The mapping of points from an N-D space to a M-D subspace (M < N)

We need a rule for mapping points resulting of this transform back onto our plane z = 1.

We will identify points by lines through the origin of the 3-D space that we have embedded our plane within.

Thus,

Since the origin lies on all of these lines (and thus cannot be uniquely specified) we will disallow it. This is no big loss since it wasn't on our selected plane anyway (This is the real reason that we chose a plane not containing the origin).

If we want to find the coordinate of any point in our selected plane we need only scale it such that it's third coordinate, w, is 1.