Perspective Projection - Transformations and Projections in Computer Graphics - page 118

(instruments) and exterior (the view from the cockpit) in real time. This section is
concerned with displaying the view from the cockpit, and we show that this task is an
application of the important concept of viewing volume .

k

Viewing
volume

L 1

sky projected

z

pilot

L 2

ground

(a)

(b)

Figure 3.40: (a) Two Fields of View. (b) A Viewing Volume.

Figure 3.40a shows part of a typical World War II bomber. It is obvious that the
field of view of the pilots in the cockpit is restricted. They see a lot of sky and part
of the airplane, but only distant parts of the ground in front and on the sides. The
bombardier, however, has almost a 180 ◦ field of view and can see all the way from 6
o'clock (the ground below their feet) to 12 o'clock (straight up).
Figure 3.40b is a schematic diagram showing the viewing volume of the pilot (ig-
noring the curvature of the Earth). We assume that the flight simulator has to display
the pilot's view on a screen placed k units in front of the pilot. It is obvious that the
view depends on the precise shape of the aircraft. (This determines the orientation of
lines L 1 and L 2 .) Most of the screen in the figure is a projection of the sky and only a
small part shows a projection of the ground in front of the aircraft. It is also trivial to
use similar triangles to obtain the basic perspective expression [Equation (3.1)]

z + k
y

k
y ∗

ky
z + k

y
z/k +1 .

y ∗ =

= or =

3.11 Stereoscopic Images

We now turn to an important application of transformations and perspective projection,
namely stereoscopic view. This section explains the principles and theory of stereoscopic
images, how to create them, and how to view them.

Stereo (from the Greek στρoσ )—solid, three-dimensional.

It is generally agreed that the concepts of stereoscopy were discovered in 1833 by
Charles Wheatstone, who is mostly known for the Wheatstone bridge (an electrical
circuit for the precise comparison of resistances). His 1833 lecture to the Royal Society