Timeline for Can we reconstruct the region in the xy plane by length measurements?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Aug 7, 2016 at 14:14 | comment | added | Joseph O'Rourke | @ToddTrimble: I think nonconvexity introduces significant complications. Not certain of the status. Might be unsolved. | |
| Aug 7, 2016 at 14:09 | comment | added | Todd Trimble | Okay, thanks, that's helpful! On the second page it seems to indicate that no set of three directions will suffice, but there are sets of four directions which will work for all curves with convex interior. Would that extend to all simple closed curves, convex or not? | |
| Aug 7, 2016 at 14:02 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
added 302 characters in body
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| Aug 7, 2016 at 14:00 | comment | added | Joseph O'Rourke | @ToddTrimble: This is a version of "Hammer’s X-ray reconstruction problem." I will edit my response. | |
| Aug 7, 2016 at 13:57 | comment | added | Todd Trimble | Yes... but now choose a third direction. I thought the question was asking if there are a finite number of directions we could choose that would determine the curve. (Admittedly, the question could stand some more clarification.) | |
| Aug 7, 2016 at 13:54 | comment | added | Joseph O'Rourke | @ToddTrimble: You are right; I misinterpreted. Then rotate the blue rays $90^\circ$. They yield the same length intersections. So two directions do not always suffice. | |
| Aug 7, 2016 at 13:52 | comment | added | Todd Trimble | My understanding is that we are supposed to consider lengths coming from multiple directions, not just the ones from segments parallel to the y-axis. | |
| Aug 7, 2016 at 13:50 | comment | added | Joseph O'Rourke | @ToddTrimble: Unless I misunderstand the question, one cannot reconstruct $S$ from the lengths of parallel ray intersections. | |
| Aug 7, 2016 at 13:48 | comment | added | Todd Trimble | But to what extent does this answer the question? | |
| Aug 7, 2016 at 13:47 | history | answered | Joseph O'Rourke | CC BY-SA 3.0 |