G4CylindricalSurface.cc

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//
// $Id$
//
// ----------------------------------------------------------------------
// GEANT 4 class source file
//
// G4CylindricalSurface.cc
//
// ----------------------------------------------------------------------

#include "G4CylindricalSurface.hh"
#include "G4Sort.hh"
#include "G4Globals.hh"

G4CylindricalSurface::G4CylindricalSurface() : G4Surface()
{  
  // default constructor
  // default axis is ( 1.0, 0.0, 0.0 ), default radius is 1.0

  axis = G4Vector3D( 1.0, 0.0, 0.0 );
  radius = 1.0;
}


G4CylindricalSurface::G4CylindricalSurface( const G4Vector3D& o, 
                                            const G4Vector3D& a,
                                            G4double r )
  : G4Surface()
{ 
  // Normal constructor
  // require axis to be a unit vector

  G4double amag = a.mag();
  if ( amag != 0.0 )
  {
    axis = a * (1/ amag);  // this makes the axis a unit vector
  }
  else 
  {
    std::ostringstream message;
    message << "Axis has zero length." << G4endl
            << "Default axis ( 1.0, 0.0, 0.0 ) is used.";    
    G4Exception("G4CylindricalSurface::G4CylindricalSurface()",
                "GeomSolids1001", JustWarning, message);
    
    axis = G4Vector3D( 1.0, 0.0, 0.0 );
  }

  //  Require radius to be non-negative
  //
  if ( r >= 0.0 )
  {
    radius = r;
  }
  else 
  {
    std::ostringstream message;
    message << "Negative radius." << G4endl
            << "Default radius of 1.0 is used.";    
    G4Exception("G4CylindricalSurface::G4CylindricalSurface()",
                "GeomSolids1001", JustWarning, message);

    radius = 1.0;
  }

  origin =o;
}


G4CylindricalSurface::~G4CylindricalSurface()
{
}


G4CylindricalSurface::G4CylindricalSurface( const G4CylindricalSurface& c )
  : G4Surface(), axis(c.axis), radius(c.radius)
{
}


G4CylindricalSurface&
G4CylindricalSurface::operator=( const G4CylindricalSurface& c )
{
  if (&c == this)  { return *this; }
  axis     = c.axis;
  radius   = c.radius;

  return *this;
}


const char* G4CylindricalSurface::NameOf() const
{
  return "G4CylindricalSurface";
}

void G4CylindricalSurface::PrintOn( std::ostream& os ) const
{
  os << "G4CylindricalSurface surface with origin: " << origin << "\t"
     << "radius: " << radius << "\tand axis " << axis << "\n";
}

G4int G4CylindricalSurface::Intersect(const G4Ray& ry)
{
  //  Distance along a Ray (straight line with G4ThreeVec) to leave or enter
  //  a G4CylindricalSurface.  The input variable which_way should be set 
  //  to +1 to indicate leaving a G4CylindricalSurface, -1 to indicate 
  //  entering a G4CylindricalSurface.
  //  p is the point of intersection of the Ray with the G4CylindricalSurface.
  //  If the G4Vector3D of the Ray is opposite to that of the Normal to
  //  the G4CylindricalSurface at the intersection point, it will not leave 
  //  the G4CylindricalSurface.
  //  Similarly, if the G4Vector3D of the Ray is along that of the Normal 
  //  to the G4CylindricalSurface at the intersection point, it will not enter
  //  the G4CylindricalSurface.
  //  This method is called by all finite shapes sub-classed to 
  //  G4CylindricalSurface.
  //  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=1;
  
  if(!Inside(ry.GetStart()))  { which_way = -1; }
  
  distance = kInfinity;
  G4Vector3D lv ( kInfinity, kInfinity, kInfinity );
  
  closest_hit = lv;

  //  Origin and G4Vector3D unit vector of Ray.
  //
  G4Vector3D x    = ry.GetStart();
  G4Vector3D dhat = ry.GetDir();

  //  Axis unit vector of the G4CylindricalSurface.
  //
  G4Vector3D ahat = GetAxis();
  G4int isoln   = 0, 
        maxsoln = 2;
  
  //  Array of solutions in distance along the Ray.
  //
  G4double sol[2];
  sol[0] = -1.0; 
  sol[1] = -1.0 ;

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

  G4double dsq  = d * d;
  G4double da   = d * ahat;
  G4double dasq = da * da;
  G4double rsq  = radiu * radiu;
  G4double qsq  = dsq - dasq;
  G4double dira = dhat * ahat;
  G4double a    = 1.0 - dira * dira;
  
  if ( a <= 0.0 )  { return 0; }

  G4double b       = 2. * ( d * dhat - da * dira );
  G4double c       = rsq - qsq;
  G4double radical = b * b + 4. * a * c; 
        
  if ( radical < 0.0 )  { return 0; }

  G4double root = std::sqrt( radical );
  sol[0] = ( - b + root ) / ( 2. * a );
  sol[1] = ( - b - root ) / ( 2. * a );

  //  Order the possible solutions by increasing distance along the Ray
  //
  sort_double( sol, 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 G4CylindricalSurface at the intersection point
  //
  for ( isoln = 0; isoln < maxsoln; isoln++ ) 
  {
    if ( sol[isoln] >= kCarTolerance*0.5 ) 
    {
      if ( sol[isoln] >= kInfinity )  // quit if too large
        { return 0; }

      distance = sol[isoln];
      closest_hit = ry.GetPoint( distance );
      G4double  tmp =  dhat * (Normal( closest_hit ));
      
      if ((tmp * which_way) >= 0.0 )
      {
        if ( 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
  //
  distance = kInfinity;
  closest_hit = lv;

  return 0;
}


G4double G4CylindricalSurface::HowNear( const G4Vector3D& x ) const
{
  //  Distance from the point x to the infinite G4CylindricalSurface.
  //  The distance will be positive if the point is Inside the 
  //  G4CylindricalSurface, negative if the point is outside.
  //  Note that this may not be correct for a bounded cylindrical object
  //  subclassed to G4CylindricalSurface.

  G4Vector3D d = x - origin;
  G4double dA = d * axis;
  G4double rds = std::sqrt( d.mag2() - dA*dA );
  G4double hownear = std::fabs( radius - rds );
 
  return hownear;
}


/*
G4double G4CylindricalSurface::
distanceAlongRay( G4int which_way, const G4Ray* ry, G4Vector3D& p ) const 
{
  // Distance along a Ray (straight line with G4Vector3D) to leave or enter
  // a G4CylindricalSurface.  The input variable which_way should be set to +1
  // to indicate leaving a G4CylindricalSurface, -1 to indicate entering a
  // G4CylindricalSurface.
  // p is the point of intersection of the Ray with the G4CylindricalSurface.
  // If the G4Vector3D of the Ray is opposite to that of the Normal to
  // the G4CylindricalSurface at the intersection point, it will not leave the
  // G4CylindricalSurface.
  // Similarly, if the G4Vector3D of the Ray is along that of the Normal 
  // to the G4CylindricalSurface at the intersection point, it will not enter
  // the G4CylindricalSurface.
  // This method is called by all finite shapes sub-classed to
  // G4CylindricalSurface.
  // 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 = kInfinity;
  G4Vector3D lv ( kInfinity, kInfinity, kInfinity );
  p = lv;

  // Origin and G4Vector3D unit vector of Ray.
  //
  G4Vector3D x = ry->Position();
  G4Vector3D dhat = ry->Direction( 0.0 );

  // Axis unit vector of the G4CylindricalSurface.
  //
  G4Vector3D ahat = GetAxis();
  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 = x - GetOrigin();
  G4double radius = GetRadius();

  // Quit with no intersection if radius of the G4CylindricalSurface is zero
  //
  if ( radius <= 0.0 )  { return Dist; }

  G4double dsq = d * d;
  G4double da = d * ahat;
  G4double dasq = da * da;
  G4double rsq = radius * radius;
  G4double qsq = dsq - dasq;
  G4double dira = dhat * ahat;
  G4double a = 1.0 - dira * dira;
  if ( a <= 0.0 )  { return Dist; }

  G4double b = 2. * ( d * dhat - da * dira );
  G4double c = rsq - qsq;
  G4double radical = b * b + 4. * a * c; 
  if ( radical < 0.0 )  { return Dist; }

  G4double root = std::sqrt( radical );
  s[0] = ( - b + root ) / ( 2. * a );
  s[1] = ( - b - root ) / ( 2. * a );

  // Order the possible solutions by increasing distance along the Ray
  //
  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 G4CylindricalSurface at the intersection point
  //
  for ( isoln = 0; isoln < maxsoln; isoln++ )
  {
    if ( s[isoln] >= 0.0 )
    {
      if ( s[isoln] >= kInfinity )  // 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 kInfinity;
}


G4double G4CylindricalSurface::
distanceAlongHelix( G4int which_way, const Helix* hx, G4Vector3D& p ) const
{
  // Distance along a Helix to leave or enter a G4CylindricalSurface.
  // The input variable which_way should be set to +1 to
  // indicate leaving a G4CylindricalSurface, -1 to indicate entering a
  // G4CylindricalSurface.
  // p is the point of intersection of the Helix with the G4CylindricalSurface.
  // If the G4Vector3D of the Helix is opposite to that of the Normal to
  // the G4CylindricalSurface at the intersection point, it will not leave the
  // G4CylindricalSurface.
  // Similarly, if the G4Vector3D of the Helix is along that of the Normal 
  // to the G4CylindricalSurface at the intersection point, it will not enter
  // the G4CylindricalSurface.
  // This method is called by all finite shapes sub-classed to
  // G4CylindricalSurface.
  // 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 = kInfinity;
  G4Vector3D lv ( kInfinity, kInfinity, kInfinity );
  G4Vector3D zerovec;  // zero G4Vector3D

  p = lv;
  G4int isoln = 0, maxsoln = 4;

  // Array of solutions in turning angle
  //
  G4double s[4];s[0]=-1.0;s[1]= -1.0;s[2]= -1.0;s[3]= -1.0;

  // Flag set to 1 if exact solution is found
  //
  G4int exact = 0;

  // Helix parameters
  //
  G4double rh = hx->GetRadius();          // radius of Helix
  G4Vector3D ah = hx->GetAxis();          // axis of Helix
  G4Vector3D oh = hx->position();         // origin of Helix
  G4Vector3D dh = hx->direction( 0.0 );   // initial G4Vector3D of Helix
  G4Vector3D prp = hx->getPerp();         // perpendicular vector
  G4double prpmag = prp.Magnitude();
  G4double rhp = rh / prpmag;

  // G4CylindricalSurface parameters
  //
  G4double rc = GetRadius();              // radius of G4CylindricalSurface
  if ( rc == 0.0 )  { return Dist; }      // quit if zero radius
    
  G4Vector3D oc = GetOrigin();            // origin of G4CylindricalSurface
  G4Vector3D ac = GetAxis();              // axis of G4CylindricalSurface

  // Calculate quantities of use later on
  //
  G4Vector3D alpha = rhp * prp;
  G4Vector3D beta = rhp * dh;
  G4Vector3D gamma = oh - oc;

  // Declare variables used later on in several places
  //
  G4double rcd2 = 0.0, alpha2 = 0.0;
  G4double A = 0.0, B = 0.0, C = 0.0, F = 0.0, G = 0.0, H = 0.0;
  G4double CoverB = 0.0, radical = 0.0, root = 0.0, s1 = 0.0, s2 = 0.0;
  G4Vector3D ghat;

  // Set flag for special cases
  //
  G4int special_case = 0;  // 0 means general case

  // Test to see if axes of Helix and G4CylindricalSurface are parallel,
  // in which case there are exact solutions
  //
  if ( ( std::fabs( ah.AngleBetween(ac) ) < kAngTolerance )
    || ( std::fabs( ah.AngleBetween(ac) - pi ) < kAngTolerance ) )
  {
    special_case = 1;

    // If, in addition, gamma is a zero vector or is parallel to the
    // G4CylindricalSurface axis, this simplifies the previous case
    //
    if ( gamma == zerovec )
    {
      special_case = 3;
      ghat = gamma;
    }
    else
    {
      ghat = gamma / gamma.Magnitude();
      if ( ( std::fabs( ghat.AngleBetween(ac) ) < kAngTolerance )
        || ( std::fabs( ghat.AngleBetween(ac) - pi ) < kAngTolerance ) )
      {
        special_case = 3;
      }
    }

    // Test to see if, in addition to the axes of the Helix and
    // G4CylindricalSurface being parallel, the axis of the surface is
    // perpendicular to the initial G4Vector3D of the Helix
    //
    if ( std::fabs( ( ac * dh ) ) < kAngTolerance )
    {
      // And, if, in addition to all this, the difference in origins of the
      // Helix and G4CylindricalSurface is  perpendicular to the initial
      // G4Vector3D of the Helix, there is a separate special case
      //
      if ( std::fabs( ( ghat * dh ) ) < kAngTolerance )
      {
        special_case = 4;
      }
    }
  }  // end of section with axes of Helix and G4CylindricalSurface parallel

  // Another peculiar case occurs if the axis of the G4CylindricalSurface and
  // the initial G4Vector3D of the Helix line up and their origins are the same.
  // This will require a higher order approximation than the general case
  //
  if ( ( ( std::fabs( dh.AngleBetween(ac) ) < kAngTolerance )
      || ( std::fabs( dh.AngleBetween(ac) - pi ) < kAngTolerance ) )
      && ( gamma == zerovec ) )
  {
    special_case = 2;
  }

  // Now all the special cases have been tagged, so solutions are found
  // for each case.  Exact solutions are indicated by setting exact = 1.
  // [For some reason switch doesn't work here, so do series of if's.]

  if ( special_case == 0  )    // approximate quadratic solutions
  {
    A = beta * beta - ( beta * ac ) * ( beta * ac )
      + gamma * alpha - ( gamma * ac ) * ( alpha * ac );
    B = 2.0 * gamma * beta 
      - 2.0 * ( gamma * ac ) * ( beta * ac );
    C = gamma * gamma 
      - ( gamma * ac ) * ( gamma * ac ) - rc * rc;

    if ( std::fabs( A ) < kCarTolerance )    // no quadratic term
    {
      if ( B == 0.0 )  // no intersection, quit
      {
        return Dist;
      }
      else             // B != 0
      {
        s[0] = -C / B;
      }
    }
    else               // A != 0, general quadratic solution
    {
      radical = B * B - 4.0 * A * C;
      if ( radical < 0.0 )  // no solution, quit
      {
        return Dist;
      }
      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] + 2.0 * pi;
      s[3] = s[1] + 2.0 * pi;
    }
  }
  else if ( special_case == 1 )    // exact solutions
  {
    exact = 1;
    H = 2.0 * ( alpha * alpha + gamma * alpha );
    F = gamma * gamma - ( ( gamma * ac ) * ( gamma * ac ) ) - rc * rc  + H;
    G = 2.0 * rhp * ( gamma * dh - ( gamma * ac ) * ( ac * dh ) );
    A = G * G  + H * H;
    B = -2.0 * F * H;
    C = F * F - G * G;

    if ( std::fabs( A ) < kCarTolerance )    // no quadratic term
    {
      if ( B == 0.0 )  // no intersection, quit
      {
        return Dist;
      }
      else             // B != 0
      {
        CoverB = -C / B;
        if ( std::fabs( CoverB ) > 1.0 )
        {
          return Dist;
        }
        s[0] = std::acos( CoverB );
      }
    }
  }
  else                 // A != 0, general quadratic solution
  {
    // Try a different method of calculation using F, G, and H to avoid
    // precision problems.

    // radical = B * B - 4.0 * A * C;
    // if ( radical < 0.0 )
    // {
    if ( std::fabs( H ) > kCarTolerance )
    {
      G4double r1 = G / H;
      G4double r2 = F / H;
      G4double radsq = 1.0 + r1*r1 - r2*r2;
      if ( radsq < 0.0 )  { return Dist; }
      root = G * std::sqrt( radsq );

      G4double denominator = H * ( 1.0 + r1*r1 );
      s1 = ( F + root ) / denominator;
      s2 = ( F - root ) / denominator;
    }
    else
    {
      return Dist;
    }
    // }  //  end radical < 0 condition
    // else
    // {
    //   root = std::sqrt( radical );
    //   s1 = ( -B + root ) / ( 2.0 * A );
    //   s2 = ( -B - root ) / ( 2.0 * A );
    // }
    if ( std::fabs( s1 ) <= 1.0 )
    {
      s[0] = std::acos( s1 );
      s[2] = 2.0 * pi - s[0];
    }
    if ( std::fabs( s2 ) <= 1.0 )
    {
      s[1] = std::acos( s2 );
      s[3] = 2.0 * pi - s[1];
    }

    // Must take only solutions which satisfy original unsquared equation:
    // Gsin(s) - Hcos(s) + F = 0.  Take best solution of pair and set false
    // solutions to -1.  Only do this if the result is significantly different
    // from zero.

    G4double temp1 = 0.0, temp2 = 0.0;
    G4double rsign = 1.0;
    if ( rh < 0.0 ) rsign = -1.0;
    if ( s[0] > 0.0 )
    {
      temp1 =  G * rsign * std::sin( s[0] ) - H * std::cos( s[0] ) + F;
      temp2 =  G * rsign * std::sin( s[2] ) - H * std::cos( s[2] ) + F;
      if ( std::fabs( temp1 ) > std::fabs( temp2 ) )
      {
        if ( std::fabs( temp1 ) > kAngTolerance )  {  s[0] = -1.0; }
        else if ( std::fabs( temp2 ) > kAngTolerance )  { s[2] = -1.0; }
      }
    }
    if ( s[1] > 0.0 )
    {
      temp1 =  G * rsign * std::sin( s[1] ) - H * std::cos( s[1] ) + F;
      temp2 =  G * rsign * std::sin( s[3] ) - H * std::cos( s[3] ) + F;
      if ( std::fabs( temp1 ) > std::fabs( temp2 ) )
      {
        if ( std::fabs( temp1 ) > kAngTolerance )  { s[1] = -1.0; }
        else if ( std::fabs( temp2 ) > kAngTolerance )  { s[3] = -1.0; }
      }
    }
  }
  else if ( special_case == 2 )    // approximate solution
  {
    G4Vector3D e = ah.cross( ac );
    G4double re = std::fabs( rhp ) * e.Magnitude();
    s[0] = std::sqrt( 2.0 * rc / re );
  }
  else if ( special_case == 3 )    // exact solutions
  {
    exact = 1;
    alpha2 = alpha * alpha;
    rcd2 = rhp * rhp * ( 1.0 - ( (ac*dh) * (ac*dh) ) );
    A = alpha2 - rcd2;
    B = - 2.0 * alpha2;
    C = alpha2 + rcd2 - rc*rc;
    if ( std::fabs( A ) < kCarTolerance )    // no quadratic term
    {
      if ( B == 0.0 )  { return Dist; }      // no intersection, quit
      else
      {
        CoverB = -C / B;
        if ( std::fabs( CoverB ) > 1.0 )  { return Dist; }
        s[0] = std::acos( CoverB );
      }
    }
    else    // A != 0, general quadratic solution
    {
      radical = B * B - 4.0 * A * C;
      if ( radical < 0.0 )  { return Dist; }
      root = std::sqrt( radical );
      s1 = ( -B + root ) / ( 2.0 * A );
      s2 = ( -B - root ) / ( 2.0 * A );
      if ( std::fabs( s1 ) <= 1.0 )  { s[0] = std::acos( s1 ); }
      if ( std::fabs( s2 ) <= 1.0 )  { s[1] = std::acos( s2 ); }
    }
  }
  else if ( special_case == 4 )    // exact solution
  {
    exact = 1;
    F = gamma * gamma - ( ( gamma * ac ) * ( gamma * ac ) ) - rc * rc;
    G = 2.0 * ( rhp * rhp  +  gamma * alpha );
    if ( G == 0.0 )  { return Dist; }               // no intersection, quit
                                
    G4double cs = 1.0 + ( F / G );
    if ( std::fabs( cs ) > 1.0 )  { return Dist; }  // no intersection, quit
    s[0] = std::acos( cs );
  }
  else                                // shouldn't get here
  {
    return Dist;
  }

  // **************************************************************************
  //
  //  Order the possible solutions by increasing turning angle
  //
  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 );
      if ( exact == 0 )    //  only for approximate solutions
      {
        // 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 = 0.0;  
        G4double delta0 = kInfinity;
        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 G4CylindricalSurface.
          // This generally occurs if Helix curls too tightly to Intersect it.
          //
          if ( iter > 50 )
          {
            Dist = kInfinity;
            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 G4CylindricalSurface.
          //
          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; }

          // If 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 surface 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 G4CylindricalSurface.

          if ( std::fabs( delta ) > std::fabs( delta0 ) )
          {
            Dist = std::fabs( rhp ) * gropeAlongHelix( hx );
            if ( Dist < 0.0 )
            {
              Dist = kInfinity;
              p = lv;
            }
            else
            {
              p = hx->position( Dist );
            }
            break;
          }

          // Set old delta to new one
          //
          delta0 = delta;

          // Add distance to G4CylindricalSurface to distance along Helix
          //
          Dist += delta;

          // Negative distance along Helix means Helix doesn't Intersect
          // G4CylindricalSurface.
          // Reset distance to large number, indicating no intersection with
          // G4CylindricalSurface.
          //
          if ( Dist < 0.0 )
          {
            Dist = kInfinity;
            p = lv;
            break;
          }

          // Recalculate point along Helix and the G4Vector3D
          //
          p = hx->position( Dist );
          d = hx->direction( Dist );
        }  //  end of while loop
      }  //  end of exact == 0 condition

      // 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 G4CylindricalSurface.

      if ( ( Dist < kInfinity ) &&
           ( ( 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 = kInfinity;
  p = lv;

  return Dist;
}
*/


G4Vector3D G4CylindricalSurface::Normal( const G4Vector3D& p ) const
{ 
  //  return the Normal unit vector to the G4CylindricalSurface 
  //  at a point p on (or nearly on) the G4CylindricalSurface
 
  G4Vector3D n = ( p - origin ) - ( ( p - origin ) * axis ) * axis;
  G4double nmag = n.mag();
 
  if ( nmag != 0.0 )  { n = n * (1/nmag); }
  
  return n;
}


G4Vector3D G4CylindricalSurface::SurfaceNormal( const G4Point3D& p ) const
{
  //  return the Normal unit vector to the G4CylindricalSurface at a point 
  //  p on (or nearly on) the G4CylindricalSurface
  
  G4Vector3D n = ( p - origin ) - ( ( p - origin ) * axis ) * axis;
  G4double nmag = n.mag();
  
  if ( nmag != 0.0 )  { n = n * (1/nmag); }
  
  return n;
}


G4int G4CylindricalSurface::Inside ( const G4Vector3D& x ) const
{ 
  //  Return 0 if point x is outside G4CylindricalSurface, 1 if Inside.
  //  Outside means that the distance to the G4CylindricalSurface would 
  //  be negative. Use the HowNear function to calculate this distance.

  if ( HowNear( x ) >= -0.5*kCarTolerance )
    { return 1; }
  else
    { return 0; }
}


G4int G4CylindricalSurface::WithinBoundary( const G4Vector3D& x ) const
{ 
  //  return 1 if point x is on the G4CylindricalSurface, otherwise return zero
  //  base this on the surface precision factor

  if ( std::fabs( HowNear( x ) / Scale() ) <= SURFACE_PRECISION )
    { return 1; }
  else
    { return 0; }
}


G4double G4CylindricalSurface::Scale() const
{
  //  Returns the radius of a G4CylindricalSurface unless it is zero, in which
  //  case returns the arbitrary number 1.0.
  //  This is ok since derived finite-sized classes will overwrite this.
  //  Used for Scale-invariant tests of surface thickness.

  if ( radius == 0.0 )
    { return 1.0; }
  else
    { return radius; }
}

/*
void G4CylindricalSurface::
rotate( G4double alpha, G4double beta, G4double gamma,
        G4ThreeMat& m, G4int inverse )
{
  // Rotate G4CylindricalSurface  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 );
  axis = m * axis;
}

void G4CylindricalSurface::
rotate( G4double alpha, G4double beta, G4double gamma, G4int inverse )
{
  // Rotate G4CylindricalSurface  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 );
  axis = m * axis;
}
*/

void G4CylindricalSurface::SetRadius( G4double r )
{ 
  //  Reset the radius of the G4CylindricalSurface
  //  Require radius to be non-negative

  if ( r >= 0.0 )  { radius = r; }
  else   // Use old value (do not change radius) if out of the range, 
  {      // but print warning message
    std::ostringstream message;
    message << "Negative radius." << G4endl
            << "Default radius of " << radius << " is used.";    
    G4Exception("G4CylindricalSurface::SetRadius()",
                "GeomSolids1001", JustWarning, message);
  }
}

/*
G4double G4CylindricalSurface::gropeAlongHelix( const Helix* hx ) const
{
  // Grope for a solution of a Helix intersecting a G4CylindricalSurface.
  // 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
  // G4CylindricalSurface, 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.Magnitude();
  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 = 2.0 * pi * 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 G4CylindricalSurface,
      // 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;
}
*/

---