anchor.diff:  
   ---
   [NOTE, indent=2]
  -.Note
  +.Side Note
   ====
   This claim actually has 2 sides. Let me go a little be more in details in math term: 
   (1). For any 3D rotation equivalent to a rotation angle stem:[θ] along axis stem:[\vec{v}], there exists a unit quaternion stem:[q=(sin⁡\frac{θ}{2}\vec{v},cos⁡\frac{θ}{2})] to describe this rotation. 
  
positive.code: ++++
  {q_c}{q_c}=(\vec{c},0)(\vec{c},0)=(\vec{c}×\vec{c},-(\vec{c}·\vec{c}))=(\vec{0},-1)=-I
  ++++ 
  It shows that the combined rotation can be composed by flip stem:[q_a] and stem:[q_b], which tells the combined rotation is a rotation of angle stem:[2<vec{a},vec{b}>] along axis stem:[\vec{u}=\frac{\vec{a}×\vec{b}}{\left|\vec{a}×\vec{b}\right|}].
  
  .Figure 4
  image::https://github.com/lxjk/lxjk.github.io/raw/master/images/quaternions/fig4.png[, 400,align="center"]
  
negative.code: [stem]
  ++++
  \begin{align*}
  \vec{v'}&={q_1}\vec{v}{q_1^{-1}}\\
  \vec{v''}&={q_2}\vec{v'}{q_2^{-1}}\\
  &={q_2}{q_1}\vec{v}{q_1^{-1}}{q_2^{-1}}\\
  &=({q_2}{q_1})\vec{v}({q_2}{q_1})^{-1}\\
  \end{align*}
  