Re:Show HN: Test your shape rotation skills
by whatshisface on Sunday February 20, 2022 @11:42PM
(#30412045)
Right-handed rotation is different from left-handed rotation no matter what coordinate system you choose.
Re:Show HN: Test your shape rotation skills
by crdrost on Tuesday February 22, 2022 @12:47PM
(#30430944)
WLOG 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.
Re:Show HN: Test your shape rotation skills
by emschlr on Monday February 21, 2022 @01:02AM
(#30412419)
The 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.
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...