inline void G4Parabola::Init(const G4Axis2Placement3D& position0,
			     G4double focalDist0) {
  position= position0;
  focalDist= focalDist0;

  // focus
  F= position.GetLocation()+focalDist*position.GetPX();
  // line
  L0= position.GetLocation()-focalDist*position.GetPX();
  //l= position.GetPY();
}

inline double G4Parabola::GetFocalDist() const {
  return focalDist;
}

//////////////////////////////////////////////////////////////////////////////

inline G4double G4Parabola::GetPMax() {
  return -1;
}

inline G4Point3D G4Parabola::GetPoint(G4double param) {
  return position.GetLocation()
    + focalDist* (param*param*position.GetPX() + 2*param*position.GetPY());
}

inline G4double G4Parabola::GetPPoint(const G4Point3D& pt) {
  G4Point3D ptLocal= position.GetToPlacementCoordinates()*pt;
  return ptLocal.y()/(2*focalDist);
}

//////////////////////////////////////////////////////////////////////////////

#include "G4CurveRayIntersection.hh"

inline void G4Parabola::IntersectRay2D(const G4Ray& ray,
				       G4CurveRayIntersection& is)
{
  is.Init(*this, ray);

  const G4Point3D& S= ray.GetStart();
  const G4Vector3D& d= ray.GetDir();

  const G4Vector3D& l= position.GetPY();

  // a == 1
  G4Vector3D SMinusF= S-F;
  G4double bHalf= SMinusF*d - (d.x()*l.y()-d.y()*l.x());
  G4double c= SMinusF.mag2() + ( (S.x()-L0.x())*l.y() - (S.y()-L0.y())*l.x() );

  G4double discr= bHalf*bHalf-c;
  if (discr >= 0) {

    // 2 intersections (maybe 1, but this case is rare)
    G4double sqrtdiscr= sqrt(discr);
    // find the smallest positive i
    G4double i= -bHalf-sqrtdiscr;
    if (i<kCarTolerance) {
      i= -bHalf+sqrtdiscr;
      if (i<kCarTolerance) {
	return;
      }
    }
    G4CurveRayIntersection isTmp(*this, ray);
    isTmp.ResetDistance(i);
    is.Update(isTmp);

  }
}