Vertex:Control point or knot?

[IDIMITRIOUD883D]

Trying to insert a new point at (1,0), the one at the left remains unchanged but the one to the right gets a new position at (2.3333,0) (see picture). When i manually calculate the new positions for Uvec=[0,1,2,4,6,8,...) i get the new control points :P1= (0,0) for the first ,Pnew=(0.5,0) for the new one and P2=(2.3333,0) for the one to the right. 

Is there something i am missing?

Thanks in advance

[IDIMITRIOUD883D · Accepted solution]

I found out  that edge (knot)  insertion is quite different compairing with the usuall internal knot insertion. But bibliography is so deficient.

[IDIMITRIOUD883D · Accepted solution]

In the following picture  we have an equalspaced index while control points start with a double zero (p1=p2). If i do this then i have an agreement with the first picture from FUSION 360. Does anybody agree with this?