Game Development Reference
In-Depth Information
2
rl
+
0
0
rl
rl
P
2
tb
+
 
x
0
0
 
tb
tb
f
P
y
 
=
PM P
=
.
(5.58)
ortho
2
+
n P
 
z
0
0
 
f
n
f
n
1
 
0
0
0
1
The matrix orth M in Equation (5.58) is the OpenGL orthographic projection
matrix generated by the glOrtho() function. Note that the w coordinate re-
mains 1 after the transformation, and thus no perspective projection takes place.
5.5.3 Extracting Frustum Planes
It is remarkably simple to extract the four-dimensional vectors corresponding to
the six camera-space view frustum planes from an arbitrary projection matrix M .
The technique presented here derives from the fact that the planes are always the
same in clip space. They are actually rather trivial since, as shown in Figure 5.18,
each plane's normal is parallel to one of the principal axes.
x =−
1
x =
1
z =
1
0, 0,
1
1, 0, 0
1, 0, 0
0, 0,1
z =−
1
Figure 5.18. These are the normal vectors for the left, right, near, and far planes bound-
ing the cube-shaped homogeneous clip space. The normal vectors for the top and bottom
planes point in and out of the page.
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