Matlab curve fitting a set of 2D points

Question

Currently I have a set of 2D points as shown below.

I need to obtain fitted curve of the points to determine the shape of the object.

Matlab offers a spline fitting function . I have to applied it to the set of points. However, the results I am obtaining is shown below. .

         xx = linspace(-10,10,20);
         pp2 = splinefit(PV(:,1),PV(:,2),8,5);
         y2 = ppval(pp2,xx);

         plot(x,y,'.',xx,y2), grid on
         axis([-10 10 -10 10]);

PV is the data points. I am unsure where the problem lies.

Answer 1

You are trying to fit PV(:,1) = f( PV(:,2) ) that is, fitting directly y=f(x) . But as you can see from your points, there are multiple values of y for certain values of x (around x=0 and x=-15 ). Thus, you cannot mathematically fit y=f(x) for any function f(.) here.

What you can do is fit a parametric curve using an auxiliary parameter t :

t = linspace(0, 1, size(PV,1));
ppx = splinefit(PV(:,1),t,8,5);  % x = f_x(t)
ppy = splinefit(PV(:,2),t,8,5);  % y = f_y(t)

Now you can plot the curve (f_x(t), f_y(t)) :

tt = linspace(0, 1, 50);
x2 = ppval(ppx, tt);
y2 = ppval(ppy, tt);
plot( PV(:,1), PV(:,2), '.', x2, y2); grid on;
axis([-10 10 -10 10]);

Note :
This fitting scheme is based on the assumption that the points in PV are ordered : That is, the curve should follow from PV(1,:) to PV(2,:) and then to PV(3,:) and so on. If this is not the case (eg, PV(1,:) has x value of ~-10, PV(2,:) has x value of ~0 and PV(3,:) jumps back to x ~-10) then you are in deep s&#t.