
2.3 Cameras 57
The slightly more complicated conversion for u
has to do with the switch from right-
handed to left-handed coordinates.
The depth values d
∈ [0, 1] can also be mapped to a depth r ange that is a subset
of [0, 1]. Section 2.3.1 introduced the depth range interval [p
n
, p
f
]⊆[0, 1] . The new
depth values for this range are
δ =
p
f
− p
n
d
+ p
n
(2.72)
Equations (2.71) and (2.72) may be combined into a single 4-tuple, which I will
call the window coordinates of the corresponding clip-space point:
X
window
1
=
⎡
⎢
⎢
⎢
⎢
⎣
W(p
r
−p
)
2
00
W(p
r
+p
)
2
0
H(p
b
−p
t
)
2
0
H(2−p
t
−p
b
)
2
00p
f
− p
n
p
n
000 1
⎤
⎥
⎥
⎥
⎥
⎦
X
ndc
1
= H
window
X
ndc
1
(2.73)
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