I have seen many methods of rotation such as $p' = qpq^{-1}$ and $q = \cos (pi/2),v \sin (pi/2)$ , but I became slightly confused by how a unit quaternion is performed around a vector line.

  • $\begingroup$ Have you looked at the wikipedia article Quaternions and spacial rotation? What is your confusion? $\endgroup$ – Somos Apr 10 at 14:03
  • $\begingroup$ Yes, but I do not really understand what p' = qpq^-1 actually represents when we perform a rotation. $\endgroup$ – Guy Gershon Apr 11 at 10:53
  • $\begingroup$ The article states "it can be shown that the desired rotation can be applied to an ordinary vector p ... considered as a quaternion with a real coordinate equal to zero, by evaluating the conjugation of p by q: p' = qp$q^{-1}$ ... where p' is the new position vector of the point after rotation." What part of that do you not understand? $\endgroup$ – Somos Apr 11 at 12:03
  • $\begingroup$ Where the inverse quaternion comes into play in the equation (q^-1). $\endgroup$ – Guy Gershon Apr 11 at 12:18
  • $\begingroup$ Because multiplication by q and $q^{-1}$ leaves the real part of quaternions fixed. $\endgroup$ – Somos Apr 11 at 13:04

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