Solution:

In 3-D space, a physical point is located and if we want to change from one coordinate to another frame then we need to use a 4 X 4 homogenous transformation matrix.

As mentioned earlier, in regard to 3D computer graphics, homogeneous coordinates are useful in certain situations. We will look at some of those situations here.

It consists of 4 sub-matrices as given below:

$3 \mathrm{X} 3$ sub - matrix $\mathrm{R}$ is a rotation matrix

$3 \mathrm{X} 1$ column vector $\mathrm{p}$ is a translation matrix

$1 \mathrm{X} 3 \eta^{\mathrm{T}}$ is a perspective vector

Scalar $\sigma$ is a non-zero scale factor set to unity.

$ \mathrm{T}=\left[\begin{array}{ll} R & P \\ \eta & \sigma \end{array}\right]\\ $