Anamorphic 2D Images That Look Three-Dimensional from a Particular Viewpoint

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This Demonstration illustrates flat images that look three-dimensional when seen from the appropriate viewpoint. These kind of images are used in anamorphic art. Changing the viewpoint shows that the graph on the left is three-dimensional while the graph on the right is totally flat, although they look identical when is equal to zero or . The main reason for this effect is a distortion on the 2D graph; however, the effect is also enhanced with the coloring and transparency of the surfaces.

Contributed by: José Luis Gómez-Muñoz (March 2011)
Open content licensed under CC BY-NC-SA


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A flat anamorphic image corresponding to the viewpoint with coordinates can be obtained from the original 3D image by multiplying each 3D point by this transformation matrix:

.

An example of anamorphic images in art is the famous distorted skull that can be identified only from a particular viewpoint in the painting "The Ambassadors", by Hans Holbein the Younger, painted in 1533. It is in exhibition in the National Gallery, London.

A more recent example is Julian Beever, an artist who creates chalk drawings on pavement surfaces. His works are created using anamorphosis, giving the illusion of three dimensions when viewed from the correct viewpoint. See his website for some examples.



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