fitCircle.C: Generate points distributed with some errors around a circle

//Generate points distributed with some errors around a circle
//Fit a circle through the points and draw
//To run the script, do, eg
//   root > .x fitCircle.C   (10000 points by default)
//   root > .x fitCircle.C(100);  (with only 100 points
//   root > .x fitCircle.C(100000);  with ACLIC
//
//Author: Rene Brun

#include "TCanvas.h"
#include "TRandom3.h"
#include "TGraph.h"
#include "TMath.h"
#include "TArc.h"
#include "TVirtualFitter.h"

TGraph *gr;

//____________________________________________________________________
void myfcn(Int_t &, Double_t *, Double_t &f, Double_t *par, Int_t) {
   //minimisation function computing the sum of squares of residuals
   Int_t np = gr->GetN();
   f = 0;
   Double_t *x = gr->GetX();
   Double_t *y = gr->GetY();
   for (Int_t i=0;i<np;i++) {
      Double_t u = x[i] - par[0];
      Double_t v = y[i] - par[1];
      Double_t dr = par[2] - TMath::Sqrt(u*u+v*v);
      f += dr*dr;
   }
}

//____________________________________________________________________
void fitCircle(Int_t n=10000) {
   //generates n points around a circle and fit them
   TCanvas *c1 = new TCanvas("c1","c1",600,600);
   c1->SetGrid();
   gr = new TGraph(n);
   if (n> 999) gr->SetMarkerStyle(1);
   else        gr->SetMarkerStyle(3);
   TRandom3 r;
   Double_t x,y;
   for (Int_t i=0;i<n;i++) {
      r.Circle(x,y,r.Gaus(4,0.3));
      gr->SetPoint(i,x,y);
   }
   c1->DrawFrame(-5,-5,5,5);
   gr->Draw("p");

   //Fit a circle to the graph points
   TVirtualFitter::SetDefaultFitter("Minuit");  //default is Minuit
   TVirtualFitter *fitter = TVirtualFitter::Fitter(0, 3);
   fitter->SetFCN(myfcn);

   fitter->SetParameter(0, "x0",   0, 0.1, 0,0);
   fitter->SetParameter(1, "y0",   0, 0.1, 0,0);
   fitter->SetParameter(2, "R",    1, 0.1, 0,0);

   Double_t arglist[1] = {0};
   fitter->ExecuteCommand("MIGRAD", arglist, 0);

   //Draw the circle on top of the points
   TArc *arc = new TArc(fitter->GetParameter(0),
      fitter->GetParameter(1),fitter->GetParameter(2));
   arc->SetLineColor(kRed);
   arc->SetLineWidth(4);
   arc->Draw();
}