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}