Fit Circle to Weighted (x,y,w) Data

This program fits a circle to weighted set of 2D data.

weightedFitCircle Fits a circle to a list of datapoints X, Y, and weights W using fminsearch with specifiable options. Initial parameters are obtained using SVD (SVD approach inspired by https://people.cas.uab.edu/~mosya/cl/TaubinSVD.m).

Returns

CXCYout: XY of circle center

Rout: Radius of circle

RMS: Orthogonal, weighted, root mean squared error

exitFlag: Exit condition of fit

Example code showing that fitting is fast and accurate:

X = 1./rand(1, 6); Y = 1./rand(1, 6); W = rand(1, 6);
tic
[CXCYout, Rout, RMSE] = ...
    weightedFitCircle(X, Y, W, optimset('Display', 'Iter')); 
toc
disp(['(X,Y,R) = ', num2str([CXCYout, Rout])])
disp(['RMSE    = ', num2str(RMSE)])
plot(CXCYout(1) + Rout*cos(0:0.00001:2.001*pi), ...
    CXCYout(2) + Rout*sin(0:0.00001:2.001*pi), '--k')
hold on
scatter(X, Y, W/max(W)*75, 'r')
axis equal