forum.alglib.net

I have a very applied problem.
There is a real world line (made of one kind of metal) and a lot of 2D points, taken from the line with some errors with non-regular step.
I need to represent the line with some spline.
The spline must reflect the next real line property: it should not have "curved areas" shorter then some value (point steps can be mach shorter then this value)
"Curved areas" means areas with same curvature direction (cw, ccw).

I can use a weighted 2D spline but have no any ideas how to estimate the weights.

As I can see point should have smaller weight in two cases:
a. it lies within series with short steps between points;
b. it's location measures with large error.
In both cases such point (if not to reduce it's weight) will result in short spline bend.

Could you advise me something?
Thank you.

PS Sorry for poor English.

Do you really need to enforce such requirement, or you just try to prevent spline from being "too flexible"? There are much more convenient ways of regularizing spline....

Sergey,
If there is relativly simple way "to prevent spline from being "too flexible" I hope it will help me
(it will result in smth like what I want from my data, The next step of my "algorithm strategy" is to locate "curved areas" and I want them not to be too small and "frequent").

Thank you for interest.

I recommend to use spline1dfitcubicwc() function. You can constrain flexibility of a spline by specifying small number of degrees of freedom. Alternatively, you can use penalized regression splines. However, ALGLIB doesn't include penalized regression splines yet, so you have to implement them yourself.