geodemo.C

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/// \file
/// \ingroup tutorial_geometry
/// GUI to draw the geometry shapes.
///
/// \macro_code
///
/// \author Andrei Gheata
 
#include "TMath.h"
#include "TControlBar.h"
#include "TRandom3.h"
#include "TROOT.h"
#include "TSystem.h"
#include "TVirtualPad.h"
#include "TCanvas.h"
#include "TVirtualGeoPainter.h"
#include "TGeoManager.h"
#include "TGeoNode.h"
#include "TView.h"
#include "TPaveText.h"
#include "TGeoBBox.h"
#include "TGeoPara.h"
#include "TGeoTube.h"
#include "TGeoCone.h"
#include "TGeoEltu.h"
#include "TGeoSphere.h"
#include "TGeoTorus.h"
#include "TGeoTrd1.h"
#include "TGeoTrd2.h"
#include "TGeoParaboloid.h"
#include "TGeoHype.h"
#include "TGeoPcon.h"
#include "TGeoPgon.h"
#include "TGeoArb8.h"
#include "TGeoXtru.h"
#include "TGeoCompositeShape.h"
#include "TGeoTessellated.h"
#include "TGeoPhysicalNode.h"
 
Bool_t comments = kTRUE;
Bool_t raytracing = kFALSE;
Bool_t grotate = kFALSE;
Bool_t axis = kTRUE;
 
//______________________________________________________________________________
void MakePicture()
{
   TView *view = gPad->GetView();
   if (view) {
      //      view->RotateView(248,66);
      if (axis)
         view->ShowAxis();
   }
   Bool_t is_raytracing = gGeoManager->GetTopVolume()->IsRaytracing();
   if (is_raytracing != raytracing) {
      gGeoManager->GetTopVolume()->SetVisRaytrace(raytracing);
      gPad->Modified();
      gPad->Update();
   }
}
 
//______________________________________________________________________________
void AddMemberInfo(TPaveText *pave, const char *datamember, Double_t value, const char *comment)
{
   TString line = datamember;
   while (line.Length() < 10)
      line.Append(" ");
   line.Append(TString::Format("= %5.2f  => %s", value, comment));
   TText *text = pave->AddText(line.Data());
   //   text->SetTextColor(4);
   text->SetTextAlign(12); // 12
}
 
//______________________________________________________________________________
void AddMemberInfo(TPaveText *pave, const char *datamember, Int_t value, const char *comment)
{
   TString line = datamember;
   while (line.Length() < 10)
      line.Append(" ");
   line.Append(TString::Format("= %5d  => %s", value, comment));
   TText *text = pave->AddText(line.Data());
   //   text->SetTextColor(4);
   text->SetTextAlign(12);
}
 
//______________________________________________________________________________
void AddFinderInfo(TPaveText *pave, TObject *pf, Int_t iaxis)
{
   TGeoPatternFinder *finder = dynamic_cast<TGeoPatternFinder *>(pf);
   if (!pave || !pf || !iaxis)
      return;
   TGeoVolume *volume = finder->GetVolume();
   TGeoShape *sh = volume->GetShape();
   TText *text = pave->AddText(
      TString::Format("Division of %s on axis %d (%s)", volume->GetName(), iaxis, sh->GetAxisName(iaxis)));
   text->SetTextColor(3);
   text->SetTextAlign(12);
   AddMemberInfo(pave, "fNdiv", finder->GetNdiv(), "number of divisions");
   AddMemberInfo(pave, "fStart", finder->GetStart(), "start divisioning position");
   AddMemberInfo(pave, "fStep", finder->GetStep(), "division step");
}
 
//______________________________________________________________________________
void AddExecInfo(TPaveText *pave, const char *name = nullptr, const char *axisinfo = nullptr)
{
   if (name && axisinfo) {
      auto text = pave->AddText(TString::Format("Execute: %s(iaxis, ndiv, start, step) to divide this.", name));
      text->SetTextColor(4);
      pave->AddText(TString::Format("----- IAXIS can be %s", axisinfo));
      pave->AddText("----- NDIV must be a positive integer");
      pave->AddText("----- START must be a valid axis offset within shape range on divided axis");
      pave->AddText("----- STEP is the division step. START+NDIV*STEP must be in range also");
      pave->AddText("----- If START and STEP are omitted, all range of the axis will be divided");
      pave->SetAllWith("-----", "color", 2);
      pave->SetAllWith("-----", "font", 72);
      pave->SetAllWith("-----", "size", 0.04);
   } else if (name) {
      auto text = pave->AddText(TString::Format("Execute: %s()", name));
      text->SetTextColor(4);
   }
 
   pave->AddText(" ");
   pave->SetTextSize(0.044);
   pave->SetTextAlign(12);
}
 
//______________________________________________________________________________
void SavePicture(const char *name, TObject *objcanvas, TObject *objvol, Int_t iaxis, Double_t step)
{
   TCanvas *c = (TCanvas *)objcanvas;
   TGeoVolume *vol = (TGeoVolume *)objvol;
   if (!c || !vol)
      return;
   c->cd();
   TString fname;
   if (iaxis == 0)
      fname.Form("t_%s.gif", name);
   else if (step == 0)
      fname.Form("t_%sdiv%s.gif", name, vol->GetShape()->GetAxisName(iaxis));
   else
      fname.Form("t_%sdivstep%s.gif", name, vol->GetShape()->GetAxisName(iaxis));
 
   c->Print(fname.Data());
}
 
//______________________________________________________________________________
Int_t randomColor()
{
   Double_t color = 7. * gRandom->Rndm();
   return (1 + Int_t(color));
}
 
//______________________________________________________________________________
void raytrace()
{
   raytracing = !raytracing;
   if (gGeoManager && gPad) {
      auto top = gGeoManager->GetTopVolume();
      bool drawn = gPad->GetListOfPrimitives()->FindObject(top);
      if (drawn)
         top->SetVisRaytrace(raytracing);
      gPad->Modified();
      gPad->Update();
   }
}
 
//______________________________________________________________________________
void help()
{
 
   auto c = (TCanvas *)gROOT->GetListOfCanvases()->FindObject("geom_help");
   if (c) {
      c->Clear();
      c->Update();
      c->cd();
   } else {
      c = new TCanvas("geom_help", "Help to run demos", 200, 10, 700, 600);
   }
 
   TPaveText *welcome = new TPaveText(.1, .8, .9, .97);
   welcome->AddText("Welcome to the new geometry package");
   welcome->SetTextFont(32);
   welcome->SetTextColor(4);
   welcome->SetFillColor(24);
   welcome->Draw();
 
   TPaveText *hdemo = new TPaveText(.05, .05, .95, .7);
   hdemo->SetTextAlign(12);
   hdemo->SetTextFont(52);
   hdemo->AddText("- Demo for building TGeo basic shapes and simple geometry. Shape parameters are");
   hdemo->AddText("  displayed in the right pad");
   hdemo->AddText("- Click left mouse button to execute one demo");
   hdemo->AddText("- While pointing the mouse to the pad containing the geometry, do:");
   hdemo->AddText("- .... click-and-move to rotate");
   hdemo->AddText("- .... press j/k to zoom/unzoom");
   hdemo->AddText("- .... press l/h/u/i to move the view center around");
   hdemo->AddText("- Click Ray-trace ON/OFF to toggle ray-tracing");
   hdemo->AddText("- Use <View>/<View With>/<OpenGL> for an external 3D view");
   hdemo->AddText("- .... use the OpenGL viewer controls to rotate/zoom/move the view");
   hdemo->AddText("- Execute box(1,8) to divide a box in 8 equal slices along X");
   hdemo->AddText("- Most shapes can be divided on X,Y,Z,Rxy or Phi :");
   hdemo->AddText("- .... root[0] <shape>(IAXIS, NDIV, START, STEP);");
   hdemo->AddText("  .... IAXIS = 1,2,3 meaning (X,Y,Z) or (Rxy, Phi, Z)");
   hdemo->AddText("  .... NDIV  = number of slices");
   hdemo->AddText("  .... START = start slicing position");
   hdemo->AddText("  .... STEP  = division step");
   hdemo->AddText("- Click Comments ON/OFF to toggle comments");
   hdemo->AddText("- Click Ideal/Align geometry to see how alignment works");
   hdemo->AddText(" ");
   hdemo->SetAllWith("....", "color", 2);
   hdemo->SetAllWith("....", "font", 72);
   hdemo->SetAllWith("....", "size", 0.03);
 
   hdemo->Draw();
 
   c->Update();
}
 
//______________________________________________________________________________
void autorotate()
{
   grotate = !grotate;
   if (!grotate) {
      gROOT->SetInterrupt(kTRUE);
      return;
   }
   if (!gPad)
      return;
   TView *view = gPad->GetView();
   if (!view)
      return;
   if (!gGeoManager)
      return;
   TVirtualGeoPainter *painter = gGeoManager->GetGeomPainter();
   if (!painter)
      return;
   Double_t longit = view->GetLongitude();
   //   Double_t lat = view->GetLatitude();
   //   Double_t psi = view->GetPsi();
   Double_t dphi = 1.;
   Int_t irep;
   TProcessEventTimer *timer = new TProcessEventTimer(5);
   gROOT->SetInterrupt(kFALSE);
   while (grotate) {
      if (timer->ProcessEvents())
         break;
      if (gROOT->IsInterrupted())
         break;
      longit += dphi;
      if (longit > 360)
         longit -= 360.;
      if (!gPad) {
         grotate = kFALSE;
         return;
      }
      view = gPad->GetView();
      if (!view) {
         grotate = kFALSE;
         return;
      }
      view->SetView(longit, view->GetLatitude(), view->GetPsi(), irep);
      gPad->Modified();
      gPad->Update();
   }
   delete timer;
}
 
//______________________________________________________________________________
void axes()
{
   axis = !axis;
   TView *view = gPad ? gPad->GetView() : nullptr;
   if (view)
      view->ShowAxis();
}
 
//______________________________________________________________________________
TCanvas *create_canvas(const char *title)
{
   auto c = (TCanvas *)gROOT->GetListOfCanvases()->FindObject("geom_draw");
   if (c) {
      c->Clear();
      c->Update();
      c->SetTitle(title);
   } else {
      c = new TCanvas("geom_draw", title, 700, 1000);
   }
   if (comments) {
      c->Divide(1, 2, 0, 0);
      c->GetPad(2)->SetPad(0, 0, 1, 0.4);
      c->GetPad(1)->SetPad(0, 0.4, 1, 1);
      c->cd(1);
   }
 
   return c;
}
 
//______________________________________________________________________________
void box(Int_t iaxis = 0, Int_t ndiv = 8, Double_t start = 0, Double_t step = 0)
{
   auto c = create_canvas("A simple box");
 
   if (gGeoManager)
      delete gGeoManager;
   new TGeoManager("box", "A simple box");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98, 13, 2.7);
   TGeoMedium *med = new TGeoMedium("MED", 1, mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP", med, 100, 100, 100);
   gGeoManager->SetTopVolume(top);
   TGeoVolume *vol = gGeoManager->MakeBox("BOX", med, 20, 30, 40);
   vol->SetLineColor(randomColor());
   vol->SetLineWidth(2);
   top->AddNode(vol, 1);
   if ((iaxis > 0) && (iaxis < 4)) {
      TGeoVolume *slice = vol->Divide("SLICE", iaxis, ndiv, start, step);
      if (!slice)
         return;
      slice->SetLineColor(randomColor());
   }
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
 
   top->Draw();
 
   MakePicture();
   if (!comments)
      return;
   c->cd(2);
   TPaveText *pt = new TPaveText(0.01, 0.01, 0.99, 0.99);
   pt->SetLineColor(1);
   TGeoBBox *box = (TGeoBBox *)vol->GetShape();
   TText *text = pt->AddText("TGeoBBox - box class");
   text->SetTextColor(2);
   AddMemberInfo(pt, "fDX", box->GetDX(), "half length in X");
   AddMemberInfo(pt, "fDY", box->GetDY(), "half length in Y");
   AddMemberInfo(pt, "fDZ", box->GetDZ(), "half length in Z");
   AddMemberInfo(pt, "fOrigin[0]", (box->GetOrigin())[0], "box origin on X");
   AddMemberInfo(pt, "fOrigin[1]", (box->GetOrigin())[1], "box origin on Y");
   AddMemberInfo(pt, "fOrigin[2]", (box->GetOrigin())[2], "box origin on Z");
   AddFinderInfo(pt, vol->GetFinder(), iaxis);
   AddExecInfo(pt, "box", "1, 2 or 3 (X, Y, Z)");
   pt->Draw();
   //   SavePicture("box",c,vol,iaxis,step);
   c->cd(1);
}
 
//______________________________________________________________________________
void para(Int_t iaxis = 0, Int_t ndiv = 8, Double_t start = 0, Double_t step = 0)
{
   auto c = create_canvas("A parallelepiped");
 
   if (gGeoManager)
      delete gGeoManager;
   new TGeoManager("para", "A parallelepiped");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98, 13, 2.7);
   TGeoMedium *med = new TGeoMedium("MED", 1, mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP", med, 100, 100, 100);
   gGeoManager->SetTopVolume(top);
   TGeoVolume *vol = gGeoManager->MakePara("PARA", med, 20, 30, 40, 30, 15, 30);
   vol->SetLineColor(randomColor());
   vol->SetLineWidth(2);
   top->AddNode(vol, 1);
   if ((iaxis > 0) && (iaxis < 4)) {
      TGeoVolume *slice = vol->Divide("SLICE", iaxis, ndiv, start, step);
      if (!slice)
         return;
      slice->SetLineColor(randomColor());
   } else if (iaxis) {
      printf("Wrong division axis %d. Allowed range is 1-3.\n", iaxis);
      return;
   }
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
 
   top->Draw();
 
   MakePicture();
   if (!comments)
      return;
   c->cd(2);
   TPaveText *pt = new TPaveText(0.01, 0.01, 0.99, 0.99);
   pt->SetLineColor(1);
   TGeoPara *para = (TGeoPara *)vol->GetShape();
   TText *text = pt->AddText("TGeoPara - parallelepiped class");
   text->SetTextColor(2);
   AddMemberInfo(pt, "fX", para->GetX(), "half length in X");
   AddMemberInfo(pt, "fY", para->GetY(), "half length in Y");
   AddMemberInfo(pt, "fZ", para->GetZ(), "half length in Z");
   AddMemberInfo(pt, "fAlpha", para->GetAlpha(), "angle about Y of the Z bases");
   AddMemberInfo(pt, "fTheta", para->GetTheta(), "inclination of para axis about Z");
   AddMemberInfo(pt, "fPhi", para->GetPhi(), "phi angle of para axis");
   AddFinderInfo(pt, vol->GetFinder(), iaxis);
   AddExecInfo(pt, "para", "1, 2 or 3 (X, Y, Z)");
   pt->Draw();
   c->cd(1);
   //   SavePicture("para",c,vol,iaxis,step);
}
 
//______________________________________________________________________________
void tube(Int_t iaxis = 0, Int_t ndiv = 8, Double_t start = 0, Double_t step = 0)
{
   auto c = create_canvas("A tube");
 
   if (gGeoManager)
      delete gGeoManager;
   new TGeoManager("tube", "poza2");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98, 13, 2.7);
   TGeoMedium *med = new TGeoMedium("MED", 1, mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP", med, 100, 100, 100);
   gGeoManager->SetTopVolume(top);
   TGeoVolume *vol = gGeoManager->MakeTube("TUBE", med, 20, 30, 40);
   vol->SetLineColor(randomColor());
   vol->SetLineWidth(2);
   top->AddNode(vol, 1);
   if ((iaxis > 0) && (iaxis < 4)) {
      TGeoVolume *slice = vol->Divide("SLICE", iaxis, ndiv, start, step);
      if (!slice)
         return;
      slice->SetLineColor(randomColor());
   } else if (iaxis) {
      printf("Wrong division axis %d. Allowed range is 1-3.\n", iaxis);
      return;
   }
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
 
   top->Draw();
 
   MakePicture();
   if (!comments)
      return;
   c->cd(2);
   TPaveText *pt = new TPaveText(0.01, 0.01, 0.99, 0.99);
   pt->SetLineColor(1);
   TGeoTube *tube = (TGeoTube *)(vol->GetShape());
   TText *text = pt->AddText("TGeoTube - tube class");
   text->SetTextColor(2);
   AddMemberInfo(pt, "fRmin", tube->GetRmin(), "minimum radius");
   AddMemberInfo(pt, "fRmax", tube->GetRmax(), "maximum radius");
   AddMemberInfo(pt, "fDZ", tube->GetDZ(), "half length in Z");
   AddFinderInfo(pt, vol->GetFinder(), iaxis);
   AddExecInfo(pt, "tube", "1, 2 or 3 (Rxy, Phi, Z)");
   pt->Draw();
   c->cd(1);
   //   SavePicture("tube",c,vol,iaxis,step);
}
 
//______________________________________________________________________________
void tubeseg(Int_t iaxis = 0, Int_t ndiv = 8, Double_t start = 0, Double_t step = 0)
{
   auto c = create_canvas("A tube segment");
 
   if (gGeoManager)
      delete gGeoManager;
   new TGeoManager("tubeseg", "poza3");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98, 13, 2.7);
   TGeoMedium *med = new TGeoMedium("MED", 1, mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP", med, 100, 100, 100);
   gGeoManager->SetTopVolume(top);
   TGeoVolume *vol = gGeoManager->MakeTubs("TUBESEG", med, 20, 30, 40, -30, 270);
   vol->SetLineColor(randomColor());
   if ((iaxis > 0) && (iaxis < 4)) {
      TGeoVolume *slice = vol->Divide("SLICE", iaxis, ndiv, start, step);
      if (!slice)
         return;
      slice->SetLineColor(randomColor());
   } else if (iaxis) {
      printf("Wrong division axis %d. Allowed range is 1-3.\n", iaxis);
      return;
   }
 
   vol->SetLineWidth(2);
   top->AddNode(vol, 1);
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
 
   top->Draw();
 
   MakePicture();
   if (!comments)
      return;
   c->cd(2);
   TPaveText *pt = new TPaveText(0.01, 0.01, 0.99, 0.99);
   pt->SetLineColor(1);
   TGeoTubeSeg *tubeseg = (TGeoTubeSeg *)(vol->GetShape());
   TText *text = pt->AddText("TGeoTubeSeg - tube segment class");
   text->SetTextColor(2);
   AddMemberInfo(pt, "fRmin", tubeseg->GetRmin(), "minimum radius");
   AddMemberInfo(pt, "fRmax", tubeseg->GetRmax(), "maximum radius");
   AddMemberInfo(pt, "fDZ", tubeseg->GetDZ(), "half length in Z");
   AddMemberInfo(pt, "fPhi1", tubeseg->GetPhi1(), "first phi limit");
   AddMemberInfo(pt, "fPhi2", tubeseg->GetPhi2(), "second phi limit");
   AddFinderInfo(pt, vol->GetFinder(), iaxis);
   AddExecInfo(pt, "tubeseg", "1, 2 or 3 (Rxy, Phi, Z)");
   pt->Draw();
   c->cd(1);
   //   SavePicture("tubeseg",c,vol,iaxis,step);
}
 
//______________________________________________________________________________
void ctub(Int_t iaxis = 0, Int_t ndiv = 8, Double_t start = 0, Double_t step = 0)
{
   auto c = create_canvas("A cut tube segment");
 
   if (gGeoManager)
      delete gGeoManager;
   new TGeoManager("ctub", "poza3");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98, 13, 2.7);
   TGeoMedium *med = new TGeoMedium("MED", 1, mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP", med, 100, 100, 100);
   gGeoManager->SetTopVolume(top);
   Double_t theta = 160. * TMath::Pi() / 180.;
   Double_t phi = 30. * TMath::Pi() / 180.;
   Double_t nlow[3];
   nlow[0] = TMath::Sin(theta) * TMath::Cos(phi);
   nlow[1] = TMath::Sin(theta) * TMath::Sin(phi);
   nlow[2] = TMath::Cos(theta);
   theta = 20. * TMath::Pi() / 180.;
   phi = 60. * TMath::Pi() / 180.;
   Double_t nhi[3];
   nhi[0] = TMath::Sin(theta) * TMath::Cos(phi);
   nhi[1] = TMath::Sin(theta) * TMath::Sin(phi);
   nhi[2] = TMath::Cos(theta);
   TGeoVolume *vol =
      gGeoManager->MakeCtub("CTUB", med, 20, 30, 40, -30, 250, nlow[0], nlow[1], nlow[2], nhi[0], nhi[1], nhi[2]);
   vol->SetLineColor(randomColor());
   if (iaxis == 1 || iaxis == 2) {
      TGeoVolume *slice = vol->Divide("SLICE", iaxis, ndiv, start, step);
      if (!slice)
         return;
      slice->SetLineColor(randomColor());
   } else if (iaxis) {
      printf("Wrong division axis %d. Allowed range is 1-2.\n", iaxis);
      return;
   }
 
   vol->SetLineWidth(2);
   top->AddNode(vol, 1);
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
 
   top->Draw();
 
   MakePicture();
   if (!comments)
      return;
   c->cd(2);
   TPaveText *pt = new TPaveText(0.01, 0.01, 0.99, 0.99);
   pt->SetLineColor(1);
   TGeoTubeSeg *tubeseg = (TGeoTubeSeg *)(vol->GetShape());
   TText *text = pt->AddText("TGeoTubeSeg - tube segment class");
   text->SetTextColor(2);
   AddMemberInfo(pt, "fRmin", tubeseg->GetRmin(), "minimum radius");
   AddMemberInfo(pt, "fRmax", tubeseg->GetRmax(), "maximum radius");
   AddMemberInfo(pt, "fDZ", tubeseg->GetDZ(), "half length in Z");
   AddMemberInfo(pt, "fPhi1", tubeseg->GetPhi1(), "first phi limit");
   AddMemberInfo(pt, "fPhi2", tubeseg->GetPhi2(), "second phi limit");
   AddFinderInfo(pt, vol->GetFinder(), iaxis);
   AddExecInfo(pt, "ctub", "1 or 2");
   pt->Draw();
   c->cd(1);
   //   SavePicture("tubeseg",c,vol,iaxis,step);
}
 
//______________________________________________________________________________
void cone(Int_t iaxis = 0, Int_t ndiv = 8, Double_t start = 0, Double_t step = 0)
{
   auto c = create_canvas("A cone");
 
   if (gGeoManager)
      delete gGeoManager;
   new TGeoManager("cone", "poza4");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98, 13, 2.7);
   TGeoMedium *med = new TGeoMedium("MED", 1, mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP", med, 100, 100, 100);
   gGeoManager->SetTopVolume(top);
   TGeoVolume *vol = gGeoManager->MakeCone("CONE", med, 40, 10, 20, 35, 45);
   vol->SetLineColor(randomColor());
   vol->SetLineWidth(2);
   if (iaxis == 2 || iaxis == 3) {
      TGeoVolume *slice = vol->Divide("SLICE", iaxis, ndiv, start, step);
      if (!slice)
         return;
      slice->SetLineColor(randomColor());
   } else if (iaxis) {
      printf("Wrong division axis %d. Allowed range is 2-3.\n", iaxis);
      return;
   }
   top->AddNode(vol, 1);
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
 
   top->Draw();
 
   MakePicture();
   if (!comments)
      return;
   c->cd(2);
   TPaveText *pt = new TPaveText(0.01, 0.01, 0.99, 0.99);
   pt->SetLineColor(1);
   TGeoCone *cone = (TGeoCone *)(vol->GetShape());
   TText *text = pt->AddText("TGeoCone - cone class");
   text->SetTextColor(2);
   AddMemberInfo(pt, "fDZ", cone->GetDZ(), "half length in Z");
   AddMemberInfo(pt, "fRmin1", cone->GetRmin1(), "inner radius at -dz");
   AddMemberInfo(pt, "fRmax1", cone->GetRmax1(), "outer radius at -dz");
   AddMemberInfo(pt, "fRmin2", cone->GetRmin2(), "inner radius at +dz");
   AddMemberInfo(pt, "fRmax2", cone->GetRmax2(), "outer radius at +dz");
   AddFinderInfo(pt, vol->GetFinder(), iaxis);
   AddExecInfo(pt, "cone", "2 or 3 (Phi, Z)");
   pt->Draw();
   c->cd(1);
   //   SavePicture("cone",c,vol,iaxis,step);
}
 
//______________________________________________________________________________
void coneseg(Int_t iaxis = 0, Int_t ndiv = 8, Double_t start = 0, Double_t step = 0)
{
   auto c = create_canvas("A cone segment");
 
   if (gGeoManager)
      delete gGeoManager;
   new TGeoManager("coneseg", "poza5");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98, 13, 2.7);
   TGeoMedium *med = new TGeoMedium("MED", 1, mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP", med, 100, 100, 100);
   gGeoManager->SetTopVolume(top);
   TGeoVolume *vol = gGeoManager->MakeCons("CONESEG", med, 40, 30, 40, 10, 20, -30, 250);
   vol->SetLineColor(randomColor());
   //   vol->SetLineWidth(2);
   top->AddNode(vol, 1);
   if (iaxis >= 2 && iaxis <= 3) {
      TGeoVolume *slice = vol->Divide("SLICE", iaxis, ndiv, start, step);
      if (!slice)
         return;
      slice->SetLineColor(randomColor());
   } else if (iaxis) {
      printf("Wrong division axis %d. Allowed range is 2-3.\n", iaxis);
      return;
   }
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
 
   top->Draw();
 
   MakePicture();
   if (!comments)
      return;
   c->cd(2);
   TPaveText *pt = new TPaveText(0.01, 0.01, 0.99, 0.99);
   pt->SetLineColor(1);
   TGeoConeSeg *coneseg = (TGeoConeSeg *)(vol->GetShape());
   TText *text = pt->AddText("TGeoConeSeg - coneseg class");
   text->SetTextColor(2);
   AddMemberInfo(pt, "fDZ", coneseg->GetDZ(), "half length in Z");
   AddMemberInfo(pt, "fRmin1", coneseg->GetRmin1(), "inner radius at -dz");
   AddMemberInfo(pt, "fRmax1", coneseg->GetRmax1(), "outer radius at -dz");
   AddMemberInfo(pt, "fRmin2", coneseg->GetRmin1(), "inner radius at +dz");
   AddMemberInfo(pt, "fRmax2", coneseg->GetRmax1(), "outer radius at +dz");
   AddMemberInfo(pt, "fPhi1", coneseg->GetPhi1(), "first phi limit");
   AddMemberInfo(pt, "fPhi2", coneseg->GetPhi2(), "second phi limit");
   AddFinderInfo(pt, vol->GetFinder(), iaxis);
   AddExecInfo(pt, "coneseg", "2 or 3 (Phi, Z)");
   pt->Draw();
   c->cd(1);
   //   SavePicture("coneseg",c,vol,iaxis,step);
}
 
//______________________________________________________________________________
void eltu(Int_t iaxis = 0, Int_t ndiv = 8, Double_t start = 0, Double_t step = 0)
{
   auto c = create_canvas("An Elliptical tube");
 
   if (gGeoManager)
      delete gGeoManager;
   new TGeoManager("eltu", "poza6");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98, 13, 2.7);
   TGeoMedium *med = new TGeoMedium("MED", 1, mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP", med, 100, 100, 100);
   gGeoManager->SetTopVolume(top);
   TGeoVolume *vol = gGeoManager->MakeEltu("ELTU", med, 30, 10, 40);
   vol->SetLineColor(randomColor());
   //   vol->SetLineWidth(2);
   top->AddNode(vol, 1);
   if (iaxis >= 2 && iaxis <= 3) {
      TGeoVolume *slice = vol->Divide("SLICE", iaxis, ndiv, start, step);
      if (!slice)
         return;
      slice->SetLineColor(randomColor());
   } else if (iaxis) {
      printf("Wrong division axis %d. Allowed range is 2-3.\n", iaxis);
      return;
   }
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
 
   top->Draw();
 
   MakePicture();
   if (!comments)
      return;
   c->cd(2);
   TPaveText *pt = new TPaveText(0.01, 0.01, 0.99, 0.99);
   pt->SetLineColor(1);
   TGeoEltu *eltu = (TGeoEltu *)(vol->GetShape());
   TText *text = pt->AddText("TGeoEltu - eltu class");
   text->SetTextColor(2);
   AddMemberInfo(pt, "fA", eltu->GetA(), "semi-axis along x");
   AddMemberInfo(pt, "fB", eltu->GetB(), "semi-axis along y");
   AddMemberInfo(pt, "fDZ", eltu->GetDZ(), "half length in Z");
   AddFinderInfo(pt, vol->GetFinder(), iaxis);
   AddExecInfo(pt, "eltu", "2 or 3 (Phi, Z)");
   pt->Draw();
   c->cd(1);
   //   SavePicture("eltu",c,vol,iaxis,step);
}
 
//______________________________________________________________________________
void sphere()
{
   auto c = create_canvas("A spherical sector");
 
   if (gGeoManager)
      delete gGeoManager;
   new TGeoManager("sphere", "poza7");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98, 13, 2.7);
   TGeoMedium *med = new TGeoMedium("MED", 1, mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP", med, 100, 100, 100);
   gGeoManager->SetTopVolume(top);
   TGeoVolume *vol = gGeoManager->MakeSphere("SPHERE", med, 30, 40, 60, 120, 30, 240);
   vol->SetLineColor(randomColor());
   vol->SetLineWidth(2);
   top->AddNode(vol, 1);
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
 
   top->Draw();
 
   MakePicture();
   if (!comments)
      return;
   c->cd(2);
   TPaveText *pt = new TPaveText(0.01, 0.01, 0.99, 0.99);
   pt->SetLineColor(1);
   TGeoSphere *sphere = (TGeoSphere *)(vol->GetShape());
   TText *text = pt->AddText("TGeoSphere- sphere class");
   text->SetTextColor(2);
   AddMemberInfo(pt, "fRmin", sphere->GetRmin(), "inner radius");
   AddMemberInfo(pt, "fRmax", sphere->GetRmax(), "outer radius");
   AddMemberInfo(pt, "fTheta1", sphere->GetTheta1(), "lower theta limit");
   AddMemberInfo(pt, "fTheta2", sphere->GetTheta2(), "higher theta limit");
   AddMemberInfo(pt, "fPhi1", sphere->GetPhi1(), "lower phi limit");
   AddMemberInfo(pt, "fPhi2", sphere->GetPhi2(), "higher phi limit");
   AddExecInfo(pt, "sphere");
   pt->Draw();
   c->cd(1);
   //   SavePicture("sphere",c,vol,iaxis,step);
}
 
//______________________________________________________________________________
void torus()
{
   auto c = create_canvas("A toroidal segment");
 
   if (gGeoManager)
      delete gGeoManager;
   new TGeoManager("torus", "poza2");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98, 13, 2.7);
   TGeoMedium *med = new TGeoMedium("MED", 1, mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP", med, 100, 100, 100);
   gGeoManager->SetTopVolume(top);
   TGeoVolume *vol = gGeoManager->MakeTorus("TORUS", med, 40, 20, 25, 0, 270);
   vol->SetLineColor(randomColor());
   top->AddNode(vol, 1);
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
 
   top->Draw();
 
   MakePicture();
   if (!comments)
      return;
   c->cd(2);
   TPaveText *pt = new TPaveText(0.01, 0.01, 0.99, 0.99);
   pt->SetLineColor(1);
   TGeoTorus *tor = (TGeoTorus *)(vol->GetShape());
   TText *text = pt->AddText("TGeoTorus - torus class");
   text->SetTextColor(2);
   AddMemberInfo(pt, "fR", tor->GetR(), "radius of the ring");
   AddMemberInfo(pt, "fRmin", tor->GetRmin(), "minimum radius");
   AddMemberInfo(pt, "fRmax", tor->GetRmax(), "maximum radius");
   AddMemberInfo(pt, "fPhi1", tor->GetPhi1(), "starting phi angle");
   AddMemberInfo(pt, "fDphi", tor->GetDphi(), "phi range");
   AddExecInfo(pt, "torus");
   pt->Draw();
   c->cd(1);
}
 
//______________________________________________________________________________
void trd1(Int_t iaxis = 0, Int_t ndiv = 8, Double_t start = 0, Double_t step = 0)
{
   auto c = create_canvas("A trapezoid with dX varying");
 
   if (gGeoManager)
      delete gGeoManager;
   new TGeoManager("trd1", "poza8");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98, 13, 2.7);
   TGeoMedium *med = new TGeoMedium("MED", 1, mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP", med, 100, 100, 100);
   gGeoManager->SetTopVolume(top);
   TGeoVolume *vol = gGeoManager->MakeTrd1("Trd1", med, 10, 20, 30, 40);
   vol->SetLineColor(randomColor());
   vol->SetLineWidth(2);
   top->AddNode(vol, 1);
   if (iaxis == 2 || iaxis == 3) {
      TGeoVolume *slice = vol->Divide("SLICE", iaxis, ndiv, start, step);
      if (!slice)
         return;
      slice->SetLineColor(randomColor());
   } else if (iaxis) {
      printf("Wrong division axis %d. Allowed range is 2-3.\n", iaxis);
      return;
   }
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
 
   top->Draw();
 
   MakePicture();
   if (!comments)
      return;
   c->cd(2);
   TPaveText *pt = new TPaveText(0.01, 0.01, 0.99, 0.99);
   pt->SetLineColor(1);
   TGeoTrd1 *trd1 = (TGeoTrd1 *)vol->GetShape();
   TText *text = pt->AddText("TGeoTrd1 - Trd1 class");
   text->SetTextColor(2);
   AddMemberInfo(pt, "fDx1", trd1->GetDx1(), "half length in X at lower Z surface(-dz)");
   AddMemberInfo(pt, "fDx2", trd1->GetDx2(), "half length in X at higher Z surface(+dz)");
   AddMemberInfo(pt, "fDy", trd1->GetDy(), "half length in Y");
   AddMemberInfo(pt, "fDz", trd1->GetDz(), "half length in Z");
   AddFinderInfo(pt, vol->GetFinder(), iaxis);
   AddExecInfo(pt, "trd1", "2 or 3 (Y, Z)");
   pt->Draw();
   c->cd(1);
   //   SavePicture("trd1",c,vol,iaxis,step);
}
 
//______________________________________________________________________________
void parab()
{
   auto c = create_canvas("A paraboloid segment");
 
   if (gGeoManager)
      delete gGeoManager;
   new TGeoManager("parab", "paraboloid");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98, 13, 2.7);
   TGeoMedium *med = new TGeoMedium("MED", 1, mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP", med, 100, 100, 100);
   gGeoManager->SetTopVolume(top);
   TGeoVolume *vol = gGeoManager->MakeParaboloid("PARAB", med, 0, 40, 50);
   TGeoParaboloid *par = (TGeoParaboloid *)vol->GetShape();
   vol->SetLineColor(randomColor());
   vol->SetLineWidth(2);
   top->AddNode(vol, 1);
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
 
   top->Draw();
 
   MakePicture();
   if (!comments)
      return;
   c->cd(2);
   TPaveText *pt = new TPaveText(0.01, 0.01, 0.99, 0.99);
   pt->SetLineColor(1);
   TText *text = pt->AddText("TGeoParaboloid - Paraboloid class");
   text->SetTextColor(2);
   AddMemberInfo(pt, "fRlo", par->GetRlo(), "radius at Z=-dz");
   AddMemberInfo(pt, "fRhi", par->GetRhi(), "radius at Z=+dz");
   AddMemberInfo(pt, "fDz", par->GetDz(), "half-length on Z axis");
   pt->AddText("----- A paraboloid is described by the equation:");
   pt->AddText("-----    z = a*r*r + b;   where: r = x*x + y*y");
   pt->AddText("----- Create with:    TGeoParaboloid *parab = new TGeoParaboloid(rlo, rhi, dz);");
   pt->AddText("-----    dz:  half-length in Z (range from -dz to +dz");
   pt->AddText("-----    rlo: radius at z=-dz given by: -dz = a*rlo*rlo + b");
   pt->AddText("-----    rhi: radius at z=+dz given by:  dz = a*rhi*rhi + b");
   pt->AddText("-----      rlo != rhi; both >= 0");
   AddExecInfo(pt, "parab");
   pt->Draw();
   c->cd(1);
}
 
//______________________________________________________________________________
void hype()
{
   auto c = create_canvas("A hyperboloid");
 
   if (gGeoManager)
      delete gGeoManager;
   new TGeoManager("hype", "hyperboloid");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98, 13, 2.7);
   TGeoMedium *med = new TGeoMedium("MED", 1, mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP", med, 100, 100, 100);
   gGeoManager->SetTopVolume(top);
   TGeoVolume *vol = gGeoManager->MakeHype("HYPE", med, 10, 45, 20, 45, 40);
   TGeoHype *hype = (TGeoHype *)vol->GetShape();
   vol->SetLineColor(randomColor());
   vol->SetLineWidth(2);
   top->AddNode(vol, 1);
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
 
   top->Draw();
 
   MakePicture();
   if (!comments)
      return;
   c->cd(2);
   TPaveText *pt = new TPaveText(0.01, 0.01, 0.99, 0.99);
   pt->SetLineColor(1);
   TText *text = pt->AddText("TGeoHype - Hyperboloid class");
   text->SetTextColor(2);
   AddMemberInfo(pt, "fRmin", hype->GetRmin(), "minimum inner radius");
   AddMemberInfo(pt, "fStIn", hype->GetStIn(), "inner surface stereo angle [deg]");
   AddMemberInfo(pt, "fRmax", hype->GetRmax(), "minimum outer radius");
   AddMemberInfo(pt, "fStOut", hype->GetStOut(), "outer surface stereo angle [deg]");
   AddMemberInfo(pt, "fDz", hype->GetDz(), "half-length on Z axis");
   pt->AddText("----- A hyperboloid is described by the equation:");
   pt->AddText("-----    r^2 - (tan(stereo)*z)^2 = rmin^2;   where: r = x*x + y*y");
   pt->AddText("----- Create with:    TGeoHype *hype = new TGeoHype(rin, stin, rout, stout, dz);");
   pt->AddText("-----      rin < rout; rout > 0");
   pt->AddText("-----      rin = 0; stin > 0 => inner surface conical");
   pt->AddText("-----      stin/stout = 0 => corresponding surface cylindrical");
   AddExecInfo(pt, "hype");
   pt->Draw();
   c->cd(1);
}
 
//______________________________________________________________________________
void pcon(Int_t iaxis = 0, Int_t ndiv = 8, Double_t start = 0, Double_t step = 0)
{
   auto c = create_canvas("A polycone");
 
   if (gGeoManager)
      delete gGeoManager;
   new TGeoManager("pcon", "poza10");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98, 13, 2.7);
   TGeoMedium *med = new TGeoMedium("MED", 1, mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP", med, 100, 100, 100);
   gGeoManager->SetTopVolume(top);
   TGeoVolume *vol = gGeoManager->MakePcon("PCON", med, -30.0, 300, 4);
   TGeoPcon *pcon = (TGeoPcon *)(vol->GetShape());
   pcon->DefineSection(0, 0, 15, 20);
   pcon->DefineSection(1, 20, 15, 20);
   pcon->DefineSection(2, 20, 15, 25);
   pcon->DefineSection(3, 50, 15, 20);
   vol->SetLineColor(randomColor());
   vol->SetLineWidth(2);
   top->AddNode(vol, 1);
   if (iaxis == 2 || iaxis == 3) {
      TGeoVolume *slice = vol->Divide("SLICE", iaxis, ndiv, start, step);
      if (!slice)
         return;
      slice->SetLineColor(randomColor());
   }
   if (iaxis) {
      printf("Wrong division axis %d. Allowed range is 2-3.\n", iaxis);
      return;
   }
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
 
   top->Draw();
 
   MakePicture();
   if (!comments)
      return;
   c->cd(2);
   TPaveText *pt = new TPaveText(0.01, 0.01, 0.99, 0.99);
   pt->SetLineColor(1);
   TText *text = pt->AddText("TGeoPcon - pcon class");
   text->SetTextColor(2);
   AddMemberInfo(pt, "fPhi1", pcon->GetPhi1(), "lower phi limit");
   AddMemberInfo(pt, "fDphi", pcon->GetDphi(), "phi range");
   AddMemberInfo(pt, "fNz", pcon->GetNz(), "number of z planes");
   for (Int_t j = 0; j < pcon->GetNz(); j++) {
      auto line = TString::Format("fZ[%i]=%5.2f  fRmin[%i]=%5.2f  fRmax[%i]=%5.2f", j, pcon->GetZ()[j], j,
                                  pcon->GetRmin()[j], j, pcon->GetRmax()[j]);
      text = pt->AddText(line.Data());
      text->SetTextColor(4);
      text->SetTextAlign(12);
   }
   AddFinderInfo(pt, vol->GetFinder(), iaxis);
   AddExecInfo(pt, "pcon", "2 or 3 (Phi, Z)");
   pt->Draw();
   c->cd(1);
   //   SavePicture("pcon",c,vol,iaxis,step);
}
 
//______________________________________________________________________________
void pgon(Int_t iaxis = 0, Int_t ndiv = 8, Double_t start = 0, Double_t step = 0)
{
   auto c = create_canvas("A polygone");
 
   if (gGeoManager)
      delete gGeoManager;
   new TGeoManager("pgon", "poza11");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98, 13, 2.7);
   TGeoMedium *med = new TGeoMedium("MED", 1, mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP", med, 150, 150, 100);
   gGeoManager->SetTopVolume(top);
   TGeoVolume *vol = gGeoManager->MakePgon("PGON", med, -45.0, 270.0, 4, 4);
   TGeoPgon *pgon = (TGeoPgon *)(vol->GetShape());
   pgon->DefineSection(0, -70, 45, 50);
   pgon->DefineSection(1, 0, 35, 40);
   pgon->DefineSection(2, 0, 30, 35);
   pgon->DefineSection(3, 70, 90, 100);
   vol->SetLineColor(randomColor());
   vol->SetLineWidth(2);
   top->AddNode(vol, 1);
   if (iaxis == 2 || iaxis == 3) {
      TGeoVolume *slice = vol->Divide("SLICE", iaxis, ndiv, start, step);
      if (!slice)
         return;
      slice->SetLineColor(randomColor());
   }
   if (iaxis) {
      printf("Wrong division axis %d. Allowed range is 2-3.\n", iaxis);
      return;
   }
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
 
   top->Draw();
 
   MakePicture();
   if (!comments)
      return;
   c->cd(2);
   TPaveText *pt = new TPaveText(0.01, 0.01, 0.99, 0.99);
   pt->SetLineColor(1);
   TText *text = pt->AddText("TGeoPgon - pgon class");
   text->SetTextColor(2);
   AddMemberInfo(pt, "fPhi1", pgon->GetPhi1(), "lower phi limit");
   AddMemberInfo(pt, "fDphi", pgon->GetDphi(), "phi range");
   AddMemberInfo(pt, "fNedges", pgon->GetNedges(), "number of edges");
   AddMemberInfo(pt, "fNz", pgon->GetNz(), "number of z planes");
   for (Int_t j = 0; j < pgon->GetNz(); j++) {
      auto line = TString::Format("fZ[%i]=%5.2f  fRmin[%i]=%5.2f  fRmax[%i]=%5.2f", j, pgon->GetZ()[j], j,
                                  pgon->GetRmin()[j], j, pgon->GetRmax()[j]);
      text = pt->AddText(line.Data());
      text->SetTextColor(4);
      text->SetTextAlign(12);
   }
   AddFinderInfo(pt, vol->GetFinder(), iaxis);
   AddExecInfo(pt, "pgon", "2 or 3 (Phi, Z)");
   pt->Draw();
   c->cd(1);
   //   SavePicture("pgon",c,vol,iaxis,step);
}
 
//______________________________________________________________________________
void arb8()
{
   auto c = create_canvas("An arbitrary polyhedron");
 
   if (gGeoManager)
      delete gGeoManager;
   new TGeoManager("arb8", "poza12");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98, 13, 2.7);
   TGeoMedium *med = new TGeoMedium("MED", 1, mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP", med, 100, 100, 100);
   gGeoManager->SetTopVolume(top);
   TGeoArb8 *arb = new TGeoArb8(20);
   arb->SetVertex(0, -30, -25);
   arb->SetVertex(1, -25, 25);
   arb->SetVertex(2, 5, 25);
   arb->SetVertex(3, 25, -25);
   arb->SetVertex(4, -28, -23);
   arb->SetVertex(5, -23, 27);
   arb->SetVertex(6, -23, 27);
   arb->SetVertex(7, 13, -27);
   TGeoVolume *vol = new TGeoVolume("ARB8", arb, med);
   vol->SetLineColor(randomColor());
   vol->SetLineWidth(2);
   top->AddNode(vol, 1);
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
 
   top->Draw();
 
   MakePicture();
   if (!comments)
      return;
   c->cd(2);
   TPaveText *pt = new TPaveText(0.01, 0.01, 0.99, 0.99);
   pt->SetLineColor(1);
   TText *text = pt->AddText("TGeoArb8 - arb8 class");
   text->SetTextColor(2);
   AddMemberInfo(pt, "fDz", arb->GetDz(), "Z half length");
   Double_t *vert = arb->GetVertices();
   text = pt->AddText("Vertices on lower Z plane:");
   text->SetTextColor(3);
   for (Int_t i = 0; i < 4; i++) {
      text = pt->AddText(TString::Format("   fXY[%d] = (%5.2f, %5.2f)", i, vert[2 * i], vert[2 * i + 1]));
      text->SetTextSize(0.043);
      text->SetTextColor(4);
   }
   text = pt->AddText("Vertices on higher Z plane:");
   text->SetTextColor(3);
   for (Int_t i = 4; i < 8; i++) {
      text = pt->AddText(TString::Format("   fXY[%d] = (%5.2f, %5.2f)", i, vert[2 * i], vert[2 * i + 1]));
      text->SetTextSize(0.043);
      text->SetTextColor(4);
   }
 
   AddExecInfo(pt, "arb8");
   pt->Draw();
   c->cd(1);
   //   SavePicture("arb8",c,vol,iaxis,step);
}
 
//______________________________________________________________________________
void trd2(Int_t iaxis = 0, Int_t ndiv = 8, Double_t start = 0, Double_t step = 0)
{
   auto c = create_canvas("A trapezoid with dX and dY varying with Z");
 
   if (gGeoManager)
      delete gGeoManager;
   new TGeoManager("trd2", "poza9");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98, 13, 2.7);
   TGeoMedium *med = new TGeoMedium("MED", 1, mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP", med, 100, 100, 100);
   gGeoManager->SetTopVolume(top);
   TGeoVolume *vol = gGeoManager->MakeTrd2("Trd2", med, 10, 20, 30, 10, 40);
   vol->SetLineColor(randomColor());
   vol->SetLineWidth(2);
   top->AddNode(vol, 1);
   if (iaxis == 3) {
      TGeoVolume *slice = vol->Divide("SLICE", iaxis, ndiv, start, step);
      if (!slice)
         return;
      slice->SetLineColor(randomColor());
   } else if (iaxis) {
      printf("Wrong division axis %d. Allowed is only 3.\n", iaxis);
      return;
   }
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
 
   top->Draw();
 
   MakePicture();
   if (!comments)
      return;
   c->cd(2);
   TPaveText *pt = new TPaveText(0.01, 0.01, 0.99, 0.99);
   pt->SetLineColor(1);
   TGeoTrd2 *trd2 = (TGeoTrd2 *)(vol->GetShape());
   TText *text = pt->AddText("TGeoTrd2 - Trd2 class");
   text->SetTextColor(2);
   AddMemberInfo(pt, "fDx1", trd2->GetDx1(), "half length in X at lower Z surface(-dz)");
   AddMemberInfo(pt, "fDx2", trd2->GetDx2(), "half length in X at higher Z surface(+dz)");
   AddMemberInfo(pt, "fDy1", trd2->GetDy1(), "half length in Y at lower Z surface(-dz)");
   AddMemberInfo(pt, "fDy2", trd2->GetDy2(), "half length in Y at higher Z surface(-dz)");
   AddMemberInfo(pt, "fDz", trd2->GetDz(), "half length in Z");
   AddFinderInfo(pt, vol->GetFinder(), iaxis);
   AddExecInfo(pt, "trd2", "only 3 (Z)");
   pt->Draw();
   c->cd(1);
   //   SavePicture("trd2",c,vol,iaxis,step);
}
 
//______________________________________________________________________________
void trap(Int_t iaxis = 0, Int_t ndiv = 8, Double_t start = 0, Double_t step = 0)
{
   auto c = create_canvas("A more general trapezoid");
 
   if (gGeoManager)
      delete gGeoManager;
   new TGeoManager("trap", "poza10");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98, 13, 2.7);
   TGeoMedium *med = new TGeoMedium("MED", 1, mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP", med, 100, 100, 100);
   gGeoManager->SetTopVolume(top);
   TGeoVolume *vol = gGeoManager->MakeTrap("Trap", med, 30, 15, 30, 20, 10, 15, 0, 20, 10, 15, 0);
   vol->SetLineColor(randomColor());
   vol->SetLineWidth(2);
   top->AddNode(vol, 1);
   if (iaxis == 3) {
      TGeoVolume *slice = vol->Divide("SLICE", iaxis, ndiv, start, step);
      if (!slice)
         return;
      slice->SetLineColor(randomColor());
   } else if (iaxis) {
      printf("Wrong division axis %d. Allowed is only 3.\n", iaxis);
      return;
   }
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
 
   top->Draw();
 
   MakePicture();
   if (!comments)
      return;
   c->cd(2);
   TPaveText *pt = new TPaveText(0.01, 0.01, 0.99, 0.99);
   pt->SetLineColor(1);
   TGeoTrap *trap = (TGeoTrap *)(vol->GetShape());
   TText *text = pt->AddText("TGeoTrap - Trapezoid class");
   text->SetTextColor(2);
   AddMemberInfo(pt, "fDz", trap->GetDz(), "half length in Z");
   AddMemberInfo(pt, "fTheta", trap->GetTheta(), "theta angle of trapezoid axis");
   AddMemberInfo(pt, "fPhi", trap->GetPhi(), "phi angle of trapezoid axis");
   AddMemberInfo(pt, "fH1", trap->GetH1(), "half length in y at -fDz");
   AddMemberInfo(pt, "fAlpha1", trap->GetAlpha1(), "angle between centers of x edges and y axis at -fDz");
   AddMemberInfo(pt, "fBl1", trap->GetBl1(), "half length in x at -dZ and y=-fH1");
   AddMemberInfo(pt, "fTl1", trap->GetTl1(), "half length in x at -dZ and y=+fH1");
   AddMemberInfo(pt, "fH2", trap->GetH2(), "half length in y at +fDz");
   AddMemberInfo(pt, "fBl2", trap->GetBl2(), "half length in x at +dZ and y=-fH1");
   AddMemberInfo(pt, "fTl2", trap->GetTl2(), "half length in x at +dZ and y=+fH1");
   AddMemberInfo(pt, "fAlpha2", trap->GetAlpha2(), "angle between centers of x edges and y axis at +fDz");
   AddFinderInfo(pt, vol->GetFinder(), iaxis);
   AddExecInfo(pt, "trap", "only 3 (Z)");
   pt->Draw();
   c->cd(1);
   //   SavePicture("trap",c,vol,iaxis,step);
}
 
//______________________________________________________________________________
void gtra(Int_t iaxis = 0, Int_t ndiv = 8, Double_t start = 0, Double_t step = 0)
{
   auto c = create_canvas("A twisted trapezoid");
 
   if (gGeoManager)
      delete gGeoManager;
   new TGeoManager("gtra", "poza11");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98, 13, 2.7);
   TGeoMedium *med = new TGeoMedium("MED", 1, mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP", med, 100, 100, 100);
   gGeoManager->SetTopVolume(top);
   TGeoVolume *vol = gGeoManager->MakeGtra("Gtra", med, 30, 15, 30, 30, 20, 10, 15, 0, 20, 10, 15, 0);
   vol->SetLineColor(randomColor());
   vol->SetLineWidth(2);
   top->AddNode(vol, 1);
   if (iaxis == 3) {
      TGeoVolume *slice = vol->Divide("SLICE", iaxis, ndiv, start, step);
      if (!slice)
         return;
      slice->SetLineColor(randomColor());
   } else if (iaxis) {
      printf("Wrong division axis %d. Allowed is only 3.\n", iaxis);
      return;
   }
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
 
   top->Draw();
 
   MakePicture();
   if (!comments)
      return;
   c->cd(2);
   TPaveText *pt = new TPaveText(0.01, 0.01, 0.99, 0.99);
   pt->SetLineColor(1);
   TGeoGtra *trap = (TGeoGtra *)(vol->GetShape());
   TText *text = pt->AddText("TGeoGtra - Twisted trapezoid class");
   text->SetTextColor(2);
   AddMemberInfo(pt, "fDz", trap->GetDz(), "half length in Z");
   AddMemberInfo(pt, "fTheta", trap->GetTheta(), "theta angle of trapezoid axis");
   AddMemberInfo(pt, "fPhi", trap->GetPhi(), "phi angle of trapezoid axis");
   AddMemberInfo(pt, "fTwist", trap->GetTwistAngle(), "twist angle");
   AddMemberInfo(pt, "fH1", trap->GetH1(), "half length in y at -fDz");
   AddMemberInfo(pt, "fAlpha1", trap->GetAlpha1(), "angle between centers of x edges and y axis at -fDz");
   AddMemberInfo(pt, "fBl1", trap->GetBl1(), "half length in x at -dZ and y=-fH1");
   AddMemberInfo(pt, "fTl1", trap->GetTl1(), "half length in x at -dZ and y=+fH1");
   AddMemberInfo(pt, "fH2", trap->GetH2(), "half length in y at +fDz");
   AddMemberInfo(pt, "fBl2", trap->GetBl2(), "half length in x at +dZ and y=-fH1");
   AddMemberInfo(pt, "fTl2", trap->GetTl2(), "half length in x at +dZ and y=+fH1");
   AddMemberInfo(pt, "fAlpha2", trap->GetAlpha2(), "angle between centers of x edges and y axis at +fDz");
   AddFinderInfo(pt, vol->GetFinder(), iaxis);
   AddExecInfo(pt, "gtra", "only 3 (Z)");
   pt->Draw();
   c->cd(1);
   //   SavePicture("gtra",c,vol,iaxis,step);
}
 
//______________________________________________________________________________
void xtru()
{
   auto c = create_canvas("A twisted trapezoid");
 
   if (gGeoManager)
      delete gGeoManager;
   new TGeoManager("xtru", "poza12");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98, 13, 2.7);
   TGeoMedium *med = new TGeoMedium("MED", 1, mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP", med, 100, 100, 100);
   gGeoManager->SetTopVolume(top);
   TGeoVolume *vol = gGeoManager->MakeXtru("XTRU", med, 4);
   TGeoXtru *xtru = (TGeoXtru *)vol->GetShape();
   Double_t x[8] = {-30, -30, 30, 30, 15, 15, -15, -15};
   Double_t y[8] = {-30, 30, 30, -30, -30, 15, 15, -30};
   xtru->DefinePolygon(8, x, y);
   xtru->DefineSection(0, -40, -20., 10., 1.5);
   xtru->DefineSection(1, 10, 0., 0., 0.5);
   xtru->DefineSection(2, 10, 0., 0., 0.7);
   xtru->DefineSection(3, 40, 10., 20., 0.9);
   vol->SetLineColor(randomColor());
   vol->SetLineWidth(2);
   top->AddNode(vol, 1);
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
 
   top->Draw();
 
   MakePicture();
   if (!comments)
      return;
   c->cd(2);
   TPaveText *pt = new TPaveText(0.01, 0.01, 0.99, 0.99);
   pt->SetLineColor(1);
   TText *text = pt->AddText("TGeoXtru - Polygonal extrusion class");
   text->SetTextColor(2);
   AddMemberInfo(pt, "fNvert", xtru->GetNvert(), "number of polygone vertices");
   AddMemberInfo(pt, "fNz", xtru->GetNz(), "number of Z sections");
   pt->AddText("----- Any Z section is an arbitrary polygone");
   pt->AddText("----- The shape can have an arbitrary number of Z sections, as for pcon/pgon");
   pt->AddText("----- Create with:    TGeoXtru *xtru = new TGeoXtru(nz);");
   pt->AddText("----- Define the blueprint polygon :");
   pt->AddText("-----                 Double_t x[8] = {-30,-30,30,30,15,15,-15,-15};");
   pt->AddText("-----                 Double_t y[8] = {-30,30,30,-30,-30,15,15,-30};");
   pt->AddText("-----                 xtru->DefinePolygon(8,x,y);");
   pt->AddText("----- Define translations/scales of the blueprint for Z sections :");
   pt->AddText("-----                 xtru->DefineSection(i, Zsection, x0, y0, scale);");
   pt->AddText("----- Sections have to be defined in increasing Z order");
   pt->AddText("----- 2 sections can be defined at same Z (not for first/last sections)");
   AddExecInfo(pt, "xtru");
   pt->Draw();
   c->cd(1);
}
 
//______________________________________________________________________________
void tessellated()
{
   // Create a [triacontahedron solid](https://en.wikipedia.org/wiki/Rhombic_triacontahedron)
 
   auto c = create_canvas("A tessellated shape");
 
   if (gGeoManager)
      delete gGeoManager;
   new TGeoManager("tessellated", "tessellated");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98, 13, 2.7);
   TGeoMedium *med = new TGeoMedium("MED", 1, mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP", med, 10, 10, 10);
   gGeoManager->SetTopVolume(top);
   TGeoTessellated *tsl = new TGeoTessellated("triaconthaedron", 30);
   const Double_t sqrt5 = TMath::Sqrt(5.);
   std::vector<Tessellated::Vertex_t> vert;
   vert.reserve(120);
   vert.emplace_back(0, 0.5 * (1 + sqrt5), -1);
   vert.emplace_back(0, 0.5 * (-1 + sqrt5), 0.5 * (-1 - sqrt5));
   vert.emplace_back(-1, 0, 0.5 * (-1 - sqrt5));
   vert.emplace_back(-1, 1, -1);
   vert.emplace_back(1, 1, -1);
   vert.emplace_back(0, 0.5 * (1 + sqrt5), -1);
   vert.emplace_back(0, 0.5 * (-1 + sqrt5), 0.5 * (-1 - sqrt5));
   vert.emplace_back(1, 0, 0.5 * (-1 - sqrt5));
   vert.emplace_back(1, 1, -1);
   vert.emplace_back(0, 0.5 * (1 + sqrt5), -1);
   vert.emplace_back(0.5 * (-1 + sqrt5), 0.5 * (1 + sqrt5), 0);
   vert.emplace_back(0.5 * (1 + sqrt5), 1, 0);
   vert.emplace_back(0.5 * (1 - sqrt5), 0.5 * (1 + sqrt5), 0);
   vert.emplace_back(0, 0.5 * (1 + sqrt5), -1);
   vert.emplace_back(0.5 * (-1 + sqrt5), 0.5 * (1 + sqrt5), 0);
   vert.emplace_back(0, 0.5 * (1 + sqrt5), 1);
   vert.emplace_back(0.5 * (1 - sqrt5), 0.5 * (1 + sqrt5), 0);
   vert.emplace_back(0, 0.5 * (1 + sqrt5), -1);
   vert.emplace_back(-1, 1, -1);
   vert.emplace_back(0.5 * (-1 - sqrt5), 1, 0);
   vert.emplace_back(1, 1, -1);
   vert.emplace_back(0.5 * (1 + sqrt5), 1, 0);
   vert.emplace_back(0.5 * (1 + sqrt5), 0, 0.5 * (1 - sqrt5));
   vert.emplace_back(1, 0, 0.5 * (-1 - sqrt5));
   vert.emplace_back(0.5 * (1 + sqrt5), 0, 0.5 * (1 - sqrt5));
   vert.emplace_back(0.5 * (1 + sqrt5), -1, 0);
   vert.emplace_back(1, -1, -1);
   vert.emplace_back(1, 0, 0.5 * (-1 - sqrt5));
   vert.emplace_back(1, -1, -1);
   vert.emplace_back(0, 0.5 * (-1 - sqrt5), -1);
   vert.emplace_back(0, 0.5 * (1 - sqrt5), 0.5 * (-1 - sqrt5));
   vert.emplace_back(1, 0, 0.5 * (-1 - sqrt5));
   vert.emplace_back(1, 0, 0.5 * (-1 - sqrt5));
   vert.emplace_back(0, 0.5 * (-1 + sqrt5), 0.5 * (-1 - sqrt5));
   vert.emplace_back(-1, 0, 0.5 * (-1 - sqrt5));
   vert.emplace_back(0, 0.5 * (1 - sqrt5), 0.5 * (-1 - sqrt5));
   vert.emplace_back(0.5 * (-1 + sqrt5), 0.5 * (1 + sqrt5), 0);
   vert.emplace_back(0.5 * (1 + sqrt5), 1, 0);
   vert.emplace_back(1, 1, 1);
   vert.emplace_back(0, 0.5 * (1 + sqrt5), 1);
   vert.emplace_back(0.5 * (1 + sqrt5), 1, 0);
   vert.emplace_back(1, 1, 1);
   vert.emplace_back(1, 0, 0.5 * (1 + sqrt5));
   vert.emplace_back(0.5 * (1 + sqrt5), 0, 0.5 * (-1 + sqrt5));
   vert.emplace_back(0.5 * (1 + sqrt5), 0, 0.5 * (1 - sqrt5));
   vert.emplace_back(0.5 * (1 + sqrt5), 1, 0);
   vert.emplace_back(0.5 * (1 + sqrt5), 0, 0.5 * (-1 + sqrt5));
   vert.emplace_back(0.5 * (1 + sqrt5), -1, 0);
   vert.emplace_back(0.5 * (1 - sqrt5), 0.5 * (1 + sqrt5), 0);
   vert.emplace_back(0, 0.5 * (1 + sqrt5), 1);
   vert.emplace_back(-1, 1, 1);
   vert.emplace_back(0.5 * (-1 - sqrt5), 1, 0);
   vert.emplace_back(0, 0.5 * (1 + sqrt5), 1);
   vert.emplace_back(0, 0.5 * (-1 + sqrt5), 0.5 * (1 + sqrt5));
   vert.emplace_back(-1, 0, 0.5 * (1 + sqrt5));
   vert.emplace_back(-1, 1, 1);
   vert.emplace_back(1, 1, 1);
   vert.emplace_back(0, 0.5 * (1 + sqrt5), 1);
   vert.emplace_back(0, 0.5 * (-1 + sqrt5), 0.5 * (1 + sqrt5));
   vert.emplace_back(1, 0, 0.5 * (1 + sqrt5));
   vert.emplace_back(0, 0.5 * (1 - sqrt5), 0.5 * (1 + sqrt5));
   vert.emplace_back(-1, 0, 0.5 * (1 + sqrt5));
   vert.emplace_back(0, 0.5 * (-1 + sqrt5), 0.5 * (1 + sqrt5));
   vert.emplace_back(1, 0, 0.5 * (1 + sqrt5));
   vert.emplace_back(0, 0.5 * (1 - sqrt5), 0.5 * (1 + sqrt5));
   vert.emplace_back(1, 0, 0.5 * (1 + sqrt5));
   vert.emplace_back(1, -1, 1);
   vert.emplace_back(0, 0.5 * (-1 - sqrt5), 1);
   vert.emplace_back(0.5 * (1 + sqrt5), 0, 0.5 * (-1 + sqrt5));
   vert.emplace_back(0.5 * (1 + sqrt5), -1, 0);
   vert.emplace_back(1, -1, 1);
   vert.emplace_back(1, 0, 0.5 * (1 + sqrt5));
   vert.emplace_back(-1, 0, 0.5 * (1 + sqrt5));
   vert.emplace_back(-1, 1, 1);
   vert.emplace_back(0.5 * (-1 - sqrt5), 1, 0);
   vert.emplace_back(0.5 * (-1 - sqrt5), 0, 0.5 * (-1 + sqrt5));
   vert.emplace_back(-1, -1, 1);
   vert.emplace_back(-1, 0, 0.5 * (1 + sqrt5));
   vert.emplace_back(0.5 * (-1 - sqrt5), 0, 0.5 * (-1 + sqrt5));
   vert.emplace_back(0.5 * (-1 - sqrt5), -1, 0);
   vert.emplace_back(0, 0.5 * (1 - sqrt5), 0.5 * (1 + sqrt5));
   vert.emplace_back(-1, 0, 0.5 * (1 + sqrt5));
   vert.emplace_back(-1, -1, 1);
   vert.emplace_back(0, 0.5 * (-1 - sqrt5), 1);
   vert.emplace_back(0.5 * (-1 - sqrt5), -1, 0);
   vert.emplace_back(0.5 * (-1 - sqrt5), 0, 0.5 * (1 - sqrt5));
   vert.emplace_back(0.5 * (-1 - sqrt5), 1, 0);
   vert.emplace_back(0.5 * (-1 - sqrt5), 0, 0.5 * (-1 + sqrt5));
   vert.emplace_back(0.5 * (-1 - sqrt5), -1, 0);
   vert.emplace_back(0.5 * (-1 - sqrt5), 0, 0.5 * (1 - sqrt5));
   vert.emplace_back(-1, 0, 0.5 * (-1 - sqrt5));
   vert.emplace_back(-1, -1, -1);
   vert.emplace_back(0, 0.5 * (-1 - sqrt5), -1);
   vert.emplace_back(0.5 * (1 - sqrt5), 0.5 * (-1 - sqrt5), 0);
   vert.emplace_back(0.5 * (-1 - sqrt5), -1, 0);
   vert.emplace_back(-1, -1, -1);
   vert.emplace_back(0.5 * (1 - sqrt5), 0.5 * (-1 - sqrt5), 0);
   vert.emplace_back(0.5 * (-1 - sqrt5), -1, 0);
   vert.emplace_back(-1, -1, 1);
   vert.emplace_back(0, 0.5 * (-1 - sqrt5), 1);
   vert.emplace_back(-1, 1, -1);
   vert.emplace_back(-1, 0, 0.5 * (-1 - sqrt5));
   vert.emplace_back(0.5 * (-1 - sqrt5), 0, 0.5 * (1 - sqrt5));
   vert.emplace_back(0.5 * (-1 - sqrt5), 1, 0);
   vert.emplace_back(0, 0.5 * (-1 - sqrt5), -1);
   vert.emplace_back(0, 0.5 * (1 - sqrt5), 0.5 * (-1 - sqrt5));
   vert.emplace_back(-1, 0, 0.5 * (-1 - sqrt5));
   vert.emplace_back(-1, -1, -1);
   vert.emplace_back(0, 0.5 * (-1 - sqrt5), -1);
   vert.emplace_back(0.5 * (1 - sqrt5), 0.5 * (-1 - sqrt5), 0);
   vert.emplace_back(0, 0.5 * (-1 - sqrt5), 1);
   vert.emplace_back(0.5 * (-1 + sqrt5), 0.5 * (-1 - sqrt5), 0);
   vert.emplace_back(1, -1, -1);
   vert.emplace_back(0.5 * (1 + sqrt5), -1, 0);
   vert.emplace_back(0.5 * (-1 + sqrt5), 0.5 * (-1 - sqrt5), 0);
   vert.emplace_back(0, 0.5 * (-1 - sqrt5), -1);
   vert.emplace_back(0.5 * (1 + sqrt5), -1, 0);
   vert.emplace_back(1, -1, 1);
   vert.emplace_back(0, 0.5 * (-1 - sqrt5), 1);
   vert.emplace_back(0.5 * (-1 + sqrt5), 0.5 * (-1 - sqrt5), 0);
 
   tsl->AddFacet(vert[0], vert[1], vert[2], vert[3]);
   tsl->AddFacet(vert[4], vert[7], vert[6], vert[5]);
   tsl->AddFacet(vert[8], vert[9], vert[10], vert[11]);
   tsl->AddFacet(vert[12], vert[15], vert[14], vert[13]);
   tsl->AddFacet(vert[16], vert[17], vert[18], vert[19]);
   tsl->AddFacet(vert[20], vert[21], vert[22], vert[23]);
   tsl->AddFacet(vert[24], vert[25], vert[26], vert[27]);
   tsl->AddFacet(vert[28], vert[29], vert[30], vert[31]);
   tsl->AddFacet(vert[32], vert[35], vert[34], vert[33]);
   tsl->AddFacet(vert[36], vert[39], vert[38], vert[37]);
   tsl->AddFacet(vert[40], vert[41], vert[42], vert[43]);
   tsl->AddFacet(vert[44], vert[45], vert[46], vert[47]);
   tsl->AddFacet(vert[48], vert[51], vert[50], vert[49]);
   tsl->AddFacet(vert[52], vert[55], vert[54], vert[53]);
   tsl->AddFacet(vert[56], vert[57], vert[58], vert[59]);
   tsl->AddFacet(vert[60], vert[63], vert[62], vert[61]);
   tsl->AddFacet(vert[64], vert[67], vert[66], vert[65]);
   tsl->AddFacet(vert[68], vert[71], vert[70], vert[69]);
   tsl->AddFacet(vert[72], vert[73], vert[74], vert[75]);
   tsl->AddFacet(vert[76], vert[77], vert[78], vert[79]);
   tsl->AddFacet(vert[80], vert[81], vert[82], vert[83]);
   tsl->AddFacet(vert[84], vert[87], vert[86], vert[85]);
   tsl->AddFacet(vert[88], vert[89], vert[90], vert[91]);
   tsl->AddFacet(vert[92], vert[93], vert[94], vert[95]);
   tsl->AddFacet(vert[96], vert[99], vert[98], vert[97]);
   tsl->AddFacet(vert[100], vert[101], vert[102], vert[103]);
   tsl->AddFacet(vert[104], vert[107], vert[106], vert[105]);
   tsl->AddFacet(vert[108], vert[111], vert[110], vert[109]);
   tsl->AddFacet(vert[112], vert[113], vert[114], vert[115]);
   tsl->AddFacet(vert[116], vert[117], vert[118], vert[119]);
 
   TGeoVolume *vol = new TGeoVolume("TRIACONTHAEDRON", tsl, med);
   vol->SetLineColor(randomColor());
   vol->SetLineWidth(2);
   top->AddNode(vol, 1);
   gGeoManager->CloseGeometry();
 
   top->Draw();
 
   MakePicture();
   if (!comments)
      return;
   c->cd(2);
   TPaveText *pt = new TPaveText(0.01, 0.01, 0.99, 0.99);
   pt->SetLineColor(1);
   TText *text = pt->AddText("TGeoTessellated - Tessellated shape class");
   text->SetTextColor(2);
   AddMemberInfo(pt, "fNfacets", tsl->GetNfacets(), "number of facets");
   AddMemberInfo(pt, "fNvertices", tsl->GetNvertices(), "number of vertices");
   pt->AddText("----- A tessellated shape is defined by the number of facets");
   pt->AddText("-----    facets can be added using AddFacet");
   pt->AddText("----- Create with:    TGeoTessellated *tsl = new TGeoTessellated(nfacets);");
   AddExecInfo(pt, "tessellated");
   pt->Draw();
   c->cd(1);
}
 
//______________________________________________________________________________
void composite()
{
   auto c = create_canvas("A Boolean shape composition");
 
   if (gGeoManager)
      delete gGeoManager;
   new TGeoManager("xtru", "poza12");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98, 13, 2.7);
   TGeoMedium *med = new TGeoMedium("MED", 1, mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP", med, 100, 100, 100);
   gGeoManager->SetTopVolume(top);
   // define shape components with names
   TGeoPgon *pgon = new TGeoPgon("pg", 0., 360., 6, 2);
   pgon->DefineSection(0, 0, 0, 20);
   pgon->DefineSection(1, 30, 0, 20);
   new TGeoSphere("sph", 40., 45.);
   // define named geometrical transformations with names
   TGeoTranslation *tr = new TGeoTranslation(0., 0., 45.);
   tr->SetName("tr");
   // register all used transformations
   tr->RegisterYourself();
   // create the composite shape based on a Boolean expression
   TGeoCompositeShape *cs = new TGeoCompositeShape("mir", "sph:tr*pg");
   TGeoVolume *vol = new TGeoVolume("COMP", cs);
   vol->SetLineColor(randomColor());
   top->AddNode(vol, 1);
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(100);
 
   top->Draw();
 
   MakePicture();
   if (!comments)
      return;
   c->cd(2);
   TPaveText *pt = new TPaveText(0.01, 0.01, 0.99, 0.99);
   pt->SetLineColor(1);
   TText *text = pt->AddText("TGeoCompositeShape - composite shape class");
   text->SetTextColor(2);
   pt->AddText("----- Define the shape components and don't forget to name them");
   pt->AddText("----- Define geometrical transformations that apply to shape components");
   pt->AddText("----- Name all transformations and register them");
   pt->AddText("----- Define the composite shape based on a Boolean expression");
   pt->AddText("                TGeoCompositeShape(\"someName\", \"expression\")");
   pt->AddText("----- Expression is made of <shapeName:transfName> components related by Boolean operators");
   pt->AddText("----- Boolean operators can be: (+) union, (-) subtraction and (*) intersection");
   pt->AddText("----- Use parenthesis in the expression to force precedence");
   AddExecInfo(pt, "composite");
   pt->Draw();
   c->cd(1);
}
 
//______________________________________________________________________________
void ideal()
{
   // This is an ideal geometry. In real life, some geometry pieces are moved/rotated
   // with respect to their ideal positions. This is called alignment. Alignment
   // operations can be handled by TGeo starting from a CLOSED geometry (applied a posteriori)
   // Alignment is handled by PHYSICAL NODES, representing an unique object in geometry.
   //
   // Creating physical nodes:
   // 1. TGeoPhysicalNode *node = gGeoManager->MakePhysicalNode(const char *path)
   //   - creates a physical node represented by path
   //   - path can be : TOP_1/A_2/B_3
   //   - B_3 is the 'final node' e.g. the logical node represented by this physical node
   // 2. TGeoPhysicalNode *node = gGeoManager->MakePhysicalNode()
   //   - creates a physical node representing the current modeller state
 
   // Setting visualisation options for TGeoPhysicalNode *node:
   // 1.   node->SetVisibility(Bool_t flag); // set node visible(*) or invisible
   // 2.   node->SetIsVolAtt(Bool_t flag);   // set line attributes to match the ones of the volumes in the branch
   //    - default - TRUE
   //    - when called with FALSE - the attributes defined for the physical node will be taken
   //       node->SetLineColor(color);
   //       node->SetLineWidth(width);
   //       node->SetLineStyle(style);
   // 3.   node->SetVisibleFull(Bool_t flag); // not only last node in the branch is visible (default)
   //
   // Activating/deactivating physical nodes drawing - not needed in case of alignment
 
   // Aligning physical nodes
   //==========================
   //      node->Align(TGeoMatrix *newmat, TGeoShape *newshape, Bool_t check=kFALSE);
   //   newmat = new matrix to replace final node LOCAL matrix
   //   newshape = new shape to replace final node shape
   //   check = optional check if the new aligned node is overlapping
   // gGeoManager->SetDrawExtraPaths(Bool_t flag)
 
   auto c = create_canvas("Ideal geometry");
 
   if (gGeoManager)
      delete gGeoManager;
   new TGeoManager("alignment", "Ideal geometry");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98, 13, 2.7);
   TGeoMedium *med = new TGeoMedium("MED", 1, mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP", med, 100, 100, 10);
   gGeoManager->SetTopVolume(top);
   TGeoVolume *slicex = top->Divide("SX", 1, 10, -100, 10);
   TGeoVolume *slicey = slicex->Divide("SY", 2, 10, -100, 10);
   TGeoVolume *vol = gGeoManager->MakePgon("CELL", med, 0., 360., 6, 2);
   TGeoPgon *pgon = (TGeoPgon *)(vol->GetShape());
   pgon->DefineSection(0, -5, 0., 2.);
   pgon->DefineSection(1, 5, 0., 2.);
   vol->SetLineColor(randomColor());
   slicey->AddNode(vol, 1);
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
 
   top->Draw();
 
   MakePicture();
   if (!comments)
      return;
   c->cd(2);
   TPaveText *pt = new TPaveText(0.01, 0.01, 0.99, 0.99);
   pt->SetLineColor(1);
   TText *text = pt->AddText("Ideal / Aligned geometry");
   text->SetTextColor(2);
   pt->AddText("-- Create physical nodes for the objects you want to align");
   pt->AddText("-- You must start from a valid CLOSED geometry");
   pt->AddText("    TGeoPhysicalNode *node = gGeoManager->MakePhysicalNode(const char *path)");
   pt->AddText("    + creates a physical node represented by path, e.g. TOP_1/A_2/B_3");
   pt->AddText("    node->Align(TGeoMatrix *newmat, TGeoShape *newshape, Bool_t check=kFALSE)");
   pt->AddText("    + newmat = new matrix to replace final node LOCAL matrix");
   pt->AddText("    + newshape = new shape to replace final node shape");
   pt->AddText("    + check = optional check if the new aligned node is overlapping");
   pt->AddText(" ");
   pt->SetAllWith("--", "color", 4);
   pt->SetAllWith("--", "font", 72);
   pt->SetAllWith("--", "size", 0.04);
   pt->SetAllWith("+", "color", 2);
   pt->SetAllWith("+", "font", 72);
   pt->SetAllWith("+", "size", 0.04);
   pt->SetTextAlign(12);
   pt->SetTextSize(0.044);
   pt->Draw();
   c->cd(1);
}
 
//______________________________________________________________________________
void align()
{
   if (!gGeoManager)
      return;
   if (strcmp(gGeoManager->GetName(), "alignment")) {
      printf("Click: <Ideal geometry> first\n");
      return;
   }
   TObjArray *list = gGeoManager->GetListOfPhysicalNodes();
   for (Int_t i = 1; i <= 10; i++) {
      for (Int_t j = 1; j <= 10; j++) {
         TGeoPhysicalNode *node = nullptr;
         auto name = TString::Format("TOP_1/SX_%d/SY_%d/CELL_1", i, j);
         if (list)
            node = (TGeoPhysicalNode *)list->At(10 * (i - 1) + j - 1);
         if (!node)
            node = gGeoManager->MakePhysicalNode(name.Data());
         TGeoTranslation *tr;
         if (node->IsAligned()) {
            tr = (TGeoTranslation *)node->GetNode()->GetMatrix();
            tr->SetTranslation(2. * gRandom->Rndm(), 2. * gRandom->Rndm(), 0.);
         } else {
            tr = new TGeoTranslation(2. * gRandom->Rndm(), 2. * gRandom->Rndm(), 0.);
         }
         node->Align(tr);
      }
   }
   if (gPad) {
      gPad->Modified();
      gPad->Update();
   }
}
 
//______________________________________________________________________________
void geodemo()
{
   // root[0] .x geodemo.C
   // root[1] box();   //draw a TGeoBBox with description
   //
   // The box can be divided on one axis.
   //
   // root[2] box(iaxis, ndiv, start, step);
   //
   // where: iaxis = 1,2 or 3, meaning (X,Y,Z) or (Rxy, phi, Z) depending on shape type
   //        ndiv  = number of slices
   //        start = starting position (must be in shape range)
   //        step  = division step
   // If step=0, all range of a given axis will be divided
   //
   // The same can procedure can be performed for visualizing other shapes.
   // When drawing one shape after another, the old geometry/canvas will be deleted.
   TControlBar *bar = new TControlBar("vertical", "TGeo shapes", 10, 10);
   bar->AddButton("How to run  ", "help()", "Instructions for running this macro");
   bar->AddButton("Arb8        ", "arb8()",
                  "An arbitrary polyhedron defined by vertices (max 8) sitting on 2 parallel planes");
   bar->AddButton("Box         ", "box()", "A box shape.");
   bar->AddButton("Composite   ", "composite()", "A composite shape");
   bar->AddButton("Cone        ", "cone()", "A conical tube");
   bar->AddButton("Cone segment", "coneseg()", "A conical segment");
   bar->AddButton("Cut tube    ", "ctub()", "A cut tube segment");
   bar->AddButton("Elliptical tube", "eltu()", "An elliptical tube");
   bar->AddButton("Extruded poly", "xtru()", "A general polygone extrusion");
   bar->AddButton("Hyperboloid  ", "hype()", "A hyperboloid");
   bar->AddButton("Paraboloid  ", "parab()", "A paraboloid");
   bar->AddButton("Polycone    ", "pcon()", "A polycone shape");
   bar->AddButton("Polygone    ", "pgon()", "A polygone");
   bar->AddButton("Parallelepiped", "para()", "A parallelepiped shape");
   bar->AddButton("Sphere      ", "sphere()", "A spherical sector");
   bar->AddButton("Trd1        ", "trd1()", "A trapezoid with dX varying with Z");
   bar->AddButton("Trd2        ", "trd2()", "A trapezoid with both dX and dY varying with Z");
   bar->AddButton("Trapezoid   ", "trap()", "A general trapezoid");
   bar->AddButton("Torus       ", "torus()", "A toroidal segment");
   bar->AddButton("Tube        ", "tube()", "A tube with inner and outer radius");
   bar->AddButton("Tube segment", "tubeseg()", "A tube segment");
   bar->AddButton("Twisted trap", "gtra()", "A twisted trapezoid");
   bar->AddButton("Tessellated ", "tessellated()", "A tessellated shape");
   bar->AddButton("Aligned (ideal)", "ideal()", "An ideal (un-aligned) geometry");
   bar->AddButton("Un-aligned", "align()", "Some alignment operation");
   bar->AddButton("RAY-TRACE ON/OFF", "raytrace()", "Toggle ray-tracing mode");
   bar->AddButton("COMMENTS  ON/OFF", "comments = !comments;", "Toggle explanations pad ON/OFF");
   bar->AddButton("AXES ON/OFF", "axes()", "Toggle axes ON/OFF");
   bar->AddButton("AUTOROTATE ON/OFF", "autorotate()", "Toggle autorotation ON/OFF");
   bar->Show();
   gROOT->SaveContext();
   gRandom = new TRandom3();
}