Logo ROOT  
Reference Guide
waves.C
Go to the documentation of this file.
1/// \file
2/// \ingroup tutorial_graphs
3/// \notebook
4/// Hint: Spherical waves
5///
6/// \macro_image
7/// \macro_code
8///
9/// \author Otto Schaile
10
11#include "TROOT.h"
12#include "TCanvas.h"
13#include "TColor.h"
14#include "TArc.h"
15#include "TGraph.h"
16#include "TF2.h"
17#include "TLine.h"
18#include "TLatex.h"
19#include "TMath.h"
20#include "TStyle.h"
21
22//______________________________________________________________
23Double_t interference( Double_t *x, Double_t *par)
24{
25 Double_t x_p2 = x[0] * x[0];
26 Double_t d_2 = 0.5 * par[2];
27 Double_t ym_p2 = (x[1] - d_2) * (x[1] - d_2);
28 Double_t yp_p2 = (x[1] + d_2) * (x[1] + d_2);
29 Double_t tpi_l = TMath::Pi() / par[1];
30 Double_t amplitude = par[0] * (cos(tpi_l * sqrt(x_p2 + ym_p2))
31 + par[3] * cos(tpi_l * sqrt(x_p2 + yp_p2)));
32 return amplitude * amplitude;
33}
34
35
36//_____________________________________________________________
38{
39 Double_t xint[2];
40 Double_t maxintens = 0, xcur = 14;
41 Double_t dlambda = 0.1 * par[1];
42 for(Int_t i=0; i<10; i++){
43 xint[0] = xcur;
44 xint[1] = x[1];
45 Double_t intens = interference(xint, par);
46 if(intens > maxintens) maxintens = intens;
47 xcur -= dlambda;
48 }
49 return maxintens;
50}
51
52
53//_____________________________________________________________
54void waves( Double_t d = 3, Double_t lambda = 1, Double_t amp = 10)
55{
56 TCanvas *c1 = new TCanvas("waves", "A double slit experiment", 300, 40, 1004, 759);
57 c1->Range(0, -10, 30, 10);
58 c1->SetFillColor(0);
59 TPad *pad = new TPad("pr","pr", 0.5, 0 , 1., 1);
60 pad->Range(0, -10, 15, 10);
61 pad->Draw();
62
63 const Int_t colNum = 30;
64 Int_t palette[colNum];
65 for (Int_t i=0;i<colNum;i++) {
66 Float_t level = 1.*i/colNum;
67 palette[i] = TColor::GetColor((Float_t) TMath::Power(level,0.3), (Float_t) TMath::Power(level,0.3), (Float_t) 0.5*level);
68 // palette[i] = 1001+i;
69 }
70 gStyle->SetPalette(colNum, palette);
71
72 c1->cd();
73
74 TF2 *f0 = new TF2("ray_source",interference, 0.02, 15, -8, 8, 4);
75 f0->SetParameters(amp, lambda, 0, 0);
76 f0->SetNpx(200);
77 f0->SetNpy(200);
78 f0->SetContour(colNum-2);
79 f0->Draw("samecol");
80
81 TLatex title;
82 title.DrawLatex(1.6, 8.5, "A double slit experiment");
83
84 TGraph *graph = new TGraph(4);
85 graph->SetFillColor(0);
86 graph->SetFillStyle(1001);
87 graph->SetLineWidth(0);
88 graph->SetPoint(0, 0., 0.1);
89 graph->SetPoint(1, 14.8, 8);
90 graph->SetPoint(2, 0, 8);
91 graph->SetPoint(3, 0, 0.1);
92 graph->Draw("F");
93
94 graph = new TGraph(4);
95 graph->SetFillColor(0);
96 graph->SetFillStyle(1001);
97 graph->SetLineWidth(0);
98 graph->SetPoint(0, 0, -0.1);
99 graph->SetPoint(1, 14.8, -8);
100 graph->SetPoint(2, 0, -8);
101 graph->SetPoint(3, 0, -0.1);
102 graph->Draw("F");
103
104 TLine * line = new TLine(15,-10, 15, 0 - 0.5*d -0.2);
105 line->SetLineWidth(10);
106 line->Draw();
107
108 line = new TLine(15, 0 - 0.5*d +0.2 ,15, 0 + 0.5*d -0.2);
109 line->SetLineWidth(10);
110 line->Draw();
111
112 line = new TLine(15,0 + 0.5*d + 0.2,15, 10);
113 line->SetLineWidth(10);
114 line->Draw();
115
116 pad ->cd();
117
118 TF2 *finter = new TF2("interference",interference, 0.01, 14, -10, 10, 4);
119 finter->SetParameters(amp, lambda, d, 1);
120 finter->SetNpx(200);
121 finter->SetNpy(200);
122 finter->SetContour(colNum-2);
123 finter->Draw("samecol");
124
125 TArc arc;
126 arc.SetFillStyle(0);
127 arc.SetLineWidth(2);
128 arc.SetLineColor(5);
129 Float_t r = 0.5 * lambda, dr = lambda;
130 for (Int_t i = 0; i < 16; i++) {
131 arc.DrawArc(0, 0.5*d, r, 0., 360., "only");
132 arc.DrawArc(0, -0.5*d, r, 0., 360., "only");
133 r += dr;
134 }
135
136 pad ->cd();
137
138 TF2 *fresult = new TF2("result",result, 14, 15, -10, 10, 4);
139 fresult->SetParameters(amp, lambda, d, 1);
140 fresult->SetNpx(300);
141 fresult->SetNpy(300);
142 fresult->SetContour(colNum-2);
143 fresult->Draw("samecol");
144
145 line = new TLine(13.8,-10, 14, 10);
147 c1->Modified(kTRUE);
148 c1->Update();
149 c1->SetEditable(kTRUE);
150}
#define d(i)
Definition: RSha256.hxx:102
int Int_t
Definition: RtypesCore.h:45
float Float_t
Definition: RtypesCore.h:57
double Double_t
Definition: RtypesCore.h:59
const Bool_t kTRUE
Definition: RtypesCore.h:100
Option_t Option_t TPoint TPoint const char GetTextMagnitude GetFillStyle GetLineColor GetLineWidth GetMarkerStyle GetTextAlign GetTextColor GetTextSize void char Point_t Rectangle_t WindowAttributes_t Float_t r
Option_t Option_t TPoint TPoint const char GetTextMagnitude GetFillStyle GetLineColor GetLineWidth GetMarkerStyle GetTextAlign GetTextColor GetTextSize void char Point_t Rectangle_t WindowAttributes_t Float_t Float_t Float_t Int_t Int_t UInt_t UInt_t Rectangle_t result
R__EXTERN TStyle * gStyle
Definition: TStyle.h:414
Create an Arc.
Definition: TArc.h:26
virtual TArc * DrawArc(Double_t x1, Double_t y1, Double_t radius, Double_t phimin=0, Double_t phimax=360, Option_t *option="")
Draw this arc with new coordinates.
Definition: TArc.cxx:79
virtual void SetFillStyle(Style_t fstyle)
Set the fill area style.
Definition: TAttFill.h:39
virtual void SetLineWidth(Width_t lwidth)
Set the line width.
Definition: TAttLine.h:43
virtual void SetLineColor(Color_t lcolor)
Set the line color.
Definition: TAttLine.h:40
The Canvas class.
Definition: TCanvas.h:23
static Int_t GetColor(const char *hexcolor)
Static method returning color number for color specified by hex color string of form: "#rrggbb",...
Definition: TColor.cxx:1823
virtual void SetNpx(Int_t npx=100)
Set the number of points used to draw the function.
Definition: TF1.cxx:3477
virtual void SetParameters(const Double_t *params)
Definition: TF1.h:649
A 2-Dim function with parameters.
Definition: TF2.h:29
virtual void SetContour(Int_t nlevels=20, const Double_t *levels=nullptr)
Set the number and values of contour levels.
Definition: TF2.cxx:919
virtual void SetNpy(Int_t npy=100)
Set the number of points used to draw the function.
Definition: TF2.cxx:954
void Draw(Option_t *option="") override
Draw this function with its current attributes.
Definition: TF2.cxx:259
A TGraph is an object made of two arrays X and Y with npoints each.
Definition: TGraph.h:41
To draw Mathematical Formula.
Definition: TLatex.h:18
TLatex * DrawLatex(Double_t x, Double_t y, const char *text)
Make a copy of this object with the new parameters And copy object attributes.
Definition: TLatex.cxx:1928
Use the TLine constructor to create a simple line.
Definition: TLine.h:22
virtual void Draw(Option_t *option="")
Default Draw method for all objects.
Definition: TObject.cxx:274
The most important graphics class in the ROOT system.
Definition: TPad.h:28
void Range(Double_t x1, Double_t y1, Double_t x2, Double_t y2) override
Set world coordinate system for the pad.
Definition: TPad.cxx:5165
TVirtualPad * cd(Int_t subpadnumber=0) override
Set Current pad.
Definition: TPad.cxx:598
void Draw(Option_t *option="") override
Draw Pad in Current pad (re-parent pad if necessary).
Definition: TPad.cxx:1268
void SetPalette(Int_t ncolors=kBird, Int_t *colors=nullptr, Float_t alpha=1.)
See TColor::SetPalette.
Definition: TStyle.cxx:1781
TLine * line
RVec< PromoteType< T > > cos(const RVec< T > &v)
Definition: RVec.hxx:1798
return c1
Definition: legend1.C:41
Double_t x[n]
Definition: legend1.C:17
VecExpr< UnaryOp< Sqrt< T >, VecExpr< A, T, D >, T >, T, D > sqrt(const VecExpr< A, T, D > &rhs)
LongDouble_t Power(LongDouble_t x, LongDouble_t y)
Returns x raised to the power y.
Definition: TMath.h:719
constexpr Double_t Pi()
Definition: TMath.h:37
Definition: graph.py:1