G4Polyhedra.cc

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//
// Implementation of G4Polyhedra, a CSG polyhedra,
// as an inherited class of G4VCSGfaceted.
//
// Utility classes:
//    * G4EnclosingCylinder: decided a quick check of geometry would be a
//      good idea (for CPU speed). If the quick check fails, the regular
//      full-blown G4VCSGfaceted version is invoked.
//    * G4ReduciblePolygon: Really meant as a check of input parameters,
//      this utility class also "converts" the GEANT3-like PGON/PCON
//      arguments into the newer ones.
// Both these classes are implemented outside this file because they are
// shared with G4Polycone.
//
// Author: David C. Williams (davidw@scipp.ucsc.edu)
// --------------------------------------------------------------------
 
#include "G4Polyhedra.hh"
 
#if !defined(G4GEOM_USE_UPOLYHEDRA)
 
#include "G4PolyhedraSide.hh"
#include "G4PolyPhiFace.hh"
 
#include "G4GeomTools.hh"
#include "G4VoxelLimits.hh"
#include "G4AffineTransform.hh"
#include "G4BoundingEnvelope.hh"
 
#include "G4QuickRand.hh"
 
#include "G4EnclosingCylinder.hh"
#include "G4ReduciblePolygon.hh"
#include "G4VPVParameterisation.hh"
 
namespace
{
  G4Mutex surface_elementsMutex = G4MUTEX_INITIALIZER;
}
 
using namespace CLHEP;
 
// Constructor (GEANT3 style parameters)
//
// GEANT3 PGON radii are specified in the distance to the norm of each face.
//
G4Polyhedra::G4Polyhedra( const G4String& name,
                                G4double phiStart,
                                G4double thePhiTotal,
                                G4int theNumSide,
                                G4int numZPlanes,
                          const G4double zPlane[],
                          const G4double rInner[],
                          const G4double rOuter[]  )
  : G4VCSGfaceted( name )
{
  if (theNumSide <= 0)
  {
    std::ostringstream message;
    message << "Solid must have at least one side - " << GetName() << G4endl
            << "        No sides specified !";
    G4Exception("G4Polyhedra::G4Polyhedra()", "GeomSolids0002",
                FatalErrorInArgument, message);
  }
 
  //
  // Calculate conversion factor from G3 radius to G4 radius
  //
  G4double phiTotal = thePhiTotal;
  if ( (phiTotal <=0) || (phiTotal >= twopi*(1-DBL_EPSILON)) )
    { phiTotal = twopi; }
  G4double convertRad = std::cos(0.5*phiTotal/theNumSide);
 
  //
  // Some historical stuff
  //
  original_parameters = new G4PolyhedraHistorical;
 
  original_parameters->numSide = theNumSide;
  original_parameters->Start_angle = phiStart;
  original_parameters->Opening_angle = phiTotal;
  original_parameters->Num_z_planes = numZPlanes;
  original_parameters->Z_values = new G4double[numZPlanes];
  original_parameters->Rmin = new G4double[numZPlanes];
  original_parameters->Rmax = new G4double[numZPlanes];
 
  for (G4int 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])   )
      {
        DumpInfo();
        std::ostringstream message;
        message << "Cannot create a Polyhedra with no contiguous segments."
                << G4endl
                << "        Segments are not contiguous !" << G4endl
                << "        rMin[" << i << "] = " << rInner[i]
                << " -- rMax[" << i+1 << "] = " << rOuter[i+1] << G4endl
                << "        rMin[" << i+1 << "] = " << rInner[i+1]
                << " -- rMax[" << i << "] = " << rOuter[i];
        G4Exception("G4Polyhedra::G4Polyhedra()", "GeomSolids0002",
                    FatalErrorInArgument, message);
      }
    }
    original_parameters->Z_values[i] = zPlane[i];
    original_parameters->Rmin[i] = rInner[i]/convertRad;
    original_parameters->Rmax[i] = rOuter[i]/convertRad;
  }
 
 
  //
  // Build RZ polygon using special PCON/PGON GEANT3 constructor
  //
  G4ReduciblePolygon* rz =
    new G4ReduciblePolygon( rInner, rOuter, zPlane, numZPlanes );
  rz->ScaleA( 1/convertRad );
 
  //
  // Do the real work
  //
  Create( phiStart, phiTotal, theNumSide, rz );
 
  delete rz;
}
 
// Constructor (generic parameters)
//
G4Polyhedra::G4Polyhedra( const G4String& name,
                                G4double phiStart,
                                G4double phiTotal,
                                G4int    theNumSide,
                                G4int    numRZ,
                          const G4double r[],
                          const G4double z[]   )
  : G4VCSGfaceted( name ), genericPgon(true)
{
  if (theNumSide <= 0)
  {
    std::ostringstream message;
    message << "Solid must have at least one side - " << GetName() << G4endl
            << "        No sides specified !";
    G4Exception("G4Polyhedra::G4Polyhedra()", "GeomSolids0002",
                FatalErrorInArgument, message);
  }
 
  G4ReduciblePolygon* rz = new G4ReduciblePolygon( r, z, numRZ );
 
  Create( phiStart, phiTotal, theNumSide, rz );
 
  // Set original_parameters struct for consistency
  //
  SetOriginalParameters(rz);
 
  delete rz;
}
 
// Create
//
// Generic create routine, called by each constructor
// after conversion of arguments
//
void G4Polyhedra::Create( G4double phiStart,
                          G4double phiTotal,
                          G4int    theNumSide,
                          G4ReduciblePolygon* rz  )
{
  //
  // Perform checks of rz values
  //
  if (rz->Amin() < 0.0)
  {
    std::ostringstream message;
    message << "Illegal input parameters - " << GetName() << G4endl
            << "        All R values must be >= 0 !";
    G4Exception("G4Polyhedra::Create()", "GeomSolids0002",
                FatalErrorInArgument, message);
  }
 
  G4double rzArea = rz->Area();
  if (rzArea < -kCarTolerance)
  {
    rz->ReverseOrder();
  }
  else if (rzArea < kCarTolerance)
  {
    std::ostringstream message;
    message << "Illegal input parameters - " << GetName() << G4endl
            << "        R/Z cross section is zero or near zero: " << rzArea;
    G4Exception("G4Polyhedra::Create()", "GeomSolids0002",
                FatalErrorInArgument, message);
  }
 
  if ( (!rz->RemoveDuplicateVertices( kCarTolerance ))
    || (!rz->RemoveRedundantVertices( kCarTolerance )) )
  {
    std::ostringstream message;
    message << "Illegal input parameters - " << GetName() << G4endl
            << "        Too few unique R/Z values !";
    G4Exception("G4Polyhedra::Create()", "GeomSolids0002",
                FatalErrorInArgument, message);
  }
 
  if (rz->CrossesItself( 1/kInfinity ))
  {
    std::ostringstream message;
    message << "Illegal input parameters - " << GetName() << G4endl
            << "        R/Z segments cross !";
    G4Exception("G4Polyhedra::Create()", "GeomSolids0002",
                FatalErrorInArgument, message);
  }
 
  numCorner = rz->NumVertices();
 
 
  startPhi = phiStart;
  while( startPhi < 0 )    // Loop checking, 13.08.2015, G.Cosmo
    startPhi += twopi;
  //
  // Phi opening? Account for some possible roundoff, and interpret
  // nonsense value as representing no phi opening
  //
  if ( (phiTotal <= 0) || (phiTotal > twopi*(1-DBL_EPSILON)) )
  {
    phiIsOpen = false;
    endPhi = startPhi + twopi;
  }
  else
  {
    phiIsOpen = true;
    endPhi = startPhi + phiTotal;
  }
 
  //
  // Save number sides
  //
  numSide = theNumSide;
 
  //
  // Allocate corner array.
  //
  corners = new G4PolyhedraSideRZ[numCorner];
 
  //
  // Copy corners
  //
  G4ReduciblePolygonIterator iterRZ(rz);
 
  G4PolyhedraSideRZ *next = corners;
  iterRZ.Begin();
  do    // Loop checking, 13.08.2015, G.Cosmo
  {
    next->r = iterRZ.GetA();
    next->z = iterRZ.GetB();
  } while( ++next, iterRZ.Next() );
 
  //
  // Allocate face pointer array
  //
  numFace = phiIsOpen ? numCorner+2 : numCorner;
  faces = new G4VCSGface*[numFace];
 
  //
  // Construct side faces
  //
  // To do so properly, we need to keep track of four successive RZ
  // corners.
  //
  // But! Don't construct a face if both points are at zero radius!
  //
  G4PolyhedraSideRZ* corner = corners,
                   * prev = corners + numCorner-1,
                   * nextNext;
  G4VCSGface** face = faces;
  do    // Loop checking, 13.08.2015, G.Cosmo
  {
    next = corner+1;
    if (next >= corners+numCorner) next = corners;
    nextNext = next+1;
    if (nextNext >= corners+numCorner) nextNext = corners;
 
    if (corner->r < 1/kInfinity && next->r < 1/kInfinity) continue;
/*
    // We must decide here if we can dare declare one of our faces
    // as having a "valid" normal (i.e. allBehind = true). This
    // is never possible if the face faces "inward" in r *unless*
    // we have only one side
    //
    G4bool allBehind;
    if ((corner->z > next->z) && (numSide > 1))
    {
      allBehind = false;
    }
    else
    {
      //
      // Otherwise, it is only true if the line passing
      // through the two points of the segment do not
      // split the r/z cross section
      //
      allBehind = !rz->BisectedBy( corner->r, corner->z,
                                   next->r, next->z, kCarTolerance );
    }
*/
    *face++ = new G4PolyhedraSide( prev, corner, next, nextNext,
                 numSide, startPhi, endPhi-startPhi, phiIsOpen );
  } while( prev=corner, corner=next, corner > corners );
 
  if (phiIsOpen)
  {
    //
    // Construct phi open edges
    //
    *face++ = new G4PolyPhiFace( rz, startPhi, phiTotal/numSide, endPhi );
    *face++ = new G4PolyPhiFace( rz, endPhi,   phiTotal/numSide, startPhi );
  }
 
  //
  // We might have dropped a face or two: recalculate numFace
  //
  numFace = face-faces;
 
  //
  // Make enclosingCylinder
  //
  enclosingCylinder =
    new G4EnclosingCylinder( rz, phiIsOpen, phiStart, phiTotal );
}
 
// Fake default constructor - sets only member data and allocates memory
//                            for usage restricted to object persistency.
//
G4Polyhedra::G4Polyhedra( __void__& a )
  : G4VCSGfaceted(a), startPhi(0.), endPhi(0.)
{
}
 
// Destructor
//
G4Polyhedra::~G4Polyhedra()
{
  delete [] corners;
  delete original_parameters;
  delete enclosingCylinder;
  delete fElements;
  delete fpPolyhedron;
  corners = nullptr;
  original_parameters = nullptr;
  enclosingCylinder = nullptr;
  fElements = nullptr;
  fpPolyhedron = nullptr;
}
 
// Copy constructor
//
G4Polyhedra::G4Polyhedra( const G4Polyhedra& source )
  : G4VCSGfaceted( source )
{
  CopyStuff( source );
}
 
// Assignment operator
//
G4Polyhedra &G4Polyhedra::operator=( const G4Polyhedra& source )
{
  if (this == &source) return *this;
 
  G4VCSGfaceted::operator=( source );
 
  delete [] corners;
  delete original_parameters;
  delete enclosingCylinder;
 
  CopyStuff( source );
 
  return *this;
}
 
// CopyStuff
//
void G4Polyhedra::CopyStuff( const G4Polyhedra& source )
{
  //
  // Simple stuff
  //
  numSide    = source.numSide;
  startPhi   = source.startPhi;
  endPhi     = source.endPhi;
  phiIsOpen  = source.phiIsOpen;
  numCorner  = source.numCorner;
  genericPgon= source.genericPgon;
 
  //
  // The corner array
  //
  corners = new G4PolyhedraSideRZ[numCorner];
 
  G4PolyhedraSideRZ* corn = corners,
                   * sourceCorn = source.corners;
  do    // Loop checking, 13.08.2015, G.Cosmo
  {
    *corn = *sourceCorn;
  } while( ++sourceCorn, ++corn < corners+numCorner );
 
  //
  // Original parameters
  //
  if (source.original_parameters)
  {
    original_parameters =
      new G4PolyhedraHistorical( *source.original_parameters );
  }
 
  //
  // Enclosing cylinder
  //
  enclosingCylinder = new G4EnclosingCylinder( *source.enclosingCylinder );
 
  //
  // Surface elements
  //
  delete fElements;
  fElements = nullptr;
 
  //
  // Polyhedron
  //
  fRebuildPolyhedron = false;
  delete fpPolyhedron;
  fpPolyhedron = nullptr;
}
 
// Reset
//
// Recalculates and reshapes the solid, given pre-assigned scaled
// original_parameters.
//
G4bool G4Polyhedra::Reset()
{
  if (genericPgon)
  {
    std::ostringstream message;
    message << "Solid " << GetName() << " built using generic construct."
            << G4endl << "Not applicable to the generic construct !";
    G4Exception("G4Polyhedra::Reset()", "GeomSolids1001",
                JustWarning, message, "Parameters NOT resetted.");
    return true;
  }
 
  //
  // Clear old setup
  //
  G4VCSGfaceted::DeleteStuff();
  delete [] corners;
  delete enclosingCylinder;
  delete fElements;
  corners = nullptr;
  fElements = nullptr;
  enclosingCylinder = nullptr;
 
  //
  // Rebuild polyhedra
  //
  G4ReduciblePolygon* rz =
    new G4ReduciblePolygon( original_parameters->Rmin,
                            original_parameters->Rmax,
                            original_parameters->Z_values,
                            original_parameters->Num_z_planes );
  Create( original_parameters->Start_angle,
          original_parameters->Opening_angle,
          original_parameters->numSide, rz );
  delete rz;
 
  return false;
}
 
// Inside
//
// This is an override of G4VCSGfaceted::Inside, created in order
// to speed things up by first checking with G4EnclosingCylinder.
//
EInside G4Polyhedra::Inside( const G4ThreeVector& p ) const
{
  //
  // Quick test
  //
  if (enclosingCylinder->MustBeOutside(p)) return kOutside;
 
  //
  // Long answer
  //
  return G4VCSGfaceted::Inside(p);
}
 
// DistanceToIn
//
// This is an override of G4VCSGfaceted::Inside, created in order
// to speed things up by first checking with G4EnclosingCylinder.
//
G4double G4Polyhedra::DistanceToIn( const G4ThreeVector& p,
                                    const G4ThreeVector& v ) const
{
  //
  // Quick test
  //
  if (enclosingCylinder->ShouldMiss(p,v))
    return kInfinity;
 
  //
  // Long answer
  //
  return G4VCSGfaceted::DistanceToIn( p, v );
}
 
// DistanceToIn
//
G4double G4Polyhedra::DistanceToIn( const G4ThreeVector& p ) const
{
  return G4VCSGfaceted::DistanceToIn(p);
}
 
// Get bounding box
//
void G4Polyhedra::BoundingLimits(G4ThreeVector& pMin,
                                 G4ThreeVector& pMax) const
{
  G4double rmin = kInfinity, rmax = -kInfinity;
  G4double zmin = kInfinity, zmax = -kInfinity;
  for (G4int i=0; i<GetNumRZCorner(); ++i)
  {
    G4PolyhedraSideRZ corner = GetCorner(i);
    if (corner.r < rmin) rmin = corner.r;
    if (corner.r > rmax) rmax = corner.r;
    if (corner.z < zmin) zmin = corner.z;
    if (corner.z > zmax) zmax = corner.z;
  }
 
  G4double sphi    = GetStartPhi();
  G4double ephi    = GetEndPhi();
  G4double dphi    = IsOpen() ? ephi-sphi : twopi;
  G4int    ksteps  = GetNumSide();
  G4double astep   = dphi/ksteps;
  G4double sinStep = std::sin(astep);
  G4double cosStep = std::cos(astep);
 
  G4double sinCur = GetSinStartPhi();
  G4double cosCur = GetCosStartPhi();
  if (!IsOpen()) rmin = 0.;
  G4double xmin = rmin*cosCur, xmax = xmin;
  G4double ymin = rmin*sinCur, ymax = ymin;
  for (G4int k=0; k<ksteps+1; ++k)
  {
    G4double x = rmax*cosCur;
    if (x < xmin) xmin = x;
    if (x > xmax) xmax = x;
    G4double y = rmax*sinCur;
    if (y < ymin) ymin = y;
    if (y > ymax) ymax = y;
    if (rmin > 0)
    {
      G4double xx = rmin*cosCur;
      if (xx < xmin) xmin = xx;
      if (xx > xmax) xmax = xx;
      G4double yy = rmin*sinCur;
      if (yy < ymin) ymin = yy;
      if (yy > ymax) ymax = yy;
    }
    G4double sinTmp = sinCur;
    sinCur = sinCur*cosStep + cosCur*sinStep;
    cosCur = cosCur*cosStep - sinTmp*sinStep;
  }
  pMin.set(xmin,ymin,zmin);
  pMax.set(xmax,ymax,zmax);
 
  // Check correctness of the bounding box
  //
  if (pMin.x() >= pMax.x() || pMin.y() >= pMax.y() || pMin.z() >= pMax.z())
  {
    std::ostringstream message;
    message << "Bad bounding box (min >= max) for solid: "
            << GetName() << " !"
            << "\npMin = " << pMin
            << "\npMax = " << pMax;
    G4Exception("G4Polyhedra::BoundingLimits()", "GeomMgt0001",
                JustWarning, message);
    DumpInfo();
  }
}
 
// Calculate extent under transform and specified limit
//
G4bool G4Polyhedra::CalculateExtent(const EAxis pAxis,
                                    const G4VoxelLimits& pVoxelLimit,
                                    const G4AffineTransform& pTransform,
                                    G4double& pMin, G4double& pMax) const
{
  G4ThreeVector bmin, bmax;
  G4bool exist;
 
  // Check bounding box (bbox)
  //
  BoundingLimits(bmin,bmax);
  G4BoundingEnvelope bbox(bmin,bmax);
#ifdef G4BBOX_EXTENT
  return bbox.CalculateExtent(pAxis,pVoxelLimit,pTransform,pMin,pMax);
#endif
  if (bbox.BoundingBoxVsVoxelLimits(pAxis,pVoxelLimit,pTransform,pMin,pMax))
  {
    return exist = (pMin < pMax) ? true : false;
  }
 
  // To find the extent, RZ contour of the polycone is subdivided
  // in triangles. The extent is calculated as cumulative extent of
  // all sub-polycones formed by rotation of triangles around Z
  //
  G4TwoVectorList contourRZ;
  G4TwoVectorList triangles;
  std::vector<G4int> iout;
  G4double eminlim = pVoxelLimit.GetMinExtent(pAxis);
  G4double emaxlim = pVoxelLimit.GetMaxExtent(pAxis);
 
  // get RZ contour, ensure anticlockwise order of corners
  for (G4int i=0; i<GetNumRZCorner(); ++i)
  {
    G4PolyhedraSideRZ corner = GetCorner(i);
    contourRZ.push_back(G4TwoVector(corner.r,corner.z));
  }
  G4GeomTools::RemoveRedundantVertices(contourRZ,iout,2*kCarTolerance);
  G4double area = G4GeomTools::PolygonArea(contourRZ);
  if (area < 0.) std::reverse(contourRZ.begin(),contourRZ.end());
 
  // triangulate RZ countour
  if (!G4GeomTools::TriangulatePolygon(contourRZ,triangles))
  {
    std::ostringstream message;
    message << "Triangulation of RZ contour has failed for solid: "
            << GetName() << " !"
            << "\nExtent has been calculated using boundary box";
    G4Exception("G4Polyhedra::CalculateExtent()",
                "GeomMgt1002",JustWarning,message);
    return bbox.CalculateExtent(pAxis,pVoxelLimit,pTransform,pMin,pMax);
  }
 
  // set trigonometric values
  G4double sphi     = GetStartPhi();
  G4double ephi     = GetEndPhi();
  G4double dphi     = IsOpen() ? ephi-sphi : twopi;
  G4int    ksteps   = GetNumSide();
  G4double astep    = dphi/ksteps;
  G4double sinStep  = std::sin(astep);
  G4double cosStep  = std::cos(astep);
  G4double sinStart = GetSinStartPhi();
  G4double cosStart = GetCosStartPhi();
 
  // allocate vector lists
  std::vector<const G4ThreeVectorList *> polygons;
  polygons.resize(ksteps+1);
  for (G4int k=0; k<ksteps+1; ++k)
  {
    polygons[k] = new G4ThreeVectorList(3);
  }
 
  // main loop along triangles
  pMin =  kInfinity;
  pMax = -kInfinity;
  G4int ntria = triangles.size()/3;
  for (G4int i=0; i<ntria; ++i)
  {
    G4double sinCur = sinStart;
    G4double cosCur = cosStart;
    G4int i3 = i*3;
    for (G4int k=0; k<ksteps+1; ++k) // rotate triangle
    {
      G4ThreeVectorList* ptr = const_cast<G4ThreeVectorList*>(polygons[k]);
      G4ThreeVectorList::iterator iter = ptr->begin();
      iter->set(triangles[i3+0].x()*cosCur,
                triangles[i3+0].x()*sinCur,
                triangles[i3+0].y());
      iter++;
      iter->set(triangles[i3+1].x()*cosCur,
                triangles[i3+1].x()*sinCur,
                triangles[i3+1].y());
      iter++;
      iter->set(triangles[i3+2].x()*cosCur,
                triangles[i3+2].x()*sinCur,
                triangles[i3+2].y());
 
      G4double sinTmp = sinCur;
      sinCur = sinCur*cosStep + cosCur*sinStep;
      cosCur = cosCur*cosStep - sinTmp*sinStep;
    }
 
    // set sub-envelope and adjust extent
    G4double emin,emax;
    G4BoundingEnvelope benv(polygons);
    if (!benv.CalculateExtent(pAxis,pVoxelLimit,pTransform,emin,emax)) continue;
    if (emin < pMin) pMin = emin;
    if (emax > pMax) pMax = emax;
    if (eminlim > pMin && emaxlim < pMax) break; // max possible extent
  }
  // free memory
  for (G4int k=0; k<ksteps+1; ++k) { delete polygons[k]; polygons[k]=0;}
  return (pMin < pMax);
}
 
// ComputeDimensions
//
void G4Polyhedra::ComputeDimensions(       G4VPVParameterisation* p,
                                     const G4int n,
                                     const G4VPhysicalVolume* pRep )
{
  p->ComputeDimensions(*this,n,pRep);
}
 
// GetEntityType
//
G4GeometryType G4Polyhedra::GetEntityType() const
{
  return G4String("G4Polyhedra");
}
 
// Make a clone of the object
//
G4VSolid* G4Polyhedra::Clone() const
{
  return new G4Polyhedra(*this);
}
 
// Stream object contents to an output stream
//
std::ostream& G4Polyhedra::StreamInfo( std::ostream& os ) const
{
  G4int oldprc = os.precision(16);
  os << "-----------------------------------------------------------\n"
     << "    *** Dump for solid - " << GetName() << " ***\n"
     << "    ===================================================\n"
     << " Solid type: G4Polyhedra\n"
     << " Parameters: \n"
     << "    starting phi angle : " << startPhi/degree << " degrees \n"
     << "    ending phi angle   : " << endPhi/degree << " degrees \n"
     << "    number of sides    : " << numSide << " \n";
  G4int i=0;
  if (!genericPgon)
  {
    G4int numPlanes = original_parameters->Num_z_planes;
    os << "    number of Z planes: " << numPlanes << "\n"
       << "              Z values: \n";
    for (i=0; i<numPlanes; ++i)
    {
      os << "              Z plane " << i << ": "
         << original_parameters->Z_values[i] << "\n";
    }
    os << "              Tangent distances to inner surface (Rmin): \n";
    for (i=0; i<numPlanes; ++i)
    {
      os << "              Z plane " << i << ": "
         << original_parameters->Rmin[i] << "\n";
    }
    os << "              Tangent distances to outer surface (Rmax): \n";
    for (i=0; i<numPlanes; ++i)
    {
      os << "              Z plane " << i << ": "
         << original_parameters->Rmax[i] << "\n";
    }
  }
  os << "    number of RZ points: " << numCorner << "\n"
     << "              RZ values (corners): \n";
     for (i=0; i<numCorner; ++i)
     {
       os << "                         "
          << corners[i].r << ", " << corners[i].z << "\n";
     }
  os << "-----------------------------------------------------------\n";
  os.precision(oldprc);
 
  return os;
}
 
//
// Return volume
 
G4double G4Polyhedra::GetCubicVolume()
{
  if (fCubicVolume == 0.)
  {
    G4double total = 0.;
    G4int nrz = GetNumRZCorner();
    G4PolyhedraSideRZ a = GetCorner(nrz - 1);
    for (G4int i=0; i<nrz; ++i)
    {
      G4PolyhedraSideRZ b = GetCorner(i);
      total += (b.r*b.r + b.r*a.r + a.r*a.r)*(b.z - a.z);
      a = b;
    }
    fCubicVolume = std::abs(total)*
      std::sin((GetEndPhi() - GetStartPhi())/GetNumSide())*GetNumSide()/6.;
  }
  return fCubicVolume;
}
 
//
// Return surface area
 
G4double G4Polyhedra::GetSurfaceArea()
{
  if (fSurfaceArea == 0.)
  {
    G4double total = 0.;
    G4int nrz = GetNumRZCorner();
    if (IsOpen())
    {
      G4PolyhedraSideRZ a = GetCorner(nrz - 1);
      for (G4int i=0; i<nrz; ++i)
      {
        G4PolyhedraSideRZ b = GetCorner(i);
        total += a.r*b.z - a.z*b.r;
        a = b;
      }
      total = std::abs(total);
    }
    G4double alp = (GetEndPhi() - GetStartPhi())/GetNumSide();
    G4double cosa = std::cos(alp);
    G4double sina = std::sin(alp);
    G4PolyhedraSideRZ a = GetCorner(nrz - 1);
    for (G4int i=0; i<nrz; ++i)
    {
      G4PolyhedraSideRZ b = GetCorner(i);
      G4ThreeVector p1(a.r, 0, a.z);
      G4ThreeVector p2(a.r*cosa, a.r*sina, a.z);
      G4ThreeVector p3(b.r*cosa, b.r*sina, b.z);
      G4ThreeVector p4(b.r, 0, b.z);
      total += GetNumSide()*(G4GeomTools::QuadAreaNormal(p1, p2, p3, p4)).mag();
      a = b;
    }
    fSurfaceArea = total;
  }
  return fSurfaceArea;
}
 
//
// Set vector of surface elements, auxiliary method for sampling
// random points on surface
 
void G4Polyhedra::SetSurfaceElements() const
{
  fElements = new std::vector<G4Polyhedra::surface_element>;
  G4double total = 0.;
  G4int nrz = GetNumRZCorner();
 
  // set lateral surface elements
  G4double dphi = (GetEndPhi() - GetStartPhi())/GetNumSide();
  G4double cosa = std::cos(dphi);
  G4double sina = std::sin(dphi);
  G4int ia = nrz - 1;
  for (G4int ib=0; ib<nrz; ++ib)
  {
    G4PolyhedraSideRZ a = GetCorner(ia);
    G4PolyhedraSideRZ b = GetCorner(ib);
    G4Polyhedra::surface_element selem;
    selem.i0 = ia;
    selem.i1 = ib;
    ia = ib;
    if (a.r == 0. && b.r == 0.) continue;
    G4ThreeVector p1(a.r, 0, a.z);
    G4ThreeVector p2(a.r*cosa, a.r*sina, a.z);
    G4ThreeVector p3(b.r*cosa, b.r*sina, b.z);
    G4ThreeVector p4(b.r, 0, b.z);
    if (a.r > 0.)
    {
      selem.i2 = -1;
      total += GetNumSide()*(G4GeomTools::TriangleAreaNormal(p1, p2, p3)).mag();
      selem.area = total;
      fElements->push_back(selem);
    }
    if (b.r > 0.)
    {
      selem.i2 = -2;
      total += GetNumSide()*(G4GeomTools::TriangleAreaNormal(p1, p3, p4)).mag();
      selem.area = total;
      fElements->push_back(selem);
    }
  }
 
  // set elements for phi cuts
  if (IsOpen())
  {
    G4TwoVectorList contourRZ;
    std::vector<G4int> triangles;
    for (G4int i=0; i<nrz; ++i)
    {
      G4PolyhedraSideRZ corner = GetCorner(i);
      contourRZ.push_back(G4TwoVector(corner.r, corner.z));
    }
    G4GeomTools::TriangulatePolygon(contourRZ, triangles);
    G4int ntria = triangles.size();
    for (G4int i=0; i<ntria; i+=3)
    {
      G4Polyhedra::surface_element selem;
      selem.i0 = triangles[i];
      selem.i1 = triangles[i+1];
      selem.i2 = triangles[i+2];
      G4PolyhedraSideRZ a = GetCorner(selem.i0);
      G4PolyhedraSideRZ b = GetCorner(selem.i1);
      G4PolyhedraSideRZ c = GetCorner(selem.i2);
      G4double stria =
        std::abs(G4GeomTools::TriangleArea(a.r, a.z, b.r, b.z, c.r, c.z));
      total += stria;
      selem.area = total;
      fElements->push_back(selem); // start phi
      total += stria;
      selem.area = total;
      selem.i0 += nrz;
      fElements->push_back(selem); // end phi
    }
  }
}
 
//
// Generate random point on surface
 
G4ThreeVector G4Polyhedra::GetPointOnSurface() const
{
  // Set surface elements
  if (!fElements)
  {
    G4AutoLock l(&surface_elementsMutex);
    SetSurfaceElements();
    l.unlock();
  }
 
  // Select surface element
  G4Polyhedra::surface_element selem;
  selem = fElements->back();
  G4double select = selem.area*G4QuickRand();
  auto it = std::lower_bound(fElements->begin(), fElements->end(), select,
                             [](const G4Polyhedra::surface_element& x, G4double val)
                             -> G4bool { return x.area < val; });
 
  // Generate random point
  G4double x = 0, y = 0, z = 0;
  G4double u = G4QuickRand();
  G4double v = G4QuickRand();
  if (u + v > 1.) { u = 1. - u; v = 1. - v; }
  G4int i0 = (*it).i0;
  G4int i1 = (*it).i1;
  G4int i2 = (*it).i2;
  if (i2 < 0) // lateral surface
  {
    // sample point
    G4int nside = GetNumSide();
    G4double dphi = (GetEndPhi() - GetStartPhi())/nside;
    G4double cosa = std::cos(dphi);
    G4double sina = std::sin(dphi);
    G4PolyhedraSideRZ a = GetCorner(i0);
    G4PolyhedraSideRZ b = GetCorner(i1);
    G4ThreeVector p0(a.r, 0, a.z);
    G4ThreeVector p1(b.r, 0, b.z);
    G4ThreeVector p2(b.r*cosa, b.r*sina, b.z);
    if (i2 == -1) p1.set(a.r*cosa, a.r*sina, a.z);
    p0 += (p1 - p0)*u + (p2 - p0)*v;
    // find selected side and rotate point
    G4double scurr = (*it).area;
    G4double sprev = (it == fElements->begin()) ? 0. : (*(--it)).area;
    G4int iside = nside*(select - sprev)/(scurr - sprev);
    if (iside == 0 && GetStartPhi() == 0.)
    {
      x = p0.x();
      y = p0.y();
      z = p0.z();
    }
    else
    {
      if (iside == nside) --iside; // iside must be less then nside
      G4double phi = iside*dphi + GetStartPhi();
      G4double cosphi = std::cos(phi);
      G4double sinphi = std::sin(phi);
      x = p0.x()*cosphi - p0.y()*sinphi;
      y = p0.x()*sinphi + p0.y()*cosphi;
      z = p0.z();
    }
  }
  else // phi cut
  {
    G4int nrz = GetNumRZCorner();
    G4double phi = (i0 < nrz) ? GetStartPhi() : GetEndPhi();
    if (i0 >= nrz) { i0 -= nrz; }
    G4PolyhedraSideRZ p0 = GetCorner(i0);
    G4PolyhedraSideRZ p1 = GetCorner(i1);
    G4PolyhedraSideRZ p2 = GetCorner(i2);
    G4double r = (p1.r - p0.r)*u + (p2.r - p0.r)*v + p0.r;
    x = r*std::cos(phi);
    y = r*std::sin(phi);
    z = (p1.z - p0.z)*u + (p2.z - p0.z)*v + p0.z;
  }
  return G4ThreeVector(x, y, z);
}
 
//
// CreatePolyhedron
 
G4Polyhedron* G4Polyhedra::CreatePolyhedron() const
{
  std::vector<G4TwoVector> rz(numCorner);
  for (G4int i = 0; i < numCorner; ++i)
    rz[i].set(corners[i].r, corners[i].z);
  return new G4PolyhedronPgon(startPhi, endPhi - startPhi, numSide, rz);
}
 
// SetOriginalParameters
//
void G4Polyhedra::SetOriginalParameters(G4ReduciblePolygon* rz)
{
  G4int numPlanes = numCorner;
  G4bool isConvertible = true;
  G4double Zmax=rz->Bmax();
  rz->StartWithZMin();
 
  // Prepare vectors for storage
  //
  std::vector<G4double> Z;
  std::vector<G4double> Rmin;
  std::vector<G4double> Rmax;
 
  G4int countPlanes=1;
  G4int icurr=0;
  G4int icurl=0;
 
  // first plane Z=Z[0]
  //
  Z.push_back(corners[0].z);
  G4double 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
  //
  G4int inextr=0, inextl=0;
  for (G4int 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; }
 
    G4double Zleft = corners[inextl].z;
    G4double Zright = corners[inextr].z;
    if(Zright>Zleft)
    {
      Z.push_back(Zleft);
      countPlanes++;
      G4double difZr=corners[inextr].z - corners[icurr].z;
      G4double difZl=corners[inextl].z - corners[icurl].z;
 
      if(std::fabs(difZl) < kCarTolerance)
      {
        if(std::fabs(difZr) < kCarTolerance)
        {
          Rmin.push_back(corners[inextl].r);
          Rmax.push_back(corners[icurr].r);
        }
        else
        {
          Rmin.push_back(corners[inextl].r);
          Rmax.push_back(corners[icurr].r + (Zleft-corners[icurr].z)/difZr
                                *(corners[inextr].r - corners[icurr].r));
        }
      }
      else if (difZl >= kCarTolerance)
      {
        if(std::fabs(difZr) < kCarTolerance)
        {
          Rmin.push_back(corners[icurl].r);
          Rmax.push_back(corners[icurr].r);
        }
        else
        {
          Rmin.push_back(corners[icurl].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)<kCarTolerance)  // 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;
 
      G4double difZr=corners[inextr].z - corners[icurr].z;
      G4double difZl=corners[inextl].z - corners[icurl].z;
      if(std::fabs(difZr) < kCarTolerance)
      {
        if(std::fabs(difZl) < kCarTolerance)
        {
          Rmax.push_back(corners[inextr].r);
          Rmin.push_back(corners[icurr].r);
        }
        else
        {
          Rmin.push_back(corners[icurl].r + (Zright-corners[icurl].z)/difZl
                                * (corners[inextl].r - corners[icurl].r));
          Rmax.push_back(corners[inextr].r);
        }
        ++icurr;
      }           // plate
      else if (difZr >= kCarTolerance)
      {
        if(std::fabs(difZl) < kCarTolerance)
        {
          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;
 
  Rmax.push_back(corners[inextr].r);
  Rmin.push_back(corners[inextl].r);
 
  // Set original parameters Rmin,Rmax,Z
  //
  if(isConvertible)
  {
   original_parameters = new G4PolyhedraHistorical;
   original_parameters->numSide = numSide;
   original_parameters->Z_values = new G4double[countPlanes];
   original_parameters->Rmin = new G4double[countPlanes];
   original_parameters->Rmax = new G4double[countPlanes];
 
   for(G4int j=0; j < countPlanes; ++j)
   {
     original_parameters->Z_values[j] = Z[j];
     original_parameters->Rmax[j] = Rmax[j];
     original_parameters->Rmin[j] = Rmin[j];
   }
   original_parameters->Start_angle = startPhi;
   original_parameters->Opening_angle = endPhi-startPhi;
   original_parameters->Num_z_planes = countPlanes;
 
  }
  else  // Set parameters(r,z) with Rmin==0 as convention
  {
#ifdef G4SPECSDEBUG
    std::ostringstream message;
    message << "Polyhedra " << GetName() << G4endl
      << "cannot be converted to Polyhedra with (Rmin,Rmaz,Z) parameters!";
    G4Exception("G4Polyhedra::SetOriginalParameters()",
                "GeomSolids0002", JustWarning, message);
#endif
    original_parameters = new G4PolyhedraHistorical;
    original_parameters->numSide = numSide;
    original_parameters->Z_values = new G4double[numPlanes];
    original_parameters->Rmin = new G4double[numPlanes];
    original_parameters->Rmax = new G4double[numPlanes];
 
    for(G4int j=0; j < numPlanes; ++j)
    {
      original_parameters->Z_values[j] = corners[j].z;
      original_parameters->Rmax[j] = corners[j].r;
      original_parameters->Rmin[j] = 0.0;
    }
    original_parameters->Start_angle = startPhi;
    original_parameters->Opening_angle = endPhi-startPhi;
    original_parameters->Num_z_planes = numPlanes;
  }
}
 
#endif