Can i control all gradients of a spline, not just the end points?

PROBLEM CONTEXT: I am trying to estimate the y-coordinates of some physical system given that I know x-coordinates and the slopes/gradient of the data (will be <= 10 coordinates). I chose splines so that I do not get over fitting problems with potentially 9th order polynomials!

I would also rather use spline than pchip as I want the gradient curve to be smooth.

If for now I assume that the coordinates are equi-spaced in x and another controlling factor is that the arclength of the spline will be constant does anyone know any way to estimate (iteratively or otherwise) the y-positions? if I can gain some control over the gradients of the spline I believe I should be able to recover the possible y-positions? (i.e. swap my known information from the usual x,y, positions and use the spline to find the gradients and instead use the gradients and x positions to find the y?)

I know this is a second question but its intrinsically linked to the other problem!

Cheers,

Edd

Answer 1

[Matt J]

The control over the derivatives that you want is possible through

http://www.mathworks.com/matlabcentral/fileexchange/24443-slm-shape-language-modeling

Arc-length would probably be more work. You would probably need to formulate your own constrained problem using fmincon, I imagine.

[Edd Hirons]

Matt, Many thanks for your reply I will need to get some toolboxes it would seem!

Regards, Edd