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Cylindrical Anamorphosis of Parametric Surfaces

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].

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In this Demonstration, the mirror is a circular right cylinder with radius parallel to the axis. The viewer's eye is at at a distance and a height .
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 , perpendicular to the cylinder at , the intersection with the cylinder of the view line between the viewpoint and the image point .
The viewer perceives the anamorphic point as the point . The artist makes the anamorphic point from the reflected point . Both and are in the same horizontal plane and at the same distance from .
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.
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