G4Tet.cc

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//
// ********************************************************************
// * License and Disclaimer                                           *
// *                                                                  *
// * The  Geant4 software  is  copyright of the Copyright Holders  of *
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// *                                                                  *
// * Neither the authors of this software system, nor their employing *
// * institutes,nor the agencies providing financial support for this *
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// * regarding  this  software system or assume any liability for its *
// * use.  Please see the license in the file  LICENSE  and URL above *
// * for the full disclaimer and the limitation of liability.         *
// *                                                                  *
// * This  code  implementation is the  intellectual property  of the *
// * Vanderbilt University Free Electron Laser Center                 *
// * Vanderbilt University, Nashville, TN, USA                        *
// * Development supported by:                                        *
// * United States MFEL program  under grant FA9550-04-1-0045         *
// * and NASA under contract number NNG04CT05P                        *
// * Written by Marcus H. Mendenhall and Robert A. Weller.            *
// *                                                                  *
// * Contributed to the Geant4 Core, January, 2005.                   *
// *                                                                  *
// ********************************************************************
//
// $Id$
//
// class G4Tet
//
// Implementation for G4Tet class
//
// History:
//
//  20040903 - Marcus Mendenhall, created G4Tet
//  20041101 - Marcus Mendenhall, optimized constant dot products with
//             fCdotNijk values
//  20041101 - MHM removed tracking error by clipping DistanceToOut to 0
//             for surface cases
//  20041101 - MHM many speed optimizations in if statements
//  20041101 - MHM changed vdotn comparisons to 1e-12 instead of 0.0 to
//             avoid nearly-parallel problems
//  20041102 - MHM Added extra distance into solid to DistanceToIn(p,v)
//             hit testing
//  20041102 - MHM added ability to check for degeneracy without throwing
//             G4Exception
//  20041103 - MHM removed many unused variables from class
//  20040803 - Dionysios Anninos, added GetPointOnSurface() method
//  20061112 - MHM added code for G4VSolid GetSurfaceArea()
//  20100920 - Gabriele Cosmo added copy-ctor and operator=()
//
// --------------------------------------------------------------------
 
#include "G4Tet.hh"
 
const char G4Tet::CVSVers[]="$Id: G4Tet.cc,v 1.16 2010-10-20 08:54:18 gcosmo Exp $";
 
#include "G4VoxelLimits.hh"
#include "G4AffineTransform.hh"
 
#include "G4VPVParameterisation.hh"
 
#include "Randomize.hh"
 
#include "G4VGraphicsScene.hh"
#include "G4Polyhedron.hh"
#include "G4NURBS.hh"
#include "G4NURBSbox.hh"
#include "G4VisExtent.hh"
 
#include "G4ThreeVector.hh"
 
#include <cmath>
 
using namespace CLHEP;
 
////////////////////////////////////////////////////////////////////////
//
// Constructor - create a tetrahedron
// This class is implemented separately from general polyhedra,
// because the simplex geometry can be computed very quickly,
// which may become important in situations imported from mesh generators,
// in which a very large number of G4Tets are created.
// A Tet has all of its geometrical information precomputed
 
G4Tet::G4Tet(const G4String& pName,
                   G4ThreeVector anchor,
                   G4ThreeVector p2,
                   G4ThreeVector p3,
                   G4ThreeVector p4, G4bool *degeneracyFlag)
  : G4VSolid(pName), fpPolyhedron(0), warningFlag(0)
{
  // fV<x><y> is vector from vertex <y> to vertex <x>
  //
  G4ThreeVector fV21=p2-anchor;
  G4ThreeVector fV31=p3-anchor;
  G4ThreeVector fV41=p4-anchor;
 
  // make sure this is a correctly oriented set of points for the tetrahedron
  //
  G4double signed_vol=fV21.cross(fV31).dot(fV41);
  if(signed_vol<0.0)
  {
    G4ThreeVector temp(p4);
    p4=p3;
    p3=temp;
    temp=fV41;
    fV41=fV31;
    fV31=temp; 
  }
  fCubicVolume = std::fabs(signed_vol) / 6.;
 
  G4ThreeVector fV24=p2-p4;
  G4ThreeVector fV43=p4-p3;
  G4ThreeVector fV32=p3-p2;
 
  fXMin=std::min(std::min(std::min(anchor.x(), p2.x()),p3.x()),p4.x());
  fXMax=std::max(std::max(std::max(anchor.x(), p2.x()),p3.x()),p4.x());
  fYMin=std::min(std::min(std::min(anchor.y(), p2.y()),p3.y()),p4.y());
  fYMax=std::max(std::max(std::max(anchor.y(), p2.y()),p3.y()),p4.y());
  fZMin=std::min(std::min(std::min(anchor.z(), p2.z()),p3.z()),p4.z());
  fZMax=std::max(std::max(std::max(anchor.z(), p2.z()),p3.z()),p4.z());
 
  fDx=(fXMax-fXMin)*0.5; fDy=(fYMax-fYMin)*0.5; fDz=(fZMax-fZMin)*0.5;
 
  fMiddle=G4ThreeVector(fXMax+fXMin, fYMax+fYMin, fZMax+fZMin)*0.5;
  fMaxSize=std::max(std::max(std::max((anchor-fMiddle).mag(),
                                      (p2-fMiddle).mag()),
                             (p3-fMiddle).mag()),
                    (p4-fMiddle).mag());
 
  G4bool degenerate=std::fabs(signed_vol) < 1e-9*fMaxSize*fMaxSize*fMaxSize;
 
  if(degeneracyFlag) *degeneracyFlag=degenerate;
  else if (degenerate)
  {
    G4Exception("G4Tet::G4Tet()", "GeomSolids0002", FatalException,
                "Degenerate tetrahedron not allowed.");
  }
 
  fTol=1e-9*(std::fabs(fXMin)+std::fabs(fXMax)+std::fabs(fYMin)
            +std::fabs(fYMax)+std::fabs(fZMin)+std::fabs(fZMax));
  //fTol=kCarTolerance;
 
  fAnchor=anchor;
  fP2=p2;
  fP3=p3;
  fP4=p4;
 
  G4ThreeVector fCenter123=(anchor+p2+p3)*(1.0/3.0); // face center
  G4ThreeVector fCenter134=(anchor+p4+p3)*(1.0/3.0);
  G4ThreeVector fCenter142=(anchor+p4+p2)*(1.0/3.0);
  G4ThreeVector fCenter234=(p2+p3+p4)*(1.0/3.0);
 
  // compute area of each triangular face by cross product
  // and sum for total surface area
 
  G4ThreeVector normal123=fV31.cross(fV21);
  G4ThreeVector normal134=fV41.cross(fV31);
  G4ThreeVector normal142=fV21.cross(fV41);
  G4ThreeVector normal234=fV32.cross(fV43);
 
  fSurfaceArea=(
      normal123.mag()+
      normal134.mag()+
      normal142.mag()+
      normal234.mag()
  )/2.0;
 
  fNormal123=normal123.unit();
  fNormal134=normal134.unit();
  fNormal142=normal142.unit();
  fNormal234=normal234.unit();
 
  fCdotN123=fCenter123.dot(fNormal123);
  fCdotN134=fCenter134.dot(fNormal134);
  fCdotN142=fCenter142.dot(fNormal142);
  fCdotN234=fCenter234.dot(fNormal234);
}
 
//////////////////////////////////////////////////////////////////////////
//
// Fake default constructor - sets only member data and allocates memory
//                            for usage restricted to object persistency.
//
G4Tet::G4Tet( __void__& a )
  : G4VSolid(a), fCubicVolume(0.), fSurfaceArea(0.), fpPolyhedron(0),
    fAnchor(0,0,0), fP2(0,0,0), fP3(0,0,0), fP4(0,0,0), fMiddle(0,0,0),
    fNormal123(0,0,0), fNormal142(0,0,0), fNormal134(0,0,0),
    fNormal234(0,0,0), warningFlag(0),
    fCdotN123(0.), fCdotN142(0.), fCdotN134(0.), fCdotN234(0.),
    fXMin(0.), fXMax(0.), fYMin(0.), fYMax(0.), fZMin(0.), fZMax(0.),
    fDx(0.), fDy(0.), fDz(0.), fTol(0.), fMaxSize(0.)
{
}
 
//////////////////////////////////////////////////////////////////////////
//
// Destructor
 
G4Tet::~G4Tet()
{
  delete fpPolyhedron;
}
 
///////////////////////////////////////////////////////////////////////////////
//
// Copy constructor
 
G4Tet::G4Tet(const G4Tet& rhs)
  : G4VSolid(rhs),
    fCubicVolume(rhs.fCubicVolume), fSurfaceArea(rhs.fSurfaceArea),
    fpPolyhedron(0), fAnchor(rhs.fAnchor),
    fP2(rhs.fP2), fP3(rhs.fP3), fP4(rhs.fP4), fMiddle(rhs.fMiddle),
    fNormal123(rhs.fNormal123), fNormal142(rhs.fNormal142),
    fNormal134(rhs.fNormal134), fNormal234(rhs.fNormal234),
    warningFlag(rhs.warningFlag), fCdotN123(rhs.fCdotN123),
    fCdotN142(rhs.fCdotN142), fCdotN134(rhs.fCdotN134),
    fCdotN234(rhs.fCdotN234), fXMin(rhs.fXMin), fXMax(rhs.fXMax),
    fYMin(rhs.fYMin), fYMax(rhs.fYMax), fZMin(rhs.fZMin), fZMax(rhs.fZMax),
    fDx(rhs.fDx), fDy(rhs.fDy), fDz(rhs.fDz), fTol(rhs.fTol),
    fMaxSize(rhs.fMaxSize)
{
}
 
 
///////////////////////////////////////////////////////////////////////////////
//
// Assignment operator
 
G4Tet& G4Tet::operator = (const G4Tet& rhs) 
{
   // Check assignment to self
   //
   if (this == &rhs)  { return *this; }
 
   // Copy base class data
   //
   G4VSolid::operator=(rhs);
 
   // Copy data
   //
   fCubicVolume = rhs.fCubicVolume; fSurfaceArea = rhs.fSurfaceArea;
   fpPolyhedron = 0; fAnchor = rhs.fAnchor;
   fP2 = rhs.fP2; fP3 = rhs.fP3; fP4 = rhs.fP4; fMiddle = rhs.fMiddle;
   fNormal123 = rhs.fNormal123; fNormal142 = rhs.fNormal142;
   fNormal134 = rhs.fNormal134; fNormal234 = rhs.fNormal234;
   warningFlag = rhs.warningFlag; fCdotN123 = rhs.fCdotN123;
   fCdotN142 = rhs.fCdotN142; fCdotN134 = rhs.fCdotN134;
   fCdotN234 = rhs.fCdotN234; fXMin = rhs.fXMin; fXMax = rhs.fXMax;
   fYMin = rhs.fYMin; fYMax = rhs.fYMax; fZMin = rhs.fZMin; fZMax = rhs.fZMax;
   fDx = rhs.fDx; fDy = rhs.fDy; fDz = rhs.fDz; fTol = rhs.fTol;
   fMaxSize = rhs.fMaxSize;
 
   return *this;
}
 
//////////////////////////////////////////////////////////////////////////
//
// CheckDegeneracy
 
G4bool G4Tet::CheckDegeneracy( G4ThreeVector anchor,
                               G4ThreeVector p2,
                               G4ThreeVector p3,
                               G4ThreeVector p4 )
{
  G4bool result;
  G4Tet *object=new G4Tet("temp",anchor,p2,p3,p4,&result);
  delete object;
  return result;
}
 
//////////////////////////////////////////////////////////////////////////
//
// Dispatch to parameterisation for replication mechanism dimension
// computation & modification.
 
void G4Tet::ComputeDimensions(G4VPVParameterisation* ,
                              const G4int ,
                              const G4VPhysicalVolume* )
{
}
 
//////////////////////////////////////////////////////////////////////////
//
// Calculate extent under transform and specified limit
 
G4bool G4Tet::CalculateExtent(const EAxis pAxis,
                              const G4VoxelLimits& pVoxelLimit,
                              const G4AffineTransform& pTransform,
                                    G4double& pMin, G4double& pMax) const
{
  G4double xMin,xMax;
  G4double yMin,yMax;
  G4double zMin,zMax;
 
  if (pTransform.IsRotated())
  {
    G4ThreeVector pp0=pTransform.TransformPoint(fAnchor);
    G4ThreeVector pp1=pTransform.TransformPoint(fP2);
    G4ThreeVector pp2=pTransform.TransformPoint(fP3);
    G4ThreeVector pp3=pTransform.TransformPoint(fP4);
 
    xMin    = std::min(std::min(std::min(pp0.x(), pp1.x()),pp2.x()),pp3.x());
    xMax    = std::max(std::max(std::max(pp0.x(), pp1.x()),pp2.x()),pp3.x());
    yMin    = std::min(std::min(std::min(pp0.y(), pp1.y()),pp2.y()),pp3.y());
    yMax    = std::max(std::max(std::max(pp0.y(), pp1.y()),pp2.y()),pp3.y());
    zMin    = std::min(std::min(std::min(pp0.z(), pp1.z()),pp2.z()),pp3.z());
    zMax    = std::max(std::max(std::max(pp0.z(), pp1.z()),pp2.z()),pp3.z());
 
  }
  else
  {
    G4double xoffset = pTransform.NetTranslation().x() ;
    xMin    = xoffset + fXMin;
    xMax    = xoffset + fXMax;
    G4double yoffset = pTransform.NetTranslation().y() ;
    yMin    = yoffset + fYMin;
    yMax    = yoffset + fYMax;
    G4double zoffset = pTransform.NetTranslation().z() ;
    zMin    = zoffset + fZMin;
    zMax    = zoffset + fZMax;
  }
 
  if (pVoxelLimit.IsXLimited())
  {
    if ( (xMin > pVoxelLimit.GetMaxXExtent()+fTol) || 
         (xMax < pVoxelLimit.GetMinXExtent()-fTol)  )  { return false; }
    else
    {
      xMin = std::max(xMin, pVoxelLimit.GetMinXExtent());
      xMax = std::min(xMax, pVoxelLimit.GetMaxXExtent());
    }
  }
 
  if (pVoxelLimit.IsYLimited())
  {
    if ( (yMin > pVoxelLimit.GetMaxYExtent()+fTol) ||
         (yMax < pVoxelLimit.GetMinYExtent()-fTol)  )  { return false; }
    else
    {
      yMin = std::max(yMin, pVoxelLimit.GetMinYExtent());
      yMax = std::min(yMax, pVoxelLimit.GetMaxYExtent());
    }
    }
 
    if (pVoxelLimit.IsZLimited())
    {
      if ( (zMin > pVoxelLimit.GetMaxZExtent()+fTol) ||
           (zMax < pVoxelLimit.GetMinZExtent()-fTol)  )  { return false; }
    else
    {
      zMin = std::max(zMin, pVoxelLimit.GetMinZExtent());
      zMax = std::min(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;
  }
 
  return true;
} 
 
/////////////////////////////////////////////////////////////////////////
//
// Return whether point inside/outside/on surface, using tolerance
 
EInside G4Tet::Inside(const G4ThreeVector& p) const
{
  G4double r123, r134, r142, r234;
 
  // this is written to allow if-statement truncation so the outside test
  // (where most of the world is) can fail very quickly and efficiently
 
  if ( (r123=p.dot(fNormal123)-fCdotN123) > fTol ||
       (r134=p.dot(fNormal134)-fCdotN134) > fTol ||
       (r142=p.dot(fNormal142)-fCdotN142) > fTol ||
       (r234=p.dot(fNormal234)-fCdotN234) > fTol )
  {
    return kOutside; // at least one is out!
  }
  else if( (r123 < -fTol)&&(r134 < -fTol)&&(r142 < -fTol)&&(r234 < -fTol) )
  {
    return kInside; // all are definitively inside
  }
  else
  {
    return kSurface; // too close to tell
  }
}
 
///////////////////////////////////////////////////////////////////////
//
// Calculate side nearest to p, and return normal
// If two sides are equidistant, normal of first side (x/y/z) 
// encountered returned.
// This assumes that we are looking from the inside!
 
G4ThreeVector G4Tet::SurfaceNormal( const G4ThreeVector& p) const
{
  G4double r123=std::fabs(p.dot(fNormal123)-fCdotN123);
  G4double r134=std::fabs(p.dot(fNormal134)-fCdotN134);
  G4double r142=std::fabs(p.dot(fNormal142)-fCdotN142);
  G4double r234=std::fabs(p.dot(fNormal234)-fCdotN234);
 
  if( (r123<=r134) && (r123<=r142) && (r123<=r234) )  { return fNormal123; }
  else if ( (r134<=r142) && (r134<=r234) )  { return fNormal134; }
  else if (r142 <= r234)  { return fNormal142; }
  return fNormal234;
}
 
///////////////////////////////////////////////////////////////////////////
//
// Calculate distance to box from an outside point
// - return kInfinity if no intersection.
// All this is very unrolled, for speed.
 
G4double G4Tet::DistanceToIn(const G4ThreeVector& p,
                             const G4ThreeVector& v) const
{
    G4ThreeVector vu(v.unit()), hp;
    G4double vdotn, t, tmin=kInfinity;
 
    G4double extraDistance=10.0*fTol; // a little ways into the solid
 
    vdotn=-vu.dot(fNormal123);
    if(vdotn > 1e-12)
    { // this is a candidate face, since it is pointing at us
      t=(p.dot(fNormal123)-fCdotN123)/vdotn; // #  distance to intersection
      if( (t>=-fTol) && (t<tmin) )
      { // if not true, we're going away from this face or it's not close
        hp=p+vu*(t+extraDistance); // a little beyond point of intersection
        if ( ( hp.dot(fNormal134)-fCdotN134 < 0.0 ) &&
             ( hp.dot(fNormal142)-fCdotN142 < 0.0 ) &&
             ( hp.dot(fNormal234)-fCdotN234 < 0.0 ) )
        {
          tmin=t;
        }
      }
    }
 
    vdotn=-vu.dot(fNormal134);
    if(vdotn > 1e-12)
    { // # this is a candidate face, since it is pointing at us
      t=(p.dot(fNormal134)-fCdotN134)/vdotn; // #  distance to intersection
      if( (t>=-fTol) && (t<tmin) )
      { // if not true, we're going away from this face
        hp=p+vu*(t+extraDistance); // a little beyond point of intersection
        if ( ( hp.dot(fNormal123)-fCdotN123 < 0.0 ) && 
             ( hp.dot(fNormal142)-fCdotN142 < 0.0 ) &&
             ( hp.dot(fNormal234)-fCdotN234 < 0.0 ) )
        {
          tmin=t;
        }
      }
    }
 
    vdotn=-vu.dot(fNormal142);
    if(vdotn > 1e-12)
    { // # this is a candidate face, since it is pointing at us
      t=(p.dot(fNormal142)-fCdotN142)/vdotn; // #  distance to intersection
      if( (t>=-fTol) && (t<tmin) )
      { // if not true, we're going away from this face
        hp=p+vu*(t+extraDistance); // a little beyond point of intersection
        if ( ( hp.dot(fNormal123)-fCdotN123 < 0.0 ) &&
             ( hp.dot(fNormal134)-fCdotN134 < 0.0 ) &&
             ( hp.dot(fNormal234)-fCdotN234 < 0.0 ) )
        {
          tmin=t;
        }
      }
    }
 
    vdotn=-vu.dot(fNormal234);
    if(vdotn > 1e-12)
    { // # this is a candidate face, since it is pointing at us
      t=(p.dot(fNormal234)-fCdotN234)/vdotn; // #  distance to intersection
      if( (t>=-fTol) && (t<tmin) )
      { // if not true, we're going away from this face
        hp=p+vu*(t+extraDistance); // a little beyond point of intersection
        if ( ( hp.dot(fNormal123)-fCdotN123 < 0.0 ) &&
             ( hp.dot(fNormal134)-fCdotN134 < 0.0 ) &&
             ( hp.dot(fNormal142)-fCdotN142 < 0.0 ) )
        {
          tmin=t;
        }
      }
    }
 
  return std::max(0.0,tmin);
}
 
//////////////////////////////////////////////////////////////////////////
// 
// Approximate distance to tet.
// returns distance to sphere centered on bounding box
// - If inside return 0
 
G4double G4Tet::DistanceToIn(const G4ThreeVector& p) const
{
  G4double dd=(p-fMiddle).mag() - fMaxSize - fTol;
  return std::max(0.0, dd);
}
 
/////////////////////////////////////////////////////////////////////////
//
// Calcluate distance to surface of box from inside
// by calculating distances to box's x/y/z planes.
// Smallest distance is exact distance to exiting.
 
G4double G4Tet::DistanceToOut( const G4ThreeVector& p,const G4ThreeVector& v,
                               const G4bool calcNorm,
                                     G4bool *validNorm, G4ThreeVector *n) const
{
    G4ThreeVector vu(v.unit());
    G4double t1=kInfinity,t2=kInfinity,t3=kInfinity,t4=kInfinity, vdotn, tt;
 
    vdotn=vu.dot(fNormal123);
    if(vdotn > 1e-12)  // #we're heading towards this face, so it is a candidate
    {
      t1=(fCdotN123-p.dot(fNormal123))/vdotn; // #  distance to intersection
    }
 
    vdotn=vu.dot(fNormal134);
    if(vdotn > 1e-12) // #we're heading towards this face, so it is a candidate
    {
      t2=(fCdotN134-p.dot(fNormal134))/vdotn; // #  distance to intersection
    }
 
    vdotn=vu.dot(fNormal142);
    if(vdotn > 1e-12) // #we're heading towards this face, so it is a candidate
    {
      t3=(fCdotN142-p.dot(fNormal142))/vdotn; // #  distance to intersection
    }
 
    vdotn=vu.dot(fNormal234);
    if(vdotn > 1e-12) // #we're heading towards this face, so it is a candidate
    {
      t4=(fCdotN234-p.dot(fNormal234))/vdotn; // #  distance to intersection
    }
 
    tt=std::min(std::min(std::min(t1,t2),t3),t4);
 
    if (warningFlag && (tt == kInfinity || tt < -fTol))
    {
      DumpInfo();
      std::ostringstream message;
      message << "No good intersection found or already outside!?" << G4endl
              << "p = " << p / mm << "mm" << G4endl
              << "v = " << v  << G4endl
              << "t1, t2, t3, t4 (mm) "
              << t1/mm << ", " << t2/mm << ", " << t3/mm << ", " << t4/mm;
      G4Exception("G4Tet::DistanceToOut(p,v,...)", "GeomSolids1002",
                  JustWarning, message);
      if(validNorm)
      {
        *validNorm=false; // flag normal as meaningless
      }
    }
    else if(calcNorm && n)
    {
      static G4ThreeVector normal;
      if(tt==t1)        { normal=fNormal123; }
      else if (tt==t2)  { normal=fNormal134; }
      else if (tt==t3)  { normal=fNormal142; }
      else if (tt==t4)  { normal=fNormal234; }
      n=&normal;
      if(validNorm) { *validNorm=true; }
    }
 
    return std::max(tt,0.0); // avoid tt<0.0 by a tiny bit
                             // if we are right on a face
}
 
////////////////////////////////////////////////////////////////////////////
//
// Calculate exact shortest distance to any boundary from inside
// - If outside return 0
 
G4double G4Tet::DistanceToOut(const G4ThreeVector& p) const
{
  G4double t1,t2,t3,t4;
  t1=fCdotN123-p.dot(fNormal123); //  distance to plane, positive if inside
  t2=fCdotN134-p.dot(fNormal134); //  distance to plane
  t3=fCdotN142-p.dot(fNormal142); //  distance to plane
  t4=fCdotN234-p.dot(fNormal234); //  distance to plane
 
  // if any one of these is negative, we are outside,
  // so return zero in that case
 
  G4double tmin=std::min(std::min(std::min(t1,t2),t3),t4);
  return (tmin < fTol)? 0:tmin;
}
 
////////////////////////////////////////////////////////////////////////
//
// Create a List containing the transformed vertices
// Note: Caller has deletion responsibility
 
G4ThreeVectorList*
G4Tet::CreateRotatedVertices(const G4AffineTransform& pTransform) const
{
  G4ThreeVectorList* vertices = new G4ThreeVectorList();
 
  if (vertices)
  {
    vertices->reserve(4);
    G4ThreeVector vertex0(fAnchor);
    G4ThreeVector vertex1(fP2);
    G4ThreeVector vertex2(fP3);
    G4ThreeVector vertex3(fP4);
 
    vertices->push_back(pTransform.TransformPoint(vertex0));
    vertices->push_back(pTransform.TransformPoint(vertex1));
    vertices->push_back(pTransform.TransformPoint(vertex2));
    vertices->push_back(pTransform.TransformPoint(vertex3));
  }
  else
  {
    DumpInfo();
    G4Exception("G4Tet::CreateRotatedVertices()",
                "GeomSolids0003", FatalException,
                "Error in allocation of vertices. Out of memory !");
  }
  return vertices;
}
 
//////////////////////////////////////////////////////////////////////////
//
// GetEntityType
 
G4GeometryType G4Tet::GetEntityType() const
{
  return G4String("G4Tet");
}
 
//////////////////////////////////////////////////////////////////////////
//
// Make a clone of the object
 
G4VSolid* G4Tet::Clone() const
{
  return new G4Tet(*this);
}
 
//////////////////////////////////////////////////////////////////////////
//
// Stream object contents to an output stream
 
std::ostream& G4Tet::StreamInfo(std::ostream& os) const
{
  G4int oldprc = os.precision(16);
  os << "-----------------------------------------------------------\n"
  << "    *** Dump for solid - " << GetName() << " ***\n"
  << "    ===================================================\n"
  << " Solid type: G4Tet\n"
  << " Parameters: \n"
  << "    anchor: " << fAnchor/mm << " mm \n"
  << "    p2: " << fP2/mm << " mm \n"
  << "    p3: " << fP3/mm << " mm \n"
  << "    p4: " << fP4/mm << " mm \n"
  << "    normal123: " << fNormal123 << " \n"
  << "    normal134: " << fNormal134 << " \n"
  << "    normal142: " << fNormal142 << " \n"
  << "    normal234: " << fNormal234 << " \n"
  << "-----------------------------------------------------------\n";
  os.precision(oldprc);
 
  return os;
}
 
 
////////////////////////////////////////////////////////////////////////
//
// GetPointOnFace
//
// Auxiliary method for get point on surface
 
G4ThreeVector G4Tet::GetPointOnFace(G4ThreeVector p1, G4ThreeVector p2,
                                    G4ThreeVector p3, G4double& area) const
{
  G4double lambda1,lambda2;
  G4ThreeVector v, w;
 
  v = p3 - p1;
  w = p1 - p2;
 
  lambda1 = RandFlat::shoot(0.,1.);
  lambda2 = RandFlat::shoot(0.,lambda1);
 
  area = 0.5*(v.cross(w)).mag();
 
  return (p2 + lambda1*w + lambda2*v);
}
 
////////////////////////////////////////////////////////////////////////////
//
// GetPointOnSurface
 
G4ThreeVector G4Tet::GetPointOnSurface() const
{
  G4double chose,aOne,aTwo,aThree,aFour;
  G4ThreeVector p1, p2, p3, p4;
  
  p1 = GetPointOnFace(fAnchor,fP2,fP3,aOne);
  p2 = GetPointOnFace(fAnchor,fP4,fP3,aTwo);
  p3 = GetPointOnFace(fAnchor,fP4,fP2,aThree);
  p4 = GetPointOnFace(fP4,fP3,fP2,aFour);
  
  chose = RandFlat::shoot(0.,aOne+aTwo+aThree+aFour);
  if( (chose>=0.) && (chose <aOne) ) {return p1;}
  else if( (chose>=aOne) && (chose < aOne+aTwo) ) {return p2;}
  else if( (chose>=aOne+aTwo) && (chose<aOne+aTwo+aThree) ) {return p3;}
  return p4;
}
 
////////////////////////////////////////////////////////////////////////
//
// GetVertices
 
std::vector<G4ThreeVector> G4Tet::GetVertices() const 
{
  std::vector<G4ThreeVector> vertices(4);
  vertices[0] = fAnchor;
  vertices[1] = fP2;
  vertices[2] = fP3;
  vertices[3] = fP4;
 
  return vertices;
}
 
////////////////////////////////////////////////////////////////////////
//
// GetCubicVolume
 
G4double G4Tet::GetCubicVolume()
{
  return fCubicVolume;
}
 
////////////////////////////////////////////////////////////////////////
//
// GetSurfaceArea
 
G4double G4Tet::GetSurfaceArea()
{
  return fSurfaceArea;
}
 
// Methods for visualisation
 
////////////////////////////////////////////////////////////////////////
//
// DescribeYourselfTo
 
void G4Tet::DescribeYourselfTo (G4VGraphicsScene& scene) const 
{
  scene.AddSolid (*this);
}
 
////////////////////////////////////////////////////////////////////////
//
// GetExtent
 
G4VisExtent G4Tet::GetExtent() const 
{
  return G4VisExtent (fXMin, fXMax, fYMin, fYMax, fZMin, fZMax);
}
 
////////////////////////////////////////////////////////////////////////
//
// CreatePolyhedron
 
G4Polyhedron* G4Tet::CreatePolyhedron () const 
{
  G4Polyhedron *ph=new G4Polyhedron;
  G4double xyz[4][3];
  static G4int faces[4][4]={{1,3,2,0},{1,4,3,0},{1,2,4,0},{2,3,4,0}};
  xyz[0][0]=fAnchor.x(); xyz[0][1]=fAnchor.y(); xyz[0][2]=fAnchor.z();
  xyz[1][0]=fP2.x(); xyz[1][1]=fP2.y(); xyz[1][2]=fP2.z();
  xyz[2][0]=fP3.x(); xyz[2][1]=fP3.y(); xyz[2][2]=fP3.z();
  xyz[3][0]=fP4.x(); xyz[3][1]=fP4.y(); xyz[3][2]=fP4.z();
 
  ph->createPolyhedron(4,4,xyz,faces);
 
  return ph;
}
 
////////////////////////////////////////////////////////////////////////
//
// CreateNURBS
 
G4NURBS* G4Tet::CreateNURBS () const 
{
  return new G4NURBSbox (fDx, fDy, fDz);
}
 
////////////////////////////////////////////////////////////////////////
//
// GetPolyhedron
 
G4Polyhedron* G4Tet::GetPolyhedron () const
{
  if (!fpPolyhedron ||
      fpPolyhedron->GetNumberOfRotationStepsAtTimeOfCreation() !=
      fpPolyhedron->GetNumberOfRotationSteps())
    {
      delete fpPolyhedron;
      fpPolyhedron = CreatePolyhedron();
    }
  return fpPolyhedron;
}