WireLine Class Reference

A three dimensional limited line represented by its closest approach to the z-axes (reference position ) and its skew parameter. More...

#include <WireLine.h>

Public Member Functions
	WireLine ()
	Default constructor initialising to all members to zero.
	WireLine (const ROOT::Math::XYZVector &forward, const ROOT::Math::XYZVector &backward, double sagCoeff)
	Constructor for a wire line between forward and backward point.
WireLine	movedBy (const ROOT::Math::XYZVector &offset) const
	Returns a copy of the wire line moved by a three dimensional offset.
WireLine	movedBy (const ROOT::Math::XYVector &offset) const
	Returns a copy of the wire line moved by a two dimensional offset.
ROOT::Math::XYZVector	nominalPos3DAtZ (const double z) const
	Gives the three dimensional position without wire sag effect of the line at the given z value.
ROOT::Math::XYVector	nominalPos2DAtZ (const double z) const
	Gives the two dimensional position without wire sag effect of the line at the given z value.
ROOT::Math::XYZVector	sagPos3DAtZ (const double z) const
	Gives the three dimensional position with wire sag effect of the line at the given z value.
ROOT::Math::XYVector	sagPos2DAtZ (const double z) const
	Gives the two dimensional position with wire sag effect of the line at the given z value.
const ROOT::Math::XYVector &	nominalMovePerZ () const
	Gives the positional move in the xy projection per unit z.
ROOT::Math::XYVector	sagMovePerZ (const double z) const
	Gives the two dimensional position with wire sag effect of the line at the given z value.
double	nominalDistance (const ROOT::Math::XYZVector &pos3D) const
	Calculates the distance of the given point to the wire without wire sag effect.
double	sagDistance (const ROOT::Math::XYZVector &pos3D) const
	Calculates the distance of the given point to the wire with wire sag effect.
ROOT::Math::XYZVector	nominalClosest3D (const ROOT::Math::XYZVector &point) const
	Returns the closest approach on the wire without wire sag effect to the give point.
ROOT::Math::XYZVector	sagClosest3D (const ROOT::Math::XYZVector &point) const
	Returns the closest approach on the wire with wire sag effect to the give point.
ROOT::Math::XYZVector	forward3D () const
	Gives the position of the forward point.
ROOT::Math::XYVector	forward2D () const
	Gives the xy position of the forward point.
ROOT::Math::XYZVector	backward3D () const
	Gives the position of the backward point.
ROOT::Math::XYVector	backward2D () const
	Gives the xy position of the backward point.
ROOT::Math::XYZVector	wireVector () const
	Getter for the vector from backward to the forward position.
double	forwardZ () const
	Gives the forward z coordinate.
double	backwardZ () const
	Gives the backward z coordinate.
double	deltaZ () const
	Returns the difference between forward and backward z.
double	outOfZBoundsFactor (double z) const
	Returns the amount how much the given z position is outside the bounds in units of the wire length.
double	forwardPhi () const
	Gives the forward azimuth angle.
double	backwardPhi () const
	Gives the backward azimuth angle.
double	forwardCylindricalR () const
	Gives the cylindrical radius of the forward position.
double	backwardCylindricalR () const
	Gives the cylindrical radius of the backward position.
double	forwardPhiToRef () const
	Gives the azimuth angle of the forward position relative to the reference position.
double	backwardPhiToRef () const
	Gives the azimuth angle of the backward position relative to the reference position.
double	backwardToForwardAngle () const
	Gives the azimuth angle difference from backward to forward position.
double	tanLambda () const
	Returns the nominal tan lambda of the line. Also know as dz / ds.
double	lambda () const
	Returns the nominal lambda angle of the line.
double	tanTheta () const
	Returns the tangent of the opening angle between tangential vector and the z axes Also know as ds / dz.
double	theta () const
	Returns the nominal opening angle between tangential vector and the z axes.
double	nominalPerigeeZ () const
	Returns the z coordinate of the point of nominal closest approach to the z axes.
ROOT::Math::XYZVector	nominalPerigee3D () const
	Returns the point of nominal closest approach to the z axes.
ROOT::Math::XYVector	nominalPerigee2D () const
	Returns the point of nominal closest approach to the z axes.
double	refX () const
	Returns the the x coordinate of the reference point.
double	refY () const
	Returns the the y coordinate of the reference point.
double	refZ () const
	Returns the the z coordinate of the reference point.
double	refCylindricalRSquared () const
	Returns the cylindrical radius of the reference position.
const ROOT::Math::XYVector &	refPos2D () const
	Returns the xy vector of the reference position.
const ROOT::Math::XYZVector &	refPos3D () const
	Returns the reference position.
double	sagCoeff () const
	Returns the wire sag coefficient due to gravity.

Private Attributes
ROOT::Math::XYZVector	m_refPos3D
	Memory for the reference position.
ROOT::Math::XYVector	m_refPos2D
	Memory for the 2D reference position (to avoid [-Wreturn-stack-address] in refPos2D())
ROOT::Math::XYVector	m_nominalMovePerZ
	Memory for the nominal movement of the xy position per z unit off the reference.
double	m_forwardZ = 0.0
	Memory for the forward end z coordinate.
double	m_backwardZ = 0.0
	Memory for the backward end z coordinate.
double	m_sagCoeff = 0.0
	Memory for the wire sag coefficient.

Detailed Description

A three dimensional limited line represented by its closest approach to the z-axes (reference position ) and its skew parameter.

The representation is only suitable for lines out of the xy plane. The endpoints are stored encoded by their z position. The end point with the higher z value is called forward, the one with the smaller is called backward. This class is mainly used to describe the cdc wires with as few parameters as possible and simplifies the retrieval of the two dimensional track reference position, which is taken at the closest approach to the beam z-axes.

A three dimensional limited line

Definition at line 33 of file WireLine.h.

Constructor & Destructor Documentation

WireLine() [1/2]

WireLine ( )

inline

Default constructor initialising to all members to zero.

Definition at line 37 of file WireLine.h.

      {}

WireLine() [2/2]

WireLine	(	const ROOT::Math::XYZVector &	forward,
		const ROOT::Math::XYZVector &	backward,
		double	sagCoeff )

Constructor for a wire line between forward and backward point.

Definition at line 15 of file WireLine.cc.

  : m_refPos3D{(backward * forward.z() - forward * backward.z()) / (forward.z() - backward.z()) }
  , m_forwardZ{forward.z()}
  , m_backwardZ{backward.z()}
  , m_sagCoeff(sagCoeff)
{
  m_refPos2D = ROOT::Math::XYVector(m_refPos3D.x(), m_refPos3D.y());
  const double deltaZ = forward.z() - backward.z();
  m_nominalMovePerZ = ROOT::Math::XYVector((forward.x() - backward.x()) / deltaZ, (forward.y() - backward.y()) / deltaZ);
 
  B2ASSERT("Wire reference position is not at 0", m_refPos3D.z() == 0);
}

Member Function Documentation

backward2D()

ROOT::Math::XYVector backward2D ( ) const

inline

Gives the xy position of the backward point.

Definition at line 137 of file WireLine.h.

      { return nominalPos2DAtZ(backwardZ()); }

backward3D()

ROOT::Math::XYZVector backward3D ( ) const

inline

Gives the position of the backward point.

Definition at line 133 of file WireLine.h.

      { return nominalPos3DAtZ(backwardZ()); }

backwardCylindricalR()

double backwardCylindricalR ( ) const

inline

Gives the cylindrical radius of the backward position.

Definition at line 176 of file WireLine.h.

      { return backward2D().R(); }

backwardPhi()

double backwardPhi ( ) const

inline

Gives the backward azimuth angle.

Definition at line 168 of file WireLine.h.

      { return backward2D().Phi(); }

backwardPhiToRef()

double backwardPhiToRef ( ) const

inline

Gives the azimuth angle of the backward position relative to the reference position.

Definition at line 184 of file WireLine.h.

      { return VectorUtil::Angle(backward2D(), refPos2D()); }

backwardToForwardAngle()

double backwardToForwardAngle ( ) const

inline

Gives the azimuth angle difference from backward to forward position.

Definition at line 190 of file WireLine.h.

      { return VectorUtil::Angle(backward2D(), forward2D()); }

backwardZ()

double backwardZ ( ) const

inline

Gives the backward z coordinate.

Definition at line 152 of file WireLine.h.

      { return m_backwardZ; }

deltaZ()

double deltaZ ( ) const

inline

Returns the difference between forward and backward z.

Definition at line 156 of file WireLine.h.

      { return forwardZ() - backwardZ(); }

forward2D()

ROOT::Math::XYVector forward2D ( ) const

inline

Gives the xy position of the forward point.

Definition at line 129 of file WireLine.h.

      { return nominalPos2DAtZ(forwardZ()); }

forward3D()

ROOT::Math::XYZVector forward3D ( ) const

inline

Gives the position of the forward point.

Definition at line 125 of file WireLine.h.

      { return nominalPos3DAtZ(forwardZ()); }

forwardCylindricalR()

double forwardCylindricalR ( ) const

inline

Gives the cylindrical radius of the forward position.

Definition at line 172 of file WireLine.h.

      { return forward2D().R(); }

forwardPhi()

double forwardPhi ( ) const

inline

Gives the forward azimuth angle.

Definition at line 164 of file WireLine.h.

      { return forward2D().Phi(); }

forwardPhiToRef()

double forwardPhiToRef ( ) const

inline

Gives the azimuth angle of the forward position relative to the reference position.

Definition at line 180 of file WireLine.h.

      { return VectorUtil::Angle(forward2D(), refPos2D()); }

forwardZ()

double forwardZ ( ) const

inline

Gives the forward z coordinate.

Definition at line 148 of file WireLine.h.

      { return m_forwardZ; }

lambda()

double lambda ( ) const

inline

Returns the nominal lambda angle of the line.

Definition at line 198 of file WireLine.h.

      { return std::atan(tanLambda()); }

movedBy() [1/2]

WireLine movedBy

(

const ROOT::Math::XYVector &

offset

)

const

Returns a copy of the wire line moved by a two dimensional offset.

Definition at line 40 of file WireLine.cc.

{
  WireLine moved = *this;
  moved.m_refPos3D += ROOT::Math::XYZVector(offset.X(), offset.Y(), 0);
  return moved;
}

movedBy() [2/2]

WireLine movedBy

(

const ROOT::Math::XYZVector &

offset

)

const

Returns a copy of the wire line moved by a three dimensional offset.

Definition at line 30 of file WireLine.cc.

{
  WireLine moved = *this;
  const ROOT::Math::XYVector tmp = nominalMovePerZ();
  moved.m_refPos3D += ROOT::Math::XYZVector(offset.X(), offset.Y(), 0) + ROOT::Math::XYZVector(tmp.X(), tmp.Y(), 0)  * offset.z();
  moved.m_forwardZ += offset.z();
  moved.m_backwardZ += offset.z();
  return moved;
}

nominalClosest3D()

ROOT::Math::XYZVector nominalClosest3D ( const ROOT::Math::XYZVector & point ) const

inline

Returns the closest approach on the wire without wire sag effect to the give point.

Definition at line 109 of file WireLine.h.

      {
        return refPos3D() - ROOT::Math::VectorUtil::ProjVector((point - refPos3D()), ROOT::Math::XYZVector(nominalMovePerZ().X(),
                                                               nominalMovePerZ().Y(), 1));
      }

nominalDistance()

double nominalDistance ( const ROOT::Math::XYZVector & pos3D ) const

inline

Calculates the distance of the given point to the wire without wire sag effect.

Definition at line 94 of file WireLine.h.

      {
        return ROOT::Math::VectorUtil::Perp((pos3D - refPos3D()), ROOT::Math::XYZVector(nominalMovePerZ().X(), nominalMovePerZ().Y(), 1));
      }

nominalMovePerZ()

const ROOT::Math::XYVector & nominalMovePerZ ( ) const

inline

Gives the positional move in the xy projection per unit z.

Definition at line 79 of file WireLine.h.

      { return m_nominalMovePerZ; }

nominalPerigee2D()

ROOT::Math::XYVector nominalPerigee2D ( ) const

inline

Returns the point of nominal closest approach to the z axes.

Definition at line 221 of file WireLine.h.

      { return VectorUtil::orthogonalVector(refPos2D(), nominalMovePerZ()); }

nominalPerigee3D()

ROOT::Math::XYZVector nominalPerigee3D ( ) const

inline

Returns the point of nominal closest approach to the z axes.

Definition at line 217 of file WireLine.h.

      { return nominalPos3DAtZ(nominalPerigeeZ()); }

nominalPerigeeZ()

double nominalPerigeeZ ( ) const

inline

Returns the z coordinate of the point of nominal closest approach to the z axes.

Definition at line 213 of file WireLine.h.

      { return -refPos2D().Dot(nominalMovePerZ()) / nominalMovePerZ().Mag2(); }

nominalPos2DAtZ()

ROOT::Math::XYVector nominalPos2DAtZ ( const double z ) const

inline

Gives the two dimensional position without wire sag effect of the line at the given z value.

Definition at line 57 of file WireLine.h.

      { return refPos2D() + nominalMovePerZ() * z; }

nominalPos3DAtZ()

ROOT::Math::XYZVector nominalPos3DAtZ ( const double z ) const

inline

Gives the three dimensional position without wire sag effect of the line at the given z value.

Definition at line 50 of file WireLine.h.

      {
        const ROOT::Math::XYVector& tmp = nominalPos2DAtZ(z);
        return ROOT::Math::XYZVector(tmp.X(), tmp.Y(), z);
      }

outOfZBoundsFactor()

double outOfZBoundsFactor ( double z ) const

inline

Returns the amount how much the given z position is outside the bounds in units of the wire length.

Definition at line 160 of file WireLine.h.

      { return std::fmax(backwardZ() - z, z - forwardZ()) / deltaZ(); }

refCylindricalRSquared()

double refCylindricalRSquared ( ) const

inline

Returns the cylindrical radius of the reference position.

Definition at line 237 of file WireLine.h.

      { return m_refPos3D.Perp2(); }

refPos2D()

const ROOT::Math::XYVector & refPos2D ( ) const

inline

Returns the xy vector of the reference position.

Definition at line 241 of file WireLine.h.

      { return m_refPos2D; }

refPos3D()

const ROOT::Math::XYZVector & refPos3D ( ) const

inline

Returns the reference position.

Definition at line 245 of file WireLine.h.

      { return m_refPos3D; }

refX()

double refX ( ) const

inline

Returns the the x coordinate of the reference point.

Definition at line 225 of file WireLine.h.

      { return m_refPos3D.x(); }

refY()

double refY ( ) const

inline

Returns the the y coordinate of the reference point.

Definition at line 229 of file WireLine.h.

      { return m_refPos3D.y(); }

refZ()

double refZ ( ) const

inline

Returns the the z coordinate of the reference point.

Definition at line 233 of file WireLine.h.

      { return m_refPos3D.z(); }

sagClosest3D()

ROOT::Math::XYZVector sagClosest3D ( const ROOT::Math::XYZVector & point ) const

inline

Returns the closest approach on the wire with wire sag effect to the give point.

Definition at line 116 of file WireLine.h.

      {
        const ROOT::Math::XYZVector& wirePos3D = sagPos3DAtZ(point.z());
        const ROOT::Math::XYVector& tmp = sagMovePerZ(point.z());
        const ROOT::Math::XYZVector movePerZ(tmp.X(), tmp.Y(), 1);
        return  wirePos3D - ROOT::Math::VectorUtil::ProjVector((point - wirePos3D), movePerZ);
      }

sagCoeff()

double sagCoeff ( ) const

inline

Returns the wire sag coefficient due to gravity.

Definition at line 249 of file WireLine.h.

      { return m_sagCoeff; }

sagDistance()

double sagDistance ( const ROOT::Math::XYZVector & pos3D ) const

inline

Calculates the distance of the given point to the wire with wire sag effect.

Definition at line 100 of file WireLine.h.

      {
        const ROOT::Math::XYZVector& wirePos3D = sagPos3DAtZ(pos3D.z());
        const ROOT::Math::XYVector& tmp = sagMovePerZ(pos3D.z());
        const ROOT::Math::XYZVector movePerZ(tmp.X(), tmp.Y(), 1);
        return ROOT::Math::VectorUtil::Perp((pos3D - wirePos3D), movePerZ);
      }

sagMovePerZ()

ROOT::Math::XYVector sagMovePerZ ( const double z ) const

inline

Gives the two dimensional position with wire sag effect of the line at the given z value.

Efficient version without divisions

Definition at line 83 of file WireLine.h.

      {
        ROOT::Math::XYVector movePerZ = nominalMovePerZ();
        double xzFactorSquared = 1 + nominalMovePerZ().X() * nominalMovePerZ().X();
        double sagDYDZ = - sagCoeff() * xzFactorSquared * (forwardZ() + backwardZ() - 2 * z);
        movePerZ.SetY(movePerZ.Y() + sagDYDZ);
        return movePerZ;
      }

sagPos2DAtZ()

ROOT::Math::XYVector sagPos2DAtZ ( const double z ) const

inline

Gives the two dimensional position with wire sag effect of the line at the given z value.

Efficient version without divisions

Definition at line 68 of file WireLine.h.

      {
        ROOT::Math::XYVector pos2D = nominalPos2DAtZ(z);
        double xzFactorSquared = 1 + nominalMovePerZ().X() * nominalMovePerZ().X();
        double sagY = - sagCoeff() * xzFactorSquared * (forwardZ() - z) * (z - backwardZ());
        pos2D.SetY(pos2D.Y() + sagY);
        return pos2D;
      }

sagPos3DAtZ()

ROOT::Math::XYZVector sagPos3DAtZ ( const double z ) const

inline

Gives the three dimensional position with wire sag effect of the line at the given z value.

Definition at line 61 of file WireLine.h.

      {
        const ROOT::Math::XYVector& tmp = sagPos2DAtZ(z);
        return ROOT::Math::XYZVector(tmp.X(), tmp.Y(), z);
      }

tanLambda()

double tanLambda ( ) const

inline

Returns the nominal tan lambda of the line. Also know as dz / ds.

Definition at line 194 of file WireLine.h.

      { return 1 / nominalMovePerZ().R(); }

tanTheta()

double tanTheta ( ) const

inline

Returns the tangent of the opening angle between tangential vector and the z axes Also know as ds / dz.

Definition at line 205 of file WireLine.h.

      { return std::atan(nominalMovePerZ().R()); }

theta()

double theta ( ) const

inline

Returns the nominal opening angle between tangential vector and the z axes.

Definition at line 209 of file WireLine.h.

      { return std::atan(nominalMovePerZ().R()); }

wireVector()

ROOT::Math::XYZVector wireVector ( ) const

inline

Getter for the vector from backward to the forward position.

Definition at line 141 of file WireLine.h.

      {
        const ROOT::Math::XYVector& tmp = nominalMovePerZ() * deltaZ();
        return ROOT::Math::XYZVector(tmp.X(), tmp.Y(), deltaZ());
      }

Member Data Documentation

m_backwardZ

double m_backwardZ = 0.0

private

Memory for the backward end z coordinate.

Definition at line 266 of file WireLine.h.

m_forwardZ

double m_forwardZ = 0.0

private

Memory for the forward end z coordinate.

Definition at line 263 of file WireLine.h.

m_nominalMovePerZ

ROOT::Math::XYVector m_nominalMovePerZ

private

Memory for the nominal movement of the xy position per z unit off the reference.

Definition at line 260 of file WireLine.h.

m_refPos2D

ROOT::Math::XYVector m_refPos2D

private

Memory for the 2D reference position (to avoid [-Wreturn-stack-address] in refPos2D())

Definition at line 257 of file WireLine.h.

m_refPos3D

ROOT::Math::XYZVector m_refPos3D

private

Memory for the reference position.

Definition at line 254 of file WireLine.h.

m_sagCoeff

double m_sagCoeff = 0.0

private

Memory for the wire sag coefficient.

Definition at line 269 of file WireLine.h.

---

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

• cdc/topology/include/WireLine.h
• cdc/topology/src/WireLine.cc