Perspective Projection Matrix

r-1 r-l

0 2n t+b 0

t-b t-b

0 0 -(f+n) -2fn

f-n f-n

0 0 -1 0

Note that after multiplication by [x y z w] that the transformed W will not be equal to the old W. New W will be equal to

Wnew = Zold * -2fn/(f-n)

f = far, n = near, l = left, r = right, t = top, b = bottom