anchor.diff:  
   [stem]
   ++++
  --q=(-sin⁡\frac{θ}{2}\vec{v},-cos⁡\frac{θ}{2})\\
  -=(-sin⁡\frac{2π-θ}{2}\vec{v},cos⁡\frac{2π-θ}{2})\\
  -=(sin⁡\frac{-(2π-θ)}{2}\vec{v},cos⁡\frac{-(2π-θ)}{2})\\
  +-q&=(-sin⁡\frac{θ}{2}\vec{v},-cos⁡\frac{θ}{2})\\
  +&=(-sin⁡\frac{2π-θ}{2}\vec{v},cos⁡\frac{2π-θ}{2})\\
  +&=(sin⁡\frac{-(2π-θ)}{2}\vec{v},cos⁡\frac{-(2π-θ)}{2})\\
   ++++
   
   Recall that stem:[sin⁡θ=sin(π-θ)] and stem:[-cos⁡θ=cos(π-θ)], then stem:[-sin⁡θ=sin(-θ)] and stem:[cos⁡θ=cos(-θ)].
  
positive.code: 
  The order of stem:[q=-{q_b}{q_a}] on the right hand side is important. It means flip along stem:[\vec{a}] first and then stem:[\vec{b}]. Actually all unit quaternion multiplication needs to be “read” from right to left when we are thinking about the order of applying those rotations.
  
  [NOTE, indent=2]
  .Note
  ====
  
negative.code: 
  [stem]
  ++++
  q&=(sin⁡\frac{θ}{2}\vec{v},cos⁡\frac{θ}{2})\\
  &=(\vec{a}×\vec{b},\vec{a}·\vec{b})\\
  &=-(-\vec{a}×\vec{b},-\vec{a}·\vec{b})\\
  &=(\vec{b}×\vec{a},-\vec{a}·\vec{b})\\
  &=-{q_b}{q_a}
  ++++
  
  Here you can also clearly see why we are using stem:[sin⁡\frac{θ}{2}] and stem:[cos⁡\frac{θ}{2}] in quaternions.
  