2d Polar Histogram

ROOT
1

I am attempting to draw a 2d polar histogram using the “pol” option. When I do, the axes appear messed up. The script below generates a 2d plot, then attempts to display it as a polar histogram.

I have tried various options, I do not get the plot that I would expect. With the y parameter varying from 1.1 to 3.5, and with x varying from -pi to pi, I would expect a polar plot to show an annulus. This is based on my reading of the sentence “The X coordinate is mapped on the angle and the Y coordinate on the radius.” from the documentation of THistPainter, describing the “POL” option. When I plot it with just “colz”, I see the two blobs that I generated. When I plot it with “colz pol”, I only see one, and the regions start moving off the pad.

I tried using the “lego2” option along with “pol”, hoping that I could make a 3d plot, then rotate it until I am looking down from the top. However, the lego2 plot puts the innermost bin at radius 0, rather than at radius 1.1, as was specified in the plot.

{
  TH2F* polar_hist = new TH2F("polar_hist","polar_hist",
                              32, -TMath::Pi(), TMath::Pi(),
                              24, 1.1, 3.5);

  // Generate some data
  for(int i=0; i<1e5; i++) {
    double x = gRandom->Gaus(0.0, 0.3);
    double y = gRandom->Gaus(1.2, 0.3);
    double r = std::sqrt(x*x + y*y);
    double theta = std::atan2(y,x);

    polar_hist->Fill(theta, r);

    x = gRandom->Gaus(0.0, 0.3);
    y = gRandom->Gaus(-1.2, 0.3);
    r = std::sqrt(x*x + y*y);
    theta = std::atan2(y,x);

    polar_hist->Fill(theta, r);
  }
  polar_hist->SetStats(0);

  // Plot it 4 ways
  TCanvas* can = new TCanvas;
  can->Divide(2,2);
  can->cd(1);
  polar_hist->SetTitle("colz");
  polar_hist->DrawCopy("colz");
  can->cd(2);
  polar_hist->SetTitle("colz pol");
  polar_hist->DrawCopy("colz pol");
  can->cd(3);
  polar_hist->SetTitle("lego2 pol");
  polar_hist->DrawCopy("lego2 pol");
  can->cd(4);
  polar_hist->SetTitle("lego2 pol colz");
  polar_hist->DrawCopy("lego2 pol colz");
}

How should I go about making a polar plot?

2

The option “COLZ POL” is clearly wrong (going outside the pad.)
But “POL LEGO2” seems ok for me.
I produced a picture (attached) showing this plot from top and you can
see these 2 structures centred on Pi/2 and -Pi/2 as in the Cartesian plot shown above.
Also along the radius it reflects what is shown above.

Screen Shot 2016-11-30 at 09.43.47.png1594×1930 257 KB

3

the complete macro would be:

void polar2d()
{
   TH2F* polar_hist = new TH2F("polar_hist","polar_hist",
                           32, -TMath::Pi(), TMath::Pi(),
                           24, 1.1, 3.5);

   // Generate some data
   for(int i=0; i<1e5; i++) {
      double x = gRandom->Gaus(0.0, 0.3);
      double y = gRandom->Gaus(1.2, 0.3);
      double r = std::sqrt(x*x + y*y);
      double theta = std::atan2(y,x);

      polar_hist->Fill(theta, r);

      x = gRandom->Gaus(0.0, 0.3);
      y = gRandom->Gaus(-1.2, 0.3);
      r = std::sqrt(x*x + y*y);
      theta = std::atan2(y,x);

      polar_hist->Fill(theta, r);
   }
   polar_hist->SetStats(0);

   TCanvas* can = new TCanvas("c","c",800,1200);
   can->Divide(1,3);
   can->cd(1);
   polar_hist->SetTitle("colz");
   polar_hist->DrawCopy("colz");

   TPad *p = (TPad*)can->cd(2);
   p->SetTheta(90.);
   p->SetPhi(0.);
   polar_hist->SetTitle("lego2 pol");
   polar_hist->DrawCopy("lego2 pol");

   can->cd(3);
   gPad->DrawFrame(-3.5, -3.5,3.5, 3.5);
   polar_hist->SetTitle("colz pol");
   polar_hist->DrawCopy("same colz pol");
}

Screen Shot 2016-11-30 at 10.23.34.png1550×2306 307 KB

4

Thank you. It looks like the call to “DrawFrame” was the important one, and with that, I can reproduce the plot you made. As a clarification, the reason why I said that “pol lego2” was incorrect, was that it shows bins filling in all the way to the center. I want to innermost radius of the plot to be at 1.1, whereas that range is being ignored in the lego2 plot.

Is there a way to make the “pol colz” option automatically make the call to “gPad->DrawFrame” before drawing itself? It seems rather silly to have the default behavior draw the plot so poorly, and to need the workaround.

5

Right now the DrawFrame is needed. But you are right a more automatic way would be better.
If you have several histogram to be drawn this way you can encapsulate what is required into a function:

void DrawPolCol (TH2F *h)
{
   Double_t max = h->GetYaxis()->GetXmax();
   gPad->DrawFrame(-max, -max, max, max);
   h->DrawCopy("same colz pol");
}

void polar2d()
{
   TH2F* polar_hist = new TH2F("polar_hist","polar_hist",
                           32, -TMath::Pi(), TMath::Pi(),
                           24, 1.1, 3.5);

   // Generate some data
   for(int i=0; i<1e5; i++) {
      double x = gRandom->Gaus(0.0, 0.3);
      double y = gRandom->Gaus(1.2, 0.3);
      double r = std::sqrt(x*x + y*y);
      double theta = std::atan2(y,x);

      polar_hist->Fill(theta, r);

      x = gRandom->Gaus(0.0, 0.3);
      y = gRandom->Gaus(-1.2, 0.3);
      r = std::sqrt(x*x + y*y);
      theta = std::atan2(y,x);

      polar_hist->Fill(theta, r);
   }
   polar_hist->SetStats(0);

   TCanvas* can = new TCanvas("c","c",800,1200);
   can->Divide(1,3);
   can->cd(1);
   polar_hist->SetTitle("colz");
   polar_hist->DrawCopy("colz");

   TPad *p = (TPad*)can->cd(2);
   p->SetTheta(90.);
   p->SetPhi(0.);
   polar_hist->SetTitle("lego2 pol");
   polar_hist->DrawCopy("lego2 pol");

   can->cd(3);
   DrawPolCol(polar_hist);
}
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