gr201_waves.C

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/// \file
/// \ingroup tutorial_graphs
/// \notebook
/// \preview Draw spherical waves interference. Two closed TGraphs filled with white are used
/// here to draw triangles on top of a 2D function in order to hide parts of it.
///
/// \macro_image
/// \macro_code
/// \author Otto Schaile
 
#include "TROOT.h"
#include "TCanvas.h"
#include "TColor.h"
#include "TArc.h"
#include "TGraph.h"
#include "TF2.h"
#include "TLine.h"
#include "TLatex.h"
#include "TMath.h"
#include "TStyle.h"
 
//______________________________________________________________
Double_t interference( Double_t *x, Double_t *par)
{
   Double_t x_p2 = x[0] * x[0];
   Double_t d_2 = 0.5 * par[2];
   Double_t ym_p2 = (x[1] - d_2) * (x[1] - d_2);
   Double_t yp_p2 = (x[1] + d_2) * (x[1] + d_2);
   Double_t  tpi_l = TMath::Pi() /  par[1];
   Double_t amplitude = par[0] * (cos(tpi_l  * sqrt(x_p2 + ym_p2))
                      + par[3] * cos(tpi_l  * sqrt(x_p2 + yp_p2)));
   return amplitude * amplitude;
}
 
 
//_____________________________________________________________
Double_t result( Double_t *x, Double_t *par)
{
   Double_t xint[2];
   Double_t  maxintens = 0, xcur = 14;
   Double_t dlambda = 0.1 * par[1];
   for(Int_t i=0; i<10; i++){
      xint[0] = xcur;
      xint[1] = x[1];
      Double_t  intens = interference(xint, par);
      if(intens > maxintens) maxintens = intens;
      xcur -= dlambda;
   }
   return maxintens;
}
 
 
//_____________________________________________________________
void gr201_waves( Double_t d = 3, Double_t lambda = 1, Double_t amp = 10)
{
   TCanvas *c1 = new TCanvas("gr201_waves", "A double slit experiment", 300, 40, 1004, 759);
   c1->Range(0, -10,  30, 10);
   c1->SetFillColor(0);
   TPad *pad = new TPad("pr", "pr", 0.5, 0, 1., 1);
   pad->Range(0, -10, 15, 10);
   pad->Draw();
 
   const Int_t colNum = 30;
   Int_t palette[colNum];
   for (Int_t i = 0; i < colNum; i++) {
      Float_t level = 1.*i/colNum;
      palette[i] = TColor::GetColor((Float_t) TMath::Power(level,0.3), (Float_t) TMath::Power(level,0.3), (Float_t) 0.5*level);
      // palette[i] = 1001+i;
   }
   gStyle->SetPalette(colNum, palette);
 
   c1->cd();
 
   // For the incoming waves, on the left side, we use a TF2 and increase the number
   // of points used for drawing to 200 (default is 100) for better resolution
   TF2 *f0 = new TF2("ray_source", interference, 0.02, 15, -8, 8, 4);
   f0->SetParameters(amp, lambda, 0, 0);
   f0->SetNpx(200);
   f0->SetNpy(200);
   f0->SetContour(colNum-2);
   f0->Draw("samecol");
 
   TLatex title;
   title.DrawLatex(1.6, 8.5, "A double slit experiment");
 
   // Draw 2 white triangles to cover parts of f0, simulating a cone
   // (change the fill color to see these)
   TGraph *graph = new TGraph(4);
   graph->SetFillColor(1);
   graph->SetFillStyle(1001);
   graph->SetLineWidth(0);
   graph->SetPoint(0, 0., 0.1);
   graph->SetPoint(1, 14.8, 8);
   graph->SetPoint(2, 0, 8);
   graph->SetPoint(3, 0, 0.1);
   graph->Draw("F");
 
   graph = new TGraph(4);
   graph->SetFillColor(1);
   graph->SetFillStyle(1001);
   graph->SetLineWidth(0);
   graph->SetPoint(0, 0, -0.1);
   graph->SetPoint(1, 14.8, -8);
   graph->SetPoint(2, 0, -8);
   graph->SetPoint(3, 0, -0.1);
   graph->Draw("F");
 
   // To represent the wall with 2 openings, we draw 3 black vertical lines
   TLine * line = new TLine(15,-10, 15, 0 - 0.5*d - 0.2);
   line->SetLineWidth(10);
   line->Draw();
 
   line = new TLine(15, 0 - 0.5*d + 0.2, 15, 0 + 0.5*d - 0.2);
   line->SetLineWidth(10);
   line->Draw();
 
   line = new TLine(15, 0 + 0.5*d + 0.2, 15, 10);
   line->SetLineWidth(10);
   line->Draw();
 
   pad->cd();
 
   // Interference plot, on the centre-right side
   TF2 *finter = new TF2("interference",interference, 0.01, 14, -10, 10, 4);
   finter->SetParameters(amp, lambda, d, 1);
   finter->SetNpx(200);
   finter->SetNpy(200);
   finter->SetContour(colNum-2);
   finter->Draw("samecol");
 
   // Some lines
   TArc arc;
   arc.SetFillStyle(0);
   arc.SetLineWidth(2);
   arc.SetLineColor(5);
   Float_t r = 0.5 * lambda, dr = lambda;
   for (Int_t i = 0; i < 16; i++) {
      arc.DrawArc(0,  0.5*d, r, 0., 360., "only");
      arc.DrawArc(0, -0.5*d, r, 0., 360., "only");
      r += dr;
   }
 
   pad->cd();
 
   // Result, on the right edge
   TF2 *fresult = new TF2("result",result, 14, 15, -10, 10, 4);
   fresult->SetParameters(amp, lambda, d, 1);
   fresult->SetNpx(300);
   fresult->SetNpy(300);
   fresult->SetContour(colNum-2);
   fresult->Draw("samecol");
 
   // Vertical white line on the right side
   line = new TLine(14,-10, 14, 10);
   line->SetLineWidth(10); line->SetLineColor(0); line->Draw();
   c1->Modified(kTRUE);
   c1->Update();
   c1->SetEditable(kTRUE);
}