Graphics Programs Reference
In-Depth Information
Figure 3.44c yields
x
e
k
+
z
−
=
x
L
−
w
1+
z/k
+
e
=
x
+
ez/k
x
−
e
or
x
L
=
1+
z/k
,
k
and, similarly, from Figure 3.44d we get
x
+
e
k
+
z
=
x
R
+
w
k
x
+
e
1+
z/k
−
e
=
x
ez/k
1+
z/k
.
−
or
x
R
=
Since both eyes are at
y
=0,the
y
∗
coordinates of both
P
L
and
P
R
are given by
y
1+
z/k
.
y
∗
=
We thus obtain the transformation matrices
T
L
and
T
R
that transform
P
to
P
L
and
P
R
,
⎛
⎞
⎛
⎞
1000
0100
e/k
001
/k
0001
1000
0100
−e/k
001
/k
0001
⎝
⎠
⎝
⎠
T
L
=
,
T
R
=
.
(3.19)
x
left eye
P
P
L
20
3
P
R
θ
left eye
z
right eye
z
k
right eye
(a)
(b)
x
x
x
x
L
x
x
R
e
z
z
z
e
k
(c)
(d)
Figure 3.44: Perspective Projection of a Stereo Pair.
Figure 3.44b shows how to select reasonable values for
e
and
k
. We first assume that
the distance between the eyes is about 75 mm (about 3 in). Normal reading distance is
Search WWH ::
Custom Search