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Comment by onion2k | Hacker News Reader

I'm struggling to understand why the illustration at the bottom left of https://im-possible.info/english/library/grey/grey4.html is impossible. If you don't assume the two horizontal bars are parallel, and the top one is farther back than the bottom one, it make seems to make sense.

Eg it has a side profile of;

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I guess it's because the bottom and top bar look like their edges are actually touching which should be impossible with the middle bar going between them without it being squished.

I was able to recreate it in FreeCAD:

https://i.imgur.com/atOSXbc.gif

I don't think your idea would work in an ortho projection (like the one in the drawing). If the two horizontal bars were separated vertically you would have to see a space between them instead of the them sharing an edge. You idea should work if there is perspective distortion involved and the top bar is closer to the viewer and is also longer than the other.

The "bottom" and "top" pieces have the same length (transversal in your projection), as the 3d figure shows. But if you try to place the pieces so that their edges match on a projection, then they cannot start and end at the same point (one is "nearer" the camera than the other).

A agree, and I just reproduced it physically using three rectangular objects that were to hand on my desk.

Presumably the impossibility is meant to be that the edges of the two parallel bars are actually touching, rather than just being aligned in the angle of view. But it is certainly possible to reproduce this physically.

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