Example 8. From homogeneoues coordinates find Cartesian coordinates of real point M=(2,6,4,2) and of vector a=MN,N=(2,8,10,2).

Solution. Cartesian coordinates of the real point M form a triple of real numbers

M = ( a 1 a 0 , a 2 a 0 , a 3 a 0 ) = ( 2 2 , 6 2 , 4 2 ) = ( 1, 3, 2 )

where a0=2 is the last homogeneous coordinate.

Cartesian coordinates of the vector a=MN can be derived from the Cartesian coordinates of the endpoints, while

N = ( 2 2 , 8 2 , 10 2 ) = ( 1,4,5 )

and coordinates of the vetor are

a = M N = N M = ( 1 , 4,5 ) ( 1, 3,2 ) = ( 2 ,7,3 )

ex8
Figure 1: Cartesian coordinates