anchor.diff:  It becomes harder to visualize stem:[\vec{a}] and stem:[\vec{b}] if we go this way, and the negative sign does not really introduce a lot of difficulties, so we will stick with that negative sign in this article.
   
   ****
  +---
   
   
   === Flip Vector
  
positive.code: 
  *_Any 3D rotation is equivalent a unit quaternion stem:[q] that stem:[\left|q\right|=1]._*
  
  .Side Note
  ****
  This claim actually has 2 sides. Let me go a little be more in details in math term: 
  
negative.code: (2). For any unit quaternion stem:[q=(x,y,z,w)], it describes a rotation of angle stem:[θ=2cos^{-1}w] along axis stem:[\vec{v}=\frac{(x,y,z)}{\sqrt{1-w^{2}}}].
  
  ****
  ---
  
  From now on, any quaternion stem:[q] used in this article is by default a unit quaternion, and we will use stem:[q] to describe rotations.
  
  