I want to create Nurbs curves which approximate a periodic planar curve well, while having a degree of 2 and as few control points as possible. What i have done so far is determine where the inflection points on the original curve are, and then set the minimal Nurbs control points to 2*inflection_points. from there, I manually adjust each control point so that the Nurbs curve approximates the original curve well, as shown below:

The black curve is the original planar curve which is baked into the Rhino environment. The red curve is a Nurbs curve with 8 manually moved control points, this process took half an hour.

Contrarily, this is what it looks like to use the Rebuild Curve function with degree set to two and 8 control points:

You can see that this is a significantly worse result. But I do not want to spend 30 minutes on every curve optimizing the control points. Any idea how to do this?

Below is the necessary files to play with. Thanks (14.6 KB) FitReducedNurbs.3dm (3.8 MB)FitReducedNurbs.gh (14.6 KB)