M.C. Escher for Real
Gershon Elber .................. The work of M.C. Escher needs no introduction. We have all learned to appreciate the impossibilities that this master of illusion's artwork presents to the layman's eye. Nevertheless, it may come as a surprise for some, but many of the so-called 'impossible' drawings of M. C. Escher can be realized as actual physical objects. These objects will resemble the Escher's drawing, of the same name, from a certain viewing direction. This work below presents some of these three-dimensional models that were designed and built using geometric modeling and computer graphics tools.
Metamorphose ...........M.C. Escher (Maurits Cornelis) ........... Documentary
In the following sequences, figures are frequently presented in pairs. The left figure in each pair is the front view-Escher's drawing's direction, whereas the right figure gives a general view. Whenever a real, tangible model has been created, it will be presented as a second pair to the right of the pair of computer rendered images. The objects were physically realized with the aid of layered manufacturing systems: a Z402 3D Printer from Zcorporation and a Stratasys FDM3000 printing machine.
The Penrose Triangle:
The Penrose Rectangle:
The Pennrose Pentagon:
The Penrose Triangle II:
Here is an movie that shows this model rotated.
Escher's (Louis Albert Necker's) Cube:
And here is an movie that shows this model rotated.
Escher's Moebius Strip - Ducks:
Escher's Moebius Strip - Ants:
To better understand this, examine the pictures on the left. The rightmost image shows the Penrose triangle only, from above; the leftmost image shows the original Waterfall scene; and the middle image is a blend of the two. In fact, the original Waterfall model presents three different and connected such triangles. Also interesting in this image is the house. When we examine the original Waterfall drawing, we see that the house ends up behind the middle corner of the water path. In order to accomplish this in our constructed image, the house's geometry is warped so as to look straight only from the proper viewing direction. The house, as well as the S shaped rods that look vertical from the original viewing direction, were modeled as generalized sweeps by the geometric modeler.
Here is our physical realization of Escher's Belvedere drawing. Again, this model looks like the original Escher drawing from one direction only, whereas the (not so) vertical poles stretch from the far top to the near bottom sides and vice-versa. This trick is somewhat similar to the trick we used in the Penrose triangle but is somewhat simpler.
Gershon ElberDepartment of Computer ScienceTechnion, Israel Institute of TechnologyHaifa, 32000Israel
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