source: trunk/source/geometry/solids/BREPS/src/G4SphericalSurface.cc@ 1321

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// $Id: G4SphericalSurface.cc,v 1.10 2006/06/29 18:42:41 gunter Exp $
// GEANT4 tag $Name: geant4-09-03 $
//
// ----------------------------------------------------------------------
// GEANT 4 class source file
//
// G4SphericalSurface.cc
//
// ----------------------------------------------------------------------

#include "G4SphericalSurface.hh"


/*
G4SphericalSurface::G4SphericalSurface() : G4Surface()
{  // default constructor
   // default x_axis is ( 1.0, 0.0, 0.0 ), z_axis is ( 0.0, 0.0, 1.0 ),
   // default radius is 1.0
   // default phi_1 is 0, phi_2 is 2*PI
   // default theta_1 is 0, theta_2 is PI
        x_axis = G4Vector3D( 1.0, 0.0, 0.0 );
        z_axis = G4Vector3D( 0.0, 0.0, 1.0 );
        radius = 1.0;
        phi_1 = 0.0;
        phi_2 = 2*pi;
        theta_1 = 0.0;
        theta_2 = pi;
        //      OuterBoundary = new G4BREPPolyline();
    }
*/


G4SphericalSurface::G4SphericalSurface( const G4Vector3D&, 
                                        const G4Vector3D& xhat,
                                        const G4Vector3D& zhat,
                                        G4double r, 
                                        G4double ph1, G4double ph2, 
                                        G4double th1, G4double th2) 
  //: G4Surface( o )
{ 
  // Require both x_axis and z_axis to be unit vectors
  G4double xhatmag = xhat.mag();
  if ( xhatmag != 0.0 )
    x_axis = xhat * (1/ xhatmag); // this makes the x_axis a unit vector
  else
  {
    G4cerr << "Error in G4SphericalSurface::G4SphericalSurface--"
           <<"x_axis has zero length\n"
           << "\tDefault x_axis of (1, 0, 0) is used.\n";
  
    x_axis = G4Vector3D( 1.0, 0.0, 0.0 );
  }     

  G4double zhatmag = zhat.mag();
  
  if (zhatmag != 0.0)
    z_axis = zhat *(1/ zhatmag);  // this makes the z_axis a unit vector
  else 
  {
    G4cerr << "Error in G4SphericalSurface::G4SphericalSurface--"
           <<"z_axis has zero length\n"
           << "\tDefault z_axis of (0, 0, 1) is used. \n";
    
    z_axis = G4Vector3D( 0.0, 0.0, 1.0 );
  }
  
  //  Require radius to be non-negative
  if ( r >= 0.0 )
    radius = r;
  else 
  {
    G4cerr << "Error in G4SphericalSurface::G4SphericalSurface"
           << "--radius cannot be less than zero.\n"
           << "\tDefault radius of 1.0 is used.\n";
    
    radius = 1.0;
  }

  //  Require phi_1 in the range: 0 <= phi_1 < 2*PI
  //  and phi_2 in the range: phi_1 < phi_2 <= phi_1 + 2*PI
  if ( ( ph1 >= 0.0 ) && ( ph1 < 2*pi ) )
    phi_1 = ph1;        
  else 
  {
    G4cerr << "Error in G4SphericalSurface::G4SphericalSurface"
           << "--lower azimuthal limit is out of range\n"
           << "\tDefault angle of 0 is used.\n";
    
    phi_1 = 0.0;
  }     
        
  if ( ( ph2 > phi_1 ) && ( ph2 <=  ( phi_1 + twopi ) ) ) 
    phi_2 = ph2;                 
  else 
  {
    G4cerr << "Error in G4SphericalSurface::G4SphericalSurface"
           << "--upper azimuthal limit is out of range\n"
           << "\tDefault angle of 2*PI is used.\n";
    
    phi_2 = twopi;
  }
         
  //  Require theta_1 in the range: 0 <= theta_1 < PI 
  //  and theta-2 in the range: theta_1 < theta_2 <= theta_1 + PI
  if ( ( th1 >= 0.0 ) && ( th1 < pi ) ) 
    theta_1 = th1;
  else
  {
    G4cerr << "Error in G4SphericalSurface::G4SphericalSurface"
           << "--lower polar limit is out of range\n"
           << "\tDefault angle of 0 is used.\n";
    
    theta_1 = 0.0;
  }       
  
  if  ( ( th2 > theta_1 ) && ( th2 <= ( theta_1 + pi ) ) ) 
    theta_2 =th2;             
  else 
  {
    G4cerr << "Error in G4SphericalSurface::G4SphericalSurface"
           << "--upper polar limit is out of range\n"
           << "\tDefault angle of PI is used.\n";
    
    theta_2 = pi;
  } 
}


G4SphericalSurface::~G4SphericalSurface()
{
}

/*
G4SphericalSurface::G4SphericalSurface( const G4SphericalSurface& s )
 : G4Surface( s.origin )
{ x_axis = s.x_axis;
  z_axis = s.z_axis;
  radius = s.radius;
  phi_1 = s.phi_1;
  phi_2 = s.phi_2;
  theta_1 = s.theta_1;
  theta_2 = s.theta_2;
}                                                      
*/

const char* G4SphericalSurface::NameOf() const
{
  return "G4SphericalSurface";
}

void G4SphericalSurface::PrintOn( std::ostream& os ) const
{  
  //  printing function using C++ std::ostream class
  os << "G4SphericalSurface surface with origin: " << origin << "\t"
     << "radius: " << radius << "\n"
     << "\t local x_axis: " << x_axis
     << "\t local z_axis: " << z_axis << "\n" 
     << "\t lower azimuthal limit: " << phi_1 << " radians\n"
     << "\t upper azimuthal limit: " << phi_2 << " radians\n"
     << "\t lower polar limit    : " << theta_1 << " radians\n"
     << "\t upper polar limit    : " << theta_2 << " radians\n";
}


G4double G4SphericalSurface::HowNear( const G4Vector3D& x ) const
{
  //  Distance from the point x to the G4SphericalSurface.
  //  The distance will be positive if the point is Inside the 
  //  G4SphericalSurface, negative if the point is outside.
  G4Vector3D d = G4Vector3D( x - origin );
  G4double rad = d.mag();
  return (radius - rad);
}


/*
G4double G4SphericalSurface::distanceAlongRay( G4int which_way,
                                               const G4Ray* ry,
                                               G4Vector3D& p ) const
{  //  Distance along a Ray (straight line with G4Vector3D) to leave or enter
   //  a G4SphericalSurface.  The input variable which_way should be set to +1 to
   //  indicate leaving a G4SphericalSurface, -1 to indicate entering the surface.
   //  p is the point of intersection of the Ray with the G4SphericalSurface.
   //  If the G4Vector3D of the Ray is opposite to that of the Normal to
   //  the G4SphericalSurface at the intersection point, it will not leave the
   //  G4SphericalSurface.
   //  Similarly, if the G4Vector3D of the Ray is along that of the Normal 
   //  to the G4SphericalSurface at the intersection point, it will not enter the
   //  G4SphericalSurface.
   //  This method is called by all finite shapes sub-classed to G4SphericalSurface.
   //  Use the virtual function table to check if the intersection point
   //  is within the boundary of the finite shape.
   //  A negative result means no intersection.
   //  If no valid intersection point is found, set the distance
   //  and intersection point to large numbers.
        G4double Dist = FLT_MAXX;
        G4Vector3D lv ( FLT_MAXX, FLT_MAXX, FLT_MAXX );
        p = lv;
//  Origin and G4Vector3D unit vector of Ray.
        G4Vector3D x = ry->Position( 0.0 );
        G4Vector3D dhat = ry->Direction( 0.0 );
        G4int isoln = 0, maxsoln = 2;
//  array of solutions in distance along the Ray
//      G4double s[2] = { -1.0, -1.0 };
        G4double s[2];s[0] = -1.0; s[1]= -1.0 ;
//  calculate the two solutions (quadratic equation)
        G4Vector3D d = x - GetOrigin();
        G4double radius = GetRadius();
//  quit with no intersection if the radius of the G4SphericalSurface is zero
        if ( radius <= 0.0 )
                return Dist;
        G4double dsq = d * d;
        G4double rsq = radius * radius;
        G4double b = d * dhat;
        G4double c = dsq - rsq;
        G4double radical = b * b - c;
//  quit with no intersection if the radical is negative
        if ( radical < 0.0 )
                return Dist;
        G4double root = std::sqrt( radical );
        s[0] = -b + root;
        s[1] = -b - root;
//  order the possible solutions by increasing distance along the Ray
//  (G4Sorting routines are in support/G4Sort.h)
        G4Sort_double( s, isoln, maxsoln-1 );
//  now loop over each positive solution, keeping the first one (smallest
//  distance along the Ray) which is within the boundary of the sub-shape
//  and which also has the correct G4Vector3D with respect to the Normal to
//  the G4SphericalSurface at the intersection point
        for ( isoln = 0; isoln < maxsoln; isoln++ ) {
                if ( s[isoln] >= 0.0 ) {
                        if ( s[isoln] >= FLT_MAXX )  // quit if too large
                                return Dist;
                        Dist = s[isoln];
                        p = ry->Position( Dist );
                        if ( ( ( dhat * Normal( p ) * which_way ) >= 0.0 )
                          && ( WithinBoundary( p ) == 1 ) )
                                return Dist;
                }
        }
//  get here only if there was no solution within the boundary, Reset
//  distance and intersection point to large numbers
        p = lv;
        return FLT_MAXX;
}                 
*/


void G4SphericalSurface::CalcBBox()
{
  G4double x_min = origin.x() - radius;
  G4double y_min = origin.y() - radius;
  G4double z_min = origin.z() - radius;
  G4double x_max = origin.x() + radius;
  G4double y_max = origin.y() + radius;
  G4double z_max = origin.z() + radius;  
    
  G4Point3D Min(x_min, y_min, z_min);
  G4Point3D Max(x_max, y_max, z_max);  
  bbox = new G4BoundingBox3D( Min, Max); 
}


G4int G4SphericalSurface::Intersect( const G4Ray& ry )
{
  //  Distance along a Ray (straight line with G4Vector3D) to leave or enter
  //  a G4SphericalSurface.  The input variable which_way should be set to +1 
  //  to indicate leaving a G4SphericalSurface, -1 to indicate entering a 
  //  G4SphericalSurface.
  //  p is the point of intersection of the Ray with the G4SphericalSurface.
  //  If the G4Vector3D of the Ray is opposite to that of the Normal to
  //  the G4SphericalSurface at the intersection point, it will not leave the
  //  G4SphericalSurface.
  //  Similarly, if the G4Vector3D of the Ray is along that of the Normal 
  //  to the G4SphericalSurface at the intersection point, it will not enter 
  //  the G4SphericalSurface.
  //  This method is called by all finite shapes sub-classed to 
  //  G4SphericalSurface.
  //  Use the virtual function table to check if the intersection point
  //  is within the boundary of the finite shape.
  //  A negative result means no intersection.
  //  If no valid intersection point is found, set the distance
  //  and intersection point to large numbers.

  G4int which_way = (G4int)HowNear(ry.GetStart());
  //Originally a parameter.Read explanation above. 
  
  if(!which_way)which_way =-1;
  distance = FLT_MAXX;
  
  G4Vector3D lv ( FLT_MAXX, FLT_MAXX, FLT_MAXX );

  //    p = lv; 
  closest_hit = lv;

  //  Origin and G4Vector3D unit vector of Ray.
  //    G4Vector3D x = ry->position( 0.0 );     
  G4Vector3D x= G4Vector3D( ry.GetStart() );

  //    G4Vector3D dhat = ry->direction( 0.0 );
  G4Vector3D dhat = ry.GetDir();
  G4int isoln = 0, maxsoln = 2;

  //  array of solutions in distance along the Ray
  G4double s[2];
  s[0] = -1.0 ; 
  s[1] = -1.0 ;

  //  calculate the two solutions (quadratic equation)
  G4Vector3D d = G4Vector3D( x - GetOrigin() );
  G4double r = GetRadius();

//  quit with no intersection if the radius of the G4SphericalSurface is zero
  if ( r <= 0.0 )
    return 0;
  
  G4double dsq     = d * d;
  G4double rsq     = r * r;
  G4double b       = d * dhat;
  G4double c       = dsq - rsq;
  G4double radical = b * b - c;
  
//  quit with no intersection if the radical is negative
  if ( radical < 0.0 )
    return 0;
  
  G4double root = std::sqrt( radical );
  s[0] = -b + root;
  s[1] = -b - root;

  //  order the possible solutions by increasing distance along the Ray
  //  (G4Sorting routines are in support/G4Sort.h)
  //    G4Sort_double( s, isoln, maxsoln-1 );
  if(s[0] > s[1])
  {
    G4double tmp =s[0];
    s[0] = s[1];
    s[1] = tmp;
  }

  //  now loop over each positive solution, keeping the first one (smallest
  //  distance along the Ray) which is within the boundary of the sub-shape
  //  and which also has the correct G4Vector3D with respect to the Normal to
  //  the G4SphericalSurface at the intersection point
  for ( isoln = 0; isoln < maxsoln; isoln++ ) 
  {
    if ( s[isoln] >= kCarTolerance*0.5 ) 
    {
      if ( s[isoln] >= FLT_MAXX )  // quit if too large
        return 0;
      
      distance = s[isoln];
      closest_hit = ry.GetPoint( distance );
      if ( ( ( dhat * Normal( closest_hit ) * which_way ) >= 0.0 ) && 
           ( WithinBoundary( closest_hit ) == 1 )                      )
      {
        distance =  distance*distance;                      
        return 1;
      }
    }
  }
  
  //  get here only if there was no solution within the boundary, Reset
  //  distance and intersection point to large numbers
  //    p = lv;
  //    return FLT_MAXX;
  distance = FLT_MAXX;
  closest_hit = lv;
  return 0;
}                 


/*
G4double G4SphericalSurface::distanceAlongHelix( G4int which_way,
                                                 const Helix* hx,
                                                 G4Vector3D& p ) const
{  //  Distance along a Helix to leave or enter a G4SphericalSurface.
   //  The input variable which_way should be set to +1 to
   //  indicate leaving a G4SphericalSurface, -1 to indicate entering a G4SphericalSurface.
   //  p is the point of intersection of the Helix with the G4SphericalSurface.
   //  If the G4Vector3D of the Helix is opposite to that of the Normal to
   //  the G4SphericalSurface at the intersection point, it will not leave the
   //  G4SphericalSurface.
   //  Similarly, if the G4Vector3D of the Helix is along that of the Normal 
   //  to the G4SphericalSurface at the intersection point, it will not enter the
   //  G4SphericalSurface.
   //  This method is called by all finite shapes sub-classed to G4SphericalSurface.
   //  Use the virtual function table to check if the intersection point
   //  is within the boundary of the finite shape.
   //  If no valid intersection point is found, set the distance
   //  and intersection point to large numbers.
   //  Possible negative distance solutions are discarded.
        G4double Dist = FLT_MAXX;
        G4Vector3D lv ( FLT_MAXX, FLT_MAXX, FLT_MAXX );
        p = lv;
        G4int isoln = 0, maxsoln = 4;
//  Array of solutions in turning angle
//      G4double s[4] = { -1.0, -1.0, -1.0, -1.0 };
        G4double s[4];s[0] = -1.0; s[1]= -1.0 ;s[2] = -1.0; s[3]= -1.0 ;

//  Helix parameters
        G4double rh = hx->GetRadius();  // radius of Helix
        G4Vector3D oh = hx->position( 0.0 );  // origin of Helix
        G4Vector3D dh = hx->direction( 0.0 );  // initial G4Vector3D of Helix
        G4Vector3D prp = hx->getPerp(); // perpendicular vector
        G4double prpmag = prp.mag();
        G4double rhp = rh / prpmag;
//  G4SphericalSurface parameters
        G4double rs = GetRadius();  // radius of G4SphericalSurface
        if ( rs == 0.0 )   // quit if zero radius
                return Dist;
        G4Vector3D os = GetOrigin();  // origin of G4SphericalSurface
//
//  Calculate quantities of use later on
        G4Vector3D alpha = rhp * prp;
        G4Vector3D beta = rhp * dh;
        G4Vector3D gamma = oh - os;
//
//  Only consider approximate solutions to quadratic order in the turning
//  angle along the Helix
        G4double A = beta * beta  +  gamma * alpha;
        G4double B = 2.0 * gamma * beta;
        G4double C = gamma * gamma  -  rs * rs;
//  Case if quadratic term is zero
        if ( std::fabs( A ) < FLT_EPSILO ) {
                if ( B == 0.0 )  // no intersection, quit
                        return Dist;
                else             // B != 0
                        s[0] = -C / B;
        }
//  General quadratic solution, A != 0
        else {
                G4double radical = B * B  -  4.0 * A * C;
                if ( radical < 0.0 )  // no intersection, quit
                        return Dist;
                G4double root = std::sqrt( radical );
                s[0] = ( -B + root ) / ( 2.0 * A );                  
                s[1] = ( -B - root ) / ( 2.0 * A );                  
                if ( rh < 0.0 ) {
                        s[0] = -s[0];
                        s[1] = -s[1];
                }
                s[2] = s[0] + twopi;
                s[3] = s[1] + twopi;
        }
//
//  Order the possible solutions by increasing turning angle
//  (G4Sorting routines are in support/G4Sort.h).
        G4Sort_double( s, isoln, maxsoln-1 );
//
//  Now loop over each positive solution, keeping the first one (smallest
//  distance along the Helix) which is within the boundary of the sub-shape.
        for ( isoln = 0; isoln < maxsoln; isoln++ ) {
                if ( s[isoln] >= 0.0 ) {
//  Calculate distance along Helix and position and G4Vector3D vectors.
                        Dist = s[isoln] * std::fabs( rhp );
                        p = hx->position( Dist );
                        G4Vector3D d = hx->direction( Dist );
//  Now do approximation to get remaining distance to correct this solution
//  iterate it until the accuracy is below the user-set surface precision.
                        G4double delta = 0.;  
                        G4double delta0 = FLT_MAXX;
                        G4int dummy = 1;
                        G4int iter = 0;
                        G4int in0 = Inside( hx->position ( 0.0 ) );
                        G4int in1 = Inside( p );
                        G4double sc = Scale();
                        while ( dummy ) {
                                iter++;
//  Terminate loop after 50 iterations and Reset distance to large number,
//  indicating no intersection with G4SphericalSurface.
//  This generally occurs if the Helix curls too tightly to Intersect it.
                                if ( iter > 50 ) {
                                        Dist = FLT_MAXX;
                                        p = lv;
                                        break;
                                }
//  Find distance from the current point along the above-calculated
//  G4Vector3D using a Ray.
//  The G4Vector3D of the Ray and the Sign of the distance are determined
//  by whether the starting point of the Helix is Inside or outside of
//  the G4SphericalSurface.
                                in1 = Inside( p );
                                if ( in1 ) {  //  current point Inside
                                   if ( in0 ) {  //  starting point Inside
                                      Ray* r = new Ray( p, d );
                                      delta = 
                                          distanceAlongRay( 1, r, p );
                                      delete r;
                                   }
                                   else {       //  starting point outside
                                      Ray* r = new Ray( p, -d );
                                      delta = 
                                         -distanceAlongRay( 1, r, p );
                                      delete r;
                                   }
                                }
                                else {        //  current point outside
                                   if ( in0 ) {  //  starting point Inside
                                      Ray* r = new Ray( p, -d );
                                      delta = 
                                         -distanceAlongRay( -1, r, p );
                                      delete r;
                                   }
                                   else {        //  starting point outside
                                      Ray* r = new Ray( p, d );
                                      delta = 
                                          distanceAlongRay( -1, r, p );
                                      delete r;
                                   }
                                }
//  Test if distance is less than the surface precision, if so Terminate loop.
                                if ( std::fabs( delta / sc ) <= SURFACE_PRECISION )
                                        break;
//  Ff delta has not changed sufficiently from the previous iteration, 
//  skip out of this loop.
                                if ( std::fabs( ( delta - delta0 ) / sc ) <=
                                                           SURFACE_PRECISION )
                                        break;
//  If delta has increased in absolute value from the previous iteration
//  either the Helix doesn't Intersect the G4SphericalSurface or the approximate
//  solution is too far from the real solution.  Try groping for a solution.
//  If not found, Reset distance to large number, indicating no intersection
//  with the G4SphericalSurface.
                                if ( ( std::fabs( delta ) > std::fabs( delta0 ) ) ) {
                                        Dist = std::fabs( rhp ) * 
                                               gropeAlongHelix( hx );
                                        if ( Dist < 0.0 ) {
                                                Dist = FLT_MAXX;
                                                p = lv;
                                        }
                                        else
                                                p = hx->position( Dist );
                                        break;
                                }
//  Set old delta to new one.
                                delta0 = delta;
//  Add distance to G4SphericalSurface to distance along Helix.
                                Dist += delta;
//  Negative distance along Helix means Helix doesn't Intersect G4SphericalSurface.
//  Reset distance to large number, indicating no intersection with G4SphericalSurface.
                                if ( Dist < 0.0 ) {
                                        Dist = FLT_MAXX;
                                        p = lv;
                                        break;
                                }
//  Recalculate point along Helix and the G4Vector3D.
                                p = hx->position( Dist );
                                d = hx->direction( Dist );
                           }  //  end of while loop
//  Now have best value of distance along Helix and position for this
//  solution, so test if it is within the boundary of the sub-shape
//  and require that it point in the correct G4Vector3D with respect to
//  the Normal to the G4SphericalSurface.
                        if ( ( Dist < FLT_MAXX ) &&
                             ( ( hx->direction( Dist ) * Normal( p ) *
                                 which_way ) >= 0.0 ) &&
                             ( WithinBoundary( p ) == 1 ) )
                                return Dist;
                }  // end of if s[isoln] >= 0.0 condition
        }  // end of for loop over solutions
//  If one gets here, there is no solution, so set distance along Helix
//  and position to large numbers.
        Dist = FLT_MAXX;
        p = lv;
        return Dist;
}
*/


/*
G4Vector3D G4SphericalSurface::Normal( const G4Vector3D& p ) const
{  //  Return the Normal unit vector to the G4SphericalSurface at a point p on
   //  (or nearly on) the G4SphericalSurface.
        G4Vector3D n = p - origin;
        G4double nmag = n.mag();
        if ( nmag != 0.0 )
                n = n / nmag;
//  If the point p happens to coincide with the origin (which is possible
//  if the radius is zero), set the Normal to the z-axis unit vector.
        else
                n = G4Vector3D( 0.0, 0.0, 1.0 );
        return n;
}
*/

         
G4Vector3D G4SphericalSurface::Normal( const G4Vector3D& p ) const
{ 
  //  Return the Normal unit vector to the G4SphericalSurface at a point p on
  //  (or nearly on) the G4SphericalSurface.
  G4Vector3D n = G4Vector3D( p - origin );
  G4double nmag = n.mag();
  
  if ( nmag != 0.0 )
    n = n * (1/ nmag);

  //  If the point p happens to coincide with the origin (which is possible
  //  if the radius is zero), set the Normal to the z-axis unit vector.
  else
    n = G4Vector3D( 0.0, 0.0, 1.0 );
  
  return n;
}


G4Vector3D G4SphericalSurface::SurfaceNormal( const G4Point3D& p ) const
{ 
  //  Return the Normal unit vector to the G4SphericalSurface at a point p on
  //  (or nearly on) the G4SphericalSurface.
  G4Vector3D n = G4Vector3D( p - origin );
  G4double nmag = n.mag();
  
  if ( nmag != 0.0 )
    n = n * (1/ nmag);
  
  //  If the point p happens to coincide with the origin (which is possible
  //  if the radius is zero), set the Normal to the z-axis unit vector.
  else
    n = G4Vector3D( 0.0, 0.0, 1.0 );
  
  return n;
}


G4int G4SphericalSurface::Inside ( const G4Vector3D& x ) const
{
  //  Return 0 if point x is outside G4SphericalSurface, 1 if Inside.
  //  Outside means that the distance to the G4SphericalSurface would 
  //  be negative.
  //  Use the HowNear function to calculate this distance.
  if ( HowNear( x ) >= 0.0 )
    return 1;
  else
    return 0; 
}


G4int G4SphericalSurface::WithinBoundary( const G4Vector3D& x ) const
{ 
  //  return 1 if point x is on the G4SphericalSurface, otherwise return zero
  //  (x is assumed to lie on the surface of the G4SphericalSurface, so one 
  //  only checks the angular limits)
  G4Vector3D y_axis = G4Vector3D( z_axis.cross( x_axis ) );

  //  components of x in the local coordinate system of the G4SphericalSurface
  G4double px = x * x_axis;
  G4double py = x * y_axis;
  G4double pz = x * z_axis;

  //  check if within polar angle limits
  G4double theta = std::acos( pz / x.mag() );  // acos in range 0 to PI
  
  //  Normal case
  if ( theta_2 <= pi ) 
  {
    if ( ( theta < theta_1 ) || ( theta > theta_2 ) )
      return 0;
  }

  //  this is for the case that theta_2 is greater than PI
  else 
  {
    theta += pi;
    if ( ( theta < theta_1 ) || ( theta > theta_2 ) )
      return 0;
  }

  //  now check if within azimuthal angle limits
  G4double phi = std::atan2( py, px );  // atan2 in range -PI to PI
  
  if ( phi < 0.0 )
    phi += twopi;
  
  //  Normal case
  if ( ( phi >= phi_1 )  &&  ( phi <= phi_2 ) )
    return 1;
  
  //  this is for the case that phi_2 is greater than 2*PI
  phi += twopi;
  
  if ( ( phi >= phi_1 )  &&  ( phi <= phi_2 ) )
    return 1;
  //  get here if not within azimuthal limits                   
 
 return 0;
}


G4double G4SphericalSurface::Scale() const
{
  //  Returns the radius of a G4SphericalSurface unless it is zero, in which
  //  case returns the arbitrary number 1.0.
  //  Used for Scale-invariant tests of surface thickness.
  if ( radius == 0.0 )
    return 1.0;
  else
    return radius;
}


G4double G4SphericalSurface::Area() const
{
  //  Returns the Area of a G4SphericalSurface
  return ( 2.0*( theta_2 - theta_1 )*( phi_2 - phi_1)*radius*radius/pi );
}


void G4SphericalSurface::resize( G4double r, 
                                 G4double ph1, G4double ph2,
                                 G4double th1, G4double th2 )
{ 
  //  Resize the G4SphericalSurface to new radius r, new lower and upper 
  //  azimuthal angle limits ph1 and ph2, and new lower and upper polar 
  //  angle limits th1 and th2.
  
  //  Require radius to be non-negative
  if ( r >= 0.0 )
    radius = r;        
  else 
  {
    G4cerr << "Error in G4SphericalSurface::resize"
           << "--radius cannot be less than zero.\n"
           << "\tOriginal value of " << radius << " is retained.\n";
  }

  //  Require azimuthal angles to be within bounds
  
  if ( ( ph1 >= 0.0 ) && ( ph1 < twopi ) )
    phi_1 = ph1;
  else 
  {
    G4cerr << "Error in G4SphericalSurface::resize"
           << "--lower azimuthal limit out of range\n"
           << "\tOriginal value of " << phi_1 << " is retained.\n";
  }
  
  if ( ( ph2 > phi_1 ) && ( ph2 <= ( phi_1 + twopi ) ) )
    phi_2 = ph2;
  else 
  {
    ph2 = ( phi_2 <= phi_1 ) ? ( phi_1 + FLT_EPSILO ) : phi_2;
    phi_2 = ph2;
    G4cerr << "Error in G4SphericalSurface::resize"
           << "--upper azimuthal limit out of range\n"
           << "\tValue of " << phi_2 << " is used.\n";
  }

  //  Require polar angles to be within bounds
  if ( ( th1 >= 0.0 ) && ( th1 < pi ) )
    theta_1 = th1;
  else 
  {
    G4cerr << "Error in G4SphericalSurface::resize"
           << "--lower polar limit out of range\n"
           << "\tOriginal value of " << theta_1 << " is retained.\n";
  }
  
  if ( ( th2 > theta_1 ) && ( th2 <= ( theta_1 + pi ) ) )
    theta_2 = th2;
  else
  {
    th2 = ( theta_2 <= theta_1 ) ? ( theta_1 + FLT_EPSILO ) : theta_2;
    theta_2 = th2;
    G4cerr << "Error in G4SphericalSurface::resize"
           << "--upper polar limit out of range\n"
           << "\tValue of " << theta_2 << " is used.\n";
  }
}


/*
void G4SphericalSurface::rotate( G4double alpha, G4double beta,
                        G4double gamma, G4ThreeMat& m, G4int inverse )
{  //  rotate G4SphericalSurface first about global x_axis by angle alpha,
   //                  second about global y-axis by angle beta,
   //               and third about global z_axis by angle gamma
   //  by creating and using G4ThreeMat objects in Surface::rotate
   //  angles are assumed to be given in radians
   //  if inverse is non-zero, the order of rotations is reversed
   //  the axis is rotated here, the origin is rotated by calling
   //  Surface::rotate
        G4Surface::rotate( alpha, beta, gamma, m, inverse );
        x_axis = m * x_axis;
        z_axis = m * z_axis;
}
*/


/*
void G4SphericalSurface::rotate( G4double alpha, G4double beta,
                        G4double gamma, G4int inverse )
{  //  rotate G4SphericalSurface first about global x_axis by angle alpha,
   //                  second about global y-axis by angle beta,
   //               and third about global z_axis by angle gamma
   //  by creating and using G4ThreeMat objects in Surface::rotate
   //  angles are assumed to be given in radians
   //  if inverse is non-zero, the order of rotations is reversed
   //  the axis is rotated here, the origin is rotated by calling
   //  Surface::rotate
        G4ThreeMat m;
        G4Surface::rotate( alpha, beta, gamma, m, inverse );
        x_axis = m * x_axis;
        z_axis = m * z_axis;
}
*/


/*
G4double G4SphericalSurface::gropeAlongHelix( const Helix* hx ) const
{  //  Grope for a solution of a Helix intersecting a G4SphericalSurface.
   //  This function returns the turning angle (in radians) where the
   //  intersection occurs with only positive values allowed, or -1.0 if
   //  no intersection is found.
//  The idea is to start at the beginning of the Helix, then take steps
//  of some fraction of a turn.  If at the end of a Step, the current position
//  along the Helix and the previous position are on opposite sides of the
//  G4SphericalSurface, then the solution must lie somewhere in between.
        G4int one_over_f = 8;  // one over fraction of a turn to go in each Step
        G4double turn_angle = 0.0;
        G4double dist_along = 0.0;
        G4double d_new;
        G4double fk = 1.0 / G4double( one_over_f );
        G4double scal = Scale();
        G4double d_old = HowNear( hx->position( dist_along ) );
        G4double rh = hx->GetRadius();    // radius of Helix
        G4Vector3D prp = hx->getPerp(); // perpendicular vector
        G4double prpmag = prp.mag();
        G4double rhp = rh / prpmag;
        G4int max_iter = one_over_f * HELIX_MAX_TURNS;
//  Take up to a user-settable number of turns along the Helix,
//  groping for an intersection point.
        for ( G4int k = 1; k < max_iter; k++ ) {
                turn_angle = twopi * k / one_over_f;
                dist_along = turn_angle * std::fabs( rhp );
                d_new = HowNear( hx->position( dist_along ) );
                if ( ( d_old < 0.0 && d_new > 0.0 ) ||
                     ( d_old > 0.0 && d_new < 0.0 ) ) {
                        d_old = d_new;
//  Old and new points are on opposite sides of the G4SphericalSurface, therefore
//  a solution lies in between, use a binary search to pin the point down
//  to the surface precision, but don't do more than 50 iterations.
                        G4int itr = 0;
                        while ( std::fabs( d_new / scal ) > SURFACE_PRECISION ) {
                                itr++;
                                if ( itr > 50 )
                                        return turn_angle;
                                turn_angle -= fk * pi;
                                dist_along = turn_angle * std::fabs( rhp );
                                d_new = HowNear( hx->position( dist_along ) );
                                if ( ( d_old < 0.0 && d_new > 0.0 ) ||
                                     ( d_old > 0.0 && d_new < 0.0 ) )
                                        fk *= -0.5;
                                else
                                        fk *=  0.5;
                                d_old = d_new;
                        }  //  end of while loop
                        return turn_angle;  // this is the best solution
                }  //  end of if condition
        }  //  end of for loop
//  Get here only if no solution is found, so return -1.0 to indicate that.
        return -1.0;
}
*/