This is just a request for clarification, an attempt to penetrate the notation.
Is this what you have in mind? If so, the operation is not definite:
any point $P_{k+1,j}$ on the circle arc between $P_{k,j}$ and $P_{k,j+1}$ forms a
right angle.
After the OP's correction of the problem statement:
![ngon corrected][2]