G4Trd.cc

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//
// $Id: G4Trd.cc 81636 2014-06-04 09:06:08Z gcosmo $
//
//
// Implementation for G4Trd class
//
// History:
//
// 28.04.05 V.Grichine: new SurfaceNormal according to J. Apostolakis proposal 
// 26.04.05, V.Grichine, new SurfaceNoramal is default
// 07.12.04, V.Grichine, SurfaceNoramal with edges/vertices.
// 07.05.00, V.Grichine, in d = DistanceToIn(p,v), if d<0.5*kCarTolerance, d=0
//    ~1996, V.Grichine, 1st implementation based on old code of P.Kent
//

#include "G4Trd.hh"

#if !defined(G4GEOM_USE_UTRD)

#include "G4VPVParameterisation.hh"
#include "G4VoxelLimits.hh"
#include "G4AffineTransform.hh"
#include "Randomize.hh"

#include "G4VGraphicsScene.hh"

using namespace CLHEP;

//
// Constructor - check & set half widths

G4Trd::G4Trd( const G4String& pName,
                    G4double pdx1,  G4double pdx2,
                    G4double pdy1,  G4double pdy2,
                    G4double pdz )
  : G4CSGSolid(pName)
{
  CheckAndSetAllParameters (pdx1, pdx2, pdy1, pdy2, pdz);
}

//
// Set and check (coplanarity) of trd parameters

void G4Trd::CheckAndSetAllParameters ( G4double pdx1,  G4double pdx2,
                                       G4double pdy1,  G4double pdy2,
                                       G4double pdz ) 
{
  if ( pdx1>0&&pdx2>0&&pdy1>0&&pdy2>0&&pdz>0 )
  {
    fDx1=pdx1; fDx2=pdx2;
    fDy1=pdy1; fDy2=pdy2;
    fDz=pdz;
  }
  else
  {
    if ( pdx1>=0 && pdx2>=0 && pdy1>=0 && pdy2>=0 && pdz>=0 )
    {
      // G4double  Minimum_length= (1+per_thousand) * kCarTolerance/2.;
      // FIX-ME : temporary solution for ZERO or very-small parameters
      //
      G4double  Minimum_length= kCarTolerance/2.;
      fDx1=std::max(pdx1,Minimum_length); 
      fDx2=std::max(pdx2,Minimum_length); 
      fDy1=std::max(pdy1,Minimum_length); 
      fDy2=std::max(pdy2,Minimum_length); 
      fDz=std::max(pdz,Minimum_length);
    }
    else
    {
      std::ostringstream message;
      message << "Invalid negative dimensions for Solid: " << GetName()
              << G4endl
              << "          X - " << pdx1 << ", " << pdx2 << G4endl
              << "          Y - " << pdy1 << ", " << pdy2 << G4endl
              << "          Z - " << pdz;
      G4Exception("G4Trd::CheckAndSetAllParameters()",
                  "GeomSolids0002", FatalException, message);
    }
  }
  fCubicVolume= 0.;
  fSurfaceArea= 0.;
  fpPolyhedron = 0;
}

//
// Fake default constructor - sets only member data and allocates memory
//                            for usage restricted to object persistency.
//
G4Trd::G4Trd( __void__& a )
  : G4CSGSolid(a), fDx1(0.), fDx2(0.), fDy1(0.), fDy2(0.), fDz(0.)
{
}

//
// Destructor

G4Trd::~G4Trd()
{
}

//
// Copy constructor

G4Trd::G4Trd(const G4Trd& rhs)
  : G4CSGSolid(rhs), fDx1(rhs.fDx1), fDx2(rhs.fDx2),
    fDy1(rhs.fDy1), fDy2(rhs.fDy2), fDz(rhs.fDz)
{
   fpPolyhedron = GetPolyhedron();
}

//
// Assignment operator

G4Trd& G4Trd::operator = (const G4Trd& rhs) 
{
   // Check assignment to self
   //
   if (this == &rhs)  { return *this; }

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

   // Copy data
   //
   fDx1 = rhs.fDx1; fDx2 = rhs.fDx2;
   fDy1 = rhs.fDy1; fDy2 = rhs.fDy2;
   fDz = rhs.fDz;
   fpPolyhedron = GetPolyhedron();

   return *this;
}

//
//

void G4Trd::SetAllParameters ( G4double pdx1, G4double pdx2, G4double pdy1, 
                               G4double pdy2, G4double pdz ) 
{
  CheckAndSetAllParameters (pdx1, pdx2, pdy1, pdy2, pdz);
}


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

void G4Trd::ComputeDimensions(       G4VPVParameterisation* p,
                               const G4int n,
                               const G4VPhysicalVolume* pRep )
{
  p->ComputeDimensions(*this,n,pRep);
}


//
// Calculate extent under transform and specified limit

G4bool G4Trd::CalculateExtent( const EAxis pAxis,
                               const G4VoxelLimits& pVoxelLimit,
                               const G4AffineTransform& pTransform,
                                     G4double& pMin, G4double& pMax ) const
{
  if (!pTransform.IsRotated())
  {
    // Special case handling for unrotated solids
    // 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;

    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();
        }
      }
    }
    xoffset=pTransform.NetTranslation().x();
    if (fDx2 >= fDx1)
    { 
      xMax =  xoffset+(fDx1+fDx2)/2+(zMax-zoffset)*(fDx2-fDx1)/(2*fDz) ;
      xMin = 2*xoffset - xMax ;
    }
    else
    {
      xMax =  xoffset+(fDx1+fDx2)/2+(zMin-zoffset)*(fDx2-fDx1)/(2*fDz) ;
      xMin =  2*xoffset - xMax ;
    }   
    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() ;
    if(fDy2 >= fDy1)
    {
      yMax = yoffset+(fDy2+fDy1)/2+(zMax-zoffset)*(fDy2-fDy1)/(2*fDz) ;
      yMin = 2*yoffset - yMax ;
    }
    else
    {
      yMax = yoffset+(fDy2+fDy1)/2+(zMin-zoffset)*(fDy2-fDy1)/(2*fDz) ;
      yMin = 2*yoffset - yMax ;  
    }  
    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();
        }
      }
    }

    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;
    }

    // Add 2*Tolerance to avoid precision troubles ?
    //
    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;
  }
}

//
// Return whether point inside/outside/on surface, using tolerance

EInside G4Trd::Inside( const G4ThreeVector& p ) const
{  
  EInside in=kOutside;
  G4double x,y,zbase1,zbase2;
    
  if (std::fabs(p.z())<=fDz-kCarTolerance/2)
  {
    zbase1=p.z()+fDz;  // Dist from -ve z plane
    zbase2=fDz-p.z();  // Dist from +ve z plane

    // Check whether inside x tolerance
    //
    x=0.5*(fDx2*zbase1+fDx1*zbase2)/fDz - kCarTolerance/2;
    if (std::fabs(p.x())<=x)
    {
      y=0.5*((fDy2*zbase1+fDy1*zbase2))/fDz - kCarTolerance/2;
      if (std::fabs(p.y())<=y)
      {
        in=kInside;
      }
      else if (std::fabs(p.y())<=y+kCarTolerance)
      {
        in=kSurface;
      }
    }
    else if (std::fabs(p.x())<=x+kCarTolerance)
    {
      // y = y half width of shape at z of point + tolerant boundary
      //
      y=0.5*((fDy2*zbase1+fDy1*zbase2))/fDz + kCarTolerance/2;
      if (std::fabs(p.y())<=y)
      {
        in=kSurface;
      }
    }
  }
  else if (std::fabs(p.z())<=fDz+kCarTolerance/2)
  {
    // Only need to check outer tolerant boundaries
    //
    zbase1=p.z()+fDz;  // Dist from -ve z plane
    zbase2=fDz-p.z();   // Dist from +ve z plane

    // x = x half width of shape at z of point plus tolerance
    //
    x=0.5*(fDx2*zbase1+fDx1*zbase2)/fDz + kCarTolerance/2;
    if (std::fabs(p.x())<=x)
    {
      // y = y half width of shape at z of point
      //
      y=0.5*((fDy2*zbase1+fDy1*zbase2))/fDz + kCarTolerance/2;
      if (std::fabs(p.y())<=y) in=kSurface;
    }
  }  
  return in;
}

//
// Calculate side nearest to p, and return normal
// If two sides are equidistant, normal of first side (x/y/z) 
// encountered returned

G4ThreeVector G4Trd::SurfaceNormal( const G4ThreeVector& p ) const
{
  G4ThreeVector norm, sumnorm(0.,0.,0.);
  G4int noSurfaces = 0; 
  G4double z = 2.0*fDz, tanx, secx, newpx, widx;
  G4double tany, secy, newpy, widy;
  G4double distx, disty, distz, fcos;
  G4double delta = 0.5*kCarTolerance;

  tanx  = (fDx2 - fDx1)/z;
  secx  = std::sqrt(1.0+tanx*tanx);
  newpx = std::fabs(p.x())-p.z()*tanx;
  widx  = fDx2 - fDz*tanx;

  tany  = (fDy2 - fDy1)/z;
  secy  = std::sqrt(1.0+tany*tany);
  newpy = std::fabs(p.y())-p.z()*tany;
  widy  = fDy2 - fDz*tany;

  distx = std::fabs(newpx-widx)/secx;       // perp. distance to x side
  disty = std::fabs(newpy-widy)/secy;       //                to y side
  distz = std::fabs(std::fabs(p.z())-fDz);  //                to z side

  fcos              = 1.0/secx;
  G4ThreeVector nX  = G4ThreeVector( fcos,0,-tanx*fcos);
  G4ThreeVector nmX = G4ThreeVector(-fcos,0,-tanx*fcos);

  fcos              = 1.0/secy;
  G4ThreeVector nY  = G4ThreeVector(0, fcos,-tany*fcos);
  G4ThreeVector nmY = G4ThreeVector(0,-fcos,-tany*fcos);
  G4ThreeVector nZ  = G4ThreeVector( 0, 0,  1.0);
 
  if (distx <= delta)      
  {
    noSurfaces ++;
    if ( p.x() >= 0.) sumnorm += nX;
    else              sumnorm += nmX;   
  }
  if (disty <= delta)
  {
    noSurfaces ++;
    if ( p.y() >= 0.) sumnorm += nY;
    else              sumnorm += nmY;   
  }
  if (distz <= delta)  
  {
    noSurfaces ++;
    if ( p.z() >= 0.) sumnorm += nZ;
    else              sumnorm -= nZ; 
  }
  if ( noSurfaces == 0 )
  {
#ifdef G4CSGDEBUG
    G4Exception("G4Trd::SurfaceNormal(p)", "GeomSolids1002", JustWarning, 
                "Point p is not on surface !?" );
#endif 
     norm = ApproxSurfaceNormal(p);
  }
  else if ( noSurfaces == 1 ) norm = sumnorm;
  else                        norm = sumnorm.unit();
  return norm;   
}


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

G4ThreeVector G4Trd::ApproxSurfaceNormal( const G4ThreeVector& p ) const
{
  G4ThreeVector norm;
  G4double z,tanx,secx,newpx,widx;
  G4double tany,secy,newpy,widy;
  G4double distx,disty,distz,fcos;

  z=2.0*fDz;

  tanx=(fDx2-fDx1)/z;
  secx=std::sqrt(1.0+tanx*tanx);
  newpx=std::fabs(p.x())-p.z()*tanx;
  widx=fDx2-fDz*tanx;

  tany=(fDy2-fDy1)/z;
  secy=std::sqrt(1.0+tany*tany);
  newpy=std::fabs(p.y())-p.z()*tany;
  widy=fDy2-fDz*tany;

  distx=std::fabs(newpx-widx)/secx;  // perpendicular distance to x side
  disty=std::fabs(newpy-widy)/secy;  //                        to y side
  distz=std::fabs(std::fabs(p.z())-fDz);  //                        to z side

  // find closest side
  //
  if (distx<=disty)
  { 
    if (distx<=distz) 
    {
      // Closest to X
      //
      fcos=1.0/secx;
      // normal=(+/-std::cos(ang),0,-std::sin(ang))
      if (p.x()>=0)
        norm=G4ThreeVector(fcos,0,-tanx*fcos);
      else
        norm=G4ThreeVector(-fcos,0,-tanx*fcos);
    }
    else
    {
      // Closest to Z
      //
      if (p.z()>=0)
        norm=G4ThreeVector(0,0,1);
      else
        norm=G4ThreeVector(0,0,-1);
    }
  }
  else
  {  
    if (disty<=distz)
    {
      // Closest to Y
      //
      fcos=1.0/secy;
      if (p.y()>=0)
        norm=G4ThreeVector(0,fcos,-tany*fcos);
      else
        norm=G4ThreeVector(0,-fcos,-tany*fcos);
    }
    else 
    {
      // Closest to Z
      //
      if (p.z()>=0)
        norm=G4ThreeVector(0,0,1);
      else
        norm=G4ThreeVector(0,0,-1);
    }
  }
  return norm;   
}

//
// Calculate distance to shape from outside
// - return kInfinity if no intersection
//
// ALGORITHM:
// For each component, calculate pair of minimum and maximum intersection
// values for which the particle is in the extent of the shape
// - The smallest (MAX minimum) allowed distance of the pairs is intersect
// - Z plane intersectin uses tolerance
// - XZ YZ planes use logic & *SLIGHTLY INCORRECT* tolerance
//   (this saves at least 1 sqrt, 1 multiply and 1 divide... in applicable
//    cases)
// - Note: XZ and YZ planes each divide space into four regions,
//   characterised by ss1 ss2
// NOTE:
//
// `Inside' safe - meaningful answers given if point is inside the exact
// shape.

G4double G4Trd::DistanceToIn( const G4ThreeVector& p,
                              const G4ThreeVector& v ) const
{  
  G4double snxt = kInfinity ;    // snxt = default return value
  G4double smin,smax;
  G4double s1,s2,tanxz,tanyz,ds1,ds2;
  G4double ss1,ss2,sn1=0.,sn2=0.,Dist;

  if ( v.z() )  // Calculate valid z intersect range
  {
    if ( v.z() > 0 )   // Calculate smax: must be +ve or no intersection.
    {
      Dist = fDz - p.z() ;  // to plane at +dz

      if (Dist >= 0.5*kCarTolerance)
      {
        smax = Dist/v.z() ;
        smin = -(fDz + p.z())/v.z() ;
      }
      else  return snxt ;
    }
    else // v.z <0
    {
      Dist=fDz+p.z();  // plane at -dz

      if ( Dist >= 0.5*kCarTolerance )
      {
        smax = -Dist/v.z() ;
        smin = (fDz - p.z())/v.z() ;
      }
      else return snxt ; 
    }
    if (smin < 0 ) smin = 0 ;
  }
  else // v.z=0
  {
    if (std::fabs(p.z()) >= fDz ) return snxt ;     // Outside & no intersect
    else
    {
      smin = 0 ;    // Always inside z range
      smax = kInfinity;
    }
  }

  // Calculate x intersection range
  //
  // Calc half width at p.z, and components towards planes

  tanxz = (fDx2 - fDx1)*0.5/fDz ;
  s1    = 0.5*(fDx1+fDx2) + tanxz*p.z() ;  // x half width at p.z
  ds1   = v.x() - tanxz*v.z() ;       // Components of v towards faces at +-x
  ds2   = v.x() + tanxz*v.z() ;
  ss1   = s1 - p.x() ;         // -delta x to +ve plane
                               // -ve when outside
  ss2   = -s1 - p.x() ;        // -delta x to -ve plane
                               // +ve when outside
    
  if (ss1 < 0 && ss2 <= 0 )
  {
    if (ds1 < 0)   // In +ve coord Area
    {
      sn1 = ss1/ds1 ;

      if ( ds2 < 0 ) sn2 = ss2/ds2 ;           
      else           sn2 = kInfinity ;
    }
    else return snxt ;
  }
  else if ( ss1 >= 0 && ss2 > 0 )
  {
    if ( ds2 > 0 )  // In -ve coord Area
    {
      sn1 = ss2/ds2 ;

      if (ds1 > 0)  sn2 = ss1/ds1 ;      
      else          sn2 = kInfinity;      
        
    }
    else   return snxt ;
  }
  else if (ss1 >= 0 && ss2 <= 0 )
  {
    // Inside Area - calculate leaving distance
    // *Don't* use exact distance to side for tolerance
    //                                             = ss1*std::cos(ang xz)
    //                                             = ss1/std::sqrt(1.0+tanxz*tanxz)
    sn1 = 0 ;

    if ( ds1 > 0 )
    {
      if (ss1 > 0.5*kCarTolerance) sn2 = ss1/ds1 ; // Leave +ve side extent
      else                         return snxt ;   // Leave immediately by +ve 
    }
    else  sn2 = kInfinity ;
      
    if ( ds2 < 0 )
    {
      if ( ss2 < -0.5*kCarTolerance )
      {
        Dist = ss2/ds2 ;            // Leave -ve side extent
        if ( Dist < sn2 ) sn2 = Dist ;
      }
      else  return snxt ;
    }    
  }
  else if (ss1 < 0 && ss2 > 0 )
  {
    // Within +/- plane cross-over areas (not on boundaries ss1||ss2==0)

    if ( ds1 >= 0 || ds2 <= 0 )
    {   
      return snxt ;
    }
    else  // Will intersect & stay inside
    {
      sn1  = ss1/ds1 ;
      Dist = ss2/ds2 ;
      if (Dist > sn1 ) sn1 = Dist ;
      sn2 = kInfinity ;
    }
  }

  // Reduce allowed range of distances as appropriate

  if ( sn1 > smin ) smin = sn1 ;
  if ( sn2 < smax ) smax = sn2 ;

  // Check for incompatible ranges (eg z intersects between 50 ->100 and x
  // only 10-40 -> no intersection)

  if ( smax < smin ) return snxt ;

  // Calculate valid y intersection range 
  // (repeat of x intersection code)

  tanyz = (fDy2-fDy1)*0.5/fDz ;
  s2    = 0.5*(fDy1+fDy2) + tanyz*p.z() ;  // y half width at p.z
  ds1   = v.y() - tanyz*v.z() ;       // Components of v towards faces at +-y
  ds2   = v.y() + tanyz*v.z() ;
  ss1   = s2 - p.y() ;         // -delta y to +ve plane
  ss2   = -s2 - p.y() ;        // -delta y to -ve plane
    
  if ( ss1 < 0 && ss2 <= 0 )
  {
    if (ds1 < 0 ) // In +ve coord Area
    {
      sn1 = ss1/ds1 ;
      if ( ds2 < 0 )  sn2 = ss2/ds2 ;
      else            sn2 = kInfinity ;
    }
    else   return snxt ;
  }
  else if ( ss1 >= 0 && ss2 > 0 )
  {
    if ( ds2 > 0 )  // In -ve coord Area
    {
      sn1 = ss2/ds2 ;
      if ( ds1 > 0 )  sn2 = ss1/ds1 ;
      else            sn2 = kInfinity ;      
    }
    else   return snxt ;
  }
  else if (ss1 >= 0 && ss2 <= 0 )
  {
    // Inside Area - calculate leaving distance
    // *Don't* use exact distance to side for tolerance
    //                                          = ss1*std::cos(ang yz)
    //                                          = ss1/std::sqrt(1.0+tanyz*tanyz)
    sn1 = 0 ;

    if ( ds1 > 0 )
    {
      if (ss1 > 0.5*kCarTolerance) sn2 = ss1/ds1 ; // Leave +ve side extent
      else                         return snxt ;   // Leave immediately by +ve
    }
    else  sn2 = kInfinity ;
      
    if ( ds2 < 0 )
    {
      if ( ss2 < -0.5*kCarTolerance )
      {
        Dist = ss2/ds2 ; // Leave -ve side extent
        if (Dist < sn2) sn2=Dist;
      }
      else  return snxt ;
    }    
  }
  else if (ss1 < 0 && ss2 > 0 )
  {
    // Within +/- plane cross-over areas (not on boundaries ss1||ss2==0)

    if (ds1 >= 0 || ds2 <= 0 )  
    {
      return snxt ;
    }
    else  // Will intersect & stay inside
    {
      sn1 = ss1/ds1 ;
      Dist = ss2/ds2 ;
      if (Dist > sn1 ) sn1 = Dist ;
      sn2 = kInfinity ;
    }
  }
  
  // Reduce allowed range of distances as appropriate

  if ( sn1 > smin) smin = sn1 ;
  if ( sn2 < smax) smax = sn2 ;

  // Check for incompatible ranges (eg x intersects between 50 ->100 and y
  // only 10-40 -> no intersection). Set snxt if ok

  if ( smax > smin ) snxt = smin ;
  if (snxt < 0.5*kCarTolerance ) snxt = 0.0 ;

  return snxt ;
}

//
// Approximate distance to shape
// Calculate perpendicular distances to z/x/y surfaces, return largest
// which is the most fast estimation of shortest distance to Trd
//  - Safe underestimate
//  - If point within exact shape, return 0 

G4double G4Trd::DistanceToIn( const G4ThreeVector& p ) const
{
  G4double safe=0.0;
  G4double tanxz,distx,safx;
  G4double tanyz,disty,safy;
  G4double zbase;

  safe=std::fabs(p.z())-fDz;
  if (safe<0) safe=0;      // Also used to ensure x/y distances
                           // POSITIVE 

  zbase=fDz+p.z();

  // Find distance along x direction to closest x plane
  //
  tanxz=(fDx2-fDx1)*0.5/fDz;
  //    widx=fDx1+tanxz*(fDz+p.z()); // x width at p.z
  //    distx=std::fabs(p.x())-widx;      // distance to plane
  distx=std::fabs(p.x())-(fDx1+tanxz*zbase);
  if (distx>safe)
  {
    safx=distx/std::sqrt(1.0+tanxz*tanxz); // vector Dist=Dist*std::cos(ang)
    if (safx>safe) safe=safx;
  }

  // Find distance along y direction to slanted wall
  tanyz=(fDy2-fDy1)*0.5/fDz;
  //    widy=fDy1+tanyz*(fDz+p.z()); // y width at p.z
  //    disty=std::fabs(p.y())-widy;      // distance to plane
  disty=std::fabs(p.y())-(fDy1+tanyz*zbase);
  if (disty>safe)    
  {
    safy=disty/std::sqrt(1.0+tanyz*tanyz); // distance along vector
    if (safy>safe) safe=safy;
  }
  return safe;
}

//
// Calcluate distance to surface of shape from inside
// Calculate distance to x/y/z planes - smallest is exiting distance
// - z planes have std. check for tolerance
// - xz yz planes have check based on distance || to x or y axis
//   (not corrected for slope of planes)
// ?BUG? If v.z==0 are there cases when snside not set????

G4double G4Trd::DistanceToOut( const G4ThreeVector& p,
                               const G4ThreeVector& v,
                               const G4bool calcNorm,
                                     G4bool *validNorm,
                                     G4ThreeVector *n ) const
{
  ESide side = kUndefined, snside = kUndefined;
  G4double snxt,pdist;
  G4double central,ss1,ss2,ds1,ds2,sn=0.,sn2=0.;
  G4double tanxz=0.,cosxz=0.,tanyz=0.,cosyz=0.;

  if (calcNorm) *validNorm=true; // All normals are valid

  // Calculate z plane intersection
  if (v.z()>0)
  {
    pdist=fDz-p.z();
    if (pdist>kCarTolerance/2)
    {
      snxt=pdist/v.z();
      side=kPZ;
    }
    else
    {
      if (calcNorm)
      {
        *n=G4ThreeVector(0,0,1);
      }
      return snxt=0;
    }
  }
  else if (v.z()<0) 
  {
    pdist=fDz+p.z();
    if (pdist>kCarTolerance/2)
    {
      snxt=-pdist/v.z();
      side=kMZ;
    }
    else
    {
      if (calcNorm)
      {
        *n=G4ThreeVector(0,0,-1);
      }
      return snxt=0;
    }
  }
  else
  {
    snxt=kInfinity;
  }

  //
  // Calculate x intersection
  //
  tanxz=(fDx2-fDx1)*0.5/fDz;
  central=0.5*(fDx1+fDx2);

  // +ve plane (1)
  //
  ss1=central+tanxz*p.z()-p.x();  // distance || x axis to plane
                                  // (+ve if point inside)
  ds1=v.x()-tanxz*v.z();    // component towards plane at +x
                            // (-ve if +ve -> -ve direction)
  // -ve plane (2)
  //
  ss2=-tanxz*p.z()-p.x()-central;  //distance || x axis to plane
                                   // (-ve if point inside)
  ds2=tanxz*v.z()+v.x();    // component towards plane at -x

  if (ss1>0&&ss2<0)
  {
    // Normal case - entirely inside region
    if (ds1<=0&&ds2<0)
    {   
      if (ss2<-kCarTolerance/2)
      {
        sn=ss2/ds2;  // Leave by -ve side
        snside=kMX;
      }
      else
      {
        sn=0; // Leave immediately by -ve side
        snside=kMX;
      }
    }
    else if (ds1>0&&ds2>=0)
    {
      if (ss1>kCarTolerance/2)
      {
        sn=ss1/ds1;  // Leave by +ve side
        snside=kPX;
      }
      else
      {
        sn=0; // Leave immediately by +ve side
        snside=kPX;
      }
    }
    else if (ds1>0&&ds2<0)
    {
      if (ss1>kCarTolerance/2)
      {
        // sn=ss1/ds1;  // Leave by +ve side
        if (ss2<-kCarTolerance/2)
        {
          sn=ss1/ds1;  // Leave by +ve side
          sn2=ss2/ds2;
          if (sn2<sn)
          {
            sn=sn2;
            snside=kMX;
          }
          else
          {
            snside=kPX;
          }
        }
        else
        {
          sn=0; // Leave immediately by -ve
          snside=kMX;
        }      
      }
      else
      {
        sn=0; // Leave immediately by +ve side
        snside=kPX;
      }
    }
    else
    {
      // Must be || to both
      //
      sn=kInfinity;    // Don't leave by either side
    }
  }
  else if (ss1<=0&&ss2<0)
  {
    // Outside, in +ve Area
    
    if (ds1>0)
    {
      sn=0;       // Away from shape
                  // Left by +ve side
      snside=kPX;
    }
    else
    {
      if (ds2<0)
      {
        // Ignore +ve plane and use -ve plane intersect
        //
        sn=ss2/ds2; // Leave by -ve side
        snside=kMX;
      }
      else
      {
        // Must be || to both -> exit determined by other axes
        //
        sn=kInfinity; // Don't leave by either side
      }
    }
  }
  else if (ss1>0&&ss2>=0)
  {
    // Outside, in -ve Area

    if (ds2<0)
    {
      sn=0;       // away from shape
                  // Left by -ve side
      snside=kMX;
    }
    else
    {
      if (ds1>0)
      {
        // Ignore +ve plane and use -ve plane intersect
        //
        sn=ss1/ds1; // Leave by +ve side
        snside=kPX;
      }
      else
      {
        // Must be || to both -> exit determined by other axes
        //
        sn=kInfinity; // Don't leave by either side
      }
    }
  }

  // Update minimum exit distance

  if (sn<snxt)
  {
    snxt=sn;
    side=snside;
  }
  if (snxt>0)
  {
    // Calculate y intersection

    tanyz=(fDy2-fDy1)*0.5/fDz;
    central=0.5*(fDy1+fDy2);

    // +ve plane (1)
    //
    ss1=central+tanyz*p.z()-p.y(); // distance || y axis to plane
                                   // (+ve if point inside)
    ds1=v.y()-tanyz*v.z();  // component towards +ve plane
                            // (-ve if +ve -> -ve direction)
    // -ve plane (2)
    //
    ss2=-tanyz*p.z()-p.y()-central; // distance || y axis to plane
                                    // (-ve if point inside)
    ds2=tanyz*v.z()+v.y();  // component towards -ve plane

    if (ss1>0&&ss2<0)
    {
      // Normal case - entirely inside region

      if (ds1<=0&&ds2<0)
      {   
        if (ss2<-kCarTolerance/2)
        {
          sn=ss2/ds2;  // Leave by -ve side
          snside=kMY;
        }
        else
        {
          sn=0; // Leave immediately by -ve side
          snside=kMY;
        }
      }
      else if (ds1>0&&ds2>=0)
      {
        if (ss1>kCarTolerance/2)
        {
          sn=ss1/ds1;  // Leave by +ve side
          snside=kPY;
        }
        else
        {
          sn=0; // Leave immediately by +ve side
          snside=kPY;
        }
      }
      else if (ds1>0&&ds2<0)
      {
        if (ss1>kCarTolerance/2)
        {
          // sn=ss1/ds1;  // Leave by +ve side
          if (ss2<-kCarTolerance/2)
          {
            sn=ss1/ds1;  // Leave by +ve side
            sn2=ss2/ds2;
            if (sn2<sn)
            {
              sn=sn2;
              snside=kMY;
            }
            else
            {
              snside=kPY;
            }
          }
          else
          {
            sn=0; // Leave immediately by -ve
            snside=kMY;
          }
        }
        else
        {
          sn=0; // Leave immediately by +ve side
          snside=kPY;
        }
      }
      else
      {
        // Must be || to both
        //
        sn=kInfinity;    // Don't leave by either side
      }
    }
    else if (ss1<=0&&ss2<0)
    {
      // Outside, in +ve Area

      if (ds1>0)
      {
        sn=0;       // Away from shape
                    // Left by +ve side
        snside=kPY;
      }
      else
      {
        if (ds2<0)
        {
          // Ignore +ve plane and use -ve plane intersect
          //
          sn=ss2/ds2; // Leave by -ve side
          snside=kMY;
        }
        else
        {
          // Must be || to both -> exit determined by other axes
          //
          sn=kInfinity; // Don't leave by either side
        }
      }
    }
    else if (ss1>0&&ss2>=0)
    {
      // Outside, in -ve Area
      if (ds2<0)
      {
        sn=0;       // away from shape
                    // Left by -ve side
        snside=kMY;
      }
      else
      {
        if (ds1>0)
        {
          // Ignore +ve plane and use -ve plane intersect
          //
          sn=ss1/ds1; // Leave by +ve side
          snside=kPY;
        }
        else
        {
          // Must be || to both -> exit determined by other axes
          //
          sn=kInfinity; // Don't leave by either side
        }
      }
    }

    // Update minimum exit distance

    if (sn<snxt)
    {
      snxt=sn;
      side=snside;
    }
  }

  if (calcNorm)
  {
    switch (side)
    {
      case kPX:
        cosxz=1.0/std::sqrt(1.0+tanxz*tanxz);
        *n=G4ThreeVector(cosxz,0,-tanxz*cosxz);
        break;
      case kMX:
        cosxz=-1.0/std::sqrt(1.0+tanxz*tanxz);
        *n=G4ThreeVector(cosxz,0,tanxz*cosxz);
        break;
      case kPY:
        cosyz=1.0/std::sqrt(1.0+tanyz*tanyz);
        *n=G4ThreeVector(0,cosyz,-tanyz*cosyz);
        break;
      case kMY:
        cosyz=-1.0/std::sqrt(1.0+tanyz*tanyz);
        *n=G4ThreeVector(0,cosyz,tanyz*cosyz);
        break;
      case kPZ:
        *n=G4ThreeVector(0,0,1);
        break;
      case kMZ:
        *n=G4ThreeVector(0,0,-1);
        break;
      default:
        DumpInfo();
        G4Exception("G4Trd::DistanceToOut(p,v,..)",
                    "GeomSolids1002", JustWarning, 
                    "Undefined side for valid surface normal to solid.");
        break;
    }
  }
  return snxt; 
}

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

G4double G4Trd::DistanceToOut( const G4ThreeVector& p ) const
{
  G4double safe=0.0;
  G4double tanxz,xdist,saf1;
  G4double tanyz,ydist,saf2;
  G4double zbase;

#ifdef G4CSGDEBUG
  if( Inside(p) == kOutside )
  {
     G4int oldprc = G4cout.precision(16) ;
     G4cout << G4endl ;
     DumpInfo();
     G4cout << "Position:"  << G4endl << G4endl ;
     G4cout << "p.x() = "   << p.x()/mm << " mm" << G4endl ;
     G4cout << "p.y() = "   << p.y()/mm << " mm" << G4endl ;
     G4cout << "p.z() = "   << p.z()/mm << " mm" << G4endl << G4endl ;
     G4cout.precision(oldprc) ;
     G4Exception("G4Trd::DistanceToOut(p)", "GeomSolids1002", JustWarning, 
                 "Point p is outside !?" );
  }
#endif

  safe=fDz-std::fabs(p.z());  // z perpendicular Dist

  zbase=fDz+p.z();

  // xdist = distance perpendicular to z axis to closest x plane from p
  //       = (x half width of shape at p.z) - std::fabs(p.x)
  //
  tanxz=(fDx2-fDx1)*0.5/fDz;
  xdist=fDx1+tanxz*zbase-std::fabs(p.x());
  saf1=xdist/std::sqrt(1.0+tanxz*tanxz); // x*std::cos(ang_xz) =
                                    // shortest (perpendicular)
                                    // distance to plane
  tanyz=(fDy2-fDy1)*0.5/fDz;
  ydist=fDy1+tanyz*zbase-std::fabs(p.y());
  saf2=ydist/std::sqrt(1.0+tanyz*tanyz);

  // Return minimum x/y/z distance
  //
  if (safe>saf1) safe=saf1;
  if (safe>saf2) safe=saf2;

  if (safe<0) safe=0;
  return safe;     
}

//
// 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 resposibility

G4ThreeVectorList*
G4Trd::CreateRotatedVertices( const G4AffineTransform& pTransform ) const
{
  G4ThreeVectorList *vertices;
  vertices=new G4ThreeVectorList();
  if (vertices)
  {
    vertices->reserve(8);
    G4ThreeVector vertex0(-fDx1,-fDy1,-fDz);
    G4ThreeVector vertex1(fDx1,-fDy1,-fDz);
    G4ThreeVector vertex2(fDx1,fDy1,-fDz);
    G4ThreeVector vertex3(-fDx1,fDy1,-fDz);
    G4ThreeVector vertex4(-fDx2,-fDy2,fDz);
    G4ThreeVector vertex5(fDx2,-fDy2,fDz);
    G4ThreeVector vertex6(fDx2,fDy2,fDz);
    G4ThreeVector vertex7(-fDx2,fDy2,fDz);

    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
  {
    DumpInfo();
    G4Exception("G4Trd::CreateRotatedVertices()",
                "GeomSolids0003", FatalException,
                "Error in allocation of vertices. Out of memory !");
  }
  return vertices;
}

//
// GetEntityType

G4GeometryType G4Trd::GetEntityType() const
{
  return G4String("G4Trd");
}

//
// Make a clone of the object
//
G4VSolid* G4Trd::Clone() const
{
  return new G4Trd(*this);
}

//
// Stream object contents to an output stream

std::ostream& G4Trd::StreamInfo( std::ostream& os ) const
{
  G4int oldprc = os.precision(16);
  os << "-----------------------------------------------------------\n"
     << "    *** Dump for solid - " << GetName() << " ***\n"
     << "    ===================================================\n"
     << " Solid type: G4Trd\n"
     << " Parameters: \n"
     << "    half length X, surface -dZ: " << fDx1/mm << " mm \n"
     << "    half length X, surface +dZ: " << fDx2/mm << " mm \n"
     << "    half length Y, surface -dZ: " << fDy1/mm << " mm \n"
     << "    half length Y, surface +dZ: " << fDy2/mm << " mm \n"
     << "    half length Z             : " << fDz/mm << " mm \n"
     << "-----------------------------------------------------------\n";
  os.precision(oldprc);

  return os;
}


//
// GetPointOnSurface
//
// Return a point (G4ThreeVector) randomly and uniformly
// selected on the solid surface

G4ThreeVector G4Trd::GetPointOnSurface() const
{
  G4double px, py, pz, tgX, tgY, secX, secY, select, sumS, tmp;
  G4double Sxy1, Sxy2, Sxy, Sxz, Syz;

  tgX  = 0.5*(fDx2-fDx1)/fDz;
  secX = std::sqrt(1+tgX*tgX);
  tgY  = 0.5*(fDy2-fDy1)/fDz;
  secY = std::sqrt(1+tgY*tgY);

  // calculate 0.25 of side surfaces, sumS is 0.25 of total surface

  Sxy1 = fDx1*fDy1; 
  Sxy2 = fDx2*fDy2;
  Sxy  = Sxy1 + Sxy2; 
  Sxz  = (fDx1 + fDx2)*fDz*secY; 
  Syz  = (fDy1 + fDy2)*fDz*secX;
  sumS = Sxy + Sxz + Syz;

  select = sumS*G4UniformRand();
 
  if( select < Sxy )                  // Sxy1 or Sxy2
  {
    if( select < Sxy1 ) 
    {
      pz = -fDz;
      px = -fDx1 + 2*fDx1*G4UniformRand();
      py = -fDy1 + 2*fDy1*G4UniformRand();
    }
    else      
    {
      pz =  fDz;
      px = -fDx2 + 2*fDx2*G4UniformRand();
      py = -fDy2 + 2*fDy2*G4UniformRand();
    }
  }
  else if ( ( select - Sxy ) < Sxz )    // Sxz
  {
    pz  = -fDz  + 2*fDz*G4UniformRand();
    tmp =  fDx1 + (pz + fDz)*tgX;
    px  = -tmp  + 2*tmp*G4UniformRand();
    tmp =  fDy1 + (pz + fDz)*tgY;

    if(G4UniformRand() > 0.5) { py =  tmp; }
    else                      { py = -tmp; }
  }
  else                                   // Syz
  {
    pz  = -fDz  + 2*fDz*G4UniformRand();
    tmp =  fDy1 + (pz + fDz)*tgY;
    py  = -tmp  + 2*tmp*G4UniformRand();
    tmp =  fDx1 + (pz + fDz)*tgX;

    if(G4UniformRand() > 0.5) { px =  tmp; }
    else                      { px = -tmp; }
  } 
  return G4ThreeVector(px,py,pz);
}

//
// Methods for visualisation

void G4Trd::DescribeYourselfTo ( G4VGraphicsScene& scene ) const
{
  scene.AddSolid (*this);
}

G4Polyhedron* G4Trd::CreatePolyhedron () const
{
  return new G4PolyhedronTrd2 (fDx1, fDx2, fDy1, fDy2, fDz);
}

#endif