The Camera - Essentials of Interactive Computer Graphics - page 374

Projection ray toward
the camera p osition

Image Plane
(near plane)

Object in
visible
volume

Camera
Position

Object in
visible
volume

Projection rays t oward
the camera pos ition

Figure 14.12.

Perspective projection.

or

tan ( β )= aspect ratio × tan ( α ) ,

or

W dc
H dc ×

tan ( β )= tan ( α ) . (14.1)

It is important to note that although we do not explicitly specify the value for β ,

the graphics API does ensure the above relationship.
In computer graphics, we always perform perspective projection when the
visible volume is specified as a viewing frustum. Figure 14.12 shows that per-
spective projection collapses each object toward the camera position. Notice that
the projection direction is from the object toward the camera position. Conceptu-
ally, a projection ray is formed from each position on an object. This projection
ray is a straight line between the position and the camera position. The position
is collapsed onto the image plane along its projection ray. This means that the
projection rays are distinct for different parts of an object and for objects located
at different locations. This is in contrast to the orthographic projection, where
all objects are projected along the same view vector direction. A direct result of
per-object projection direction is that the projected object size differs depending
on objects' position. As shown in Figure 14.12, in perspective projection, objects
that are farther from the camera appear to be smaller. Perspective projection gen-
erates images that resemble photographs and thus are appealing to regular users.