Suppose P be the point object along with the coordinate (x,y,z). We want to translate such object point to the new position as, P'(x',y',z') through the translation Vector as V=t_x.I+t_y.J+t_z.K , here t_x , t_y and t_z  are the translation factor into the x, y, and z directions correspondingly, as demonstrated in Figure 8. It is, a point (x,y,z) is shifted to (x+ t_x,y+ t_y,z+ t_z). Hence the new coordinates of a point can be written:

In terms of homogeneous coordinates, above equation  becomes:

That is: P'_h = P_h.T_v