Mathematical Topics from 3D Graphics - 3D Math Primer for Graphics and Game Development - page 365

Figure 10.3
The 3D view frustum

more complicated, but essentially it has to do with how the depth buffer
values are assigned. As an example, if the depth buffer entries are 16-
bit fixed point, then the largest depth value that can be stored is 65,535.
The far clip establishes what (floating point) z value in camera space will
correspond to the maximum value that can be stored in the depth buffer.
The motivation for the near clip plane will have to wait until we discuss
clip space in Section 10.3.2.
Notice that each of the clipping planes are planes, with emphasis on the
fact that they extend infinitely. The view volume is the intersection of the
six half-spaces defined by the clip planes.

10.2.4 Field of View and Zoom

A camera has position and orientation, just like any other object in the
world. However, it also has an additional property known as field of view.
Another term you probably know is zoom. Intuitively, you already know
what it means to “zoom in” and “zoom out.” When you zoom in, the
object you are looking at appears bigger on screen, and when you zoom
out, the apparent size of the object is smaller. Let's see if we can develop
this intuition into a more precise definition.
The field of view (FOV) is the angle that is intercepted by the view
frustum. We actually need two angles: a horizontal field of view, and a
vertical field of view. Let's drop back to 2D briefly and consider just one of
these angles. Figure 10.4 shows the view frustum from above, illustrating
precisely the angle that the horizontal field of view measures. The labeling
of the axes is illustrative of camera space, which is discussed in Section 10.3.
Zoom measures the ratio of the apparent size of the object relative to a
90 o field of view. For example, a zoom of 2.0 means that object will appear