Example 7. From Cartesian coordinates find homogeneous coordinates of real point M=(7,3,4) and ideal point U determined by direction of vector a=MN,N=(2,3,4).

Solution. Homogeneous coordinates of the real point M form a class of equivalent quadruples

M = k . ( 7 , 3, 4,1 ) , k 0

where the last coordinate a0=1 in the normal form.

Homogeneous coordinates of the ideal point U are defined from the coordinates of the endpoint M and N of direction vector a in the normal form

a = M N = N M = ( 2, 3, 4,1 ) ( 7,3, 4,1 ) = ( 9,0,0,0 )

and they form a class of equivalent quadruples

U = k . ( 9 ,0,0 ,0 ) , k 0

ex7
Figure 1: Homogeneous coordinates