I first became aware of Aitken’s Graphical Construction of Lagrange Parabolic interpolation from an article that appeared in the Design News Magazine.
The article presented a graphical construction for the generation of points on a parabola. The significant feature was that the construction presented a method for generating exact point on the parabola. And it pointed out that the construction was an analog for the Lagrange Three Point Polynomial.
I was able to rework their construction into a more useful form and I also created a FORTRAN statement function which I then used to reproduce the construction.
And here is more detail about the FORTRAN FLINE Statement function.