Graphics Reference
In-Depth Information
9.3 Pseudo fish-eye projection
A pseudo fish-eye projection is readily achieved by projecting onto a spherical projection surface.
The geometry for this is shown in Fig. 9.6, where the projection radius of curvature is given by
r and the centre of curvature is located at the origin.
P
p
Y
Q
q
Z
D
d
j
k
O
i
X
Figure 9.6.
We begin by declaring the following conditions:
=
−
OD
=
−
OQ
=
−
OP
d
=
d
k q
=
r
p
We define
q
in terms of
p
,sowelet
q
=
p
(9.12)
But it is obvious that
q
=
r for all points. Therefore,
q
=
p
and
=
q
r
=
p
p
Substituting in Eq. (9.12) gives
r
q
=
p
p
Therefore,
rx
P
x
P
+
ry
P
x
P
+
x
Q
=
y
Q
=
y
P
+
z
P
y
P
+
z
P
where r is the radius of curvature of the lens.
