The simplest model for the generation of an image is the
so-called pinhole camera. In this camera, light is let into a box
through a pinhole and projected on a light sensitive screen on the
back end of the box at a distance 
away from the pinhole.
Thus, if 
are the 3-D coordinates of a point in the world and
be the 2-D coordinates on the screen, the relation between
these quantities is given by
The image is inverted both left-right and up-down as indicated by the minus signs in this equation. These equations represent what is known as perspective projection.
Under perspective projection, parallel lines (train tracks)
converge to a point on the horizon. To prove this let us consider a
line in the 3 D world passing through 
in the
direction 
. This is given by 
for 
. The
projection of this line on the image plane has coordinates from
equation 1 given by
In equation 2 as 
this
converges to 
. This point
depends only on the direction coordinates 
of the
line. Thus all lines with these direction coordinates will appear to
converge to the same point 
!
