Utility for propagation of a particle along helix. More...

#include <HelixSwimmer.h>

Public Member Functions
	HelixSwimmer ()
	default constructor

void	set (const ROOT::Math::XYZPoint &position, const ROOT::Math::XYZVector &momentum, double charge, double Bz)
	Sets the helix.

void	setTransformation (const ROOT::Math::Transform3D &transform)
	Sets transformation from the frame in which helix is constructed (nominal frame) to module local frame.

void	moveReferencePosition (double length)
	Moves reference position along helix by length.

ROOT::Math::XYZPoint	getPosition (double length) const
	Returns particle position at given length.

ROOT::Math::XYZVector	getDirection (double length) const
	Returns particle direction at given length.

double	getDistanceToPlane (const ROOT::Math::XYZPoint &point, const ROOT::Math::XYZVector &normal) const
	Returns the distance along helix to the nearest intersection with the plane nearly parallel to z axis.

Private Member Functions
double	shortestDistance (double cosAlpha, double phi) const
	Returns shortest distance.

double	withinSingleTurn (double t) const
	Returns helix length within a single turn.

Private Attributes
double	m_R = 0
	helix radius

double	m_xc = 0
	helix axis position in x

double	m_yc = 0
	helix axis position in y

double	m_omega = 0
	angular speed [1/cm]

double	m_kz = 0
	slope in z

double	m_phi0 = 0
	phi of reference position

double	m_z0 = 0
	z of reference position

double	m_T0 = 0
	helix length of single turn

double &	x0 = m_xc
	x of reference position for zero magnetic field

double &	y0 = m_yc
	y of reference position for zero magnetic field

double &	z0 = m_z0
	z of reference position for zero magnetic field

double &	kx = m_R
	direction in x for zero magnetic field

double &	ky = m_phi0
	direction in y for zero magnetic field

double &	kz = m_kz
	direction in z for zero magnetic field

ROOT::Math::Transform3D	m_transformInv
	transformation from nominal to local frame

Detailed Description

Utility for propagation of a particle along helix.

Helix representation here differs from the official one. Running parameter is the signed distance along helix measured from the reference position. Negative distance means propagating back in time.

Definition at line 30 of file HelixSwimmer.h.

Constructor & Destructor Documentation

◆ HelixSwimmer()

HelixSwimmer ( )

inline

default constructor

Definition at line 37 of file HelixSwimmer.h.

38 {}

Member Function Documentation

◆ getDirection()

XYZVector getDirection ( double length ) const

Returns particle direction at given length.

Parameters

length distance along helix measured from the reference position

Returns: direction (in module local frame if transformation is set)

Definition at line 75 of file HelixSwimmer.cc.

    {
      if (m_omega != 0) {
        double phi = m_phi0 + m_omega * length;
        double k_T = m_omega * m_R;
        XYZVector vec(-k_T * sin(phi), k_T * cos(phi), m_kz);
        return m_transformInv * vec;
      } else {
        XYZVector vec(kx, ky, kz);
        return m_transformInv * vec;
      }
    }

◆ getDistanceToPlane()

double getDistanceToPlane	(	const ROOT::Math::XYZPoint &	point,
		const ROOT::Math::XYZVector &	normal
	)		const

Returns the distance along helix to the nearest intersection with the plane nearly parallel to z axis.

Parameters

point	point on the plane
normal	plane normal

Returns: signed distance (NaN if cross-section doesn't exist)

Definition at line 88 of file HelixSwimmer.cc.

    {
      if (m_omega != 0) {
        auto r = point - XYZPoint(m_xc, m_yc, m_z0);
        double phi = normal.Phi();
        double s = r.Dot(normal);
        if (std::abs(s) > m_R) return std::numeric_limits<double>::quiet_NaN(); // no solution
 
        double t = shortestDistance(s / m_R, phi);
        double v = m_kz * normal.Z();
        if (v == 0) return t;
 
        double t_prev = t;
        double dt_prev = 0;
        for (int i = 0; i < 100; i++) {
          double cosAlpha = (s - v * t) / m_R;
          if (std::abs(cosAlpha) > 1) {
            return std::numeric_limits<double>::quiet_NaN(); // no solution
          }
          t = shortestDistance(cosAlpha, phi);
          double dt = t - t_prev;
          if (dt == 0 or (dt + dt_prev) == 0) return t;
          t_prev = t;
          dt_prev = dt;
        }
        if (std::abs(dt_prev) < 1e-6) {
          B2DEBUG(20, "TOP::HelixSwimmer::getDistanceToPlane: not converged"
                  << LogVar("v", v) << LogVar("dt", dt_prev));
          return t;
        } else {
          B2DEBUG(20, "TOP::HelixSwimmer::getDistanceToPlane: not converged"
                  << LogVar("v", v) << LogVar("dt", dt_prev));
          return std::numeric_limits<double>::quiet_NaN();
        }
      } else {
        auto r = point - XYZPoint(x0, y0, z0);
        auto v = XYZVector(kx, ky, kz);
        return r.Dot(normal) / v.Dot(normal);
      }
    }

◆ getPosition()

XYZPoint getPosition ( double length ) const

Returns particle position at given length.

Parameters

length distance along helix measured from the reference position

Returns: position (in module local frame if transformation is set)

Definition at line 63 of file HelixSwimmer.cc.

    {
      if (m_omega != 0) {
        double phi = m_phi0 + m_omega * length;
        XYZPoint vec(m_xc + m_R * cos(phi), m_yc + m_R * sin(phi), m_z0 + m_kz * length);
        return m_transformInv * vec;
      } else {
        XYZPoint vec(x0 + kx * length, y0 + ky * length, z0 + kz * length);
        return m_transformInv * vec;
      }
    }

◆ moveReferencePosition()

void moveReferencePosition ( double length )

Moves reference position along helix by length.

Parameters

length distance along helix measured from current reference position

Definition at line 51 of file HelixSwimmer.cc.

    {
      if (m_omega != 0) {
        m_phi0 += m_omega * length;
        m_z0 += m_kz * length;
      } else {
        x0 += kx * length;
        y0 += ky * length;
        z0 += kz * length;
      }
    }

◆ set()

void set	(	const ROOT::Math::XYZPoint &	position,
		const ROOT::Math::XYZVector &	momentum,
		double	charge,
		double	Bz
	)

Sets the helix.

Parameters

position	particle position (= default reference position)
momentum	particle momentum
charge	particle charge in units of elementary charge
Bz	magnetic field z-component (we assume other two are negligible)

Definition at line 26 of file HelixSwimmer.cc.

    {
      double p = momentum.R();
      double pT = momentum.Rho();
      double b = -Bz * charge * Const::speedOfLight;
      if (std::abs(b / Unit::T) > pT) { // helix for R < 100 m
        m_R = pT / std::abs(b);
        m_omega = b / p;
        m_kz = momentum.Z() / p;
        m_phi0 = momentum.Phi() - copysign(M_PI / 2, m_omega);
        m_xc = position.X() - m_R * cos(m_phi0);
        m_yc = position.Y() - m_R * sin(m_phi0);
        m_z0 = position.Z();
        m_T0 = 2 * M_PI / std::abs(m_omega);
      } else { // straight line
        m_omega = 0; // distinguisher between straight line and helix
        x0 = position.X();
        y0 = position.Y();
        z0 = position.Z();
        kx = momentum.X() / p;
        ky = momentum.Y() / p;
        kz = momentum.Z() / p;
      }
    }

◆ setTransformation()

void setTransformation ( const ROOT::Math::Transform3D & transform )

inline

Sets transformation from the frame in which helix is constructed (nominal frame) to module local frame.

Parameters

transform transformation from local to nominal frame

Definition at line 53 of file HelixSwimmer.h.

53{m_transformInv = transform.Inverse();}

◆ shortestDistance()

double shortestDistance	(	double	cosAlpha,
		double	phi
	)		const

inlineprivate

Returns shortest distance.

Parameters

cosAlpha	cosine of alpha
phi	phi of plane

Returns: signed shortest distance

Definition at line 121 of file HelixSwimmer.h.

    {
      double alpha = acos(cosAlpha);
      double t1 = withinSingleTurn((phi - m_phi0 - alpha) / m_omega);
      double t2 = withinSingleTurn((phi - m_phi0 + alpha) / m_omega);
      double ta = std::min(t1, t2);
      double tb = std::max(t1 - m_T0, t2 - m_T0);
      double t = (std::abs(ta) < std::abs(tb)) ? ta : tb;
      return t;
    }

◆ withinSingleTurn()

double withinSingleTurn ( double t ) const

inlineprivate

Returns helix length within a single turn.

Parameters

t	helix length

Returns: helix length within single turn

Definition at line 132 of file HelixSwimmer.h.

    {
      t = fmod(t, m_T0);
      if (t < 0) t += m_T0;
      return t;
    }

Member Data Documentation

◆ kx

double& kx = m_R

private

direction in x for zero magnetic field

Definition at line 112 of file HelixSwimmer.h.

◆ ky

double& ky = m_phi0

private

direction in y for zero magnetic field

Definition at line 113 of file HelixSwimmer.h.

◆ kz

double& kz = m_kz

private

direction in z for zero magnetic field

Definition at line 114 of file HelixSwimmer.h.

◆ m_kz

double m_kz = 0

private

slope in z

Definition at line 104 of file HelixSwimmer.h.

◆ m_omega

double m_omega = 0

private

angular speed [1/cm]

Definition at line 103 of file HelixSwimmer.h.

◆ m_phi0

double m_phi0 = 0

private

phi of reference position

Definition at line 105 of file HelixSwimmer.h.

◆ m_R

double m_R = 0

private

helix radius

Definition at line 100 of file HelixSwimmer.h.

◆ m_T0

double m_T0 = 0

private

helix length of single turn

Definition at line 107 of file HelixSwimmer.h.

◆ m_transformInv

ROOT::Math::Transform3D m_transformInv

private

transformation from nominal to local frame

Definition at line 116 of file HelixSwimmer.h.

◆ m_xc

double m_xc = 0

private

helix axis position in x

Definition at line 101 of file HelixSwimmer.h.

◆ m_yc

double m_yc = 0

private

helix axis position in y

Definition at line 102 of file HelixSwimmer.h.

◆ m_z0

double m_z0 = 0

private

z of reference position

Definition at line 106 of file HelixSwimmer.h.

◆ x0

double& x0 = m_xc

private

x of reference position for zero magnetic field

Definition at line 109 of file HelixSwimmer.h.

◆ y0

double& y0 = m_yc

private

y of reference position for zero magnetic field

Definition at line 110 of file HelixSwimmer.h.

◆ z0

double& z0 = m_z0

private

z of reference position for zero magnetic field

Definition at line 111 of file HelixSwimmer.h.

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

top/reconstruction_cpp/include/HelixSwimmer.h
top/reconstruction_cpp/src/HelixSwimmer.cc

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ HelixSwimmer()

Member Function Documentation

◆ getDirection()

◆ getDistanceToPlane()

◆ getPosition()

◆ moveReferencePosition()

◆ set()

◆ setTransformation()

◆ shortestDistance()

◆ withinSingleTurn()

Member Data Documentation

◆ kx

◆ ky

◆ kz

◆ m_kz

◆ m_omega

◆ m_phi0

◆ m_R

◆ m_T0

◆ m_transformInv

◆ m_xc

◆ m_yc

◆ m_z0

◆ x0

◆ y0

◆ z0