Helper class representing a helical track. More...

#include <HelixHelper.h>

Public Member Functions
	HelixHelper (float z0, float d0, float omega, float cotTheta, float phi)
	construct a helix with given helix parameters, as defined for Track objects

	HelixHelper (const ROOT::Math::XYZVector &poca, const ROOT::Math::XYZVector &momentum_in_poca, int charge)
	construct a helix at an arbitrary position 'poca' (helices built at different points are not comparable)

double	pathLengthToPoint (const ROOT::Math::XYZVector &p) const
	returns the path length (along the helix) to the helix point closest to p.

double	pathLengthToLine (const ROOT::Math::XYZVector &a, const ROOT::Math::XYZVector &b) const
	returns the path length (along the helix) to the helix point closest to the line going through points a and b.

ROOT::Math::XYZVector	momentum (double s=0) const
	momentum of the particle, at the helix point corresponding to a flown path length s (from poca).

ROOT::Math::XYZVector	position (double s) const
	point on helix corresponding to a flown path length s (from poca)

Static Private Member Functions
static double	distanceToPoint (double s)
	minimization function, calculates distance to minimize_distance_to_point

static double	distanceToLine (double s)
	same as distanceToPoint, but ignoring z coordinate

Private Attributes
float	m_z0
	minimal z distance of point of closest approach to origin

float	m_d0
	minimal r distance of point of closest approach to origin

float	m_omega
	signed curvature

float	m_cotTheta
	cotangens of polar angle

float	m_phi
	Phi at the perigee [-pi, pi].

ROOT::Math::XYZVector	m_poca
	point of closest approach to origin

Static Private Attributes
static constexpr double	c_cTimesB = (1.5 * 0.00299792458)
	magnetic filed times speed of light

static constexpr double	c_maxFlightLength = 150.0
	maximal path length (from origin) considered for extrapolation

static ROOT::Math::XYZVector	minimize_distance_to_point
	user supplied point we're trying to find the nearest helix point to

static ROOT::Math::XYZVector	minimize_distance_to_line_a
	first user supplied line we're trying to find the nearest helix point to

static ROOT::Math::XYZVector	minimize_distance_to_line_b
	second user supplied line we're trying to find the nearest helix point to

static HelixHelper const *	helix_object
	keep a 'this' pointer around for minimization

Detailed Description

Helper class representing a helical track.

It is used as an alternative to Genfit's track representation and provides much faster replacements for its extrapolateToLine/ extrapolateToPoint() methods.

Definition at line 28 of file HelixHelper.h.

Constructor & Destructor Documentation

◆ HelixHelper() [1/2]

HelixHelper	(	float	z0,
		float	d0,
		float	omega,
		float	cotTheta,
		float	phi
	)

inline

construct a helix with given helix parameters, as defined for Track objects

Definition at line 34 of file HelixHelper.h.

                                                                           :
      m_z0(z0), m_d0(d0), m_omega(omega), m_cotTheta(cotTheta), m_phi(phi),
      m_poca(d0 * sin(phi), -d0 * cos(phi), z0)
    { }

◆ HelixHelper() [2/2]

HelixHelper	(	const ROOT::Math::XYZVector &	poca,
		const ROOT::Math::XYZVector &	momentum_in_poca,
		int	charge
	)

inline

construct a helix at an arbitrary position 'poca' (helices built at different points are not comparable)

Definition at line 41 of file HelixHelper.h.

                                                                                                     :
      m_poca(poca)
    {
      const double pt = momentum_in_poca.Rho();
      const double R = pt / c_cTimesB; //c and magnetic field, should come from some common database later...
 
      const ROOT::Math::XYZVector& dirInPoca = momentum_in_poca.Unit();
 
      //determine the angle phi, distribute it from -pi to pi
      m_phi = atan2(dirInPoca.Y(), dirInPoca.X());
 
      //determine sign of d0
      //calculate the sign of the projection of pt(dirInPoca) at d0(poca)
      const double d0Sign = TMath::Sign(1., poca.X() * dirInPoca.X()
                                        + poca.Y() * dirInPoca.Y());
 
      //Now set the helix parameters
      m_d0 = d0Sign * poca.Rho();
      m_omega = 1 / R * charge;
      m_z0 = poca.Z();
      m_cotTheta = dirInPoca.Z() / dirInPoca.Rho();
    }

Member Function Documentation

◆ distanceToLine()

static double distanceToLine ( double s )

inlinestaticprivate

same as distanceToPoint, but ignoring z coordinate

Definition at line 153 of file HelixHelper.h.

    {
      const ROOT::Math::XYZVector& p = helix_object->position(s);
      // d = |(p-a) \times (p-b)| / |b-a|
      return ((p - minimize_distance_to_line_a).Cross(p - minimize_distance_to_line_b)).R() / (minimize_distance_to_line_b -
             minimize_distance_to_line_a).R();
    }

◆ distanceToPoint()

static double distanceToPoint ( double s )

inlinestaticprivate

minimization function, calculates distance to minimize_distance_to_point

Definition at line 147 of file HelixHelper.h.

    {
      return (helix_object->position(s) - minimize_distance_to_point).R();
    }

◆ momentum()

ROOT::Math::XYZVector momentum ( double s = 0 ) const

inline

momentum of the particle, at the helix point corresponding to a flown path length s (from poca).

Definition at line 109 of file HelixHelper.h.

    {
      const float pt = c_cTimesB / TMath::Abs(m_omega);
      return ROOT::Math::XYZVector(
               pt * cos(m_phi - 2 * m_omega * s),
               pt * sin(m_phi - 2 * m_omega * s),
               pt * m_cotTheta
             );
    }

◆ pathLengthToLine()

double pathLengthToLine	(	const ROOT::Math::XYZVector &	a,
		const ROOT::Math::XYZVector &	b
	)		const

inline

returns the path length (along the helix) to the helix point closest to the line going through points a and b.

Definition at line 87 of file HelixHelper.h.

    {
      minimize_distance_to_line_a = a;
      minimize_distance_to_line_b = b;
 
      helix_object = this; //ok, this is ugly
      //TODO create a functor object to wrap everything up
 
      ROOT::Math::Functor1D functor(&distanceToLine);
      ROOT::Math::BrentMinimizer1D bm;
      bm.SetFunction(functor, 0.0, c_maxFlightLength);
      bm.Minimize(100); //#iterations, abs. error, rel. error
 
      //bm.FValMinimum() is shortest distance
      //bm.XMinimum() is corresponding path length
      return bm.XMinimum();
    }

◆ pathLengthToPoint()

double pathLengthToPoint ( const ROOT::Math::XYZVector & p ) const

inline

returns the path length (along the helix) to the helix point closest to p.

a path length of 0 corresponds to p = poca

Definition at line 68 of file HelixHelper.h.

    {
      minimize_distance_to_point = p;
      helix_object = this; //ok, this is ugly
      //TODO create a functor object to wrap everything up
 
      ROOT::Math::Functor1D functor(&distanceToPoint);
      ROOT::Math::BrentMinimizer1D bm;
      bm.SetFunction(functor, 0.0, c_maxFlightLength);
      bm.Minimize(100); //#iterations, abs. error, rel. error
 
      //bm.FValMinimum() is shortest distance
      //bm.XMinimum() is corresponding path length
      return bm.XMinimum();
    }

◆ position()

ROOT::Math::XYZVector position ( double s ) const

inline

point on helix corresponding to a flown path length s (from poca)

Definition at line 120 of file HelixHelper.h.

    {
      //approximation (but it does work for straight tracks)
      return m_poca + ROOT::Math::XYZVector(
               s * s * m_omega / 2 * sin(m_phi) + s * cos(m_phi),
               -s * s * m_omega / 2 * cos(m_phi) + s * sin(m_phi),
               s * m_cotTheta
             );
    }

Member Data Documentation

◆ c_cTimesB

constexpr double c_cTimesB = (1.5 * 0.00299792458)

staticconstexprprivate

magnetic filed times speed of light

Definition at line 29 of file HelixHelper.h.

◆ c_maxFlightLength

constexpr double c_maxFlightLength = 150.0

staticconstexprprivate

maximal path length (from origin) considered for extrapolation

Definition at line 30 of file HelixHelper.h.

◆ m_cotTheta

float m_cotTheta

private

cotangens of polar angle

Definition at line 139 of file HelixHelper.h.

◆ m_d0

float m_d0

private

minimal r distance of point of closest approach to origin

Definition at line 135 of file HelixHelper.h.

◆ m_omega

float m_omega

private

signed curvature

Definition at line 137 of file HelixHelper.h.

◆ m_phi

float m_phi

private

Phi at the perigee [-pi, pi].

Definition at line 141 of file HelixHelper.h.

◆ m_poca

ROOT::Math::XYZVector m_poca

private

point of closest approach to origin

Definition at line 144 of file HelixHelper.h.

◆ m_z0

float m_z0

private

minimal z distance of point of closest approach to origin

Definition at line 133 of file HelixHelper.h.

The documentation for this class was generated from the following file:

reconstruction/modules/VXDDedxPID/include/HelixHelper.h

Public Member Functions

Static Private Member Functions

Private Attributes

Static Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ HelixHelper() [1/2]

◆ HelixHelper() [2/2]

Member Function Documentation

◆ distanceToLine()

◆ distanceToPoint()

◆ momentum()

◆ pathLengthToLine()

◆ pathLengthToPoint()

◆ position()

Member Data Documentation

◆ c_cTimesB

◆ c_maxFlightLength

◆ m_cotTheta

◆ m_d0

◆ m_omega

◆ m_phi

◆ m_poca

◆ m_z0