Graphics Reference
In-Depth Information
y
Up
(
2
1, 1,
2
1)
(
2
1, 1, 0)
2
(1, 1,
1)
(1, 1, 0)
2
1
)
(0, 0,
Look
z
Back clip plane
at
Z
52
1
(
2
1,
2
1, 0)
(
2
1,
2
1,
2
1)
x
Front clip plane
at
Z
5
0
(1,
2
1,
2
1)
(1,
2
1, 0)
Figure 13.8: The standard parallel view volume.
y
1
2
1
2
1
z
1
2
1
y
x
1
2
1
2
1
z
1
2
1
x
Figure 13.9: The unhinging transformation.
Our
standard parallel view volume
(see Figure 13.8) is a parallelepiped that
ranges from
−
1to1in
x
and
y
, and from 0 to
−
1in
z
. Its near clipping plane is
z
=
0; its far clipping plane is
z
=
1. (This differs from the parallel view volume
used in either Direct3D or OpenGL, but only slightly.)
Now we'll transform the portion of the standard perspective view volume
between the transformed near and far planes (i.e., the portion between
z
=
−
−
n
/
f
and
z
=
1) to the standard parallel view volume. The transformation we use
will be a
projective
transformation in which all the rays passing from the view
volume toward the origin are transformed into rays passing from the view volume
toward the
xy
-plane in the positive-
z
direction (see Figure 13.9). (This is some-
times called an
unhinging
transformation, because the planes defining opposite
sides of the view frustum meet along a “hinge line,” which this transformation
“sends to infinity.”)
−
