TGeoPgon.cxx

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// @(#)root/geom:$Id$
// Author: Andrei Gheata   31/01/02
// TGeoPgon::Contains() implemented by Mihaela Gheata
 
/*************************************************************************
 * Copyright (C) 1995-2000, Rene Brun and Fons Rademakers.               *
 * All rights reserved.                                                  *
 *                                                                       *
 * For the licensing terms see $ROOTSYS/LICENSE.                         *
 * For the list of contributors see $ROOTSYS/README/CREDITS.             *
 *************************************************************************/
 
/** \class TGeoPgon
\ingroup Shapes_classes
 
Polygons are defined in the same way as polycones, the difference being
just that the segments between consecutive Z planes are regular
polygons. The phi segmentation is preserved and the shape is defined in
a similar manner, just that `rmin` and `rmax` represent the radii of the
circles inscribed in the inner/outer polygon.
 
Begin_Macro
{
   TCanvas *c = new TCanvas("c", "c",0,0,600,600);
   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->SetLineWidth(2);
   top->AddNode(vol,1);
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
   top->Draw();
   TView *view = gPad->GetView();
   view->ShowAxis();
}
End_Macro
 
The constructor of a polygon has the form:
 
~~~{.cpp}
TGeoPgon(Double_t phi1,Double_t dphi,Int_t nedges,Int_t nz);
~~~
 
The extra parameter `nedges` represent the number of equal edges of the
polygons, between `phi1` and `phi1+dphi.`
 
*/
 
#include "TGeoPgon.h"
 
#include <iostream>
 
#include "TGeoManager.h"
#include "TGeoVolume.h"
#include "TVirtualGeoPainter.h"
#include "TGeoTube.h"
#include "TBuffer3D.h"
#include "TBuffer3DTypes.h"
#include "TMath.h"
 
ClassImp(TGeoPgon);
 
////////////////////////////////////////////////////////////////////////////////
/// Constructor.
 
TGeoPgon::ThreadData_t::ThreadData_t() : fIntBuffer(nullptr), fDblBuffer(nullptr) {}
 
////////////////////////////////////////////////////////////////////////////////
/// Destructor.
 
TGeoPgon::ThreadData_t::~ThreadData_t()
{
   delete[] fIntBuffer;
   delete[] fDblBuffer;
}
 
////////////////////////////////////////////////////////////////////////////////
 
TGeoPgon::ThreadData_t &TGeoPgon::GetThreadData() const
{
   Int_t tid = TGeoManager::ThreadId();
   return *fThreadData[tid];
}
 
////////////////////////////////////////////////////////////////////////////////
 
void TGeoPgon::ClearThreadData() const
{
   std::lock_guard<std::mutex> guard(fMutex);
   std::vector<ThreadData_t *>::iterator i = fThreadData.begin();
   while (i != fThreadData.end()) {
      delete *i;
      ++i;
   }
   fThreadData.clear();
   fThreadSize = 0;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Create thread data for n threads max.
 
void TGeoPgon::CreateThreadData(Int_t nthreads)
{
   if (fThreadSize)
      ClearThreadData();
   std::lock_guard<std::mutex> guard(fMutex);
   fThreadData.resize(nthreads);
   fThreadSize = nthreads;
   for (Int_t tid = 0; tid < nthreads; tid++) {
      if (fThreadData[tid] == nullptr) {
         fThreadData[tid] = new ThreadData_t;
         fThreadData[tid]->fIntBuffer = new Int_t[fNedges + 10];
         fThreadData[tid]->fDblBuffer = new Double_t[fNedges + 10];
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// dummy ctor
 
TGeoPgon::TGeoPgon()
{
   SetShapeBit(TGeoShape::kGeoPgon);
   fNedges = 0;
   fThreadSize = 0;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Default constructor
 
TGeoPgon::TGeoPgon(Double_t phi, Double_t dphi, Int_t nedges, Int_t nz) : TGeoPcon(phi, dphi, nz)
{
   SetShapeBit(TGeoShape::kGeoPgon);
   fNedges = nedges;
   fThreadSize = 0;
   CreateThreadData(1);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Default constructor
 
TGeoPgon::TGeoPgon(const char *name, Double_t phi, Double_t dphi, Int_t nedges, Int_t nz)
   : TGeoPcon(name, phi, dphi, nz)
{
   SetShapeBit(TGeoShape::kGeoPgon);
   fNedges = nedges;
   fThreadSize = 0;
   CreateThreadData(1);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Default constructor in GEANT3 style
///  - param[0] = phi1
///  - param[1] = dphi
///  - param[2] = nedges
///  - param[3] = nz
///  - param[4] = z1
///  - param[5] = Rmin1
///  - param[6] = Rmax1
/// ...
 
TGeoPgon::TGeoPgon(Double_t *param) : TGeoPcon("")
{
   SetShapeBit(TGeoShape::kGeoPgon);
   SetDimensions(param);
   ComputeBBox();
   fThreadSize = 0;
   CreateThreadData(1);
}
 
////////////////////////////////////////////////////////////////////////////////
/// destructor
 
TGeoPgon::~TGeoPgon()
{
   ClearThreadData();
}
 
////////////////////////////////////////////////////////////////////////////////
/// Computes capacity of the shape in [length^3]
 
Double_t TGeoPgon::Capacity() const
{
   Int_t ipl;
   Double_t rmin1, rmax1, rmin2, rmax2, dphi, dz;
   Double_t capacity = 0.;
   dphi = fDphi / fNedges; // [deg]
   Double_t tphi2 = TMath::Tan(0.5 * dphi * TMath::DegToRad());
   for (ipl = 0; ipl < fNz - 1; ipl++) {
      dz = fZ[ipl + 1] - fZ[ipl];
      if (dz < TGeoShape::Tolerance())
         continue;
      rmin1 = fRmin[ipl];
      rmax1 = fRmax[ipl];
      rmin2 = fRmin[ipl + 1];
      rmax2 = fRmax[ipl + 1];
      capacity += fNedges * (tphi2 / 3.) * dz *
                  (rmax1 * rmax1 + rmax1 * rmax2 + rmax2 * rmax2 - rmin1 * rmin1 - rmin1 * rmin2 - rmin2 * rmin2);
   }
   return capacity;
}
 
////////////////////////////////////////////////////////////////////////////////
/// compute bounding box for a polygone
/// Check if the sections are in increasing Z order
 
void TGeoPgon::ComputeBBox()
{
   for (Int_t isec = 0; isec < fNz - 1; isec++) {
      if (fZ[isec] > fZ[isec + 1]) {
         InspectShape();
         Fatal("ComputeBBox", "Wrong section order");
      }
   }
   // Check if the last sections are valid
   if (TMath::Abs(fZ[1] - fZ[0]) < TGeoShape::Tolerance() ||
       TMath::Abs(fZ[fNz - 1] - fZ[fNz - 2]) < TGeoShape::Tolerance()) {
      InspectShape();
      Fatal("ComputeBBox", "Shape %s at index %d: Not allowed first two or last two sections at same Z", GetName(),
            gGeoManager->GetListOfShapes()->IndexOf(this));
   }
   Double_t zmin = TMath::Min(fZ[0], fZ[fNz - 1]);
   Double_t zmax = TMath::Max(fZ[0], fZ[fNz - 1]);
   // find largest rmax an smallest rmin
   Double_t rmin, rmax;
   Double_t divphi = fDphi / fNedges;
   // find the radius of the outscribed circle
   rmin = fRmin[TMath::LocMin(fNz, fRmin)];
   rmax = fRmax[TMath::LocMax(fNz, fRmax)];
   rmax = rmax / TMath::Cos(0.5 * divphi * TMath::DegToRad());
   Double_t phi1 = fPhi1;
   Double_t phi2 = phi1 + fDphi;
 
   Double_t xc[4];
   Double_t yc[4];
   xc[0] = rmax * TMath::Cos(phi1 * TMath::DegToRad());
   yc[0] = rmax * TMath::Sin(phi1 * TMath::DegToRad());
   xc[1] = rmax * TMath::Cos(phi2 * TMath::DegToRad());
   yc[1] = rmax * TMath::Sin(phi2 * TMath::DegToRad());
   xc[2] = rmin * TMath::Cos(phi1 * TMath::DegToRad());
   yc[2] = rmin * TMath::Sin(phi1 * TMath::DegToRad());
   xc[3] = rmin * TMath::Cos(phi2 * TMath::DegToRad());
   yc[3] = rmin * TMath::Sin(phi2 * TMath::DegToRad());
 
   Double_t xmin = xc[TMath::LocMin(4, &xc[0])];
   Double_t xmax = xc[TMath::LocMax(4, &xc[0])];
   Double_t ymin = yc[TMath::LocMin(4, &yc[0])];
   Double_t ymax = yc[TMath::LocMax(4, &yc[0])];
 
   Double_t ddp = -phi1;
   if (ddp < 0)
      ddp += 360;
   if (ddp <= fDphi)
      xmax = rmax;
   ddp = 90 - phi1;
   if (ddp < 0)
      ddp += 360;
   if (ddp <= fDphi)
      ymax = rmax;
   ddp = 180 - phi1;
   if (ddp < 0)
      ddp += 360;
   if (ddp <= fDphi)
      xmin = -rmax;
   ddp = 270 - phi1;
   if (ddp < 0)
      ddp += 360;
   if (ddp <= fDphi)
      ymin = -rmax;
   fOrigin[0] = 0.5 * (xmax + xmin);
   fOrigin[1] = 0.5 * (ymax + ymin);
   fOrigin[2] = 0.5 * (zmax + zmin);
   fDX = 0.5 * (xmax - xmin);
   fDY = 0.5 * (ymax - ymin);
   fDZ = 0.5 * (zmax - zmin);
   SetShapeBit(kGeoClosedShape);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Compute normal to closest surface from POINT.
 
void TGeoPgon::ComputeNormal(const Double_t *point, const Double_t *dir, Double_t *norm)
{
   memset(norm, 0, 3 * sizeof(Double_t));
   Double_t phi1 = 0, phi2 = 0, c1 = 0, s1 = 0, c2 = 0, s2 = 0;
   Double_t dz, rmin1, rmin2;
   Bool_t is_seg = (fDphi < 360) ? kTRUE : kFALSE;
   if (is_seg) {
      phi1 = fPhi1;
      if (phi1 < 0)
         phi1 += 360;
      phi2 = phi1 + fDphi;
      phi1 *= TMath::DegToRad();
      phi2 *= TMath::DegToRad();
      c1 = TMath::Cos(phi1);
      s1 = TMath::Sin(phi1);
      c2 = TMath::Cos(phi2);
      s2 = TMath::Sin(phi2);
      if (TGeoShape::IsCloseToPhi(1E-5, point, c1, s1, c2, s2)) {
         TGeoShape::NormalPhi(point, dir, norm, c1, s1, c2, s2);
         return;
      }
   } // Phi done
 
   Int_t ipl = TMath::BinarySearch(fNz, fZ, point[2]);
   if (ipl == (fNz - 1) || ipl < 0) {
      // point outside Z range
      norm[2] = TMath::Sign(1., dir[2]);
      return;
   }
   Int_t iplclose = ipl;
   if ((fZ[ipl + 1] - point[2]) < (point[2] - fZ[ipl]))
      iplclose++;
   dz = TMath::Abs(fZ[iplclose] - point[2]);
 
   Double_t divphi = fDphi / fNedges;
   Double_t phi = TMath::ATan2(point[1], point[0]) * TMath::RadToDeg();
   while (phi < fPhi1)
      phi += 360.;
   Double_t ddp = phi - fPhi1;
   Int_t ipsec = Int_t(ddp / divphi);
   Double_t ph0 = (fPhi1 + divphi * (ipsec + 0.5)) * TMath::DegToRad();
   // compute projected distance
   Double_t r, rsum, rpgon, ta, calf;
   r = TMath::Abs(point[0] * TMath::Cos(ph0) + point[1] * TMath::Sin(ph0));
   if (dz < 1E-5) {
      if (iplclose == 0 || iplclose == (fNz - 1)) {
         norm[2] = TMath::Sign(1., dir[2]);
         return;
      }
      if (iplclose == ipl && TGeoShape::IsSameWithinTolerance(fZ[ipl], fZ[ipl - 1])) {
         if (r < TMath::Max(fRmin[ipl], fRmin[ipl - 1]) || r > TMath::Min(fRmax[ipl], fRmax[ipl - 1])) {
            norm[2] = TMath::Sign(1., dir[2]);
            return;
         }
      } else {
         if (TGeoShape::IsSameWithinTolerance(fZ[iplclose], fZ[iplclose + 1])) {
            if (r < TMath::Max(fRmin[iplclose], fRmin[iplclose + 1]) ||
                r > TMath::Min(fRmax[iplclose], fRmax[iplclose + 1])) {
               norm[2] = TMath::Sign(1., dir[2]);
               return;
            }
         }
      }
   } //-> Z done
 
   dz = fZ[ipl + 1] - fZ[ipl];
   rmin1 = fRmin[ipl];
   rmin2 = fRmin[ipl + 1];
   rsum = rmin1 + rmin2;
   Double_t safe = TGeoShape::Big();
   if (rsum > 1E-10) {
      ta = (rmin2 - rmin1) / dz;
      calf = 1. / TMath::Sqrt(1 + ta * ta);
      rpgon = rmin1 + (point[2] - fZ[ipl]) * ta;
      safe = TMath::Abs(r - rpgon);
      norm[0] = calf * TMath::Cos(ph0);
      norm[1] = calf * TMath::Sin(ph0);
      norm[2] = -calf * ta;
   }
   ta = (fRmax[ipl + 1] - fRmax[ipl]) / dz;
   calf = 1. / TMath::Sqrt(1 + ta * ta);
   rpgon = fRmax[ipl] + (point[2] - fZ[ipl]) * ta;
   if (safe > TMath::Abs(rpgon - r)) {
      norm[0] = calf * TMath::Cos(ph0);
      norm[1] = calf * TMath::Sin(ph0);
      norm[2] = -calf * ta;
   }
   if (norm[0] * dir[0] + norm[1] * dir[1] + norm[2] * dir[2] < 0) {
      norm[0] = -norm[0];
      norm[1] = -norm[1];
      norm[2] = -norm[2];
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// test if point is inside this shape
/// check total z range
 
Bool_t TGeoPgon::Contains(const Double_t *point) const
{
   if (point[2] < fZ[0])
      return kFALSE;
   if (point[2] > fZ[fNz - 1])
      return kFALSE;
   Double_t divphi = fDphi / fNedges;
   // now check phi
   Double_t phi = TMath::ATan2(point[1], point[0]) * TMath::RadToDeg();
   while (phi < fPhi1)
      phi += 360.0;
   Double_t ddp = phi - fPhi1;
   if (ddp > fDphi)
      return kFALSE;
   // now find phi division
   Int_t ipsec = TMath::Min(Int_t(ddp / divphi), fNedges - 1);
   Double_t ph0 = (fPhi1 + divphi * (ipsec + 0.5)) * TMath::DegToRad();
   // now check projected distance
   Double_t r = point[0] * TMath::Cos(ph0) + point[1] * TMath::Sin(ph0);
   // find in which Z section the point is in
   Int_t iz = TMath::BinarySearch(fNz, fZ, point[2]);
   if (iz == fNz - 1) {
      if (r < fRmin[iz])
         return kFALSE;
      if (r > fRmax[iz])
         return kFALSE;
      return kTRUE;
   }
   Double_t dz = fZ[iz + 1] - fZ[iz];
   Double_t rmin, rmax;
   if (dz < 1E-8) {
      // we are at a radius-changing plane
      rmin = TMath::Min(fRmin[iz], fRmin[iz + 1]);
      rmax = TMath::Max(fRmax[iz], fRmax[iz + 1]);
      if (r < rmin)
         return kFALSE;
      if (r > rmax)
         return kFALSE;
      return kTRUE;
   }
   // now compute rmin and rmax and test the value of r
   Double_t dzrat = (point[2] - fZ[iz]) / dz;
   rmin = fRmin[iz] + dzrat * (fRmin[iz + 1] - fRmin[iz]);
   // is the point inside the 'hole' at the center of the volume ?
   if (r < rmin)
      return kFALSE;
   rmax = fRmax[iz] + dzrat * (fRmax[iz + 1] - fRmax[iz]);
   if (r > rmax)
      return kFALSE;
 
   return kTRUE;
}
 
////////////////////////////////////////////////////////////////////////////////
/// compute distance from inside point to surface of the polygone
/// first find out in which Z section the point is in
 
Double_t
TGeoPgon::DistFromInside(const Double_t *point, const Double_t *dir, Int_t iact, Double_t step, Double_t *safe) const
{
   if (iact < 3 && safe) {
      *safe = Safety(point, kTRUE);
      if (iact == 0)
         return TGeoShape::Big();
      if (iact == 1 && step < *safe)
         return TGeoShape::Big();
   }
   // find current Z section
   Int_t ipl, ipsec;
   ipl = TMath::BinarySearch(fNz, fZ, point[2]);
   if (ipl == fNz - 1) {
      if (dir[2] >= 0)
         return 0.;
      ipl--;
   }
   if (ipl < 0) {
      // point out
      if (dir[2] <= 0)
         return 0.;
      ipl++;
   }
   Double_t stepmax = step;
   if (!fThreadSize)
      ((TGeoPgon *)this)->CreateThreadData(1);
   ThreadData_t &td = GetThreadData();
   Double_t *sph = td.fDblBuffer;
   Int_t *iph = td.fIntBuffer;
   // locate current phi sector [0,fNedges-1]; -1 for dead region
   LocatePhi(point, ipsec);
   if (ipsec < 0) {
      // Point on a phi boundary - entering or exiting ?
      Double_t phi1 = fPhi1 * TMath::DegToRad();
      Double_t phi2 = (fPhi1 + fDphi) * TMath::DegToRad();
      if ((point[0] * dir[1] - point[1] * dir[0]) > 0) {
         // phi1 next crossing
         if ((point[0] * TMath::Cos(phi1) + point[1] * TMath::Sin(phi1)) <
             (point[0] * TMath::Cos(phi2) + point[1] * TMath::Sin(phi2))) {
            // close to phimax
            return 0.0;
         } else {
            // close to phi1 - ignore it
            ipsec = 0;
         }
      } else {
         // phimax next crossing
         if ((point[0] * TMath::Cos(phi1) + point[1] * TMath::Sin(phi1)) >
             (point[0] * TMath::Cos(phi2) + point[1] * TMath::Sin(phi2))) {
            // close to phi1
            return 0.0;
         } else {
            // close to phimax - ignore it
            ipsec = fNedges - 1;
         }
      }
   }
   Int_t ipln = -1;
   if (TGeoShape::IsSameWithinTolerance(fZ[ipl], fZ[ipl + 1])) {
      ipln = ipl;
   } else {
      if (fNz > 3 && ipl >= 0 && ipl < fNz - 3 && TGeoShape::IsSameWithinTolerance(fZ[ipl + 1], fZ[ipl + 2]) &&
          TMath::Abs(point[2] - fZ[ipl + 1]) < 1.E-8) {
         ipln = ipl + 1;
      } else {
         if (ipl > 1 && TGeoShape::IsSameWithinTolerance(fZ[ipl], fZ[ipl - 1]) &&
             TMath::Abs(point[2] - fZ[ipl]) < 1.E-8)
            ipln = ipl - 1;
      }
   }
   if (ipln > 0) {
      // point between segments
      Double_t divphi = fDphi / fNedges;
      Double_t phi = (fPhi1 + (ipsec + 0.5) * divphi) * TMath::DegToRad();
      Double_t cphi = TMath::Cos(phi);
      Double_t sphi = TMath::Sin(phi);
      Double_t rproj = point[0] * cphi + point[1] * sphi;
      if (dir[2] > 0) {
         ipl = ipln + 1;
         if (rproj > fRmin[ipln] && rproj < fRmin[ipln + 1])
            return 0.0;
         if (rproj < fRmax[ipln] && rproj > fRmax[ipln + 1])
            return 0.0;
      } else {
         ipl = ipln - 1;
         if (rproj < fRmin[ipln] && rproj > fRmin[ipln + 1])
            return 0.0;
         if (rproj > fRmax[ipln] && rproj < fRmax[ipln + 1])
            return 0.0;
      }
   }
 
   Int_t icrossed;
   icrossed = GetPhiCrossList(point, dir, ipsec, sph, iph, stepmax);
   Double_t snext;
   if (TMath::Abs(dir[2]) < TGeoShape::Tolerance()) {
      if (SliceCrossingInZ(point, dir, icrossed, iph, sph, snext, stepmax))
         return snext;
      if (snext > TGeoShape::Tolerance())
         return TGeoShape::Big();
      return 0.;
   }
   if (SliceCrossingIn(point, dir, ipl, icrossed, iph, sph, snext, stepmax))
      return snext;
   if (snext > TGeoShape::Tolerance())
      return TGeoShape::Big();
   return 0.;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Locates index IPSEC of the phi sector containing POINT.
 
void TGeoPgon::LocatePhi(const Double_t *point, Int_t &ipsec) const
{
   Double_t phi = TMath::ATan2(point[1], point[0]) * TMath::RadToDeg();
   while (phi < fPhi1)
      phi += 360.;
   ipsec = Int_t(fNedges * (phi - fPhi1) / fDphi); // [0, fNedges-1]
   if (ipsec > fNedges - 1)
      ipsec = -1; // in gap
}
 
////////////////////////////////////////////////////////////////////////////////
/// Returns lists of PGON phi crossings for a ray starting from POINT.
 
Int_t TGeoPgon::GetPhiCrossList(const Double_t *point, const Double_t *dir, Int_t istart, Double_t *sphi, Int_t *iphi,
                                Double_t stepmax) const
{
   Double_t rxy, phi, cph, sph;
   Int_t icrossed = 0;
   if ((1. - TMath::Abs(dir[2])) < 1E-8) {
      // ray is going parallel with Z
      iphi[0] = istart;
      sphi[0] = stepmax;
      return 1;
   }
   Bool_t shootorig = (TMath::Abs(point[0] * dir[1] - point[1] * dir[0]) < 1E-8) ? kTRUE : kFALSE;
   Double_t divphi = fDphi / fNedges;
   if (shootorig) {
      Double_t rdotn = point[0] * dir[0] + point[1] * dir[1];
      if (rdotn > 0) {
         sphi[0] = stepmax;
         iphi[0] = istart;
         return 1;
      }
      sphi[0] = TMath::Sqrt((point[0] * point[0] + point[1] * point[1]) / (1. - dir[2] * dir[2]));
      iphi[0] = istart;
      if (sphi[0] > stepmax) {
         sphi[0] = stepmax;
         return 1;
      }
      phi = TMath::ATan2(dir[1], dir[0]) * TMath::RadToDeg();
      while (phi < fPhi1)
         phi += 360.;
      istart = Int_t((phi - fPhi1) / divphi);
      if (istart > fNedges - 1)
         istart = -1;
      iphi[1] = istart;
      sphi[1] = stepmax;
      return 2;
   }
   Int_t incsec = Int_t(TMath::Sign(1., point[0] * dir[1] - point[1] * dir[0]));
   Int_t ist;
   if (istart < 0)
      ist = (incsec > 0) ? 0 : fNedges;
   else
      ist = (incsec > 0) ? (istart + 1) : istart;
   Bool_t crossing = kTRUE;
   Bool_t gapdone = kFALSE;
   divphi *= TMath::DegToRad();
   Double_t phi1 = fPhi1 * TMath::DegToRad();
   while (crossing) {
      if (istart < 0)
         gapdone = kTRUE;
      phi = phi1 + ist * divphi;
      cph = TMath::Cos(phi);
      sph = TMath::Sin(phi);
      crossing = IsCrossingSemiplane(point, dir, cph, sph, sphi[icrossed], rxy);
      if (!crossing)
         sphi[icrossed] = stepmax;
      iphi[icrossed++] = istart;
      if (crossing) {
         if (sphi[icrossed - 1] > stepmax) {
            sphi[icrossed - 1] = stepmax;
            return icrossed;
         }
         if (istart < 0) {
            istart = (incsec > 0) ? 0 : (fNedges - 1);
         } else {
            istart += incsec;
            if (istart > fNedges - 1)
               istart = (fDphi < 360.) ? (-1) : 0;
            else if (istart < 0 && TGeoShape::IsSameWithinTolerance(fDphi, 360))
               istart = fNedges - 1;
         }
         if (istart < 0) {
            if (gapdone)
               return icrossed;
            ist = (incsec > 0) ? 0 : fNedges;
         } else {
            ist = (incsec > 0) ? (istart + 1) : istart;
         }
      }
   }
   return icrossed;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Performs ray propagation between Z segments.
 
Bool_t TGeoPgon::SliceCrossingInZ(const Double_t *point, const Double_t *dir, Int_t nphi, Int_t *iphi,
                                  Double_t *stepphi, Double_t &snext, Double_t stepmax) const
{
   snext = 0.;
   if (!nphi)
      return kFALSE;
   Int_t i;
   Double_t rmin, rmax;
   Double_t apg, bpg;
   Double_t pt[3];
   if (iphi[0] < 0 && nphi == 1)
      return kFALSE;
   // Get current Z segment
   Int_t ipl = TMath::BinarySearch(fNz, fZ, point[2]);
   if (ipl < 0 || ipl == fNz - 1)
      return kFALSE;
   if (TMath::Abs(point[2] - fZ[ipl]) < TGeoShape::Tolerance()) {
      if (ipl < fNz - 2 && TGeoShape::IsSameWithinTolerance(fZ[ipl], fZ[ipl + 1])) {
         rmin = TMath::Min(fRmin[ipl], fRmin[ipl + 1]);
         rmax = TMath::Max(fRmax[ipl], fRmax[ipl + 1]);
      } else if (ipl > 1 && TGeoShape::IsSameWithinTolerance(fZ[ipl], fZ[ipl - 1])) {
         rmin = TMath::Min(fRmin[ipl], fRmin[ipl + 1]);
         rmax = TMath::Max(fRmax[ipl], fRmax[ipl + 1]);
      } else {
         rmin = fRmin[ipl];
         rmax = fRmax[ipl];
      }
   } else {
      rmin = Rpg(point[2], ipl, kTRUE, apg, bpg);
      rmax = Rpg(point[2], ipl, kFALSE, apg, bpg);
   }
   Int_t iphcrt;
   Double_t divphi = TMath::DegToRad() * fDphi / fNedges;
   Double_t rproj, ndot, dist;
   Double_t phi1 = fPhi1 * TMath::DegToRad();
   Double_t cosph, sinph;
   Double_t snextphi = 0.;
   Double_t step = 0;
   Double_t phi;
   memcpy(pt, point, 3 * sizeof(Double_t));
   for (iphcrt = 0; iphcrt < nphi; iphcrt++) {
      if (step > stepmax) {
         snext = step;
         return kFALSE;
      }
      if (iphi[iphcrt] < 0) {
         snext = step;
         return kTRUE;
      }
      // check crossing
      snextphi = stepphi[iphcrt];
      phi = phi1 + (iphi[iphcrt] + 0.5) * divphi;
      cosph = TMath::Cos(phi);
      sinph = TMath::Sin(phi);
      rproj = pt[0] * cosph + pt[1] * sinph;
      dist = TGeoShape::Big();
      ndot = dir[0] * cosph + dir[1] * sinph;
      if (!TGeoShape::IsSameWithinTolerance(ndot, 0)) {
         dist = (ndot > 0) ? ((rmax - rproj) / ndot) : ((rmin - rproj) / ndot);
         if (dist < 0)
            dist = 0.;
      }
      if (dist < (snextphi - step)) {
         snext = step + dist;
         if (snext < stepmax)
            return kTRUE;
         return kFALSE;
      }
      step = snextphi;
      for (i = 0; i < 3; i++)
         pt[i] = point[i] + step * dir[i];
   }
   snext = step;
   return kFALSE;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Performs ray propagation between Z segments.
 
Bool_t TGeoPgon::SliceCrossingZ(const Double_t *point, const Double_t *dir, Int_t nphi, Int_t *iphi, Double_t *stepphi,
                                Double_t &snext, Double_t stepmax) const
{
   if (!nphi)
      return kFALSE;
   Int_t i;
   Double_t rmin, rmax;
   Double_t apg, bpg;
   Double_t pt[3];
   if (iphi[0] < 0 && nphi == 1)
      return kFALSE;
   // Get current Z segment
   Int_t ipl = TMath::BinarySearch(fNz, fZ, point[2]);
   if (ipl < 0 || ipl == fNz - 1)
      return kFALSE;
   if (TMath::Abs(point[2] - fZ[ipl]) < TGeoShape::Tolerance()) {
      if (ipl < fNz - 2 && TGeoShape::IsSameWithinTolerance(fZ[ipl], fZ[ipl + 1])) {
         rmin = TMath::Min(fRmin[ipl], fRmin[ipl + 1]);
         rmax = TMath::Max(fRmax[ipl], fRmax[ipl + 1]);
      } else if (ipl > 1 && TGeoShape::IsSameWithinTolerance(fZ[ipl], fZ[ipl - 1])) {
         rmin = TMath::Min(fRmin[ipl], fRmin[ipl + 1]);
         rmax = TMath::Max(fRmax[ipl], fRmax[ipl + 1]);
      } else {
         rmin = fRmin[ipl];
         rmax = fRmax[ipl];
      }
   } else {
      rmin = Rpg(point[2], ipl, kTRUE, apg, bpg);
      rmax = Rpg(point[2], ipl, kFALSE, apg, bpg);
   }
   Int_t iphcrt;
   Double_t divphi = TMath::DegToRad() * fDphi / fNedges;
   Double_t rproj, ndot, dist;
   Double_t phi1 = fPhi1 * TMath::DegToRad();
   Double_t cosph, sinph;
   Double_t snextphi = 0.;
   Double_t step = 0;
   Double_t phi;
   memcpy(pt, point, 3 * sizeof(Double_t));
   for (iphcrt = 0; iphcrt < nphi; iphcrt++) {
      if (step > stepmax)
         return kFALSE;
      snextphi = stepphi[iphcrt];
      if (iphi[iphcrt] < 0) {
         if (iphcrt == nphi - 1)
            return kFALSE;
         if (snextphi > stepmax)
            return kFALSE;
         for (i = 0; i < 3; i++)
            pt[i] = point[i] + snextphi * dir[i];
         phi = phi1 + (iphi[iphcrt + 1] + 0.5) * divphi;
         cosph = TMath::Cos(phi);
         sinph = TMath::Sin(phi);
         rproj = pt[0] * cosph + pt[1] * sinph;
         if (rproj < rmin || rproj > rmax) {
            step = snextphi;
            continue;
         }
         snext = snextphi;
         return kTRUE;
      }
      // check crossing
      phi = phi1 + (iphi[iphcrt] + 0.5) * divphi;
      cosph = TMath::Cos(phi);
      sinph = TMath::Sin(phi);
      rproj = pt[0] * cosph + pt[1] * sinph;
      dist = TGeoShape::Big();
      ndot = dir[0] * cosph + dir[1] * sinph;
      if (rproj < rmin) {
         dist = (ndot > 0) ? ((rmin - rproj) / ndot) : TGeoShape::Big();
      } else {
         dist = (ndot < 0) ? ((rmax - rproj) / ndot) : TGeoShape::Big();
      }
      if (dist < 1E10) {
         snext = step + dist;
         if (snext < stepmax)
            return kTRUE;
      }
      step = snextphi;
      for (i = 0; i < 3; i++)
         pt[i] = point[i] + step * dir[i];
   }
   return kFALSE;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Check boundary crossing inside phi slices. Return distance snext to first crossing
/// if smaller than stepmax.
/// Protection in case point is in phi gap or close to phi boundaries and exiting
 
Bool_t TGeoPgon::SliceCrossingIn(const Double_t *point, const Double_t *dir, Int_t ipl, Int_t nphi, Int_t *iphi,
                                 Double_t *stepphi, Double_t &snext, Double_t stepmax) const
{
   snext = 0.;
   if (!nphi)
      return kFALSE;
   Int_t i;
   Int_t iphstart = 0;
   Double_t pt[3];
   if (iphi[0] < 0) {
      if (stepphi[0] > TGeoShape::Tolerance())
         return kFALSE;
      iphstart = 1;
   }
   if (nphi > 1 && iphi[1] < 0 && stepphi[0] < TGeoShape::Tolerance()) {
      snext = stepphi[0];
      return kTRUE;
   }
   // Get current Z segment
   Double_t snextphi = 0.;
   Double_t step = 0;
   Int_t incseg = (dir[2] > 0) ? 1 : -1; // dir[2] is never 0 here
   // Compute the projected radius from starting point
   Int_t iplstart = ipl;
   Int_t iphcrt = 0;
   Double_t apr = TGeoShape::Big(), bpr = 0, db = 0;
   Double_t rpg = 0, rnew = 0, znew = 0;
   Double_t rpgin = 0, rpgout = 0, apgin = 0, apgout = 0, bpgin = 0, bpgout = 0;
   Double_t divphi = TMath::DegToRad() * fDphi / fNedges;
   Double_t phi1 = fPhi1 * TMath::DegToRad();
   Double_t phi = 0, dz = 0;
   Double_t cosph = 0, sinph = 0;
   Double_t distz = 0, distr = 0, din = 0, dout = 0;
   Double_t invdir = 1. / dir[2];
   memcpy(pt, point, 3 * sizeof(Double_t));
   for (iphcrt = iphstart; iphcrt < nphi; iphcrt++) {
      // check if step to current checked slice is too big
      if (step > stepmax) {
         snext = step;
         return kFALSE;
      }
      if (iphi[iphcrt] < 0) {
         snext = snextphi;
         return kTRUE;
      }
      snextphi = stepphi[iphcrt];
      phi = phi1 + (iphi[iphcrt] + 0.5) * divphi;
      cosph = TMath::Cos(phi);
      sinph = TMath::Sin(phi);
      Double_t rproj = Rproj(pt[2], pt, dir, cosph, sinph, apr, bpr);
      // compute distance to next Z plane
      while (ipl >= 0 && ipl < fNz - 1) {
         din = dout = TGeoShape::Big();
         // dist to last boundary of current segment according dir
         distz = (fZ[ipl + ((1 + incseg) >> 1)] - pt[2]) * invdir;
         // length of current segment
         dz = fZ[ipl + 1] - fZ[ipl];
         if (dz < TGeoShape::Tolerance()) {
            rnew = apr + bpr * fZ[ipl];
            rpg = (rnew - fRmin[ipl]) * (rnew - fRmin[ipl + 1]);
            if (rpg <= 0)
               din = distz;
            rpg = (rnew - fRmax[ipl]) * (rnew - fRmax[ipl + 1]);
            if (rpg <= 0)
               dout = distz;
            distr = TMath::Min(din, dout);
         } else {
            rpgin = Rpg(pt[2], ipl, kTRUE, apgin, bpgin);
            db = bpgin - bpr;
            if (TMath::Abs(db) > TGeoShape::Tolerance()) {
               znew = (apr - apgin) / db;
               din = (znew - pt[2]) * invdir;
            }
            rpgout = Rpg(pt[2], ipl, kFALSE, apgout, bpgout);
            db = bpgout - bpr;
            if (TMath::Abs(db) > TGeoShape::Tolerance()) {
               znew = (apr - apgout) / db;
               dout = (znew - pt[2]) * invdir;
            }
            // protection for the first segment
            Double_t dinp = (din > TMath::Abs(snext - TGeoShape::Tolerance())) ? din : TGeoShape::Big();
            Double_t doutp = (dout > TMath::Abs(snext - TGeoShape::Tolerance())) ? dout : TGeoShape::Big();
            distr = TMath::Min(dinp, doutp);
            if (iphcrt == iphstart && ipl == iplstart) {
               if (rproj < rpgin + 1.E-8) {
                  Double_t ndotd = dir[0] * cosph + dir[1] * sinph + dir[2] * (fRmin[ipl] - fRmin[ipl + 1]) / dz;
                  if (ndotd < 0) {
                     snext = (din < 0) ? step : (step + din);
                     return kTRUE;
                  } else {
                     // Ignore din
                     din = -TGeoShape::Big();
                  }
                  distr = TMath::Max(din, dout);
                  if (distr < TGeoShape::Tolerance())
                     distr = TGeoShape::Big();
               } else if (rproj > rpgout - 1.E-8) {
                  Double_t ndotd = dir[0] * cosph + dir[1] * sinph + dir[2] * (fRmax[ipl] - fRmax[ipl + 1]) / dz;
                  if (ndotd > 0) {
                     snext = (dout < 0) ? step : (step + dout);
                     return kTRUE;
                  } else {
                     // Ignore dout
                     dout = -TGeoShape::Big();
                  }
                  distr = TMath::Max(din, dout);
                  if (distr < TGeoShape::Tolerance())
                     distr = TGeoShape::Big();
               }
            }
         }
         if (distr < snext - TGeoShape::Tolerance())
            distr = TGeoShape::Big();
         if (snextphi < step + TMath::Min(distz, distr)) {
            for (i = 0; i < 3; i++)
               pt[i] = point[i] + snextphi * dir[i];
            step = snextphi;
            snext = 0.0;
            break;
         }
         if (distr <= distz + TGeoShape::Tolerance()) {
            step += distr;
            snext = step;
            return (step > stepmax) ? kFALSE : kTRUE;
         }
         // we have crossed a Z boundary
         snext = distz;
         if ((ipl + incseg < 0) || (ipl + incseg > fNz - 2)) {
            // it was the last boundary
            step += distz;
            snext = step;
            return (step > stepmax) ? kFALSE : kTRUE;
         }
         ipl += incseg;
      } // end loop Z
   }    // end loop phi
   snext = TGeoShape::Big();
   return kFALSE;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Check boundary crossing inside phi slices. Return distance snext to first crossing
/// if smaller than stepmax.
 
Bool_t TGeoPgon::SliceCrossing(const Double_t *point, const Double_t *dir, Int_t nphi, Int_t *iphi, Double_t *stepphi,
                               Double_t &snext, Double_t stepmax) const
{
   if (!nphi)
      return kFALSE;
   Int_t i;
   Double_t pt[3];
   if (iphi[0] < 0 && nphi == 1)
      return kFALSE;
 
   Double_t snextphi = 0.;
   Double_t step = 0;
   // Get current Z segment
   Int_t incseg = (dir[2] > 0) ? 1 : -1; // dir[2] is never 0 here
   Int_t ipl = TMath::BinarySearch(fNz, fZ, point[2]);
   if (ipl < 0) {
      ipl = 0; // this should never happen
      if (incseg < 0)
         return kFALSE;
   } else {
      if (ipl == fNz - 1) {
         ipl = fNz - 2; // nor this
         if (incseg > 0)
            return kFALSE;
      } else {
         if (TMath::Abs(point[2] - fZ[ipl]) < TGeoShape::Tolerance()) {
            // we are at the sector edge, but never inside the pgon
            if ((ipl + incseg) < 0 || (ipl + incseg) > fNz - 1)
               return kFALSE;
            if (TGeoShape::IsSameWithinTolerance(fZ[ipl], fZ[ipl + incseg]))
               ipl += incseg;
            // move to next clean segment if downwards
            if (incseg < 0) {
               if (TGeoShape::IsSameWithinTolerance(fZ[ipl], fZ[ipl + 1]))
                  ipl--;
            }
         }
      }
   }
   // Compute the projected radius from starting point
   Int_t iphcrt;
   Double_t apg, bpg;
   Double_t rpgin;
   Double_t rpgout;
   Double_t divphi = TMath::DegToRad() * fDphi / fNedges;
   Double_t phi1 = fPhi1 * TMath::DegToRad();
   Double_t phi;
   Double_t cosph, sinph;
   Double_t rproj;
   memcpy(pt, point, 3 * sizeof(Double_t));
   for (iphcrt = 0; iphcrt < nphi; iphcrt++) {
      // check if step to current checked slice is too big
      if (step > stepmax)
         return kFALSE;
      // jump over the dead sector
      snextphi = stepphi[iphcrt];
      if (iphi[iphcrt] < 0) {
         if (iphcrt == nphi - 1)
            return kFALSE;
         if (snextphi > stepmax)
            return kFALSE;
         for (i = 0; i < 3; i++)
            pt[i] = point[i] + snextphi * dir[i];
         // we have a new z, so check again iz
         if (incseg > 0) {
            // loop z planes
            while (pt[2] > fZ[ipl + 1]) {
               ipl++;
               if (ipl > fNz - 2)
                  return kFALSE;
            }
         } else {
            while (pt[2] < fZ[ipl]) {
               ipl--;
               if (ipl < 0)
                  return kFALSE;
            }
         }
         // check if we have a crossing when entering new sector
         rpgin = Rpg(pt[2], ipl, kTRUE, apg, bpg);
         rpgout = Rpg(pt[2], ipl, kFALSE, apg, bpg);
         phi = phi1 + (iphi[iphcrt + 1] + 0.5) * divphi;
         cosph = TMath::Cos(phi);
         sinph = TMath::Sin(phi);
 
         rproj = pt[0] * cosph + pt[1] * sinph;
         if (rproj < rpgin || rproj > rpgout) {
            step = snextphi;
            continue;
         }
         snext = snextphi;
         return kTRUE;
      }
      if (IsCrossingSlice(point, dir, iphi[iphcrt], step, ipl, snext, TMath::Min(snextphi, stepmax)))
         return kTRUE;
      step = snextphi;
   }
   return kFALSE;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Check crossing of a given pgon slice, from a starting point inside the slice
 
Bool_t TGeoPgon::IsCrossingSlice(const Double_t *point, const Double_t *dir, Int_t iphi, Double_t sstart, Int_t &ipl,
                                 Double_t &snext, Double_t stepmax) const
{
   if (ipl < 0 || ipl > fNz - 2)
      return kFALSE;
   if (sstart > stepmax)
      return kFALSE;
   Double_t pt[3];
   memcpy(pt, point, 3 * sizeof(Double_t));
   if (sstart > 0)
      for (Int_t i = 0; i < 3; i++)
         pt[i] += sstart * dir[i];
   stepmax -= sstart;
   Double_t step;
   Int_t incseg = (dir[2] > 0) ? 1 : -1;
   Double_t invdir = 1. / dir[2];
   Double_t divphi = TMath::DegToRad() * fDphi / fNedges;
   Double_t phi = fPhi1 * TMath::DegToRad() + (iphi + 0.5) * divphi;
   Double_t cphi = TMath::Cos(phi);
   Double_t sphi = TMath::Sin(phi);
   Double_t apr = TGeoShape::Big();
   Double_t bpr = 0.;
   Rproj(pt[2], point, dir, cphi, sphi, apr, bpr);
   Double_t dz;
   // loop segments
   Int_t icrtseg = ipl;
   Int_t isegstart = ipl;
   Int_t iseglast = (incseg > 0) ? (fNz - 1) : -1;
   Double_t din, dout, rdot, rnew, apg, bpg, db, znew;
 
   for (ipl = isegstart; ipl != iseglast; ipl += incseg) {
      step = (fZ[ipl + 1 - ((1 + incseg) >> 1)] - pt[2]) * invdir;
      if (step > 0) {
         if (step > stepmax) {
            ipl = icrtseg;
            return kFALSE;
         }
         icrtseg = ipl;
      }
      din = dout = TGeoShape::Big();
      dz = fZ[ipl + 1] - fZ[ipl];
 
      //      rdot = (rproj-fRmin[ipl])*dz - (pt[2]-fZ[ipl])*(fRmin[ipl+1]-fRmin[ipl]);
      if (TGeoShape::IsSameWithinTolerance(dz, 0))
         rdot = dir[2] * TMath::Sign(1., fRmin[ipl] - fRmin[ipl + 1]);
      else
         rdot = dir[0] * cphi + dir[1] * sphi + dir[2] * (fRmin[ipl] - fRmin[ipl + 1]) / dz;
      if (rdot > 0) {
         // inner surface visible ->check crossing
         //         printf("   inner visible\n");
         if (TGeoShape::IsSameWithinTolerance(dz, 0)) {
            rnew = apr + bpr * fZ[ipl];
            Double_t rpg = (rnew - fRmin[ipl]) * (rnew - fRmin[ipl + 1]);
            if (rpg <= 0)
               din = (fZ[ipl] - pt[2]) * invdir;
         } else {
            Rpg(pt[2], ipl, kTRUE, apg, bpg);
            db = bpg - bpr;
            if (!TGeoShape::IsSameWithinTolerance(db, 0)) {
               znew = (apr - apg) / db;
               if (znew > fZ[ipl] && znew < fZ[ipl + 1]) {
                  din = (znew - pt[2]) * invdir;
                  if (din < 0)
                     din = TGeoShape::Big();
               }
            }
         }
      }
      //      printf("   din=%f\n", din);
      //      rdot = (rproj-fRmax[ipl])*dz - (pt[2]-fZ[ipl])*(fRmax[ipl+1]-fRmax[ipl]);
      if (TGeoShape::IsSameWithinTolerance(dz, 0))
         rdot = dir[2] * TMath::Sign(1., fRmax[ipl] - fRmax[ipl + 1]);
      else
         rdot = dir[0] * cphi + dir[1] * sphi + dir[2] * (fRmax[ipl] - fRmax[ipl + 1]) / dz;
      if (rdot < 0) {
         //         printf("   outer visible\n");
         // outer surface visible ->check crossing
         if (TGeoShape::IsSameWithinTolerance(dz, 0)) {
            rnew = apr + bpr * fZ[ipl];
            Double_t rpg = (rnew - fRmax[ipl]) * (rnew - fRmax[ipl + 1]);
            if (rpg <= 0)
               dout = (fZ[ipl] - pt[2]) * invdir;
         } else {
            Rpg(pt[2], ipl, kFALSE, apg, bpg);
            db = bpg - bpr;
            if (!TGeoShape::IsSameWithinTolerance(db, 0)) {
               znew = (apr - apg) / db;
               if (znew > fZ[ipl] && znew < fZ[ipl + 1])
                  dout = (znew - pt[2]) * invdir;
               if (dout < 0)
                  dout = TGeoShape::Big();
            }
         }
      }
      //      printf("   dout=%f\n", dout);
      step = TMath::Min(din, dout);
      if (step < 1E10) {
         // there is a crossing within this segment
         if (step > stepmax) {
            ipl = icrtseg;
            return kFALSE;
         }
         snext = sstart + step;
         return kTRUE;
      }
   }
   ipl = icrtseg;
   return kFALSE;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Compute distance from outside point to surface of the polygone
 
Double_t
TGeoPgon::DistFromOutside(const Double_t *point, const Double_t *dir, Int_t iact, Double_t step, Double_t *safe) const
{
   if (iact < 3 && safe) {
      *safe = Safety(point, kFALSE);
      if (iact == 0)
         return TGeoShape::Big(); // just safety computed
      if (iact == 1 && step < *safe)
         return TGeoShape::Big(); // safety mode
   }
   // Check if the bounding box is crossed within the requested distance
   Double_t sdist = TGeoBBox::DistFromOutside(point, dir, fDX, fDY, fDZ, fOrigin, step);
   if (sdist >= step)
      return TGeoShape::Big();
   // Protection for points on last Z sections
   if (dir[2] <= 0 && TMath::Abs(point[2] - fZ[0]) < TGeoShape::Tolerance())
      return TGeoShape::Big();
   if (dir[2] >= 0 && TMath::Abs(point[2] - fZ[fNz - 1]) < TGeoShape::Tolerance())
      return TGeoShape::Big();
   // copy the current point
   Double_t pt[3];
   memcpy(pt, point, 3 * sizeof(Double_t));
   // find current Z section
   Int_t ipl;
   Int_t i, ipsec;
   ipl = TMath::BinarySearch(fNz, fZ, pt[2]);
 
   Double_t divphi = fDphi / fNedges;
   // check if ray may intersect outer cylinder
   Double_t snext = 0.;
   Double_t stepmax = step;
   Double_t rpr, snewcross;
   Double_t r2 = pt[0] * pt[0] + pt[1] * pt[1];
   Double_t radmax = fRmax[TMath::LocMax(fNz, fRmax)];
   radmax = radmax / TMath::Cos(0.5 * divphi * TMath::DegToRad());
   radmax += 1E-8;
   if (r2 > (radmax * radmax) || pt[2] < fZ[0] || pt[2] > fZ[fNz - 1]) {
      pt[2] -= 0.5 * (fZ[0] + fZ[fNz - 1]);
      snext = TGeoTube::DistFromOutsideS(pt, dir, 0., radmax, 0.5 * (fZ[fNz - 1] - fZ[0]));
      if (snext > 1E10)
         return TGeoShape::Big();
      if (snext > stepmax)
         return TGeoShape::Big();
      stepmax -= snext;
      pt[2] = point[2];
      for (i = 0; i < 3; i++)
         pt[i] += snext * dir[i];
      Bool_t checkz = (ipl < 0 && TMath::Abs(pt[2] - fZ[0]) < 1E-8) ? kTRUE : kFALSE;
      if (!checkz)
         checkz = (ipl == fNz - 1 && TMath::Abs(pt[2] - fZ[fNz - 1]) < 1E-8) ? kTRUE : kFALSE;
      if (checkz) {
         Double_t rmin, rmax;
         if (ipl < 0) {
            rmin = fRmin[0];
            rmax = fRmax[0];
         } else {
            rmin = fRmin[fNz - 1];
            rmax = fRmax[fNz - 1];
         }
         Double_t phi = TMath::ATan2(pt[1], pt[0]) * TMath::RadToDeg();
         while (phi < fPhi1)
            phi += 360.0;
         Double_t ddp = phi - fPhi1;
         if (ddp <= fDphi) {
            ipsec = Int_t(ddp / divphi);
            Double_t ph0 = (fPhi1 + divphi * (ipsec + 0.5)) * TMath::DegToRad();
            rpr = pt[0] * TMath::Cos(ph0) + pt[1] * TMath::Sin(ph0);
            if (rpr >= rmin && rpr <= rmax)
               return snext;
         }
      }
   }
   if (!fThreadSize)
      ((TGeoPgon *)this)->CreateThreadData(1);
   ThreadData_t &td = GetThreadData();
   Double_t *sph = td.fDblBuffer;
   Int_t *iph = td.fIntBuffer;
   Int_t icrossed;
   // locate current phi sector [0,fNedges-1]; -1 for dead region
   // if ray is perpendicular to Z, solve this particular case
   if (TMath::Abs(dir[2]) < TGeoShape::Tolerance()) {
      LocatePhi(pt, ipsec);
      icrossed = GetPhiCrossList(pt, dir, ipsec, sph, iph, stepmax);
      if (SliceCrossingZ(pt, dir, icrossed, iph, sph, snewcross, stepmax))
         return (snext + snewcross);
      return TGeoShape::Big();
   }
   // Locate phi and get the phi crossing list
   divphi *= TMath::DegToRad();
   Bool_t inphi = kTRUE;
   Double_t ph = TMath::ATan2(pt[1], pt[0]) * TMath::RadToDeg();
   while (ph < fPhi1)
      ph += 360.;
   ipsec = Int_t(fNedges * (ph - fPhi1) / fDphi); // [0, fNedges-1]
   if (ipsec > fNedges - 1)
      ipsec = -1; // in gap
   Double_t phim = fPhi1 + 0.5 * fDphi;
   Double_t ddp = TMath::Abs(ph - phim);
   if (fDphi < 360.0) {
      inphi = (ddp < 0.5 * fDphi + TGeoShape::Tolerance()) ? kTRUE : kFALSE;
   }
   ipl = TMath::BinarySearch(fNz, fZ, pt[2]);
   if (ipl < 0)
      ipl = 0;
   if (ipl == fNz - 1)
      ipl--;
   Bool_t inz = kTRUE;
   if (pt[2] > fZ[fNz - 1] + TGeoShape::Tolerance())
      inz = kFALSE;
   if (pt[2] < fZ[0] - TGeoShape::Tolerance())
      inz = kFALSE;
   Bool_t onphi = kFALSE;
   if (inphi && inz) {
      Bool_t done = kFALSE;
      Double_t dz = fZ[ipl + 1] - fZ[ipl];
      Double_t phi = fPhi1 * TMath::DegToRad() + (ipsec + 0.5) * divphi;
      Double_t cphi = TMath::Cos(phi);
      Double_t sphi = TMath::Sin(phi);
      Double_t rproj = pt[0] * cphi + pt[1] * sphi;
      if (TGeoShape::IsSameWithinTolerance(dz, 0)) {
         if (rproj < fRmin[ipl] && rproj > fRmin[ipl + 1] && dir[2] > 0)
            return 0.0;
         if (rproj > fRmin[ipl] && rproj < fRmin[ipl + 1] && dir[2] < 0)
            return 0.0;
         if (rproj > fRmax[ipl] && rproj < fRmax[ipl + 1] && dir[2] > 0)
            return 0.0;
         if (rproj < fRmax[ipl] && rproj > fRmax[ipl + 1] && dir[2] < 0)
            return 0.0;
         done = kTRUE;
      }
      if (!done) {
         Double_t apgout, bpgout;
         Double_t rpgout = Rpg(pt[2], ipl, kFALSE, apgout, bpgout);
         if (rproj < rpgout + 1.E-8) {
            Double_t apgin, bpgin;
            Double_t rpgin = Rpg(pt[2], ipl, kTRUE, apgin, bpgin);
            if (rproj > rpgin - 1.E-8) {
               Double_t safrmin = rproj - rpgin;
               Double_t safrmax = rpgout - rproj;
               Double_t safz = TMath::Min(pt[2] - fZ[ipl], fZ[ipl + 1] - pt[2]);
               Double_t safphi = TGeoShape::Big();
               if (fDphi < 360) {
                  safphi = rproj * TMath::Sin((ddp - 0.5 * fDphi) * TMath::DegToRad());
                  safphi = TMath::Abs(safphi);
               }
               //               printf("inside pgon: safrmin=%f, safrmax=%f, safphi=%f,
               //               safz=%f\n",safrmin,safrmax,safphi,safz);
               Double_t dzinv = 1. / dz;
               if (safrmin < safz && safrmin < safrmax && safrmin < safphi) {
                  // on inner boundary
                  Double_t ndotd = dir[0] * cphi + dir[1] * sphi + dir[2] * (fRmin[ipl] - fRmin[ipl + 1]) * dzinv;
                  //                  printf("   - inner ndotd=%f (>0 ->0)\n",ndotd);
                  if (ndotd > 0)
                     return snext;
                  done = kTRUE;
               }
               if (!done && safrmax < safz && safrmax < safphi) {
                  Double_t ndotd = dir[0] * cphi + dir[1] * sphi + dir[2] * (fRmax[ipl] - fRmax[ipl + 1]) * dzinv;
                  //                  printf("   - outer ndotd=%f (<0 ->0)\n",ndotd);
                  if (ndotd < 0)
                     return snext;
                  done = kTRUE;
               }
               if (!done && safz < safphi) {
                  done = kTRUE;
                  Int_t iplc = ipl;
                  if (TMath::Abs(pt[2] - fZ[ipl]) > TMath::Abs(fZ[ipl + 1] - pt[2]))
                     iplc++;
                  if (iplc == 0 || iplc == fNz - 1) {
                     if (pt[2] * dir[2] < 0)
                        return snext;
                     return TGeoShape::Big();
                  } else {
                     if (TGeoShape::IsSameWithinTolerance(fZ[iplc], fZ[iplc + 1])) {
                        if (dir[2] > 0) {
                           if (rproj < fRmin[iplc] && rproj > fRmin[iplc + 1])
                              return snext;
                           if (rproj > fRmax[iplc] && rproj < fRmax[iplc + 1])
                              return snext;
                        } else {
                           if (rproj > fRmin[iplc] && rproj < fRmin[iplc + 1])
                              return snext;
                           if (rproj < fRmax[iplc] && rproj > fRmax[iplc + 1])
                              return snext;
                        }
                     } else if (TGeoShape::IsSameWithinTolerance(fZ[iplc], fZ[iplc - 1])) {
                        if (dir[2] > 0) {
                           if (rproj < fRmin[iplc - 1] && rproj > fRmin[iplc])
                              return snext;
                           if (rproj > fRmax[iplc - 1] && rproj < fRmax[iplc])
                              return snext;
                        } else {
                           if (rproj > fRmin[iplc - 1] && rproj < fRmin[iplc])
                              return snext;
                           if (rproj < fRmax[iplc - 1] && rproj > fRmax[iplc])
                              return snext;
                        }
                     }
                  }
               }
               if (!done) {
                  // point on phi boundary
                  onphi = kTRUE;
               }
            }
         }
      }
   }
   icrossed = GetPhiCrossList(pt, dir, ipsec, sph, iph, stepmax);
   if (onphi) {
      if (!icrossed)
         return snext;
      if (iph[0] < 0 && sph[0] < TGeoShape::Tolerance())
         return (snext + sph[0]);
      if (iph[0] >= 0 && sph[0] > 1.E-8)
         return snext;
   }
   // Fire-up slice crossing algorithm
   if (SliceCrossing(pt, dir, icrossed, iph, sph, snewcross, stepmax)) {
      snext += snewcross;
      return snext;
   }
   return TGeoShape::Big();
}
 
////////////////////////////////////////////////////////////////////////////////
/// compute closest distance from point px,py to each corner
 
Int_t TGeoPgon::DistancetoPrimitive(Int_t px, Int_t py)
{
   Int_t n = fNedges + 1;
   const Int_t numPoints = 2 * n * fNz;
   return ShapeDistancetoPrimitive(numPoints, px, py);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Divide this polygone shape belonging to volume "voldiv" into ndiv volumes
/// called divname, from start position with the given step. Returns pointer
/// to created division cell volume in case of Z divisions. Phi divisions are
/// allowed only if nedges%ndiv=0 and create polygone "segments" with nedges/ndiv edges.
/// Z divisions can be performed if the divided range is in between two consecutive Z planes.
/// In case a wrong division axis is supplied, returns pointer to volume that was divided.
 
TGeoVolume *
TGeoPgon::Divide(TGeoVolume *voldiv, const char *divname, Int_t iaxis, Int_t ndiv, Double_t start, Double_t step)
{
   //   printf("Dividing %s : nz=%d nedges=%d phi1=%g dphi=%g (ndiv=%d iaxis=%d start=%g step=%g)\n",
   //          voldiv->GetName(), fNz, fNedges, fPhi1, fDphi, ndiv, iaxis, start, step);
   TGeoShape *shape;          //--- shape to be created
   TGeoVolume *vol;           //--- division volume to be created
   TGeoVolumeMulti *vmulti;   //--- generic divided volume
   TGeoPatternFinder *finder; //--- finder to be attached
   TString opt = "";          //--- option to be attached
   Int_t nedges = fNedges;
   Double_t zmin = start;
   Double_t zmax = start + ndiv * step;
   Int_t isect = -1;
   Int_t is, id, ipl;
   switch (iaxis) {
   case 1: //---                R division
      Error("Divide", "makes no sense dividing a pgon on radius");
      return nullptr;
   case 2: //---                Phi division
      if (fNedges % ndiv) {
         Error("Divide", "ndiv should divide number of pgon edges");
         return nullptr;
      }
      nedges = fNedges / ndiv;
      finder = new TGeoPatternCylPhi(voldiv, ndiv, start, start + ndiv * step);
      vmulti = gGeoManager->MakeVolumeMulti(divname, voldiv->GetMedium());
      voldiv->SetFinder(finder);
      finder->SetDivIndex(voldiv->GetNdaughters());
      shape = new TGeoPgon(-step / 2, step, nedges, fNz);
      vol = new TGeoVolume(divname, shape, voldiv->GetMedium());
      vmulti->AddVolume(vol);
      for (is = 0; is < fNz; is++)
         ((TGeoPgon *)shape)->DefineSection(is, fZ[is], fRmin[is], fRmax[is]);
      opt = "Phi";
      for (id = 0; id < ndiv; id++) {
         voldiv->AddNodeOffset(vol, id, start + id * step + step / 2, opt.Data());
         ((TGeoNodeOffset *)voldiv->GetNodes()->At(voldiv->GetNdaughters() - 1))->SetFinder(finder);
      }
      return vmulti;
   case 3: // ---                Z division
      // find start plane
      for (ipl = 0; ipl < fNz - 1; ipl++) {
         if (start < fZ[ipl])
            continue;
         else {
            if ((start + ndiv * step) > fZ[ipl + 1])
               continue;
         }
         isect = ipl;
         zmin = fZ[isect];
         zmax = fZ[isect + 1];
         break;
      }
      if (isect < 0) {
         Error("Divide", "cannot divide pcon on Z if divided region is not between 2 consecutive planes");
         return nullptr;
      }
      finder = new TGeoPatternZ(voldiv, ndiv, start, start + ndiv * step);
      vmulti = gGeoManager->MakeVolumeMulti(divname, voldiv->GetMedium());
      voldiv->SetFinder(finder);
      finder->SetDivIndex(voldiv->GetNdaughters());
      opt = "Z";
      for (id = 0; id < ndiv; id++) {
         Double_t z1 = start + id * step;
         Double_t z2 = start + (id + 1) * step;
         Double_t rmin1 = (fRmin[isect] * (zmax - z1) - fRmin[isect + 1] * (zmin - z1)) / (zmax - zmin);
         Double_t rmax1 = (fRmax[isect] * (zmax - z1) - fRmax[isect + 1] * (zmin - z1)) / (zmax - zmin);
         Double_t rmin2 = (fRmin[isect] * (zmax - z2) - fRmin[isect + 1] * (zmin - z2)) / (zmax - zmin);
         Double_t rmax2 = (fRmax[isect] * (zmax - z2) - fRmax[isect + 1] * (zmin - z2)) / (zmax - zmin);
         shape = new TGeoPgon(fPhi1, fDphi, nedges, 2);
         ((TGeoPgon *)shape)->DefineSection(0, -step / 2, rmin1, rmax1);
         ((TGeoPgon *)shape)->DefineSection(1, step / 2, rmin2, rmax2);
         vol = new TGeoVolume(divname, shape, voldiv->GetMedium());
         vmulti->AddVolume(vol);
         voldiv->AddNodeOffset(vol, id, start + id * step + step / 2, opt.Data());
         ((TGeoNodeOffset *)voldiv->GetNodes()->At(voldiv->GetNdaughters() - 1))->SetFinder(finder);
      }
      return vmulti;
   default: Error("Divide", "Wrong axis type for division"); return nullptr;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Fill vector param[4] with the bounding cylinder parameters. The order
/// is the following : Rmin, Rmax, Phi1, Phi2
 
void TGeoPgon::GetBoundingCylinder(Double_t *param) const
{
   param[0] = fRmin[0]; // Rmin
   param[1] = fRmax[0]; // Rmax
   for (Int_t i = 1; i < fNz; i++) {
      if (fRmin[i] < param[0])
         param[0] = fRmin[i];
      if (fRmax[i] > param[1])
         param[1] = fRmax[i];
   }
   Double_t divphi = fDphi / fNedges;
   param[1] /= TMath::Cos(0.5 * divphi * TMath::DegToRad());
   param[0] *= param[0];
   param[1] *= param[1];
   if (TGeoShape::IsSameWithinTolerance(fDphi, 360)) {
      param[2] = 0.;
      param[3] = 360.;
      return;
   }
   param[2] = (fPhi1 < 0) ? (fPhi1 + 360.) : fPhi1; // Phi1
   param[3] = param[2] + fDphi;                     // Phi2
}
 
////////////////////////////////////////////////////////////////////////////////
/// Inspect the PGON parameters.
 
void TGeoPgon::InspectShape() const
{
   printf("*** Shape %s: TGeoPgon ***\n", GetName());
   printf("    Nedges = %i\n", fNedges);
   TGeoPcon::InspectShape();
}
 
////////////////////////////////////////////////////////////////////////////////
/// Creates a TBuffer3D describing *this* shape.
/// Coordinates are in local reference frame.
 
TBuffer3D *TGeoPgon::MakeBuffer3D() const
{
   Int_t nbPnts, nbSegs, nbPols;
   GetMeshNumbers(nbPnts, nbSegs, nbPols);
 
   if (nbPnts <= 0)
      return nullptr;
 
   TBuffer3D *buff =
      new TBuffer3D(TBuffer3DTypes::kGeneric, nbPnts, 3 * nbPnts, nbSegs, 3 * nbSegs, nbPols, 6 * nbPols);
   if (buff) {
      SetPoints(buff->fPnts);
      SetSegsAndPols(*buff);
   }
 
   return buff;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Fill TBuffer3D structure for segments and polygons.
 
void TGeoPgon::SetSegsAndPols(TBuffer3D &buff) const
{
   if (!HasInsideSurface()) {
      SetSegsAndPolsNoInside(buff);
      return;
   }
 
   Int_t i, j;
   const Int_t n = GetNedges() + 1;
   Int_t nz = GetNz();
   if (nz < 2)
      return;
   Int_t nbPnts = nz * 2 * n;
   if (nbPnts <= 0)
      return;
   Double_t dphi = GetDphi();
   Bool_t specialCase = TGeoShape::IsSameWithinTolerance(dphi, 360);
 
   Int_t c = GetBasicColor();
 
   Int_t indx = 0, indx2, k;
 
   // inside & outside circles, number of segments: 2*nz*(n-1)
   //             special case number of segments: 2*nz*n
   for (i = 0; i < nz * 2; i++) {
      indx2 = i * n;
      for (j = 1; j < n; j++) {
         buff.fSegs[indx++] = c;
         buff.fSegs[indx++] = indx2 + j - 1;
         buff.fSegs[indx++] = indx2 + j;
      }
      if (specialCase) {
         buff.fSegs[indx++] = c;
         buff.fSegs[indx++] = indx2 + j - 1;
         buff.fSegs[indx++] = indx2;
      }
   }
 
   // bottom & top lines, number of segments: 2*n
   for (i = 0; i < 2; i++) {
      indx2 = i * (nz - 1) * 2 * n;
      for (j = 0; j < n; j++) {
         buff.fSegs[indx++] = c;
         buff.fSegs[indx++] = indx2 + j;
         buff.fSegs[indx++] = indx2 + n + j;
      }
   }
 
   // inside & outside cylinders, number of segments: 2*(nz-1)*n
   for (i = 0; i < (nz - 1); i++) {
      // inside cylinder
      indx2 = i * n * 2;
      for (j = 0; j < n; j++) {
         buff.fSegs[indx++] = c + 2;
         buff.fSegs[indx++] = indx2 + j;
         buff.fSegs[indx++] = indx2 + n * 2 + j;
      }
      // outside cylinder
      indx2 = i * n * 2 + n;
      for (j = 0; j < n; j++) {
         buff.fSegs[indx++] = c + 3;
         buff.fSegs[indx++] = indx2 + j;
         buff.fSegs[indx++] = indx2 + n * 2 + j;
      }
   }
 
   // left & right sections, number of segments: 2*(nz-2)
   //          special case number of segments: 0
   if (!specialCase) {
      for (i = 1; i < (nz - 1); i++) {
         for (j = 0; j < 2; j++) {
            buff.fSegs[indx++] = c;
            buff.fSegs[indx++] = 2 * i * n + j * (n - 1);
            buff.fSegs[indx++] = (2 * i + 1) * n + j * (n - 1);
         }
      }
   }
 
   Int_t m = n - 1 + (specialCase ? 1 : 0);
   indx = 0;
 
   // bottom & top, number of polygons: 2*(n-1)
   // special case number of polygons: 2*n
   i = 0;
   for (j = 0; j < n - 1; j++) {
      buff.fPols[indx++] = c + 3;
      buff.fPols[indx++] = 4;
      buff.fPols[indx++] = 2 * nz * m + i * n + j;
      buff.fPols[indx++] = i * (nz * 2 - 2) * m + m + j;
      buff.fPols[indx++] = 2 * nz * m + i * n + j + 1;
      buff.fPols[indx++] = i * (nz * 2 - 2) * m + j;
   }
   if (specialCase) {
      buff.fPols[indx++] = c + 3;
      buff.fPols[indx++] = 4;
      buff.fPols[indx++] = 2 * nz * m + i * n + j;
      buff.fPols[indx++] = i * (nz * 2 - 2) * m + m + j;
      buff.fPols[indx++] = 2 * nz * m + i * n;
      buff.fPols[indx++] = i * (nz * 2 - 2) * m + j;
   }
   i = 1;
   for (j = 0; j < n - 1; j++) {
      buff.fPols[indx++] = c + 3;
      buff.fPols[indx++] = 4;
      buff.fPols[indx++] = i * (nz * 2 - 2) * m + j;
      buff.fPols[indx++] = 2 * nz * m + i * n + j + 1;
      buff.fPols[indx++] = i * (nz * 2 - 2) * m + m + j;
      buff.fPols[indx++] = 2 * nz * m + i * n + j;
   }
   if (specialCase) {
      buff.fPols[indx++] = c + 3;
      buff.fPols[indx++] = 4;
      buff.fPols[indx++] = i * (nz * 2 - 2) * m + j;
      buff.fPols[indx++] = 2 * nz * m + i * n;
      buff.fPols[indx++] = i * (nz * 2 - 2) * m + m + j;
      buff.fPols[indx++] = 2 * nz * m + i * n + j;
   }
 
   // inside & outside, number of polygons: (nz-1)*2*(n-1)
   for (k = 0; k < (nz - 1); k++) {
      i = 0;
      for (j = 0; j < n - 1; j++) {
         buff.fPols[indx++] = c + i;
         buff.fPols[indx++] = 4;
         buff.fPols[indx++] = nz * 2 * m + (2 * k + i * 1 + 2) * n + j + 1;
         buff.fPols[indx++] = (2 * k + i * 1 + 2) * m + j;
         buff.fPols[indx++] = nz * 2 * m + (2 * k + i * 1 + 2) * n + j;
         buff.fPols[indx++] = (2 * k + i * 1) * m + j;
      }
      if (specialCase) {
         buff.fPols[indx++] = c + i;
         buff.fPols[indx++] = 4;
         buff.fPols[indx++] = nz * 2 * m + (2 * k + i * 1 + 2) * n;
         buff.fPols[indx++] = (2 * k + i * 1 + 2) * m + j;
         buff.fPols[indx++] = nz * 2 * m + (2 * k + i * 1 + 2) * n + j;
         buff.fPols[indx++] = (2 * k + i * 1) * m + j;
      }
      i = 1;
      for (j = 0; j < n - 1; j++) {
         buff.fPols[indx++] = c + i;
         buff.fPols[indx++] = 4;
         buff.fPols[indx++] = (2 * k + i * 1) * m + j;
         buff.fPols[indx++] = nz * 2 * m + (2 * k + i * 1 + 2) * n + j;
         buff.fPols[indx++] = (2 * k + i * 1 + 2) * m + j;
         buff.fPols[indx++] = nz * 2 * m + (2 * k + i * 1 + 2) * n + j + 1;
      }
      if (specialCase) {
         buff.fPols[indx++] = c + i;
         buff.fPols[indx++] = 4;
         buff.fPols[indx++] = (2 * k + i * 1) * m + j;
         buff.fPols[indx++] = nz * 2 * m + (2 * k + i * 1 + 2) * n + j;
         buff.fPols[indx++] = (2 * k + i * 1 + 2) * m + j;
         buff.fPols[indx++] = nz * 2 * m + (2 * k + i * 1 + 2) * n;
      }
   }
 
   // left & right sections, number of polygons: 2*(nz-1)
   //          special case number of polygons: 0
   if (!specialCase) {
      indx2 = nz * 2 * (n - 1);
      for (k = 0; k < (nz - 1); k++) {
         buff.fPols[indx++] = c + 2;
         buff.fPols[indx++] = 4;
         buff.fPols[indx++] = k == 0 ? indx2 : indx2 + 2 * nz * n + 2 * (k - 1);
         buff.fPols[indx++] = indx2 + 2 * (k + 1) * n;
         buff.fPols[indx++] = indx2 + 2 * nz * n + 2 * k;
         buff.fPols[indx++] = indx2 + (2 * k + 3) * n;
 
         buff.fPols[indx++] = c + 2;
         buff.fPols[indx++] = 4;
         buff.fPols[indx++] = k == 0 ? indx2 + n - 1 : indx2 + 2 * nz * n + 2 * (k - 1) + 1; // a
         buff.fPols[indx++] = indx2 + (2 * k + 3) * n + n - 1;                               // d
         buff.fPols[indx++] = indx2 + 2 * nz * n + 2 * k + 1;                                // c
         buff.fPols[indx++] = indx2 + 2 * (k + 1) * n + n - 1;                               // b
      }
      buff.fPols[indx - 8] = indx2 + n;
      buff.fPols[indx - 2] = indx2 + 2 * n - 1;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Fill TBuffer3D structure for segments and polygons, when no inner surface exists
 
void TGeoPgon::SetSegsAndPolsNoInside(TBuffer3D &buff) const
{
   const Int_t n = GetNedges() + 1;
   const Int_t nz = GetNz();
   const Int_t nbPnts = nz * n + 2;
 
   if ((nz < 2) || (nbPnts <= 0) || (n < 2))
      return;
 
   Int_t c = GetBasicColor();
 
   Int_t indx = 0, indx1 = 0, indx2 = 0, i, j;
 
   //  outside circles, number of segments: nz*n
   for (i = 0; i < nz; i++) {
      indx2 = i * n;
      for (j = 1; j < n; j++) {
         buff.fSegs[indx++] = c;
         buff.fSegs[indx++] = indx2 + j - 1;
         buff.fSegs[indx++] = indx2 + j % (n - 1);
      }
   }
 
   indx2 = 0;
   // bottom lines
   for (j = 0; j < n; j++) {
      buff.fSegs[indx++] = c;
      buff.fSegs[indx++] = indx2 + j % (n - 1);
      buff.fSegs[indx++] = nbPnts - 2;
   }
 
   indx2 = (nz - 1) * n;
   // top lines
   for (j = 0; j < n; j++) {
      buff.fSegs[indx++] = c;
      buff.fSegs[indx++] = indx2 + j % (n - 1);
      buff.fSegs[indx++] = nbPnts - 1;
   }
 
   // outside cylinders, number of segments: (nz-1)*n
   for (i = 0; i < (nz - 1); i++) {
      // outside cylinder
      indx2 = i * n;
      for (j = 0; j < n; j++) {
         buff.fSegs[indx++] = c;
         buff.fSegs[indx++] = indx2 + j % (n - 1);
         buff.fSegs[indx++] = indx2 + n + j % (n - 1);
      }
   }
 
   indx = 0;
 
   // bottom cap
   indx1 = 0; // start of first z layer
   indx2 = nz * (n - 1);
   for (j = 0; j < n - 1; j++) {
      buff.fPols[indx++] = c;
      buff.fPols[indx++] = 3;
      buff.fPols[indx++] = indx1 + j;
      buff.fPols[indx++] = indx2 + (j + 1) % (n - 1);
      buff.fPols[indx++] = indx2 + j;
   }
 
   // top cap
   indx1 = (nz - 1) * (n - 1); // start last z layer
   indx2 = nz * (n - 1) + n;
   for (j = 0; j < n - 1; j++) {
      buff.fPols[indx++] = c;
      buff.fPols[indx++] = 3;
      buff.fPols[indx++] = indx1 + j; // last z layer
      buff.fPols[indx++] = indx2 + j;
      buff.fPols[indx++] = indx2 + (j + 1) % (n - 1);
   }
 
   // outside, number of polygons: (nz-1)*(n-1)
   for (Int_t k = 0; k < (nz - 1); k++) {
      indx1 = k * (n - 1);
      indx2 = nz * (n - 1) + n * 2 + k * n;
      for (j = 0; j < n - 1; j++) {
         buff.fPols[indx++] = c;
         buff.fPols[indx++] = 4;
         buff.fPols[indx++] = indx1 + j;
         buff.fPols[indx++] = indx2 + j;
         buff.fPols[indx++] = indx1 + j + (n - 1);
         buff.fPols[indx++] = indx2 + (j + 1) % (n - 1);
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Computes projected pgon radius (inner or outer) corresponding to a given Z
/// value. Fills corresponding coefficients of:
///  `Rpg(z) = a + b*z`
///
/// Note: ipl must be in range [0,fNz-2]
 
Double_t TGeoPgon::Rpg(Double_t z, Int_t ipl, Bool_t inner, Double_t &a, Double_t &b) const
{
   Double_t rpg;
   if (ipl < 0 || ipl > fNz - 2) {
      Fatal("Rpg", "Plane index parameter ipl=%i out of range\n", ipl);
      return 0;
   }
   Double_t dz = fZ[ipl + 1] - fZ[ipl];
   if (dz < TGeoShape::Tolerance()) {
      // radius-changing region
      rpg = (inner) ? TMath::Min(fRmin[ipl], fRmin[ipl + 1]) : TMath::Max(fRmax[ipl], fRmax[ipl + 1]);
      a = rpg;
      b = 0.;
      return rpg;
   }
   Double_t r1 = 0, r2 = 0;
   if (inner) {
      r1 = fRmin[ipl];
      r2 = fRmin[ipl + 1];
   } else {
      r1 = fRmax[ipl];
      r2 = fRmax[ipl + 1];
   }
   Double_t dzinv = 1. / dz;
   a = (r1 * fZ[ipl + 1] - r2 * fZ[ipl]) * dzinv;
   b = (r2 - r1) * dzinv;
   return (a + b * z);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Computes projected distance at a given Z for a given ray inside a given sector
/// and fills coefficients:
///   `Rproj = a + b*z`
 
Double_t TGeoPgon::Rproj(Double_t z, const Double_t *point, const Double_t *dir, Double_t cphi, Double_t sphi,
                         Double_t &a, Double_t &b) const
{
   if (TMath::Abs(dir[2]) < TGeoShape::Tolerance()) {
      a = b = TGeoShape::Big();
      return TGeoShape::Big();
   }
   Double_t invdirz = 1. / dir[2];
   a = ((point[0] * dir[2] - point[2] * dir[0]) * cphi + (point[1] * dir[2] - point[2] * dir[1]) * sphi) * invdirz;
   b = (dir[0] * cphi + dir[1] * sphi) * invdirz;
   return (a + b * z);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Compute safety from POINT to segment between planes ipl, ipl+1 within safmin.
 
Double_t TGeoPgon::SafetyToSegment(const Double_t *point, Int_t ipl, Int_t iphi, Bool_t in, Double_t safphi,
                                   Double_t safmin) const
{
   Double_t saf[3];
   Double_t safe;
   Int_t i;
   Double_t r, rpgon, ta, calf;
   if (ipl < 0 || ipl > fNz - 2)
      return (safmin + 1.); // error in input plane
                            // Get info about segment.
   Double_t dz = fZ[ipl + 1] - fZ[ipl];
   if (dz < 1E-9)
      return 1E9; // skip radius-changing segment
   Double_t znew = point[2] - 0.5 * (fZ[ipl] + fZ[ipl + 1]);
   saf[0] = 0.5 * dz - TMath::Abs(znew);
   if (-saf[0] > safmin)
      return TGeoShape::Big(); // means: stop checking further segments
   Double_t rmin1 = fRmin[ipl];
   Double_t rmax1 = fRmax[ipl];
   Double_t rmin2 = fRmin[ipl + 1];
   Double_t rmax2 = fRmax[ipl + 1];
   Double_t divphi = fDphi / fNedges;
   if (iphi < 0) {
      Double_t f = 1. / TMath::Cos(0.5 * divphi * TMath::DegToRad());
      rmax1 *= f;
      rmax2 *= f;
      r = TMath::Sqrt(point[0] * point[0] + point[1] * point[1]);
      Double_t ro1 = 0.5 * (rmin1 + rmin2);
      Double_t tg1 = (rmin2 - rmin1) / dz;
      Double_t cr1 = 1. / TMath::Sqrt(1. + tg1 * tg1);
      Double_t ro2 = 0.5 * (rmax1 + rmax2);
      Double_t tg2 = (rmax2 - rmax1) / dz;
      Double_t cr2 = 1. / TMath::Sqrt(1. + tg2 * tg2);
      Double_t rin = tg1 * znew + ro1;
      Double_t rout = tg2 * znew + ro2;
      saf[1] = (ro1 > 0) ? ((r - rin) * cr1) : TGeoShape::Big();
      saf[2] = (rout - r) * cr2;
      for (i = 0; i < 3; i++)
         saf[i] = -saf[i];
      safe = saf[TMath::LocMax(3, saf)];
      safe = TMath::Max(safe, safphi);
      if (safe < 0)
         safe = 0;
      return safe;
   }
   Double_t ph0 = (fPhi1 + divphi * (iphi + 0.5)) * TMath::DegToRad();
   r = point[0] * TMath::Cos(ph0) + point[1] * TMath::Sin(ph0);
   if (rmin1 + rmin2 > 1E-10) {
      ta = (rmin2 - rmin1) / dz;
      calf = 1. / TMath::Sqrt(1 + ta * ta);
      rpgon = rmin1 + (point[2] - fZ[ipl]) * ta;
      saf[1] = (r - rpgon) * calf;
   } else {
      saf[1] = TGeoShape::Big();
   }
   ta = (rmax2 - rmax1) / dz;
   calf = 1. / TMath::Sqrt(1 + ta * ta);
   rpgon = rmax1 + (point[2] - fZ[ipl]) * ta;
   saf[2] = (rpgon - r) * calf;
   if (in) {
      safe = saf[TMath::LocMin(3, saf)];
      safe = TMath::Min(safe, safphi);
   } else {
      for (i = 0; i < 3; i++)
         saf[i] = -saf[i];
      safe = saf[TMath::LocMax(3, saf)];
      safe = TMath::Max(safe, safphi);
   }
   if (safe < 0)
      safe = 0;
   return safe;
}
 
////////////////////////////////////////////////////////////////////////////////
/// computes the closest distance from given point to this shape, according
/// to option. The matching point on the shape is stored in spoint.
 
Double_t TGeoPgon::Safety(const Double_t *point, Bool_t in) const
{
   Double_t safmin, saftmp, safphi;
   Double_t dz;
   Int_t ipl, iplane, iphi;
   LocatePhi(point, iphi);
   safphi = TGeoShape::SafetyPhi(point, in, fPhi1, fPhi1 + fDphi);
   if (in) {
      //---> point is inside pgon
      ipl = TMath::BinarySearch(fNz, fZ, point[2]);
      if (ipl == (fNz - 1))
         return 0; // point on last Z boundary
      if (ipl < 0)
         return 0; // point on first Z boundary
      dz = 0.5 * (fZ[ipl + 1] - fZ[ipl]);
      if (dz < 1E-8)
         return 0;
      // Check safety for current segment
      safmin = SafetyToSegment(point, ipl, iphi, in, safphi);
      if (safmin > 1E10) {
         //  something went wrong - point is not inside current segment
         return TGeoShape::Big();
      }
      if (safmin < 1E-6)
         return TMath::Abs(safmin); // point on radius-changing plane
      // check increasing iplanes
      iplane = ipl + 1;
      saftmp = 0.;
      while ((iplane < fNz - 1) && saftmp < 1E10) {
         saftmp = TMath::Abs(SafetyToSegment(point, iplane, iphi, kFALSE, safphi, safmin));
         if (saftmp < safmin)
            safmin = saftmp;
         iplane++;
      }
      // now decreasing nplanes
      iplane = ipl - 1;
      saftmp = 0.;
      while ((iplane >= 0) && saftmp < 1E10) {
         saftmp = TMath::Abs(SafetyToSegment(point, iplane, iphi, kFALSE, safphi, safmin));
         if (saftmp < safmin)
            safmin = saftmp;
         iplane--;
      }
      return safmin;
   }
   //---> point is outside pgon
   ipl = TMath::BinarySearch(fNz, fZ, point[2]);
   if (ipl < 0)
      ipl = 0;
   else if (ipl == fNz - 1)
      ipl = fNz - 2;
   dz = 0.5 * (fZ[ipl + 1] - fZ[ipl]);
   if (dz < 1E-8) {
      ipl++;
      if (ipl > fNz - 2)
         return 0.; // invalid last section
      dz = 0.5 * (fZ[ipl + 1] - fZ[ipl]);
   }
   // Check safety for current segment
   safmin = SafetyToSegment(point, ipl, iphi, kFALSE, safphi);
   if (safmin < 1E-6)
      return TMath::Abs(safmin); // point on radius-changing plane
   // check increasing iplanes
   iplane = ipl + 1;
   saftmp = 0.;
   while ((iplane < fNz - 1) && saftmp < 1E10) {
      saftmp = TMath::Abs(SafetyToSegment(point, iplane, iphi, kFALSE, safphi, safmin));
      if (saftmp < safmin)
         safmin = saftmp;
      iplane++;
   }
   // now decreasing nplanes
   iplane = ipl - 1;
   saftmp = 0.;
   while ((iplane >= 0) && saftmp < 1E10) {
      saftmp = TMath::Abs(SafetyToSegment(point, iplane, iphi, kFALSE, safphi, safmin));
      if (saftmp < safmin)
         safmin = saftmp;
      iplane--;
   }
   return safmin;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Save a primitive as a C++ statement(s) on output stream "out".
 
void TGeoPgon::SavePrimitive(std::ostream &out, Option_t * /*option*/ /*= ""*/)
{
   if (TObject::TestBit(kGeoSavePrimitive))
      return;
   out << "   // Shape: " << GetName() << " type: " << ClassName() << std::endl;
   out << "   phi1    = " << fPhi1 << ";" << std::endl;
   out << "   dphi    = " << fDphi << ";" << std::endl;
   out << "   nedges = " << fNedges << ";" << std::endl;
   out << "   nz      = " << fNz << ";" << std::endl;
   out << "   auto " << GetPointerName() << " = new TGeoPgon(\"" << GetName() << "\", phi1, dphi, nedges, nz);"
       << std::endl;
   for (Int_t i = 0; i < fNz; i++) {
      out << "      z     = " << fZ[i] << ";" << std::endl;
      out << "      rmin  = " << fRmin[i] << ";" << std::endl;
      out << "      rmax  = " << fRmax[i] << ";" << std::endl;
      out << "   " << GetPointerName() << "->DefineSection(" << i << ", z, rmin, rmax);" << std::endl;
   }
   TObject::SetBit(TGeoShape::kGeoSavePrimitive);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Set PGON dimensions starting from an array.
 
void TGeoPgon::SetDimensions(Double_t *param)
{
   fPhi1 = param[0];
   fDphi = param[1];
   fNedges = (Int_t)param[2];
   fNz = (Int_t)param[3];
   if (fNz < 2) {
      Error("SetDimensions", "Pgon %s: Number of Z sections must be > 2", GetName());
      return;
   }
   if (fRmin)
      delete[] fRmin;
   if (fRmax)
      delete[] fRmax;
   if (fZ)
      delete[] fZ;
   fRmin = new Double_t[fNz];
   fRmax = new Double_t[fNz];
   fZ = new Double_t[fNz];
   memset(fRmin, 0, fNz * sizeof(Double_t));
   memset(fRmax, 0, fNz * sizeof(Double_t));
   memset(fZ, 0, fNz * sizeof(Double_t));
   for (Int_t i = 0; i < fNz; i++)
      DefineSection(i, param[4 + 3 * i], param[5 + 3 * i], param[6 + 3 * i]);
}
 
////////////////////////////////////////////////////////////////////////////////
/// create polygone mesh points
 
void TGeoPgon::SetPoints(Double_t *points) const
{
   Double_t phi, dphi;
   Int_t n = fNedges + 1;
   dphi = fDphi / (n - 1);
   Double_t factor = 1. / TMath::Cos(TMath::DegToRad() * dphi / 2);
   Int_t i, j;
   Int_t indx = 0;
 
   Bool_t hasInside = HasInsideSurface();
 
   if (points) {
      for (i = 0; i < GetNz(); i++) {
         if (hasInside)
            for (j = 0; j < n; j++) {
               phi = (fPhi1 + j * dphi) * TMath::DegToRad();
               points[indx++] = factor * fRmin[i] * TMath::Cos(phi);
               points[indx++] = factor * fRmin[i] * TMath::Sin(phi);
               points[indx++] = fZ[i];
            }
         for (j = 0; j < n; j++) {
            phi = (fPhi1 + j * dphi) * TMath::DegToRad();
            points[indx++] = factor * fRmax[i] * TMath::Cos(phi);
            points[indx++] = factor * fRmax[i] * TMath::Sin(phi);
            points[indx++] = fZ[i];
         }
      }
 
      if (!hasInside) {
         points[indx++] = 0;
         points[indx++] = 0;
         points[indx++] = fZ[0];
 
         points[indx++] = 0;
         points[indx++] = 0;
         points[indx++] = fZ[GetNz() - 1];
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// create polygone mesh points
 
void TGeoPgon::SetPoints(Float_t *points) const
{
   Double_t phi, dphi;
   Int_t n = fNedges + 1;
   dphi = fDphi / (n - 1);
   Double_t factor = 1. / TMath::Cos(TMath::DegToRad() * dphi / 2);
   Int_t i, j;
   Int_t indx = 0;
 
   Bool_t hasInside = HasInsideSurface();
 
   if (points) {
      for (i = 0; i < fNz; i++) {
         if (hasInside)
            for (j = 0; j < n; j++) {
               phi = (fPhi1 + j * dphi) * TMath::DegToRad();
               points[indx++] = factor * fRmin[i] * TMath::Cos(phi);
               points[indx++] = factor * fRmin[i] * TMath::Sin(phi);
               points[indx++] = fZ[i];
            }
         for (j = 0; j < n; j++) {
            phi = (fPhi1 + j * dphi) * TMath::DegToRad();
            points[indx++] = factor * fRmax[i] * TMath::Cos(phi);
            points[indx++] = factor * fRmax[i] * TMath::Sin(phi);
            points[indx++] = fZ[i];
         }
      }
 
      if (!hasInside) {
         points[indx++] = 0;
         points[indx++] = 0;
         points[indx++] = fZ[0];
 
         points[indx++] = 0;
         points[indx++] = 0;
         points[indx++] = fZ[GetNz() - 1];
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Returns numbers of vertices, segments and polygons composing the shape mesh.
 
void TGeoPgon::GetMeshNumbers(Int_t &nvert, Int_t &nsegs, Int_t &npols) const
{
   nvert = nsegs = npols = 0;
 
   Int_t n = GetNedges() + 1;
   Int_t nz = GetNz();
 
   if (nz < 2)
      return;
 
   if (HasInsideSurface()) {
      Bool_t specialCase = TGeoShape::IsSameWithinTolerance(GetDphi(), 360);
      nvert = nz * 2 * n;
      nsegs = 4 * (nz * n - 1 + (specialCase ? 1 : 0));
      npols = 2 * (nz * n - 1 + (specialCase ? 1 : 0));
   } else {
      nvert = nz * n + 2;
      nsegs = nz * (n - 1) + n * 2 + (nz - 1) * n;
      npols = 2 * (n - 1) + (nz - 1) * (n - 1);
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Return number of vertices of the mesh representation
 
Int_t TGeoPgon::GetNmeshVertices() const
{
   Int_t nvert, nsegs, npols;
 
   GetMeshNumbers(nvert, nsegs, npols);
 
   return nvert;
}
 
////////////////////////////////////////////////////////////////////////////////
/// fill size of this 3-D object
 
void TGeoPgon::Sizeof3D() const {}
 
////////////////////////////////////////////////////////////////////////////////
/// Fills a static 3D buffer and returns a reference.
 
const TBuffer3D &TGeoPgon::GetBuffer3D(Int_t reqSections, Bool_t localFrame) const
{
   static TBuffer3D buffer(TBuffer3DTypes::kGeneric);
 
   TGeoBBox::FillBuffer3D(buffer, reqSections, localFrame);
 
   if (reqSections & TBuffer3D::kRawSizes) {
      Int_t nbPnts, nbSegs, nbPols;
      GetMeshNumbers(nbPnts, nbSegs, nbPols);
      if (nbPnts > 0) {
         if (buffer.SetRawSizes(nbPnts, 3 * nbPnts, nbSegs, 3 * nbSegs, nbPols, 6 * nbPols)) {
            buffer.SetSectionsValid(TBuffer3D::kRawSizes);
         }
      }
   }
   // TODO: Push down to TGeoShape?? Would have to do raw sizes set first..
   // can rest of TGeoShape be deferred until after this?
   if ((reqSections & TBuffer3D::kRaw) && buffer.SectionsValid(TBuffer3D::kRawSizes)) {
      SetPoints(buffer.fPnts);
      if (!buffer.fLocalFrame) {
         TransformPoints(buffer.fPnts, buffer.NbPnts());
      }
 
      SetSegsAndPols(buffer);
      buffer.SetSectionsValid(TBuffer3D::kRaw);
   }
 
   return buffer;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Check the inside status for each of the points in the array.
/// Input: Array of point coordinates + vector size
/// Output: Array of Booleans for the inside of each point
 
void TGeoPgon::Contains_v(const Double_t *points, Bool_t *inside, Int_t vecsize) const
{
   for (Int_t i = 0; i < vecsize; i++)
      inside[i] = Contains(&points[3 * i]);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Compute the normal for an array o points so that norm.dot.dir is positive
/// Input: Arrays of point coordinates and directions + vector size
/// Output: Array of normal directions
 
void TGeoPgon::ComputeNormal_v(const Double_t *points, const Double_t *dirs, Double_t *norms, Int_t vecsize)
{
   for (Int_t i = 0; i < vecsize; i++)
      ComputeNormal(&points[3 * i], &dirs[3 * i], &norms[3 * i]);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Compute distance from array of input points having directions specified by dirs. Store output in dists
 
void TGeoPgon::DistFromInside_v(const Double_t *points, const Double_t *dirs, Double_t *dists, Int_t vecsize,
                                Double_t *step) const
{
   for (Int_t i = 0; i < vecsize; i++)
      dists[i] = DistFromInside(&points[3 * i], &dirs[3 * i], 3, step[i]);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Compute distance from array of input points having directions specified by dirs. Store output in dists
 
void TGeoPgon::DistFromOutside_v(const Double_t *points, const Double_t *dirs, Double_t *dists, Int_t vecsize,
                                 Double_t *step) const
{
   for (Int_t i = 0; i < vecsize; i++)
      dists[i] = DistFromOutside(&points[3 * i], &dirs[3 * i], 3, step[i]);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Compute safe distance from each of the points in the input array.
/// Input: Array of point coordinates, array of statuses for these points, size of the arrays
/// Output: Safety values
 
void TGeoPgon::Safety_v(const Double_t *points, const Bool_t *inside, Double_t *safe, Int_t vecsize) const
{
   for (Int_t i = 0; i < vecsize; i++)
      safe[i] = Safety(&points[3 * i], inside[i]);
}