Graphics Programs Reference
In-Depth Information
x
P
*
m
P
z
θ
Figure 4.42: Microscopic Projection.
Computing
x
∗
therefore involves the two steps
θ
=arctan(
x/
(
z
+
k
)) and
x
∗
=
(
z
+
k
) tan(
mθ
). For small angles, tan
θ
is close to
θ
, so we can write as an approximation
x
∗
z
+
k
x
z
+
k
x
∗
=
mx.
=
m
or
This is a linear scaling transformation where both
x
and
y
are scaled by a factor of
m
,
while
z
is left unchanged. The transformation matrix is
⎛
⎝
⎞
⎠
m
000
0
m
00
0010
0001
.
Nature composes some of her loveliest poems for the microscope
and the telescope.
—Theodore Roszak,
Where the Wasteland Ends
(1972)
4.13 Anamorphosis
An anamorphosis is a distorted image that can be visualized and perceived only when
viewed in a special way. The two most common types of anamorphosis are oblique and
catoptric. The former type has to be viewed from an unusual angle or from a specific
location or distance. The latter has to be seen reflected in a special mirror.
Anamorphosis
A distorted or monstrous projection or representation of an image on a plane or curved
surface, which, when viewed from a certain point, or as reflected from a curved mirror
or through a polyhedron, appears regular and in proportion; a deformation of an
image.
—From
Webster's Dictionary
(1913)
Figure 4.43 illustrates oblique anamorphosis. We imagine the artist painting a
subject as if seen through a window. A conventional window is perpendicular to the
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