Class representing a helix curve.

A helix is a curve defined by the following equations:

x = (1/c) * COS(q*phi)
y = (1/c) * SIN(q*phi)
z = s * alfa

where:

c = 1/Rxy  - curvature in XY plane
phi        - phi angle
S = 2*PI*s - vertical separation between helix loops
q = +/- 1  - (+)=left-handed, (-)=right-handed

In particular, a helix describes the trajectory of a charged particle in magnetic field. In such case, the helix is right-handed for negative particle charge. To define a helix, one must define:

the curvature - positive defined
the Z step made after one full turn of the helix
the particle charge sign
the initial particle position and direction (force normalization to unit)
the magnetic field direction

A helix provides:

propagation to a given Z position (in global frame) Double_t *point = TGeoHelix::PropagateToZ(Double_t z);
propagation to an arbitrary plane, returning also the new point
propagation in a geometry until the next crossed surface
computation of the total track length along a helix

Definition at line 20 of file TGeoHelix.h.

Public Types
enum	EGeoHelixTypes { kHelixNeedUpdate = BIT(16) , kHelixStraight = BIT(17) , kHelixCircle = BIT(18) }

Public Types inherited from TObject
enum	{ kIsOnHeap = 0x01000000 , kNotDeleted = 0x02000000 , kZombie = 0x04000000 , kInconsistent = 0x08000000 , kBitMask = 0x00ffffff }

enum	{ kSingleKey = BIT(0) , kOverwrite = BIT(1) , kWriteDelete = BIT(2) }

enum	EDeprecatedStatusBits { kObjInCanvas = BIT(3) }

enum	EStatusBits { kCanDelete = BIT(0) , kMustCleanup = BIT(3) , kIsReferenced = BIT(4) , kHasUUID = BIT(5) , kCannotPick = BIT(6) , kNoContextMenu = BIT(8) , kInvalidObject = BIT(13) }

Public Member Functions
	TGeoHelix ()
	Dummy constructor. More...

	TGeoHelix (Double_t curvature, Double_t step, Int_t charge=1)
	Normal constructor. More...

virtual	~TGeoHelix ()
	Destructor. More...

Double_t	ComputeSafeStep (Double_t epsil=1E-6) const
	Compute safe linear step that can be made such that the error between linear-helix extrapolation is less than EPSIL. More...

const Double_t *	GetCurrentDirection () const

const Double_t *	GetCurrentPoint () const

Double_t	GetStep () const

Double_t	GetTotalCurvature () const
	Compute helix total curvature. More...

Double_t	GetXYcurvature () const

void	InitDirection (Double_t *dir, Bool_t is_normalized=kTRUE)
	Initialize particle direction (tangent on the helix in initial point) More...

void	InitDirection (Double_t dirx, Double_t diry, Double_t dirz, Bool_t is_normalized=kTRUE)
	Initialize particle direction (tangent on the helix in initial point) More...

void	InitPoint (Double_t *point)
	Set initial point on the helix. More...

void	InitPoint (Double_t x0, Double_t y0, Double_t z0)
	Initialize coordinates of a point on the helix. More...

Bool_t	IsRightHanded () const

void	ResetStep ()
	Reset current point/direction to initial values. More...

void	SetCharge (Int_t charge)
	Positive charge means left-handed helix. More...

void	SetField (Double_t bx, Double_t by, Double_t bz, Bool_t is_normalized=kTRUE)
	Initialize particle direction (tangent on the helix in initial point) More...

void	SetHelixStep (Double_t hstep)
	Set Z step of the helix on a complete turn. Positive or null. More...

void	SetXYcurvature (Double_t curvature)
	Set XY curvature: c = 1/Rxy. More...

void	Step (Double_t step)
	Make a step from current point along the helix and compute new point, direction and angle To reach a plane/ shape boundary, one has to: More...

Double_t	StepToPlane (Double_t point, Double_t norm)
	Propagate initial point up to a given Z position in MARS. More...

void	UpdateHelix ()
	Update the local helix matrix. More...

Public Member Functions inherited from TObject
	TObject ()
	TObject constructor. More...

	TObject (const TObject &object)
	TObject copy ctor. More...

virtual	~TObject ()
	TObject destructor. More...

void	AbstractMethod (const char *method) const
	Use this method to implement an "abstract" method that you don't want to leave purely abstract. More...

virtual void	AppendPad (Option_t *option="")
	Append graphics object to current pad. More...

virtual void	Browse (TBrowser *b)
	Browse object. May be overridden for another default action. More...

ULong_t	CheckedHash ()
	Check and record whether this class has a consistent Hash/RecursiveRemove setup (*) and then return the regular Hash value for this object. More...

virtual const char *	ClassName () const
	Returns name of class to which the object belongs. More...

virtual void	Clear (Option_t *="")

virtual TObject *	Clone (const char *newname="") const
	Make a clone of an object using the Streamer facility. More...

virtual Int_t	Compare (const TObject *obj) const
	Compare abstract method. More...

virtual void	Copy (TObject &object) const
	Copy this to obj. More...

virtual void	Delete (Option_t *option="")
	Delete this object. More...

virtual Int_t	DistancetoPrimitive (Int_t px, Int_t py)
	Computes distance from point (px,py) to the object. More...

virtual void	Draw (Option_t *option="")
	Default Draw method for all objects. More...

virtual void	DrawClass () const
	Draw class inheritance tree of the class to which this object belongs. More...

virtual TObject *	DrawClone (Option_t *option="") const
	Draw a clone of this object in the current selected pad for instance with: `gROOT->SetSelectedPad(gPad)`. More...

virtual void	Dump () const
	Dump contents of object on stdout. More...

virtual void	Error (const char method, const char msgfmt,...) const
	Issue error message. More...

virtual void	Execute (const char method, const char params, Int_t *error=0)
	Execute method on this object with the given parameter string, e.g. More...

virtual void	Execute (TMethod method, TObjArray params, Int_t *error=0)
	Execute method on this object with parameters stored in the TObjArray. More...

virtual void	ExecuteEvent (Int_t event, Int_t px, Int_t py)
	Execute action corresponding to an event at (px,py). More...

virtual void	Fatal (const char method, const char msgfmt,...) const
	Issue fatal error message. More...

virtual TObject *	FindObject (const char *name) const
	Must be redefined in derived classes. More...

virtual TObject *	FindObject (const TObject *obj) const
	Must be redefined in derived classes. More...

virtual Option_t *	GetDrawOption () const
	Get option used by the graphics system to draw this object. More...

virtual const char *	GetIconName () const
	Returns mime type name of object. More...

virtual const char *	GetName () const
	Returns name of object. More...

virtual char *	GetObjectInfo (Int_t px, Int_t py) const
	Returns string containing info about the object at position (px,py). More...

virtual Option_t *	GetOption () const

virtual const char *	GetTitle () const
	Returns title of object. More...

virtual UInt_t	GetUniqueID () const
	Return the unique object id. More...

virtual Bool_t	HandleTimer (TTimer *timer)
	Execute action in response of a timer timing out. More...

virtual ULong_t	Hash () const
	Return hash value for this object. More...

Bool_t	HasInconsistentHash () const
	Return true is the type of this object is known to have an inconsistent setup for Hash and RecursiveRemove (i.e. More...

virtual void	Info (const char method, const char msgfmt,...) const
	Issue info message. More...

virtual Bool_t	InheritsFrom (const char *classname) const
	Returns kTRUE if object inherits from class "classname". More...

virtual Bool_t	InheritsFrom (const TClass *cl) const
	Returns kTRUE if object inherits from TClass cl. More...

virtual void	Inspect () const
	Dump contents of this object in a graphics canvas. More...

void	InvertBit (UInt_t f)

virtual Bool_t	IsEqual (const TObject *obj) const
	Default equal comparison (objects are equal if they have the same address in memory). More...

virtual Bool_t	IsFolder () const
	Returns kTRUE in case object contains browsable objects (like containers or lists of other objects). More...

R__ALWAYS_INLINE Bool_t	IsOnHeap () const

virtual Bool_t	IsSortable () const

R__ALWAYS_INLINE Bool_t	IsZombie () const

virtual void	ls (Option_t *option="") const
	The ls function lists the contents of a class on stdout. More...

void	MayNotUse (const char *method) const
	Use this method to signal that a method (defined in a base class) may not be called in a derived class (in principle against good design since a child class should not provide less functionality than its parent, however, sometimes it is necessary). More...

virtual Bool_t	Notify ()
	This method must be overridden to handle object notification. More...

void	Obsolete (const char method, const char asOfVers, const char *removedFromVers) const
	Use this method to declare a method obsolete. More...

void	operator delete (void *ptr)
	Operator delete. More...

void	operator delete[] (void *ptr)
	Operator delete []. More...

void *	operator new (size_t sz)

void *	operator new (size_t sz, void *vp)

void *	operator new[] (size_t sz)

void *	operator new[] (size_t sz, void *vp)

TObject &	operator= (const TObject &rhs)
	TObject assignment operator. More...

virtual void	Paint (Option_t *option="")
	This method must be overridden if a class wants to paint itself. More...

virtual void	Pop ()
	Pop on object drawn in a pad to the top of the display list. More...

virtual void	Print (Option_t *option="") const
	This method must be overridden when a class wants to print itself. More...

virtual Int_t	Read (const char *name)
	Read contents of object with specified name from the current directory. More...

virtual void	RecursiveRemove (TObject *obj)
	Recursively remove this object from a list. More...

void	ResetBit (UInt_t f)

virtual void	SaveAs (const char filename="", Option_t option="") const
	Save this object in the file specified by filename. More...

virtual void	SavePrimitive (std::ostream &out, Option_t *option="")
	Save a primitive as a C++ statement(s) on output stream "out". More...

void	SetBit (UInt_t f)

void	SetBit (UInt_t f, Bool_t set)
	Set or unset the user status bits as specified in f. More...

virtual void	SetDrawOption (Option_t *option="")
	Set drawing option for object. More...

virtual void	SetUniqueID (UInt_t uid)
	Set the unique object id. More...

virtual void	SysError (const char method, const char msgfmt,...) const
	Issue system error message. More...

R__ALWAYS_INLINE Bool_t	TestBit (UInt_t f) const

Int_t	TestBits (UInt_t f) const

virtual void	UseCurrentStyle ()
	Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked. More...

virtual void	Warning (const char method, const char msgfmt,...) const
	Issue warning message. More...

virtual Int_t	Write (const char *name=0, Int_t option=0, Int_t bufsize=0)
	Write this object to the current directory. More...

virtual Int_t	Write (const char *name=0, Int_t option=0, Int_t bufsize=0) const
	Write this object to the current directory. More...

Private Member Functions
	TGeoHelix (const TGeoHelix &)=delete

TGeoHelix &	operator= (const TGeoHelix &)=delete

Private Attributes
Double_t	fB [3]

Double_t	fC

Double_t	fDir [3]

Double_t	fDirInit [3]

TGeoHMatrix *	fMatrix {nullptr}

Double_t	fPhi

Double_t	fPoint [3]

Double_t	fPointInit [3]

Int_t	fQ

Double_t	fS

Double_t	fStep

Additional Inherited Members
Static Public Member Functions inherited from TObject
static Long_t	GetDtorOnly ()
	Return destructor only flag. More...

static Bool_t	GetObjectStat ()
	Get status of object stat flag. More...

static void	SetDtorOnly (void *obj)
	Set destructor only flag. More...

static void	SetObjectStat (Bool_t stat)
	Turn on/off tracking of objects in the TObjectTable. More...

Protected Types inherited from TObject
enum	{ kOnlyPrepStep = BIT(3) }

Protected Member Functions inherited from TObject
virtual void	DoError (int level, const char location, const char fmt, va_list va) const
	Interface to ErrorHandler (protected). More...

void	MakeZombie ()

#include <TGeoHelix.h>

Inheritance diagram for TGeoHelix:

[legend]

Member Enumeration Documentation

◆ EGeoHelixTypes

enum TGeoHelix::EGeoHelixTypes

Enumerator
kHelixNeedUpdate
kHelixStraight
kHelixCircle

Definition at line 38 of file TGeoHelix.h.

Constructor & Destructor Documentation

◆ TGeoHelix() [1/3]

TGeoHelix::TGeoHelix ( const TGeoHelix & )

privatedelete

◆ TGeoHelix() [2/3]

TGeoHelix::TGeoHelix ( )

Dummy constructor.

Definition at line 62 of file TGeoHelix.cxx.

◆ TGeoHelix() [3/3]

TGeoHelix::TGeoHelix	(	Double_t	curvature,
		Double_t	step,
		Int_t	charge = `1`
	)

Normal constructor.

Definition at line 83 of file TGeoHelix.cxx.

◆ ~TGeoHelix()

TGeoHelix::~TGeoHelix ( )

virtual

Destructor.

Definition at line 105 of file TGeoHelix.cxx.

Member Function Documentation

◆ ComputeSafeStep()

Double_t TGeoHelix::ComputeSafeStep ( Double_t epsil = 1E-6 ) const

Compute safe linear step that can be made such that the error between linear-helix extrapolation is less than EPSIL.

Definition at line 114 of file TGeoHelix.cxx.

◆ GetCurrentDirection()

const Double_t * TGeoHelix::GetCurrentDirection ( ) const

inline

Definition at line 56 of file TGeoHelix.h.

◆ GetCurrentPoint()

const Double_t * TGeoHelix::GetCurrentPoint ( ) const

inline

Definition at line 55 of file TGeoHelix.h.

◆ GetStep()

Double_t TGeoHelix::GetStep ( ) const

inline

Definition at line 58 of file TGeoHelix.h.

◆ GetTotalCurvature()

Double_t TGeoHelix::GetTotalCurvature ( ) const

Compute helix total curvature.

Definition at line 166 of file TGeoHelix.cxx.

◆ GetXYcurvature()

Double_t TGeoHelix::GetXYcurvature ( ) const

inline

Definition at line 57 of file TGeoHelix.h.

◆ InitDirection() [1/2]

void TGeoHelix::InitDirection	(	Double_t *	dir,
		Bool_t	is_normalized = `kTRUE`
	)

Initialize particle direction (tangent on the helix in initial point)

Definition at line 158 of file TGeoHelix.cxx.

◆ InitDirection() [2/2]

void TGeoHelix::InitDirection	(	Double_t	dirx,
		Double_t	diry,
		Double_t	dirz,
		Bool_t	is_normalized = `kTRUE`
	)

Initialize particle direction (tangent on the helix in initial point)

Definition at line 144 of file TGeoHelix.cxx.

◆ InitPoint() [1/2]

void TGeoHelix::InitPoint ( Double_t * point )

Set initial point on the helix.

Definition at line 136 of file TGeoHelix.cxx.

◆ InitPoint() [2/2]

void TGeoHelix::InitPoint	(	Double_t	x0,
		Double_t	y0,
		Double_t	z0
	)

Initialize coordinates of a point on the helix.

Definition at line 125 of file TGeoHelix.cxx.

◆ IsRightHanded()

Bool_t TGeoHelix::IsRightHanded ( ) const

inline

Definition at line 60 of file TGeoHelix.h.

◆ operator=()

TGeoHelix & TGeoHelix::operator= ( const TGeoHelix & )

privatedelete

◆ ResetStep()

void TGeoHelix::ResetStep ( )

Reset current point/direction to initial values.

Definition at line 235 of file TGeoHelix.cxx.

◆ SetCharge()

void TGeoHelix::SetCharge ( Int_t charge )

Positive charge means left-handed helix.

Definition at line 192 of file TGeoHelix.cxx.

◆ SetField()

void TGeoHelix::SetField	(	Double_t	bx,
		Double_t	by,
		Double_t	bz,
		Bool_t	is_normalized = `kTRUE`
	)

Initialize particle direction (tangent on the helix in initial point)

Definition at line 207 of file TGeoHelix.cxx.

◆ SetHelixStep()

void TGeoHelix::SetHelixStep ( Double_t hstep )

Set Z step of the helix on a complete turn. Positive or null.

Definition at line 221 of file TGeoHelix.cxx.

◆ SetXYcurvature()

void TGeoHelix::SetXYcurvature ( Double_t curvature )

Set XY curvature: c = 1/Rxy.

Definition at line 175 of file TGeoHelix.cxx.

◆ Step()

void TGeoHelix::Step ( Double_t step )

Make a step from current point along the helix and compute new point, direction and angle To reach a plane/ shape boundary, one has to:

Compute the safety to the plane/boundary
Define / update a helix according local field and particle state (position, direction, charge)
Compute the magnetic safety (maximum distance for which the field can be considered constant)
Call TGeoHelix::Step() having as argument the minimum between 1. and 3.
Repeat from 1. until the step to be made is small enough.
Add to the total step the distance along a straight line from the last point to the plane/shape boundary

Definition at line 253 of file TGeoHelix.cxx.

◆ StepToPlane()

Double_t TGeoHelix::StepToPlane	(	Double_t *	point,
		Double_t *	norm
	)

Propagate initial point up to a given Z position in MARS.

Definition at line 285 of file TGeoHelix.cxx.

◆ UpdateHelix()

void TGeoHelix::UpdateHelix ( )

Update the local helix matrix.

Definition at line 339 of file TGeoHelix.cxx.

Member Data Documentation

◆ fB

Double_t TGeoHelix::fB[3]

private

Definition at line 31 of file TGeoHelix.h.

◆ fC

Double_t TGeoHelix::fC

private

Definition at line 23 of file TGeoHelix.h.

◆ fDir

Double_t TGeoHelix::fDir[3]

private

Definition at line 30 of file TGeoHelix.h.

◆ fDirInit

Double_t TGeoHelix::fDirInit[3]

private

Definition at line 28 of file TGeoHelix.h.

◆ fMatrix

TGeoHMatrix* TGeoHelix::fMatrix {nullptr}

private

Definition at line 33 of file TGeoHelix.h.

◆ fPhi

Double_t TGeoHelix::fPhi

private

Definition at line 26 of file TGeoHelix.h.

◆ fPoint

Double_t TGeoHelix::fPoint[3]

private

Definition at line 29 of file TGeoHelix.h.

◆ fPointInit

Double_t TGeoHelix::fPointInit[3]

private

Definition at line 27 of file TGeoHelix.h.

◆ fQ

Int_t TGeoHelix::fQ

private

Definition at line 32 of file TGeoHelix.h.

◆ fS

Double_t TGeoHelix::fS

private

Definition at line 24 of file TGeoHelix.h.

◆ fStep

Double_t TGeoHelix::fStep

private

Definition at line 25 of file TGeoHelix.h.

Libraries for TGeoHelix:

[legend]

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Member Enumeration Documentation

◆ EGeoHelixTypes

Constructor & Destructor Documentation

◆ TGeoHelix() [1/3]

◆ TGeoHelix() [2/3]

◆ TGeoHelix() [3/3]

◆ ~TGeoHelix()

Member Function Documentation

◆ ComputeSafeStep()

◆ GetCurrentDirection()

◆ GetCurrentPoint()

◆ GetStep()

◆ GetTotalCurvature()

◆ GetXYcurvature()

◆ InitDirection() [1/2]

◆ InitDirection() [2/2]

◆ InitPoint() [1/2]

◆ InitPoint() [2/2]

◆ IsRightHanded()

◆ operator=()

◆ ResetStep()

◆ SetCharge()

◆ SetField()

◆ SetHelixStep()

◆ SetXYcurvature()

◆ Step()

◆ StepToPlane()

◆ UpdateHelix()

Member Data Documentation

◆ fB

◆ fC

◆ fDir

◆ fDirInit

◆ fMatrix

◆ fPhi

◆ fPoint

◆ fPointInit

◆ fQ

◆ fS

◆ fStep