- If by chance you'll have time to apply this 2nd derivative constraint until the next week, this would be great :-) Then I'll include the better approximation in a coming conference paper.

- you are right; I was just confused by several plateaus observed in the 1st derivative. But as it is already emphasized in the help-file, this means the monotonicity in the sense "=>0' (or "<=0"), not just ">" or "<".

- OK, the total arc length constraint is not vitally important while I have a good number of points to interpolate (and for me it is not a problem to take many points from the test data).

Thank you very much for this tool! I use it to fit the test data for the bent shape of a textile stripe loaded by its own weight, and SLM the best fitting I used for this!

However :-) I would be happy yet more if you extend the files to include the following properties:

1) monotonic increase/decrease of the curvarure (in my case the condition of decreasing curvarure is very important, since I take the 2nd derivative to calculate the bending stiffness of the stripe). Now I need to make a double fiitting: first for the bent shape and then for the slope; otherwise the curvature has too large jumps. But even after this the result is still not perfect :-(

2) controlled length of the curve (similarly to the integral option). This is not so important in my case but could improve the fitting, since this condition has a sound physical sense in my problem).

Property of the monotonic increase/decrease of the 1st derivative could also be useful IMHO.