anchor.diff:  ****
   
   
  -== Flip Vector
  +=== Flip Vector
   
   Given a flip stem:[q_a=(\vec{a},0)] and vector stem:[\vec{v}], we are ready to calculate the result of the flip stem:[\vec{v'}].
   
  
positive.code: 
  We slightly touched quaternion multiplication, and we proved an important equation stem:[{q_1^{-1}}{q_2^{-1}}=({q_2}{q_1})^{-1}].
  
  == Appendix: Derive Quaternion Multiplication
  
  This part is not very important for understanding quaternion. It is a bit calculation heavy and is more for fun. Feel free to skip.
  
  
negative.code: 
  This representation means if we fully understand flip, which is easier to visualize, we can fully understand rotation and quaternions, since any quaternion can be broken down to flips.
  
  === Quaternion and Flip
  
  Now let’s recall the quaternion vector form stem:[q=(sin⁡\frac{θ}{2}\vec{v},cos⁡\frac{θ}{2})]. With the discussion of flips above, you can almost immediately see why we are using stem:[\frac{θ}{2}] here.
  
  