Sorry, as I mentioned, I do not do discussions via PM. It excludes everyone else here, which means the idea to run a forum is canceled.
You have sent a link with a German Illustrator path explanation (don’t worry, I speak German), which would be a Spline in Cinema 4D. Those can work with interpolations between or among points.
Edges of objects in Cinema 4D are always straight. No exception. The subdivision surface creates new points, like with the interpolated Splines, and connects those with straight edges until you get more polygons.
The appearance of roundness is then given with the Phong Tag, which is an idea of smoothness, but not in terms of the underlying geometry. The Silhouette of the object will show that. There is, however, a sweet spot, where subdivision allows the Silhouette of the object to show up smooth, without going too dense. Always depended on how close the camera is and the given rendered resolution.
There are applications, primarily in engineering, which create these surfaces based on mathematical definitions (NURBS). However, when it gets exported into a polygon object, this smoothness depends on the given parameters.
In Cinema 4D, the SDS is not a full NURBS (non-uniform-rational B-spline) surface.
All the best