anchor.diff:  {q_1}{q_2}=(\vec{v_1},w_1)(\vec{v_2},w_2)=(w_1\vec{v_2} + w_2\vec{v_1} + \vec{v_1}×\vec{v_2}, {w_1}{w_2}-\vec{v_1}·\vec{v_2})
   ++++
   
  -Note here stem:[q_1] and stem:[q_2] are not necessarily unit quaternion, so even I’m using vector form, there’s no need to put stem:[sin⁡\frac{θ}{2}] and stem:[cos⁡\frac{θ}{2}] as we did for unit quaternions. It’s hard to explain this definition without introducing the algebra structure of quaternions, so I will skip that. If you are interesting to know how this is derived, quaternion https://en.wikipedia.org/wiki/Quaternion#Definition[Wiki page] has a very straight forward introduction.
  +Note here stem:[q_1] and stem:[q_2] are not necessarily unit quaternion, so even I’m using vector form, there’s no need to put stem:[\sin⁡\frac{θ}{2}] and stem:[\cos⁡\frac{θ}{2}] as we did for unit quaternions. It’s hard to explain this definition without introducing the algebra structure of quaternions, so I will skip that. If you are interesting to know how this is derived, quaternion https://en.wikipedia.org/wiki/Quaternion#Definition[Wiki page] has a very straight forward introduction.
   
   We are not going to use this general quaternion multiplication in Part 1. Here we only need to know a simpler form, the multiplication of flips. Let stem:[q_a=(\vec{a},0)], stem:[q_b=(\vec{b},0)] then
   
  
positive.code: 
  With flip multiplication defined, we can rewrite our flip composition rule again:
  
  *_Any 3D rotation stem:[q=(sin⁡\frac{θ}{2}\vec{v},cos⁡\frac{θ}{2})] can be represented as a sequence of 2 flips stem:[q_a=(\vec{a},0)] and stem:[q_b=(\vec{b},0)], such that_*
  [stem]
  ++++
  q=-{q_b}{q_a}
  
negative.code: ****
  We can however get rid of the negative sign by choosing stem:[\vec{a}] and stem:[\vec{b}] differently.
  
  _Any 3D rotation stem:[q=(\sin⁡\frac{θ}{2}\vec{v},\cos⁡\frac{θ}{2})] can be represented as a sequence of 2 flips stem:[q_a=(\vec{a},0)] and stem:[q_b=(\vec{b},0)], such that
  stem:[q={q_b}{q_a}]
  where stem:[\vec{a}·\vec{v}=0], stem:[\vec{b}·\vec{v}=0] and the angle from stem:[\vec{a}] to stem:[\vec{b}]: stem:[<\vec{a},\vec{b}>=\frac{θ}{2}-π]._
  
  