2.4.6.2. Homogeneous Matrices in 3-D

Homogeneous coordinate transformation matrices in three dimensions are similar to the two dimensional matrix with extra row and column. It is a 4-by-4 containing a 3-by-3 rotation matrix and a 3-by-1 translation column vector.

\[\begin{split}T = \begin{bmatrix} {} & {} & {} & x_t \\ {} & R_{3\times3} & {} & y_t \\ {} & {} & {} & z_t \\ 0 & 0 & 0 & 1 \end{bmatrix}\end{split}\]