MATLAB: Fitting smooth closed spline to scattered 2D points

Question

Hi everyone,

I have a set of points scattered in a 2D plane. The points are scattered in a somwhat circular/elipptical way, but I would like to fit some arbitrarily (but smoothed) shaped spline. The points are distributed like:

To enable closing of a spline, the last and first data points are the same.

As said I would like to fit a closed smoothed spline to this curve. I've tried the cscvn-option giving me the below, but I would like something a bit more smoothened out (cscvn forces the spline to go exactly through each and every point):

Reading up in the help, csaps seem to enable smoothing (to be fair, I'm not really sure how), but if trying this on my data I get a smoothed non-closed curve like below:

The last option I've looked at is creating a new parameter to which I fit both my (x,y)-data (as suggested in an earlier thread: http://www.mathworks.com/matlabcentral/newsreader/view_thread/33868 ), but this actually gives me an even more jagged curve:

However I might be applying the parametrization in an incorrect way…

So, to my question. Does anyone have a good way of creating a closed smoothed spline to my data? Any suggestion or help would be very much appreciated. (P.S: I'm trying to create an automatized code, so I'm preferably looking for executable code than GUI in the curve fitting toolbox (but I understand that they are somewhat connected…)).

Thanks for the help!

/David

Answer 1

If you don't want or require the curve to go through every point exactly, you can use a Savitzky-Golay filter on the parameterized data.

% Now smooth with a Savitzky-Golay sliding polynomial filter
windowWidth = 35
polynomialOrder = 2
smoothX = sgolayfilt(x, polynomialOrder, windowWidth);
smoothY = sgolayfilt(y, polynomialOrder, windowWidth);