Can I make a spline both smoothing *and* periodic?

Hi all,

I would like to make a smoothing spline through data, and enforce point and gradient equality at either end of my spline. Here's the data:

XYpts = [...
    10     5    -5   -10    -5    0    10
     0     9     9     0    -9    0     0];
figure, plot(XYpts(1,:), XYpts(2,:),'bo')
axis equal, grid on, hold on

And here I can do a smoothing spline without the constraints to make it periodic (note that it smooths the original data nicely, but meets a nasty sharp turn at the end):

dt = sum((diff(XYpts,[],2).^2));
t = cumsum([0,dt.^(0.25)]);
smoothingSpline = spaps(t,XYpts,1);
fnplt(smoothingSpline,'-r.')

And here I can do an interpolating spline with the correct continuity constraints I'm looking for:

interpolatingSpline = csape(t,XYpts,'periodic') 
fnplt(interpolatingSpline,'-g.')

But neither of these do both at the same time (smooth the data and enforce continuity). Can you help?

The only way I can think of so far is a bit messy: repeat the starting/ending points of my data so that the smoothed spline wraps back over itself, and then only sample it within the "original" domain. Is there a better/cleaner way?

Thanks, Sven.

Answer 1

[Matt J]

This FEX file advertises all kinds of convenient options for constraining spline fits,

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

You need the Optimization Toolbox, though.

[Sven]

Ha, thanks Matt, I actually had this toolbox, just never thought to apply it to 2d data.

The (minor) downside is that the fit needs to be applied separately to each X,Y channel, but it certainly fits the bill.

Thanks, Sven.