Game Development Reference

In-Depth Information

f

C

n

Figure 5.8.
The view frustum encloses the space bounded by the near plane lying at a

distance
n
from the camera, the far plane lying at a distance
f
from the camera, and four

side planes that pass through the camera position
C
.

a rectangular window—the computer screen. The view frustum is bounded by six

planes, four of which correspond to the edges of the screen and are called the
left
,

right
,
bottom
, and
top
frustum planes. The remaining two planes are called the

near
and
far
frustum planes, and define the minimum and maximum distances at

which objects in a scene are visible to the camera.

The view frustum is aligned to
camera space
. Camera space, also called
eye

space
, is the coordinate system in which the camera lies at the origin, the
x
axis

points to the right, and the
y
axis points upward. The direction in which the
z
axis

points depends on the 3D graphics library being used. Within the OpenGL li-

brary, the
z
axis points in the direction opposite that in which the camera points.

This forms a right-handed coordinate system and is shown in Figure 5.9. (Under

Direct3D, the
z
axis points in the same direction that the camera points and forms

a left-handed coordinate system.)

5.3.1 Field of View

The projection plane, shown in Figure 5.10, is a plane that is perpendicular to the

camera's viewing direction and lies at the distance
e
from the camera where the

left and right frustum planes intersect it at

. The distance
e,
which

is sometimes called the
focal length
of the camera, depends on the angle
α

=−

1

and

=

1

x

x

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