Cylindrical Anamorphosis of Parametric Surfaces

​
parametric surface
ellipsoid
torus
two tori
Klein bottle
size
0.75
vertical offset
0.15
axis of rotation
x axis
z axis
angle of rotation
0
view distance
16.
viewpoint
default
top
side
front
Mirror anamorphosis is a distorted projection that a viewer sees as a normal undeformed image when reflected[1].
This Demonstration deals with the artist's process: given a realistic 3D surface, make a new surface of the deformed, anamorphic image as reflected in the cylindrical mirror. The surfaces used are parametric surfaces defined by the built-in Mathematica function ParametricPlot3D.
The technique of 3D cylindrical anamorphosis is used by many graphic artists[2].

Details

In this Demonstration, the mirror is a circular right cylinder with radius
1
parallel to the
z
axis. The viewer's eye is at
V
at a distance
y
v
and a height
z
v
.
A point of the object is reflected by the mirror toward the observer's eye. The light path forms equal angles with the normal vector
n
, perpendicular to the cylinder at
Q
, the intersection with the cylinder of the view line between the viewpoint
V
and the image point
ℐ
.
The viewer perceives the anamorphic point
R
as the point
ℐ
. The artist makes the anamorphic point
R
from the reflected point
ℐ
. Both
R
and
ℐ
are in the same horizontal plane and at the same distance from
Q
.

References

[1] J. Britton. "Cylindrical Mirror Anamorphoses." Department of Mathematics, Camosun College, Victoria, BC, Canada. britton.disted.camosun.bc.ca/anamorphic/cylmirror.html.
[2] J. Hurwitz. "Catropic Anamorphosis." (Jun 20, 2017) www.jontyhurwitz.com/anamorphosis.

External Links

Cylindrical Anamorphosis of Some Popular Images

Permanent Citation

Erik Mahieu
​
​"Cylindrical Anamorphosis of Parametric Surfaces"​
​http://demonstrations.wolfram.com/CylindricalAnamorphosisOfParametricSurfaces/​
​Wolfram Demonstrations Project​
​Published: June 27, 2017