.. _homogen3d:

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.

.. math:: T = \begin{bmatrix}
                 {}  & {} & {} & x_t \\ 
                 {}  & R_{3\times3} & {} & y_t \\ 
                 {}  & {} & {} & z_t \\ 
                 0  & 0 & 0 & 1
              \end{bmatrix}