3.2.2. Homogeneous Matrices in 3-DΒΆ

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.

T = \spalignmat{{}, {}, {},x_t; {}, R_{3\times3}, {}, y_t; {}, {}, {}, z_t; 0, 0, 0, 1}