A study in reconstruction of paradoxical objects (1992)

Pavol Elias

Human perceptions system keeps amazing people all around the world. Many artists are attracted to it, many of them learned to use its features to attract the audience. M.C. Escher is probably the best example - many of his works (Belvedere. Waterfall, ...) use features of human perception to provoke, showing so called "impossible" objects. Impossible objects contain what we perceive as paradox (or several of them) - water flows up (Waterfall), man on a ladder climbs from inside of the building to outside and back inside again (Belvedere), cuboid shows what we see as a cube in impossible and contradictory setup. When people are presented with such images most of them are very confident that such objects are not possible in our 3D world. Obviously they are not right - such paradoxical objects can indeed exist in 3D world. To shown them they are wrong (and provoke their visual perception some more) was a goal of this project...

Gallery of  images - cuboid in motion

One of the basic ideas in modeling "impossible" objects is to divide figures into consistent parts, that means to reduce a paradox. Reduced figures which don't contain paradox can be easily modeled using standard methods. The second step consist of merging all parts to the final (paradoxically looking) model. In case of cuboid it is easy to place both "bases" of the cube into the proper "cuboid" position . The vertical "edges" they join the corresponding vertices. The wire edges are then expanded to form a solid structure. This is slightly more involved, but it can be done by keeping geometric relationships between adjacent vertices. The faces of the resulting object are not planar rectangles, they are twisted.



Animation of a rotating cuboid


Shockwave3D interactive cuboid (requires Macromedia Shockwave Player) 

The idea of modeling cuboid as one of the "impossible" objects on Escher's Belvedere drawing was inspired by a video from Eurographics conference where the whole model of Belvedere was reconstructed. Being motivated by peers I took this as a challenge and attempted (successfully) to recreate a 3D model of cuboid - cube in "impossible" position. The results achieved with fully custom build software for all modeling, animation and playback (virtually no 3D technology was available to us at that time :-) keep amazing people many years afterwards. BTW a real world model of the cuboid was constructed out of wires - unfortunately the model hasn't survived the attention it generated and it has felt apart...

There were more independent attempts to reconstruct paradoxical objects. More information can be found on following links:

Escher Revisited in VR Valley

Escher's Belvedere in Lego

Dunako (c) 2002