You cannot fit a spline directly to data of that form. (I don't have your data, so I cannot give an example using it.) But for example:
theta = linspace(-pi/2,pi/2,15)';
x = cos(theta);
y = sin(theta);
what happens when we just use a spline, or interp1, for that matter on the (x,y) curve? It fails, and fails, miserably! I'll even use the method David suggested.
airfoil=fit(x,y,'smoothingspline');
plot(airfoil)
Why did it fail so badly? Becua the (x,y) pairs here are not in the form of a single valued function, that is, y(x). So for ANY x, we need to see a single value for y. But in your airfoil, you don't have that. You have a relationship that is essentially multi-valued.
So what happens is interp1 internally SORTS your data on x, then assumes y is a single valued function of x. NOT TRUE FOR YOU. And that will cause it to fail in unfortunate ways.
The common answer, IF you have a parametric form, is to use that. So, if we were to fit x(theta) and y(theta), so both functions of a third parameter that drives both x and y, then we can make it work. But you won't have that, or at least, you probably won't have it.
So what can you do? You can download my interparc function from the File Exchange.
xyint = interparc(100,x,y,'spline');
plot(x,y,'bo',xyint(:,1),xyint(:,2),'r-')
If you have the curve fitting toolbox, you can use cscvn, which is able to handle a set of points that lie along a completely general path in the plane like this.
fnplt(cscvn([x,y ]'))
