G4Para.cc

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//
// $Id: G4Para.cc 107555 2017-11-22 15:26:59Z gcosmo $
//
// class G4Para
//
// Implementation for G4Para class
//
// History:
//
// 29.05.17 E.Tcherniaev: complete revision, speed-up
// 23.09.16 E.Tcherniaev: use G4BoundingEnvelope for CalculateExtent(),
//                      removed CreateRotatedVertices()
// 23.10.05 V.Grichine: bug fixed in DistanceToOut(p,v,...) for the v.x()<0 case
// 28.04.05 V.Grichine: new SurfaceNormal according to J. Apostolakis proposal
// 30.11.04 V.Grichine: modifications in SurfaceNormal for edges/vertices and
//                      in constructor with vertices
// 14.02.02 V.Grichine: bug fixed in Inside according to proposal of D.Wright
// 18.11.99 V.Grichine: kUndef was added to ESide
// 31.10.96 V.Grichine: Modifications according G4Box/Tubs before to commit
// 21.03.95 P.Kent: Modified for `tolerant' geom
//

#include "G4Para.hh"

#if !defined(G4GEOM_USE_UPARA)

#include "G4VoxelLimits.hh"
#include "G4AffineTransform.hh"
#include "G4BoundingEnvelope.hh"
#include "Randomize.hh"

#include "G4VPVParameterisation.hh"

#include "G4VGraphicsScene.hh"

using namespace CLHEP;

//
//  Constructor - set & check half widths

G4Para::G4Para(const G4String& pName,
                     G4double pDx, G4double pDy, G4double pDz,
                     G4double pAlpha, G4double pTheta, G4double pPhi)
  : G4CSGSolid(pName), halfCarTolerance(0.5*kCarTolerance)
{
  SetAllParameters(pDx, pDy, pDz, pAlpha, pTheta, pPhi);
  fRebuildPolyhedron = false;  // default value for G4CSGSolid
}

//
// Constructor - design of trapezoid based on 8 vertices

G4Para::G4Para( const G4String& pName,
                const G4ThreeVector pt[8] )
  : G4CSGSolid(pName), halfCarTolerance(0.5*kCarTolerance)
{
  // Find dimensions and trigonometric values
  // 
  fDx = (pt[3].x() - pt[2].x())*0.5;
  fDy = (pt[2].y() - pt[1].y())*0.5;
  fDz = pt[7].z();
  CheckParameters(); // check dimensions

  fTalpha = (pt[2].x() + pt[3].x() - pt[1].x() - pt[0].x())*0.25/fDy;
  fTthetaCphi = (pt[4].x() + fDy*fTalpha + fDx)/fDz;
  fTthetaSphi = (pt[4].y() + fDy)/fDz;
  MakePlanes();

  // Recompute vertices
  //
  G4ThreeVector v[8];
  G4double DyTalpha = fDy*fTalpha;
  G4double DzTthetaSphi = fDz*fTthetaSphi;
  G4double DzTthetaCphi = fDz*fTthetaCphi;
  v[0].set(-DzTthetaCphi-DyTalpha-fDx, -DzTthetaSphi-fDy, -fDz);
  v[1].set(-DzTthetaCphi-DyTalpha+fDx, -DzTthetaSphi-fDy, -fDz);
  v[2].set(-DzTthetaCphi+DyTalpha-fDx, -DzTthetaSphi+fDy, -fDz);
  v[3].set(-DzTthetaCphi+DyTalpha+fDx, -DzTthetaSphi+fDy, -fDz);
  v[4].set( DzTthetaCphi-DyTalpha-fDx,  DzTthetaSphi-fDy,  fDz);
  v[5].set( DzTthetaCphi-DyTalpha+fDx,  DzTthetaSphi-fDy,  fDz);
  v[6].set( DzTthetaCphi+DyTalpha-fDx,  DzTthetaSphi+fDy,  fDz);
  v[7].set( DzTthetaCphi+DyTalpha+fDx,  DzTthetaSphi+fDy,  fDz);

  // Compare with original vertices
  //
  for (G4int i=0; i<8; ++i)
  {
    G4double delx = std::abs(pt[i].x() - v[i].x());
    G4double dely = std::abs(pt[i].y() - v[i].y());
    G4double delz = std::abs(pt[i].z() - v[i].z());
    G4double discrepancy = std::max(std::max(delx,dely),delz);
    if (discrepancy > 0.1*kCarTolerance)
    {
      std::ostringstream message;
      G4int oldprc = message.precision(16);
      message << "Invalid vertice coordinates for Solid: " << GetName()
              << "\nVertix #" << i << ", discrepancy = " << discrepancy
              << "\n  original   : " << pt[i]
              << "\n  recomputed : " << v[i];
      G4cout.precision(oldprc);
      G4Exception("G4Para::G4Para()", "GeomSolids0002",
                  FatalException, message);

    }
  }
}

//
// Fake default constructor - sets only member data and allocates memory
//                            for usage restricted to object persistency

G4Para::G4Para( __void__& a )
  : G4CSGSolid(a), halfCarTolerance(0.5*kCarTolerance)
{
  SetAllParameters(1., 1., 1., 0., 0., 0.);
  fRebuildPolyhedron = false; // default value for G4CSGSolid
}

//
// Destructor

G4Para::~G4Para()
{
}

//
// Copy constructor

G4Para::G4Para(const G4Para& rhs)
  : G4CSGSolid(rhs), halfCarTolerance(rhs.halfCarTolerance),
    fDx(rhs.fDx), fDy(rhs.fDy), fDz(rhs.fDz), fTalpha(rhs.fTalpha),
    fTthetaCphi(rhs.fTthetaCphi),fTthetaSphi(rhs.fTthetaSphi)
{
  for (G4int i=0; i<4; ++i) { fPlanes[i] = rhs.fPlanes[i]; }
}

//
// Assignment operator

G4Para& G4Para::operator = (const G4Para& rhs)
{
   // Check assignment to self
   //
   if (this == &rhs)  { return *this; }

   // Copy base class data
   //
   G4CSGSolid::operator=(rhs);

   // Copy data
   //
   halfCarTolerance = rhs.halfCarTolerance;
   fDx = rhs.fDx;
   fDy = rhs.fDy;
   fDz = rhs.fDz;
   fTalpha = rhs.fTalpha;
   fTthetaCphi = rhs.fTthetaCphi;
   fTthetaSphi = rhs.fTthetaSphi;
   for (G4int i=0; i<4; ++i) { fPlanes[i] = rhs.fPlanes[i]; }

   return *this;
}

//
// Set all parameters, as for constructor - set and check half-widths

void G4Para::SetAllParameters(G4double pDx, G4double pDy, G4double pDz,
                              G4double pAlpha, G4double pTheta, G4double pPhi)
{
  // Reset data of the base class
  fCubicVolume = 0;
  fSurfaceArea = 0;
  fRebuildPolyhedron = true;

  // Set parameters
  fDx = pDx;
  fDy = pDy;
  fDz = pDz;
  fTalpha = std::tan(pAlpha);
  fTthetaCphi = std::tan(pTheta)*std::cos(pPhi);
  fTthetaSphi = std::tan(pTheta)*std::sin(pPhi);

  CheckParameters();
  MakePlanes();
}

//
// Check dimensions

void G4Para::CheckParameters()
{
  if (fDx < 2*kCarTolerance ||
      fDy < 2*kCarTolerance ||
      fDz < 2*kCarTolerance)
  {
    std::ostringstream message;
    message << "Invalid (too small or negative) dimensions for Solid: "
            << GetName()
            << "\n  X - " << fDx
            << "\n  Y - " << fDy
            << "\n  Z - " << fDz;
    G4Exception("G4Para::CheckParameters()", "GeomSolids0002",
                FatalException, message);
  }
}

//
// Set side planes

void G4Para::MakePlanes()
{
  G4ThreeVector vx(1, 0, 0);
  G4ThreeVector vy(fTalpha, 1, 0);
  G4ThreeVector vz(fTthetaCphi, fTthetaSphi, 1);

  // Set -Y & +Y planes
  //
  G4ThreeVector ynorm = (vx.cross(vz)).unit();

  fPlanes[0].a = 0.;
  fPlanes[0].b = ynorm.y();
  fPlanes[0].c = ynorm.z();
  fPlanes[0].d = fPlanes[0].b*fDy; // point (0,fDy,0) is on plane

  fPlanes[1].a =  0.;
  fPlanes[1].b = -fPlanes[0].b;
  fPlanes[1].c = -fPlanes[0].c;
  fPlanes[1].d =  fPlanes[0].d;

  // Set -X & +X planes
  //
  G4ThreeVector xnorm = (vz.cross(vy)).unit();

  fPlanes[2].a = xnorm.x();
  fPlanes[2].b = xnorm.y();
  fPlanes[2].c = xnorm.z();
  fPlanes[2].d = fPlanes[2].a*fDx; // point (fDx,0,0) is on plane

  fPlanes[3].a = -fPlanes[2].a;
  fPlanes[3].b = -fPlanes[2].b;
  fPlanes[3].c = -fPlanes[2].c;
  fPlanes[3].d =  fPlanes[2].d;
}

//
// Get volume

G4double G4Para::GetCubicVolume()
{
  // It is like G4Box, since para transformations keep the volume to be const
  if (fCubicVolume == 0)
  {
    fCubicVolume = 8*fDx*fDy*fDz;
  }
  return fCubicVolume;
}

//
// Get surface area

G4double G4Para::GetSurfaceArea()
{
  if(fSurfaceArea == 0)
  {
    G4ThreeVector vx(fDx, 0, 0);
    G4ThreeVector vy(fDy*fTalpha, fDy, 0);
    G4ThreeVector vz(fDz*fTthetaCphi, fDz*fTthetaSphi, fDz);

    G4double sxy = fDx*fDy; // (vx.cross(vy)).mag();
    G4double sxz = (vx.cross(vz)).mag();
    G4double syz = (vy.cross(vz)).mag();

    fSurfaceArea = 8*(sxy+sxz+syz);
  }
  return fSurfaceArea;
}

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

void G4Para::ComputeDimensions(      G4VPVParameterisation* p,
                                const G4int n,
                                const G4VPhysicalVolume* pRep )
{
  p->ComputeDimensions(*this,n,pRep);
}

//
// Get bounding box

void G4Para::BoundingLimits(G4ThreeVector& pMin, G4ThreeVector& pMax) const
{
  G4double dz = GetZHalfLength();
  G4double dx = GetXHalfLength();
  G4double dy = GetYHalfLength();

  G4double x0 = dz*fTthetaCphi;
  G4double x1 = dy*GetTanAlpha();
  G4double xmin =
    std::min(
    std::min(
    std::min(-x0-x1-dx,-x0+x1-dx),x0-x1-dx),x0+x1-dx);
  G4double xmax =
    std::max(
    std::max(
    std::max(-x0-x1+dx,-x0+x1+dx),x0-x1+dx),x0+x1+dx);

  G4double y0 = dz*fTthetaSphi;
  G4double ymin = std::min(-y0-dy,y0-dy);
  G4double ymax = std::max(-y0+dy,y0+dy);

  pMin.set(xmin,ymin,-dz);
  pMax.set(xmax,ymax, dz);

  // Check correctness of the bounding box
  //
  if (pMin.x() >= pMax.x() || pMin.y() >= pMax.y() || pMin.z() >= pMax.z())
  {
    std::ostringstream message;
    message << "Bad bounding box (min >= max) for solid: "
            << GetName() << " !"
            << "\npMin = " << pMin
            << "\npMax = " << pMax;
    G4Exception("G4Para::BoundingLimits()", "GeomMgt0001",
                JustWarning, message);
    DumpInfo();
  }
}

//
// Calculate extent under transform and specified limit

G4bool G4Para::CalculateExtent( const EAxis pAxis,
                                const G4VoxelLimits& pVoxelLimit,
                                const G4AffineTransform& pTransform,
                                     G4double& pMin, G4double& pMax ) const
{
  G4ThreeVector bmin, bmax;
  G4bool exist;

  // Check bounding box (bbox)
  //
  BoundingLimits(bmin,bmax);
  G4BoundingEnvelope bbox(bmin,bmax);
#ifdef G4BBOX_EXTENT
  if (true) return bbox.CalculateExtent(pAxis,pVoxelLimit,pTransform,pMin,pMax);
#endif
  if (bbox.BoundingBoxVsVoxelLimits(pAxis,pVoxelLimit,pTransform,pMin,pMax))
  {
    return exist = (pMin < pMax) ? true : false;
  }

  // Set bounding envelope (benv) and calculate extent
  //
  G4double dz = GetZHalfLength();
  G4double dx = GetXHalfLength();
  G4double dy = GetYHalfLength();

  G4double x0 = dz*fTthetaCphi;
  G4double x1 = dy*GetTanAlpha();
  G4double y0 = dz*fTthetaSphi;

  G4ThreeVectorList baseA(4), baseB(4);
  baseA[0].set(-x0-x1-dx,-y0-dy,-dz);
  baseA[1].set(-x0-x1+dx,-y0-dy,-dz);
  baseA[2].set(-x0+x1+dx,-y0+dy,-dz);
  baseA[3].set(-x0+x1-dx,-y0+dy,-dz);

  baseB[0].set(+x0-x1-dx, y0-dy, dz);
  baseB[1].set(+x0-x1+dx, y0-dy, dz);
  baseB[2].set(+x0+x1+dx, y0+dy, dz);
  baseB[3].set(+x0+x1-dx, y0+dy, dz);

  std::vector<const G4ThreeVectorList *> polygons(2);
  polygons[0] = &baseA;
  polygons[1] = &baseB;

  G4BoundingEnvelope benv(bmin,bmax,polygons);
  exist = benv.CalculateExtent(pAxis,pVoxelLimit,pTransform,pMin,pMax);
  return exist;
}

//
// Determine where is point p, inside/on_surface/outside
//

EInside G4Para::Inside( const G4ThreeVector& p ) const
{
  G4double xx = fPlanes[2].a*p.x()+fPlanes[2].b*p.y()+fPlanes[2].c*p.z();
  G4double dx = std::abs(xx) + fPlanes[2].d;

  G4double yy = fPlanes[0].b*p.y()+fPlanes[0].c*p.z();
  G4double dy = std::abs(yy) + fPlanes[0].d;
  G4double dxy = std::max(dx,dy);

  G4double dz = std::abs(p.z())-fDz;
  G4double dist = std::max(dxy,dz);

  if (dist > halfCarTolerance) return kOutside;
  return (dist > -halfCarTolerance) ? kSurface : kInside;
}

//
// Determine side where point is, and return corresponding normal

G4ThreeVector G4Para::SurfaceNormal( const G4ThreeVector& p ) const
{
  G4int nsurf = 0; // number of surfaces where p is placed

  // Check Z faces
  //
  G4double nz = 0;
  G4double dz = std::abs(p.z()) - fDz;
  if (std::abs(dz) <= halfCarTolerance)
  {
    nz = (p.z() < 0) ? -1 : 1;
    ++nsurf;
  }

  // Check Y faces
  //
  G4double ny = 0;
  G4double yy = fPlanes[0].b*p.y()+fPlanes[0].c*p.z();
  if (std::abs(fPlanes[0].d + yy) <= halfCarTolerance)
  {
    ny  = fPlanes[0].b;
    nz += fPlanes[0].c;
    ++nsurf;
  }
  else if (std::abs(fPlanes[1].d - yy) <= halfCarTolerance)
  {
    ny  = fPlanes[1].b;
    nz += fPlanes[1].c;
    ++nsurf;
  }

  // Check X faces
  //
  G4double nx = 0;
  G4double xx = fPlanes[2].a*p.x()+fPlanes[2].b*p.y()+fPlanes[2].c*p.z();
  if (std::abs(fPlanes[2].d + xx) <= halfCarTolerance)
  {
    nx  = fPlanes[2].a;
    ny += fPlanes[2].b;
    nz += fPlanes[2].c;
    ++nsurf;
  }
  else if (std::abs(fPlanes[3].d - xx) <= halfCarTolerance)
  {
    nx  = fPlanes[3].a;
    ny += fPlanes[3].b;
    nz += fPlanes[3].c;
    ++nsurf;
  }

  // Return normal
  //
  if (nsurf == 1)      return G4ThreeVector(nx,ny,nz);
  else if (nsurf != 0) return G4ThreeVector(nx,ny,nz).unit(); // edge or corner
  else
  {
    // Point is not on the surface
    //
#ifdef G4CSGDEBUG
    std::ostringstream message;
    G4int oldprc = message.precision(16);
    message << "Point p is not on surface (!?) of solid: "
            << GetName() << G4endl;
    message << "Position:\n";
    message << "   p.x() = " << p.x()/mm << " mm\n";
    message << "   p.y() = " << p.y()/mm << " mm\n";
    message << "   p.z() = " << p.z()/mm << " mm";
    G4cout.precision(oldprc) ;
    G4Exception("G4Para::SurfaceNormal(p)", "GeomSolids1002",
                JustWarning, message );
    DumpInfo();
#endif
    return ApproxSurfaceNormal(p);
  }
}

//
// Algorithm for SurfaceNormal() following the original specification
// for points not on the surface

G4ThreeVector G4Para::ApproxSurfaceNormal( const G4ThreeVector& p ) const
{
  G4double dist = -DBL_MAX;
  G4int iside = 0;
  for (G4int i=0; i<4; ++i)
  {
    G4double d = fPlanes[i].a*p.x() +
                 fPlanes[i].b*p.y() +
                 fPlanes[i].c*p.z() + fPlanes[i].d;
    if (d > dist) { dist = d; iside = i; }
  }

  G4double distz = std::abs(p.z()) - fDz;
  if (dist > distz)
    return G4ThreeVector(fPlanes[iside].a, fPlanes[iside].b, fPlanes[iside].c);
  else
    return G4ThreeVector(0, 0, (p.z() < 0) ? -1 : 1);
}

//
// Calculate distance to shape from outside
//  - return kInfinity if no intersection

G4double G4Para::DistanceToIn(const G4ThreeVector& p,
                              const G4ThreeVector& v ) const
{
  // Z intersections
  //
  if ((std::abs(p.z()) - fDz) >= -halfCarTolerance && p.z()*v.z() >= 0)
    return kInfinity;
  G4double invz = (-v.z() == 0) ? DBL_MAX : -1./v.z();
  G4double dz = (invz < 0) ? fDz : -fDz; 
  G4double tzmin = (p.z() + dz)*invz;
  G4double tzmax = (p.z() - dz)*invz;

  // Y intersections
  //
  G4double tmin0 = tzmin, tmax0 = tzmax;
  G4double cos0 = fPlanes[0].b*v.y() + fPlanes[0].c*v.z();
  G4double disy = fPlanes[0].b*p.y() + fPlanes[0].c*p.z();
  G4double dis0 = fPlanes[0].d + disy;
  if (dis0 >= -halfCarTolerance)
  {
    if (cos0 >= 0) return kInfinity;
    G4double tmp  = -dis0/cos0;
    if (tmin0 < tmp) tmin0 = tmp;
  }
  else if (cos0 > 0)
  {
    G4double tmp  = -dis0/cos0;
    if (tmax0 > tmp) tmax0 = tmp;
  }

  G4double tmin1 = tmin0, tmax1 = tmax0;
  G4double cos1 = -cos0;
  G4double dis1 = fPlanes[1].d - disy;
  if (dis1 >= -halfCarTolerance)
  {
    if (cos1 >= 0) return kInfinity;
    G4double tmp  = -dis1/cos1;
    if (tmin1 < tmp) tmin1 = tmp;
  }
  else if (cos1 > 0)
  {
    G4double tmp  = -dis1/cos1;
    if (tmax1 > tmp) tmax1 = tmp;
  }

  // X intersections
  //
  G4double tmin2 = tmin1, tmax2 = tmax1;
  G4double cos2 = fPlanes[2].a*v.x() + fPlanes[2].b*v.y() + fPlanes[2].c*v.z();
  G4double disx = fPlanes[2].a*p.x() + fPlanes[2].b*p.y() + fPlanes[2].c*p.z();
  G4double dis2 = fPlanes[2].d + disx;
  if (dis2 >= -halfCarTolerance)
  {
    if (cos2 >= 0) return kInfinity;
    G4double tmp  = -dis2/cos2;
    if (tmin2 < tmp) tmin2 = tmp;
  }
  else if (cos2 > 0)
  {
    G4double tmp  = -dis2/cos2;
    if (tmax2 > tmp) tmax2 = tmp;
  }

  G4double tmin3 = tmin2, tmax3 = tmax2;
  G4double cos3 = -cos2;
  G4double dis3 = fPlanes[3].d - disx;
  if (dis3 >= -halfCarTolerance)
  {
    if (cos3 >= 0) return kInfinity;
    G4double tmp  = -dis3/cos3;
    if (tmin3 < tmp) tmin3 = tmp;
  }
  else if (cos3 > 0)
  {
    G4double tmp  = -dis3/cos3;
    if (tmax3 > tmp) tmax3 = tmp;
  }

  // Find distance
  //
  G4double tmin = tmin3, tmax = tmax3;
  if (tmax <= tmin + halfCarTolerance) return kInfinity; // touch or no hit
  return (tmin < halfCarTolerance ) ? 0. : tmin;
}

//
// Calculate exact shortest distance to any boundary from outside
// - returns 0 is point inside

G4double G4Para::DistanceToIn( const G4ThreeVector& p ) const
{
  G4double xx = fPlanes[2].a*p.x()+fPlanes[2].b*p.y()+fPlanes[2].c*p.z();
  G4double dx = std::abs(xx) + fPlanes[2].d;

  G4double yy = fPlanes[0].b*p.y()+fPlanes[0].c*p.z();
  G4double dy = std::abs(yy) + fPlanes[0].d;
  G4double dxy = std::max(dx,dy);

  G4double dz = std::abs(p.z())-fDz;
  G4double dist = std::max(dxy,dz);

  return (dist > 0) ? dist : 0.;
}

//
// Calculate distance to surface of shape from inside and, if required,
// find normal at exit point
// - when leaving the surface, return 0

G4double G4Para::DistanceToOut(const G4ThreeVector& p, const G4ThreeVector& v,
                               const G4bool calcNorm,
                                     G4bool *validNorm, G4ThreeVector *n) const
{
  // Z intersections
  //
  if ((std::abs(p.z()) - fDz) >= -halfCarTolerance && p.z()*v.z() > 0)
  {
    if (calcNorm)
    {
      *validNorm = true;
      n->set(0, 0, (p.z() < 0) ? -1 : 1);
    }
    return 0.;
  }
  G4double vz = v.z();
  G4double tmax = (vz == 0) ? DBL_MAX : (std::copysign(fDz,vz) - p.z())/vz;
  G4int iside = (vz < 0) ? -4 : -2; // little trick: (-4+3)=-1, (-2+3)=+1

  // Y intersections
  //
  G4double cos0 = fPlanes[0].b*v.y() + fPlanes[0].c*v.z();
  if (cos0 > 0)
  {
    G4double dis0 = fPlanes[0].b*p.y() + fPlanes[0].c*p.z() + fPlanes[0].d;
    if (dis0 >= -halfCarTolerance)
    {
      if (calcNorm)
      {
        *validNorm = true;
        n->set(0, fPlanes[0].b, fPlanes[0].c);
      }
      return 0.;
    }
    G4double tmp = -dis0/cos0;
    if (tmax > tmp) { tmax = tmp; iside = 0; }
  }

  G4double cos1 = -cos0;
  if (cos1 > 0)
  {
    G4double dis1 = fPlanes[1].b*p.y() + fPlanes[1].c*p.z() + fPlanes[1].d;
    if (dis1 >= -halfCarTolerance)
    {
      if (calcNorm)
      {
        *validNorm = true;
        n->set(0, fPlanes[1].b, fPlanes[1].c);
      }
      return 0.;
    }
    G4double tmp = -dis1/cos1;
    if (tmax > tmp) { tmax = tmp; iside = 1; }
  }

  // X intersections
  //
  G4double cos2 = fPlanes[2].a*v.x() + fPlanes[2].b*v.y() + fPlanes[2].c*v.z();
  if (cos2 > 0)
  {
    G4double dis2 = fPlanes[2].a*p.x()+fPlanes[2].b*p.y()+fPlanes[2].c*p.z()+fPlanes[2].d;
    if (dis2 >= -halfCarTolerance)
    {
      if (calcNorm)
      {
         *validNorm = true;
         n->set(fPlanes[2].a, fPlanes[2].b, fPlanes[2].c);
      }
      return 0.;
    }
    G4double tmp = -dis2/cos2;
    if (tmax > tmp) { tmax = tmp; iside = 2; }
  }

  G4double cos3 = -cos2;
  if (cos3 > 0)
  {
    G4double dis3 = fPlanes[3].a*p.x()+fPlanes[3].b*p.y()+fPlanes[3].c*p.z()+fPlanes[3].d;
    if (dis3 >= -halfCarTolerance)
    {
      if (calcNorm)
      {
         *validNorm = true;
         n->set(fPlanes[3].a, fPlanes[3].b, fPlanes[3].c);
      }
      return 0.;
    }
    G4double tmp = -dis3/cos3;
    if (tmax > tmp) { tmax = tmp; iside = 3; }
  }

  // Set normal, if required, and return distance
  //
  if (calcNorm) 
  {
    *validNorm = true;
    if (iside < 0)
      n->set(0, 0, iside + 3); // (-4+3)=-1, (-2+3)=+1
    else
      n->set(fPlanes[iside].a, fPlanes[iside].b, fPlanes[iside].c);
  }
  return tmax;
}

//
// Calculate exact shortest distance to any boundary from inside
// - returns 0 is point outside

G4double G4Para::DistanceToOut( const G4ThreeVector& p ) const
{
#ifdef G4CSGDEBUG
  if( Inside(p) == kOutside )
  {
    std::ostringstream message;
    G4int oldprc = message.precision(16);
    message << "Point p is outside (!?) of solid: " << GetName() << G4endl;
    message << "Position:\n";
    message << "   p.x() = " << p.x()/mm << " mm\n";
    message << "   p.y() = " << p.y()/mm << " mm\n";
    message << "   p.z() = " << p.z()/mm << " mm";
    G4cout.precision(oldprc) ;
    G4Exception("G4Para::DistanceToOut(p)", "GeomSolids1002",
                JustWarning, message );
    DumpInfo();
    }
#endif
  G4double xx = fPlanes[2].a*p.x()+fPlanes[2].b*p.y()+fPlanes[2].c*p.z();
  G4double dx = std::abs(xx) + fPlanes[2].d;

  G4double yy = fPlanes[0].b*p.y()+fPlanes[0].c*p.z();
  G4double dy = std::abs(yy) + fPlanes[0].d;
  G4double dxy = std::max(dx,dy);

  G4double dz = std::abs(p.z())-fDz;
  G4double dist = std::max(dxy,dz);

  return (dist < 0) ? -dist : 0.;
}

//
// GetEntityType

G4GeometryType G4Para::GetEntityType() const
{
  return G4String("G4Para");
}

//
// Make a clone of the object
//
G4VSolid* G4Para::Clone() const
{
  return new G4Para(*this);
}

//
// Stream object contents to an output stream

std::ostream& G4Para::StreamInfo( std::ostream& os ) const
{
  G4double alpha = std::atan(fTalpha);
  G4double theta = std::atan(std::sqrt(fTthetaCphi*fTthetaCphi +
                                       fTthetaSphi*fTthetaSphi));
  G4double phi   = std::atan2(fTthetaSphi,fTthetaCphi);
  G4String signDegree = "\u00B0";

  G4int oldprc = os.precision(16);
  os << "-----------------------------------------------------------\n"
     << "    *** Dump for solid - " << GetName() << " ***\n"
     << "    ===================================================\n"
     << " Solid type: G4Para\n"
     << " Parameters:\n"
     << "    half length X: " << fDx/mm << " mm\n"
     << "    half length Y: " << fDy/mm << " mm\n"
     << "    half length Z: " << fDz/mm << " mm\n"
     << "    alpha: " << alpha/degree << signDegree << "\n"
     << "    theta: " << theta/degree << signDegree << "\n"
     << "    phi: " << phi/degree << signDegree << "\n"
     << "-----------------------------------------------------------\n";
  os.precision(oldprc);

  return os;
}

//
// Return a point randomly and uniformly selected on the solid surface

G4ThreeVector G4Para::GetPointOnSurface() const
{
  G4double DyTalpha = fDy*fTalpha;
  G4double DzTthetaSphi = fDz*fTthetaSphi;
  G4double DzTthetaCphi = fDz*fTthetaCphi;

  // Set vertices
  //
  G4ThreeVector pt[8];
  pt[0].set(-DzTthetaCphi-DyTalpha-fDx, -DzTthetaSphi-fDy, -fDz);
  pt[1].set(-DzTthetaCphi-DyTalpha+fDx, -DzTthetaSphi-fDy, -fDz);
  pt[2].set(-DzTthetaCphi+DyTalpha-fDx, -DzTthetaSphi+fDy, -fDz);
  pt[3].set(-DzTthetaCphi+DyTalpha+fDx, -DzTthetaSphi+fDy, -fDz);
  pt[4].set( DzTthetaCphi-DyTalpha-fDx,  DzTthetaSphi-fDy,  fDz);
  pt[5].set( DzTthetaCphi-DyTalpha+fDx,  DzTthetaSphi-fDy,  fDz);
  pt[6].set( DzTthetaCphi+DyTalpha-fDx,  DzTthetaSphi+fDy,  fDz);
  pt[7].set( DzTthetaCphi+DyTalpha+fDx,  DzTthetaSphi+fDy,  fDz);

  // Set areas (-Z, -Y, +Y, -X, +X, +Z)
  //
  G4ThreeVector vx(fDx, 0, 0);
  G4ThreeVector vy(DyTalpha, fDy, 0);
  G4ThreeVector vz(DzTthetaCphi, DzTthetaSphi, fDz);

  G4double sxy = fDx*fDy; // (vx.cross(vy)).mag();
  G4double sxz = (vx.cross(vz)).mag();
  G4double syz = (vy.cross(vz)).mag();
  
  G4double sface[6] = { sxy, syz, syz, sxz, sxz, sxy };
  for (G4int i=1; i<6; ++i) { sface[i] += sface[i-1]; }

  // Select face
  //
  G4double select = sface[5]*G4UniformRand();
  G4int k = 5;
  if (select <= sface[4]) k = 4;
  if (select <= sface[3]) k = 3;
  if (select <= sface[2]) k = 2;
  if (select <= sface[1]) k = 1;
  if (select <= sface[0]) k = 0;

  // Generate point
  //
  G4int ip[6][3] = {{0,1,2}, {0,4,1}, {2,3,6}, {0,2,4}, {1,5,3}, {4,6,5}};
  G4double u = G4UniformRand();
  G4double v = G4UniformRand();
  return (1.-u-v)*pt[ip[k][0]] + u*pt[ip[k][1]] + v*pt[ip[k][2]];
}

//
// Methods for visualisation

void G4Para::DescribeYourselfTo ( G4VGraphicsScene& scene ) const
{
  scene.AddSolid (*this);
}

G4Polyhedron* G4Para::CreatePolyhedron () const
{
  G4double phi = std::atan2(fTthetaSphi, fTthetaCphi);
  G4double alpha = std::atan(fTalpha);
  G4double theta = std::atan(std::sqrt(fTthetaCphi*fTthetaCphi +
                                       fTthetaSphi*fTthetaSphi));
    
  return new G4PolyhedronPara(fDx, fDy, fDz, alpha, theta, phi);
}
#endif