UPolycone.cc

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//
// ********************************************************************
// * This Software is part of the AIDA Unified Solids Library package *
// * See: https://aidasoft.web.cern.ch/USolids                        *
// ********************************************************************
//
// $Id:$
//
// --------------------------------------------------------------------
//
// UPolycone
//
// 19.04.13 Marek Gayer
//          Created from original implementation in Geant4
// --------------------------------------------------------------------

#include "UUtils.hh"
#include <string>
#include <cmath>
#include <sstream>
#include "UPolycone.hh"

#include "UEnclosingCylinder.hh"
#include "UReduciblePolygon.hh"

#include "UTubs.hh"
#include "UCons.hh"
#include "UTransform3D.hh"

using namespace std;

UPolycone::UPolycone(const std::string& name,
                     double phiStart,
                     double phiTotal,
                     int numZPlanes,
                     const double zPlane[],
                     const double rInner[],
                     const double rOuter[])
  : VUSolid(name)  //, fNumSides(0)
{
  fCubicVolume = 0;
  fSurfaceArea = 0;
  Init(phiStart, phiTotal, numZPlanes, zPlane, rInner, rOuter);

}

UPolycone::UPolycone(const std::string& name,
                     double phiStart,
                     double phiTotal,
                     int    numRZ,
                     const double r[],
                     const double z[])
  : VUSolid(name)
{
  UReduciblePolygon* rz = new UReduciblePolygon(r, z, numRZ);

  // Create( phiStart, phiTotal, rz );

  // Set original_parameters struct for consistency
  //

  bool convertible = SetOriginalParameters(rz);

  if (!convertible)
  {
    std::ostringstream message;
    message << "Polycone " << GetName() << "cannot be converted" << std::endl
            << "to Polycone with (Rmin,Rmaz,Z) parameters! Use GenericPolycone" ;
    UUtils::Exception("UPolycone::UPolycone()", "GeomSolids0002",
                      FatalError, 1, message.str().c_str());
    // JustWarning, message, "Use G4GenericPolycone instead!");

  }
  else
  {
    std::cout << "INFO: Converting polycone " << GetName() << std::endl
              << "to optimized polycone with (Rmin,Rmaz,Z) parameters !"
              << std::endl;
    double* Z, *R1, *R2;
    int num = fOriginalParameters->fNumZPlanes;
    Z = new double[num];
    R1 = new double[num];
    R2 = new double[num];
    for (int i = 0; i < num; i++)
    {
      Z[i] = fOriginalParameters->fZValues[i];
      R1[i] = fOriginalParameters->Rmin[i];
      R2[i] = fOriginalParameters->Rmax[i];
    }

    delete(fOriginalParameters);
    Init(phiStart, phiTotal, num, Z, R1, R2);
    delete [] R1;
    delete [] Z;
    delete [] R2;
  }

  delete rz;
}


//
// Constructor (GEANT3 style parameters)
//
void UPolycone::Init(double phiStart,
                     double phiTotal,
                     int numZPlanes,
                     const double zPlane[],
                     const double rInner[],
                     const double rOuter[])
{
  //Convertion for angles
  
  if (phiTotal <= 0 || phiTotal > UUtils::kTwoPi-1E-10)
   {
     phiIsOpen=false;
     startPhi = 0;
     endPhi = UUtils::kTwoPi;
   }
   else
   {
     //
     // Convert phi into our convention
     //
     phiIsOpen=true;
     startPhi = phiStart;
     while( startPhi < 0 ) startPhi += UUtils::kTwoPi;
     
     endPhi = phiStart+phiTotal;
     while( endPhi < startPhi ) endPhi += UUtils::kTwoPi;
  }
  // Set Parameters
  fOriginalParameters = new UPolyconeHistorical();
  fOriginalParameters->fStartAngle = startPhi;
  fOriginalParameters->fOpeningAngle = endPhi-startPhi;
  fOriginalParameters->fNumZPlanes = numZPlanes;
  fOriginalParameters->fZValues.resize(numZPlanes);
  fOriginalParameters->Rmin.resize(numZPlanes);
  fOriginalParameters->Rmax.resize(numZPlanes);

  // Calculate RMax of Polycone in order to determine convexity of sections
  //
  double RMaxextent=rOuter[0];
  for (int j=1; j < numZPlanes; j++)
  {
    if (rOuter[j] > RMaxextent) RMaxextent=rOuter[j];
    if (rInner[j]>rOuter[j])
    {
      std::ostringstream message;
      message << "Cannot create Polycone with rInner > rOuter for the same Z"
              << std::endl
              << "        rInner > rOuter for the same Z !" << std::endl
              << "        rMin[" << j << "] = " << rInner[j]
              << " -- rMax[" << j << "] = " << rOuter[j];
       UUtils::Exception("UPolycone::UPolycone()", "GeomSolids0002",
                         FatalErrorInArguments, 1, message.str().c_str());
    }
  }
  //
  double prevZ = 0, prevRmax = 0, prevRmin = 0;
  int dirZ = 1;
  if (zPlane[1] < zPlane[0])dirZ = -1;
//  int curSolid = 0;

  int i;
  for (i = 0; i < numZPlanes; i++)
  {
    if ((i < numZPlanes - 1) && (zPlane[i] == zPlane[i + 1]))
    {
      if ((rInner[i]  > rOuter[i + 1])
          || (rInner[i + 1] > rOuter[i]))
      {

        std::ostringstream message;
        message << "Cannot create a Polycone with no contiguous segments."
                << std::endl
                << "                            Segments are not contiguous !" << std::endl
                << "                            rMin[" << i << "] = " << rInner[i]
                << " -- rMax[" << i + 1 << "] = " << rOuter[i + 1] << std::endl
                << "                            rMin[" << i + 1 << "] = " << rInner[i + 1]
                << " -- rMax[" << i << "] = " << rOuter[i];
        UUtils::Exception("UPolycone::UPolycone()", "GeomSolids0002",
                          FatalErrorInArguments, 1, message.str().c_str());
      }
    }



    double rMin = rInner[i];
    double rMax = rOuter[i];
    double z = zPlane[i];

    if (i > 0)
    {
      if (z > prevZ)
      {
        if (dirZ < 0)
        {
          std::ostringstream message;
          message << "Cannot create a Polycone with different Z directions.Use GenericPolycone."
                  << std::endl
                  << "                          ZPlane is changing direction  !" << std::endl
                  << "  zPlane[0] = " << zPlane[0]
                  << " -- zPlane[1] = " << zPlane[1] << std::endl
                  << "  zPlane[" << i - 1 << "] = " << zPlane[i - 1]
                  << " -- rPlane[" << i << "] = " << zPlane[i];
          UUtils::Exception("UPolycone::UPolycone()", "GeomSolids0002",
                            FatalErrorInArguments, 1, message.str().c_str());



        }
        VUSolid* solid;
        double dz = (z - prevZ) / 2;

        bool tubular = (rMin == prevRmin && prevRmax == rMax);

//        if (fNumSides == 0)
        {
          if (tubular)
          {
            solid = new UTubs("", rMin, rMax, dz, phiStart, phiTotal);
          }
          else
          {
            solid = new UCons("", prevRmin, prevRmax, rMin, rMax, dz, phiStart, phiTotal);
          }
        }
//        else
//        {
//          solid = new UHedra("", prevRmin, prevRmax, rMin, rMax, dz, phiStart, phiTotal, fNumSides);
//        }

        fZs.push_back(z);

        int zi = fZs.size() - 1;
        double shift = fZs[zi - 1] + 0.5 * (fZs[zi] - fZs[zi - 1]);

        UPolyconeSection section;
        section.shift = shift;
        section.tubular = tubular;
        section.solid = solid;
        if(tubular)
        {
          if (rMax < RMaxextent) { section.convex = false;}
          else { section.convex = true;}
        }
        else
        {
          if ((rMax<prevRmax)||(rMax < RMaxextent)||(prevRmax < RMaxextent))
            { section.convex = false;}
          else
            { section.convex = true;}
        }
        fSections.push_back(section);
      }
      else
      {
        ;// i = i;
      }
    }
    else fZs.push_back(z);

    fOriginalParameters->fZValues[i] = zPlane[i];
    fOriginalParameters->Rmin[i] = rInner[i];
    fOriginalParameters->Rmax[i] = rOuter[i];

    prevZ = z;
    prevRmin = rMin;
    prevRmax = rMax;
  }

  fMaxSection = fZs.size() - 2;

  //
  // Build RZ polygon using special PCON/PGON GEANT3 constructor
  //
  UReduciblePolygon* rz = new UReduciblePolygon(rInner, rOuter, zPlane, numZPlanes);

  double mxy = rz->Amax();
//  double alfa = UUtils::kPi / fNumSides;

  double r = rz->Amax();
//
// Perform checks of rz values
//
  if (rz->Amin() < 0.0)
  {
     std::ostringstream message;
     message << "Illegal input parameters - " << GetName() << std::endl
             << "        All R values must be >= 0 !";
     UUtils::Exception("UPolycone::Init()", "GeomSolids0002",
                       FatalErrorInArguments,1, message.str().c_str());
  }
    
  
   /*
  if (fNumSides != 0)
  {
    // mxy *= std::sqrt(2.0); // this is old and wrong, works only for n = 4
    // double k = std::tan(alfa) * mxy;
    double l = mxy / std::cos(alfa);
    mxy = l;
    r = l;
  }
  */

  mxy += fgTolerance;

  fBox.Set(mxy, mxy, (rz->Bmax() - rz->Bmin()) / 2);

  //
  // Make enclosingCylinder
  //

  enclosingCylinder = new UEnclosingCylinder(r, rz->Bmax(), rz->Bmin(), phiIsOpen, phiStart, phiTotal);

  delete rz;
}


/*
//
// Constructor (generic parameters)
//
UPolycone3::UPolycone3( const std::string& name,
                              double phiStart,
                              double phiTotal,
                              int   numRZ,
                        const double r[],
                        const double z[]   )
  : VUSolid( name )
{
  UReduciblePolygon *rz = new UReduciblePolygon( r, z, numRZ );

  box.Set(rz->Amax(), rz->Amax(), (rz->Bmax() - rz->Bmin()) /2);

  // Set fOriginalParameters struct for consistency
  //
  SetOriginalParameters();

  delete rz;
}
*/


//
// Destructor
//
UPolycone::~UPolycone()
{
  //delete [] corners;
  //delete fOriginalParameters;
}



//
// Stream object contents to an output stream
//
std::ostream& UPolycone::StreamInfo(std::ostream& os) const
{
  int oldprc = os.precision(16);
  os << "-----------------------------------------------------------\n"
     << "               *** Dump for solid - " << GetName() << " ***\n"
     << "               ===================================================\n"
     << " Solid type: UPolycone3\n"
     << " Parameters: \n"
     << "               starting phi angle : " << startPhi / (UUtils::kPi / 180.0) << " degrees \n"
     << "               ending phi angle         : " << endPhi / (UUtils::kPi / 180.0) << " degrees \n";
  int i = 0;
  int numPlanes = fOriginalParameters->fNumZPlanes;
    os << "             number of Z planes: " << numPlanes << "\n"
       << "                                                     Z values: \n";
    for (i = 0; i < numPlanes; i++)
    {
      os << "                                                   Z plane " << i << ": "
         << fOriginalParameters->fZValues[i] << "\n";
    }
    os << "                                                     Tangent distances to inner surface (Rmin): \n";
    for (i = 0; i < numPlanes; i++)
    {
      os << "                                                   Z plane " << i << ": "
         << fOriginalParameters->Rmin[i] << "\n";
    }
    os << "                                                     Tangent distances to outer surface (Rmax): \n";
    for (i = 0; i < numPlanes; i++)
    {
      os << "                                                   Z plane " << i << ": "
         << fOriginalParameters->Rmax[i] << "\n";
    }
  os << "-----------------------------------------------------------\n";
  os.precision(oldprc);

  return os;
}


VUSolid::EnumInside UPolycone::InsideSection(int index, const UVector3& p) const
{
  const UPolyconeSection& section = fSections[index];
  UVector3 ps(p.x, p.y, p.z - section.shift);

//  if (fNumSides) return section.solid->Inside(ps);

  double rMinPlus, rMaxPlus; //, rMinMinus, rMaxMinus;
  double dz;
  static double halfTolerance = fgTolerance * 0.5;

  if (section.tubular)
  {
    UTubs* tubs = (UTubs*) section.solid;
    rMinPlus = tubs->GetRMin() + halfTolerance;
    rMaxPlus = tubs->GetRMax() + halfTolerance;
    dz = tubs->GetDz();//GetZHalfLength();
  }
  else
  {
    UCons* cons = (UCons*) section.solid;

    double rMax1 = cons->GetRmax1();
    double rMax2 = cons->GetRmax2();
    double rMin1 = cons->GetRmin1();
    double rMin2 = cons->GetRmin2();

    dz = cons->GetDz();
    double ratio = (ps.z + dz) / (2 * dz);
    rMinPlus = rMin1 + (rMin2 - rMin1) * ratio + halfTolerance;
    rMaxPlus = rMax1 + (rMax2 - rMax1) * ratio + halfTolerance;
  }

  double rMinMinus = rMinPlus - fgTolerance;
  double rMaxMinus = rMaxPlus - fgTolerance;

  double r2 = p.x * p.x + p.y * p.y;

  if (r2 < rMinMinus * rMinMinus || r2 > rMaxPlus * rMaxPlus) return eOutside;
  if (r2 < rMinPlus * rMinPlus || r2 > rMaxMinus * rMaxMinus) return eSurface;

  if (! phiIsOpen )
  {
    if (ps.z < -dz + halfTolerance || ps.z > dz - halfTolerance)
      return eSurface;
    return eInside;
  }

  if (r2 < 1e-10) return eInside;

  double phi = std::atan2(p.y, p.x); // * UUtils::kTwoPi;
  if ((phi < 0)||(endPhi > UUtils::kTwoPi)) phi += UUtils::kTwoPi;

  double ddp = phi - startPhi;
  if (ddp < 0) ddp += UUtils::kTwoPi;
  if ((phi <= endPhi + frTolerance)&&(phi>= startPhi-frTolerance))
  {
    if (ps.z < -dz + halfTolerance || ps.z > dz - halfTolerance)
      return eSurface;

    if (std::fabs(endPhi - phi) < frTolerance)
      return eSurface;
    if (std::fabs(startPhi - phi) < frTolerance)
      return eSurface;

    return eInside;
  }
  return eOutside;
}


VUSolid::EnumInside UPolycone::Inside(const UVector3& p) const
{
  double shift = fZs[0] + fBox.GetZHalfLength();
  UVector3 pb(p.x, p.y, p.z - shift);
  if (fBox.Inside(pb) == eOutside)
    return eOutside;

  static const double htolerance = 0.5 * fgTolerance;
  int index = GetSection(p.z);

  EnumInside pos = InsideSection(index, p);
  if (pos == eInside) return eInside;

  int nextSection;
  EnumInside nextPos;

  if (index > 0 && p.z  - fZs[index] < htolerance)
  {
    nextSection = index - 1;
    nextPos = InsideSection(nextSection, p);
  }
  else if (index < fMaxSection && fZs[index + 1] - p.z < htolerance)
  {
    nextSection = index + 1;
    nextPos = InsideSection(nextSection, p);
  }
  else
    return pos;

  if (nextPos == eInside) return eInside;

  if (pos == eSurface && nextPos == eSurface)
  {
    UVector3 n, n2;
    NormalSection(index, p, n);
    NormalSection(nextSection, p, n2);
    if ((n +  n2).Mag2() < 1000 * frTolerance)
      return eInside;
  }

  return (nextPos == eSurface || pos == eSurface) ? eSurface : eOutside;

//  return (res == VUSolid::eOutside) ? nextPos : res;
}

/*
if (p.z < fZs.front() - htolerance || p.z > fZs.back() + htolerance) return VUSolid::eOutside;
*/

double UPolycone::DistanceToIn(const UVector3& p,
                               const UVector3& v, double) const
{
  double shift = fZs[0] + fBox.GetZHalfLength();
  UVector3 pb(p.x, p.y, p.z - shift);

  double idistance;

  idistance = fBox.DistanceToIn(pb, v);
    // using only box, this appears
    // to be faster than: idistance = enclosingCylinder->DistanceTo(pb, v);
  if (idistance >= UUtils::kInfinity) return idistance;

  // this line can be here or not. not a big difference in performance
  // TODO: fix enclosingCylinder for polyhedra!!! - the current radius
  // appears to be too small
  //  if (enclosingCylinder->ShouldMiss(p, v)) return UUtils::kInfinity;

  // this just takes too much time
  //  idistance = enclosingCylinder->DistanceTo(pb, v);
  //  if (idistance == UUtils::kInfinity) return idistance;

  pb = p + idistance * v;
  int index = GetSection(pb.z);
  pb = p;
  int increment = (v.z > 0) ? 1 : -1;
  if (std::fabs(v.z) < fgTolerance) increment = 0;

  double distance = UUtils::kInfinity;
  do
  {
    const UPolyconeSection& section = fSections[index];
    pb.z -= section.shift;
    distance = section.solid->DistanceToIn(pb, v);
    if (distance < UUtils::kInfinity || !increment)
      break;
    index += increment;
    pb.z += section.shift;
  }
  while (index >= 0 && index <= fMaxSection);
  //if(Inside(p)==eInside)return UUtils::kInfinity;
  return distance;
}

double UPolycone::DistanceToOut(const UVector3&  p, const UVector3& v,
                                UVector3& n, bool& convex, double /*aPstep*/) const
{
  UVector3 pn(p);
  if (fOriginalParameters->fNumZPlanes == 2)
  {
    const UPolyconeSection& section = fSections[0];
    pn.z -= section.shift;
    return section.solid->DistanceToOut(pn, v, n, convex);
  }
  int index =  GetSection(p.z);
  double totalDistance = 0;
  int increment = (v.z > 0) ? 1 : -1;
  bool convexloc=true;

  do
  {
    const UPolyconeSection& section = fSections[index];
    if (totalDistance != 0)
    {
      pn = p + (totalDistance /*+ 0 * 1e-8*/) * v; // point must be shifted,
                                                   // so it could eventually
      pn.z -= section.shift;                       // get into another solid
      if (section.solid->Inside(pn) == eOutside)
      {
        break;
      }
    }
    else pn.z -= section.shift;

    double distance = section.solid->DistanceToOut(pn, v, n, convex);
    if ((convexloc) && (section.convex)) { convexloc = true; }
    else { convexloc = false; }

    totalDistance += distance;
    index += increment;
  }
  while (index >= 0 && index <= fMaxSection);
  
  convex=convexloc;
  if (convex)
  {
    // Check final convexity for dz
    //
    pn = p + (totalDistance) * v;
    double dz1 = std::fabs(pn.z-fZs[index]);
    double dz2 = std::fabs(pn.z-fZs[index+1]);
    double halfTolerance=0.5*fgTolerance;
    if((dz1 < halfTolerance) && (index>0)) convex = false;
    if((dz2 < halfTolerance) && (index<fMaxSection)) convex = false;
  }
  
  return totalDistance;
}

double UPolycone::SafetyFromInside(const UVector3& p, bool) const
{
  int index = UVoxelizer::BinarySearch(fZs, p.z);
  if (index < 0 || index > fMaxSection) return 0;

  double minSafety = SafetyFromInsideSection(index, p);
  if (minSafety == UUtils::kInfinity) return 0;
  if (minSafety < 1e-6) return 0;

  double zbase = fZs[index + 1];
  for (int i = index + 1; i <= fMaxSection; ++i)
  {
    double dz = fZs[i] - zbase;
    if (dz >= minSafety) break;
    double safety = SafetyFromOutsideSection(i, p); // safety from Inside cannot be called in this context, because point is not inside, we have to call SafetyFromOutside for given section
    if (safety < minSafety) minSafety = safety;
  }

  if (index > 0)
  {
    zbase = fZs[index - 1];
    for (int i = index - 1; i >= 0; --i)
    {
      double dz = zbase - fZs[i];
      if (dz >= minSafety) break;
      double safety = SafetyFromOutsideSection(i, p);
      if (safety < minSafety) minSafety = safety;
    }
  }
  return minSafety;
}


double UPolycone::SafetyFromOutside(const UVector3& p, bool aAccurate) const
{
  if (!aAccurate)
    return enclosingCylinder->SafetyFromOutside(p);

  int index = GetSection(p.z);
  double minSafety = SafetyFromOutsideSection(index, p);
  if (minSafety < 1e-6) return minSafety;

  double zbase = fZs[index + 1];
  for (int i = index + 1; i <= fMaxSection; ++i)
  {
    double dz = fZs[i] - zbase;
    if (dz >= minSafety) break;
    double safety = SafetyFromOutsideSection(i, p);
    if (safety < minSafety) minSafety = safety;
  }

  zbase = fZs[index - 1];
  for (int i = index - 1; i >= 0; --i)
  {
    double dz = zbase - fZs[i];
    if (dz >= minSafety) break;
    double safety = SafetyFromOutsideSection(i, p);
    if (safety < minSafety) minSafety = safety;
  }
  return minSafety;
}

bool UPolycone::Normal(const UVector3& p, UVector3& n) const
{
  double htolerance = 0.5 * fgTolerance;
  int index = GetSection(p.z);

  EnumInside nextPos;
  int nextSection;

  if (index > 0 && p.z  - fZs[index] < htolerance)
  {
    nextSection = index - 1;
    nextPos = InsideSection(nextSection, p);
  }
  else if (index < fMaxSection && fZs[index + 1] - p.z < htolerance)
  {
    nextSection = index + 1;
    nextPos = InsideSection(nextSection, p);
  }
  else
  {
    const UPolyconeSection& section = fSections[index];
    UVector3 ps(p.x, p.y, p.z - section.shift);
    bool res = section.solid->Normal(ps, n);

    return res;

    // the code bellow is not used can be deleted

    nextPos = section.solid->Inside(ps);
    if (nextPos == eSurface)
    {
      return res;
    }
    else
    {
      //TODO: here should be implementation for case point was not on surface. We would have to look also at other sections. It is not clear if it is possible to solve this problem at all, since we would need precise safety... If it is outside, than it might be OK, but if it is inside..., than I beleive we do not have precise safety

      // ... or we should at least warn that this case is not supported. actually,
      //  i do not see any algorithm which would obtain right normal of point closest to surface.;

      return false;
    }
  }

  // even if it says we are on the surface, actually it do not have to be

//  "TODO special case when point is on the border of two z-sections",
//    "we should implement this after safety's";

  EnumInside pos = InsideSection(index, p);

  if (nextPos == eInside)
  {
    //UVector3 n;
    NormalSection(index, p, n);
    return false;
  }

  if (pos == eSurface && nextPos == eSurface)
  {
    //UVector3 n, n2;
    UVector3 n2;
    NormalSection(index, p, n);
    NormalSection(nextSection, p, n2);
    if ((n + n2).Mag2() < 1000 * frTolerance)
    {
      // "we are inside. see TODO above";
      NormalSection(index, p, n);
      return false;
    }
  }

  if (nextPos == eSurface || pos == eSurface)
  {
    if (pos != eSurface) index = nextSection;
    bool res = NormalSection(index, p, n);
    return res;
  }

  NormalSection(index, p, n);
  // "we are outside. see TODO above";
  return false;
}


void UPolycone::Extent(UVector3& aMin, UVector3& aMax) const
{
  double r = enclosingCylinder->radius;
  aMin.Set(-r, -r, fZs.front());
  aMax.Set(r, r, fZs.back());
}

double UPolycone::Capacity()
{
  if (fCubicVolume != 0.)
  {
    ;
  }
  else
  {
    for (int i = 0; i < fMaxSection; i++)
    {
      UPolyconeSection& section = fSections[i];
      fCubicVolume += section.solid->Capacity();
    }
  }
  return fCubicVolume;
}

double UPolycone::SurfaceArea()
{
  if (fSurfaceArea != 0)
  {
    ;
  }
  else
  {
    double Area = 0, totArea = 0;
    int i = 0;
    int numPlanes = fOriginalParameters->fNumZPlanes;


    std::vector<double> areas;       // (numPlanes+1);
    std::vector<UVector3> points; // (numPlanes-1);

    areas.push_back(UUtils::kPi * (UUtils::sqr(fOriginalParameters->Rmax[0])
                                   - UUtils::sqr(fOriginalParameters->Rmin[0])));

    for (i = 0; i < numPlanes - 1; i++)
    {
      Area = (fOriginalParameters->Rmin[i] + fOriginalParameters->Rmin[i + 1])
             * std::sqrt(UUtils::sqr(fOriginalParameters->Rmin[i]
                                     - fOriginalParameters->Rmin[i + 1]) +
                         UUtils::sqr(fOriginalParameters->fZValues[i + 1]
                                     - fOriginalParameters->fZValues[i]));

      Area += (fOriginalParameters->Rmax[i] + fOriginalParameters->Rmax[i + 1])
              * std::sqrt(UUtils::sqr(fOriginalParameters->Rmax[i]
                                      - fOriginalParameters->Rmax[i + 1]) +
                          UUtils::sqr(fOriginalParameters->fZValues[i + 1]
                                      - fOriginalParameters->fZValues[i]));

      Area *= 0.5 * (endPhi - startPhi);

      if (startPhi == 0. && endPhi == 2 * UUtils::kPi)
      {
        Area += std::fabs(fOriginalParameters->fZValues[i + 1]
                          - fOriginalParameters->fZValues[i]) *
                (fOriginalParameters->Rmax[i]
                 + fOriginalParameters->Rmax[i + 1]
                 - fOriginalParameters->Rmin[i]
                 - fOriginalParameters->Rmin[i + 1]);
      }
      areas.push_back(Area);
      totArea += Area;
    }

    areas.push_back(UUtils::kPi * (UUtils::sqr(fOriginalParameters->Rmax[numPlanes - 1]) -
                                   UUtils::sqr(fOriginalParameters->Rmin[numPlanes - 1])));

    totArea += (areas[0] + areas[numPlanes]);
    fSurfaceArea = totArea;

  }

  return fSurfaceArea;
}

//
// GetPointOnSurface
//
// GetPointOnCone
//
// Auxiliary method for Get Point On Surface
//
UVector3 UPolycone::GetPointOnCone(double fRmin1, double fRmax1,
                                   double fRmin2, double fRmax2,
                                   double zOne,   double zTwo,
                                   double& totArea) const
{
  // declare working variables
  //
  double Aone, Atwo, Afive, phi, zRand, fDPhi, cosu, sinu;
  double rRand1, rmin, rmax, chose, rone, rtwo, qone, qtwo;
  double fDz = (zTwo - zOne) / 2., afDz = std::fabs(fDz);
  UVector3 point, offset = UVector3(0., 0., 0.5 * (zTwo + zOne));
  fDPhi = endPhi - startPhi;
  rone = (fRmax1 - fRmax2) / (2.*fDz);
  rtwo = (fRmin1 - fRmin2) / (2.*fDz);
  if (fRmax1 == fRmax2)
  {
    qone = 0.;
  }
  else
  {
    qone = fDz * (fRmax1 + fRmax2) / (fRmax1 - fRmax2);
  }
  if (fRmin1 == fRmin2)
  {
    qtwo = 0.;
  }
  else
  {
    qtwo = fDz * (fRmin1 + fRmin2) / (fRmin1 - fRmin2);
  }
  Aone   = 0.5 * fDPhi * (fRmax2 + fRmax1) * (UUtils::sqr(fRmin1 - fRmin2) + UUtils::sqr(zTwo - zOne));
  Atwo   = 0.5 * fDPhi * (fRmin2 + fRmin1) * (UUtils::sqr(fRmax1 - fRmax2) + UUtils::sqr(zTwo - zOne));
  Afive  = fDz * (fRmax1 - fRmin1 + fRmax2 - fRmin2);
  totArea = Aone + Atwo + 2.*Afive;

  phi  = UUtils::Random(startPhi, endPhi);
  cosu = std::cos(phi);
  sinu = std::sin(phi);


  if ((startPhi == 0) && (endPhi == 2 * UUtils::kPi))
  {
    Afive = 0;
  }
  chose = UUtils::Random(0., Aone + Atwo + 2.*Afive);
  if ((chose >= 0) && (chose < Aone))
  {
    if (fRmax1 != fRmax2)
    {
      zRand = UUtils::Random(-1.*afDz, afDz);
      point = UVector3(rone * cosu * (qone - zRand),
                       rone * sinu * (qone - zRand), zRand);
    }
    else
    {
      point = UVector3(fRmax1 * cosu, fRmax1 * sinu,
                       UUtils::Random(-1.*afDz, afDz));

    }
  }
  else if (chose >= Aone && chose < Aone + Atwo)
  {
    if (fRmin1 != fRmin2)
    {
      zRand = UUtils::Random(-1.*afDz, afDz);
      point = UVector3(rtwo * cosu * (qtwo - zRand),
                       rtwo * sinu * (qtwo - zRand), zRand);

    }
    else
    {
      point = UVector3(fRmin1 * cosu, fRmin1 * sinu,
                       UUtils::Random(-1.*afDz, afDz));
    }
  }
  else if ((chose >= Aone + Atwo + Afive) && (chose < Aone + Atwo + 2.*Afive))
  {
    zRand  = UUtils::Random(-1.*afDz, afDz);
    rmin   = fRmin2 - ((zRand - fDz) / (2.*fDz)) * (fRmin1 - fRmin2);
    rmax   = fRmax2 - ((zRand - fDz) / (2.*fDz)) * (fRmax1 - fRmax2);
    rRand1 = std::sqrt(UUtils::Random() * (UUtils::sqr(rmax) - UUtils::sqr(rmin)) + UUtils::sqr(rmin));
    point  = UVector3(rRand1 * std::cos(startPhi),
                      rRand1 * std::sin(startPhi), zRand);
  }
  else
  {
    zRand  = UUtils::Random(-1.*afDz, afDz);
    rmin   = fRmin2 - ((zRand - fDz) / (2.*fDz)) * (fRmin1 - fRmin2);
    rmax   = fRmax2 - ((zRand - fDz) / (2.*fDz)) * (fRmax1 - fRmax2);
    rRand1 = std::sqrt(UUtils::Random() * (UUtils::sqr(rmax) - UUtils::sqr(rmin)) + UUtils::sqr(rmin));
    point  = UVector3(rRand1 * std::cos(endPhi),
                      rRand1 * std::sin(endPhi), zRand);

  }

  return point + offset;
}


//
// GetPointOnTubs
//
// Auxiliary method for GetPoint On Surface
//
UVector3 UPolycone::GetPointOnTubs(double fRMin, double fRMax,
                                   double zOne,  double zTwo,
                                   double& totArea) const
{
  double xRand, yRand, zRand, phi, cosphi, sinphi, chose,
         aOne, aTwo, aFou, rRand, fDz, fSPhi, fDPhi;
  fDz = std::fabs(0.5 * (zTwo - zOne));
  fSPhi = startPhi;
  fDPhi = endPhi - startPhi;

  aOne = 2.*fDz * fDPhi * fRMax;
  aTwo = 2.*fDz * fDPhi * fRMin;
  aFou = 2.*fDz * (fRMax - fRMin);
  totArea = aOne + aTwo + 2.*aFou;
  phi    = UUtils::Random(startPhi, endPhi);
  cosphi = std::cos(phi);
  sinphi = std::sin(phi);
  rRand  = fRMin + (fRMax - fRMin) * std::sqrt(UUtils::Random());

  if (startPhi == 0 && endPhi == 2 * UUtils::kPi)
    aFou = 0;

  chose  = UUtils::Random(0., aOne + aTwo + 2.*aFou);
  if ((chose >= 0) && (chose < aOne))
  {
    xRand = fRMax * cosphi;
    yRand = fRMax * sinphi;
    zRand = UUtils::Random(-1.*fDz, fDz);
    return UVector3(xRand, yRand, zRand + 0.5 * (zTwo + zOne));
  }
  else if ((chose >= aOne) && (chose < aOne + aTwo))
  {
    xRand = fRMin * cosphi;
    yRand = fRMin * sinphi;
    zRand = UUtils::Random(-1.*fDz, fDz);
    return UVector3(xRand, yRand, zRand + 0.5 * (zTwo + zOne));
  }
  else if ((chose >= aOne + aTwo) && (chose < aOne + aTwo + aFou))
  {
    xRand = rRand * std::cos(fSPhi + fDPhi);
    yRand = rRand * std::sin(fSPhi + fDPhi);
    zRand = UUtils::Random(-1.*fDz, fDz);
    return UVector3(xRand, yRand, zRand + 0.5 * (zTwo + zOne));
  }

  // else

  xRand = rRand * std::cos(fSPhi + fDPhi);
  yRand = rRand * std::sin(fSPhi + fDPhi);
  zRand = UUtils::Random(-1.*fDz, fDz);
  return UVector3(xRand, yRand, zRand + 0.5 * (zTwo + zOne));
}


//
// GetPointOnRing
//
// Auxiliary method for GetPoint On Surface
//
UVector3 UPolycone::GetPointOnRing(double fRMin1, double fRMax1,
                                   double fRMin2, double fRMax2,
                                   double zOne) const
{
  double xRand, yRand, phi, cosphi, sinphi, rRand1, rRand2, A1, Atot, rCh;
  phi    = UUtils::Random(startPhi, endPhi);
  cosphi = std::cos(phi);
  sinphi = std::sin(phi);

  if (fRMin1 == fRMin2)
  {
    rRand1 = fRMin1;
    A1 = 0.;
  }
  else
  {
    rRand1 = UUtils::Random(fRMin1, fRMin2);
    A1 = std::fabs(fRMin2 * fRMin2 - fRMin1 * fRMin1);
  }
  if (fRMax1 == fRMax2)
  {
    rRand2 = fRMax1;
    Atot = A1;
  }
  else
  {
    rRand2 = UUtils::Random(fRMax1, fRMax2);
    Atot   = A1 + std::fabs(fRMax2 * fRMax2 - fRMax1 * fRMax1);
  }
  rCh   = UUtils::Random(0., Atot);

  if (rCh > A1)
  {
    rRand1 = rRand2;
  }

  xRand = rRand1 * cosphi;
  yRand = rRand1 * sinphi;

  return UVector3(xRand, yRand, zOne);
}


//
// GetPointOnCut
//
// Auxiliary method for Get Point On Surface
//
UVector3 UPolycone::GetPointOnCut(double fRMin1, double fRMax1,
                                  double fRMin2, double fRMax2,
                                  double zOne,  double zTwo,
                                  double& totArea) const
{
  if (zOne == zTwo)
  {
    return GetPointOnRing(fRMin1, fRMax1, fRMin2, fRMax2, zOne);
  }
  if ((fRMin1 == fRMin2) && (fRMax1 == fRMax2))
  {
    return GetPointOnTubs(fRMin1, fRMax1, zOne, zTwo, totArea);
  }
  return GetPointOnCone(fRMin1, fRMax1, fRMin2, fRMax2, zOne, zTwo, totArea);
}


//
// GetPointOnSurface
//
UVector3 UPolycone::GetPointOnSurface() const
{
  double Area = 0, totArea = 0, Achose1 = 0, Achose2 = 0, phi, cosphi, sinphi, rRand;
  int i = 0;
  int numPlanes = fOriginalParameters->fNumZPlanes;

  phi = UUtils::Random(startPhi, endPhi);
  cosphi = std::cos(phi);
  sinphi = std::sin(phi);

  rRand = fOriginalParameters->Rmin[0] +
          ((fOriginalParameters->Rmax[0] - fOriginalParameters->Rmin[0])
           * std::sqrt(UUtils::Random()));

  std::vector<double> areas;       // (numPlanes+1);
  std::vector<UVector3> points; // (numPlanes-1);

  areas.push_back(UUtils::kPi * (UUtils::sqr(fOriginalParameters->Rmax[0])
                                 - UUtils::sqr(fOriginalParameters->Rmin[0])));

  for (i = 0; i < numPlanes - 1; i++)
  {
    Area = (fOriginalParameters->Rmin[i] + fOriginalParameters->Rmin[i + 1])
           * std::sqrt(UUtils::sqr(fOriginalParameters->Rmin[i]
                                   - fOriginalParameters->Rmin[i + 1]) +
                       UUtils::sqr(fOriginalParameters->fZValues[i + 1]
                                   - fOriginalParameters->fZValues[i]));

    Area += (fOriginalParameters->Rmax[i] + fOriginalParameters->Rmax[i + 1])
            * std::sqrt(UUtils::sqr(fOriginalParameters->Rmax[i]
                                    - fOriginalParameters->Rmax[i + 1]) +
                        UUtils::sqr(fOriginalParameters->fZValues[i + 1]
                                    - fOriginalParameters->fZValues[i]));

    Area *= 0.5 * (endPhi - startPhi);

    if (startPhi == 0. && endPhi == 2 * UUtils::kPi)
    {
      Area += std::fabs(fOriginalParameters->fZValues[i + 1]
                        - fOriginalParameters->fZValues[i]) *
              (fOriginalParameters->Rmax[i]
               + fOriginalParameters->Rmax[i + 1]
               - fOriginalParameters->Rmin[i]
               - fOriginalParameters->Rmin[i + 1]);
    }
    areas.push_back(Area);
    totArea += Area;
  }

  areas.push_back(UUtils::kPi * (UUtils::sqr(fOriginalParameters->Rmax[numPlanes - 1]) -
                                 UUtils::sqr(fOriginalParameters->Rmin[numPlanes - 1])));

  totArea += (areas[0] + areas[numPlanes]);
  double chose = UUtils::Random(0., totArea);

  if ((chose >= 0.) && (chose < areas[0]))
  {
    return UVector3(rRand * cosphi, rRand * sinphi,
                    fOriginalParameters->fZValues[0]);
  }

  for (i = 0; i < numPlanes - 1; i++)
  {
    Achose1 += areas[i];
    Achose2 = (Achose1 + areas[i + 1]);
    if (chose >= Achose1 && chose < Achose2)
    {
      return GetPointOnCut(fOriginalParameters->Rmin[i],
                           fOriginalParameters->Rmax[i],
                           fOriginalParameters->Rmin[i + 1],
                           fOriginalParameters->Rmax[i + 1],
                           fOriginalParameters->fZValues[i],
                           fOriginalParameters->fZValues[i + 1], Area);
    }
  }

  rRand = fOriginalParameters->Rmin[numPlanes - 1] +
          ((fOriginalParameters->Rmax[numPlanes - 1] - fOriginalParameters->Rmin[numPlanes - 1])
           * std::sqrt(UUtils::Random()));

  return UVector3(rRand * cosphi, rRand * sinphi,
                  fOriginalParameters->fZValues[numPlanes - 1]);

}

//
// UPolyconeHistorical stuff
//

UPolyconeHistorical::UPolyconeHistorical()
  : fStartAngle(0.), fOpeningAngle(0.), fNumZPlanes(0),
    fZValues(0), Rmin(0), Rmax(0)
{
}

UPolyconeHistorical::~UPolyconeHistorical()
{
}

UPolyconeHistorical::
UPolyconeHistorical(const UPolyconeHistorical& source)
{
  fStartAngle  = source.fStartAngle;
  fOpeningAngle = source.fOpeningAngle;
  fNumZPlanes = source.fNumZPlanes;

  fZValues.resize(fNumZPlanes);
  Rmin.resize(fNumZPlanes);
  Rmax.resize(fNumZPlanes);

  for (int i = 0; i < fNumZPlanes; i++)
  {
    fZValues[i] = source.fZValues[i];
    Rmin[i]    = source.Rmin[i];
    Rmax[i]    = source.Rmax[i];
  }
}

UPolyconeHistorical&
UPolyconeHistorical::operator=(const UPolyconeHistorical& right)
{
  if (&right == this) return *this;

  if (&right)
  {
    fStartAngle  = right.fStartAngle;
    fOpeningAngle = right.fOpeningAngle;
    fNumZPlanes = right.fNumZPlanes;

    fZValues.resize(fNumZPlanes);
    Rmin.resize(fNumZPlanes);
    Rmax.resize(fNumZPlanes);

    for (int i = 0; i < fNumZPlanes; i++)
    {
      fZValues[i] = right.fZValues[i];
      Rmin[i]    = right.Rmin[i];
      Rmax[i]    = right.Rmax[i];
    }
  }
  return *this;
}

VUSolid* UPolycone::Clone() const
{
  return new UPolycone(*this);
}
//
// Copy constructor
//
UPolycone::UPolycone(const UPolycone& source): VUSolid(source)
{
  CopyStuff(source);
}


//
// Assignment operator
//
UPolycone& UPolycone::operator=(const UPolycone& source)
{
  if (this == &source) return *this;

  //VUSolid::operator=( source );

  //delete [] corners;

  delete enclosingCylinder;

  CopyStuff(source);

  return *this;
}
//
// CopyStuff
//
void UPolycone::CopyStuff(const UPolycone& source)
{
  //
  // Simple stuff
  //

  startPhi  = source.startPhi;
  endPhi    = source.endPhi;
  phiIsOpen = source.phiIsOpen;
  fCubicVolume    = source.fCubicVolume;
  fSurfaceArea    = source.fSurfaceArea;
  fBox = source.fBox;
  //
  // The array of planes
  //
  fOriginalParameters = source.fOriginalParameters;
  //
  // Enclosing cylinder
  //
  enclosingCylinder = new UEnclosingCylinder(*source.enclosingCylinder);
}
//
// Get Entity Type
//
UGeometryType UPolycone::GetEntityType() const
{
      return "Polycone";
}
//
// Set Original Parameters
//
bool  UPolycone::SetOriginalParameters(UReduciblePolygon* rz)
{
  int numPlanes = (int)numCorner;
  bool isConvertible = true;
  double Zmax = rz->Bmax();
  rz->StartWithZMin();

  // Prepare vectors for storage
  //
  std::vector<double> Z;
  std::vector<double> Rmin;
  std::vector<double> Rmax;

  int countPlanes = 1;
  int icurr = 0;
  int icurl = 0;

  // first plane Z=Z[0]
  //
  Z.push_back(corners[0].z);
  double Zprev = Z[0];
  if (Zprev == corners[1].z)
  {
    Rmin.push_back(corners[0].r);
    Rmax.push_back(corners[1].r);
    icurr = 1;
  }
  else if (Zprev == corners[numPlanes - 1].z)
  {
    Rmin.push_back(corners[numPlanes - 1].r);
    Rmax.push_back(corners[0].r);
    icurl = numPlanes - 1;
  }
  else
  {
    Rmin.push_back(corners[0].r);
    Rmax.push_back(corners[0].r);
  }

  // next planes until last
  //
  int inextr = 0, inextl = 0;
  for (int i = 0; i < numPlanes - 2; i++)
  {
    inextr = 1 + icurr;
    inextl = (icurl <= 0) ? numPlanes - 1 : icurl - 1;

    if ((corners[inextr].z >= Zmax) & (corners[inextl].z >= Zmax))
    {
      break;
    }

    double Zleft = corners[inextl].z;
    double Zright = corners[inextr].z;
    if (Zright > Zleft)
    {
      Z.push_back(Zleft);
      countPlanes++;
      double difZr = corners[inextr].z - corners[icurr].z;
      double difZl = corners[inextl].z - corners[icurl].z;

      if (std::fabs(difZl) < frTolerance)
      {
        if (corners[inextl].r >= corners[icurl].r)
        {
          Rmin.push_back(corners[icurl].r);
          Rmax.push_back(Rmax[countPlanes - 2]);
          Rmax[countPlanes - 2] = corners[icurl].r;
        }
        else
        {
          Rmin.push_back(corners[inextl].r);
          Rmax.push_back(corners[icurl].r);
        }
      }
      else if (difZl >= frTolerance)
      {
        Rmin.push_back(corners[inextl].r);
        Rmax.push_back(corners[icurr].r + (Zleft - corners[icurr].z) / difZr
                       * (corners[inextr].r - corners[icurr].r));
      }
      else
      {
        isConvertible = false;
        break;
      }
      icurl = (icurl == 0) ? numPlanes - 1 : icurl - 1;
    }
    else if (std::fabs(Zright - Zleft) < frTolerance) // Zright=Zleft
    {
      Z.push_back(Zleft);
      countPlanes++;
      icurr++;

      icurl = (icurl == 0) ? numPlanes - 1 : icurl - 1;

      Rmin.push_back(corners[inextl].r);
      Rmax.push_back(corners[inextr].r);
    }
    else  // Zright<Zleft
    {
      Z.push_back(Zright);
      countPlanes++;

      double difZr = corners[inextr].z - corners[icurr].z;
      double difZl = corners[inextl].z - corners[icurl].z;
      if (std::fabs(difZr) < frTolerance)
      {
        if (corners[inextr].r >= corners[icurr].r)
        {
          Rmin.push_back(corners[icurr].r);
          Rmax.push_back(corners[inextr].r);
        }
        else
        {
          Rmin.push_back(corners[inextr].r);
          Rmax.push_back(corners[icurr].r);
          Rmax[countPlanes - 2] = corners[inextr].r;
        }
        icurr++;
      }           // plate
      else if (difZr >= frTolerance)
      {
        if (std::fabs(difZl) < frTolerance)
        {
          Rmax.push_back(corners[inextr].r);
          Rmin.push_back(corners[icurr].r);
        }
        else
        {
          Rmax.push_back(corners[inextr].r);
          Rmin.push_back(corners[icurl].r + (Zright - corners[icurl].z) / difZl
                         * (corners[inextl].r - corners[icurl].r));
        }
        icurr++;
      }
      else
      {
        isConvertible = false;
        break;
      }
    }
  }   // end for loop

  // last plane Z=Zmax
  //
  Z.push_back(Zmax);
  countPlanes++;
  inextr = 1 + icurr;
  inextl = (icurl <= 0) ? numPlanes - 1 : icurl - 1;

  if (corners[inextr].z == corners[inextl].z)
  {
    Rmax.push_back(corners[inextr].r);
    Rmin.push_back(corners[inextl].r);
  }
  else
  {
    Rmax.push_back(corners[inextr].r);
    Rmin.push_back(corners[inextl].r);
  }

  // Set original parameters Rmin,Rmax,Z
  //
  if (isConvertible)
  {
    fOriginalParameters = new UPolyconeHistorical;
    fOriginalParameters->fZValues.resize(numPlanes);
    fOriginalParameters->Rmin.resize(numPlanes);
    fOriginalParameters->Rmax.resize(numPlanes);

    for (int j = 0; j < countPlanes; j++)
    {
      fOriginalParameters->fZValues[j] = Z[j];
      fOriginalParameters->Rmax[j] = Rmax[j];
      fOriginalParameters->Rmin[j] = Rmin[j];
    }
    fOriginalParameters->fStartAngle = startPhi;
    fOriginalParameters->fOpeningAngle = endPhi - startPhi;
    fOriginalParameters->fNumZPlanes = countPlanes;

  }
  else  // Set parameters(r,z) with Rmin==0 as convention
  {
    std::ostringstream message;
    message << "Polycone " << GetName() << std::endl
            << "cannot be converted to Polycone with (Rmin,Rmaz,Z) parameters!";
    UUtils::Exception("G4Polycone::SetOriginalParameters()", "GeomSolids0002",
                      Warning, 1, "can not convert");

    fOriginalParameters = new UPolyconeHistorical;

    fOriginalParameters->fZValues.resize(numPlanes);
    fOriginalParameters->Rmin.resize(numPlanes);
    fOriginalParameters->Rmax.resize(numPlanes);

    for (int j = 0; j < numPlanes; j++)
    {
      fOriginalParameters->fZValues[j] = corners[j].z;
      fOriginalParameters->Rmax[j] = corners[j].r;
      fOriginalParameters->Rmin[j] = 0.0;
    }
    fOriginalParameters->fStartAngle = startPhi;
    fOriginalParameters->fOpeningAngle = endPhi - startPhi;
    fOriginalParameters->fNumZPlanes = numPlanes;
  }
  return isConvertible;
}
//
// Reset 
//
void UPolycone::Reset()
{
   //
   // Clear old setup
   //
   delete enclosingCylinder;
 
  fCubicVolume = 0;
  fSurfaceArea = 0;
  double phiStart=fOriginalParameters->fStartAngle;
  double* Z, *R1, *R2;
  int num = fOriginalParameters->fNumZPlanes;
    Z = new double[num];
    R1 = new double[num];
    R2 = new double[num];
    for (int i = 0; i < num; i++)
    {
      Z[i] = fOriginalParameters->fZValues[i];
      R1[i] = fOriginalParameters->Rmin[i];
      R2[i] = fOriginalParameters->Rmax[i];
    }

   Init(phiStart, phiStart+ fOriginalParameters->fOpeningAngle, num, Z, R1, R2);
    delete [] R1;
    delete [] Z;
    delete [] R2;
 
}