齐次坐标得到非齐次坐标

李群： $$SE(3)$$
$$T\in {\mathbb{R}}^{4\times 4}$$
$$T=\left[\begin{array}{cc}\mathbf{R}& \mathbf{t}\\ 0^T& 1\end{array}\right]=\left[\begin{array}{cccc}a& b& c& j\\ d& e& f& k\\ g& h& i& l\\ 0& 0& 0& 1\end{array}\right]$$
一个三维齐次坐标 $P$
$$P=\left[\begin{array}{c}{v}_1\\ v_2\\ v_3\\ 1\end{array}\right]$$
$$TP=\left[\begin{array}{c}a{v}_1+b{v}_2+c{v}_3+j\\ d{v}_1+e{v}_2+f{v}_3+k\\ g{v}_1+h{v}_2+i{v}_3+l\\ 1\end{array}\right]$$
$$T{P}_{un\_homogeneous}=\left[\begin{array}{c}a{v}_1+b{v}_2+c{v}_3+j\\ d{v}_1+e{v}_2+f{v}_3+k\\ g{v}_1+h{v}_2+i{v}_3+l\end{array}\right]$$