How to fit a curve with a circle with matlab?

Question

I would like to fit the curve bellow with a circle in a certain range with matlab. I want to fit this curve from x=0,1 to x=0,5 and to get the radius of the circle.

Do you have any ideas how to do that with matlab?

Thanks in advance

Answer 1

I consider this as a least square minimization problem. You minimize the norm of the vector function, [f1,f2,...fn] with respect to x0, y0, and r, where fi(x0,y0,r) = (xi-x0)^2 + (yi-y0)^2 - r^2. Here, xi and yi represent your data, and i=1..n.

Then first you create a vector function

function [ f ] = circle_fun( x0, y0, r, xdata, ydata, n )

f = zeros(n,1);
for i=1:n
    f(i) = abs((x0-xdata(i))^2 + (y0-ydata(i))^2 - r^2);
end
end

And use least square minimization function of MATLAB

f = @(inputs) circle_fun(inputs(1),inputs(2),inputs(3), xdata, ydata, n);
v0 = [0.1, 0.1, 0.1];
[v_opt,resnorm] = lsqnonlin(f,v0);

v0 is an initial guess and v_opt is a solution vector that has x0, y0, and r inside.

Answer 2

Besides using the equation for a circle, one could do it manually by calculating the mean center of all points in the (x,y) plane, and then calculating the mean distance between this center and all points.