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 Geometry_classes

A polygone. It has at least 10 parameters :
  - the lower phi limit;
  - the range in phi;
  - the number of equal edges on each z plane;
  - the number of z planes (at least two) where the inner/outer
    radii are changing;
  - z coordinate, inner and outer radius of the inscribed cercle
    (distance from center to edges) for each z plane

Begin_Macro(source)
{
   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
*/

#include "Riostream.h"

#include "TGeoPgon.h"

#include "TGeoManager.h"
#include "TGeoVolume.h"
#include "TVirtualGeoPainter.h"
#include "TGeoTube.h"
#include "TVirtualPad.h"
#include "TBuffer3D.h"
#include "TBuffer3DTypes.h"
#include "TMath.h"
#include "TThread.h"

ClassImp(TGeoPgon)

////////////////////////////////////////////////////////////////////////////////
/// Constructor.

TGeoPgon::ThreadData_t::ThreadData_t() :
   fIntBuffer(0), fDblBuffer(0)
{
}

////////////////////////////////////////////////////////////////////////////////
/// 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
{
   TThread::Lock();
   std::vector<ThreadData_t*>::iterator i = fThreadData.begin();
   while (i != fThreadData.end())
   {
      delete *i;
      ++i;
   }
   fThreadData.clear();
   fThreadSize = 0;
   TThread::UnLock();
}

////////////////////////////////////////////////////////////////////////////////
/// Create thread data for n threads max.

void TGeoPgon::CreateThreadData(Int_t nthreads)
{
   if (fThreadSize) ClearThreadData();
   TThread::Lock();
   fThreadData.resize(nthreads);
   fThreadSize = nthreads;
   for (Int_t tid=0; tid<nthreads; tid++) {
      if (fThreadData[tid] == 0) {
         fThreadData[tid] = new ThreadData_t;
         fThreadData[tid]->fIntBuffer = new Int_t[fNedges+10];
         fThreadData[tid]->fDblBuffer = new Double_t[fNedges+10];
      }
   }
   TThread::UnLock();
}

////////////////////////////////////////////////////////////////////////////////
/// 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[icrossed] = stepmax;
         iphi[icrossed++] = istart;
         return icrossed;
      }
      sphi[icrossed] = TMath::Sqrt((point[0]*point[0]+point[1]*point[1])/(1.-dir[2]*dir[2]));
      iphi[icrossed++] = istart;
      if (sphi[icrossed-1]>stepmax) {
         sphi[icrossed-1] = stepmax;
         return icrossed;
      }
      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[icrossed] = istart;
      sphi[icrossed] = stepmax;
      icrossed++;
      return icrossed;
   }
   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,rpg,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];
            rpg = (rnew-fRmin[ipl])*(rnew-fRmin[ipl+1]);
            if (rpg<=0) din=(fZ[ipl]-pt[2])*invdir;
         } else {
            rpg = 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];
            rpg = (rnew-fRmax[ipl])*(rnew-fRmax[ipl+1]);
            if (rpg<=0) dout=(fZ[ipl]-pt[2])*invdir;
         } else {
            rpg = 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 0;
      case 2:  //---                Phi division
         if (fNedges%ndiv) {
            Error("Divide", "ndiv should divide number of pgon edges");
            return 0;
         }
         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 0;
         }
         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 0;
   }
}

////////////////////////////////////////////////////////////////////////////////
/// 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
{
   const Int_t n = GetNsegments()+1;
   Int_t nz = GetNz();
   if (nz < 2) return 0;
   Int_t nbPnts = nz*2*n;
   if (nbPnts <= 0) return 0;
   Double_t dphi = GetDphi();
   Bool_t specialCase = kFALSE;
   if (TGeoShape::IsSameWithinTolerance(dphi,360)) specialCase = kTRUE;
   Int_t nbSegs = 4*(nz*n-1+(specialCase == kTRUE));
   Int_t nbPols = 2*(nz*n-1+(specialCase == kTRUE));

   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
{
   Int_t i, j;
   const Int_t n = GetNsegments()+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 = kFALSE;
   if (TGeoShape::IsSameWithinTolerance(dphi,360)) specialCase = kTRUE;
   Int_t c = GetBasicColor();

   Int_t indx, indx2, k;
   indx = indx2 = 0;

   //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 == kTRUE);
   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;
   }
}

////////////////////////////////////////////////////////////////////////////////
/// 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
   saftmp = 0.;
   // 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 << "   TGeoPgon *pgon = 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 << "   pgon->DefineSection(" << i << ", z,rmin,rmax);" << std::endl;
   }
   out << "   TGeoShape *" << GetPointerName() << " = pgon;" << 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;

   if (points) {
      for (i = 0; i < fNz; i++) {
         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];
         }
      }
   }
}

////////////////////////////////////////////////////////////////////////////////
/// 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;

   if (points) {
      for (i = 0; i < fNz; i++) {
         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];
         }
      }
   }
}

////////////////////////////////////////////////////////////////////////////////
/// Returns numbers of vertices, segments and polygons composing the shape mesh.

void TGeoPgon::GetMeshNumbers(Int_t &nvert, Int_t &nsegs, Int_t &npols) const
{
   Int_t n = fNedges+1;
   Int_t nz = GetNz();
   nvert = nz*2*n;
   Bool_t specialCase = (TGeoShape::IsSameWithinTolerance(GetDphi(),360));
   nsegs = 4*(nz*n-1+(specialCase == kTRUE));
   npols = 2*(nz*n-1+(specialCase == kTRUE));
}

////////////////////////////////////////////////////////////////////////////////
/// Return number of vertices of the mesh representation

Int_t TGeoPgon::GetNmeshVertices() const
{
   Int_t n = fNedges+1;
   Int_t numPoints = fNz*2*n;
   return numPoints;
}

////////////////////////////////////////////////////////////////////////////////
/// 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) {
      const Int_t n = GetNsegments()+1;
      Int_t nz = GetNz();
      Int_t nbPnts = nz*2*n;
      if (nz >= 2 && nbPnts > 0) {
         Bool_t specialCase = (TGeoShape::IsSameWithinTolerance(GetDphi(),360));
         Int_t nbSegs = 4*(nz*n-1+(specialCase == kTRUE));
         Int_t nbPols = 2*(nz*n-1+(specialCase == kTRUE));
         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]);
}