#include <HelixArbitraryPlaneCrossing2Order.h>

Inheritance diagram for HelixArbitraryPlaneCrossing2Order:

Public Types
typedef Basic3DVector< double >	DirectionTypeDouble
typedef Basic3DVector< double >	PositionTypeDouble
Public Member Functions
virtual DirectionType	direction (double s) const
DirectionTypeDouble	directionInDouble (double s) const
	HelixArbitraryPlaneCrossing2Order (const double &x0, const double &y0, const double &z0, const double &cosPhi0, const double &sinPhi0, const double &cosTheta, const double &sinTheta, const double &rho, const PropagationDirection propDir=alongMomentum)
	HelixArbitraryPlaneCrossing2Order (const PositionType &point, const DirectionType &direction, const float curvature, const PropagationDirection propDir=alongMomentum)
virtual std::pair< bool, double >	pathLength (const Plane &)
virtual PositionType	position (double s) const
PositionTypeDouble	positionInDouble (double s) const
double	smallestPathLength (const double firstPathLength, const double secondPathLength) const
virtual	~HelixArbitraryPlaneCrossing2Order ()
Private Member Functions
std::pair< bool, double >	solutionByDirection (const double dS1, const double dS2) const
Private Attributes
double	theCosPhi0
double	theCosTheta
const PropagationDirection	thePropDir
const double	theRho
double	theSinPhi0
double	theSinThetaI
const double	theX0
const double	theY0
const double	theZ0

Detailed Description

Calculates intersections of a helix with planes of any orientation using a parabolic approximation.

Definition at line 9 of file HelixArbitraryPlaneCrossing2Order.h.

Member Typedef Documentation

typedef Basic3DVector<double> HelixArbitraryPlaneCrossing2Order::DirectionTypeDouble

Definition at line 52 of file HelixArbitraryPlaneCrossing2Order.h.

typedef Basic3DVector<double> HelixArbitraryPlaneCrossing2Order::PositionTypeDouble

Definition at line 51 of file HelixArbitraryPlaneCrossing2Order.h.

Constructor & Destructor Documentation

HelixArbitraryPlaneCrossing2Order::HelixArbitraryPlaneCrossing2Order	(	const PositionType &	point,
		const DirectionType &	direction,
		const float	curvature,
		const PropagationDirection	propDir = `alongMomentum`
	)

Constructor using point, direction and (transverse!) curvature.

Definition at line 9 of file HelixArbitraryPlaneCrossing2Order.cc.

References p2, mathSSE::sqrt(), theCosPhi0, theCosTheta, theSinPhi0, theSinThetaI, Basic3DVector< T >::x(), Basic3DVector< T >::y(), and Basic3DVector< T >::z().

                                                                                                         :
  theX0(point.x()),
  theY0(point.y()),
  theZ0(point.z()),
  theRho(curvature),
  thePropDir(propDir)
{
  //
  // Components of direction vector (with correct normalisation)
  //
  double px = direction.x();
  double py = direction.y();
  double pz = direction.z();
  double pt2 = px*px+py*py;
  double p2 = pt2+pz*pz;
  double pI = 1./sqrt(p2);
  double ptI = 1./sqrt(pt2);
  theCosPhi0 = px*ptI;
  theSinPhi0 = py*ptI;
  theCosTheta = pz*pI;
  theSinThetaI = p2*pI*ptI; //  (1/(pt/p)) = p/pt = p*ptI and p = p2/p = p2*pI
}

HelixArbitraryPlaneCrossing2Order::HelixArbitraryPlaneCrossing2Order	(	const double &	x0,
		const double &	y0,
		const double &	z0,
		const double &	cosPhi0,
		const double &	sinPhi0,
		const double &	cosTheta,
		const double &	sinTheta,
		const double &	rho,
		const PropagationDirection	propDir = `alongMomentum`
	)		`[inline]`

Fast constructor (for use by HelixArbitraryPlaneCrossing).

Definition at line 21 of file HelixArbitraryPlaneCrossing2Order.h.

                                                                                        :
    theX0(x0), theY0(y0), theZ0(z0),
    theCosPhi0(cosPhi0), theSinPhi0(sinPhi0),
    theCosTheta(cosTheta), theSinThetaI(1./sinTheta),
    theRho(rho), 
    thePropDir(propDir) {}

virtual HelixArbitraryPlaneCrossing2Order::~HelixArbitraryPlaneCrossing2Order ( ) [inline, virtual]

Definition at line 33 of file HelixArbitraryPlaneCrossing2Order.h.

{}

Member Function Documentation

HelixPlaneCrossing::DirectionType HelixArbitraryPlaneCrossing2Order::direction ( double s ) const [virtual]

Direction at pathlength s from the starting point.

Implements HelixPlaneCrossing.

Definition at line 121 of file HelixArbitraryPlaneCrossing2Order.cc.

References dir, directionInDouble(), Basic3DVector< T >::x(), Basic3DVector< T >::y(), and Basic3DVector< T >::z().

                                                            {
  // use double precision result
  DirectionTypeDouble dir = directionInDouble(s);
  return DirectionType(dir.x(),dir.y(),dir.z());
}

HelixArbitraryPlaneCrossing2Order::DirectionTypeDouble HelixArbitraryPlaneCrossing2Order::directionInDouble ( double s ) const

Direction at pathlength s from the starting point in double precision.

Definition at line 130 of file HelixArbitraryPlaneCrossing2Order.cc.

References theCosPhi0, theCosTheta, theRho, theSinPhi0, and theSinThetaI.

Referenced by direction(), and HelixArbitraryPlaneCrossing::directionInDouble().

                                                                    {
  // based on delta phi
  double dph = s*theRho/theSinThetaI;
  return DirectionTypeDouble(theCosPhi0-(theSinPhi0+0.5*dph*theCosPhi0)*dph,
                             theSinPhi0+(theCosPhi0-0.5*dph*theSinPhi0)*dph,
                             theCosTheta*theSinThetaI);
}

std::pair< bool, double > HelixArbitraryPlaneCrossing2Order::pathLength ( const Plane & plane ) [virtual]

Propagation status (true if valid) and (signed) path length along the helix from the starting point to the plane. The starting point is given in the constructor.

Implements HelixPlaneCrossing.

Definition at line 39 of file HelixArbitraryPlaneCrossing2Order.cc.

References Plane::localZ(), Plane::normalVector(), solutionByDirection(), mathSSE::sqrt(), theCosPhi0, theCosTheta, theRho, theSinPhi0, theSinThetaI, theX0, theY0, theZ0, PV3DBase< T, PVType, FrameType >::x(), PV3DBase< T, PVType, FrameType >::y(), and PV3DBase< T, PVType, FrameType >::z().

Referenced by PixelForwardLayer::computeCrossings(), and HelixArbitraryPlaneCrossing::pathLength().

                                                                {
  //
  // get local z-vector in global co-ordinates and
  // distance to starting point
  //
  GlobalVector normalToPlane = plane.normalVector();
  double nPx = normalToPlane.x();
  double nPy = normalToPlane.y();
  double nPz = normalToPlane.z();
  double cP = plane.localZ(GlobalPoint(theX0,theY0,theZ0));
  //
  // coefficients of 2nd order equation to obtain intersection point
  // in approximation (without curvature-related factors).
  //
  double ceq1 = theRho*(nPx*theSinPhi0-nPy*theCosPhi0);
  double ceq2 = nPx*theCosPhi0 + nPy*theSinPhi0 + nPz*theCosTheta*theSinThetaI;
  double ceq3 = cP;
  //
  // Check for degeneration to linear equation (zero
  //   curvature, forward plane or direction perp. to plane)
  //
  double dS1,dS2;
  if ( fabs(ceq1)>FLT_MIN ) {
    double deq1 = ceq2*ceq2;
    double deq2 = ceq1*ceq3;
    if ( fabs(deq1)<FLT_MIN || fabs(deq2/deq1)>1.e-6 ) {
      //
      // Standard solution for quadratic equations
      //
      double deq = deq1+2*deq2;
      if ( deq<0. )  return std::pair<bool,double>(false,0);
      double ceq = -0.5*(ceq2+(ceq2>0?1:-1)*sqrt(deq));
      dS1 = -2*(ceq/ceq1)*theSinThetaI;
      dS2 = (ceq3/ceq)*theSinThetaI;
    }
    else {
      //
      // Solution by expansion of sqrt(1+deq)
      //
      double ceq = (ceq2/ceq1)*theSinThetaI;
      double deq = deq2/deq1;
      deq *= (1-0.5*deq);
      dS1 = -ceq*deq;
      dS2 = ceq*(2+deq);
    }
  }
  else {
    //
    // Special case: linear equation
    //
    dS1 = dS2 = -(ceq3/ceq2)*theSinThetaI;
  }
  //
  // Choose and return solution
  //
  return solutionByDirection(dS1,dS2);
}

HelixPlaneCrossing::PositionType HelixArbitraryPlaneCrossing2Order::position ( double s ) const [virtual]

Position at pathlength s from the starting point.

Implements HelixPlaneCrossing.

Definition at line 101 of file HelixArbitraryPlaneCrossing2Order.cc.

References pos, positionInDouble(), Basic3DVector< T >::x(), Basic3DVector< T >::y(), and Basic3DVector< T >::z().

Referenced by PixelForwardLayer::computeCrossings().

                                                           {
  // use double precision result
  PositionTypeDouble pos = positionInDouble(s);
  return PositionType(pos.x(),pos.y(),pos.z());
}

HelixArbitraryPlaneCrossing2Order::PositionTypeDouble HelixArbitraryPlaneCrossing2Order::positionInDouble ( double s ) const

Position at pathlength s from the starting point in double precision.

Definition at line 110 of file HelixArbitraryPlaneCrossing2Order.cc.

References theCosPhi0, theCosTheta, theRho, theSinPhi0, theSinThetaI, theX0, theY0, and theZ0.

Referenced by position(), and HelixArbitraryPlaneCrossing::positionInDouble().

                                                                   {
  // based on path length in the transverse plane
  double st = s/theSinThetaI;
  return PositionTypeDouble(theX0+(theCosPhi0-(st*0.5*theRho)*theSinPhi0)*st,
                            theY0+(theSinPhi0+(st*0.5*theRho)*theCosPhi0)*st,
                            theZ0+st*theCosTheta*theSinThetaI);
}

double HelixArbitraryPlaneCrossing2Order::smallestPathLength	(	const double	firstPathLength,
		const double	secondPathLength
	)		const `[inline]`

Pathlength to closest solution.

Definition at line 64 of file HelixArbitraryPlaneCrossing2Order.h.

Referenced by solutionByDirection().

                                                                         {
    return fabs(firstPathLength)<fabs(secondPathLength) ? firstPathLength : secondPathLength;
  }

std::pair< bool, double > HelixArbitraryPlaneCrossing2Order::solutionByDirection	(	const double	dS1,
		const double	dS2
	)		const `[private]`

Choice of one of two solutions according to the propagation direction.

Definition at line 141 of file HelixArbitraryPlaneCrossing2Order.cc.

References alongMomentum, anyDirection, printConversionInfo::aux, path(), indexGen::s2, smallestPathLength(), thePropDir, and TrackValidation_HighPurity_cff::valid.

Referenced by pathLength().

                                                                               {
  bool valid = false;
  double path = 0;
  if ( thePropDir == anyDirection ) {
    valid = true;
    path = smallestPathLength(dS1,dS2);
  }
  else {
    // use same logic for both directions (invert if necessary)
    double propSign = thePropDir==alongMomentum ? 1 : -1;
    double s1(propSign*dS1);
    double s2(propSign*dS2);
    // sort
    if ( s1 > s2 ) {
      double aux = s1;
      s1 = s2;
      s2 = aux;
    }
    // choose solution (if any with positive sign)
    if ( s1<0 && s2>=0 ) {
      // First solution in backward direction: choose second one.
      valid = true;
      path = propSign*s2;
    }
    else if ( s1>=0 ) {
      // First solution in forward direction: choose it (s2 is further away!).
      valid = true;
      path = propSign*s1;
    }
  }
  return std::pair<bool,double>(valid,path);
}