G4GenericTrap.cc

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// $Id$
//
//
// --------------------------------------------------------------------
// GEANT 4 class source file
//
// G4GenericTrap.cc
//
// Authors:
//   Tatiana Nikitina, CERN; Ivana Hrivnacova, IPN Orsay
//   Adapted from Root Arb8 implementation by Andrei Gheata, CERN 
//
// History :
// 04 August 2011 T.Nikitina Add SetReferences() and InvertFacets()
//                to CreatePolyhedron() for Visualisation of Boolean       
// --------------------------------------------------------------------
 
#include <iomanip>
 
#include "G4GenericTrap.hh"
#include "G4PhysicalConstants.hh"
#include "G4SystemOfUnits.hh"
#include "G4TessellatedSolid.hh"
#include "G4TriangularFacet.hh"
#include "G4QuadrangularFacet.hh"
#include "G4VoxelLimits.hh"
#include "G4AffineTransform.hh"
#include "Randomize.hh"
 
#include "G4VGraphicsScene.hh"
#include "G4Polyhedron.hh"
#include "G4PolyhedronArbitrary.hh"
#include "G4NURBS.hh"
#include "G4NURBSbox.hh"
#include "G4VisExtent.hh"
 
const G4int    G4GenericTrap::fgkNofVertices = 8;
const G4double G4GenericTrap::fgkTolerance = 1E-3;
 
// --------------------------------------------------------------------
 
G4GenericTrap::G4GenericTrap( const G4String& name, G4double halfZ,
                              const std::vector<G4TwoVector>&  vertices )
  : G4VSolid(name),
    fpPolyhedron(0),
    fDz(halfZ),
    fVertices(),
    fIsTwisted(false),
    fTessellatedSolid(0),
    fMinBBoxVector(G4ThreeVector(0,0,0)),
    fMaxBBoxVector(G4ThreeVector(0,0,0)),
    fVisSubdivisions(0),
    fSurfaceArea(0.),
    fCubicVolume(0.)
   
{
  // General constructor
  const G4double min_length=5*1.e-6;
  G4double length = 0.;
  G4int k=0;
  G4String errorDescription = "InvalidSetup in \" ";
  errorDescription += name;
  errorDescription += "\""; 
  
  // Check vertices size
 
  if ( G4int(vertices.size()) != fgkNofVertices )
  {
    G4Exception("G4GenericTrap::G4GenericTrap()", "GeomSolids0002",
                FatalErrorInArgument, "Number of vertices != 8");
  }            
  
  // Check dZ
  // 
  if (halfZ < kCarTolerance)
  {
     G4Exception("G4GenericTrap::G4GenericTrap()", "GeomSolids0002",
                FatalErrorInArgument, "dZ is too small or negative");
  }           
 
  // Check Ordering and Copy vertices 
  //
  if(CheckOrder(vertices))
  {
    for (G4int i=0; i<fgkNofVertices; ++i) {fVertices.push_back(vertices[i]);}
  }
  else
  { 
    for (G4int i=0; i <4; ++i) {fVertices.push_back(vertices[3-i]);}
    for (G4int i=0; i <4; ++i) {fVertices.push_back(vertices[7-i]);}
  }
 
   // Check length of segments and Adjust
  // 
  for (G4int j=0; j < 2; j++)
  {
    for (G4int i=1; i<4; ++i)
    {
      k = j*4+i;
      length = (fVertices[k]-fVertices[k-1]).mag();
      if ( ( length < min_length) && ( length > kCarTolerance ) )
      {
        std::ostringstream message;
        message << "Length segment is too small." << G4endl
                << "Distance between " << fVertices[k-1] << " and "
                << fVertices[k] << " is only " << length << " mm !"; 
        G4Exception("G4GenericTrap::G4GenericTrap()", "GeomSolids1001",
                    JustWarning, message, "Vertices will be collapsed.");
        fVertices[k]=fVertices[k-1];
      }
    }
  }
 
  // Compute Twist
  //
  for( G4int i=0; i<4; i++) { fTwist[i]=0.; }
  fIsTwisted = ComputeIsTwisted();
 
  // Compute Bounding Box 
  //
  ComputeBBox();
  
  // If not twisted - create tessellated solid 
  // (an alternative implementation for testing)
  //
#ifdef G4TESS_TEST
   if ( !fIsTwisted )  { fTessellatedSolid = CreateTessellatedSolid(); }
#endif
}
 
// --------------------------------------------------------------------
 
G4GenericTrap::G4GenericTrap( __void__& a )
  : G4VSolid(a),
    fpPolyhedron(0),
    fDz(0.),
    fVertices(),
    fIsTwisted(false),
    fTessellatedSolid(0),
    fMinBBoxVector(G4ThreeVector(0,0,0)),
    fMaxBBoxVector(G4ThreeVector(0,0,0)),
    fVisSubdivisions(0),
    fSurfaceArea(0.),
    fCubicVolume(0.)
{
  // Fake default constructor - sets only member data and allocates memory
  //                            for usage restricted to object persistency.
 
  for (size_t i=0; i<4; ++i)  { fTwist[i]=0.; }
}
 
// --------------------------------------------------------------------
 
G4GenericTrap::~G4GenericTrap()
{
  // Destructor
  delete fTessellatedSolid;
}
 
// --------------------------------------------------------------------
 
G4GenericTrap::G4GenericTrap(const G4GenericTrap& rhs)
  : G4VSolid(rhs),
    fpPolyhedron(0), fDz(rhs.fDz), fVertices(rhs.fVertices),
    fIsTwisted(rhs.fIsTwisted), fTessellatedSolid(0),
    fMinBBoxVector(rhs.fMinBBoxVector), fMaxBBoxVector(rhs.fMaxBBoxVector),
    fVisSubdivisions(rhs.fVisSubdivisions),
    fSurfaceArea(rhs.fSurfaceArea), fCubicVolume(rhs.fCubicVolume) 
{
   for (size_t i=0; i<4; ++i)  { fTwist[i] = rhs.fTwist[i]; }
#ifdef G4TESS_TEST
   if (rhs.fTessellatedSolid && !fIsTwisted )
   { fTessellatedSolid = CreateTessellatedSolid(); } 
#endif
}
 
// --------------------------------------------------------------------
 
G4GenericTrap& G4GenericTrap::operator = (const G4GenericTrap& rhs) 
{
   // Check assignment to self
   //
   if (this == &rhs)  { return *this; }
 
   // Copy base class data
   //
   G4VSolid::operator=(rhs);
 
   // Copy data
   //
   fpPolyhedron = 0; fDz = rhs.fDz; fVertices = rhs.fVertices;
   fIsTwisted = rhs.fIsTwisted; fTessellatedSolid = 0;
   fMinBBoxVector = rhs.fMinBBoxVector; fMaxBBoxVector = rhs.fMaxBBoxVector;
   fVisSubdivisions = rhs.fVisSubdivisions;
   fSurfaceArea = rhs.fSurfaceArea; fCubicVolume = rhs.fCubicVolume;
 
   for (size_t i=0; i<4; ++i)  { fTwist[i] = rhs.fTwist[i]; }
#ifdef G4TESS_TEST
   if (rhs.fTessellatedSolid && !fIsTwisted )
   { delete fTessellatedSolid; fTessellatedSolid = CreateTessellatedSolid(); } 
#endif
 
   return *this;
}
 
// --------------------------------------------------------------------
 
EInside
G4GenericTrap::InsidePolygone(const G4ThreeVector& p,
                              const std::vector<G4TwoVector>& poly) const 
{
  static const G4double halfCarTolerance=kCarTolerance*0.5;
  EInside  in = kInside;
  G4double cross, len2;
  G4int count=0;
 
  for (G4int i = 0; i < 4; i++)
  {
    G4int j = (i+1) % 4;
 
    cross = (p.x()-poly[i].x())*(poly[j].y()-poly[i].y())-
            (p.y()-poly[i].y())*(poly[j].x()-poly[i].x());
 
    len2=(poly[i]-poly[j]).mag2();
    if (len2 > kCarTolerance)
    {
      if(cross*cross<=len2*halfCarTolerance*halfCarTolerance)  // Surface check
      {
        G4double test;
        G4int k,l;
        if ( poly[i].y() > poly[j].y() )  { k=i; l=j; }
        else                              { k=j; l=i; }
 
        if ( poly[k].x() != poly[l].x() )
        {
          test = (p.x()-poly[l].x())/(poly[k].x()-poly[l].x())
               * (poly[k].y()-poly[l].y())+poly[l].y();
        }
        else
        {
          test = p.y();
        }
 
        // Check if point is Inside Segment
        // 
        if( (test>=(poly[l].y()-halfCarTolerance))
         && (test<=(poly[k].y()+halfCarTolerance)) )
        { 
          return kSurface;
        }
        else
        {
          return kOutside;
        }
      }
      else if (cross<0.)  { return kOutside; }
    }
    else
    {
      count++;
    }
  }
 
  // All collapsed vertices, Tet like
  //
  if(count==4)
  { 
    if ( (std::fabs(p.x()-poly[0].x())+std::fabs(p.y()-poly[0].y())) > halfCarTolerance )
    {
      in=kOutside;
    }
  }
  return in;
}
 
// --------------------------------------------------------------------
 
EInside G4GenericTrap::Inside(const G4ThreeVector& p) const
{
  // Test if point is inside this shape
 
#ifdef G4TESS_TEST
   if ( fTessellatedSolid )
   { 
     return fTessellatedSolid->Inside(p);
   }
#endif  
 
  static const G4double halfCarTolerance=kCarTolerance*0.5;
  EInside innew=kOutside;
  std::vector<G4TwoVector> xy;
 
  if (std::fabs(p.z()) <= fDz+halfCarTolerance)  // First check Z range
  {
    // Compute intersection between Z plane containing point and the shape
    //
    G4double cf = 0.5*(fDz-p.z())/fDz;
    for (G4int i=0; i<4; i++)
    {
      xy.push_back(fVertices[i+4]+cf*( fVertices[i]-fVertices[i+4]));
    }
 
    innew=InsidePolygone(p,xy);
 
    if( (innew==kInside) || (innew==kSurface) )
    { 
      if(std::fabs(p.z()) > fDz-halfCarTolerance)  { innew=kSurface; }
    }
  }
  return innew;    
} 
 
// --------------------------------------------------------------------
 
G4ThreeVector G4GenericTrap::SurfaceNormal( const G4ThreeVector& p ) const
{
  // Calculate side nearest to p, and return normal
  // If two sides are equidistant, sum of the Normal is returned
 
#ifdef G4TESS_TEST
  if ( fTessellatedSolid )
  {
    return fTessellatedSolid->SurfaceNormal(p);
  }  
#endif   
 
  static const G4double halfCarTolerance=kCarTolerance*0.5;
 
  G4ThreeVector lnorm, sumnorm(0.,0.,0.), apprnorm(0.,0.,1.),
                p0, p1, p2, r1, r2, r3, r4;
  G4int noSurfaces = 0; 
  G4double distxy,distz;
  G4bool zPlusSide=false;
 
  distz = fDz-std::fabs(p.z());
  if (distz < halfCarTolerance)
  {
    if(p.z()>0)
    {
      zPlusSide=true;
      sumnorm=G4ThreeVector(0,0,1);
    }
    else
    {
      sumnorm=G4ThreeVector(0,0,-1);
    }
    noSurfaces ++;
  } 
 
  // Check lateral planes
  //
  std:: vector<G4TwoVector> vertices;  
  G4double cf = 0.5*(fDz-p.z())/fDz;
  for (G4int i=0; i<4; i++)
  {
    vertices.push_back(fVertices[i+4]+cf*(fVertices[i]-fVertices[i+4]));
  }
 
  // Compute distance for lateral planes
  //
  for (G4int q=0; q<4; q++)
  {
    p0=G4ThreeVector(vertices[q].x(),vertices[q].y(),p.z());
    if(zPlusSide)
    {
      p1=G4ThreeVector(fVertices[q].x(),fVertices[q].y(),-fDz);
    }
    else
    {
      p1=G4ThreeVector(fVertices[q+4].x(),fVertices[q+4].y(),fDz); 
    }
    p2=G4ThreeVector(vertices[(q+1)%4].x(),vertices[(q+1)%4].y(),p.z());
 
    // Collapsed vertices
    //
    if ( (p2-p0).mag2() < kCarTolerance )
    {
      if ( std::fabs(p.z()+fDz) > kCarTolerance )
      {
        p2=G4ThreeVector(fVertices[(q+1)%4].x(),fVertices[(q+1)%4].y(),-fDz);
      }
      else
      {
        p2=G4ThreeVector(fVertices[(q+1)%4+4].x(),fVertices[(q+1)%4+4].y(),fDz);
      }
    }
    lnorm = (p1-p0).cross(p2-p0);
    lnorm = lnorm.unit();
    if(zPlusSide)  { lnorm=-lnorm; }
 
    // Adjust Normal for Twisted Surface
    //
    if ( (fIsTwisted) && (GetTwistAngle(q)!=0) )
    {
      G4double normP=(p2-p0).mag();
      if(normP)
      {
        G4double proj=(p-p0).dot(p2-p0)/normP;
        if(proj<0)     { proj=0; }
        if(proj>normP) { proj=normP; }
        G4int j=(q+1)%4;
        r1=G4ThreeVector(fVertices[q+4].x(),fVertices[q+4].y(),fDz);
        r2=G4ThreeVector(fVertices[j+4].x(),fVertices[j+4].y(),fDz);
        r3=G4ThreeVector(fVertices[q].x(),fVertices[q].y(),-fDz);
        r4=G4ThreeVector(fVertices[j].x(),fVertices[j].y(),-fDz);
        r1=r1+proj*(r2-r1)/normP;
        r3=r3+proj*(r4-r3)/normP;
        r2=r1-r3;
        r4=r2.cross(p2-p0); r4=r4.unit();
        lnorm=r4;
      }
    }   // End if fIsTwisted
 
    distxy=std::fabs((p0-p).dot(lnorm));
    if ( distxy<halfCarTolerance )
    {
      noSurfaces ++;
 
      // Negative sign for Normal is taken for Outside Normal
      //
      sumnorm=sumnorm+lnorm;
    }
 
    // For ApproxSurfaceNormal
    //
    if (distxy<distz)
    {
      distz=distxy;
      apprnorm=lnorm;
    }      
  }  // End for loop
 
  // Calculate final Normal, add Normal in the Corners and Touching Sides
  //
  if ( noSurfaces == 0 )
  {
    G4Exception("G4GenericTrap::SurfaceNormal(p)", "GeomSolids1002",
                JustWarning, "Point p is not on surface !?" );
    sumnorm=apprnorm;
    // Add Approximative Surface Normal Calculation?
  }
  else if ( noSurfaces == 1 )  { sumnorm = sumnorm; }
  else                         { sumnorm = sumnorm.unit(); }
 
  return sumnorm ; 
}    
 
// --------------------------------------------------------------------
 
G4ThreeVector G4GenericTrap::NormalToPlane( const G4ThreeVector& p,
                                            const G4int ipl ) const
{
  // Return normal to given lateral plane ipl
 
#ifdef G4TESS_TEST
  if ( fTessellatedSolid )
  { 
    return fTessellatedSolid->SurfaceNormal(p);
  }  
#endif   
 
  static const G4double halfCarTolerance=kCarTolerance*0.5; 
  G4ThreeVector lnorm, norm(0.,0.,0.), p0,p1,p2;
 
  G4double  distz = fDz-p.z();
  G4int i=ipl;  // current plane index
 
  G4TwoVector u,v;  
  G4ThreeVector r1,r2,r3,r4;
  G4double cf = 0.5*(fDz-p.z())/fDz;
  G4int j=(i+1)%4;
 
  u=fVertices[i+4]+cf*(fVertices[i]-fVertices[i+4]);
  v=fVertices[j+4]+cf*(fVertices[j]-fVertices[j+4]);
 
  // Compute cross product
  //
  p0=G4ThreeVector(u.x(),u.y(),p.z());
      
  if (std::fabs(distz)<halfCarTolerance)
  {
    p1=G4ThreeVector(fVertices[i].x(),fVertices[i].y(),-fDz);distz=-1;}
  else
  {
    p1=G4ThreeVector(fVertices[i+4].x(),fVertices[i+4].y(),fDz);
  }  
  p2=G4ThreeVector(v.x(),v.y(),p.z());
 
  // Collapsed vertices
  //
  if ( (p2-p0).mag2() < kCarTolerance )
  {
    if ( std::fabs(p.z()+fDz) > halfCarTolerance )
    {
      p2=G4ThreeVector(fVertices[j].x(),fVertices[j].y(),-fDz);
    }
    else
    {
      p2=G4ThreeVector(fVertices[j+4].x(),fVertices[j+4].y(),fDz);
    }
  }
  lnorm=-(p1-p0).cross(p2-p0);
  if (distz>-halfCarTolerance)  { lnorm=-lnorm.unit(); }
  else                          { lnorm=lnorm.unit();  }
 
  // Adjust Normal for Twisted Surface
  //
  if( (fIsTwisted) && (GetTwistAngle(ipl)!=0) )
  {
    G4double normP=(p2-p0).mag();
    if(normP)
    {
      G4double proj=(p-p0).dot(p2-p0)/normP;
      if (proj<0)     { proj=0; }
      if (proj>normP) { proj=normP; }
 
      r1=G4ThreeVector(fVertices[i+4].x(),fVertices[i+4].y(),fDz);
      r2=G4ThreeVector(fVertices[j+4].x(),fVertices[j+4].y(),fDz);
      r3=G4ThreeVector(fVertices[i].x(),fVertices[i].y(),-fDz);
      r4=G4ThreeVector(fVertices[j].x(),fVertices[j].y(),-fDz);
      r1=r1+proj*(r2-r1)/normP;
      r3=r3+proj*(r4-r3)/normP;
      r2=r1-r3;
      r4=r2.cross(p2-p0);r4=r4.unit();
      lnorm=r4;
    }
  }  // End if fIsTwisted
 
  return lnorm;
}    
 
// --------------------------------------------------------------------
 
G4double G4GenericTrap::DistToPlane(const G4ThreeVector& p,
                                    const G4ThreeVector& v,
                                    const G4int ipl) const 
{
  // Computes distance to plane ipl :
  // ipl=0 : points 0,4,1,5
  // ipl=1 : points 1,5,2,6
  // ipl=2 : points 2,6,3,7
  // ipl=3 : points 3,7,0,4
 
  static const G4double halfCarTolerance=0.5*kCarTolerance;
  G4double xa,xb,xc,xd,ya,yb,yc,yd;
  
  G4int j = (ipl+1)%4;
  
  xa=fVertices[ipl].x();
  ya=fVertices[ipl].y();
  xb=fVertices[ipl+4].x();
  yb=fVertices[ipl+4].y();
  xc=fVertices[j].x();
  yc=fVertices[j].y();
  xd=fVertices[4+j].x();
  yd=fVertices[4+j].y();
 
  G4double dz2 =0.5/fDz;
  G4double tx1 =dz2*(xb-xa);
  G4double ty1 =dz2*(yb-ya);
  G4double tx2 =dz2*(xd-xc);
  G4double ty2 =dz2*(yd-yc);
  G4double dzp =fDz+p.z();
  G4double xs1 =xa+tx1*dzp;
  G4double ys1 =ya+ty1*dzp;
  G4double xs2 =xc+tx2*dzp;
  G4double ys2 =yc+ty2*dzp;
  G4double dxs =xs2-xs1;
  G4double dys =ys2-ys1;
  G4double dtx =tx2-tx1;
  G4double dty =ty2-ty1;
 
  G4double a = (dtx*v.y()-dty*v.x()+(tx1*ty2-tx2*ty1)*v.z())*v.z();
  G4double b = dxs*v.y()-dys*v.x()+(dtx*p.y()-dty*p.x()+ty2*xs1-ty1*xs2
             + tx1*ys2-tx2*ys1)*v.z();
  G4double c=dxs*p.y()-dys*p.x()+xs1*ys2-xs2*ys1;
  G4double q=kInfinity;
  G4double x1,x2,y1,y2,xp,yp,zi;
 
  if (std::fabs(a)<kCarTolerance)
  {           
    if (std::fabs(b)<kCarTolerance)  { return kInfinity; }
    q=-c/b;
 
    // Check if Point is on the Surface
 
    if (q>-halfCarTolerance)
    {
      if (q<halfCarTolerance)
      {
        if (NormalToPlane(p,ipl).dot(v)<=0)
          { if(Inside(p) != kOutside) { return 0.; } }
        else
          { return kInfinity; }
      }
 
      // Check the Intersection
      //
      zi=p.z()+q*v.z();
      if (std::fabs(zi)<fDz)
      {
        x1=xs1+tx1*v.z()*q;
        x2=xs2+tx2*v.z()*q;
        xp=p.x()+q*v.x();
        y1=ys1+ty1*v.z()*q;
        y2=ys2+ty2*v.z()*q;
        yp=p.y()+q*v.y();
        zi = (xp-x1)*(xp-x2)+(yp-y1)*(yp-y2);
        if (zi<=halfCarTolerance)  { return q; }
      }
    }
    return kInfinity;
  }      
  G4double d=b*b-4*a*c;
  if (d>=0)
  {
    if (a>0) { q=0.5*(-b-std::sqrt(d))/a; }
    else     { q=0.5*(-b+std::sqrt(d))/a; }
 
    // Check if Point is on the Surface
    //
    if (q>-halfCarTolerance)
    {
      if(q<halfCarTolerance)
      {
        if (NormalToPlane(p,ipl).dot(v)<=0)
        {
          if(Inside(p)!= kOutside) { return 0.; }
        }
        else  // Check second root; return kInfinity
        {
          if (a>0) { q=0.5*(-b+std::sqrt(d))/a; }
          else     { q=0.5*(-b-std::sqrt(d))/a; }
          if (q<=halfCarTolerance) { return kInfinity; }
        }
      }
      // Check the Intersection
      //
      zi=p.z()+q*v.z();
      if (std::fabs(zi)<fDz)
      {
        x1=xs1+tx1*v.z()*q;
        x2=xs2+tx2*v.z()*q;
        xp=p.x()+q*v.x();
        y1=ys1+ty1*v.z()*q;
        y2=ys2+ty2*v.z()*q;
        yp=p.y()+q*v.y();
        zi = (xp-x1)*(xp-x2)+(yp-y1)*(yp-y2);
        if (zi<=halfCarTolerance)  { return q; }
      }
    }
    if (a>0)  { q=0.5*(-b+std::sqrt(d))/a; }
    else      { q=0.5*(-b-std::sqrt(d))/a; }
 
    // Check if Point is on the Surface
    //
    if (q>-halfCarTolerance)
    {
      if(q<halfCarTolerance)
      {
        if (NormalToPlane(p,ipl).dot(v)<=0)
        {
          if(Inside(p) != kOutside)  { return 0.; }
        }
        else   // Check second root; return kInfinity.
        {
          if (a>0) { q=0.5*(-b-std::sqrt(d))/a; }
          else     { q=0.5*(-b+std::sqrt(d))/a; }
          if (q<=halfCarTolerance)  { return kInfinity; }
        }
      }
      // Check the Intersection
      //
      zi=p.z()+q*v.z();
      if (std::fabs(zi)<fDz)
      {
        x1=xs1+tx1*v.z()*q;
        x2=xs2+tx2*v.z()*q;
        xp=p.x()+q*v.x();
        y1=ys1+ty1*v.z()*q;
        y2=ys2+ty2*v.z()*q;
        yp=p.y()+q*v.y();
        zi = (xp-x1)*(xp-x2)+(yp-y1)*(yp-y2);
        if (zi<=halfCarTolerance)  { return q; }
      }
    }
  }
  return kInfinity;
}      
 
// --------------------------------------------------------------------
 
G4double G4GenericTrap::DistanceToIn(const G4ThreeVector& p,
                                     const G4ThreeVector& v) const
{
#ifdef G4TESS_TEST
  if ( fTessellatedSolid )
  { 
    return fTessellatedSolid->DistanceToIn(p, v);
  }  
#endif
    
  static const G4double halfCarTolerance=kCarTolerance*0.5;
 
  G4double dist[5];
  G4ThreeVector n;
 
  // Check lateral faces
  //
  G4int i;
  for (i=0; i<4; i++)
  {
    dist[i]=DistToPlane(p, v, i);  
  }
 
  // Check Z planes
  //
  dist[4]=kInfinity;
  if (std::fabs(p.z())>fDz-halfCarTolerance)
  {
    if (v.z())
    {
      G4ThreeVector pt;
      if (p.z()>0)
      {
        dist[4] = (fDz-p.z())/v.z();
      }
      else
      {   
        dist[4] = (-fDz-p.z())/v.z();
      }   
      if (dist[4]<-halfCarTolerance)
      {
        dist[4]=kInfinity;
      }
      else
      {
        if(dist[4]<halfCarTolerance)
        {
          if(p.z()>0)  { n=G4ThreeVector(0,0,1); }
          else         { n=G4ThreeVector(0,0,-1); }
          if (n.dot(v)<0) { dist[4]=0.; }
          else            { dist[4]=kInfinity; }
        }
        pt=p+dist[4]*v;
        if (Inside(pt)==kOutside)  { dist[4]=kInfinity; }
      }
    }
  }   
  G4double distmin = dist[0];
  for (i=1;i<5;i++)
  {
    if (dist[i] < distmin)  { distmin = dist[i]; }
  }
 
  if (distmin<halfCarTolerance)  { distmin=0.; }
 
  return distmin;
}    
  
// --------------------------------------------------------------------
 
G4double G4GenericTrap::DistanceToIn(const G4ThreeVector& p) const
{
  // Computes the closest distance from given point to this shape
 
#ifdef G4TESS_TEST
  if ( fTessellatedSolid )
  {
    return fTessellatedSolid->DistanceToIn(p);
  }  
#endif
 
  G4double safz = std::fabs(p.z())-fDz;
  if(safz<0) { safz=0; }
 
  G4int iseg;
  G4double safe  = safz;
  G4double safxy = safz;
 
  for (iseg=0; iseg<4; iseg++)
  { 
    safxy = SafetyToFace(p,iseg);
    if (safxy>safe)  { safe=safxy; }
  }
 
  return safe;
}
 
// --------------------------------------------------------------------
 
G4double
G4GenericTrap::SafetyToFace(const G4ThreeVector& p, const G4int iseg) const
{
  // Estimate distance to lateral plane defined by segment iseg in range [0,3]
  // Might be negative: plane seen only from inside
 
  G4ThreeVector p1,norm;
  G4double safe;
 
  p1=G4ThreeVector(fVertices[iseg].x(),fVertices[iseg].y(),-fDz);
  
  norm=NormalToPlane(p,iseg);
  safe = (p-p1).dot(norm); // Can be negative
 
  return safe;
}
 
// --------------------------------------------------------------------
 
G4double
G4GenericTrap::DistToTriangle(const G4ThreeVector& p,
                              const G4ThreeVector& v, const G4int ipl) const
{
  static const G4double halfCarTolerance=kCarTolerance*0.5;
 
  G4double xa=fVertices[ipl].x();
  G4double ya=fVertices[ipl].y();
  G4double xb=fVertices[ipl+4].x();
  G4double yb=fVertices[ipl+4].y();
  G4int j=(ipl+1)%4;
  G4double xc=fVertices[j].x();
  G4double yc=fVertices[j].y();
  G4double zab=2*fDz;
  G4double zac=0;
  
  if ( (std::fabs(xa-xc)+std::fabs(ya-yc)) < halfCarTolerance )
  {
    xc=fVertices[j+4].x();
    yc=fVertices[j+4].y();
    zac=2*fDz;
    zab=2*fDz;
 
    //Line case
    //
    if ( (std::fabs(xb-xc)+std::fabs(yb-yc)) < halfCarTolerance )
    {
      return kInfinity;
    }
  }
  G4double a=(yb-ya)*zac-(yc-ya)*zab;
  G4double b=(xc-xa)*zab-(xb-xa)*zac;
  G4double c=(xb-xa)*(yc-ya)-(xc-xa)*(yb-ya);
  G4double d=-xa*a-ya*b+fDz*c;
  G4double t=a*v.x()+b*v.y()+c*v.z();
 
  if (t!=0)
  {
    t=-(a*p.x()+b*p.y()+c*p.z()+d)/t;
  }
  if ( (t<halfCarTolerance) && (t>-halfCarTolerance) )
  {
    if (NormalToPlane(p,ipl).dot(v)<kCarTolerance)
    {
      t=kInfinity;
    }
    else
    {
      t=0;
    }
  }
  if (Inside(p+v*t) != kSurface)  { t=kInfinity; }
 
  return t;
} 
 
// --------------------------------------------------------------------
 
G4double G4GenericTrap::DistanceToOut(const G4ThreeVector& p,
                                      const G4ThreeVector& v,
                                      const G4bool calcNorm,
                                            G4bool* validNorm,
                                            G4ThreeVector* n) const
{
#ifdef G4TESS_TEST
  if ( fTessellatedSolid )
  { 
    return fTessellatedSolid->DistanceToOut(p, v, calcNorm, validNorm, n);
  }
#endif
 
  static const G4double halfCarTolerance=kCarTolerance*0.5;
 
  G4double distmin;
  G4bool lateral_cross = false;
  ESide side = kUndefined;
 
  if (calcNorm)  { *validNorm=true; } // All normals are valid
 
  if (v.z() < 0)
  {
    distmin=(-fDz-p.z())/v.z();
    if (calcNorm) { side=kMZ; *n=G4ThreeVector(0,0,-1); }
  }
  else
  {
    if (v.z() > 0)
    { 
      distmin = (fDz-p.z())/v.z(); 
      if (calcNorm) { side=kPZ; *n=G4ThreeVector(0,0,1); } 
    }
    else            { distmin = kInfinity; }
  }      
 
  G4double dz2 =0.5/fDz;
  G4double xa,xb,xc,xd;
  G4double ya,yb,yc,yd;
 
  for (G4int ipl=0; ipl<4; ipl++)
  {
    G4int j = (ipl+1)%4;
    xa=fVertices[ipl].x();
    ya=fVertices[ipl].y();
    xb=fVertices[ipl+4].x();
    yb=fVertices[ipl+4].y();
    xc=fVertices[j].x();
    yc=fVertices[j].y();
    xd=fVertices[4+j].x();
    yd=fVertices[4+j].y();
 
    if ( ((std::fabs(xb-xd)+std::fabs(yb-yd))<halfCarTolerance)
      || ((std::fabs(xa-xc)+std::fabs(ya-yc))<halfCarTolerance) )
    {
      G4double q=DistToTriangle(p,v,ipl) ;
      if ( (q>=0) && (q<distmin) )
      {
        distmin=q;
        lateral_cross=true;
        side=ESide(ipl+1);
      }
      continue;
    }
    G4double tx1 =dz2*(xb-xa);
    G4double ty1 =dz2*(yb-ya);
    G4double tx2 =dz2*(xd-xc);
    G4double ty2 =dz2*(yd-yc);
    G4double dzp =fDz+p.z();
    G4double xs1 =xa+tx1*dzp;
    G4double ys1 =ya+ty1*dzp;
    G4double xs2 =xc+tx2*dzp;
    G4double ys2 =yc+ty2*dzp;
    G4double dxs =xs2-xs1;
    G4double dys =ys2-ys1;
    G4double dtx =tx2-tx1;
    G4double dty =ty2-ty1;
    G4double a = (dtx*v.y()-dty*v.x()+(tx1*ty2-tx2*ty1)*v.z())*v.z();
    G4double b = dxs*v.y()-dys*v.x()+(dtx*p.y()-dty*p.x()+ty2*xs1-ty1*xs2
               + tx1*ys2-tx2*ys1)*v.z();
    G4double c=dxs*p.y()-dys*p.x()+xs1*ys2-xs2*ys1;
    G4double q=kInfinity;
 
    if (std::fabs(a) < kCarTolerance)
    {           
      if (std::fabs(b) < kCarTolerance) { continue; }
      q=-c/b;
         
      // Check for Point on the Surface
      //
      if ((q > -halfCarTolerance) && (q < distmin))
      {
        if (q < halfCarTolerance)
        {
          if (NormalToPlane(p,ipl).dot(v)<0.)  { continue; }
        }
        distmin =q;
        lateral_cross=true;
        side=ESide(ipl+1);
      }   
      continue;
    }
    G4double d=b*b-4*a*c;
    if (d >= 0.)
    {
      if (a > 0)  { q=0.5*(-b-std::sqrt(d))/a; }
      else        { q=0.5*(-b+std::sqrt(d))/a; }
 
      // Check for Point on the Surface
      //
      if (q > -halfCarTolerance )
      {
        if (q < distmin)
        {
          if(q < halfCarTolerance)
          {
            if (NormalToPlane(p,ipl).dot(v)<0.)  // Check second root
            {
              if (a > 0)  { q=0.5*(-b+std::sqrt(d))/a; }
              else        { q=0.5*(-b-std::sqrt(d))/a; }
              if (( q > halfCarTolerance) && (q < distmin))
              {
                distmin=q;
                lateral_cross = true;
                side=ESide(ipl+1);
              }
              continue;
            }
          }
          distmin = q;
          lateral_cross = true;
          side=ESide(ipl+1);
        }
      }
      else
      {
        if (a > 0)  { q=0.5*(-b+std::sqrt(d))/a; }
        else        { q=0.5*(-b-std::sqrt(d))/a; }
 
        // Check for Point on the Surface
        //
        if ((q > -halfCarTolerance) && (q < distmin))
        {
          if (q < halfCarTolerance)
          {
            if (NormalToPlane(p,ipl).dot(v)<0.)  // Check second root
            {
              if (a > 0)  { q=0.5*(-b-std::sqrt(d))/a; }
              else        { q=0.5*(-b+std::sqrt(d))/a; }
              if ( ( q > halfCarTolerance) && (q < distmin) )
              {
                distmin=q;
                lateral_cross = true;
                side=ESide(ipl+1);
              }
              continue;
            }  
          }
          distmin =q;
          lateral_cross = true;
          side=ESide(ipl+1);
        }   
      }
    }
  }
  if (!lateral_cross)  // Make sure that track crosses the top or bottom
  {
    if (distmin >= kInfinity)  { distmin=kCarTolerance; }
    G4ThreeVector pt=p+distmin*v;
    
    // Check if propagated point is in the polygon
    //
    G4int i=0;
    if (v.z()>0.) { i=4; }
    std::vector<G4TwoVector> xy;
    for ( G4int j=0; j<4; j++)  { xy.push_back(fVertices[i+j]); }
 
    // Check Inside
    //
    if (InsidePolygone(pt,xy)==kOutside)
    { 
      if(calcNorm)
      {
        if (v.z()>0) {side= kPZ; *n = G4ThreeVector(0,0,1);}
        else         { side=kMZ; *n = G4ThreeVector(0,0,-1);}
      } 
      return 0.;
    }
    else
    {
      if(v.z()>0) {side=kPZ;}
      else        {side=kMZ;}
    }
  }
 
  if (calcNorm)
  {
    G4ThreeVector pt=p+v*distmin;     
    switch (side)
    {
      case kXY0:
        *n=NormalToPlane(pt,0);
        break;
      case kXY1:
        *n=NormalToPlane(pt,1);
        break;
      case kXY2:
        *n=NormalToPlane(pt,2);
        break;
      case kXY3:
        *n=NormalToPlane(pt,3);
        break;
      case kPZ:
        *n=G4ThreeVector(0,0,1);
        break;
      case kMZ:
        *n=G4ThreeVector(0,0,-1);
        break;
      default:
        DumpInfo();
        std::ostringstream message;
        G4int oldprc = message.precision(16);
        message << "Undefined side for valid surface normal to solid." << G4endl
                << "Position:" << G4endl
                << "  p.x() = "   << p.x()/mm << " mm" << G4endl
                << "  p.y() = "   << p.y()/mm << " mm" << G4endl
                << "  p.z() = "   << p.z()/mm << " mm" << G4endl
                << "Direction:" << G4endl
                << "  v.x() = "   << v.x() << G4endl
                << "  v.y() = "   << v.y() << G4endl
                << "  v.z() = "   << v.z() << G4endl
                << "Proposed distance :" << G4endl
                << "  distmin = " << distmin/mm << " mm";
        message.precision(oldprc);
        G4Exception("G4GenericTrap::DistanceToOut(p,v,..)",
                    "GeomSolids1002", JustWarning, message);
        break;
     }
  }
 
  if (distmin<halfCarTolerance)  { distmin=0.; }
 
  return distmin;
}    
 
// --------------------------------------------------------------------
 
G4double G4GenericTrap::DistanceToOut(const G4ThreeVector& p) const
{
 
#ifdef G4TESS_TEST
  if ( fTessellatedSolid )
  { 
    return fTessellatedSolid->DistanceToOut(p);
  }  
#endif
 
  G4double safz = fDz-std::fabs(p.z());
  if (safz<0) { safz = 0; }
 
  G4double safe  = safz;
  G4double safxy = safz;
 
  for (G4int iseg=0; iseg<4; iseg++)
  { 
    safxy = std::fabs(SafetyToFace(p,iseg));
    if (safxy < safe)  { safe = safxy; }
  }
 
  return safe;
}    
 
// --------------------------------------------------------------------
 
G4bool G4GenericTrap::CalculateExtent(const EAxis pAxis,
                                      const G4VoxelLimits& pVoxelLimit,
                                      const G4AffineTransform& pTransform,
                                      G4double& pMin, G4double& pMax) const
{
#ifdef G4TESS_TEST
  if ( fTessellatedSolid )
  {
    return fTessellatedSolid->CalculateExtent(pAxis, pVoxelLimit,
                                              pTransform, pMin, pMax);
  }     
#endif 
 
  // Computes bounding vectors for a shape
  //
  G4double Dx,Dy;
  G4ThreeVector minVec = GetMinimumBBox();
  G4ThreeVector maxVec = GetMaximumBBox();
  Dx = 0.5*(maxVec.x()- minVec.x());
  Dy = 0.5*(maxVec.y()- minVec.y());
 
  if (!pTransform.IsRotated())
  {
    // Special case handling for unrotated shapes
    // Compute x/y/z mins and maxs respecting limits, with early returns
    // if outside limits. Then switch() on pAxis
    //
    G4double xoffset,xMin,xMax;
    G4double yoffset,yMin,yMax;
    G4double zoffset,zMin,zMax;
 
    xoffset=pTransform.NetTranslation().x();
    xMin=xoffset-Dx;
    xMax=xoffset+Dx;
    if (pVoxelLimit.IsXLimited())
    {
      if ( (xMin>pVoxelLimit.GetMaxXExtent()+kCarTolerance)
        || (xMax<pVoxelLimit.GetMinXExtent()-kCarTolerance) )
      {
        return false;
      }
      else
      {
        if (xMin<pVoxelLimit.GetMinXExtent())
        {
          xMin=pVoxelLimit.GetMinXExtent();
        }
        if (xMax>pVoxelLimit.GetMaxXExtent())
        {
          xMax=pVoxelLimit.GetMaxXExtent();
        }
      }
    }
 
    yoffset=pTransform.NetTranslation().y();
    yMin=yoffset-Dy;
    yMax=yoffset+Dy;
    if (pVoxelLimit.IsYLimited())
    {
      if ( (yMin>pVoxelLimit.GetMaxYExtent()+kCarTolerance)
        || (yMax<pVoxelLimit.GetMinYExtent()-kCarTolerance) )
      {
        return false;
      }
      else
      {
        if (yMin<pVoxelLimit.GetMinYExtent())
        {
          yMin=pVoxelLimit.GetMinYExtent();
        }
        if (yMax>pVoxelLimit.GetMaxYExtent())
        {
          yMax=pVoxelLimit.GetMaxYExtent();
        }
      }
    }
 
    zoffset=pTransform.NetTranslation().z();
    zMin=zoffset-fDz;
    zMax=zoffset+fDz;
    if (pVoxelLimit.IsZLimited())
    {
      if ( (zMin>pVoxelLimit.GetMaxZExtent()+kCarTolerance)
        || (zMax<pVoxelLimit.GetMinZExtent()-kCarTolerance) )
      {
        return false;
      }
      else
      {
        if (zMin<pVoxelLimit.GetMinZExtent())
        {
          zMin=pVoxelLimit.GetMinZExtent();
        }
        if (zMax>pVoxelLimit.GetMaxZExtent())
        {
          zMax=pVoxelLimit.GetMaxZExtent();
        }
      }
    }
 
    switch (pAxis)
    {
      case kXAxis:
        pMin = xMin;
        pMax = xMax;
        break;
      case kYAxis:
        pMin = yMin;
        pMax = yMax;
        break;
      case kZAxis:
        pMin = zMin;
        pMax = zMax;
        break;
      default:
        break;
    }
    pMin-=kCarTolerance;
    pMax+=kCarTolerance;
 
    return true;
  }
  else
  {
    // General rotated case - create and clip mesh to boundaries
 
    G4bool existsAfterClip=false;
    G4ThreeVectorList *vertices;
 
    pMin=+kInfinity;
    pMax=-kInfinity;
 
    // Calculate rotated vertex coordinates
    //
    vertices=CreateRotatedVertices(pTransform);
    ClipCrossSection(vertices,0,pVoxelLimit,pAxis,pMin,pMax);
    ClipCrossSection(vertices,4,pVoxelLimit,pAxis,pMin,pMax);
    ClipBetweenSections(vertices,0,pVoxelLimit,pAxis,pMin,pMax);
 
    if ( (pMin!=kInfinity) || (pMax!=-kInfinity) )
    {
      existsAfterClip=true;
    
      // Add 2*tolerance to avoid precision troubles
      //
      pMin-=kCarTolerance;
      pMax+=kCarTolerance;
    }
    else
    {
      // Check for case where completely enveloping clipping volume.
      // If point inside then we are confident that the solid completely
      // envelopes the clipping volume. Hence set min/max extents according
      // to clipping volume extents along the specified axis.
      //
      G4ThreeVector clipCentre(
              (pVoxelLimit.GetMinXExtent()+pVoxelLimit.GetMaxXExtent())*0.5,
              (pVoxelLimit.GetMinYExtent()+pVoxelLimit.GetMaxYExtent())*0.5,
              (pVoxelLimit.GetMinZExtent()+pVoxelLimit.GetMaxZExtent())*0.5);
 
      if (Inside(pTransform.Inverse().TransformPoint(clipCentre))!=kOutside)
      {
        existsAfterClip=true;
        pMin=pVoxelLimit.GetMinExtent(pAxis);
        pMax=pVoxelLimit.GetMaxExtent(pAxis);
      }
    }
    delete vertices;
    return existsAfterClip;
  }
}
 
// --------------------------------------------------------------------
 
G4ThreeVectorList*
G4GenericTrap::CreateRotatedVertices(const G4AffineTransform& pTransform) const
{
  // Create a List containing the transformed vertices
  // Ordering [0-3] -fDz cross section
  //          [4-7] +fDz cross section such that [0] is below [4],
  //                                             [1] below [5] etc.
  // Note: caller has deletion responsibility
 
  G4ThreeVector Min = GetMinimumBBox();
  G4ThreeVector Max = GetMaximumBBox();
 
  G4ThreeVectorList *vertices;
  vertices=new G4ThreeVectorList();
    
  if (vertices)
  {
    vertices->reserve(8);
    G4ThreeVector vertex0(Min.x(),Min.y(),Min.z());
    G4ThreeVector vertex1(Max.x(),Min.y(),Min.z());
    G4ThreeVector vertex2(Max.x(),Max.y(),Min.z());
    G4ThreeVector vertex3(Min.x(),Max.y(),Min.z());
    G4ThreeVector vertex4(Min.x(),Min.y(),Max.z());
    G4ThreeVector vertex5(Max.x(),Min.y(),Max.z());
    G4ThreeVector vertex6(Max.x(),Max.y(),Max.z());
    G4ThreeVector vertex7(Min.x(),Max.y(),Max.z());
 
    vertices->push_back(pTransform.TransformPoint(vertex0));
    vertices->push_back(pTransform.TransformPoint(vertex1));
    vertices->push_back(pTransform.TransformPoint(vertex2));
    vertices->push_back(pTransform.TransformPoint(vertex3));
    vertices->push_back(pTransform.TransformPoint(vertex4));
    vertices->push_back(pTransform.TransformPoint(vertex5));
    vertices->push_back(pTransform.TransformPoint(vertex6));
    vertices->push_back(pTransform.TransformPoint(vertex7));
  }
  else
  {
    G4Exception("G4GenericTrap::CreateRotatedVertices()", "FatalError",
                FatalException, "Out of memory - Cannot allocate vertices!");
  }
  return vertices;
}
  
// --------------------------------------------------------------------
 
G4GeometryType G4GenericTrap::GetEntityType() const
{
  return G4String("G4GenericTrap");
}
  
// --------------------------------------------------------------------
 
G4VSolid* G4GenericTrap::Clone() const
{
  return new G4GenericTrap(*this);
}
 
// --------------------------------------------------------------------
 
std::ostream& G4GenericTrap::StreamInfo(std::ostream& os) const
{
  G4int oldprc = os.precision(16);
  os << "-----------------------------------------------------------\n"
     << "    *** Dump for solid - " << GetName() << " *** \n"
     << "    =================================================== \n"
     << " Solid geometry type: " << GetEntityType()  << G4endl
     << "   half length Z: " << fDz/mm << " mm \n"
     << "   list of vertices:\n";
     
  for ( G4int i=0; i<fgkNofVertices; ++i )
  {
    os << std::setw(5) << "#" << i 
       << "   vx = " << fVertices[i].x()/mm << " mm" 
       << "   vy = " << fVertices[i].y()/mm << " mm" << G4endl;
  }
  os.precision(oldprc);
 
  return os;
} 
 
// --------------------------------------------------------------------
 
G4ThreeVector G4GenericTrap::GetPointOnSurface() const
{
 
#ifdef G4TESS_TEST
  if ( fTessellatedSolid )
  { 
    return fTessellatedSolid->GetPointOnSurface();
  }  
#endif
 
  G4ThreeVector point;
  G4TwoVector u,v,w;
  G4double rand,area,chose,cf,lambda0,lambda1,alfa,beta,zp;
  G4int ipl,j;
 
  std::vector<G4ThreeVector> vertices;
  for (G4int i=0; i<4;i++)
  {
    vertices.push_back(G4ThreeVector(fVertices[i].x(),fVertices[i].y(),-fDz));
  }
  for (G4int i=4; i<8;i++)
  {
    vertices.push_back(G4ThreeVector(fVertices[i].x(),fVertices[i].y(),fDz));
  }
 
  // Surface Area of Planes(only estimation for twisted)
  //
  G4double Surface0=GetFaceSurfaceArea(vertices[0],vertices[1],
                                       vertices[2],vertices[3]);//-fDz plane 
  G4double Surface1=GetFaceSurfaceArea(vertices[0],vertices[1],
                                       vertices[5],vertices[4]);// Lat plane
  G4double Surface2=GetFaceSurfaceArea(vertices[3],vertices[0],
                                       vertices[4],vertices[7]);// Lat plane
  G4double Surface3=GetFaceSurfaceArea(vertices[2],vertices[3],
                                       vertices[7],vertices[6]);// Lat plane
  G4double Surface4=GetFaceSurfaceArea(vertices[2],vertices[1],
                                       vertices[5],vertices[6]);// Lat plane
  G4double Surface5=GetFaceSurfaceArea(vertices[4],vertices[5],
                                       vertices[6],vertices[7]);// fDz plane
  rand = G4UniformRand();
  area = Surface0+Surface1+Surface2+Surface3+Surface4+Surface5;
  chose = rand*area;
 
  if ( ( chose < Surface0)
    || ( chose > (Surface0+Surface1+Surface2+Surface3+Surface4)) )
  {                                        // fDz or -fDz Plane
    ipl = G4int(G4UniformRand()*4);
    j = (ipl+1)%4;
    if(chose < Surface0)
    { 
      zp = -fDz;
      u = fVertices[ipl]; v = fVertices[j];
      w = fVertices[(ipl+3)%4]; 
    }
    else
    {
      zp = fDz;
      u = fVertices[ipl+4]; v = fVertices[j+4];
      w = fVertices[(ipl+3)%4+4]; 
    }
    alfa = G4UniformRand();
    beta = G4UniformRand();
    lambda1=alfa*beta;
    lambda0=alfa-lambda1;
    v = v-u;
    w = w-u;
    v = u+lambda0*v+lambda1*w;
  }
  else                                     // Lateral Plane Twisted or Not
  {
    if (chose < Surface0+Surface1) { ipl=0; }
    else if (chose < Surface0+Surface1+Surface2) { ipl=1; }
    else if (chose < Surface0+Surface1+Surface2+Surface3) { ipl=2; }
    else { ipl=3; }
    j = (ipl+1)%4;
    zp = -fDz+G4UniformRand()*2*fDz;
    cf = 0.5*(fDz-zp)/fDz;
    u = fVertices[ipl+4]+cf*( fVertices[ipl]-fVertices[ipl+4]);
    v = fVertices[j+4]+cf*(fVertices[j]-fVertices[j+4]); 
    v = u+(v-u)*G4UniformRand();
  }
  point=G4ThreeVector(v.x(),v.y(),zp);
 
  return point;
}
 
// --------------------------------------------------------------------
 
G4double G4GenericTrap::GetCubicVolume()
{
  if(fCubicVolume != 0.) {;}
  else   { fCubicVolume = G4VSolid::GetCubicVolume(); }
  return fCubicVolume;
}
 
// --------------------------------------------------------------------
 
G4double G4GenericTrap::GetSurfaceArea()
{
  if(fSurfaceArea != 0.) {;}
  else
  {
    std::vector<G4ThreeVector> vertices;
    for (G4int i=0; i<4;i++)
    {
      vertices.push_back(G4ThreeVector(fVertices[i].x(),fVertices[i].y(),-fDz));
    }
    for (G4int i=4; i<8;i++)
    {
      vertices.push_back(G4ThreeVector(fVertices[i].x(),fVertices[i].y(),fDz));
    }
 
    // Surface Area of Planes(only estimation for twisted)
    //
    G4double fSurface0=GetFaceSurfaceArea(vertices[0],vertices[1],
                                          vertices[2],vertices[3]);//-fDz plane
    G4double fSurface1=GetFaceSurfaceArea(vertices[0],vertices[1],
                                          vertices[5],vertices[4]);// Lat plane
    G4double fSurface2=GetFaceSurfaceArea(vertices[3],vertices[0],
                                          vertices[4],vertices[7]);// Lat plane 
    G4double fSurface3=GetFaceSurfaceArea(vertices[2],vertices[3],
                                          vertices[7],vertices[6]);// Lat plane
    G4double fSurface4=GetFaceSurfaceArea(vertices[2],vertices[1],
                                          vertices[5],vertices[6]);// Lat plane
    G4double fSurface5=GetFaceSurfaceArea(vertices[4],vertices[5],
                                          vertices[6],vertices[7]);// fDz plane 
 
    // Total Surface Area
    //
    if(!fIsTwisted)
    {
      fSurfaceArea = fSurface0+fSurface1+fSurface2
                   + fSurface3+fSurface4+fSurface5;
    }
    else
    {
      fSurfaceArea = G4VSolid::GetSurfaceArea();
    }
  }
  return fSurfaceArea;
}
 
// --------------------------------------------------------------------
 
G4double G4GenericTrap::GetFaceSurfaceArea(const G4ThreeVector& p0,
                                           const G4ThreeVector& p1, 
                                           const G4ThreeVector& p2,
                                           const G4ThreeVector& p3) const
{
  // Auxiliary method for Get Surface Area of Face
  
  G4double aOne, aTwo;
  G4ThreeVector t, u, v, w, Area, normal;
 
  t = p2 - p1;
  u = p0 - p1;
  v = p2 - p3;
  w = p0 - p3;
  
  Area = w.cross(v);
  aOne = 0.5*Area.mag();
  
  Area = t.cross(u);
  aTwo = 0.5*Area.mag();
 
  return aOne + aTwo;
}
 
// --------------------------------------------------------------------
 
G4bool G4GenericTrap::ComputeIsTwisted() 
{
  // Computes tangents of twist angles (angles between projections on XY plane 
  // of corresponding -dz +dz edges). 
 
  G4bool twisted = false;
  G4double dx1, dy1, dx2, dy2;
  G4int nv = fgkNofVertices/2;
 
  for ( G4int i=0; i<4; i++ )
  {
    dx1 = fVertices[(i+1)%nv].x()-fVertices[i].x();
    dy1 = fVertices[(i+1)%nv].y()-fVertices[i].y();
    if ( (dx1 == 0) && (dy1 == 0) ) { continue; }
 
    dx2 = fVertices[nv+(i+1)%nv].x()-fVertices[nv+i].x();
    dy2 = fVertices[nv+(i+1)%nv].y()-fVertices[nv+i].y();
 
    if ( dx2 == 0 && dy2 == 0 ) { continue; }
    G4double twist_angle = std::fabs(dy1*dx2 - dx1*dy2);        
    if ( twist_angle < fgkTolerance ) { continue; }
    twisted = true;
    SetTwistAngle(i,twist_angle);
 
    // Check on big angles, potentially navigation problem
 
    twist_angle = std::acos( (dx1*dx2 + dy1*dy2)
                           / (std::sqrt(dx1*dx1+dy1*dy1)
                             * std::sqrt(dx2*dx2+dy2*dy2)) );
   
    if ( std::fabs(twist_angle) > 0.5*pi+kCarTolerance )
    {
      std::ostringstream message;
      message << "Twisted Angle is bigger than 90 degrees - " << GetName()
              << G4endl
              << "     Potential problem of malformed Solid !" << G4endl
              << "     TwistANGLE = " << twist_angle
              << "*rad  for lateral plane N= " << i;
      G4Exception("G4GenericTrap::ComputeIsTwisted()", "GeomSolids1002",
                  JustWarning, message);
    }
  }
 
  return twisted;
}
 
// --------------------------------------------------------------------
 
G4bool G4GenericTrap::CheckOrder(const std::vector<G4TwoVector>& vertices) const
{
  // Test if the vertices are in a clockwise order, if not reorder them.
  // Also test if they're well defined without crossing opposite segments
 
  G4bool clockwise_order=true;
  G4double sum1 = 0.;
  G4double sum2 = 0.;
  G4int j;
 
  for (G4int i=0; i<4; i++)
  {
    j = (i+1)%4;
    sum1 += vertices[i].x()*vertices[j].y() - vertices[j].x()*vertices[i].y();
    sum2 += vertices[i+4].x()*vertices[j+4].y()
          - vertices[j+4].x()*vertices[i+4].y();
  }
  if (sum1*sum2 < -fgkTolerance)
  {
     std::ostringstream message;
     message << "Lower/upper faces defined with opposite clockwise - "
             << GetName();
     G4Exception("G4GenericTrap::CheckOrder()", "GeomSolids0002",
                FatalException, message);
   }
   
   if ((sum1 > 0.)||(sum2 > 0.))
   {
     std::ostringstream message;
     message << "Vertices must be defined in clockwise XY planes - "
             << GetName();
     G4Exception("G4GenericTrap::CheckOrder()", "GeomSolids1001",
                 JustWarning,message, "Re-ordering...");
     clockwise_order = false;
   }
 
   // Check for illegal crossings
   //
   G4bool illegal_cross = false;
   illegal_cross = IsSegCrossingZ(vertices[0],vertices[4],
                                  vertices[1],vertices[5]);
     
   if (!illegal_cross)
   {
     illegal_cross = IsSegCrossingZ(vertices[2],vertices[6],
                                    vertices[3],vertices[7]);
   }
   // +/- dZ planes
   if (!illegal_cross)
   {
     illegal_cross = IsSegCrossing(vertices[0],vertices[1],
                                   vertices[2],vertices[3]);
   }
   if (!illegal_cross)
   {
     illegal_cross = IsSegCrossing(vertices[0],vertices[3],
                                   vertices[1],vertices[2]);
   }
   if (!illegal_cross)
   {
     illegal_cross = IsSegCrossing(vertices[4],vertices[5],
                                   vertices[6],vertices[7]);
   }
   if (!illegal_cross)
   {
     illegal_cross = IsSegCrossing(vertices[4],vertices[7],
                                   vertices[5],vertices[6]);
   }
 
   if (illegal_cross)
   {
      std::ostringstream message;
      message << "Malformed polygone with opposite sides - " << GetName();
      G4Exception("G4GenericTrap::CheckOrderAndSetup()",
                  "GeomSolids0002", FatalException, message);
   }
   return clockwise_order;
}
 
// --------------------------------------------------------------------
 
void G4GenericTrap::ReorderVertices(std::vector<G4ThreeVector>& vertices) const
{
  // Reorder the vector of vertices 
 
  std::vector<G4ThreeVector> oldVertices(vertices);
 
  for ( G4int i=0; i < G4int(oldVertices.size()); ++i )
  {
    vertices[i] = oldVertices[oldVertices.size()-1-i];
  }  
} 
 
// --------------------------------------------------------------------
 
G4bool
G4GenericTrap::IsSegCrossing(const G4TwoVector& a, const G4TwoVector& b, 
                             const G4TwoVector& c, const G4TwoVector& d) const
{ 
  // Check if segments [A,B] and [C,D] are crossing
 
  G4bool stand1 = false;
  G4bool stand2 = false;
  G4double dx1,dx2,xm=0.,ym=0.,a1=0.,a2=0.,b1=0.,b2=0.;
  dx1=(b-a).x();
  dx2=(d-c).x();
 
  if( std::fabs(dx1) < fgkTolerance )  { stand1 = true; }
  if( std::fabs(dx2) < fgkTolerance )  { stand2 = true; }
  if (!stand1)
  {
    a1 = (b.x()*a.y()-a.x()*b.y())/dx1;
    b1 = (b-a).y()/dx1;
  }
  if (!stand2)
  {
    a2 = (d.x()*c.y()-c.x()*d.y())/dx2;
    b2 = (d-c).y()/dx2;
  }   
  if (stand1 && stand2)
  {
    // Segments parallel and vertical
    //
    if (std::fabs(a.x()-c.x())<fgkTolerance)
    {
       // Check if segments are overlapping
       //
       if ( ((c.y()-a.y())*(c.y()-b.y())<-fgkTolerance)
         || ((d.y()-a.y())*(d.y()-b.y())<-fgkTolerance)
         || ((a.y()-c.y())*(a.y()-d.y())<-fgkTolerance)
         || ((b.y()-c.y())*(b.y()-d.y())<-fgkTolerance) )  { return true; }
 
       return false;
    }
    // Different x values
    //
    return false;
  }
   
  if (stand1)    // First segment vertical
  {
    xm = a.x();
    ym = a2+b2*xm; 
  }
  else
  {
    if (stand2)  // Second segment vertical
    {
      xm = c.x();
      ym = a1+b1*xm;
    }
    else  // Normal crossing
    {
      if (std::fabs(b1-b2) < fgkTolerance)
      {
        // Parallel segments, are they aligned
        //
        if (std::fabs(c.y()-(a1+b1*c.x())) > fgkTolerance)  { return false; }
 
        // Aligned segments, are they overlapping
        //
        if ( ((c.x()-a.x())*(c.x()-b.x())<-fgkTolerance)
          || ((d.x()-a.x())*(d.x()-b.x())<-fgkTolerance)
          || ((a.x()-c.x())*(a.x()-d.x())<-fgkTolerance)
          || ((b.x()-c.x())*(b.x()-d.x())<-fgkTolerance) )  { return true; }
 
        return false;
      }
      xm = (a1-a2)/(b2-b1);
      ym = (a1*b2-a2*b1)/(b2-b1);
    }
  }
 
  // Check if crossing point is both between A,B and C,D
  //
  G4double check = (xm-a.x())*(xm-b.x())+(ym-a.y())*(ym-b.y());
  if (check > -fgkTolerance)  { return false; }
  check = (xm-c.x())*(xm-d.x())+(ym-c.y())*(ym-d.y());
  if (check > -fgkTolerance)  { return false; }
 
  return true;
}
 
// --------------------------------------------------------------------
 
G4bool
G4GenericTrap::IsSegCrossingZ(const G4TwoVector& a, const G4TwoVector& b, 
                              const G4TwoVector& c, const G4TwoVector& d) const
{ 
  // Check if segments [A,B] and [C,D] are crossing when
  // A and C are on -dZ and B and D are on +dZ
 
  // Calculate the Intersection point between two lines in 3D
  //
  G4ThreeVector temp1,temp2;
  G4ThreeVector v1,v2,p1,p2,p3,p4,dv;
  G4double q,det;
  p1=G4ThreeVector(a.x(),a.y(),-fDz);
  p2=G4ThreeVector(c.x(),c.y(),-fDz);
  p3=G4ThreeVector(b.x(),b.y(),fDz);
  p4=G4ThreeVector(d.x(),d.y(),fDz);
  v1=p3-p1;
  v2=p4-p2;
  dv=p2-p1;
 
  // In case of Collapsed Vertices No crossing
  //
  if( (std::fabs(dv.x()) < kCarTolerance )&&
      (std::fabs(dv.y()) < kCarTolerance ) )  { return false; }
    
  if( (std::fabs((p4-p3).x()) < kCarTolerance )&&
      (std::fabs((p4-p3).y()) < kCarTolerance ) )  { return false; }
 
  // First estimate if Intersection is possible( if det is 0)
  //
  det = dv.x()*v1.y()*v2.z()+dv.y()*v1.z()*v2.x()
      - dv.x()*v1.z()*v2.y()-dv.y()*v1.x()*v2.z();
   
  if (std::fabs(det)<kCarTolerance)  //Intersection
  {
    temp1 = v1.cross(v2);
    temp2 = (p2-p1).cross(v2);
    if (temp1.dot(temp2) < 0)  { return false; } // intersection negative
    q = temp1.mag();
 
    if ( q < kCarTolerance )  { return false; }  // parallel lines
    q = ((dv).cross(v2)).mag()/q;
   
    if(q < 1.-kCarTolerance)  { return true; }
  }
  return false;
}
 
// --------------------------------------------------------------------
 
G4VFacet*
G4GenericTrap::MakeDownFacet(const std::vector<G4ThreeVector>& fromVertices, 
                             G4int ind1, G4int ind2, G4int ind3) const 
{
  // Create a triangular facet from the polygon points given by indices
  // forming the down side ( the normal goes in -z)
  // Do not create facet if 2 vertices are the same
 
  if ( (fromVertices[ind1] == fromVertices[ind2]) ||
       (fromVertices[ind2] == fromVertices[ind3]) ||
       (fromVertices[ind1] == fromVertices[ind3]) )  { return 0; }
 
  std::vector<G4ThreeVector> vertices;
  vertices.push_back(fromVertices[ind1]);
  vertices.push_back(fromVertices[ind2]);
  vertices.push_back(fromVertices[ind3]);
  
  // first vertex most left
  //
  G4ThreeVector cross=(vertices[1]-vertices[0]).cross(vertices[2]-vertices[1]);
 
  if ( cross.z() > 0.0 )
  {
    // Should not happen, as vertices should have been reordered at this stage
 
    std::ostringstream message;
    message << "Vertices in wrong order - " << GetName();
    G4Exception("G4GenericTrap::MakeDownFacet", "GeomSolids0002",
                FatalException, message);
  }
  
  return new G4TriangularFacet(vertices[0], vertices[1], vertices[2], ABSOLUTE);
}
 
// --------------------------------------------------------------------
 
G4VFacet*
G4GenericTrap::MakeUpFacet(const std::vector<G4ThreeVector>& fromVertices, 
                           G4int ind1, G4int ind2, G4int ind3) const     
{
  // Create a triangular facet from the polygon points given by indices
  // forming the upper side ( z>0 )
 
  // Do not create facet if 2 vertices are the same
  //
  if ( (fromVertices[ind1] == fromVertices[ind2]) ||
       (fromVertices[ind2] == fromVertices[ind3]) ||
       (fromVertices[ind1] == fromVertices[ind3]) )  { return 0; }
 
  std::vector<G4ThreeVector> vertices;
  vertices.push_back(fromVertices[ind1]);
  vertices.push_back(fromVertices[ind2]);
  vertices.push_back(fromVertices[ind3]);
  
  // First vertex most left
  //
  G4ThreeVector cross=(vertices[1]-vertices[0]).cross(vertices[2]-vertices[1]);
 
  if ( cross.z() < 0.0 )
  {
    // Should not happen, as vertices should have been reordered at this stage
 
    std::ostringstream message;
    message << "Vertices in wrong order - " << GetName();
    G4Exception("G4GenericTrap::MakeUpFacet", "GeomSolids0002",
                FatalException, message);
  }
  
  return new G4TriangularFacet(vertices[0], vertices[1], vertices[2], ABSOLUTE);
}      
 
// --------------------------------------------------------------------
 
G4VFacet*
G4GenericTrap::MakeSideFacet(const G4ThreeVector& downVertex0,
                             const G4ThreeVector& downVertex1,
                             const G4ThreeVector& upVertex1,
                             const G4ThreeVector& upVertex0) const      
{
  // Creates a triangular facet from the polygon points given by indices
  // forming the upper side ( z>0 )
 
  if ( (downVertex0 == downVertex1) && (upVertex0 == upVertex1) )
  {
    return 0;
  }
 
  if ( downVertex0 == downVertex1 )
  {
    return new G4TriangularFacet(downVertex0, upVertex1, upVertex0, ABSOLUTE);
  }
 
  if ( upVertex0 == upVertex1 )
  {
    return new G4TriangularFacet(downVertex0, downVertex1, upVertex0, ABSOLUTE);
  }
 
  return new G4QuadrangularFacet(downVertex0, downVertex1, 
                                 upVertex1, upVertex0, ABSOLUTE);   
}    
 
// --------------------------------------------------------------------
 
G4TessellatedSolid* G4GenericTrap::CreateTessellatedSolid() const
{
  // 3D vertices
  //
  G4int nv = fgkNofVertices/2;
  std::vector<G4ThreeVector> downVertices;
  for ( G4int i=0; i<nv; i++ )
  { 
    downVertices.push_back(G4ThreeVector(fVertices[i].x(),
                                         fVertices[i].y(), -fDz));
  }
 
  std::vector<G4ThreeVector> upVertices;
  for ( G4int i=nv; i<2*nv; i++ )
  { 
    upVertices.push_back(G4ThreeVector(fVertices[i].x(),
                                       fVertices[i].y(), fDz));
  }
                                         
  // Reorder vertices if they are not ordered anti-clock wise
  //
  G4ThreeVector cross 
    = (downVertices[1]-downVertices[0]).cross(downVertices[2]-downVertices[1]);
   G4ThreeVector cross1 
    = (upVertices[1]-upVertices[0]).cross(upVertices[2]-upVertices[1]);
  if ( (cross.z() > 0.0) || (cross1.z() > 0.0) )
  {
    ReorderVertices(downVertices);
    ReorderVertices(upVertices);
  }
    
  G4TessellatedSolid* tessellatedSolid = new G4TessellatedSolid(GetName());
  
  G4VFacet* facet = 0;
  facet = MakeDownFacet(downVertices, 0, 1, 2);
  if (facet)  { tessellatedSolid->AddFacet( facet ); }
  facet = MakeDownFacet(downVertices, 0, 2, 3);
  if (facet)  { tessellatedSolid->AddFacet( facet ); }
  facet = MakeUpFacet(upVertices, 0, 2, 1);
  if (facet)  { tessellatedSolid->AddFacet( facet ); }
  facet = MakeUpFacet(upVertices, 0, 3, 2);
  if (facet)  { tessellatedSolid->AddFacet( facet ); }
 
  // The quadrangular sides
  //
  for ( G4int i = 0; i < nv; ++i )
  {
    G4int j = (i+1) % nv;
    facet = MakeSideFacet(downVertices[j], downVertices[i], 
                          upVertices[i], upVertices[j]);
 
    if ( facet )  { tessellatedSolid->AddFacet( facet ); }
  }
 
  tessellatedSolid->SetSolidClosed(true);
 
  return tessellatedSolid;
}  
 
// --------------------------------------------------------------------
 
void G4GenericTrap::ComputeBBox() 
{
  // Computes bounding box for a shape.
 
  G4double minX, maxX, minY, maxY;
  minX = maxX = fVertices[0].x();
  minY = maxY = fVertices[0].y();
   
  for (G4int i=1; i< fgkNofVertices; i++)
  {
    if (minX>fVertices[i].x()) { minX=fVertices[i].x(); }
    if (maxX<fVertices[i].x()) { maxX=fVertices[i].x(); }
    if (minY>fVertices[i].y()) { minY=fVertices[i].y(); }
    if (maxY<fVertices[i].y()) { maxY=fVertices[i].y(); }
  }
  fMinBBoxVector = G4ThreeVector(minX,minY,-fDz);
  fMaxBBoxVector = G4ThreeVector(maxX,maxY, fDz);
}
 
// --------------------------------------------------------------------
 
G4Polyhedron* G4GenericTrap::GetPolyhedron () const
{
 
#ifdef G4TESS_TEST
  if ( fTessellatedSolid )
  { 
    return fTessellatedSolid->GetPolyhedron();
  }
#endif  
  
  if ( (!fpPolyhedron)
    || (fpPolyhedron->GetNumberOfRotationStepsAtTimeOfCreation() !=
        fpPolyhedron->GetNumberOfRotationSteps()) )
  {
    delete fpPolyhedron;
    fpPolyhedron = CreatePolyhedron();
  }
  return fpPolyhedron;
}    
 
// --------------------------------------------------------------------
 
void G4GenericTrap::DescribeYourselfTo(G4VGraphicsScene& scene) const
{
 
#ifdef G4TESS_TEST
  if ( fTessellatedSolid )
  { 
    return fTessellatedSolid->DescribeYourselfTo(scene);
  }
#endif  
  
  scene.AddSolid(*this);
}
 
// --------------------------------------------------------------------
 
G4VisExtent G4GenericTrap::GetExtent() const
{
  // Computes bounding vectors for the shape
 
#ifdef G4TESS_TEST
  if ( fTessellatedSolid )
  { 
    return fTessellatedSolid->GetExtent();
  } 
#endif
   
  G4double Dx,Dy;
  G4ThreeVector minVec = GetMinimumBBox();
  G4ThreeVector maxVec = GetMaximumBBox();
  Dx = 0.5*(maxVec.x()- minVec.x());
  Dy = 0.5*(maxVec.y()- minVec.y());
 
  return G4VisExtent (-Dx, Dx, -Dy, Dy, -fDz, fDz); 
}    
 
// --------------------------------------------------------------------
 
G4Polyhedron* G4GenericTrap::CreatePolyhedron() const
{
 
#ifdef G4TESS_TEST
  if ( fTessellatedSolid )
  { 
    return fTessellatedSolid->CreatePolyhedron();
  }  
#endif 
  
  // Approximation of Twisted Side
  // Construct extra Points, if Twisted Side
  //
  G4PolyhedronArbitrary* polyhedron;
  size_t nVertices, nFacets;
 
  G4int subdivisions=0;
  G4int i;
  if(fIsTwisted)
  {
    if ( GetVisSubdivisions()!= 0 )
    {
      subdivisions=GetVisSubdivisions();
    }
    else
    {
      // Estimation of Number of Subdivisions for smooth visualisation
      //
      G4double maxTwist=0.;
      for(i=0; i<4; i++)
      {
        if(GetTwistAngle(i)>maxTwist) { maxTwist=GetTwistAngle(i); }
      }
 
      // Computes bounding vectors for the shape
      //
      G4double Dx,Dy;
      G4ThreeVector minVec = GetMinimumBBox();
      G4ThreeVector maxVec = GetMaximumBBox();
      Dx = 0.5*(maxVec.x()- minVec.y());
      Dy = 0.5*(maxVec.y()- minVec.y());
      if (Dy > Dx)  { Dx=Dy; }
    
      subdivisions=8*G4int(maxTwist/(Dx*Dx*Dx)*fDz);
      if (subdivisions<4)  { subdivisions=4; }
      if (subdivisions>30) { subdivisions=30; }
    }
  }
  G4int sub4=4*subdivisions;
  nVertices = 8+subdivisions*4;
  nFacets = 6+subdivisions*4;
  G4double cf=1./(subdivisions+1);
  polyhedron = new G4PolyhedronArbitrary (nVertices, nFacets);
 
  // Add Vertex
  //
  for (i=0;i<4;i++)
  {
    polyhedron->AddVertex(G4ThreeVector(fVertices[i].x(),
                                        fVertices[i].y(),-fDz));
  }
  for( i=0;i<subdivisions;i++)
  {
    for(G4int j=0;j<4;j++)
    {
      G4TwoVector u=fVertices[j]+cf*(i+1)*( fVertices[j+4]-fVertices[j]);
      polyhedron->AddVertex(G4ThreeVector(u.x(),u.y(),-fDz+cf*2*fDz*(i+1)));
    }    
  }
  for (i=4;i<8;i++)
  {
    polyhedron->AddVertex(G4ThreeVector(fVertices[i].x(),
                                        fVertices[i].y(),fDz));
  }
 
  // Add Facets
  //
  polyhedron->AddFacet(1,4,3,2);  //Z-plane
  for (i=0;i<subdivisions+1;i++)
  {
    G4int is=i*4;
    polyhedron->AddFacet(5+is,8+is,4+is,1+is);
    polyhedron->AddFacet(8+is,7+is,3+is,4+is);
    polyhedron->AddFacet(7+is,6+is,2+is,3+is);
    polyhedron->AddFacet(6+is,5+is,1+is,2+is); 
  }
  polyhedron->AddFacet(5+sub4,6+sub4,7+sub4,8+sub4);  //Z-plane
 
  polyhedron->SetReferences();
  polyhedron->InvertFacets();
 
  return (G4Polyhedron*) polyhedron;
}
 
// --------------------------------------------------------------------
 
G4NURBS*  G4GenericTrap::CreateNURBS() const
{
#ifdef G4TESS_TEST
  if ( fTessellatedSolid )
  { 
    return fTessellatedSolid->CreateNURBS();
  }
#endif
 
  // Computes bounding vectors for the shape
  //
  G4double Dx,Dy;
  G4ThreeVector minVec = GetMinimumBBox();
  G4ThreeVector maxVec = GetMaximumBBox();
  Dx = 0.5*(maxVec.x()- minVec.y());
  Dy = 0.5*(maxVec.y()- minVec.y());
 
  return new G4NURBSbox (Dx, Dy, fDz);
}    
 
// --------------------------------------------------------------------