About Curve Degree
You can specify the curve degree when you create or edit a curve.
The minimum curve degree is:
3 when no surface curvature tangency is set.
At least 4 when surface curvature tangency is set for one end.
At least 5 when surface curvature tangency is set for two ends.
The maximum curve degree is 15.
If you apply surface curvature tangency to a curve with less than the minimum required degree for that level of tangency, the degree will automatically change to the minimum required degree. For example, if you set surface curvature tangency to one end of a curve with a degree of 3, the curve automatically changes to a degree of 4.
When the curve degree increases, the number of control points increases by one for each degree increase. When the curve degree decreases, the number of control points decreases by one for each degree.
For periodic curves, the value for the curve degree must be an odd number. When a curve of an even-numbered degree is changed to periodic, the degree increases by one.