TGeoTube.cxx

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// @(#)root/geom:$Id$
// Author: Andrei Gheata   24/10/01
// TGeoTube::Contains() and DistFromInside/In() 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 TGeoTube
\ingroup Tubes
 
Cylindrical tube  class. A tube has 3 parameters :
  - `rmin` : minimum radius
  - `rmax` : maximum radius
  - `dz` : half length
 
~~~ {.cpp}
TGeoTube(Double_t rmin,Double_t rmax,Double_t dz);
~~~
 
Begin_Macro
{
   TCanvas *c = new TCanvas("c", "c",0,0,600,600);
   new TGeoManager("tube", "poza2");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98,13,2.7);
   TGeoMedium *med = new TGeoMedium("MED",1,mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP",med,100,100,100);
   gGeoManager->SetTopVolume(top);
   TGeoVolume *vol = gGeoManager->MakeTube("TUBE",med, 20,30,40);
   vol->SetLineWidth(2);
   top->AddNode(vol,1);
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
   top->Draw();
   TView *view = gPad->GetView();
   if (view) view->ShowAxis();
}
End_Macro
*/
 
/** \class TGeoTubeSeg
\ingroup Tubes
 
A tube segment is a tube having a range in phi. The tube segment class
derives from **`TGeoTube`**, having 2 extra parameters: `phi1` and
`phi2`.
 
~~~ {.cpp}
TGeoTubeSeg(Double_t rmin,Double_t rmax,Double_t dz,
Double_t phi1,Double_t phi2);
~~~
 
Here `phi1` and `phi2 `are the starting and ending `phi `values in
degrees. The `general phi convention` is that the shape ranges from
`phi1` to `phi2` going counterclockwise. The angles can be defined with
either negative or positive values. They are stored such that `phi1` is
converted to `[0,360]` and `phi2 > phi1`.
 
Begin_Macro
{
   TCanvas *c = new TCanvas("c", "c",0,0,600,600);
   new TGeoManager("tubeseg", "poza3");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98,13,2.7);
   TGeoMedium *med = new TGeoMedium("MED",1,mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP",med,100,100,100);
   gGeoManager->SetTopVolume(top);
   TGeoVolume *vol = gGeoManager->MakeTubs("TUBESEG",med, 20,30,40,-30,270);
   vol->SetLineWidth(2);
   top->AddNode(vol,1);
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
   top->Draw();
   TView *view = gPad->GetView();
   if (view) view->ShowAxis();
}
End_Macro
*/
 
/** \class TGeoCtub
\ingroup Tubes
 
The cut tubes constructor has the form:
 
~~~ {.cpp}
TGeoCtub(Double_t rmin,Double_t rmax,Double_t dz,
Double_t phi1,Double_t phi2,
Double_t nxlow,Double_t nylow,Double_t nzlow, Double_t nxhi,
Double_t nyhi,Double_t nzhi);
~~~
 
Begin_Macro
{
   TCanvas *c = new TCanvas("c", "c",0,0,600,600);
   new TGeoManager("ctub", "poza3");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98,13,2.7);
   TGeoMedium *med = new TGeoMedium("MED",1,mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP",med,100,100,100);
   gGeoManager->SetTopVolume(top);
   Double_t theta = 160.*TMath::Pi()/180.;
   Double_t phi   = 30.*TMath::Pi()/180.;
   Double_t nlow[3];
   nlow[0] = TMath::Sin(theta)*TMath::Cos(phi);
   nlow[1] = TMath::Sin(theta)*TMath::Sin(phi);
   nlow[2] = TMath::Cos(theta);
   theta = 20.*TMath::Pi()/180.;
   phi   = 60.*TMath::Pi()/180.;
   Double_t nhi[3];
   nhi[0] = TMath::Sin(theta)*TMath::Cos(phi);
   nhi[1] = TMath::Sin(theta)*TMath::Sin(phi);
   nhi[2] = TMath::Cos(theta);
   TGeoVolume *vol = gGeoManager->MakeCtub("CTUB",med, 20,30,40,-30,250, nlow[0], nlow[1], nlow[2],
nhi[0],nhi[1],nhi[2]); vol->SetLineWidth(2); top->AddNode(vol,1); gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
   top->Draw();
   TView *view = gPad->GetView();
   if (view) view->ShowAxis();
}
End_Macro
 
A cut tube is a tube segment cut with two planes. The centers of the 2
sections are positioned at `dZ`. Each cut plane is therefore defined by
a point `(0,0,dZ)` and its normal unit vector pointing outside the
shape:
 
`Nlow=(Nx,Ny,Nz<0)`, `Nhigh=(Nx',Ny',Nz'>0)`.
*/
 
#include <iostream>
 
#include "TGeoManager.h"
#include "TGeoVolume.h"
#include "TVirtualGeoPainter.h"
#include "TGeoTube.h"
#include "TBuffer3D.h"
#include "TBuffer3DTypes.h"
#include "TMath.h"
 
 
////////////////////////////////////////////////////////////////////////////////
/// Default constructor
 
TGeoTube::TGeoTube()
{
   SetShapeBit(TGeoShape::kGeoTube);
   fRmin = 0.0;
   fRmax = 0.0;
   fDz = 0.0;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Default constructor specifying minimum and maximum radius
 
TGeoTube::TGeoTube(Double_t rmin, Double_t rmax, Double_t dz) : TGeoBBox(0, 0, 0)
{
   SetShapeBit(TGeoShape::kGeoTube);
   SetTubeDimensions(rmin, rmax, dz);
   if ((fDz < 0) || (fRmin < 0) || (fRmax < 0)) {
      SetShapeBit(kGeoRunTimeShape);
      //      if (fRmax<=fRmin) SetShapeBit(kGeoInvalidShape);
      //      printf("tube : dz=%f rmin=%f rmax=%f\n", dz, rmin, rmax);
   }
   ComputeBBox();
}
////////////////////////////////////////////////////////////////////////////////
/// Default constructor specifying minimum and maximum radius
 
TGeoTube::TGeoTube(const char *name, Double_t rmin, Double_t rmax, Double_t dz) : TGeoBBox(name, 0, 0, 0)
{
   SetShapeBit(TGeoShape::kGeoTube);
   SetTubeDimensions(rmin, rmax, dz);
   if ((fDz < 0) || (fRmin < 0) || (fRmax < 0)) {
      SetShapeBit(kGeoRunTimeShape);
      //      if (fRmax<=fRmin) SetShapeBit(kGeoInvalidShape);
      //      printf("tube : dz=%f rmin=%f rmax=%f\n", dz, rmin, rmax);
   }
   ComputeBBox();
}
 
////////////////////////////////////////////////////////////////////////////////
/// Default constructor specifying minimum and maximum radius
///  - param[0] = Rmin
///  - param[1] = Rmax
///  - param[2] = dz
 
TGeoTube::TGeoTube(Double_t *param) : TGeoBBox(0, 0, 0)
{
   SetShapeBit(TGeoShape::kGeoTube);
   SetDimensions(param);
   if ((fDz < 0) || (fRmin < 0) || (fRmax < 0))
      SetShapeBit(kGeoRunTimeShape);
   ComputeBBox();
}
 
////////////////////////////////////////////////////////////////////////////////
/// destructor
 
TGeoTube::~TGeoTube() {}
 
////////////////////////////////////////////////////////////////////////////////
/// Computes capacity of the shape in [length^3]
 
Double_t TGeoTube::Capacity() const
{
   return TGeoTube::Capacity(fRmin, fRmax, fDz);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Computes capacity of the shape in [length^3]
 
Double_t TGeoTube::Capacity(Double_t rmin, Double_t rmax, Double_t dz)
{
   Double_t capacity = 2. * TMath::Pi() * (rmax * rmax - rmin * rmin) * dz;
   return capacity;
}
 
////////////////////////////////////////////////////////////////////////////////
/// compute bounding box of the tube
 
void TGeoTube::ComputeBBox()
{
   fDX = fDY = fRmax;
   fDZ = fDz;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Compute normal to closest surface from POINT.
 
void TGeoTube::ComputeNormal(const Double_t *point, const Double_t *dir, Double_t *norm) const
{
   Double_t saf[3];
   Double_t rsq = point[0] * point[0] + point[1] * point[1];
   Double_t r = TMath::Sqrt(rsq);
   saf[0] = TMath::Abs(fDz - TMath::Abs(point[2]));
   saf[1] = (fRmin > 1E-10) ? TMath::Abs(r - fRmin) : TGeoShape::Big();
   saf[2] = TMath::Abs(fRmax - r);
   Int_t i = TMath::LocMin(3, saf);
   if (i == 0) {
      norm[0] = norm[1] = 0.;
      norm[2] = TMath::Sign(1., dir[2]);
      return;
   }
   norm[2] = 0;
   Double_t phi = TMath::ATan2(point[1], point[0]);
   norm[0] = TMath::Cos(phi);
   norm[1] = TMath::Sin(phi);
   if (norm[0] * dir[0] + norm[1] * dir[1] < 0) {
      norm[0] = -norm[0];
      norm[1] = -norm[1];
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Compute normal to closest surface from POINT.
 
void TGeoTube::ComputeNormalS(const Double_t *point, const Double_t *dir, Double_t *norm, Double_t /*rmin*/,
                              Double_t /*rmax*/, Double_t /*dz*/)
{
   norm[2] = 0;
   Double_t phi = TMath::ATan2(point[1], point[0]);
   norm[0] = TMath::Cos(phi);
   norm[1] = TMath::Sin(phi);
   if (norm[0] * dir[0] + norm[1] * dir[1] < 0) {
      norm[0] = -norm[0];
      norm[1] = -norm[1];
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// test if point is inside this tube
 
Bool_t TGeoTube::Contains(const Double_t *point) const
{
   if (TMath::Abs(point[2]) > fDz)
      return kFALSE;
   Double_t r2 = point[0] * point[0] + point[1] * point[1];
   if ((r2 < fRmin * fRmin) || (r2 > fRmax * fRmax))
      return kFALSE;
   return kTRUE;
}
 
////////////////////////////////////////////////////////////////////////////////
/// compute closest distance from point px,py to each corner
 
Int_t TGeoTube::DistancetoPrimitive(Int_t px, Int_t py)
{
   Int_t n = gGeoManager->GetNsegments();
   Int_t numPoints = 4 * n;
   if (!HasRmin())
      numPoints = 2 * (n + 1);
   return ShapeDistancetoPrimitive(numPoints, px, py);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Compute distance from inside point to surface of the tube (static)
/// Boundary safe algorithm.
/// compute distance to surface
/// Do Z
 
Double_t
TGeoTube::DistFromInsideS(const Double_t *point, const Double_t *dir, Double_t rmin, Double_t rmax, Double_t dz)
{
   Double_t sz = TGeoShape::Big();
   if (dir[2]) {
      sz = (TMath::Sign(dz, dir[2]) - point[2]) / dir[2];
      if (sz <= 0)
         return 0.0;
   }
   // Do R
   Double_t nsq = dir[0] * dir[0] + dir[1] * dir[1];
   if (TMath::Abs(nsq) < TGeoShape::Tolerance())
      return sz;
   Double_t rsq = point[0] * point[0] + point[1] * point[1];
   Double_t rdotn = point[0] * dir[0] + point[1] * dir[1];
   Double_t b, d;
   // inner cylinder
   if (rmin > 0) {
      // Protection in case point is actually outside the tube
      if (rsq <= rmin * rmin + TGeoShape::Tolerance()) {
         if (rdotn < 0)
            return 0.0;
      } else {
         if (rdotn < 0) {
            DistToTube(rsq, nsq, rdotn, rmin, b, d);
            if (d > 0) {
               Double_t sr = -b - d;
               if (sr > 0)
                  return TMath::Min(sz, sr);
            }
         }
      }
   }
   // outer cylinder
   if (rsq >= rmax * rmax - TGeoShape::Tolerance()) {
      if (rdotn >= 0)
         return 0.0;
   }
   DistToTube(rsq, nsq, rdotn, rmax, b, d);
   if (d > 0) {
      Double_t sr = -b + d;
      if (sr > 0)
         return TMath::Min(sz, sr);
   }
   return 0.;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Compute distance from inside point to surface of the tube
/// Boundary safe algorithm.
 
Double_t
TGeoTube::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) && (*safe > step))
         return TGeoShape::Big();
   }
   // compute distance to surface
   return DistFromInsideS(point, dir, fRmin, fRmax, fDz);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Static method to compute distance from outside point to a tube with given parameters
/// Boundary safe algorithm.
/// check Z planes
 
Double_t
TGeoTube::DistFromOutsideS(const Double_t *point, const Double_t *dir, Double_t rmin, Double_t rmax, Double_t dz)
{
   Double_t xi, yi, zi;
   Double_t rmaxsq = rmax * rmax;
   Double_t rminsq = rmin * rmin;
   zi = dz - TMath::Abs(point[2]);
   Bool_t in = kFALSE;
   Bool_t inz = (zi < 0) ? kFALSE : kTRUE;
   if (!inz) {
      if (point[2] * dir[2] >= 0)
         return TGeoShape::Big();
      Double_t s = -zi / TMath::Abs(dir[2]);
      xi = point[0] + s * dir[0];
      yi = point[1] + s * dir[1];
      Double_t r2 = xi * xi + yi * yi;
      if ((rminsq <= r2) && (r2 <= rmaxsq))
         return s;
   }
 
   Double_t rsq = point[0] * point[0] + point[1] * point[1];
   // check outer cyl. surface
   Double_t nsq = dir[0] * dir[0] + dir[1] * dir[1];
   Double_t rdotn = point[0] * dir[0] + point[1] * dir[1];
   Double_t b, d;
   Bool_t inrmax = kFALSE;
   Bool_t inrmin = kFALSE;
   if (rsq <= rmaxsq + TGeoShape::Tolerance())
      inrmax = kTRUE;
   if (rsq >= rminsq - TGeoShape::Tolerance())
      inrmin = kTRUE;
   in = inz & inrmin & inrmax;
   // If inside, we are most likely on a boundary within machine precision.
   if (in) {
      Bool_t checkout = kFALSE;
      Double_t r = TMath::Sqrt(rsq);
      if (zi < rmax - r) {
         if ((TGeoShape::IsSameWithinTolerance(rmin, 0)) || (zi < r - rmin)) {
            if (point[2] * dir[2] < 0)
               return 0.0;
            return TGeoShape::Big();
         }
      }
      if ((rmaxsq - rsq) < (rsq - rminsq))
         checkout = kTRUE;
      if (checkout) {
         if (rdotn >= 0)
            return TGeoShape::Big();
         return 0.0;
      }
      if (TGeoShape::IsSameWithinTolerance(rmin, 0))
         return 0.0;
      if (rdotn >= 0)
         return 0.0;
      // Ray exiting rmin -> check (+) solution for inner tube
      if (TMath::Abs(nsq) < TGeoShape::Tolerance())
         return TGeoShape::Big();
      DistToTube(rsq, nsq, rdotn, rmin, b, d);
      if (d > 0) {
         Double_t s = -b + d;
         if (s > 0) {
            zi = point[2] + s * dir[2];
            if (TMath::Abs(zi) <= dz)
               return s;
         }
      }
      return TGeoShape::Big();
   }
   // Check outer cylinder (only r>rmax has to be considered)
   if (TMath::Abs(nsq) < TGeoShape::Tolerance())
      return TGeoShape::Big();
   if (!inrmax) {
      DistToTube(rsq, nsq, rdotn, rmax, b, d);
      if (d > 0) {
         Double_t s = -b - d;
         if (s > 0) {
            zi = point[2] + s * dir[2];
            if (TMath::Abs(zi) <= dz)
               return s;
         }
      }
   }
   // check inner cylinder
   if (rmin > 0) {
      DistToTube(rsq, nsq, rdotn, rmin, b, d);
      if (d > 0) {
         Double_t s = -b + d;
         if (s > 0) {
            zi = point[2] + s * dir[2];
            if (TMath::Abs(zi) <= dz)
               return s;
         }
      }
   }
   return TGeoShape::Big();
}
 
////////////////////////////////////////////////////////////////////////////////
/// Compute distance from outside point to surface of the tube and safe distance
/// Boundary safe algorithm.
/// fist localize point w.r.t tube
 
Double_t
TGeoTube::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();
      if ((iact == 1) && (step <= *safe))
         return TGeoShape::Big();
   }
   // 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();
   // find distance to shape
   return DistFromOutsideS(point, dir, fRmin, fRmax, fDz);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Static method computing the distance to a tube with given radius, starting from
/// POINT along DIR director cosines. The distance is computed as :
///    RSQ   = point[0]*point[0]+point[1]*point[1]
///    NSQ   = dir[0]*dir[0]+dir[1]*dir[1]  ---> should NOT be 0 !!!
///    RDOTN = point[0]*dir[0]+point[1]*dir[1]
/// The distance can be computed as :
///    D = -B +/- DELTA
/// where DELTA.GT.0 and D.GT.0
 
void TGeoTube::DistToTube(Double_t rsq, Double_t nsq, Double_t rdotn, Double_t radius, Double_t &b, Double_t &delta)
{
   Double_t t1 = 1. / nsq;
   Double_t t3 = rsq - (radius * radius);
   b = t1 * rdotn;
   Double_t c = t1 * t3;
   delta = b * b - c;
   if (delta > 0) {
      delta = TMath::Sqrt(delta);
   } else {
      delta = -1;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Divide this tube 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. For radial division
/// creates all volumes with different shapes and returns pointer to volume that
/// was divided. In case a wrong division axis is supplied, returns pointer to
/// volume that was divided.
 
TGeoVolume *
TGeoTube::Divide(TGeoVolume *voldiv, const char *divname, Int_t iaxis, Int_t ndiv, Double_t start, Double_t 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 id;
   Double_t end = start + ndiv * step;
   switch (iaxis) {
   case 1: //---                R division
      finder = new TGeoPatternCylR(voldiv, ndiv, start, end);
      vmulti = gGeoManager->MakeVolumeMulti(divname, voldiv->GetMedium());
      voldiv->SetFinder(finder);
      finder->SetDivIndex(voldiv->GetNdaughters());
      for (id = 0; id < ndiv; id++) {
         shape = new TGeoTube(start + id * step, start + (id + 1) * step, fDz);
         vol = new TGeoVolume(divname, shape, voldiv->GetMedium());
         vmulti->AddVolume(vol);
         opt = "R";
         voldiv->AddNodeOffset(vol, id, 0, opt.Data());
         ((TGeoNodeOffset *)voldiv->GetNodes()->At(voldiv->GetNdaughters() - 1))->SetFinder(finder);
      }
      return vmulti;
   case 2: //---                Phi division
      finder = new TGeoPatternCylPhi(voldiv, ndiv, start, end);
      voldiv->SetFinder(finder);
      finder->SetDivIndex(voldiv->GetNdaughters());
      shape = new TGeoTubeSeg(fRmin, fRmax, fDz, -step / 2, step / 2);
      vol = new TGeoVolume(divname, shape, voldiv->GetMedium());
      vmulti = gGeoManager->MakeVolumeMulti(divname, voldiv->GetMedium());
      vmulti->AddVolume(vol);
      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
      finder = new TGeoPatternZ(voldiv, ndiv, start, start + ndiv * step);
      voldiv->SetFinder(finder);
      finder->SetDivIndex(voldiv->GetNdaughters());
      shape = new TGeoTube(fRmin, fRmax, step / 2);
      vol = new TGeoVolume(divname, shape, voldiv->GetMedium());
      vmulti = gGeoManager->MakeVolumeMulti(divname, voldiv->GetMedium());
      vmulti->AddVolume(vol);
      opt = "Z";
      for (id = 0; id < ndiv; id++) {
         voldiv->AddNodeOffset(vol, id, start + step / 2 + id * step, opt.Data());
         ((TGeoNodeOffset *)voldiv->GetNodes()->At(voldiv->GetNdaughters() - 1))->SetFinder(finder);
      }
      return vmulti;
   default: Error("Divide", "In shape %s wrong axis type for division", GetName()); return nullptr;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Returns name of axis IAXIS.
 
const char *TGeoTube::GetAxisName(Int_t iaxis) const
{
   switch (iaxis) {
   case 1: return "R";
   case 2: return "PHI";
   case 3: return "Z";
   default: return "UNDEFINED";
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Get range of shape for a given axis.
 
Double_t TGeoTube::GetAxisRange(Int_t iaxis, Double_t &xlo, Double_t &xhi) const
{
   xlo = 0;
   xhi = 0;
   Double_t dx = 0;
   switch (iaxis) {
   case 1:
      xlo = fRmin;
      xhi = fRmax;
      dx = xhi - xlo;
      return dx;
   case 2:
      xlo = 0;
      xhi = 360;
      dx = 360;
      return dx;
   case 3:
      xlo = -fDz;
      xhi = fDz;
      dx = xhi - xlo;
      return dx;
   }
   return dx;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Fill vector param[4] with the bounding cylinder parameters. The order
/// is the following : Rmin, Rmax, Phi1, Phi2, dZ
 
void TGeoTube::GetBoundingCylinder(Double_t *param) const
{
   param[0] = fRmin; // Rmin
   param[0] *= param[0];
   param[1] = fRmax; // Rmax
   param[1] *= param[1];
   param[2] = 0.;   // Phi1
   param[3] = 360.; // Phi2
}
 
////////////////////////////////////////////////////////////////////////////////
/// in case shape has some negative parameters, these has to be computed
/// in order to fit the mother
 
TGeoShape *TGeoTube::GetMakeRuntimeShape(TGeoShape *mother, TGeoMatrix * /*mat*/) const
{
   if (!TestShapeBit(kGeoRunTimeShape))
      return nullptr;
   Double_t rmin, rmax, dz;
   Double_t xmin, xmax;
   rmin = fRmin;
   rmax = fRmax;
   dz = fDz;
   if (fDz < 0) {
      mother->GetAxisRange(3, xmin, xmax);
      if (xmax < 0)
         return nullptr;
      dz = xmax;
   }
   mother->GetAxisRange(1, xmin, xmax);
   if (fRmin < 0) {
      if (xmin < 0)
         return nullptr;
      rmin = xmin;
   }
   if (fRmax < 0) {
      if (xmax <= 0)
         return nullptr;
      rmax = xmax;
   }
 
   return (new TGeoTube(GetName(), rmin, rmax, dz));
}
 
////////////////////////////////////////////////////////////////////////////////
/// print shape parameters
 
void TGeoTube::InspectShape() const
{
   printf("*** Shape %s: TGeoTube ***\n", GetName());
   printf("    Rmin = %11.5f\n", fRmin);
   printf("    Rmax = %11.5f\n", fRmax);
   printf("    dz   = %11.5f\n", fDz);
   printf(" Bounding box:\n");
   TGeoBBox::InspectShape();
}
 
////////////////////////////////////////////////////////////////////////////////
/// Creates a TBuffer3D describing *this* shape.
/// Coordinates are in local reference frame.
 
TBuffer3D *TGeoTube::MakeBuffer3D() const
{
   Int_t n = gGeoManager->GetNsegments();
   Int_t nbPnts = 4 * n;
   Int_t nbSegs = 8 * n;
   Int_t nbPols = 4 * n;
   if (!HasRmin()) {
      nbPnts = 2 * (n + 1);
      nbSegs = 5 * n;
      nbPols = 3 * n;
   }
   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 TGeoTube::SetSegsAndPols(TBuffer3D &buffer) const
{
   Int_t i, j, indx;
   Int_t n = gGeoManager->GetNsegments();
   Int_t c = (((buffer.fColor) % 8) - 1) * 4;
   if (c < 0)
      c = 0;
 
   if (HasRmin()) {
      // circle segments:
      // lower rmin circle: i=0, (0, n-1)
      // lower rmax circle: i=1, (n, 2n-1)
      // upper rmin circle: i=2, (2n, 3n-1)
      // upper rmax circle: i=1, (3n, 4n-1)
      for (i = 0; i < 4; i++) {
         for (j = 0; j < n; j++) {
            indx = 3 * (i * n + j);
            buffer.fSegs[indx] = c;
            buffer.fSegs[indx + 1] = i * n + j;
            buffer.fSegs[indx + 2] = i * n + (j + 1) % n;
         }
      }
      // Z-parallel segments
      // inner: i=4, (4n, 5n-1)
      // outer: i=5, (5n, 6n-1)
      for (i = 4; i < 6; i++) {
         for (j = 0; j < n; j++) {
            indx = 3 * (i * n + j);
            buffer.fSegs[indx] = c + 1;
            buffer.fSegs[indx + 1] = (i - 4) * n + j;
            buffer.fSegs[indx + 2] = (i - 2) * n + j;
         }
      }
      // Radial segments
      // lower: i=6, (6n, 7n-1)
      // upper: i=7, (7n, 8n-1)
      for (i = 6; i < 8; i++) {
         for (j = 0; j < n; j++) {
            indx = 3 * (i * n + j);
            buffer.fSegs[indx] = c;
            buffer.fSegs[indx + 1] = 2 * (i - 6) * n + j;
            buffer.fSegs[indx + 2] = (2 * (i - 6) + 1) * n + j;
         }
      }
      // Polygons
      i = 0;
      // Inner lateral (0, n-1)
      for (j = 0; j < n; j++) {
         indx = 6 * (i * n + j);
         buffer.fPols[indx] = c;
         buffer.fPols[indx + 1] = 4;
         buffer.fPols[indx + 2] = j;
         buffer.fPols[indx + 3] = 4 * n + (j + 1) % n;
         buffer.fPols[indx + 4] = 2 * n + j;
         buffer.fPols[indx + 5] = 4 * n + j;
      }
      i = 1;
      // Outer lateral (n,2n-1)
      for (j = 0; j < n; j++) {
         indx = 6 * (i * n + j);
         buffer.fPols[indx] = c + 1;
         buffer.fPols[indx + 1] = 4;
         buffer.fPols[indx + 2] = n + j;
         buffer.fPols[indx + 3] = 5 * n + j;
         buffer.fPols[indx + 4] = 3 * n + j;
         buffer.fPols[indx + 5] = 5 * n + (j + 1) % n;
      }
      i = 2;
      // lower disc (2n, 3n-1)
      for (j = 0; j < n; j++) {
         indx = 6 * (i * n + j);
         buffer.fPols[indx] = c;
         buffer.fPols[indx + 1] = 4;
         buffer.fPols[indx + 2] = j;
         buffer.fPols[indx + 3] = 6 * n + j;
         buffer.fPols[indx + 4] = n + j;
         buffer.fPols[indx + 5] = 6 * n + (j + 1) % n;
      }
      i = 3;
      // upper disc (3n, 4n-1)
      for (j = 0; j < n; j++) {
         indx = 6 * (i * n + j);
         buffer.fPols[indx] = c;
         buffer.fPols[indx + 1] = 4;
         buffer.fPols[indx + 2] = 2 * n + j;
         buffer.fPols[indx + 3] = 7 * n + (j + 1) % n;
         buffer.fPols[indx + 4] = 3 * n + j;
         buffer.fPols[indx + 5] = 7 * n + j;
      }
      return;
   }
   // Rmin=0 tubes
   // circle segments
   // lower rmax circle: i=0, (0, n-1)
   // upper rmax circle: i=1, (n, 2n-1)
   for (i = 0; i < 2; i++) {
      for (j = 0; j < n; j++) {
         indx = 3 * (i * n + j);
         buffer.fSegs[indx] = c;
         buffer.fSegs[indx + 1] = 2 + i * n + j;
         buffer.fSegs[indx + 2] = 2 + i * n + (j + 1) % n;
      }
   }
   // Z-parallel segments (2n,3n-1)
   for (j = 0; j < n; j++) {
      indx = 3 * (2 * n + j);
      buffer.fSegs[indx] = c + 1;
      buffer.fSegs[indx + 1] = 2 + j;
      buffer.fSegs[indx + 2] = 2 + n + j;
   }
   // Radial segments
   // Lower circle: i=3, (3n,4n-1)
   // Upper circle: i=4, (4n,5n-1)
   for (i = 3; i < 5; i++) {
      for (j = 0; j < n; j++) {
         indx = 3 * (i * n + j);
         buffer.fSegs[indx] = c;
         buffer.fSegs[indx + 1] = i - 3;
         buffer.fSegs[indx + 2] = 2 + (i - 3) * n + j;
      }
   }
   // Polygons
   // lateral (0,n-1)
   for (j = 0; j < n; j++) {
      indx = 6 * j;
      buffer.fPols[indx] = c + 1;
      buffer.fPols[indx + 1] = 4;
      buffer.fPols[indx + 2] = j;
      buffer.fPols[indx + 3] = 2 * n + j;
      buffer.fPols[indx + 4] = n + j;
      buffer.fPols[indx + 5] = 2 * n + (j + 1) % n;
   }
   // bottom triangles (n,2n-1)
   for (j = 0; j < n; j++) {
      indx = 6 * n + 5 * j;
      buffer.fPols[indx] = c;
      buffer.fPols[indx + 1] = 3;
      buffer.fPols[indx + 2] = j;
      buffer.fPols[indx + 3] = 3 * n + (j + 1) % n;
      buffer.fPols[indx + 4] = 3 * n + j;
   }
   // top triangles (2n,3n-1)
   for (j = 0; j < n; j++) {
      indx = 6 * n + 5 * n + 5 * j;
      buffer.fPols[indx] = c;
      buffer.fPols[indx + 1] = 3;
      buffer.fPols[indx + 2] = n + j;
      buffer.fPols[indx + 3] = 4 * n + j;
      buffer.fPols[indx + 4] = 4 * n + (j + 1) % n;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// 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 TGeoTube::Safety(const Double_t *point, Bool_t in) const
{
#ifndef NEVER
   Double_t r = TMath::Sqrt(point[0] * point[0] + point[1] * point[1]);
   Double_t safe, safrmin, safrmax;
   if (in) {
      safe = fDz - TMath::Abs(point[2]); // positive if inside
      if (fRmin > 1E-10) {
         safrmin = r - fRmin;
         if (safrmin < safe)
            safe = safrmin;
      }
      safrmax = fRmax - r;
      if (safrmax < safe)
         safe = safrmax;
   } else {
      safe = -fDz + TMath::Abs(point[2]);
      if (fRmin > 1E-10) {
         safrmin = -r + fRmin;
         if (safrmin > safe)
            safe = safrmin;
      }
      safrmax = -fRmax + r;
      if (safrmax > safe)
         safe = safrmax;
   }
   return safe;
#else
   Double_t saf[3];
   Double_t rsq = point[0] * point[0] + point[1] * point[1];
   Double_t r = TMath::Sqrt(rsq);
   saf[0] = fDz - TMath::Abs(point[2]); // positive if inside
   saf[1] = (fRmin > 1E-10) ? (r - fRmin) : TGeoShape::Big();
   saf[2] = fRmax - r;
   if (in)
      return saf[TMath::LocMin(3, saf)];
   for (Int_t i = 0; i < 3; i++)
      saf[i] = -saf[i];
   return saf[TMath::LocMax(3, saf)];
#endif
}
 
////////////////////////////////////////////////////////////////////////////////
/// 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 TGeoTube::SafetyS(const Double_t *point, Bool_t in, Double_t rmin, Double_t rmax, Double_t dz, Int_t skipz)
{
   Double_t saf[3];
   Double_t rsq = point[0] * point[0] + point[1] * point[1];
   Double_t r = TMath::Sqrt(rsq);
   switch (skipz) {
   case 1: // skip lower Z plane
      saf[0] = dz - point[2];
      break;
   case 2: // skip upper Z plane
      saf[0] = dz + point[2];
      break;
   case 3: // skip both
      saf[0] = TGeoShape::Big();
      break;
   default: saf[0] = dz - TMath::Abs(point[2]);
   }
   saf[1] = (rmin > 1E-10) ? (r - rmin) : TGeoShape::Big();
   saf[2] = rmax - r;
   //   printf("saf0=%g saf1=%g saf2=%g in=%d skipz=%d\n", saf[0],saf[1],saf[2],in,skipz);
   if (in)
      return saf[TMath::LocMin(3, saf)];
   for (Int_t i = 0; i < 3; i++)
      saf[i] = -saf[i];
   return saf[TMath::LocMax(3, saf)];
}
 
////////////////////////////////////////////////////////////////////////////////
/// Save a primitive as a C++ statement(s) on output stream "out".
 
void TGeoTube::SavePrimitive(std::ostream &out, Option_t * /*option*/ /*= ""*/)
{
   if (TObject::TestBit(kGeoSavePrimitive))
      return;
   out << "   // Shape: " << GetName() << " type: " << ClassName() << std::endl;
   out << "   rmin = " << fRmin << ";" << std::endl;
   out << "   rmax = " << fRmax << ";" << std::endl;
   out << "   dz   = " << fDz << ";" << std::endl;
   out << "   TGeoShape *" << GetPointerName() << " = new TGeoTube(\"" << GetName() << "\",rmin,rmax,dz);" << std::endl;
   TObject::SetBit(TGeoShape::kGeoSavePrimitive);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Set tube dimensions.
 
void TGeoTube::SetTubeDimensions(Double_t rmin, Double_t rmax, Double_t dz)
{
   fRmin = rmin;
   fRmax = rmax;
   fDz = dz;
   if (fRmin > 0 && fRmax > 0 && fRmin >= fRmax)
      Error("SetTubeDimensions", "In shape %s wrong rmin=%g rmax=%g", GetName(), rmin, rmax);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Set tube dimensions starting from a list.
 
void TGeoTube::SetDimensions(Double_t *param)
{
   Double_t rmin = param[0];
   Double_t rmax = param[1];
   Double_t dz = param[2];
   SetTubeDimensions(rmin, rmax, dz);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Fills array with n random points located on the line segments of the shape mesh.
/// The output array must be provided with a length of minimum 3*npoints. Returns
/// true if operation is implemented.
 
Bool_t TGeoTube::GetPointsOnSegments(Int_t npoints, Double_t *array) const
{
   if (npoints > (npoints / 2) * 2) {
      Error("GetPointsOnSegments", "Npoints must be even number");
      return kFALSE;
   }
   Int_t nc = 0;
   if (HasRmin())
      nc = (Int_t)TMath::Sqrt(0.5 * npoints);
   else
      nc = (Int_t)TMath::Sqrt(1. * npoints);
   Double_t dphi = TMath::TwoPi() / nc;
   Double_t phi = 0;
   Int_t ntop = 0;
   if (HasRmin())
      ntop = npoints / 2 - nc * (nc - 1);
   else
      ntop = npoints - nc * (nc - 1);
   Double_t dz = 2 * fDz / (nc - 1);
   Double_t z = 0;
   Int_t icrt = 0;
   Int_t nphi = nc;
   // loop z sections
   for (Int_t i = 0; i < nc; i++) {
      if (i == (nc - 1))
         nphi = ntop;
      z = -fDz + i * dz;
      // loop points on circle sections
      for (Int_t j = 0; j < nphi; j++) {
         phi = j * dphi;
         if (HasRmin()) {
            array[icrt++] = fRmin * TMath::Cos(phi);
            array[icrt++] = fRmin * TMath::Sin(phi);
            array[icrt++] = z;
         }
         array[icrt++] = fRmax * TMath::Cos(phi);
         array[icrt++] = fRmax * TMath::Sin(phi);
         array[icrt++] = z;
      }
   }
   return kTRUE;
}
 
////////////////////////////////////////////////////////////////////////////////
/// create tube mesh points
 
void TGeoTube::SetPoints(Double_t *points) const
{
   Double_t dz;
   Int_t j, n;
   n = gGeoManager->GetNsegments();
   Double_t dphi = 360. / n;
   Double_t phi = 0;
   dz = fDz;
   Int_t indx = 0;
   if (points) {
      if (HasRmin()) {
         // 4*n points
         // (0,n-1) lower rmin circle
         // (2n, 3n-1) upper rmin circle
         for (j = 0; j < n; j++) {
            phi = j * dphi * TMath::DegToRad();
            points[indx + 6 * n] = points[indx] = fRmin * TMath::Cos(phi);
            indx++;
            points[indx + 6 * n] = points[indx] = fRmin * TMath::Sin(phi);
            indx++;
            points[indx + 6 * n] = dz;
            points[indx] = -dz;
            indx++;
         }
         // (n, 2n-1) lower rmax circle
         // (3n, 4n-1) upper rmax circle
         for (j = 0; j < n; j++) {
            phi = j * dphi * TMath::DegToRad();
            points[indx + 6 * n] = points[indx] = fRmax * TMath::Cos(phi);
            indx++;
            points[indx + 6 * n] = points[indx] = fRmax * TMath::Sin(phi);
            indx++;
            points[indx + 6 * n] = dz;
            points[indx] = -dz;
            indx++;
         }
      } else {
         // centers of lower/upper circles (0,1)
         points[indx++] = 0.;
         points[indx++] = 0.;
         points[indx++] = -dz;
         points[indx++] = 0.;
         points[indx++] = 0.;
         points[indx++] = dz;
         // lower rmax circle (2, 2+n-1)
         // upper rmax circle (2+n, 2+2n-1)
         for (j = 0; j < n; j++) {
            phi = j * dphi * TMath::DegToRad();
            points[indx + 3 * n] = points[indx] = fRmax * TMath::Cos(phi);
            indx++;
            points[indx + 3 * n] = points[indx] = fRmax * TMath::Sin(phi);
            indx++;
            points[indx + 3 * n] = dz;
            points[indx] = -dz;
            indx++;
         }
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// create tube mesh points
 
void TGeoTube::SetPoints(Float_t *points) const
{
   Double_t dz;
   Int_t j, n;
   n = gGeoManager->GetNsegments();
   Double_t dphi = 360. / n;
   Double_t phi = 0;
   dz = fDz;
   Int_t indx = 0;
   if (points) {
      if (HasRmin()) {
         // 4*n points
         // (0,n-1) lower rmin circle
         // (2n, 3n-1) upper rmin circle
         for (j = 0; j < n; j++) {
            phi = j * dphi * TMath::DegToRad();
            points[indx + 6 * n] = points[indx] = fRmin * TMath::Cos(phi);
            indx++;
            points[indx + 6 * n] = points[indx] = fRmin * TMath::Sin(phi);
            indx++;
            points[indx + 6 * n] = dz;
            points[indx] = -dz;
            indx++;
         }
         // (n, 2n-1) lower rmax circle
         // (3n, 4n-1) upper rmax circle
         for (j = 0; j < n; j++) {
            phi = j * dphi * TMath::DegToRad();
            points[indx + 6 * n] = points[indx] = fRmax * TMath::Cos(phi);
            indx++;
            points[indx + 6 * n] = points[indx] = fRmax * TMath::Sin(phi);
            indx++;
            points[indx + 6 * n] = dz;
            points[indx] = -dz;
            indx++;
         }
      } else {
         // centers of lower/upper circles (0,1)
         points[indx++] = 0.;
         points[indx++] = 0.;
         points[indx++] = -dz;
         points[indx++] = 0.;
         points[indx++] = 0.;
         points[indx++] = dz;
         // lower rmax circle (2, 2+n-1)
         // upper rmax circle (2+n, 2+2n-1)
         for (j = 0; j < n; j++) {
            phi = j * dphi * TMath::DegToRad();
            points[indx + 3 * n] = points[indx] = fRmax * TMath::Cos(phi);
            indx++;
            points[indx + 3 * n] = points[indx] = fRmax * TMath::Sin(phi);
            indx++;
            points[indx + 3 * n] = dz;
            points[indx] = -dz;
            indx++;
         }
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Return number of vertices of the mesh representation
 
Int_t TGeoTube::GetNmeshVertices() const
{
   Int_t n = gGeoManager->GetNsegments();
   Int_t numPoints = n * 4;
   if (!HasRmin())
      numPoints = 2 * (n + 1);
   return numPoints;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Returns numbers of vertices, segments and polygons composing the shape mesh.
 
void TGeoTube::GetMeshNumbers(Int_t &nvert, Int_t &nsegs, Int_t &npols) const
{
   Int_t n = gGeoManager->GetNsegments();
   nvert = n * 4;
   nsegs = n * 8;
   npols = n * 4;
   if (!HasRmin()) {
      nvert = 2 * (n + 1);
      nsegs = 5 * n;
      npols = 3 * n;
   } else {
      nvert = n * 4;
      nsegs = n * 8;
      npols = n * 4;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// fill size of this 3-D object
 
void TGeoTube::Sizeof3D() const {}
 
////////////////////////////////////////////////////////////////////////////////
/// Fills a static 3D buffer and returns a reference.
 
const TBuffer3D &TGeoTube::GetBuffer3D(Int_t reqSections, Bool_t localFrame) const
{
   static TBuffer3DTube buffer;
   TGeoBBox::FillBuffer3D(buffer, reqSections, localFrame);
 
   if (reqSections & TBuffer3D::kShapeSpecific) {
      buffer.fRadiusInner = fRmin;
      buffer.fRadiusOuter = fRmax;
      buffer.fHalfLength = fDz;
      buffer.SetSectionsValid(TBuffer3D::kShapeSpecific);
   }
   if (reqSections & TBuffer3D::kRawSizes) {
      Int_t n = gGeoManager->GetNsegments();
      Int_t nbPnts = 4 * n;
      Int_t nbSegs = 8 * n;
      Int_t nbPols = 4 * n;
      if (!HasRmin()) {
         nbPnts = 2 * (n + 1);
         nbSegs = 5 * n;
         nbPols = 3 * n;
      }
      if (buffer.SetRawSizes(nbPnts, 3 * nbPnts, nbSegs, 3 * nbSegs, nbPols, 6 * nbPols)) {
         buffer.SetSectionsValid(TBuffer3D::kRawSizes);
      }
   }
   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 TGeoTube::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 TGeoTube::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 TGeoTube::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 TGeoTube::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 TGeoTube::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]);
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Default constructor
 
TGeoTubeSeg::TGeoTubeSeg()
   : TGeoTube(), fPhi1(0.), fPhi2(0.), fS1(0.), fC1(0.), fS2(0.), fC2(0.), fSm(0.), fCm(0.), fCdfi(0.)
{
   SetShapeBit(TGeoShape::kGeoTubeSeg);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Default constructor specifying minimum and maximum radius.
/// The segment will be from phiStart to phiEnd expressed in degree.
 
TGeoTubeSeg::TGeoTubeSeg(Double_t rmin, Double_t rmax, Double_t dz, Double_t phiStart, Double_t phiEnd)
   : TGeoTube(rmin, rmax, dz), fPhi1(0.), fPhi2(0.), fS1(0.), fC1(0.), fS2(0.), fC2(0.), fSm(0.), fCm(0.), fCdfi(0.)
{
   SetShapeBit(TGeoShape::kGeoTubeSeg);
   SetTubsDimensions(rmin, rmax, dz, phiStart, phiEnd);
   ComputeBBox();
}
 
////////////////////////////////////////////////////////////////////////////////
/// Default constructor specifying minimum and maximum radius
/// The segment will be from phiStart to phiEnd expressed in degree.
 
TGeoTubeSeg::TGeoTubeSeg(const char *name, Double_t rmin, Double_t rmax, Double_t dz, Double_t phiStart,
                         Double_t phiEnd)
   : TGeoTube(name, rmin, rmax, dz)
{
   SetShapeBit(TGeoShape::kGeoTubeSeg);
   SetTubsDimensions(rmin, rmax, dz, phiStart, phiEnd);
   ComputeBBox();
}
 
////////////////////////////////////////////////////////////////////////////////
/// Default constructor specifying minimum and maximum radius
///  - param[0] = Rmin
///  - param[1] = Rmax
///  - param[2] = dz
///  - param[3] = phi1
///  - param[4] = phi2
 
TGeoTubeSeg::TGeoTubeSeg(Double_t *param) : TGeoTube(0, 0, 0)
{
   SetShapeBit(TGeoShape::kGeoTubeSeg);
   SetDimensions(param);
   ComputeBBox();
}
 
////////////////////////////////////////////////////////////////////////////////
/// destructor
 
TGeoTubeSeg::~TGeoTubeSeg() {}
 
////////////////////////////////////////////////////////////////////////////////
/// Function called after streaming an object of this class.
 
void TGeoTubeSeg::AfterStreamer()
{
   InitTrigonometry();
}
 
////////////////////////////////////////////////////////////////////////////////
/// Init frequently used trigonometric values
 
void TGeoTubeSeg::InitTrigonometry()
{
   Double_t phi1 = fPhi1 * TMath::DegToRad();
   Double_t phi2 = fPhi2 * TMath::DegToRad();
   fC1 = TMath::Cos(phi1);
   fS1 = TMath::Sin(phi1);
   fC2 = TMath::Cos(phi2);
   fS2 = TMath::Sin(phi2);
   Double_t fio = 0.5 * (phi1 + phi2);
   fCm = TMath::Cos(fio);
   fSm = TMath::Sin(fio);
   Double_t dfi = 0.5 * (phi2 - phi1);
   fCdfi = TMath::Cos(dfi);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Computes capacity of the shape in [length^3]
 
Double_t TGeoTubeSeg::Capacity() const
{
   return TGeoTubeSeg::Capacity(fRmin, fRmax, fDz, fPhi1, fPhi2);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Computes capacity of the shape in [length^3]
 
Double_t TGeoTubeSeg::Capacity(Double_t rmin, Double_t rmax, Double_t dz, Double_t phiStart, Double_t phiEnd)
{
   Double_t capacity = TMath::Abs(phiEnd - phiStart) * TMath::DegToRad() * (rmax * rmax - rmin * rmin) * dz;
   return capacity;
}
 
////////////////////////////////////////////////////////////////////////////////
/// compute bounding box of the tube segment
 
void TGeoTubeSeg::ComputeBBox()
{
   Double_t xc[4];
   Double_t yc[4];
   xc[0] = fRmax * fC1;
   yc[0] = fRmax * fS1;
   xc[1] = fRmax * fC2;
   yc[1] = fRmax * fS2;
   xc[2] = fRmin * fC1;
   yc[2] = fRmin * fS1;
   xc[3] = fRmin * fC2;
   yc[3] = fRmin * fS2;
 
   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 dp = fPhi2 - fPhi1;
   if (dp < 0)
      dp += 360;
   Double_t ddp = -fPhi1;
   if (ddp < 0)
      ddp += 360;
   if (ddp > 360)
      ddp -= 360;
   if (ddp <= dp)
      xmax = fRmax;
   ddp = 90 - fPhi1;
   if (ddp < 0)
      ddp += 360;
   if (ddp > 360)
      ddp -= 360;
   if (ddp <= dp)
      ymax = fRmax;
   ddp = 180 - fPhi1;
   if (ddp < 0)
      ddp += 360;
   if (ddp > 360)
      ddp -= 360;
   if (ddp <= dp)
      xmin = -fRmax;
   ddp = 270 - fPhi1;
   if (ddp < 0)
      ddp += 360;
   if (ddp > 360)
      ddp -= 360;
   if (ddp <= dp)
      ymin = -fRmax;
   fOrigin[0] = (xmax + xmin) / 2;
   fOrigin[1] = (ymax + ymin) / 2;
   fOrigin[2] = 0;
   fDX = (xmax - xmin) / 2;
   fDY = (ymax - ymin) / 2;
   fDZ = fDz;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Compute normal to closest surface from POINT.
 
void TGeoTubeSeg::ComputeNormal(const Double_t *point, const Double_t *dir, Double_t *norm) const
{
   Double_t saf[3];
   Double_t rsq = point[0] * point[0] + point[1] * point[1];
   Double_t r = TMath::Sqrt(rsq);
   saf[0] = TMath::Abs(fDz - TMath::Abs(point[2]));
   saf[1] = (fRmin > 1E-10) ? TMath::Abs(r - fRmin) : TGeoShape::Big();
   saf[2] = TMath::Abs(fRmax - r);
   Int_t i = TMath::LocMin(3, saf);
   if (((fPhi2 - fPhi1) < 360.) && TGeoShape::IsCloseToPhi(saf[i], point, fC1, fS1, fC2, fS2)) {
      TGeoShape::NormalPhi(point, dir, norm, fC1, fS1, fC2, fS2);
      return;
   }
   if (i == 0) {
      norm[0] = norm[1] = 0.;
      norm[2] = TMath::Sign(1., dir[2]);
      return;
   };
   norm[2] = 0;
   Double_t phi = TMath::ATan2(point[1], point[0]);
   norm[0] = TMath::Cos(phi);
   norm[1] = TMath::Sin(phi);
   if (norm[0] * dir[0] + norm[1] * dir[1] < 0) {
      norm[0] = -norm[0];
      norm[1] = -norm[1];
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Compute normal to closest surface from POINT.
 
void TGeoTubeSeg::ComputeNormalS(const Double_t *point, const Double_t *dir, Double_t *norm, Double_t rmin,
                                 Double_t rmax, Double_t /*dz*/, Double_t c1, Double_t s1, Double_t c2, Double_t s2)
{
   Double_t saf[2];
   Double_t rsq = point[0] * point[0] + point[1] * point[1];
   Double_t r = TMath::Sqrt(rsq);
   saf[0] = (rmin > 1E-10) ? TMath::Abs(r - rmin) : TGeoShape::Big();
   saf[1] = TMath::Abs(rmax - r);
   Int_t i = TMath::LocMin(2, saf);
   if (TGeoShape::IsCloseToPhi(saf[i], point, c1, s1, c2, s2)) {
      TGeoShape::NormalPhi(point, dir, norm, c1, s1, c2, s2);
      return;
   }
   norm[2] = 0;
   Double_t phi = TMath::ATan2(point[1], point[0]);
   norm[0] = TMath::Cos(phi);
   norm[1] = TMath::Sin(phi);
   if (norm[0] * dir[0] + norm[1] * dir[1] < 0) {
      norm[0] = -norm[0];
      norm[1] = -norm[1];
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// test if point is inside this tube segment
/// first check if point is inside the tube
 
Bool_t TGeoTubeSeg::Contains(const Double_t *point) const
{
   if (!TGeoTube::Contains(point))
      return kFALSE;
   return IsInPhiRange(point, fPhi1, fPhi2);
}
 
////////////////////////////////////////////////////////////////////////////////
/// compute closest distance from point px,py to each corner
 
Int_t TGeoTubeSeg::DistancetoPrimitive(Int_t px, Int_t py)
{
   Int_t n = gGeoManager->GetNsegments() + 1;
   const Int_t numPoints = 4 * n;
   return ShapeDistancetoPrimitive(numPoints, px, py);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Compute distance from inside point to surface of the tube segment (static)
/// Boundary safe algorithm.
/// Do Z
 
Double_t TGeoTubeSeg::DistFromInsideS(const Double_t *point, const Double_t *dir, Double_t rmin, Double_t rmax,
                                      Double_t dz, Double_t c1, Double_t s1, Double_t c2, Double_t s2, Double_t cm,
                                      Double_t sm, Double_t cdfi)
{
   Double_t stube = TGeoTube::DistFromInsideS(point, dir, rmin, rmax, dz);
   if (stube <= 0)
      return 0.0;
   Double_t rsq = point[0] * point[0] + point[1] * point[1];
   Double_t r = TMath::Sqrt(rsq);
   Double_t cpsi = point[0] * cm + point[1] * sm;
   if (cpsi > r * cdfi + TGeoShape::Tolerance()) {
      Double_t sfmin = TGeoShape::DistToPhiMin(point, dir, s1, c1, s2, c2, sm, cm);
      return TMath::Min(stube, sfmin);
   }
   // Point on the phi boundary or outside
   // which one: phi1 or phi2
   Double_t ddotn, xi, yi;
   if (TMath::Abs(point[1] - s1 * r) < TMath::Abs(point[1] - s2 * r)) {
      ddotn = s1 * dir[0] - c1 * dir[1];
      if (ddotn >= 0)
         return 0.0;
      ddotn = -s2 * dir[0] + c2 * dir[1];
      if (ddotn <= 0)
         return stube;
      Double_t sfmin = s2 * point[0] - c2 * point[1];
      if (sfmin <= 0)
         return stube;
      sfmin /= ddotn;
      if (sfmin >= stube)
         return stube;
      xi = point[0] + sfmin * dir[0];
      yi = point[1] + sfmin * dir[1];
      if (yi * cm - xi * sm < 0)
         return stube;
      return sfmin;
   }
   ddotn = -s2 * dir[0] + c2 * dir[1];
   if (ddotn >= 0)
      return 0.0;
   ddotn = s1 * dir[0] - c1 * dir[1];
   if (ddotn <= 0)
      return stube;
   Double_t sfmin = -s1 * point[0] + c1 * point[1];
   if (sfmin <= 0)
      return stube;
   sfmin /= ddotn;
   if (sfmin >= stube)
      return stube;
   xi = point[0] + sfmin * dir[0];
   yi = point[1] + sfmin * dir[1];
   if (yi * cm - xi * sm > 0)
      return stube;
   return sfmin;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Compute distance from inside point to surface of the tube segment
/// Boundary safe algorithm.
 
Double_t
TGeoTubeSeg::DistFromInside(const Double_t *point, const Double_t *dir, Int_t iact, Double_t step, Double_t *safe) const
{
   if (iact < 3 && safe) {
      *safe = SafetyS(point, kTRUE, fRmin, fRmax, fDz, fPhi1, fPhi2);
      if (iact == 0)
         return TGeoShape::Big();
      if ((iact == 1) && (*safe > step))
         return TGeoShape::Big();
   }
   if ((fPhi2 - fPhi1) >= 360.)
      return TGeoTube::DistFromInsideS(point, dir, fRmin, fRmax, fDz);
 
   // compute distance to surface
   return TGeoTubeSeg::DistFromInsideS(point, dir, fRmin, fRmax, fDz, fC1, fS1, fC2, fS2, fCm, fSm, fCdfi);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Static method to compute distance to arbitrary tube segment from outside point
/// Boundary safe algorithm.
 
Double_t TGeoTubeSeg::DistFromOutsideS(const Double_t *point, const Double_t *dir, Double_t rmin, Double_t rmax,
                                       Double_t dz, Double_t c1, Double_t s1, Double_t c2, Double_t s2, Double_t cm,
                                       Double_t sm, Double_t cdfi)
{
   Double_t r2, cpsi, s;
   // check Z planes
   Double_t xi, yi, zi;
   zi = dz - TMath::Abs(point[2]);
   Double_t rmaxsq = rmax * rmax;
   Double_t rminsq = rmin * rmin;
   Double_t snxt = TGeoShape::Big();
   Bool_t in = kFALSE;
   Bool_t inz = (zi < 0) ? kFALSE : kTRUE;
   if (!inz) {
      if (point[2] * dir[2] >= 0)
         return TGeoShape::Big();
      s = -zi / TMath::Abs(dir[2]);
      xi = point[0] + s * dir[0];
      yi = point[1] + s * dir[1];
      r2 = xi * xi + yi * yi;
      if ((rminsq <= r2) && (r2 <= rmaxsq)) {
         cpsi = (xi * cm + yi * sm) / TMath::Sqrt(r2);
         if (cpsi >= cdfi)
            return s;
      }
   }
 
   // check outer cyl. surface
   Double_t rsq = point[0] * point[0] + point[1] * point[1];
   Double_t r = TMath::Sqrt(rsq);
   Double_t nsq = dir[0] * dir[0] + dir[1] * dir[1];
   Double_t rdotn = point[0] * dir[0] + point[1] * dir[1];
   Double_t b, d;
   Bool_t inrmax = kFALSE;
   Bool_t inrmin = kFALSE;
   Bool_t inphi = kFALSE;
   if (rsq <= rmaxsq + TGeoShape::Tolerance())
      inrmax = kTRUE;
   if (rsq >= rminsq - TGeoShape::Tolerance())
      inrmin = kTRUE;
   cpsi = point[0] * cm + point[1] * sm;
   if (cpsi > r * cdfi - TGeoShape::Tolerance())
      inphi = kTRUE;
   in = inz & inrmin & inrmax & inphi;
   // If inside, we are most likely on a boundary within machine precision.
   if (in) {
      Bool_t checkout = kFALSE;
      Double_t safphi = (cpsi - r * cdfi) * TMath::Sqrt(1. - cdfi * cdfi);
      //      Double_t sch, cch;
      // check if on Z boundaries
      if (zi < rmax - r) {
         if (TGeoShape::IsSameWithinTolerance(rmin, 0) || (zi < r - rmin)) {
            if (zi < safphi) {
               if (point[2] * dir[2] < 0)
                  return 0.0;
               return TGeoShape::Big();
            }
         }
      }
      if ((rmaxsq - rsq) < (rsq - rminsq))
         checkout = kTRUE;
      // check if on Rmax boundary
      if (checkout && (rmax - r < safphi)) {
         if (rdotn >= 0)
            return TGeoShape::Big();
         return 0.0;
      }
      if (TMath::Abs(nsq) < TGeoShape::Tolerance())
         return TGeoShape::Big();
      // check if on phi boundary
      if (TGeoShape::IsSameWithinTolerance(rmin, 0) || (safphi < r - rmin)) {
         // We may cross again a phi of rmin boundary
         // check first if we are on phi1 or phi2
         Double_t un;
         if (point[0] * c1 + point[1] * s1 > point[0] * c2 + point[1] * s2) {
            un = dir[0] * s1 - dir[1] * c1;
            if (un < 0)
               return 0.0;
            if (cdfi >= 0)
               return TGeoShape::Big();
            un = -dir[0] * s2 + dir[1] * c2;
            if (un < 0) {
               s = -point[0] * s2 + point[1] * c2;
               if (s > 0) {
                  s /= (-un);
                  zi = point[2] + s * dir[2];
                  if (TMath::Abs(zi) <= dz) {
                     xi = point[0] + s * dir[0];
                     yi = point[1] + s * dir[1];
                     r2 = xi * xi + yi * yi;
                     if ((rminsq <= r2) && (r2 <= rmaxsq)) {
                        if ((yi * cm - xi * sm) > 0)
                           return s;
                     }
                  }
               }
            }
         } else {
            un = -dir[0] * s2 + dir[1] * c2;
            if (un < 0)
               return 0.0;
            if (cdfi >= 0)
               return TGeoShape::Big();
            un = dir[0] * s1 - dir[1] * c1;
            if (un < 0) {
               s = point[0] * s1 - point[1] * c1;
               if (s > 0) {
                  s /= (-un);
                  zi = point[2] + s * dir[2];
                  if (TMath::Abs(zi) <= dz) {
                     xi = point[0] + s * dir[0];
                     yi = point[1] + s * dir[1];
                     r2 = xi * xi + yi * yi;
                     if ((rminsq <= r2) && (r2 <= rmaxsq)) {
                        if ((yi * cm - xi * sm) < 0)
                           return s;
                     }
                  }
               }
            }
         }
         // We may also cross rmin, (+) solution
         if (rdotn >= 0)
            return TGeoShape::Big();
         if (cdfi >= 0)
            return TGeoShape::Big();
         DistToTube(rsq, nsq, rdotn, rmin, b, d);
         if (d > 0) {
            s = -b + d;
            if (s > 0) {
               zi = point[2] + s * dir[2];
               if (TMath::Abs(zi) <= dz) {
                  xi = point[0] + s * dir[0];
                  yi = point[1] + s * dir[1];
                  if ((xi * cm + yi * sm) >= rmin * cdfi)
                     return s;
               }
            }
         }
         return TGeoShape::Big();
      }
      // we are on rmin boundary: we may cross again rmin or a phi facette
      if (rdotn >= 0)
         return 0.0;
      DistToTube(rsq, nsq, rdotn, rmin, b, d);
      if (d > 0) {
         s = -b + d;
         if (s > 0) {
            zi = point[2] + s * dir[2];
            if (TMath::Abs(zi) <= dz) {
               // now check phi range
               xi = point[0] + s * dir[0];
               yi = point[1] + s * dir[1];
               if ((xi * cm + yi * sm) >= rmin * cdfi)
                  return s;
               // now we really have to check any phi crossing
               Double_t un = -dir[0] * s1 + dir[1] * c1;
               if (un > 0) {
                  s = point[0] * s1 - point[1] * c1;
                  if (s >= 0) {
                     s /= un;
                     zi = point[2] + s * dir[2];
                     if (TMath::Abs(zi) <= dz) {
                        xi = point[0] + s * dir[0];
                        yi = point[1] + s * dir[1];
                        r2 = xi * xi + yi * yi;
                        if ((rminsq <= r2) && (r2 <= rmaxsq)) {
                           if ((yi * cm - xi * sm) <= 0) {
                              if (s < snxt)
                                 snxt = s;
                           }
                        }
                     }
                  }
               }
               un = dir[0] * s2 - dir[1] * c2;
               if (un > 0) {
                  s = (point[1] * c2 - point[0] * s2) / un;
                  if (s >= 0 && s < snxt) {
                     zi = point[2] + s * dir[2];
                     if (TMath::Abs(zi) <= dz) {
                        xi = point[0] + s * dir[0];
                        yi = point[1] + s * dir[1];
                        r2 = xi * xi + yi * yi;
                        if ((rminsq <= r2) && (r2 <= rmaxsq)) {
                           if ((yi * cm - xi * sm) >= 0) {
                              return s;
                           }
                        }
                     }
                  }
               }
               return snxt;
            }
         }
      }
      return TGeoShape::Big();
   }
   // only r>rmax has to be considered
   if (TMath::Abs(nsq) < TGeoShape::Tolerance())
      return TGeoShape::Big();
   if (rsq >= rmax * rmax) {
      if (rdotn >= 0)
         return TGeoShape::Big();
      TGeoTube::DistToTube(rsq, nsq, rdotn, rmax, b, d);
      if (d > 0) {
         s = -b - d;
         if (s > 0) {
            zi = point[2] + s * dir[2];
            if (TMath::Abs(zi) <= dz) {
               xi = point[0] + s * dir[0];
               yi = point[1] + s * dir[1];
               cpsi = xi * cm + yi * sm;
               if (cpsi >= rmax * cdfi)
                  return s;
            }
         }
      }
   }
   // check inner cylinder
   if (rmin > 0) {
      TGeoTube::DistToTube(rsq, nsq, rdotn, rmin, b, d);
      if (d > 0) {
         s = -b + d;
         if (s > 0) {
            zi = point[2] + s * dir[2];
            if (TMath::Abs(zi) <= dz) {
               xi = point[0] + s * dir[0];
               yi = point[1] + s * dir[1];
               cpsi = xi * cm + yi * sm;
               if (cpsi >= rmin * cdfi)
                  snxt = s;
            }
         }
      }
   }
   // check phi planes
   Double_t un = -dir[0] * s1 + dir[1] * c1;
   if (un > 0) {
      s = point[0] * s1 - point[1] * c1;
      if (s >= 0) {
         s /= un;
         zi = point[2] + s * dir[2];
         if (TMath::Abs(zi) <= dz) {
            xi = point[0] + s * dir[0];
            yi = point[1] + s * dir[1];
            r2 = xi * xi + yi * yi;
            if ((rminsq <= r2) && (r2 <= rmaxsq)) {
               if ((yi * cm - xi * sm) <= 0) {
                  if (s < snxt)
                     snxt = s;
               }
            }
         }
      }
   }
   un = dir[0] * s2 - dir[1] * c2;
   if (un > 0) {
      s = point[1] * c2 - point[0] * s2;
      if (s >= 0) {
         s /= un;
         zi = point[2] + s * dir[2];
         if (TMath::Abs(zi) <= dz) {
            xi = point[0] + s * dir[0];
            yi = point[1] + s * dir[1];
            r2 = xi * xi + yi * yi;
            if ((rminsq <= r2) && (r2 <= rmaxsq)) {
               if ((yi * cm - xi * sm) >= 0) {
                  if (s < snxt)
                     snxt = s;
               }
            }
         }
      }
   }
   return snxt;
}
 
////////////////////////////////////////////////////////////////////////////////
/// compute distance from outside point to surface of the tube segment
/// fist localize point w.r.t tube
 
Double_t TGeoTubeSeg::DistFromOutside(const Double_t *point, const Double_t *dir, Int_t iact, Double_t step,
                                      Double_t *safe) const
{
   if (iact < 3 && safe) {
      *safe = SafetyS(point, kFALSE, fRmin, fRmax, fDz, fPhi1, fPhi2);
      if (iact == 0)
         return TGeoShape::Big();
      if ((iact == 1) && (step <= *safe))
         return TGeoShape::Big();
   }
   // 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();
   if ((fPhi2 - fPhi1) >= 360.)
      return TGeoTube::DistFromOutsideS(point, dir, fRmin, fRmax, fDz);
 
   // find distance to shape
   return TGeoTubeSeg::DistFromOutsideS(point, dir, fRmin, fRmax, fDz, fC1, fS1, fC2, fS2, fCm, fSm, fCdfi);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Divide this tube segment 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. For radialdivision
/// creates all volumes with different shapes and returns pointer to volume that
/// was divided. In case a wrong division axis is supplied, returns pointer to
/// volume that was divided.
 
TGeoVolume *
TGeoTubeSeg::Divide(TGeoVolume *voldiv, const char *divname, Int_t iaxis, Int_t ndiv, Double_t start, Double_t 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
   Double_t dphi;
   Int_t id;
   Double_t end = start + ndiv * step;
   switch (iaxis) {
   case 1: //---                 R division
      finder = new TGeoPatternCylR(voldiv, ndiv, start, end);
      vmulti = gGeoManager->MakeVolumeMulti(divname, voldiv->GetMedium());
      voldiv->SetFinder(finder);
      finder->SetDivIndex(voldiv->GetNdaughters());
      for (id = 0; id < ndiv; id++) {
         shape = new TGeoTubeSeg(start + id * step, start + (id + 1) * step, fDz, fPhi1, fPhi2);
         vol = new TGeoVolume(divname, shape, voldiv->GetMedium());
         vmulti->AddVolume(vol);
         opt = "R";
         voldiv->AddNodeOffset(vol, id, 0, opt.Data());
         ((TGeoNodeOffset *)voldiv->GetNodes()->At(voldiv->GetNdaughters() - 1))->SetFinder(finder);
      }
      return vmulti;
   case 2: //---                 Phi division
      dphi = fPhi2 - fPhi1;
      if (dphi < 0)
         dphi += 360.;
      if (step <= 0) {
         step = dphi / ndiv;
         start = fPhi1;
         end = fPhi2;
      }
      finder = new TGeoPatternCylPhi(voldiv, ndiv, start, end);
      voldiv->SetFinder(finder);
      finder->SetDivIndex(voldiv->GetNdaughters());
      shape = new TGeoTubeSeg(fRmin, fRmax, fDz, -step / 2, step / 2);
      vol = new TGeoVolume(divname, shape, voldiv->GetMedium());
      vmulti = gGeoManager->MakeVolumeMulti(divname, voldiv->GetMedium());
      vmulti->AddVolume(vol);
      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
      finder = new TGeoPatternZ(voldiv, ndiv, start, end);
      voldiv->SetFinder(finder);
      finder->SetDivIndex(voldiv->GetNdaughters());
      shape = new TGeoTubeSeg(fRmin, fRmax, step / 2, fPhi1, fPhi2);
      vol = new TGeoVolume(divname, shape, voldiv->GetMedium());
      vmulti = gGeoManager->MakeVolumeMulti(divname, voldiv->GetMedium());
      vmulti->AddVolume(vol);
      opt = "Z";
      for (id = 0; id < ndiv; id++) {
         voldiv->AddNodeOffset(vol, id, start + step / 2 + id * step, opt.Data());
         ((TGeoNodeOffset *)voldiv->GetNodes()->At(voldiv->GetNdaughters() - 1))->SetFinder(finder);
      }
      return vmulti;
   default: Error("Divide", "In shape %s wrong axis type for division", GetName()); return nullptr;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Get range of shape for a given axis.
 
Double_t TGeoTubeSeg::GetAxisRange(Int_t iaxis, Double_t &xlo, Double_t &xhi) const
{
   xlo = 0;
   xhi = 0;
   Double_t dx = 0;
   switch (iaxis) {
   case 1:
      xlo = fRmin;
      xhi = fRmax;
      dx = xhi - xlo;
      return dx;
   case 2:
      xlo = fPhi1;
      xhi = fPhi2;
      dx = xhi - xlo;
      return dx;
   case 3:
      xlo = -fDz;
      xhi = fDz;
      dx = xhi - xlo;
      return dx;
   }
   return dx;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Fill vector param[4] with the bounding cylinder parameters. The order
/// is the following : Rmin, Rmax, Phi1, Phi2
 
void TGeoTubeSeg::GetBoundingCylinder(Double_t *param) const
{
   param[0] = fRmin;
   param[0] *= param[0];
   param[1] = fRmax;
   param[1] *= param[1];
   param[2] = fPhi1;
   param[3] = fPhi2;
}
 
////////////////////////////////////////////////////////////////////////////////
/// in case shape has some negative parameters, these has to be computed
/// in order to fit the mother
 
TGeoShape *TGeoTubeSeg::GetMakeRuntimeShape(TGeoShape *mother, TGeoMatrix * /*mat*/) const
{
   if (!TestShapeBit(kGeoRunTimeShape))
      return nullptr;
   if (!mother->TestShapeBit(kGeoTube)) {
      Error("GetMakeRuntimeShape", "Invalid mother for shape %s", GetName());
      return nullptr;
   }
   Double_t rmin, rmax, dz;
   rmin = fRmin;
   rmax = fRmax;
   dz = fDz;
   if (fDz < 0)
      dz = ((TGeoTube *)mother)->GetDz();
   if (fRmin < 0)
      rmin = ((TGeoTube *)mother)->GetRmin();
   if ((fRmax < 0) || (fRmax <= fRmin))
      rmax = ((TGeoTube *)mother)->GetRmax();
 
   return (new TGeoTubeSeg(GetName(), rmin, rmax, dz, fPhi1, fPhi2));
}
 
////////////////////////////////////////////////////////////////////////////////
/// print shape parameters
 
void TGeoTubeSeg::InspectShape() const
{
   printf("*** Shape %s: TGeoTubeSeg ***\n", GetName());
   printf("    Rmin = %11.5f\n", fRmin);
   printf("    Rmax = %11.5f\n", fRmax);
   printf("    dz   = %11.5f\n", fDz);
   printf("    phi1 = %11.5f\n", fPhi1);
   printf("    phi2 = %11.5f\n", fPhi2);
   printf(" Bounding box:\n");
   TGeoBBox::InspectShape();
}
 
////////////////////////////////////////////////////////////////////////////////
/// Creates a TBuffer3D describing *this* shape.
/// Coordinates are in local reference frame.
 
TBuffer3D *TGeoTubeSeg::MakeBuffer3D() const
{
   Int_t n = gGeoManager->GetNsegments() + 1;
   Int_t nbPnts = 4 * n;
   Int_t nbSegs = 2 * nbPnts;
   Int_t nbPols = nbPnts - 2;
 
   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 TGeoTubeSeg::SetSegsAndPols(TBuffer3D &buff) const
{
   Int_t i, j;
   Int_t n = gGeoManager->GetNsegments() + 1;
   Int_t c = GetBasicColor();
 
   memset(buff.fSegs, 0, buff.NbSegs() * 3 * sizeof(Int_t));
   for (i = 0; i < 4; i++) {
      for (j = 1; j < n; j++) {
         buff.fSegs[(i * n + j - 1) * 3] = c;
         buff.fSegs[(i * n + j - 1) * 3 + 1] = i * n + j - 1;
         buff.fSegs[(i * n + j - 1) * 3 + 2] = i * n + j;
      }
   }
   for (i = 4; i < 6; i++) {
      for (j = 0; j < n; j++) {
         buff.fSegs[(i * n + j) * 3] = c + 1;
         buff.fSegs[(i * n + j) * 3 + 1] = (i - 4) * n + j;
         buff.fSegs[(i * n + j) * 3 + 2] = (i - 2) * n + j;
      }
   }
   for (i = 6; i < 8; i++) {
      for (j = 0; j < n; j++) {
         buff.fSegs[(i * n + j) * 3] = c;
         buff.fSegs[(i * n + j) * 3 + 1] = 2 * (i - 6) * n + j;
         buff.fSegs[(i * n + j) * 3 + 2] = (2 * (i - 6) + 1) * n + j;
      }
   }
 
   Int_t indx = 0;
   memset(buff.fPols, 0, buff.NbPols() * 6 * sizeof(Int_t));
   i = 0;
   for (j = 0; j < n - 1; j++) {
      buff.fPols[indx++] = c;
      buff.fPols[indx++] = 4;
      buff.fPols[indx++] = (4 + i) * n + j + 1;
      buff.fPols[indx++] = (2 + i) * n + j;
      buff.fPols[indx++] = (4 + i) * n + j;
      buff.fPols[indx++] = i * n + j;
   }
   i = 1;
   for (j = 0; j < n - 1; j++) {
      buff.fPols[indx++] = c;
      buff.fPols[indx++] = 4;
      buff.fPols[indx++] = i * n + j;
      buff.fPols[indx++] = (4 + i) * n + j;
      buff.fPols[indx++] = (2 + i) * n + j;
      buff.fPols[indx++] = (4 + i) * n + j + 1;
   }
   i = 2;
   for (j = 0; j < n - 1; j++) {
      buff.fPols[indx++] = c + i;
      buff.fPols[indx++] = 4;
      buff.fPols[indx++] = (i - 2) * 2 * n + j;
      buff.fPols[indx++] = (4 + i) * n + j;
      buff.fPols[indx++] = ((i - 2) * 2 + 1) * n + j;
      buff.fPols[indx++] = (4 + i) * n + j + 1;
   }
   i = 3;
   for (j = 0; j < n - 1; j++) {
      buff.fPols[indx++] = c + i;
      buff.fPols[indx++] = 4;
      buff.fPols[indx++] = (4 + i) * n + j + 1;
      buff.fPols[indx++] = ((i - 2) * 2 + 1) * n + j;
      buff.fPols[indx++] = (4 + i) * n + j;
      buff.fPols[indx++] = (i - 2) * 2 * n + j;
   }
   buff.fPols[indx++] = c + 2;
   buff.fPols[indx++] = 4;
   buff.fPols[indx++] = 6 * n;
   buff.fPols[indx++] = 4 * n;
   buff.fPols[indx++] = 7 * n;
   buff.fPols[indx++] = 5 * n;
   buff.fPols[indx++] = c + 2;
   buff.fPols[indx++] = 4;
   buff.fPols[indx++] = 6 * n - 1;
   buff.fPols[indx++] = 8 * n - 1;
   buff.fPols[indx++] = 5 * n - 1;
   buff.fPols[indx++] = 7 * n - 1;
}
 
////////////////////////////////////////////////////////////////////////////////
/// computes the closest distance from given point InitTrigonometry();to this shape, according
/// to option. The matching point on the shape is stored in spoint.
 
Double_t TGeoTubeSeg::Safety(const Double_t *point, Bool_t in) const
{
   Double_t saf[3];
   Double_t rsq = point[0] * point[0] + point[1] * point[1];
   Double_t r = TMath::Sqrt(rsq);
   if (in) {
      saf[0] = fDz - TMath::Abs(point[2]);
      saf[1] = r - fRmin;
      saf[2] = fRmax - r;
      Double_t safe = saf[TMath::LocMin(3, saf)];
      if ((fPhi2 - fPhi1) >= 360.)
         return safe;
      Double_t safphi = TGeoShape::SafetyPhi(point, in, fPhi1, fPhi2);
      return TMath::Min(safe, safphi);
   }
   // Point expected to be outside
   Bool_t inphi = kFALSE;
   Double_t cpsi = point[0] * fCm + point[1] * fSm;
   saf[0] = TMath::Abs(point[2]) - fDz;
   if (cpsi > r * fCdfi - TGeoShape::Tolerance())
      inphi = kTRUE;
   if (inphi) {
      saf[1] = fRmin - r;
      saf[2] = r - fRmax;
      Double_t safe = saf[TMath::LocMax(3, saf)];
      safe = TMath::Max(0., safe);
      return safe;
   }
   // Point outside the phi range
   // Compute projected radius of the (r,phi) position vector onto
   // phi1 and phi2 edges and take the maximum for choosing the side.
   Double_t rproj = TMath::Max(point[0] * fC1 + point[1] * fS1, point[0] * fC2 + point[1] * fS2);
   saf[1] = fRmin - rproj;
   saf[2] = rproj - fRmax;
   Double_t safe = TMath::Max(saf[1], saf[2]);
   if ((fPhi2 - fPhi1) >= 360.)
      return TMath::Max(safe, saf[0]);
   if (safe > 0) {
      // rproj not within (rmin,rmax) - > no need to calculate safphi
      safe = TMath::Sqrt(rsq - rproj * rproj + safe * safe);
      return (saf[0] < 0) ? safe : TMath::Sqrt(safe * safe + saf[0] * saf[0]);
   }
   Double_t safphi = TGeoShape::SafetyPhi(point, in, fPhi1, fPhi2);
   return (saf[0] < 0) ? safphi : TMath::Sqrt(saf[0] * saf[0] + safphi * safphi);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Static method to compute the closest distance from given point to this shape.
 
Double_t TGeoTubeSeg::SafetyS(const Double_t *point, Bool_t in, Double_t rmin, Double_t rmax, Double_t dz,
                              Double_t phi1d, Double_t phi2d, Int_t skipz)
{
   Double_t saf[3];
   Double_t rsq = point[0] * point[0] + point[1] * point[1];
   Double_t r = TMath::Sqrt(rsq);
 
   switch (skipz) {
   case 1: // skip lower Z plane
      saf[0] = dz - point[2];
      break;
   case 2: // skip upper Z plane
      saf[0] = dz + point[2];
      break;
   case 3: // skip both
      saf[0] = TGeoShape::Big();
      break;
   default: saf[0] = dz - TMath::Abs(point[2]);
   }
 
   if (in) {
      saf[1] = r - rmin;
      saf[2] = rmax - r;
      Double_t safe = saf[TMath::LocMin(3, saf)];
      if ((phi2d - phi1d) >= 360.)
         return safe;
      Double_t safphi = TGeoShape::SafetyPhi(point, in, phi1d, phi2d);
      return TMath::Min(safe, safphi);
   }
   // Point expected to be outside
   saf[0] = -saf[0];
   Bool_t inphi = kFALSE;
   Double_t phi1 = phi1d * TMath::DegToRad();
   Double_t phi2 = phi2d * TMath::DegToRad();
 
   Double_t fio = 0.5 * (phi1 + phi2);
   Double_t cm = TMath::Cos(fio);
   Double_t sm = TMath::Sin(fio);
   Double_t cpsi = point[0] * cm + point[1] * sm;
   Double_t dfi = 0.5 * (phi2 - phi1);
   Double_t cdfi = TMath::Cos(dfi);
   if (cpsi > r * cdfi - TGeoShape::Tolerance())
      inphi = kTRUE;
   if (inphi) {
      saf[1] = rmin - r;
      saf[2] = r - rmax;
      Double_t safe = saf[TMath::LocMax(3, saf)];
      safe = TMath::Max(0., safe);
      return safe;
   }
   // Point outside the phi range
   // Compute projected radius of the (r,phi) position vector onto
   // phi1 and phi2 edges and take the maximum for choosing the side.
   Double_t c1 = TMath::Cos(phi1);
   Double_t s1 = TMath::Sin(phi1);
   Double_t c2 = TMath::Cos(phi2);
   Double_t s2 = TMath::Sin(phi2);
 
   Double_t rproj = TMath::Max(point[0] * c1 + point[1] * s1, point[0] * c2 + point[1] * s2);
   saf[1] = rmin - rproj;
   saf[2] = rproj - rmax;
   Double_t safe = TMath::Max(saf[1], saf[2]);
   if ((phi2d - phi1d) >= 360.)
      return TMath::Max(safe, saf[0]);
   if (safe > 0) {
      // rproj not within (rmin,rmax) - > no need to calculate safphi
      safe = TMath::Sqrt(rsq - rproj * rproj + safe * safe);
      return (saf[0] < 0) ? safe : TMath::Sqrt(safe * safe + saf[0] * saf[0]);
   }
   Double_t safphi = TGeoShape::SafetyPhi(point, in, phi1d, phi2d);
   return (saf[0] < 0) ? safphi : TMath::Sqrt(saf[0] * saf[0] + safphi * safphi);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Save a primitive as a C++ statement(s) on output stream "out".
 
void TGeoTubeSeg::SavePrimitive(std::ostream &out, Option_t * /*option*/ /*= ""*/)
{
   if (TObject::TestBit(kGeoSavePrimitive))
      return;
   out << "   // Shape: " << GetName() << " type: " << ClassName() << std::endl;
   out << "   rmin = " << fRmin << ";" << std::endl;
   out << "   rmax = " << fRmax << ";" << std::endl;
   out << "   dz   = " << fDz << ";" << std::endl;
   out << "   phi1 = " << fPhi1 << ";" << std::endl;
   out << "   phi2 = " << fPhi2 << ";" << std::endl;
   out << "   TGeoShape *" << GetPointerName() << " = new TGeoTubeSeg(\"" << GetName() << "\",rmin,rmax,dz,phi1,phi2);"
       << std::endl;
   TObject::SetBit(TGeoShape::kGeoSavePrimitive);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Set dimensions of the tube segment.
/// The segment will be from phiStart to phiEnd expressed in degree.
 
void TGeoTubeSeg::SetTubsDimensions(Double_t rmin, Double_t rmax, Double_t dz, Double_t phiStart, Double_t phiEnd)
{
   fRmin = rmin;
   fRmax = rmax;
   fDz = dz;
   fPhi1 = phiStart;
   if (fPhi1 < 0)
      fPhi1 += 360.;
   fPhi2 = phiEnd;
   while (fPhi2 <= fPhi1)
      fPhi2 += 360.;
   if (TGeoShape::IsSameWithinTolerance(fPhi1, fPhi2))
      Fatal("SetTubsDimensions", "In shape %s invalid phi1=%g, phi2=%g\n", GetName(), fPhi1, fPhi2);
   InitTrigonometry();
}
 
////////////////////////////////////////////////////////////////////////////////
/// Set dimensions of the tube segment starting from a list.
 
void TGeoTubeSeg::SetDimensions(Double_t *param)
{
   Double_t rmin = param[0];
   Double_t rmax = param[1];
   Double_t dz = param[2];
   Double_t phi1 = param[3];
   Double_t phi2 = param[4];
   SetTubsDimensions(rmin, rmax, dz, phi1, phi2);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Fills array with n random points located on the line segments of the shape mesh.
/// The output array must be provided with a length of minimum 3*npoints. Returns
/// true if operation is implemented.
 
Bool_t TGeoTubeSeg::GetPointsOnSegments(Int_t npoints, Double_t *array) const
{
   if (npoints > (npoints / 2) * 2) {
      Error("GetPointsOnSegments", "Npoints must be even number");
      return kFALSE;
   }
   Int_t nc = (Int_t)TMath::Sqrt(0.5 * npoints);
   Double_t dphi = (fPhi2 - fPhi1) * TMath::DegToRad() / (nc - 1);
   Double_t phi = 0;
   Double_t phi1 = fPhi1 * TMath::DegToRad();
   Int_t ntop = npoints / 2 - nc * (nc - 1);
   Double_t dz = 2 * fDz / (nc - 1);
   Double_t z = 0;
   Int_t icrt = 0;
   Int_t nphi = nc;
   // loop z sections
   for (Int_t i = 0; i < nc; i++) {
      if (i == (nc - 1)) {
         nphi = ntop;
         dphi = (fPhi2 - fPhi1) * TMath::DegToRad() / (nphi - 1);
      }
      z = -fDz + i * dz;
      // loop points on circle sections
      for (Int_t j = 0; j < nphi; j++) {
         phi = phi1 + j * dphi;
         array[icrt++] = fRmin * TMath::Cos(phi);
         array[icrt++] = fRmin * TMath::Sin(phi);
         array[icrt++] = z;
         array[icrt++] = fRmax * TMath::Cos(phi);
         array[icrt++] = fRmax * TMath::Sin(phi);
         array[icrt++] = z;
      }
   }
   return kTRUE;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Create tube segment mesh points.
 
void TGeoTubeSeg::SetPoints(Double_t *points) const
{
   Double_t dz;
   Int_t j, n;
   Double_t phi, phi1, phi2, dphi;
   phi1 = fPhi1;
   phi2 = fPhi2;
   if (phi2 < phi1)
      phi2 += 360.;
   n = gGeoManager->GetNsegments() + 1;
 
   dphi = (phi2 - phi1) / (n - 1);
   dz = fDz;
 
   if (points) {
      Int_t indx = 0;
 
      for (j = 0; j < n; j++) {
         phi = (phi1 + j * dphi) * TMath::DegToRad();
         points[indx + 6 * n] = points[indx] = fRmin * TMath::Cos(phi);
         indx++;
         points[indx + 6 * n] = points[indx] = fRmin * TMath::Sin(phi);
         indx++;
         points[indx + 6 * n] = dz;
         points[indx] = -dz;
         indx++;
      }
      for (j = 0; j < n; j++) {
         phi = (phi1 + j * dphi) * TMath::DegToRad();
         points[indx + 6 * n] = points[indx] = fRmax * TMath::Cos(phi);
         indx++;
         points[indx + 6 * n] = points[indx] = fRmax * TMath::Sin(phi);
         indx++;
         points[indx + 6 * n] = dz;
         points[indx] = -dz;
         indx++;
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Create tube segment mesh points.
 
void TGeoTubeSeg::SetPoints(Float_t *points) const
{
   Double_t dz;
   Int_t j, n;
   Double_t phi, phi1, phi2, dphi;
   phi1 = fPhi1;
   phi2 = fPhi2;
   if (phi2 < phi1)
      phi2 += 360.;
   n = gGeoManager->GetNsegments() + 1;
 
   dphi = (phi2 - phi1) / (n - 1);
   dz = fDz;
 
   if (points) {
      Int_t indx = 0;
 
      for (j = 0; j < n; j++) {
         phi = (phi1 + j * dphi) * TMath::DegToRad();
         points[indx + 6 * n] = points[indx] = fRmin * TMath::Cos(phi);
         indx++;
         points[indx + 6 * n] = points[indx] = fRmin * TMath::Sin(phi);
         indx++;
         points[indx + 6 * n] = dz;
         points[indx] = -dz;
         indx++;
      }
      for (j = 0; j < n; j++) {
         phi = (phi1 + j * dphi) * TMath::DegToRad();
         points[indx + 6 * n] = points[indx] = fRmax * TMath::Cos(phi);
         indx++;
         points[indx + 6 * n] = points[indx] = fRmax * TMath::Sin(phi);
         indx++;
         points[indx + 6 * n] = dz;
         points[indx] = -dz;
         indx++;
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Returns numbers of vertices, segments and polygons composing the shape mesh.
 
void TGeoTubeSeg::GetMeshNumbers(Int_t &nvert, Int_t &nsegs, Int_t &npols) const
{
   Int_t n = gGeoManager->GetNsegments() + 1;
   nvert = n * 4;
   nsegs = n * 8;
   npols = n * 4 - 2;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Return number of vertices of the mesh representation
 
Int_t TGeoTubeSeg::GetNmeshVertices() const
{
   Int_t n = gGeoManager->GetNsegments() + 1;
   Int_t numPoints = n * 4;
   return numPoints;
}
 
////////////////////////////////////////////////////////////////////////////////
/// fill size of this 3-D object
 
void TGeoTubeSeg::Sizeof3D() const {}
 
////////////////////////////////////////////////////////////////////////////////
/// Fills a static 3D buffer and returns a reference.
 
const TBuffer3D &TGeoTubeSeg::GetBuffer3D(Int_t reqSections, Bool_t localFrame) const
{
   static TBuffer3DTubeSeg buffer;
   TGeoBBox::FillBuffer3D(buffer, reqSections, localFrame);
 
   if (reqSections & TBuffer3D::kShapeSpecific) {
      // These from TBuffer3DTube / TGeoTube
      buffer.fRadiusInner = fRmin;
      buffer.fRadiusOuter = fRmax;
      buffer.fHalfLength = fDz;
      buffer.fPhiMin = fPhi1;
      buffer.fPhiMax = fPhi2;
      buffer.SetSectionsValid(TBuffer3D::kShapeSpecific);
   }
   if (reqSections & TBuffer3D::kRawSizes) {
      Int_t n = gGeoManager->GetNsegments() + 1;
      Int_t nbPnts = 4 * n;
      Int_t nbSegs = 2 * nbPnts;
      Int_t nbPols = nbPnts - 2;
      if (buffer.SetRawSizes(nbPnts, 3 * nbPnts, nbSegs, 3 * nbSegs, nbPols, 6 * nbPols)) {
         buffer.SetSectionsValid(TBuffer3D::kRawSizes);
      }
   }
   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 TGeoTubeSeg::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 TGeoTubeSeg::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 TGeoTubeSeg::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 TGeoTubeSeg::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 TGeoTubeSeg::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]);
}
 
 
TGeoCtub::TGeoCtub()
{
   // default ctor
   fNlow[0] = fNlow[1] = fNhigh[0] = fNhigh[1] = 0.;
   fNlow[2] = -1;
   fNhigh[2] = 1;
}
 
////////////////////////////////////////////////////////////////////////////////
/// constructor
 
TGeoCtub::TGeoCtub(Double_t rmin, Double_t rmax, Double_t dz, Double_t phi1, Double_t phi2, Double_t lx, Double_t ly,
                   Double_t lz, Double_t tx, Double_t ty, Double_t tz)
   : TGeoTubeSeg(rmin, rmax, dz, phi1, phi2)
{
   fNlow[0] = lx;
   fNlow[1] = ly;
   fNlow[2] = lz;
   fNhigh[0] = tx;
   fNhigh[1] = ty;
   fNhigh[2] = tz;
   SetShapeBit(kGeoCtub);
   ComputeBBox();
}
 
////////////////////////////////////////////////////////////////////////////////
/// constructor
 
TGeoCtub::TGeoCtub(const char *name, Double_t rmin, Double_t rmax, Double_t dz, Double_t phi1, Double_t phi2,
                   Double_t lx, Double_t ly, Double_t lz, Double_t tx, Double_t ty, Double_t tz)
   : TGeoTubeSeg(name, rmin, rmax, dz, phi1, phi2)
{
   fNlow[0] = lx;
   fNlow[1] = ly;
   fNlow[2] = lz;
   fNhigh[0] = tx;
   fNhigh[1] = ty;
   fNhigh[2] = tz;
   SetShapeBit(kGeoCtub);
   ComputeBBox();
}
 
////////////////////////////////////////////////////////////////////////////////
/// ctor with parameters
 
TGeoCtub::TGeoCtub(Double_t *params) : TGeoTubeSeg(0, 0, 0, 0, 0)
{
   SetCtubDimensions(params[0], params[1], params[2], params[3], params[4], params[5], params[6], params[7], params[8],
                     params[9], params[10]);
   SetShapeBit(kGeoCtub);
}
 
////////////////////////////////////////////////////////////////////////////////
/// destructor
 
TGeoCtub::~TGeoCtub() {}
 
////////////////////////////////////////////////////////////////////////////////
/// Computes capacity of the shape in [length^3]
 
Double_t TGeoCtub::Capacity() const
{
   Double_t capacity = TGeoTubeSeg::Capacity();
   return capacity;
}
 
////////////////////////////////////////////////////////////////////////////////
/// compute minimum bounding box of the ctub
 
void TGeoCtub::ComputeBBox()
{
   TGeoTubeSeg::ComputeBBox();
   if ((fNlow[2] > -(1E-10)) || (fNhigh[2] < 1E-10)) {
      Error("ComputeBBox", "In shape %s wrong definition of cut planes", GetName());
      return;
   }
   Double_t xc = 0, yc = 0;
   Double_t zmin = 0, zmax = 0;
   Double_t z1;
   Double_t z[8];
   // check if nxy is in the phi range
   Double_t phi_low = TMath::ATan2(fNlow[1], fNlow[0]) * TMath::RadToDeg();
   Double_t phi_hi = TMath::ATan2(fNhigh[1], fNhigh[0]) * TMath::RadToDeg();
   Bool_t in_range_low = kFALSE;
   Bool_t in_range_hi = kFALSE;
 
   Int_t i;
   for (i = 0; i < 2; i++) {
      if (phi_low < 0)
         phi_low += 360.;
      Double_t dphi = fPhi2 - fPhi1;
      if (dphi < 0)
         dphi += 360.;
      Double_t ddp = phi_low - fPhi1;
      if (ddp < 0)
         ddp += 360.;
      if (ddp <= dphi) {
         xc = fRmin * TMath::Cos(phi_low * TMath::DegToRad());
         yc = fRmin * TMath::Sin(phi_low * TMath::DegToRad());
         z1 = GetZcoord(xc, yc, -fDz);
         xc = fRmax * TMath::Cos(phi_low * TMath::DegToRad());
         yc = fRmax * TMath::Sin(phi_low * TMath::DegToRad());
         z1 = TMath::Min(z1, GetZcoord(xc, yc, -fDz));
         if (in_range_low)
            zmin = TMath::Min(zmin, z1);
         else
            zmin = z1;
         in_range_low = kTRUE;
      }
      phi_low += 180;
      if (phi_low > 360)
         phi_low -= 360.;
   }
 
   for (i = 0; i < 2; i++) {
      if (phi_hi < 0)
         phi_hi += 360.;
      Double_t dphi = fPhi2 - fPhi1;
      if (dphi < 0)
         dphi += 360.;
      Double_t ddp = phi_hi - fPhi1;
      if (ddp < 0)
         ddp += 360.;
      if (ddp <= dphi) {
         xc = fRmin * TMath::Cos(phi_hi * TMath::DegToRad());
         yc = fRmin * TMath::Sin(phi_hi * TMath::DegToRad());
         z1 = GetZcoord(xc, yc, fDz);
         xc = fRmax * TMath::Cos(phi_hi * TMath::DegToRad());
         yc = fRmax * TMath::Sin(phi_hi * TMath::DegToRad());
         z1 = TMath::Max(z1, GetZcoord(xc, yc, fDz));
         if (in_range_hi)
            zmax = TMath::Max(zmax, z1);
         else
            zmax = z1;
         in_range_hi = kTRUE;
      }
      phi_hi += 180;
      if (phi_hi > 360)
         phi_hi -= 360.;
   }
 
   xc = fRmin * fC1;
   yc = fRmin * fS1;
   z[0] = GetZcoord(xc, yc, -fDz);
   z[4] = GetZcoord(xc, yc, fDz);
 
   xc = fRmin * fC2;
   yc = fRmin * fS2;
   z[1] = GetZcoord(xc, yc, -fDz);
   z[5] = GetZcoord(xc, yc, fDz);
 
   xc = fRmax * fC1;
   yc = fRmax * fS1;
   z[2] = GetZcoord(xc, yc, -fDz);
   z[6] = GetZcoord(xc, yc, fDz);
 
   xc = fRmax * fC2;
   yc = fRmax * fS2;
   z[3] = GetZcoord(xc, yc, -fDz);
   z[7] = GetZcoord(xc, yc, fDz);
 
   z1 = z[TMath::LocMin(4, &z[0])];
   if (in_range_low)
      zmin = TMath::Min(zmin, z1);
   else
      zmin = z1;
 
   z1 = z[TMath::LocMax(4, &z[4]) + 4];
   if (in_range_hi)
      zmax = TMath::Max(zmax, z1);
   else
      zmax = z1;
 
   fDZ = 0.5 * (zmax - zmin);
   fOrigin[2] = 0.5 * (zmax + zmin);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Compute normal to closest surface from POINT.
 
void TGeoCtub::ComputeNormal(const Double_t *point, const Double_t *dir, Double_t *norm) const
{
   Double_t saf[4];
   Bool_t isseg = kTRUE;
   if (TMath::Abs(fPhi2 - fPhi1 - 360.) < 1E-8)
      isseg = kFALSE;
   Double_t rsq = point[0] * point[0] + point[1] * point[1];
   Double_t r = TMath::Sqrt(rsq);
 
   saf[0] = TMath::Abs(point[0] * fNlow[0] + point[1] * fNlow[1] + (fDz + point[2]) * fNlow[2]);
   saf[1] = TMath::Abs(point[0] * fNhigh[0] + point[1] * fNhigh[1] - (fDz - point[2]) * fNhigh[2]);
   saf[2] = (fRmin > 1E-10) ? TMath::Abs(r - fRmin) : TGeoShape::Big();
   saf[3] = TMath::Abs(fRmax - r);
   Int_t i = TMath::LocMin(4, saf);
   if (isseg) {
      if (TGeoShape::IsCloseToPhi(saf[i], point, fC1, fS1, fC2, fS2)) {
         TGeoShape::NormalPhi(point, dir, norm, fC1, fS1, fC2, fS2);
         return;
      }
   }
   if (i == 0) {
      memcpy(norm, fNlow, 3 * sizeof(Double_t));
      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];
      }
      return;
   }
   if (i == 1) {
      memcpy(norm, fNhigh, 3 * sizeof(Double_t));
      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];
      }
      return;
   }
 
   norm[2] = 0;
   Double_t phi = TMath::ATan2(point[1], point[0]);
   norm[0] = TMath::Cos(phi);
   norm[1] = TMath::Sin(phi);
   if (norm[0] * dir[0] + norm[1] * dir[1] < 0) {
      norm[0] = -norm[0];
      norm[1] = -norm[1];
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// check if point is contained in the cut tube
/// check the lower cut plane
 
Bool_t TGeoCtub::Contains(const Double_t *point) const
{
   Double_t zin = point[0] * fNlow[0] + point[1] * fNlow[1] + (point[2] + fDz) * fNlow[2];
   if (zin > 0)
      return kFALSE;
   // check the higher cut plane
   zin = point[0] * fNhigh[0] + point[1] * fNhigh[1] + (point[2] - fDz) * fNhigh[2];
   if (zin > 0)
      return kFALSE;
   // check radius
   Double_t r2 = point[0] * point[0] + point[1] * point[1];
   if ((r2 < fRmin * fRmin) || (r2 > fRmax * fRmax))
      return kFALSE;
   // check phi
   Double_t phi = TMath::ATan2(point[1], point[0]) * TMath::RadToDeg();
   if (phi < 0)
      phi += 360.;
   Double_t dphi = fPhi2 - fPhi1;
   Double_t ddp = phi - fPhi1;
   if (ddp < 0)
      ddp += 360.;
   //   if (ddp>360) ddp-=360;
   if (ddp > dphi)
      return kFALSE;
   return kTRUE;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Get range of shape for a given axis.
 
Double_t TGeoCtub::GetAxisRange(Int_t iaxis, Double_t &xlo, Double_t &xhi) const
{
   xlo = 0;
   xhi = 0;
   Double_t dx = 0;
   switch (iaxis) {
   case 1:
      xlo = fRmin;
      xhi = fRmax;
      dx = xhi - xlo;
      return dx;
   case 2:
      xlo = fPhi1;
      xhi = fPhi2;
      dx = xhi - xlo;
      return dx;
   }
   return dx;
}
 
////////////////////////////////////////////////////////////////////////////////
/// compute real Z coordinate of a point belonging to either lower or
/// higher caps (z should be either +fDz or -fDz)
 
Double_t TGeoCtub::GetZcoord(Double_t xc, Double_t yc, Double_t zc) const
{
   Double_t newz = 0;
   if (zc < 0)
      newz = -fDz - (xc * fNlow[0] + yc * fNlow[1]) / fNlow[2];
   else
      newz = fDz - (xc * fNhigh[0] + yc * fNhigh[1]) / fNhigh[2];
   return newz;
}
 
////////////////////////////////////////////////////////////////////////////////
/// compute distance from outside point to surface of the cut tube
 
Double_t
TGeoCtub::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();
      if ((iact == 1) && (step <= *safe))
         return TGeoShape::Big();
   }
   // 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();
   Double_t saf[2];
   saf[0] = point[0] * fNlow[0] + point[1] * fNlow[1] + (fDz + point[2]) * fNlow[2];
   saf[1] = point[0] * fNhigh[0] + point[1] * fNhigh[1] + (point[2] - fDz) * fNhigh[2];
   Double_t rsq = point[0] * point[0] + point[1] * point[1];
   Double_t r = TMath::Sqrt(rsq);
   Double_t cpsi = 0;
   Bool_t tub = kFALSE;
   if (TMath::Abs(fPhi2 - fPhi1 - 360.) < 1E-8)
      tub = kTRUE;
 
   // find distance to shape
   Double_t r2;
   Double_t calf = dir[0] * fNlow[0] + dir[1] * fNlow[1] + dir[2] * fNlow[2];
   // check Z planes
   Double_t xi, yi, zi, s;
   if (saf[0] > 0) {
      if (calf < 0) {
         s = -saf[0] / calf;
         xi = point[0] + s * dir[0];
         yi = point[1] + s * dir[1];
         r2 = xi * xi + yi * yi;
         if (((fRmin * fRmin) <= r2) && (r2 <= (fRmax * fRmax))) {
            if (tub)
               return s;
            cpsi = (xi * fCm + yi * fSm) / TMath::Sqrt(r2);
            if (cpsi >= fCdfi)
               return s;
         }
      }
   }
   calf = dir[0] * fNhigh[0] + dir[1] * fNhigh[1] + dir[2] * fNhigh[2];
   if (saf[1] > 0) {
      if (calf < 0) {
         s = -saf[1] / calf;
         xi = point[0] + s * dir[0];
         yi = point[1] + s * dir[1];
         r2 = xi * xi + yi * yi;
         if (((fRmin * fRmin) <= r2) && (r2 <= (fRmax * fRmax))) {
            if (tub)
               return s;
            cpsi = (xi * fCm + yi * fSm) / TMath::Sqrt(r2);
            if (cpsi >= fCdfi)
               return s;
         }
      }
   }
 
   // check outer cyl. surface
   Double_t nsq = dir[0] * dir[0] + dir[1] * dir[1];
   if (TMath::Abs(nsq) < 1E-10)
      return TGeoShape::Big();
   Double_t rdotn = point[0] * dir[0] + point[1] * dir[1];
   Double_t b, d;
   // only r>fRmax coming inwards has to be considered
   if (r > fRmax && rdotn < 0) {
      TGeoTube::DistToTube(rsq, nsq, rdotn, fRmax, b, d);
      if (d > 0) {
         s = -b - d;
         if (s > 0) {
            xi = point[0] + s * dir[0];
            yi = point[1] + s * dir[1];
            zi = point[2] + s * dir[2];
            if ((-xi * fNlow[0] - yi * fNlow[1] - (zi + fDz) * fNlow[2]) > 0) {
               if ((-xi * fNhigh[0] - yi * fNhigh[1] + (fDz - zi) * fNhigh[2]) > 0) {
                  if (tub)
                     return s;
                  cpsi = (xi * fCm + yi * fSm) / fRmax;
                  if (cpsi >= fCdfi)
                     return s;
               }
            }
         }
      }
   }
   // check inner cylinder
   Double_t snxt = TGeoShape::Big();
   if (fRmin > 0) {
      TGeoTube::DistToTube(rsq, nsq, rdotn, fRmin, b, d);
      if (d > 0) {
         s = -b + d;
         if (s > 0) {
            xi = point[0] + s * dir[0];
            yi = point[1] + s * dir[1];
            zi = point[2] + s * dir[2];
            if ((-xi * fNlow[0] - yi * fNlow[1] - (zi + fDz) * fNlow[2]) > 0) {
               if ((-xi * fNhigh[0] - yi * fNhigh[1] + (fDz - zi) * fNhigh[2]) > 0) {
                  if (tub)
                     return s;
                  cpsi = (xi * fCm + yi * fSm) / fRmin;
                  if (cpsi >= fCdfi)
                     snxt = s;
               }
            }
         }
      }
   }
   // check phi planes
   if (tub)
      return snxt;
   Double_t un = dir[0] * fS1 - dir[1] * fC1;
   if (un < -TGeoShape::Tolerance()) {
      s = (point[1] * fC1 - point[0] * fS1) / un;
      if (s >= 0) {
         xi = point[0] + s * dir[0];
         yi = point[1] + s * dir[1];
         zi = point[2] + s * dir[2];
         if ((-xi * fNlow[0] - yi * fNlow[1] - (zi + fDz) * fNlow[2]) > 0) {
            if ((-xi * fNhigh[0] - yi * fNhigh[1] + (fDz - zi) * fNhigh[2]) > 0) {
               r2 = xi * xi + yi * yi;
               if ((fRmin * fRmin <= r2) && (r2 <= fRmax * fRmax)) {
                  if ((yi * fCm - xi * fSm) <= 0) {
                     if (s < snxt)
                        snxt = s;
                  }
               }
            }
         }
      }
   }
   un = dir[0] * fS2 - dir[1] * fC2;
   if (un > TGeoShape::Tolerance()) {
      s = (point[1] * fC2 - point[0] * fS2) / un;
      if (s >= 0) {
         xi = point[0] + s * dir[0];
         yi = point[1] + s * dir[1];
         zi = point[2] + s * dir[2];
         if ((-xi * fNlow[0] - yi * fNlow[1] - (zi + fDz) * fNlow[2]) > 0) {
            if ((-xi * fNhigh[0] - yi * fNhigh[1] + (fDz - zi) * fNhigh[2]) > 0) {
               r2 = xi * xi + yi * yi;
               if ((fRmin * fRmin <= r2) && (r2 <= fRmax * fRmax)) {
                  if ((yi * fCm - xi * fSm) >= 0) {
                     if (s < snxt)
                        snxt = s;
                  }
               }
            }
         }
      }
   }
   return snxt;
}
 
////////////////////////////////////////////////////////////////////////////////
/// compute distance from inside point to surface of the cut tube
 
Double_t
TGeoCtub::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) && (*safe > step))
      return TGeoShape::Big();
   Double_t rsq = point[0] * point[0] + point[1] * point[1];
   Bool_t tub = kFALSE;
   if (TMath::Abs(fPhi2 - fPhi1 - 360.) < 1E-8)
      tub = kTRUE;
   // compute distance to surface
   // Do Z
   Double_t sz = TGeoShape::Big();
   Double_t saf[2];
   saf[0] = -point[0] * fNlow[0] - point[1] * fNlow[1] - (fDz + point[2]) * fNlow[2];
   saf[1] = -point[0] * fNhigh[0] - point[1] * fNhigh[1] + (fDz - point[2]) * fNhigh[2];
   Double_t calf = dir[0] * fNlow[0] + dir[1] * fNlow[1] + dir[2] * fNlow[2];
   if (calf > 0)
      sz = saf[0] / calf;
 
   calf = dir[0] * fNhigh[0] + dir[1] * fNhigh[1] + dir[2] * fNhigh[2];
   if (calf > 0) {
      Double_t sz1 = saf[1] / calf;
      if (sz1 < sz)
         sz = sz1;
   }
 
   // Do R
   Double_t nsq = dir[0] * dir[0] + dir[1] * dir[1];
   // track parallel to Z
   if (TMath::Abs(nsq) < 1E-10)
      return sz;
   Double_t rdotn = point[0] * dir[0] + point[1] * dir[1];
   Double_t sr = TGeoShape::Big();
   Double_t b, d;
   Bool_t skip_outer = kFALSE;
   // inner cylinder
   if (fRmin > 1E-10) {
      TGeoTube::DistToTube(rsq, nsq, rdotn, fRmin, b, d);
      if (d > 0) {
         sr = -b - d;
         if (sr > 0)
            skip_outer = kTRUE;
      }
   }
   // outer cylinder
   if (!skip_outer) {
      TGeoTube::DistToTube(rsq, nsq, rdotn, fRmax, b, d);
      if (d > 0) {
         sr = -b + d;
         if (sr < 0)
            sr = TGeoShape::Big();
      } else {
         return 0.; // already outside
      }
   }
   // phi planes
   Double_t sfmin = TGeoShape::Big();
   if (!tub)
      sfmin = TGeoShape::DistToPhiMin(point, dir, fS1, fC1, fS2, fC2, fSm, fCm);
   return TMath::Min(TMath::Min(sz, sr), sfmin);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Divide the tube along one axis.
 
TGeoVolume *TGeoCtub::Divide(TGeoVolume * /*voldiv*/, const char * /*divname*/, Int_t /*iaxis*/, Int_t /*ndiv*/,
                             Double_t /*start*/, Double_t /*step*/)
{
   Warning("Divide", "In shape %s division of a cut tube not implemented", GetName());
   return nullptr;
}
 
////////////////////////////////////////////////////////////////////////////////
/// in case shape has some negative parameters, these has to be computed
/// in order to fit the mother
 
TGeoShape *TGeoCtub::GetMakeRuntimeShape(TGeoShape *mother, TGeoMatrix * /*mat*/) const
{
   if (!TestShapeBit(kGeoRunTimeShape))
      return nullptr;
   if (!mother->TestShapeBit(kGeoTube)) {
      Error("GetMakeRuntimeShape", "Invalid mother for shape %s", GetName());
      return nullptr;
   }
   Double_t rmin, rmax, dz;
   rmin = fRmin;
   rmax = fRmax;
   dz = fDz;
   if (fDz < 0)
      dz = ((TGeoTube *)mother)->GetDz();
   if (fRmin < 0)
      rmin = ((TGeoTube *)mother)->GetRmin();
   if ((fRmax < 0) || (fRmax <= fRmin))
      rmax = ((TGeoTube *)mother)->GetRmax();
 
   return (new TGeoCtub(rmin, rmax, dz, fPhi1, fPhi2, fNlow[0], fNlow[1], fNlow[2], fNhigh[0], fNhigh[1], fNhigh[2]));
}
 
////////////////////////////////////////////////////////////////////////////////
/// print shape parameters
 
void TGeoCtub::InspectShape() const
{
   printf("*** Shape %s: TGeoCtub ***\n", GetName());
   printf("    lx = %11.5f\n", fNlow[0]);
   printf("    ly = %11.5f\n", fNlow[1]);
   printf("    lz = %11.5f\n", fNlow[2]);
   printf("    tx = %11.5f\n", fNhigh[0]);
   printf("    ty = %11.5f\n", fNhigh[1]);
   printf("    tz = %11.5f\n", fNhigh[2]);
   TGeoTubeSeg::InspectShape();
}
 
////////////////////////////////////////////////////////////////////////////////
/// 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 TGeoCtub::Safety(const Double_t *point, Bool_t in) const
{
   Double_t saf[4];
   Double_t rsq = point[0] * point[0] + point[1] * point[1];
   Double_t r = TMath::Sqrt(rsq);
   Bool_t isseg = kTRUE;
   if (TMath::Abs(fPhi2 - fPhi1 - 360.) < 1E-8)
      isseg = kFALSE;
 
   saf[0] = -point[0] * fNlow[0] - point[1] * fNlow[1] - (fDz + point[2]) * fNlow[2];
   saf[1] = -point[0] * fNhigh[0] - point[1] * fNhigh[1] + (fDz - point[2]) * fNhigh[2];
   saf[2] = (fRmin < 1E-10 && !isseg) ? TGeoShape::Big() : (r - fRmin);
   saf[3] = fRmax - r;
   Double_t safphi = TGeoShape::Big();
   if (isseg)
      safphi = TGeoShape::SafetyPhi(point, in, fPhi1, fPhi2);
 
   if (in) {
      Double_t safe = saf[TMath::LocMin(4, saf)];
      return TMath::Min(safe, safphi);
   }
   for (Int_t i = 0; i < 4; i++)
      saf[i] = -saf[i];
   Double_t safe = saf[TMath::LocMax(4, saf)];
   if (isseg)
      return TMath::Max(safe, safphi);
   return safe;
}
 
////////////////////////////////////////////////////////////////////////////////
/// set dimensions of a cut tube
 
void TGeoCtub::SetCtubDimensions(Double_t rmin, Double_t rmax, Double_t dz, Double_t phi1, Double_t phi2, Double_t lx,
                                 Double_t ly, Double_t lz, Double_t tx, Double_t ty, Double_t tz)
{
   SetTubsDimensions(rmin, rmax, dz, phi1, phi2);
   fNlow[0] = lx;
   fNlow[1] = ly;
   fNlow[2] = lz;
   fNhigh[0] = tx;
   fNhigh[1] = ty;
   fNhigh[2] = tz;
   ComputeBBox();
}
 
////////////////////////////////////////////////////////////////////////////////
/// Save a primitive as a C++ statement(s) on output stream "out".
 
void TGeoCtub::SavePrimitive(std::ostream &out, Option_t * /*option*/ /*= ""*/)
{
   if (TObject::TestBit(kGeoSavePrimitive))
      return;
   out << "   // Shape: " << GetName() << " type: " << ClassName() << std::endl;
   out << "   rmin = " << fRmin << ";" << std::endl;
   out << "   rmax = " << fRmax << ";" << std::endl;
   out << "   dz   = " << fDz << ";" << std::endl;
   out << "   phi1 = " << fPhi1 << ";" << std::endl;
   out << "   phi2 = " << fPhi2 << ";" << std::endl;
   out << "   lx   = " << fNlow[0] << ";" << std::endl;
   out << "   ly   = " << fNlow[1] << ";" << std::endl;
   out << "   lz   = " << fNlow[2] << ";" << std::endl;
   out << "   tx   = " << fNhigh[0] << ";" << std::endl;
   out << "   ty   = " << fNhigh[1] << ";" << std::endl;
   out << "   tz   = " << fNhigh[2] << ";" << std::endl;
   out << "   TGeoShape *" << GetPointerName() << " = new TGeoCtub(\"" << GetName()
       << "\",rmin,rmax,dz,phi1,phi2,lx,ly,lz,tx,ty,tz);" << std::endl;
   TObject::SetBit(TGeoShape::kGeoSavePrimitive);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Set dimensions of the cut tube starting from a list.
 
void TGeoCtub::SetDimensions(Double_t *param)
{
   SetCtubDimensions(param[0], param[1], param[2], param[3], param[4], param[5], param[6], param[7], param[8], param[9],
                     param[10]);
   ComputeBBox();
}
 
////////////////////////////////////////////////////////////////////////////////
/// Fills array with n random points located on the line segments of the shape mesh.
/// The output array must be provided with a length of minimum 3*npoints. Returns
/// true if operation is implemented.
 
Bool_t TGeoCtub::GetPointsOnSegments(Int_t /*npoints*/, Double_t * /*array*/) const
{
   return kFALSE;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Create mesh points for the cut tube.
 
void TGeoCtub::SetPoints(Double_t *points) const
{
   Double_t dz;
   Int_t j, n;
   Double_t phi, phi1, phi2, dphi;
   phi1 = fPhi1;
   phi2 = fPhi2;
   if (phi2 < phi1)
      phi2 += 360.;
   n = gGeoManager->GetNsegments() + 1;
 
   dphi = (phi2 - phi1) / (n - 1);
   dz = fDz;
 
   if (points) {
      Int_t indx = 0;
 
      for (j = 0; j < n; j++) {
         phi = (phi1 + j * dphi) * TMath::DegToRad();
         points[indx + 6 * n] = points[indx] = fRmin * TMath::Cos(phi);
         indx++;
         points[indx + 6 * n] = points[indx] = fRmin * TMath::Sin(phi);
         indx++;
         points[indx + 6 * n] = GetZcoord(points[indx - 2], points[indx - 1], dz);
         points[indx] = GetZcoord(points[indx - 2], points[indx - 1], -dz);
         indx++;
      }
      for (j = 0; j < n; j++) {
         phi = (phi1 + j * dphi) * TMath::DegToRad();
         points[indx + 6 * n] = points[indx] = fRmax * TMath::Cos(phi);
         indx++;
         points[indx + 6 * n] = points[indx] = fRmax * TMath::Sin(phi);
         indx++;
         points[indx + 6 * n] = GetZcoord(points[indx - 2], points[indx - 1], dz);
         points[indx] = GetZcoord(points[indx - 2], points[indx - 1], -dz);
         indx++;
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Create mesh points for the cut tube.
 
void TGeoCtub::SetPoints(Float_t *points) const
{
   Double_t dz;
   Int_t j, n;
   Double_t phi, phi1, phi2, dphi;
   phi1 = fPhi1;
   phi2 = fPhi2;
   if (phi2 < phi1)
      phi2 += 360.;
   n = gGeoManager->GetNsegments() + 1;
 
   dphi = (phi2 - phi1) / (n - 1);
   dz = fDz;
 
   if (points) {
      Int_t indx = 0;
 
      for (j = 0; j < n; j++) {
         phi = (phi1 + j * dphi) * TMath::DegToRad();
         points[indx + 6 * n] = points[indx] = fRmin * TMath::Cos(phi);
         indx++;
         points[indx + 6 * n] = points[indx] = fRmin * TMath::Sin(phi);
         indx++;
         points[indx + 6 * n] = GetZcoord(points[indx - 2], points[indx - 1], dz);
         points[indx] = GetZcoord(points[indx - 2], points[indx - 1], -dz);
         indx++;
      }
      for (j = 0; j < n; j++) {
         phi = (phi1 + j * dphi) * TMath::DegToRad();
         points[indx + 6 * n] = points[indx] = fRmax * TMath::Cos(phi);
         indx++;
         points[indx + 6 * n] = points[indx] = fRmax * TMath::Sin(phi);
         indx++;
         points[indx + 6 * n] = GetZcoord(points[indx - 2], points[indx - 1], dz);
         points[indx] = GetZcoord(points[indx - 2], points[indx - 1], -dz);
         indx++;
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Returns numbers of vertices, segments and polygons composing the shape mesh.
 
void TGeoCtub::GetMeshNumbers(Int_t &nvert, Int_t &nsegs, Int_t &npols) const
{
   TGeoTubeSeg::GetMeshNumbers(nvert, nsegs, npols);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Return number of vertices of the mesh representation
 
Int_t TGeoCtub::GetNmeshVertices() const
{
   Int_t n = gGeoManager->GetNsegments() + 1;
   Int_t numPoints = n * 4;
   return numPoints;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Fills a static 3D buffer and returns a reference.
 
const TBuffer3D &TGeoCtub::GetBuffer3D(Int_t reqSections, Bool_t localFrame) const
{
   static TBuffer3DCutTube buffer;
 
   TGeoBBox::FillBuffer3D(buffer, reqSections, localFrame);
 
   if (reqSections & TBuffer3D::kShapeSpecific) {
      // These from TBuffer3DCutTube / TGeoCtub
      buffer.fRadiusInner = fRmin;
      buffer.fRadiusOuter = fRmax;
      buffer.fHalfLength = fDz;
      buffer.fPhiMin = fPhi1;
      buffer.fPhiMax = fPhi2;
 
      for (UInt_t i = 0; i < 3; i++) {
         buffer.fLowPlaneNorm[i] = fNlow[i];
         buffer.fHighPlaneNorm[i] = fNhigh[i];
      }
      buffer.SetSectionsValid(TBuffer3D::kShapeSpecific);
   }
   if (reqSections & TBuffer3D::kRawSizes) {
      Int_t n = gGeoManager->GetNsegments() + 1;
      Int_t nbPnts = 4 * n;
      Int_t nbSegs = 2 * nbPnts;
      Int_t nbPols = nbPnts - 2;
      if (buffer.SetRawSizes(nbPnts, 3 * nbPnts, nbSegs, 3 * nbSegs, nbPols, 6 * nbPols)) {
         buffer.SetSectionsValid(TBuffer3D::kRawSizes);
      }
   }
   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 TGeoCtub::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 TGeoCtub::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 TGeoCtub::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 TGeoCtub::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 TGeoCtub::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]);
}