3 ms·

The Dirac String Trick (2015)

• nayuki 5y ago
  The first part of the article about describing sphere rotations with a direction and magnitude has some overlap with quaternion rotations, described and visualized nicely here: https://eater.net/quaternions/ https://eater.net/quaternions/ ; https://www.youtube.com/watch?v=d4EgbgTm0Bg https://www.youtube.com/watch?v=d4EgbgTm0Bg The second part of the article about untangling strings after a 720° turn is also covered in: https://www.youtube.com/watch?v=JaIR-cWk_-o https://www.youtube.com/watch?v=JaIR-cWk_-o ; https://www.youtube.com/watch?v=Nat-EsReXtQ https://www.youtube.com/watch?v=Nat-EsReXtQ ; https://www.youtube.com/watch?v=O7wvWJ3-t44 https://www.youtube.com/watch?v=O7wvWJ3-t44 ; https://www.youtube.com/watch?v=Rzt_byhgujg https://www.youtube.com/watch?v=Rzt_byhgujg
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  • phkahler 5y ago
    >> The first part of the article about describing sphere rotations with a direction and magnitude has some overlap with quaternion rotations Some? Scale the direction vector (x,y,z) to have magnitude = sin(theta) and then set w = cos theta, where theta is half the desired rotation angle. Then (w,x,y,z) is the quaternion that represents the rotation. It was hard for me to read without that relationship constantly popping into my head.
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• tobmlt 5y ago
  If this one looks to be a bit of a deep dive, try the cup trick first!