3 ms·
> The first turn can be defined as always "right" or "left," No it can’t, not in 3D... it is just a turn. You can however choose to rotate about the first seg
by crdrost 5y ago
> The first turn can be defined as always "right" or "left,"
No it can’t, not in 3D... it is just a turn.
You can however choose to rotate about the first segment until the turn is Right, then use this orientation for the rest.
In terms of normal form and restarts, who cares? Just generate the string both ways, it’s 2n computations, choose the lowest in lexicographic order, and life is good. If you get to billions of turns are humans really going to be doing the comparison? Surely we’d just stream the string into a hash function or something...
- whatshisface 5y agoRight-handed rotation is different from left-handed rotation no matter what coordinate system you choose.
- crdrost 5y agoWLOG the shape starts at the origin (0,0,0), the first kink is at (0, 0, m), and the next point is (x, y, m), where x²+y²=n² You can always rotate this to (n, 0, m) and view from the +y axis looking down, and it is a right turn. The L shape is not complex enough to be chiral, but the post is (and you are!) is claiming that you need an extra bit of information to specify “which L, the right handed one or the left handed one?” ... That is a distinctively 2D question.
- emschlr 5y agoThe keyword is "define"! You can just define the first turn to be Right no matter how it is oriented. If you are not happy with that then just rotate the first segment until it looks Right to you. Then label the other turns. If you are still not happy with the word Right to denote the first term then just make up new notation. Define the first turn to be 1. Use numbers to denote turns if you object to using Left and Right.
- kuhewa 5y ago> No it can’t, not in 3D... it is just a turn Not if it is chiral. then whatever turn is defined as right is not left