Marko Marelja's anamorphosis, 14th of December 2012.

cylindrical anamorphosis, Istvan Orosz

According to >> Wikipedia, anamorphosis "is a distorted projection or perspective requiring the viewer to use special devices or occupy a specific vantage point to reconstitute the image."

Historically (in art), especially common were the anamorphic images which could be "appropriately" seen (or reconstituted) only with the help of cylindrical mirror - only in the reflection in such a mirror were those images recognizable. The photograph above shows one such example of a modern artist >> Istvan Orosz.

From the physical point of view, it is of interest to note that mostly non-spherical, typically cylindrical, but also conical mirrors were used to these ends. Diploma work of Marko Marelja, defended yesterday on the Faculty of physics in Zagreb, dealt mostly with reflection in cylindrical and conical mirrors, but also with perspective anamorphosis. The mirrors are not needed in order to see the perspectively anamorphed image, one only needs to assume a special point of view. I was the supervisor of Marko's diploma work and I happily bring here >> the PDF file of Marko's work (in Croatian), with his permission. The images below were chosen from the work whose full title is >> Simulation of non-spherical mirrors and anamorph images using raytracing.

focus of concave cylindrical mirror

The image above shows the PovRay simulation of mirroring on the concave side of cylindrical mirror set up on the supporting plane covered with some sort of coordinate grid. One can see how the front and the back side of the cube deform and skew differently in the image space due to their different distances from the mirror. I imagine myself standing in front on one such mirror in some amusement park and I approach it. In the moment when I pass through the focal point of the mirror, I "splat" in the horizontal direction so that the width of my waist, i.e. belly diverges. Interesting ...

convex cylindrical mirror

On the image above one can see mirroring of the ping-pong ball in a convex cylindrical mirror. It can be noted that this mirror decreases the width to height ratio, so that it, contrary to concave mirror, helps in the case of unfavorable width of the belly. The left side of the image is the photograph of experimental setup, and the right side is the PovRay simulation.

slanted convex cylindrical mirror

An interesting, and analytically difficult problem, is mirroring in the slanted, inclined cylindrical mirror. The image above shows the photograph of an image in such a mirror (left) and PovRay simulation of such an optical system (right). On the photo, one can see an "experimenter" i.e. a photographer.

cylindrical mirror

The image above shows the cylindrical ring, in fact, a kitchen utensil used for cooking in an oven (e.g. to gratinate rice or similar). This is the "experimental setup" which simultaneously displays mirroring on the convex (outer) and concave (inner) side of the cylindrical mirror. The left part of the image is the experiment, and the right part is the PovRay simulation. The agreement is excellent and PovRay again proves itself here as a powerful tool to simulate classical optical systems.

horizontal cylindrical mirror

In the end, the image above shows reflection in a horizontal cylindrical mirror (its axis is parallel to the horizontal support). The upper part of the image shows the photograps of the experimental setup, and the lower part in the PovRay simulation.

More info, including examples of anamorphic images, can be found in >> Marko Marelja's diploma work (PDF, in Croatian).

Last updated on 14th of December 2012.