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
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