Timeline for How to check if a box fits in a box?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Oct 2, 2017 at 23:18 | comment | added | Joseph O'Rourke | @JeppeStigNielsen: If $A$ fits in $B$ and no vertex of $A$ touches $B$, then you could rotate $A$ so that a vertex hits. If only one vertex of $A$ touches $B$, then you could rotate until two vertices hit. So one would only need look at those orientations of $A$ for which two vertices lie on faces of $B$. | |
| Oct 2, 2017 at 23:00 | comment | added | Jeppe Stig Nielsen | @JosephO'Rourke Very naïve: One of the comments to the question holds a link that leads to the observation that if one box can be contained in another, then it can also be contained when the centers of the two boxes coincide. So without loss of generality, let the outer box and inner box have center $(0,0,0)$, and the outer box has a fixed orientation (say edges parallel to coordinate axes). Then try to rotate the inner box and see if all vertices of the inner box can fit inside the outer box. But I do not know the best way to try all (needed) rotations. | |
| Sep 27, 2017 at 19:11 | comment | added | Joseph O'Rourke | Actually, I would cite the same algorithm. I don't know that anyone has published box in box, so convex polyhedron in box may be the best bet. I wrote a paper on the minimum volume containing box, but that seems irrelevant to just deciding containment. | |
| Sep 27, 2017 at 18:52 | history | answered | coudy | CC BY-SA 3.0 |