anchor.diff:  ++++
   {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|}].
  +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"]
  
positive.code: 
  ---
  [NOTE, indent=2]
  .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. 
  
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*}
  