Spherical Mirror Anamorphosis of Regular Polygons

This Demonstration explores the spherical anamorphic map of some regular polygons and a circle. The anamorphic images can only be seen as regular polygons when reflected in a spherical mirror [1].

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With a spherical mirror centered at , is the observer's eye position, is a (real) point outside the mirror and is its perceived image point inside the mirror.
One of the reflected light rays leaving meets the mirror at in such a way that its reflection meets the eye at . But the eye at will now perceive the point at .
This mirror setup can be used for the computation of both reflection and anamorphism, and the points and form an "enantiomorphic pair" [2].
The function sphericalAnamorphMap that maps reflected points into anamorphic points uses the law of reflection [3] with the Mathematica functions ReflectionTransform and EuclideanDistance.
References
[1] M. Luque. "Images dans un miroir sphérique." (Mar 14, 2019) melusine.eu.org/syracuse/mluque/BouleMiroir/boulemiroir.html.
[2] Wiktionary. "enantiomorph." (Mar 6, 2019) en.wiktionary.org/wiki/enantiomorph.
[3] R. Ferreol, "Anamorphose en 3D," mathhcurve.com (blog). (Mar 6, 2019) www.mathcurve.com/courbes3d.gb/anamorphose/anamorphose3d.shtml.
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