Spherical Mirror Anamorphosis of Regular Polygons

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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].

Contributed by: Erik Mahieu (March 2019)
Open content licensed under CC BY-NC-SA



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.


[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.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.