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I have a question about $4D$ rotation:
I programmed a little $4D$ game and I used the classical hyper-sphere coordinates, to rotate a vector.

It works, but it has some problems:
(just for clarity I take the cartesian coordinates, translate in hypersphere coordinates, add the angle I wish than translate back to cartesian)
This procedure causes jumble locks and approximation errors.

I'm asking you if it is possible like in $3D$ to have quaterinions to manage the rotations?

I'll prefer not to use rotation matrix, which has other problems:

Thanks in advance for the help!
If you want to have a look at the game:
http://www.youtube.com/watch?v=8IUnqm8j4BE
http://www.youtube.com/watch?v=NaeqUp3jbls

Harish Chandra Rajpoot
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Pella86
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    Yes. You can use two quaternions. One acts on the space of all quaternions by left multiplication and the other acts by right multiplication. – Qiaochu Yuan Aug 21 '11 at 23:43
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    Here are two related questions: http://math.stackexchange.com/q/40088 and http://math.stackexchange.com/q/24739 – t.b. Aug 22 '11 at 00:35
  • thank you Theo! the guy really explained it well, I'll try to translate it in my program and if I have other question I'll come back here – Pella86 Aug 22 '11 at 05:57
  • For more on what Qiaochu is referring to, see the Wikipedia entry http://en.wikipedia.org/wiki/Rotations_in_4-dimensional_Euclidean_space#Algebra_of_4D_rotations – Willie Wong Aug 22 '11 at 13:04
  • I was going to ask this same question mysef, but my previous questions were quoted as references! I am using 4x4 matrix for rotations, but I was looking for something less resource intensive, like quaternions... – lvella Nov 22 '11 at 14:20

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