Comments and complaints have been made that when a curve or surface is rebuilt to a higher degree, particularly with the same or fewer control points as the input curve/surface, the control points of the resulting curve/surface can look chaotic. This “chaos” is in part due to a fundamental differences in NURBS curves and surfaces as the degree increases: the higher the degree the broader the influence of each control point for a given number of control points.
File with the examples below and more:
Degree Control Pts 01.3dm (54.8 KB)
Consider a simple 3 spand degree 3 curve with 6 control points:
Try creating an equivalent single span degree 5 curve also with 6 control points. This one was created using the development rebuild method available in the current V9 WIP, Elmo. It is close to the original curve but still has control points which are much more spread than the input degree 3 curve.
Anyone have a single span degree 5 curve which is as close to the original degree 3 curve as Elmo produced but with control points closer to the degree 3 curve locations?
Why are the control points of the single span degree 5 curve not close to the 3 span degree 3 curve? Here is a single span degree 5 curve with the same contol point locations as the degree 3 curve. It obviously has a very different shape.
Before going further let’s look at the result of the current (V8 and previous) Rebuild command. It has control points even further out than the Elmo result. This is because the current Rebuild method uses interpolation to a sparse set of points, and interpolation and produce oscillations with the magnitude of the oscillations increasing as the degree increase. Elmo using a fitting method rather than interpolation which inherently decreases, but not eliminate) oscillations away from the input curve.
To be continued.
