Game Development Reference
InDepth Information
(a)
C
F
x
(b)
Q
u
C
F
x
Figure 5.22.
(a) The modified far plane
F
given by Equation (5.63) intersects the modi
fied near plane
C
in the
x

y
plane. (b) Scaling the near plane
C
by the value
u
given by
Equation (5.66) adjusts the far plane so that the angle between the near and far planes is
as small as possible without clipping any part of the original view frustum. The shaded
area represents the volume of space that is not clipped by the modified view frustum.
cides with the point furthest from the plane
C
where two side planes meet the far
plane.
F Q
.
The only part of Equation (5.63) that we can modify is the scale of the plane
C
,
so we introduce a factor
u
as follows:
To force the far plane to contain the point
Q
, we must require that
⋅
=
0
M
.
(5.65)
F
=
2
−
u
4
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