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?