>>>>Does a simple arc circle (yellow) with moving verticaly "control points" is less legitim >>>>>

No i dont think so at this point.

What I was looking for was if the curve itself was some sort of "perfect mathematical representation" that could be found by just looking at the "dimension figures". I didnt do well in triginometry/algebra/geometry in school and sometimes (though everything can be described with the math) simple things are very easy to spot by people experienced in these areas.

The package that this has to be re-created in does Not have "control points" with it's spline tools. So when drawing, it's either a freeform curve, or you need specific "coordinates or pick points". So, I can come close, by tracing the bitmap...But if there was some kind of recognizable structure to the curve, I could place "points" at specific coordinates, then just pick those with the spline tool and the curve would be exact.

So far the consensus is that it is "just a curve".