Introduction to the Project:

Tri-Bar of Butterflies

This project was written by Weber Ofir, an undergraduate student for computer engineering, specialized in computer graphic at the Technion – Israel. The project was done in the frame of the VISL (Vision Research and Image Sciences Laboratory) lab in the department of electrical engineering and was supervised by prof. Chaim Gotsman, Computer science department. Project academic number is (Project A 044167 + Project B 044169). I started to work on this project on June 2000 and finished on October 2001.

Impossible image is a 2D image that represents a projection of a 3D environment that cannot exist in real life. Although the 3D scene is impossible, the 2D scene is possible. When the viewer looks at the impossible image he is trying to reconstruct in his mind, the 3D scene that is the source of the image. The idea of impossible images is that such a 3D scene doesn’t exist. For example, whenever we look at photos, we always try to imagine how the real 3D environment would look like. If we look at an impossible image we will not succeed imagining how the real 3D environment would look like and we will probably get confused. The artist M.C. Escher was a master in drawing such impossible images. In this project, computer software for producing impossible images is presented.

Eli Savransky gave the original idea to this project in 1999. Eli Savransky, inspired by M.C. Escher, invented a theory for composing and rendering impossible 3D object in a computer. Eli Savransky and Dan Dimerman worked on a project, in 1999, for implementing this theory. The software they wrote proved the correctness of the theory, but it was very slow and difficult to use. Only straight bars composed the models that could be created using the software. The software based on a description language that was hard to use. The software was written for the Unix platform and didn’t have a Graphic User Interface. It took a few minutes to render one frame.

The idea of this new project was to expend and improve the old theory and to implement new software. The new software was written via Microsoft Visual C++ 6.0 for the Win NT 4.0 environment and it has a Graphic User Interface. The software consist of more than 10,000 lines of code. The software makes an extensive use of the Open GL C++ library. It is extremely fast comparable to the old software. It can render up to 25 frames per second, which is 10,000 times faster than the old software. It supports complex 3D structures, given in VRML format. The software includes a modeler for making the process of modeling an impossible 3D scene easier. The software can save an impossible scene into a file using a special format. The software support Texture Mapping for producing more realistic results.

A new rendering algorithm was written in order to accelerate the rendering process. An algorithm to simplify the model and to solve visual artifacts was written. An algorithm for animation was written.

In this web site, you can see a collection of impossible images and impossible animation that produced via the Escher Software. You can also download the software and produced your own impossible images. There is information on the Theory and algorithms that the software is based on. The web site also contains a collection of some of the interesting Escher lithographs, background on M.C. Escher and links to some other Escher pages.