Let’s take an explicit example of this.
Suppose we have a cube with vertices at: (0,0,0) (10,0,0), (0,0,10)….. Suppose we transform this by rotating it by 45 degrees about the y
axis. Then the transformation matrix is: [sq2 0 –sq2 0; 0 1 0 0]. Now suppose instead we had a rectanguloid with corners at (10, 0, 0) (11,0,0),
(10, 0, 10) …. We can transform this rectanguloid into the first cube by
transforming it as: [10 0 0 -100; 0 1 0 0; 0 0 1 0; 0 0 0 1]. Then we can apply [sq2 0 –sq2 0; 0 1 0 0]
to the resulting cube, to
generate the same image. Or, we could
have combined these
two transformations into one:
[sq2 0 –sq2 0; 0 1 0 0]* [10 0 0 -100; 0 1 0 0; 0 0 1 0; 0 0 0
1]
= [10sq2 0 –sq2 0; 0 1 0 0]