Graphics Reference
In-Depth Information
p
n
p
n
Y
p
n
p
n
d
p
e
c
p
e
p
e
p
e
X
Z
α
a
y
e
= n tan(α)
a
EC
y
n
= 1.0
NDC
Figure 15.13.
The NDC ray transforms to a projection ray in EC.
where
n
is the near plane distance and
is half of the (vertical) field-of-view
angle. Substituting Equation (15.8) into Equation (15.7),
α
y
e
=
y
n
.
(
α
)
n
tan
This relationship is also true for the
x
-axis:
x
e
=
x
n
.
n
tan
(
β
)
As discussed in Section 14.2.2 and Equation (14.1),
β
is half of the horizontal
In this case, we know
p
e
is located at the near plane, or
field-of-view angle.
z
e
=
−
n
.So,
transforms
←→
p
n
p
e
or
n
.
Remember that our goal is to reconstruct the projection ray. In general, any point
x
n
y
n
0
n
tan
transforms
←→
x
n
n
tan
y
n
(
β
)
(
α
)
−
p
n
=(
x
n
,
y
n
,
0
)
in NDC space will transform to a line in EC space:
p
e
=
z
e
tan
z
e
.
(
β
)
x
n
z
e
tan
(
α
)
y
n
−
Substituting from Equation (15.6),
z
e
tan
z
e
2
×
x
dc
2
×
y
dc
(
β
)(
W
dc
−
)
(
α
)(
H
dc
−
)
−
p
e
=
1
z
e
tan
1
,
(15.9)
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