More on Matrices - 3D Math Primer for Graphics and Game Development - page 187

Figure 6.8
Viewing the
projection plane
from the side

The z values of all the projected points are the same: −d. Thus, the
result of projecting a point p through the origin onto a plane at z = −d is

Projecting onto the
plane z = −d

′

x ′ y ′ z ′

p = x y z =⇒ p = = −dx/z −dy/z −d .

In practice, the extra minus signs create unnecessary complexities, and
so we move the plane of projection to z = d, which is in front of the center
of projection, as shown in Figure 6.9. Of course, this would never work for
a real pinhole camera, since the purpose of the pinhole in the first place is

Figure 6.9
Projection plane in
front of the center of
projection