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Comment by somat | Hacker News Reader

Does it have to be straight through? I can imagine a scenario where the moving shape has to be rotated as it passes through. sort of analogous to some of those block puzzles or getting a sofa around a corner.

The article does say straight through and most analyses has been done with variation of the shadow technique, which has to be straight through. But the original bet. The thing that started this whole line of thought just said you had to get one through its copy, I think rotating is is an acceptable technique in this problem.

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This is specifically about convex polyhedra, I don't see how rotating could help.

I don't really know, I am currently farting around with blender trying to see, but that is far from rigorous. and going poorly. but let me explain my thought process.

Note the egg shape in the article. specifically the widest band around the equator. now imagine one passing straight down through the other. one edge ring would pass through the shadow if it has a slight rotation offset but it is blocked by the next edge ring up, which could also fit but requires a different offset, so if you could change that rotational offset while it is passing through would it fit?

I have the same question -- the problem of moving a couch around a corner is a nonconvex problem, but I suspect that pivoting, or perhaps a helical "rifling" motion, may avoid a vertex:face contact.

Imagine a fat corkscrew, for instance.

That is not convex

if a convex shape is rifled while it is moving the resulting cut volume could become concave(example 1). does this new concave cut volume free up enough space to meet the rupurt cut challenge where a non-rotating sweep would not?

There are also other rotation profiles, hard to say if they would help or not.

example 1. a cube rifling faces parallel would not generate a concave cut volume but moving diagonally point to far point it would. really whenever a point sticks out. Unfortunately a cube already fits and any help a convex cut volume provides is not needed.

If you passed a cube vertex-first through a regular triangle, you'd want to rotate it, right?

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