G4Paraboloid.cc

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//
// $Id: G4Paraboloid.cc 83572 2014-09-01 15:23:27Z gcosmo $
//
// class G4Paraboloid
//
// Implementation for G4Paraboloid class
//
// Author : Lukas Lindroos (CERN), July 2007
// Revised: Tatiana Nikitina (CERN)
// --------------------------------------------------------------------

#include "globals.hh"

#include "G4Paraboloid.hh"

#include "G4VoxelLimits.hh"
#include "G4AffineTransform.hh"

#include "meshdefs.hh"

#include "Randomize.hh"

#include "G4VGraphicsScene.hh"
#include "G4VisExtent.hh"

#include "G4AutoLock.hh"

namespace
{
  G4Mutex polyhedronMutex = G4MUTEX_INITIALIZER;
}

using namespace CLHEP;

//
// constructor - check parameters

G4Paraboloid::G4Paraboloid(const G4String& pName,
                                 G4double pDz,
                                 G4double pR1,
                                 G4double pR2)
 : G4VSolid(pName), fRebuildPolyhedron(false), fpPolyhedron(0),
   fSurfaceArea(0.), fCubicVolume(0.) 

{
  if( (pDz <= 0.) || (pR2 <= pR1) || (pR1 < 0.) )
  {
    std::ostringstream message;
    message << "Invalid dimensions. Negative Input Values or R1>=R2 - "
            << GetName();
    G4Exception("G4Paraboloid::G4Paraboloid()", "GeomSolids0002", 
                FatalErrorInArgument, message,
                "Z half-length must be larger than zero or R1>=R2.");
  }

  r1 = pR1;
  r2 = pR2;
  dz = pDz;

  // r1^2 = k1 * (-dz) + k2
  // r2^2 = k1 * ( dz) + k2
  // => r1^2 + r2^2 = k2 + k2 => k2 = (r2^2 + r1^2) / 2
  // and r2^2 - r1^2 = k1 * dz - k1 * (-dz) => k1 = (r2^2 - r1^2) / 2 / dz

  k1 = (r2 * r2 - r1 * r1) / 2 / dz;
  k2 = (r2 * r2 + r1 * r1) / 2;
}

//
// Fake default constructor - sets only member data and allocates memory
//                            for usage restricted to object persistency.
//
G4Paraboloid::G4Paraboloid( __void__& a )
  : G4VSolid(a), fRebuildPolyhedron(false), fpPolyhedron(0),
    fSurfaceArea(0.), fCubicVolume(0.),
    dz(0.), r1(0.), r2(0.), k1(0.), k2(0.)
{
}

//
// Destructor

G4Paraboloid::~G4Paraboloid()
{
  delete fpPolyhedron; fpPolyhedron = 0;
}

//
// Copy constructor

G4Paraboloid::G4Paraboloid(const G4Paraboloid& rhs)
  : G4VSolid(rhs), fRebuildPolyhedron(false), fpPolyhedron(0),
    fSurfaceArea(rhs.fSurfaceArea), fCubicVolume(rhs.fCubicVolume),
    dz(rhs.dz), r1(rhs.r1), r2(rhs.r2), k1(rhs.k1), k2(rhs.k2)
{
}


//
// Assignment operator

G4Paraboloid& G4Paraboloid::operator = (const G4Paraboloid& rhs) 
{
   // Check assignment to self
   //
   if (this == &rhs)  { return *this; }

   // Copy base class data
   //
   G4VSolid::operator=(rhs);

   // Copy data
   //
   fSurfaceArea = rhs.fSurfaceArea; fCubicVolume = rhs.fCubicVolume;
   dz = rhs.dz; r1 = rhs.r1; r2 = rhs.r2; k1 = rhs.k1; k2 = rhs.k2;
   fRebuildPolyhedron = false;
   delete fpPolyhedron; fpPolyhedron = 0;

   return *this;
}

//
// Dispatch to parameterisation for replication mechanism dimension
// computation & modification.

//void ComputeDimensions(       G4VPVParamerisation p,
//                        const G4Int               n,
//                        const G4VPhysicalVolume*  pRep )
//{
//  p->ComputeDimensions(*this,n,pRep) ;
//}


//
// Calculate extent under transform and specified limit

G4bool
G4Paraboloid::CalculateExtent(const EAxis pAxis,
                             const G4VoxelLimits& pVoxelLimit,
                             const G4AffineTransform& pTransform,
                                   G4double& pMin, G4double& pMax) const
{
  G4double xMin = -r2 + pTransform.NetTranslation().x(),
           xMax = r2 + pTransform.NetTranslation().x(),
           yMin = -r2 + pTransform.NetTranslation().y(),
           yMax = r2 + pTransform.NetTranslation().y(),
           zMin = -dz + pTransform.NetTranslation().z(),
           zMax = dz + pTransform.NetTranslation().z();

  if(!pTransform.IsRotated()
  || pTransform.NetRotation()(G4ThreeVector(0, 0, 1)) == G4ThreeVector(0, 0, 1))
  {
    if(pVoxelLimit.IsXLimited())
    {
      if(pVoxelLimit.GetMaxXExtent() < xMin - 0.5 * kCarTolerance
      || pVoxelLimit.GetMinXExtent() > xMax + 0.5 * kCarTolerance)
      {
        return false;
      }
      else
      {
        if(pVoxelLimit.GetMinXExtent() > xMin)
        {
          xMin = pVoxelLimit.GetMinXExtent();
        }
        if(pVoxelLimit.GetMaxXExtent() < xMax)
        {
          xMax = pVoxelLimit.GetMaxXExtent();
        }
      }
    }
    if(pVoxelLimit.IsYLimited())
    {
      if(pVoxelLimit.GetMaxYExtent() < yMin - 0.5 * kCarTolerance
      || pVoxelLimit.GetMinYExtent() > yMax + 0.5 * kCarTolerance)
      {
        return false;
      }
      else
      {
        if(pVoxelLimit.GetMinYExtent() > yMin)
        {
          yMin = pVoxelLimit.GetMinYExtent();
        }
        if(pVoxelLimit.GetMaxYExtent() < yMax)
        {
          yMax = pVoxelLimit.GetMaxYExtent();
        }
      }
    }
    if(pVoxelLimit.IsZLimited())
    {
      if(pVoxelLimit.GetMaxZExtent() < zMin - 0.5 * kCarTolerance
      || pVoxelLimit.GetMinZExtent() > zMax + 0.5 * kCarTolerance)
      {
        return false;
      }
      else
      {
        if(pVoxelLimit.GetMinZExtent() > zMin)
        {
          zMin = pVoxelLimit.GetMinZExtent();
        }
        if(pVoxelLimit.GetMaxZExtent() < zMax)
        {
          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:
        pMin = 0;
        pMax = 0;
        return false;
    }
  }
  else
  {
    G4bool existsAfterClip=true;

    // Calculate rotated vertex coordinates

    G4int noPolygonVertices=0;
    G4ThreeVectorList* vertices
      = CreateRotatedVertices(pTransform,noPolygonVertices);

    if(pAxis == kXAxis || pAxis == kYAxis || pAxis == kZAxis)
    {

      pMin =  kInfinity;
      pMax = -kInfinity;

      for(G4ThreeVectorList::iterator it = vertices->begin();
          it < vertices->end(); it++)
      {
        if(pMin > (*it)[pAxis]) pMin = (*it)[pAxis];
        if((*it)[pAxis] < pVoxelLimit.GetMinExtent(pAxis))
        {
          pMin = pVoxelLimit.GetMinExtent(pAxis);
        }
        if(pMax < (*it)[pAxis])
        {
          pMax = (*it)[pAxis];
        }
        if((*it)[pAxis] > pVoxelLimit.GetMaxExtent(pAxis))
        {
          pMax = pVoxelLimit.GetMaxExtent(pAxis);
        }
      }

      if(pMin > pVoxelLimit.GetMaxExtent(pAxis)
      || pMax < pVoxelLimit.GetMinExtent(pAxis)) { existsAfterClip = false; }
    }
    else
    {
      pMin = 0;
      pMax = 0;
      existsAfterClip = false;
    }
    delete vertices;
    return existsAfterClip;
  }
  return true;
}

//
// Return whether point inside/outside/on surface

EInside G4Paraboloid::Inside(const G4ThreeVector& p) const
{
  // First check is  the point is above or below the solid.
  //
  if(std::fabs(p.z()) > dz + 0.5 * kCarTolerance) { return kOutside; }

  G4double rho2 = p.perp2(),
           rhoSurfTimesTol2  = (k1 * p.z() + k2) * sqr(kCarTolerance),
           A = rho2 - ((k1 *p.z() + k2) + 0.25 * kCarTolerance * kCarTolerance);
 
  if(A < 0 && sqr(A) > rhoSurfTimesTol2)
  {
    // Actually checking rho < radius of paraboloid at z = p.z().
    // We're either inside or in lower/upper cutoff area.
   
    if(std::fabs(p.z()) > dz - 0.5 * kCarTolerance)
    {
      // We're in the upper/lower cutoff area, sides have a paraboloid shape
      // maybe further checks should be made to make these nicer

      return kSurface;
    }
    else
    {
      return kInside;
    }
  }
  else if(A <= 0 || sqr(A) < rhoSurfTimesTol2)
  {
    // We're in the parabolic surface.

    return kSurface;
  }
  else
  {
    return kOutside;
  }
}

//

G4ThreeVector G4Paraboloid::SurfaceNormal( const G4ThreeVector& p) const
{
  G4ThreeVector n(0, 0, 0);
  if(std::fabs(p.z()) > dz + 0.5 * kCarTolerance)
  {
    // If above or below just return normal vector for the cutoff plane.

    n = G4ThreeVector(0, 0, p.z()/std::fabs(p.z()));
  }
  else if(std::fabs(p.z()) > dz - 0.5 * kCarTolerance)
  {
    // This means we're somewhere in the plane z = dz or z = -dz.
    // (As far as the program is concerned anyway.

    if(p.z() < 0) // Are we in upper or lower plane?
    {
      if(p.perp2() > sqr(r1 + 0.5 * kCarTolerance))
      {
        n = G4ThreeVector(p.x(), p.y(), -k1 / 2).unit();
      }
      else if(r1 < 0.5 * kCarTolerance
           || p.perp2() > sqr(r1 - 0.5 * kCarTolerance))
      {
        n = G4ThreeVector(p.x(), p.y(), 0.).unit()
          + G4ThreeVector(0., 0., -1.).unit();
        n = n.unit();
      }
      else
      {
        n = G4ThreeVector(0., 0., -1.);
      }
    }
    else
    {
      if(p.perp2() > sqr(r2 + 0.5 * kCarTolerance))
      {
        n = G4ThreeVector(p.x(), p.y(), 0.).unit();
      }
      else if(r2 < 0.5 * kCarTolerance
           || p.perp2() > sqr(r2 - 0.5 * kCarTolerance))
      {
        n = G4ThreeVector(p.x(), p.y(), 0.).unit()
          + G4ThreeVector(0., 0., 1.).unit();
        n = n.unit();
      }
      else
      {
        n = G4ThreeVector(0., 0., 1.);
      }
    }
  }
  else
  {
    G4double rho2 = p.perp2();
    G4double rhoSurfTimesTol2  = (k1 * p.z() + k2) * sqr(kCarTolerance);
    G4double A = rho2 - ((k1 *p.z() + k2)
               + 0.25 * kCarTolerance * kCarTolerance);

    if(A < 0 && sqr(A) > rhoSurfTimesTol2)
    {
      // Actually checking rho < radius of paraboloid at z = p.z().
      // We're inside.

      if(p.mag2() != 0) { n = p.unit(); }
    }
    else if(A <= 0 || sqr(A) < rhoSurfTimesTol2)
    {
      // We're in the parabolic surface.

      n = G4ThreeVector(p.x(), p.y(), - k1 / 2).unit();
    }
    else
    {
      n = G4ThreeVector(p.x(), p.y(), - k1 / 2).unit();
    }
  }

  if(n.mag2() == 0)
  {
    std::ostringstream message;
    message << "No normal defined for this point p." << G4endl
            << "          p = " << 1 / mm * p << " mm";
    G4Exception("G4Paraboloid::SurfaceNormal(p)", "GeomSolids1002",
                JustWarning, message);
  }
  return n;
}

//
// Calculate distance to shape from outside, along normalised vector
// - return kInfinity if no intersection
//

G4double G4Paraboloid::DistanceToIn( const G4ThreeVector& p,
                                    const G4ThreeVector& v  ) const
{
  G4double rho2 = p.perp2(), paraRho2 = std::fabs(k1 * p.z() + k2);
  G4double tol2 = kCarTolerance*kCarTolerance;
  G4double tolh = 0.5*kCarTolerance;

  if(r2 && p.z() > - tolh + dz) 
  {
    // If the points is above check for intersection with upper edge.

    if(v.z() < 0)
    {
      G4double intersection = (dz - p.z()) / v.z(); // With plane z = dz.
      if(sqr(p.x() + v.x()*intersection)
       + sqr(p.y() + v.y()*intersection) < sqr(r2 + 0.5 * kCarTolerance))
      {
        if(p.z() < tolh + dz)
          { return 0; }
        else
          { return intersection; }
      }
    }
    else  // Direction away, no possibility of intersection
    {
      return kInfinity;
    }
  }
  else if(r1 && p.z() < tolh - dz)
  {
    // If the points is belove check for intersection with lower edge.

    if(v.z() > 0)
    {
      G4double intersection = (-dz - p.z()) / v.z(); // With plane z = -dz.
      if(sqr(p.x() + v.x()*intersection)
       + sqr(p.y() + v.y()*intersection) < sqr(r1 + 0.5 * kCarTolerance))
      {
        if(p.z() > -tolh - dz)
        {
          return 0;
        }
        else
        {
          return intersection;
        }
      }
    }
    else  // Direction away, no possibility of intersection
    {
      return kInfinity;
    }
  }

  G4double A = k1 / 2 * v.z() - p.x() * v.x() - p.y() * v.y(),
           vRho2 = v.perp2(), intersection,
           B = (k1 * p.z() + k2 - rho2) * vRho2;

  if ( ( (rho2 > paraRho2) && (sqr(rho2-paraRho2-0.25*tol2) > tol2*paraRho2) )
    || (p.z() < - dz+kCarTolerance)
    || (p.z() > dz-kCarTolerance) ) // Make sure it's safely outside.
  {
    // Is there a problem with squaring rho twice?

    if(vRho2<tol2) // Needs to be treated seperately.
    {
      intersection = ((rho2 - k2)/k1 - p.z())/v.z();
      if(intersection < 0) { return kInfinity; }
      else if(std::fabs(p.z() + v.z() * intersection) <= dz)
      {
        return intersection;
      }
      else
      {
        return kInfinity;
      }
    }
    else if(A*A + B < 0) // No real intersections.
    {
      return kInfinity;
    }
    else
    {
      intersection = (A - std::sqrt(B + sqr(A))) / vRho2;
      if(intersection < 0)
      {
        return kInfinity;
      }
      else if(std::fabs(p.z() + intersection * v.z()) < dz + tolh)
      {
        return intersection;
      }
      else
      {
        return kInfinity;
      }
    }
  }
  else if(sqr(rho2 - paraRho2 - .25 * tol2) <= tol2 * paraRho2)
  {
    // If this is true we're somewhere in the border.

    G4ThreeVector normal(p.x(), p.y(), -k1/2);
    if(normal.dot(v) <= 0)
      { return 0; }
    else
      { return kInfinity; }
  }
  else
  {
    std::ostringstream message;
    if(Inside(p) == kInside)
    {
      message << "Point p is inside! - " << GetName() << G4endl;
    }
    else
    {
      message << "Likely a problem in this function, for solid: " << GetName()
              << G4endl;
    }
    message << "          p = " << p * (1/mm) << " mm" << G4endl
            << "          v = " << v * (1/mm) << " mm";
    G4Exception("G4Paraboloid::DistanceToIn(p,v)", "GeomSolids1002",
                JustWarning, message);
    return 0;
  }
}

//
// Calculate distance (<= actual) to closest surface of shape from outside
// - Return 0 if point inside

G4double G4Paraboloid::DistanceToIn(const G4ThreeVector& p) const
{
  G4double safz = -dz+std::fabs(p.z());
  if(safz<0) { safz=0; }
  G4double safr = kInfinity;

  G4double rho = p.x()*p.x()+p.y()*p.y();
  G4double paraRho = (p.z()-k2)/k1;
  G4double sqrho = std::sqrt(rho);

  if(paraRho<0)
  {
    safr=sqrho-r2;
    if(safr>safz) { safz=safr; }
    return safz;
  }

  G4double sqprho = std::sqrt(paraRho);
  G4double dRho = sqrho-sqprho;
  if(dRho<0) { return safz; }

  G4double talf = -2.*k1*sqprho;
  G4double tmp  = 1+talf*talf;
  if(tmp<0.) { return safz; }

  G4double salf = talf/std::sqrt(tmp);
  safr = std::fabs(dRho*salf);
  if(safr>safz) { safz=safr; }

  return safz;
}

//
// Calculate distance to surface of shape from 'inside'

G4double G4Paraboloid::DistanceToOut(const G4ThreeVector& p,
                                    const G4ThreeVector& v,
                                    const G4bool calcNorm,
                                          G4bool *validNorm,
                                          G4ThreeVector *n  ) const
{
  G4double rho2 = p.perp2(), paraRho2 = std::fabs(k1 * p.z() + k2);
  G4double vRho2 = v.perp2(), intersection;
  G4double tol2 = kCarTolerance*kCarTolerance;
  G4double tolh = 0.5*kCarTolerance;

  if(calcNorm) { *validNorm = false; }

  // We have that the particle p follows the line x = p + s * v
  // meaning x = p.x() + s * v.x(), y = p.y() + s * v.y() and
  // z = p.z() + s * v.z()
  // The equation for all points on the surface (surface expanded for
  // to include all z) x^2 + y^2 = k1 * z + k2 => .. =>
  // => s = (A +- std::sqrt(A^2 + B)) / vRho2
  // where:
  //
  G4double A = k1 / 2 * v.z() - p.x() * v.x() - p.y() * v.y();
  //
  // and:
  //
  G4double B = (-rho2 + paraRho2) * vRho2;

  if ( rho2 < paraRho2 && sqr(rho2 - paraRho2 - 0.25 * tol2) > tol2 * paraRho2
    && std::fabs(p.z()) < dz - kCarTolerance)
  {
    // Make sure it's safely inside.

    if(v.z() > 0)
    {
      // It's heading upwards, check where it colides with the plane z = dz.
      // When it does, is that in the surface of the paraboloid.
      // z = p.z() + variable * v.z() for all points the particle can go.
      // => variable = (z - p.z()) / v.z() so intersection must be:

      intersection = (dz - p.z()) / v.z();
      G4ThreeVector ip = p + intersection * v; // Point of intersection.

      if(ip.perp2() < sqr(r2 + kCarTolerance))
      {
        if(calcNorm)
        {
          *n = G4ThreeVector(0, 0, 1);
          if(r2 < tolh || ip.perp2() > sqr(r2 - tolh))
          {
            *n += G4ThreeVector(ip.x(), ip.y(), - k1 / 2).unit();
            *n = n->unit();
          }
          *validNorm = true;
        }
        return intersection;
      }
    }
    else if(v.z() < 0)
    {
      // It's heading downwards, check were it colides with the plane z = -dz.
      // When it does, is that in the surface of the paraboloid.
      // z = p.z() + variable * v.z() for all points the particle can go.
      // => variable = (z - p.z()) / v.z() so intersection must be:

      intersection = (-dz - p.z()) / v.z();
      G4ThreeVector ip = p + intersection * v; // Point of intersection.

      if(ip.perp2() < sqr(r1 + tolh))
      {
        if(calcNorm)
        {
          *n = G4ThreeVector(0, 0, -1);
          if(r1 < tolh || ip.perp2() > sqr(r1 - tolh))
          {
            *n += G4ThreeVector(ip.x(), ip.y(), - k1 / 2).unit();
            *n = n->unit();
          }
          *validNorm = true;
        }
        return intersection;
      }
    }

    // Now check for collisions with paraboloid surface.

    if(vRho2 == 0) // Needs to be treated seperately.
    {
      intersection = ((rho2 - k2)/k1 - p.z())/v.z();
      if(calcNorm)
      {
        G4ThreeVector intersectionP = p + v * intersection;
        *n = G4ThreeVector(intersectionP.x(), intersectionP.y(), -k1/2);
        *n = n->unit();

        *validNorm = true;
      }
      return intersection;
    }
    else if( ((A <= 0) && (B >= sqr(A) * (sqr(vRho2) - 1))) || (A >= 0))
    {
      // intersection = (A + std::sqrt(B + sqr(A))) / vRho2;
      // The above calculation has a precision problem:
      // known problem of solving quadratic equation with small A  

      A = A/vRho2;
      B = (k1 * p.z() + k2 - rho2)/vRho2;
      intersection = B/(-A + std::sqrt(B + sqr(A)));
      if(calcNorm)
      {
        G4ThreeVector intersectionP = p + v * intersection;
        *n = G4ThreeVector(intersectionP.x(), intersectionP.y(), -k1/2);
        *n = n->unit();
        *validNorm = true;
      }
      return intersection;
    }
    std::ostringstream message;
    message << "There is no intersection between given line and solid!"
            << G4endl
            << "          p = " << p << G4endl
            << "          v = " << v;
    G4Exception("G4Paraboloid::DistanceToOut(p,v,...)", "GeomSolids1002",
                JustWarning, message);

    return kInfinity;
  }
  else if ( (rho2 < paraRho2 + kCarTolerance
         || sqr(rho2 - paraRho2 - 0.25 * tol2) < tol2 * paraRho2 )
         && std::fabs(p.z()) < dz + tolh) 
  {
    // If this is true we're somewhere in the border.
    
    G4ThreeVector normal = G4ThreeVector (p.x(), p.y(), -k1/2);

    if(std::fabs(p.z()) > dz - tolh)
    {
      // We're in the lower or upper edge
      //
      if( ((v.z() > 0) && (p.z() > 0)) || ((v.z() < 0) && (p.z() < 0)) )
      {             // If we're heading out of the object that is treated here
        if(calcNorm)
        {
          *validNorm = true;
          if(p.z() > 0)
            { *n = G4ThreeVector(0, 0, 1); }
          else
            { *n = G4ThreeVector(0, 0, -1); }
        }
        return 0;
      }

      if(v.z() == 0)
      {
        // Case where we're moving inside the surface needs to be
        // treated separately.
        // Distance until it goes out through a side is returned.

        G4double r = (p.z() > 0)? r2 : r1;
        G4double pDotV = p.dot(v);
        A = vRho2 * ( sqr(r) - sqr(p.x()) - sqr(p.y()));
        intersection = (-pDotV + std::sqrt(A + sqr(pDotV))) / vRho2;

        if(calcNorm)
        {
          *validNorm = true;

          *n = (G4ThreeVector(0, 0, p.z()/std::fabs(p.z()))
              + G4ThreeVector(p.x() + v.x() * intersection, p.y() + v.y()
              * intersection, -k1/2).unit()).unit();
        }
        return intersection;
      }
    }
    //
    // Problem in the Logic :: Following condition for point on upper surface 
    //                         and Vz<0  will return 0 (Problem #1015), but
    //                         it has to return intersection with parabolic
    //                         surface or with lower plane surface (z = -dz)
    // The logic has to be  :: If not found intersection until now,
    // do not exit but continue to search for possible intersection.
    // Only for point situated on both borders (Z and parabolic)
    // this condition has to be taken into account and done later
    //
    //
    // else if(normal.dot(v) >= 0)
    // {
    //   if(calcNorm)
    //   {
    //     *validNorm = true;
    //     *n = normal.unit();
    //   }
    //   return 0;
    // }

    if(v.z() > 0)
    {
      // Check for collision with upper edge.

      intersection = (dz - p.z()) / v.z();
      G4ThreeVector ip = p + intersection * v;

      if(ip.perp2() < sqr(r2 - tolh))
      {
        if(calcNorm)
        {
          *validNorm = true;
          *n = G4ThreeVector(0, 0, 1);
        }
        return intersection;
      }
      else if(ip.perp2() < sqr(r2 + tolh))
      {
        if(calcNorm)
        {
          *validNorm = true;
          *n = G4ThreeVector(0, 0, 1)
             + G4ThreeVector(ip.x(), ip.y(), - k1 / 2).unit();
          *n = n->unit();
        }
        return intersection;
      }
    }
    if( v.z() < 0)
    {
      // Check for collision with lower edge.

      intersection = (-dz - p.z()) / v.z();
      G4ThreeVector ip = p + intersection * v;

      if(ip.perp2() < sqr(r1 - tolh))
      {
        if(calcNorm)
        {
          *validNorm = true;
          *n = G4ThreeVector(0, 0, -1);
        }
        return intersection;
      }
      else if(ip.perp2() < sqr(r1 + tolh))
      {
        if(calcNorm)
        {
          *validNorm = true;
          *n = G4ThreeVector(0, 0, -1)
             + G4ThreeVector(ip.x(), ip.y(), - k1 / 2).unit();
          *n = n->unit();
        }
        return intersection;
      }
    }

    // Note: comparison with zero below would not be correct !
    //
    if(std::fabs(vRho2) > tol2) // precision error in the calculation of
    {                           // intersection = (A+std::sqrt(B+sqr(A)))/vRho2
      A = A/vRho2;
      B = (k1 * p.z() + k2 - rho2);
      if(std::fabs(B)>kCarTolerance)
      {
        B = (B)/vRho2;
        intersection = B/(-A + std::sqrt(B + sqr(A)));
      }
      else                      // Point is On both borders: Z and parabolic
      {                         // solution depends on normal.dot(v) sign
        if(normal.dot(v) >= 0)
        {
          if(calcNorm)
          {
            *validNorm = true;
            *n = normal.unit();
          }
          return 0;
        }
        intersection = 2.*A;
      }
    }
    else
    {
      intersection = ((rho2 - k2) / k1 - p.z()) / v.z();
    }

    if(calcNorm)
    {
      *validNorm = true;
      *n = G4ThreeVector(p.x() + intersection * v.x(), p.y()
         + intersection * v.y(), - k1 / 2);
      *n = n->unit();
    }
    return intersection;
  }
  else
  {
#ifdef G4SPECSDEBUG
    if(kOutside == Inside(p))
    {
      G4Exception("G4Paraboloid::DistanceToOut(p,v,...)", "GeomSolids1002",
                  JustWarning, "Point p is outside!");
    }
    else
      G4Exception("G4Paraboloid::DistanceToOut(p,v,...)", "GeomSolids1002",
                  JustWarning, "There's an error in this functions code.");
#endif
    return kInfinity;
  }
  return 0;
} 

//
// Calculate distance (<=actual) to closest surface of shape from inside

G4double G4Paraboloid::DistanceToOut(const G4ThreeVector& p) const
{
  G4double safe=0.0,rho,safeR,safeZ ;
  G4double tanRMax,secRMax,pRMax ;

#ifdef G4SPECSDEBUG
  if( Inside(p) == kOutside )
  {
     G4cout << G4endl ;
     DumpInfo();
     std::ostringstream message;
     G4int oldprc = message.precision(16);
     message << "Point p is outside !?" << G4endl
             << "Position:" << G4endl
             << "   p.x() = "   << p.x()/mm << " mm" << G4endl
             << "   p.y() = "   << p.y()/mm << " mm" << G4endl
             << "   p.z() = "   << p.z()/mm << " mm";
     message.precision(oldprc) ;
     G4Exception("G4Paraboloid::DistanceToOut(p)", "GeomSolids1002",
                 JustWarning, message);
  }
#endif

  rho = p.perp();
  safeZ = dz - std::fabs(p.z()) ;

  tanRMax = (r2 - r1)*0.5/dz ;
  secRMax = std::sqrt(1.0 + tanRMax*tanRMax) ;
  pRMax   = tanRMax*p.z() + (r1+r2)*0.5 ;
  safeR  = (pRMax - rho)/secRMax ;

  if (safeZ < safeR) { safe = safeZ; }
  else { safe = safeR; }
  if ( safe < 0.5 * kCarTolerance ) { safe = 0; }
  return safe ;
}

//
// G4EntityType

G4GeometryType G4Paraboloid::GetEntityType() const
{
  return G4String("G4Paraboloid");
}

//
// Make a clone of the object

G4VSolid* G4Paraboloid::Clone() const
{
  return new G4Paraboloid(*this);
}

//
// Stream object contents to an output stream

std::ostream& G4Paraboloid::StreamInfo( std::ostream& os ) const
{
  G4int oldprc = os.precision(16);
  os << "-----------------------------------------------------------\n"
     << "    *** Dump for solid - " << GetName() << " ***\n"
     << "    ===================================================\n"
     << " Solid type: G4Paraboloid\n"
     << " Parameters: \n"
     << "    z half-axis:   " << dz/mm << " mm \n"
     << "    radius at -dz: " << r1/mm << " mm \n"
     << "    radius at dz:  " << r2/mm << " mm \n"
     << "-----------------------------------------------------------\n";
  os.precision(oldprc);

  return os;
}

//
// GetPointOnSurface

G4ThreeVector G4Paraboloid::GetPointOnSurface() const
{
  G4double A = (fSurfaceArea == 0)? CalculateSurfaceArea(): fSurfaceArea;
  G4double z = RandFlat::shoot(0.,1.);
  G4double phi = RandFlat::shoot(0., twopi);
  if(pi*(sqr(r1) + sqr(r2))/A >= z)
  {
    G4double rho;
    if(pi * sqr(r1) / A > z)
    {
      rho = r1 * std::sqrt(RandFlat::shoot(0., 1.));
      return G4ThreeVector(rho * std::cos(phi), rho * std::sin(phi), -dz);
    }
    else
    {
      rho = r2 * std::sqrt(RandFlat::shoot(0., 1));
      return G4ThreeVector(rho * std::cos(phi), rho * std::sin(phi), dz);
    }
  }
  else
  {
    z = RandFlat::shoot(0., 1.)*2*dz - dz;
    return G4ThreeVector(std::sqrt(z*k1 + k2)*std::cos(phi),
                         std::sqrt(z*k1 + k2)*std::sin(phi), z);
  }
}

G4ThreeVectorList*
G4Paraboloid::CreateRotatedVertices(const G4AffineTransform& pTransform,
                                          G4int& noPolygonVertices) const
{
  G4ThreeVectorList *vertices;
  G4ThreeVector vertex;
  G4double meshAnglePhi, cosMeshAnglePhiPer2,
           crossAnglePhi, coscrossAnglePhi, sincrossAnglePhi, sAnglePhi,
           sRho, dRho, rho, lastRho = 0., swapRho;
  G4double rx, ry, rz, k3, k4, zm;
  G4int crossSectionPhi, noPhiCrossSections, noRhoSections;

  // Phi cross sections
  //
  noPhiCrossSections = G4int(twopi/kMeshAngleDefault)+1;  // =9!
/*
  if (noPhiCrossSections<kMinMeshSections)          // <3
  {
    noPhiCrossSections=kMinMeshSections;
  }
  else if (noPhiCrossSections>kMaxMeshSections)     // >37
  {
    noPhiCrossSections=kMaxMeshSections;
  }
*/
  meshAnglePhi=twopi/(noPhiCrossSections-1);

  sAnglePhi = -meshAnglePhi*0.5*0;
  cosMeshAnglePhiPer2 = std::cos(meshAnglePhi / 2.);

  noRhoSections = G4int(pi/2/kMeshAngleDefault) + 1;

  // There is no obvious value for noRhoSections, at the moment the parabola is
  // viewed as a quarter circle mean this formula for it.

  // An alternetive would be to calculate max deviation from parabola and
  // keep adding new vertices there until it was under a decided constant.

  // maxDeviation on a line between points (rho1, z1) and (rho2, z2) is given
  // by rhoMax = sqrt(k1 * z + k2) - z * (rho2 - rho1)
  //           / (z2 - z1) - (rho1 * z2 - rho2 * z1) / (z2 - z1)
  // where z is k1 / 2 * (rho1 + rho2) - k2 / k1

  sRho = r1;
  dRho = (r2 - r1) / double(noRhoSections - 1);

  vertices=new G4ThreeVectorList();

  if (vertices)
  {
    for (crossSectionPhi=0; crossSectionPhi<noPhiCrossSections;
         crossSectionPhi++)
    {
      crossAnglePhi=sAnglePhi+crossSectionPhi*meshAnglePhi;
      coscrossAnglePhi=std::cos(crossAnglePhi);
      sincrossAnglePhi=std::sin(crossAnglePhi);
      lastRho = 0;
      for (int iRho=0; iRho < noRhoSections;
           iRho++)
      {
        // Compute coordinates of cross section at section crossSectionPhi
        //
        if(iRho == noRhoSections - 1)
        {
          rho = r2;
        }
        else
        {
          rho = iRho * dRho + sRho;

          // This part is to ensure that the vertices
          // will form a volume larger than the paraboloid

          k3 = k1 / (2*rho + dRho);
          k4 = rho - k3 * (sqr(rho) - k2) / k1;
          zm = (sqr(k1 / (2 * k3)) - k2) / k1;
          rho += std::sqrt(k1 * zm + k2) - zm * k3 - k4;
        }

        rho += (1 / cosMeshAnglePhiPer2 - 1) * (iRho * dRho + sRho);

        if(rho < lastRho)
        {
          swapRho = lastRho;
          lastRho = rho + dRho;
          rho = swapRho;
        }
        else
        {
          lastRho = rho + dRho;
        }

        rx = coscrossAnglePhi*rho;
        ry = sincrossAnglePhi*rho;
        rz = (sqr(iRho * dRho + sRho) - k2) / k1;
        vertex = G4ThreeVector(rx,ry,rz);
        vertices->push_back(pTransform.TransformPoint(vertex));
      }
    }    // Phi
    noPolygonVertices = noRhoSections ;
  }
  else
  {
    DumpInfo();
    G4Exception("G4Paraboloid::CreateRotatedVertices()",
                "GeomSolids0003", FatalException,
                "Error in allocation of vertices. Out of memory !");
  }
  return vertices;
}

//
// Methods for visualisation

void G4Paraboloid::DescribeYourselfTo (G4VGraphicsScene& scene) const
{
  scene.AddSolid(*this);
}

G4Polyhedron* G4Paraboloid::CreatePolyhedron () const
{
  return new G4PolyhedronParaboloid(r1, r2, dz, 0., twopi);
}


G4Polyhedron* G4Paraboloid::GetPolyhedron () const
{
  if (!fpPolyhedron ||
      fRebuildPolyhedron ||
      fpPolyhedron->GetNumberOfRotationStepsAtTimeOfCreation() !=
      fpPolyhedron->GetNumberOfRotationSteps())
  {
    G4AutoLock l(&polyhedronMutex);
    delete fpPolyhedron;
    fpPolyhedron = CreatePolyhedron();
    fRebuildPolyhedron = false;
    l.unlock();
  }
  return fpPolyhedron;
}