ROOT   Reference Guide
Fibonacci.C
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1
2/// \file
3/// \ingroup tutorial_hist
4/// \notebook -js
5/// A TH2Poly build with Fibonacci numbers.
6///
7/// In mathematics, the Fibonacci sequence is a suite of integer in which
8/// every number is the sum of the two preceding one.
9///
10/// The first 10 Fibonacci numbers are:
11///
12/// 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...
13///
14/// This tutorial computes Fibonacci numbers and uses them to build a TH2Poly
15/// producing the "Fibonacci spiral" created by drawing circular arcs connecting
16/// the opposite corners of squares in the Fibonacci tiling.
17///
18/// \macro_image
19/// \macro_code
20///
21/// \author Olivier Couet
22
23void Arc(int n, double a, double r, double *px, double *py);
25
26void Fibonacci(int N=7) {
27 // N = number of Fibonacci numbers > 1
28
29 TCanvas *C = new TCanvas("C", "C", 800, 600);
30 C->SetFrameLineWidth(0);
31
32 TH2Poly *h2pf = new TH2Poly(); // TH2Poly containing Fibonacci bins.
33 h2pf->SetTitle(Form("The first %d Fibonacci numbers",N));
34 h2pf->SetMarkerColor(kRed-2);
35 h2pf->SetStats(0);
36
37 double f0 = 0.;
38 double f1 = 1.;
39 double ft;
40
42
43 for (int i=0; i<=N; i++) {
44 ft = f1;
45 f1 = f0 + f1;
46 f0 = ft;
48 }
49
50 h2pf->Draw("A COL L TEXT");
51}
52
53void Arc(int n, double a, double r, double *px, double *py) {
54 // Add points on a arc of circle from point 2 to n-2
55
56 double da = TMath::Pi()/(2*(n-2)); // Angle delta
57
58 for (int i = 2; i<=n-2; i++) {
59 a = a+da;
60 px[i] = r*TMath::Cos(a) + px[0];
61 py[i] = r*TMath::Sin(a) + py[0];
62 }
63}
64
65void AddFibonacciBin(TH2Poly *h2pf, double N) {
66 // Add to h2pf the bin corresponding to the Fibonacci number N
67
68 double X1 = 0.; //
69 double Y1 = 0.; // Current Fibonacci
70 double X2 = 1.; // square position.
71 double Y2 = 1.; //
72
73 static int MoveId = 0;
74
75 static double T = 1.; //Current Top limit of the bins
76 static double B = 0.; //Current Bottom limit of the bins
77 static double L = 0.; //Current Left limit of the bins
78 static double R = 1.; //Current Right limit of the bins
79
80 const int NP = 50; // Number of point to build the current bin
81 double px[NP]; // Bin's X positions
82 double py[NP]; // Bin's Y positions
83
84 double pi2 = TMath::Pi()/2;
85
86 switch (MoveId) {
87 case 1:
88 R = R+N;
89 X2 = R;
90 Y2 = T;
91 X1 = X2-N;
92 Y1 = Y2-N;
93 px[0] = X1;
94 py[0] = Y2;
95 px[1] = X1;
96 py[1] = Y1;
97 px[NP-1] = X2;
98 py[NP-1] = Y2;
99 Arc(NP,3*pi2,(double)N,px,py);
100 break;
101
102 case 2:
103 T = T+N;
104 X2 = R;
105 Y2 = T;
106 X1 = X2-N;
107 Y1 = Y2-N;
108 px[0] = X1;
109 py[0] = Y1;
110 px[1] = X2;
111 py[1] = Y1;
112 px[NP-1] = X1;
113 py[NP-1] = Y2;
114 Arc(NP,0.,(double)N,px,py);
115 break;
116
117 case 3:
118 L = L-N;
119 X1 = L;
120 Y1 = B;
121 X2 = X1+N;
122 Y2 = Y1+N;
123 px[0] = X2;
124 py[0] = Y1;
125 px[1] = X2;
126 py[1] = Y2;
127 px[NP-1] = X1;
128 py[NP-1] = Y1;
129 Arc(NP,pi2,(double)N,px,py);
130 break;
131
132 case 4:
133 B = B-N;
134 X1 = L;
135 Y1 = B;
136 X2 = X1+N;
137 Y2 = Y1+N;
138 px[0] = X2;
139 py[0] = Y2;
140 px[1] = X1;
141 py[1] = Y2;
142 px[NP-1] = X2;
143 py[NP-1] = Y1;
144 Arc(NP,2*pi2,(double)N,px,py);
145 break;
146 }
147
148 if (MoveId==0) h2pf->AddBin(X1,Y1,X2,Y2); // First bin is a square
149 else h2pf->AddBin(NP, px ,py); // Other bins have an arc of circle
150
151 h2pf->Fill((X1+X2)/2.5, (Y1+Y2)/2.5, N);
152
153 MoveId++;
154 if (MoveId==5) MoveId=1;
155}
156
157
#define R(a, b, c, d, e, f, g, h, i)
Definition: RSha256.hxx:110
@ kRed
Definition: Rtypes.h:66
#define N
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
char * Form(const char *fmt,...)
Formats a string in a circular formatting buffer.
Definition: TString.cxx:2447
virtual void SetMarkerColor(Color_t mcolor=1)
Set the marker color.
Definition: TAttMarker.h:38
The Canvas class.
Definition: TCanvas.h:23
void SetTitle(const char *title) override
Definition: TH1.cxx:6708
void Draw(Option_t *option="") override
Draw this histogram with options.
Definition: TH1.cxx:3070
virtual void SetStats(Bool_t stats=kTRUE)
Set statistics option on/off.
Definition: TH1.cxx:8865
2D Histogram with Polygonal Bins
Definition: TH2Poly.h:66
Int_t Fill(Double_t x, Double_t y) override
Increment the bin containing (x,y) by 1.
Definition: TH2Poly.cxx:589
Adds a new bin to the histogram.
Definition: TH2Poly.cxx:222
const Int_t n
Definition: legend1.C:16
TF1 * f1
Definition: legend1.C:11
static double B[]
static double C[]
double T(double x)
Definition: ChebyshevPol.h:34
static constexpr double pi2
static constexpr double L
Double_t Cos(Double_t)
Returns the cosine of an angle of x radians.
Definition: TMath.h:591
constexpr Double_t Pi()
Definition: TMath.h:37
Double_t Sin(Double_t)
Returns the sine of an angle of x radians.
Definition: TMath.h:585
auto * a
Definition: textangle.C:12