x& y& z& 1\end{array}\right]=\left[\begin{array}{cccc}u& v& w& 1\end{array}\right]*T$$

$$\begin{array}{ccccc}[r_{11}& r_{12}& r_{13}& 0;& \mathrm{...}\\ r_{21}& r_{22}& r_{23}& 0;& \mathrm{...}\\ r_{31}& r_{32}& r_{33}& 0;& \mathrm{...}\\ t_x& t_y& t_z& 1];& \end{array}$$

$$\left[\begin{array}{ccc}x& y& z\end{array}\right]=\left[\begin{array}{ccc}u& v& w\end{array}\right]*R$$

$$\left[\begin{array}{ccc}x& y& z\end{array}\right]=\left[\begin{array}{ccc}u& v& w\end{array}\right]+t$$