# 2.2.3 函数与图形

## 基本函数表达

#### root中的函数表达和C语言重合，例如:

* `sin(x)/x`
* `[0]*sin(x) + [1]*exp(-[2]*x)`
* `x + y**2`
* `x^2 + y^2`
* `[0]*pow([1],4)`
* `2*pi*sqrt(x/y)`
* `gaus(0)*expo(3) + ypol3(5)*x`
* `gausn(0)*expo(3) + ypol3(5)*x`
* `gaus(x, [0..2]) + expo(y, [3..4])`

在以上最后一个示例中：

* `gaus(0)` 是 `[0]*exp(-0.5*((x-[1])/[2])**2)` 的简写形式，`(0)` 表示从 0 开始编号参数。
* `gausn(0)` 是 `[0]*exp(-0.5*((x-[1])/[2])**2)/(sqrt(2*pi)*[2]))` 的简写形式，`(0)` 表示从 0 开始编号参数。
* `expo(3)` 是 `exp([3]+[4]*x)` 的简写形式。
* `pol3(5)` 是 `par[5]+par[6]*x+par[7]*x**2+par[8]*x**3` 的简写形式（`PolN` 表示 N 次多项式）。
* `gaus(x, [0..2])` 是 `gaus(0)` 的一种更明确的写法。
* `expo(y, [3..4])` 是 `exp([3]+[4]*y)` 的简写形式。

[`TMath`](https://root.cern/doc/master/namespaceTMath.html) 作为表达式的一部分:

* `TMath::Landau(x)*sin(x)`
* `TMath::Erf(x)`

公式可以包含常量，例如：

* `sqrt2`
* `e`
* `pi`
* `ln10`
* `infinity`

e.g. 两个简单的例子

```c
{
   auto fa1 = new TF1("fa1","sin(x)/x",0,10);
   fa1->Draw();
}
```

<figure><img src="https://1447085975-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2Fpf9IsLOaNy0SNtz1zmqo%2Fuploads%2Ft404PfPsDocTmcWzW0E1%2Fpict1_TF1_001.png?alt=media&#x26;token=5ed2c8c8-17f1-4b10-85bd-5938f15f0b9a" alt="" width="563"><figcaption></figcaption></figure>

```c
{
    auto f2 = new TF2("f2","sin(x)*sin(y)/(x*y)",0,5,0,5);
    f2->Draw();
}
```

<figure><img src="https://1447085975-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2Fpf9IsLOaNy0SNtz1zmqo%2Fuploads%2FZutsbTSf0rIXApM55BwG%2Fpict1_TF2_001.png?alt=media&#x26;token=4bc8fbe7-d6d9-466a-b85a-047a8fca6892" alt="" width="563"><figcaption></figcaption></figure>

## 直线 TLine

```
root[] l = new TLine(0.2,0.2,0.8,0.3)
root[] l->Draw()
```

<details>

<summary>仿造 python 的致密网格</summary>

```c
void DrawGrid(TString t, Int_t ngx, Int_t ngy)
{
   Double_t x1 = -10;
   Double_t x2 = 20;
   Double_t y1 = 10;
   Double_t y2 = 40;
   Double_t xs = (x2-x1)/ngx;
   Double_t ys = (y2-y1)/ngy;
   Int_t i;

   TH1F *h = gPad->DrawFrame(x1, y1, x2, y2);
   h->GetXaxis()->SetNdivisions(20);
   h->GetYaxis()->SetNdivisions(20);
   h->GetYaxis()->SetTickLength(0.);
   h->GetXaxis()->SetTickLength(0.);
   h->GetXaxis()->SetLabelSize(0.025);
   h->GetYaxis()->SetLabelSize(0.025);
   h->SetTitle(t.Data());
   gPad-> Update();

   TLine l;
   l.SetLineColor(kGray);
   Double_t x = x1+xs;
   for (i = 0; i<ngx-1; i++) {
      l.DrawLine(x,y1,x,y2);
      x = x + xs;
   }

   Double_t y = y1+xs;
   for (i = 0; i<ngy-1; i++) {
      l.DrawLine(x1,y,x2,y);
      y = y +ys;
   }
}

void ofirar()
{
   TCanvas *c = new TCanvas("c","c", 800, 800);

   Double_t x[10] = {1.,2.,3.,4.,5.,-1.,-2.,-6.,-7.,-8.};
   Double_t y[10] = {21.,21.,23.,34.,35.,21.,22.,36.,37.,28.};
   TGraph *before = new TGraph(10, x, y);
   before->SetTitle("Before");
   before->SetMarkerStyle(kFullCircle);
   before->SetMarkerColor(kBlue);
   DrawGrid("Before/After plot", 100, 100);
   before->Draw("P");

//   Double_t a[10] = {-1.,2.,-3.,4.,-5.,1.,2.,-6.,7.,-8.};
//   Double_t b[10] = {25.,24.,22.,31.,32.,27.,23.,35.,38.,22.};
   Double_t a[10] = {-1.,2.,-3.,4.,-5.,1.,2.,-6.,7.,-8.};
   Double_t b[10] = {25.,24.,22.,31.,32.,27.,23.,35.,38.,22.};
   TGraph *after = new TGraph(10, a, b);
   after->SetMarkerStyle(kFullCircle);
   after->SetMarkerColor(kRed);
   after->Draw("P");
}
```

</details>

## 箭头 TArrow

```c
TArrow *ar = new TArrow(4,0.2,4,4.5,0.02,"|>");ar->SetLineWidth(3); ar->SetArrowSize(0.02);ar->Draw();
```

箭头方向可以控制。e.g. `ar4->[SetAngle](60);`。

**参考：**[classTArrow](https://root.cern/doc/master/classTArrow.html)

## 矩形 TBox

```c
b = new TBox(0.2,0.2,0.8,0.3); b->SetFillColor(5); b->SetFillStyle(3001); b->Draw();
```

## 矩形文本框 TPaveLabel

```c
TPaveText *pave = new TPaveText(-3.78,500,-1.2,750);
	TText *t1=pave->AddText("You can move");
	t1->SetTextColor(4);
	t1->SetTextSize(0.05);
	pave->AddText("Title and Stats pads");
	pave->AddText("X and Y axis");
	pave->AddText("You can modify bin contents");
	pave->Draw();
	c1->Update();
```

## 椭圆 TEllipse

TEllipse是很强大的类，它能帮你绘制椭圆、圆、半圆、倾斜的椭圆等，其标准用如下：

```c
TEllipse *ellipse;  // 设置PSF于Pad
        ellipse = new TEllipse(Ra[i]+w2*3/5.,Dec[i]-w*3/5.,R[i]*1.51/cos(Dec[i]/57.3),R[i]*1.51,0,270,60);   // TEllipse(椭圆在Pad中的横坐标,纵坐标,长轴,短轴,phimax,phimin,theta)
        ellipse->SetFillStyle(0);   // 设置PSF的填充风格为0，意为不填充，默认不填充
        ellipse->SetLineWidth(2);   // 设置PSF线宽为2
        ellipse->SetLineColor(3);   // 设置PSF的轮廓色为3，绿色
        ellipse->Draw();    // 将PSF添加至画布

```

## 蜂巢图

<details>

<summary>e.g.</summary>

```c
void th2polyHoneycomb(){
   TCanvas *C = new TCanvas("C", "C", 1200, 600);
   C->Divide(2,1);
 
   TH2Poly *hc1 = new TH2Poly();
   hc1->Honeycomb(0, 0, .1, 5, 5);
   hc1->SetTitle("Option V (default)");
   hc1->SetStats(0);
   hc1->Fill(.1, .1, 15.);
   hc1->Fill(.4, .4, 10.);
   hc1->Fill(.5, .5, 20.);
 
   TH2Poly *hc2 = new TH2Poly();
   hc2->Honeycomb(0, 0, .1, 5, 5, "h");
   hc2->SetTitle("Option H");
   hc2->SetStats(0);
   hc2->Fill(.1, .1, 15.);
   hc2->Fill(.4, .4, 10.);
   hc2->Fill(.5, .5, 20.);
 
   C->cd(1)->SetGrid();
   hc1->Draw("colz L");
   C->cd(2)->SetGrid();
   hc2->Draw("colz L");
}
```

</details>

## 多边形

<details>

<summary>polygon</summary>

```c
{
   Double_t x[5] = {.2,.6,.7,.25,.2};
   Double_t y[5] = {.5,.1,.9,.7,.5};
   TPolyLine *pline = new TPolyLine(5,x,y);
   pline->SetFillColor(38);
   pline->SetLineColor(2);
   pline->SetLineWidth(4);
   pline->Draw("f");
   pline->Draw();
}
```

</details>

<details>

<summary>e.g.</summary>

```c
void inside() {
   auto el = new TEllipse(0.75, 0.25, .2,.15,45,315,62);
   el->Draw();
 
   auto gr = new TGraph();
   double gr_x1[5] = {0.1, 0.3388252, 0.03796561, 0.4176218, 0.1};
   double gr_y1[5] = {0.5, 0.9644737, 0.7776316, 0.6960526, 0.5};
   gr = new TGraph(5, gr_x1, gr_y1);
   gr->Draw("L");
 
   auto bx = new TBox(.7, .8, .9, .95);
   bx->Draw();
 
   auto pv = new TPave(.05, .1, .3, .2);
   pv->Draw();
 
   auto di = new TDiamond(.05, .25, .3, .4);
   di->Draw();
 
   auto cr = new TCrown(.5, .5, .1, .15);
   cr->SetFillColor(19);
   cr->Draw();
 
   for (int i = 0; i < 10000; i++) {
      double x = gRandom->Rndm();
      double y = gRandom->Rndm();
      auto p = new TMarker(x,y,7);
      p->Draw();
      if (el->IsInside(x,y) || bx->IsInside(x,y) || pv->IsInside(x,y) || di->IsInside(x,y) || cr->IsInside(x,y) ||
          gr->IsInside(x,y)) {
         p->SetMarkerColor(kGreen);
      } else {
         p->SetMarkerColor(kRed);
      }
   }
}
```

</details>

## 地图

<details>

<summary>USAmap</summary>

```csharp
void th2polyUSA()
{
   Int_t i, bin;
   const Int_t nx = 48;
   const char *states [nx] = {
      "alabama",      "arizona",        "arkansas",       "california",
      "colorado",     "connecticut",    "delaware",       "florida",
      "georgia",      "idaho",          "illinois",       "indiana",
      "iowa",         "kansas",         "kentucky",       "louisiana",
      "maine",        "maryland",       "massachusetts",  "michigan",
      "minnesota",    "mississippi",    "missouri",       "montana",
      "nebraska",     "nevada",         "new_hampshire",  "new_jersey",
      "new_mexico",   "new_york",       "north_carolina", "north_dakota",
      "ohio",         "oklahoma",       "oregon",         "pennsylvania",
      "rhode_island", "south_carolina", "south_dakota",   "tennessee",
      "texas",        "utah",           "vermont",        "virginia",
      "washington",   "west_virginia",  "wisconsin",      "wyoming"
   };
   Double_t pop[nx] = {
    4708708, 6595778,  2889450, 36961664, 5024748,  3518288,  885122, 18537969,
    9829211, 1545801, 12910409,  6423113, 3007856,  2818747, 4314113,  4492076,
    1318301, 5699478,  6593587,  9969727, 5266214,  2951996, 5987580,   974989,
    1796619, 2643085,  1324575,  8707739, 2009671, 19541453, 9380884,   646844,
   11542645, 3687050,  3825657, 12604767, 1053209,  4561242,  812383,  6296254,
   24782302, 2784572,   621760,  7882590, 6664195,  1819777, 5654774,   544270
   };
 
   TCanvas *usa = new TCanvas("USA", "USA");
   usa->ToggleEventStatus();
   Double_t lon1 = -130;
   Double_t lon2 = -65;
   Double_t lat1 = 24;
   Double_t lat2 = 50;
   TH2Poly *p = new TH2Poly("USA","USA Population",lon1,lon2,lat1,lat2);
 
   TFile::SetCacheFileDir(".");
   TFile *f = TFile::Open("http://root.cern.ch/files/usa.root", "CACHEREAD");
 
   if (!f) {
      printf("Cannot access usa.root. Is internet working ?\n");
      return;
   }
 
   // Define the TH2Poly bins.
   TMultiGraph *mg;
   TKey *key;
   TIter nextkey(gDirectory->GetListOfKeys());
   while ((key = (TKey*)nextkey())) {
      TObject *obj = key->ReadObj();
      if (obj->InheritsFrom("TMultiGraph")) {
         mg = (TMultiGraph*)obj;
         bin = p->AddBin(mg);
      }
   }
 
   // Fill TH2Poly.
   for (i=0; i<nx; i++) p->Fill(states[i], pop[i]);
 
   gStyle->SetOptStat(11);
   p->Draw("colz textn");
}

```

</details>

* 等高线绘法：<https://root-forum.cern.ch/t/th2d-contour-lines/19860>
* 经纬度绘法：<https://root-forum.cern.ch/t/problem-drawing-aitoff-and-tgraph-together/6498/3>

## 费曼图

<details>

<summary>e.g.</summary>

```c
void feynman()
{
   TCanvas *c1 = new TCanvas("c1", "A canvas", 10, 10, 600, 300);
   c1->Range(0, 0, 140, 60);
   Int_t linsav = gStyle->GetLineWidth();
   gStyle->SetLineWidth(3);
   TLatex t;
   t.SetTextAlign(22);
   t.SetTextSize(0.1);
   TLine *l;
   l = new TLine(10, 10, 30, 30);
   l->Draw();
   l = new TLine(10, 50, 30, 30);
   l->Draw();
   TCurlyArc *ginit = new TCurlyArc(30, 30, 12.5 * sqrt(2), 135, 225);
   ginit->SetWavy();
   ginit->Draw();
   t.DrawLatex(7, 6, "e^{-}");
   t.DrawLatex(7, 55, "e^{+}");
   t.DrawLatex(7, 30, "#gamma");
 
   TCurlyLine *Gamma = new TCurlyLine(30, 30, 55, 30);
   Gamma->SetWavy();
   Gamma->Draw();
   t.DrawLatex(42.5, 37.7, "#gamma");
 
   TArc *a = new TArc(70, 30, 15);
   a->Draw();
   t.DrawLatex(55, 45, "#bar{q}");
   t.DrawLatex(85, 15, "q");
   TCurlyLine *gluon = new TCurlyLine(70, 45, 70, 15);
   gluon->Draw();
   t.DrawLatex(77.5, 30, "g");
 
   TCurlyLine *z0 = new TCurlyLine(85, 30, 110, 30);
   z0->SetWavy();
   z0->Draw();
   t.DrawLatex(100, 37.5, "Z^{0}");
 
   l = new TLine(110, 30, 130, 10);
   l->Draw();
   l = new TLine(110, 30, 130, 50);
   l->Draw();
 
   TCurlyArc *gluon1 = new TCurlyArc(110, 30, 12.5 * sqrt(2), 315, 45);
   gluon1->Draw();
 
   t.DrawLatex(135, 6, "#bar{q}");
   t.DrawLatex(135, 55, "q");
   t.DrawLatex(135, 30, "g");
   c1->Update();
   gStyle->SetLineWidth(linsav);
}
```

</details>