inline void G4Hyperbola::Init(G4Axis2Placement3D position0,
			      G4double semiAxis0, G4double semiImagAxis0) {
  position= position0;
  semiAxis= semiAxis0;
  semiImagAxis= semiImagAxis0;

  ratioAxisImagAxis= semiAxis/semiImagAxis;

  // needed only for 2D hyperbolas
  toUnitHyperbola = G4Scale3D(1/semiAxis, 1/semiImagAxis, 0)
                    * position.GetToPlacementCoordinates();

  forTangent= semiAxis*semiAxis/(semiImagAxis*semiImagAxis);
}

inline G4double G4Hyperbola::GetSemiAxis() const {
  return semiAxis;
}

inline G4double G4Hyperbola::GetSemiImagAxis() const {
  return semiImagAxis;
}

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

inline G4double G4Hyperbola::GetPMax() {
  return -1;
}

inline G4Point3D G4Hyperbola::GetPoint(G4double param) {
  return position.GetLocation()
    + semiAxis*cosh(param)*position.GetPX()
    + semiImagAxis*sinh(param)*position.GetPY();
}

inline G4double G4Hyperbola::GetPPoint(const G4Point3D& pt) {
  G4Point3D ptLocal= position.GetToPlacementCoordinates()*pt;
  G4double xval= ptLocal.y()/ptLocal.x()*ratioAxisImagAxis;
  #ifdef WIN32
    G4double ppoint= 0.5*log((1+xval)/(1-xval));
  #else
    G4double ppoint= atanh(xval);
  #endif
  return ppoint;
}

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

#include "G4CurveRayIntersection.hh"

/*
inline void G4Hyperbola::IntersectRay2D(const G4Ray& ray,
					G4CurveRayIntersection& is)
{
  is.Init(*this, ray);

  // similar to G4Ellipse::IntersectRay2D

  // 2D operations would be faster
  G4Point3D s= toUnitHyperbola*ray.GetStart();
  G4Vector3D d= toUnitHyperbola*ray.GetDir();
  
  // solve (s+i*t)^2 = 1 for i (the distance)

  G4double sd= s.x()*d.x()-s.y()*d.y();
  G4double dd= d.x()*d.x()-d.y()*d.y(); // can be 0
  G4double ss= s.x()*s.x()-s.y()*s.y();

  if (abs(dd) < kCarTolerance*kCarTolerance) {

    // coeff of i^2 == 0
    G4double i= (1-ss)/(2*sd);
    G4CurveRayIntersection isTmp(*this, ray);
    isTmp.ResetDistance(i);
    is.Update(isTmp);
    return;

  }

  G4double discr= sd*sd-dd*(ss-1);
  if (discr >= 0) {

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

  }
}
*/

inline G4int G4Hyperbola::IntersectRay2D(const G4Ray& ray)
{
  // NOT VERIFIED

  // similar to G4Ellipse::IntersectRay2D

  // 2D operations would be faster
  G4Point3D s= toUnitHyperbola*ray.GetStart();
  G4Vector3D d= toUnitHyperbola*ray.GetDir();
  
  // solve (s+i*t)^2 = 1 for i (the distance)

  G4double sd= s.x()*d.x()-s.y()*d.y();
  G4double dd= d.x()*d.x()-d.y()*d.y(); // can be 0
  G4double ss= s.x()*s.x()-s.y()*s.y();

  if (abs(dd) < kCarTolerance*kCarTolerance) {

    // coeff of i^2 == 0
    return 0;

  }
  
  G4int nbinter = 0;

  G4double discr= sd*sd-dd*(ss-1);
  if (discr >= 0) 
  {
    // 2 intersections (maybe 1, but this case is rare)
    G4double sqrtdiscr= sqrt(discr);
    // find the smallest positive i
    G4double i= -sd-sqrtdiscr;
    if (i > kCarTolerance) 
      nbinter++;

    i= -sd+sqrtdiscr;
    if (i<kCarTolerance) 
      nbinter++;
  }
    
  return nbinter;
}