# fitting a circle with fitnlm

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Hoschang Noori on 4 Jul 2020
Edited: Star Strider on 4 Jul 2020
Hello, I tried to fit following data to a circle with help of fitnlm
i used following circle function to determine the center of the circle and the radius:
X = readmatrix('coordinates.txt') %you can find the coordinats.txt in the attachments
circlefun = @(X, b) (X(:,1).^2 + X(:,2).^2 + b(1)*X(:,1) + b(2)*X(:,2) + b(3));
y = zeros(length(X(:,1)),1);
beta0 = [0 0 400];
mdl = fitnlm(X,y,circlefun, beta0)
it gives me following output:
Error using nlinfit (line 219)
MODELFUN must be a function that returns a vector of fitted values the same size as Y (1000-by-1). The model function you provided returned a result that was 1-by-1.
One common reason for a size mismatch is using matrix operators (*, /, ^) in your function instead of the corresponding elementwise operators (.*, ./, .^).
Error in NonLinearModel/fitter (line 1127)
nlinfit(X,y,F,b0,opts,wtargs{:},errormodelargs{:});
Error in classreg.regr.FitObject/doFit (line 94)
model = fitter(model);
Error in NonLinearModel.fit (line 1434)
model = doFit(model);
Error in fitnlm (line 99)
model = NonLinearModel.fit(X,varargin{:});
What I already tried: I used Newton Method for multivariables and the results were quite good in my opinion, but i would like to understand how i can use fitnlm.

Star Strider on 4 Jul 2020
The arguments to ‘circlefun’ are reversed. The parameter vector must always be the first argument, and the independent variable vector (or matrix) must always be the second.
This works:
circlefun = @(b,X) (X(:,1).^2 + X(:,2).^2 + b(1)*X(:,1) + b(2)*X(:,2) + b(3));
and produces:
mdl =
Nonlinear regression model:
y ~ (x1^2 + x2^2 + b1*x1 + b2*x2 + b3)
Estimated Coefficients:
Estimate SE tStat pValue
___________ _______ _______ __________
b1 -156.27 0.79825 -195.76 0
b2 51.732 5.9203 8.7381 9.8825e-18
b3 -3.4442e+05 3394.1 -101.48 0
Number of observations: 1000, Error degrees of freedom: 997
Root Mean Squared Error: 1.08e+03
F-statistic vs. constant model: 0, p-value = 1
.
Image Analyst on 4 Jul 2020
How do you plot the fitted circle once you have the model?
Star Strider on 4 Jul 2020
Edited: Star Strider on 4 Jul 2020
Since it is an implicit equation, the intent appears to be to estimate the parameters. Everything else would be derived from them.
EDIT — (4 Jul 2020 at 17:55)
The plot is relatively straightforward:
B = mdl.Coefficients.Estimate;
Xm = -B(1)/2;
Ym = -B(2)/2;
R = sqrt((Xm^2 + Ym^2) - B(3));
A = atan2(X(:,2)-Ym, X(:,1)-Xm);
Ycir = R*sin(A) + Ym;
Xcir = R*cos(A) + Xm;
figure
plot(X(:,1), X(:,2), 'p')
hold on
plot(Xcir, Ycir, '-r', 'LineWidth',2)
hold off
grid
axis('equal')
producing:
.

Image Analyst on 4 Jul 2020
Hoschang Noori on 4 Jul 2020
Edited: Hoschang Noori on 4 Jul 2020
Thanks, I know the FAQ, i saw some posts from you about this elsewhere. :D The solution presented there works quite well for circles with few outliers, but it seems not to be robust enough for my purposes since i have some noise + some more circles in my data.