Can I make a spline both smoothing and periodic?

Question

Sven 2012-12-2

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/55401-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.