Timeline for How do you traverse a rectangular grid of points while turning as little as possible?
Current License: CC BY-SA 4.0
8 events
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| Aug 7 at 8:59 | comment | added | Tom Solberg | Thanks for bearing with me -- I just saw your edits and in fact I am indeed interested in minimizing the total amount of absolute turning angles. I'm picturing a vehicle that can move rapidly in a straight line, but where turning takes a long time. | |
| Aug 7 at 1:27 | comment | added | Yaakov Baruch | Too tired to edit, but there is a simpler example where the $3\times 3$ lattice can be traversed by a path with only 3 turns. | |
| Aug 7 at 1:19 | history | edited | Yaakov Baruch | CC BY-SA 4.0 |
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| Aug 2 at 20:55 | comment | added | Tom Solberg | Sorry, I was horribly unclear. I meant to say: as I understand it, your proof bounds the number of squares that have a turn in them, if we restrict ourselves only to movement in the north/south/east/west direction. It feels silly, but I'd like to bound the total turning if we assume any directions allowed, like there aren't any HORIZONTAL or VERTICAL squares because it's always moving at a 45-degree angle or something like that. Does that make sense? | |
| Aug 2 at 15:20 | comment | added | Yaakov Baruch | @TomSolberg : I don't understand this last question. Nowhere is there any mention of right or left hand turns... There are paths with the minimal number $n-2$ of turns containing only left turns, or only right turns, or anything in between. | |
| Jul 31 at 22:05 | comment | added | Tom Solberg | Thank you for the reply! Do you see any way to generalize this where one doesn't have to take only right hand turns? | |
| Jul 13 at 23:05 | history | edited | Yaakov Baruch | CC BY-SA 4.0 |
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| Jul 13 at 22:44 | history | answered | Yaakov Baruch | CC BY-SA 4.0 |