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

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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

Accepted Answer

Matt J
Matt J on 22 Sep 2014
The control over the derivatives that you want is possible through
Arc-length would probably be more work. You would probably need to formulate your own constrained problem using fmincon, I imagine.
  1 Comment
Edd Hirons
Edd Hirons on 22 Sep 2014
Matt, Many thanks for your reply I will need to get some toolboxes it would seem!
Regards, Edd

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