%%cpp -d
#include "TCanvas.h"
#include "TRandom3.h"
#include "TGraph.h"
#include "TMath.h"
#include "TArc.h"
#include "Fit/Fitter.h"
#include <Math/Functor.h>

int n=10000;

TCanvas *c1 = new TCanvas("c1","c1",600,600);
c1->SetGrid();
TGraph* gr = new TGraph(n);
if (n> 999) gr->SetMarkerStyle(1);
else        gr->SetMarkerStyle(3);
TRandom3 r;
double x,y;
for (int 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");


auto chi2Function = [&](const double *par) {
   //minimisation function computing the sum of squares of residuals
   // looping at the graph points
   int np = gr->GetN();
   double f = 0;
   double *x = gr->GetX();
   double *y = gr->GetY();
   for (int i=0;i<np;i++) {
      double u = x[i] - par[0];
      double v = y[i] - par[1];
      double dr = par[2] - std::sqrt(u*u+v*v);
      f += dr*dr;
   }
   return f;
};

ROOT::Math::Functor fcn(chi2Function,3);
ROOT::Fit::Fitter  fitter;


double pStart[3] = {0,0,1};
fitter.SetFCN(fcn, pStart);
fitter.Config().ParSettings(0).SetName("x0");
fitter.Config().ParSettings(1).SetName("y0");
fitter.Config().ParSettings(2).SetName("R");

bool ok = fitter.FitFCN();
if (!ok) {
   Error("line3Dfit","Line3D Fit failed");
}

const ROOT::Fit::FitResult & result = fitter.Result();
result.Print(std::cout);

TArc *arc = new TArc(result.Parameter(0),result.Parameter(1),result.Parameter(2));
arc->SetLineColor(kRed);
arc->SetLineWidth(4);
arc->SetFillStyle(0);
arc->Draw();

gROOT->GetListOfCanvases()->Draw()