#include <iostream>
#include "TRandom3.h"
#include "TCanvas.h"
#include "TStyle.h"
#include "TTree.h"

int isotropic_3d(){
  TRandom3 *ran = new TRandom3();
  const double pi = 4*atan(1.0);
  
  TTree *t = new TTree("t","tree for isotropic 3d");
  
  Double_t theta, phi, x, y, z;
  t->Branch("theta",&theta,"theta/D");
  t->Branch("phi",&phi,"phi/D");
  t->Branch("x",&x,"x/D");
  t->Branch("y",&y,"y/D");
  t->Branch("z",&z,"z/D");
  
  for (int i=0; i<50000; i++){
    theta = acos(-ran->Uniform(-1.0,1.0));
    phi   = ran->Uniform(0.0,2*pi);
    x     = sin(theta)*cos(phi);
    y     = sin(theta)*sin(phi);
    z     = cos(theta);
    t->Fill();
  }

  TCanvas *c1 = new TCanvas("c1", "c1");
  gStyle->SetPadTopMargin(0.15);
  gStyle->SetLabelSize(0.05,"XYZ");
  gStyle->SetTitleSize(0.10,"");
  gStyle->SetTitleXSize(0.05);
  gStyle->SetTitleXSize(0.05);
  gStyle->SetTitleYSize(0.05);

  c1->Divide(3,3);
  c1->cd(1);
  t->Draw("z:y:x","(x>0)&&(y>0)&&(z>0)");
  c1->cd(2);
  t->Draw("theta");
  c1->cd(3);
  t->Draw("phi");
  c1->cd(4);
  t->Draw("x");
  c1->cd(5);
  t->Draw("y");
  c1->cd(6);
  t->Draw("z");
  c1->cd(7);
  t->Draw("y:x");
  c1->cd(8);
  t->Draw("z:x");
  c1->cd(9);
  t->Draw("z:y");
  return 0;
}