THelix Class Reference

THelix has two different constructors.

If a particle with charge q passes through a point (x,y,z) with momentum (px,py,pz) with magnetic field B along an axis (nx,ny,nz), this helix can be constructed like:

THelix p(x,y,z, px,py,pz, q*B, nx,ny,nz);
(nx,ny,nz) defaults to (0,0,1).

A helix in its own frame can be defined with a pivotal point (x0,y0,z0), the velocity at that point (vx0,vy0,vz0), and an angular frequency w. Combining vx0 and vy0 to a transverse velocity vt0 one can parametrize the helix as:

x(t) = x0 - vt0 / w * sin(-w * t + phi0)
y(t) = y0 + vt0 / w * cos(-w * t + phi0)
z(t) = z0 + vz0 * t

The second constructor has 6 parameters,

Example:

THelix pl1(xyz, v, w, range, rtype, axis);

where:

• xyz : array of initial position
• v : array of initial velocity
• w : angular frequency
• range: helix range
• rtype: kHelixZ specifies allowed drawing range in helix Z direction, i.e., along B field. kLabZ specifies drawing range in lab frame. kHelixX, kHelixY, kLabX, kLabY, kUnchanged ... etc can also be specified
• axis : helix axis

Example constructing a helix with several default values and drawing it:

{
   TCanvas* helix_example_c1 = new TCanvas("helix_example_c1");
   TView *view = TView::CreateView(1);
   view->SetRange(-1,-1,-1,1,1,1);
   THelix *helix = new THelix(0., 0., 0., 1., 0., 0.3, 10.);
   helix->Draw();
}

This initializes a helix with its axis in Z direction (rtype=kHelixZ).

Definition at line 23 of file THelix.h.

Public Member Functions
	THelix ()
	Helix default constructor.
	THelix (const THelix &helix)
	Helix copy constructor.
	THelix (Double_t const *xyz, Double_t const *v, Double_t w, Double_t const *range=nullptr, EHelixRangeType rtype=kHelixZ, Double_t const *axis=nullptr)
	Helix normal constructor.
	THelix (Double_t x, Double_t y, Double_t z, Double_t vx, Double_t vy, Double_t vz, Double_t w)
	Helix normal constructor.
virtual	~THelix ()
	Helix destructor.
virtual void	Copy (TObject &helix) const
	Copy this helix to obj.
virtual void	Draw (Option_t *option="")
	Draw this helix with its current attributes.
Option_t *	GetOption () const
virtual TClass *	IsA () const
virtual void	Print (Option_t *option="") const
	Dump this helix with its attributes.
virtual void	SavePrimitive (std::ostream &out, Option_t *option="")
	Save primitive as a C++ statement(s) on output stream out.
virtual void	SetAxis (Double_t const *axis)
	Set a new axis for the helix. This will make a new rotation matrix.
virtual void	SetAxis (Double_t x, Double_t y, Double_t z)
	Set axis.
void	SetHelix (Double_t const *xyz, Double_t const *v, Double_t w, Double_t const *range=nullptr, EHelixRangeType type=kUnchanged, Double_t const *axis=nullptr)
	Set all helix parameters.
virtual void	SetOption (Option_t *option="")
virtual void	SetRange (Double_t *range, EHelixRangeType rtype=kHelixZ)
	Set a new range for the helix. This will remake the polyline.
virtual void	SetRange (Double_t r1, Double_t r2, EHelixRangeType rtype=kHelixZ)
	Set range.
virtual void	Streamer (TBuffer &)
	Stream an object of class THelix.
void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)
Public Member Functions inherited from TPolyLine3D
	TPolyLine3D ()
	3-D polyline default constructor.
	TPolyLine3D (const TPolyLine3D &polylin)
	3-D polyline copy ctor.
	TPolyLine3D (Int_t n, Double_t const *p, Option_t *option="")
	3-D polyline normal constructor.
	TPolyLine3D (Int_t n, Double_t const *x, Double_t const *y, Double_t const *z, Option_t *option="")
	3-D polyline normal constructor.
	TPolyLine3D (Int_t n, Float_t const *p, Option_t *option="")
	3-D polyline normal constructor.
	TPolyLine3D (Int_t n, Float_t const *x, Float_t const *y, Float_t const *z, Option_t *option="")
	3-D polyline normal constructor.
	TPolyLine3D (Int_t n, Option_t *option="")
	3-D polyline normal constructor with initialization to 0.
virtual	~TPolyLine3D ()
	3-D polyline destructor.
void	Copy (TObject &polyline) const override
	Copy polyline to polyline obj.
Int_t	DistancetoPrimitive (Int_t px, Int_t py) override
	Compute distance from point px,py to a 3-D polyline.
void	Draw (Option_t *option="") override
	Draw this 3-D polyline with its current attributes.
virtual void	DrawPolyLine (Int_t n, Float_t *p, Option_t *option="")
	Draw 3-D polyline with new coordinates.
void	ExecuteEvent (Int_t event, Int_t px, Int_t py) override
	Execute action corresponding to one event.
Int_t	GetLastPoint () const
Int_t	GetN () const
Option_t *	GetOption () const override
Float_t *	GetP () const
TClass *	IsA () const override
void	ls (Option_t *option="") const override
	List this 3-D polyline.
virtual Int_t	Merge (TCollection *list)
	Merge polylines in the collection in this polyline.
TPolyLine3D &	operator= (const TPolyLine3D &polylin)
	assignment operator
void	Paint (Option_t *option="") override
	Paint a TPolyLine3D.
void	Print (Option_t *option="") const override
	Dump this 3-D polyline with its attributes on stdout.
void	SavePrimitive (std::ostream &out, Option_t *option="") override
	Save primitive as a C++ statement(s) on output stream.
virtual Int_t	SetNextPoint (Double_t x, Double_t y, Double_t z)
	Set point following LastPoint to x, y, z.
virtual void	SetPoint (Int_t point, Double_t x, Double_t y, Double_t z)
	Set point n to x, y, z.
virtual void	SetPolyLine (Int_t n, Double_t *p, Option_t *option="")
	Re-initialize polyline with n points from p.
virtual void	SetPolyLine (Int_t n, Float_t *p, Option_t *option="")
	Re-initialize polyline with n points from p.
virtual void	SetPolyLine (Int_t n, Option_t *option="")
	Re-initialize polyline with n points (0,0,0).
virtual Int_t	Size () const
void	Streamer (TBuffer &) override
	Stream a 3-D polyline object.
void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)
Public Member Functions inherited from TObject
	TObject ()
	TObject constructor.
	TObject (const TObject &object)
	TObject copy ctor.
virtual	~TObject ()
	TObject destructor.
void	AbstractMethod (const char *method) const
	Use this method to implement an "abstract" method that you don't want to leave purely abstract.
virtual void	AppendPad (Option_t *option="")
	Append graphics object to current pad.
virtual void	Browse (TBrowser *b)
	Browse object. May be overridden for another default action.
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.
virtual const char *	ClassName () const
	Returns name of class to which the object belongs.
virtual void	Clear (Option_t *="")
virtual TObject *	Clone (const char *newname="") const
	Make a clone of an object using the Streamer facility.
virtual Int_t	Compare (const TObject *obj) const
	Compare abstract method.
virtual void	Delete (Option_t *option="")
	Delete this object.
virtual void	DrawClass () const
	Draw class inheritance tree of the class to which this object belongs.
virtual TObject *	DrawClone (Option_t *option="") const
	Draw a clone of this object in the current selected pad with: gROOT->SetSelectedPad(c1).
virtual void	Dump () const
	Dump contents of object on stdout.
virtual void	Error (const char *method, const char *msgfmt,...) const
	Issue error message.
virtual void	Execute (const char *method, const char *params, Int_t *error=nullptr)
	Execute method on this object with the given parameter string, e.g.
virtual void	Execute (TMethod *method, TObjArray *params, Int_t *error=nullptr)
	Execute method on this object with parameters stored in the TObjArray.
virtual void	Fatal (const char *method, const char *msgfmt,...) const
	Issue fatal error message.
virtual TObject *	FindObject (const char *name) const
	Must be redefined in derived classes.
virtual TObject *	FindObject (const TObject *obj) const
	Must be redefined in derived classes.
virtual Option_t *	GetDrawOption () const
	Get option used by the graphics system to draw this object.
virtual const char *	GetIconName () const
	Returns mime type name of object.
virtual const char *	GetName () const
	Returns name of object.
virtual char *	GetObjectInfo (Int_t px, Int_t py) const
	Returns string containing info about the object at position (px,py).
virtual const char *	GetTitle () const
	Returns title of object.
virtual UInt_t	GetUniqueID () const
	Return the unique object id.
virtual Bool_t	HandleTimer (TTimer *timer)
	Execute action in response of a timer timing out.
virtual ULong_t	Hash () const
	Return hash value for this object.
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.
virtual void	Info (const char *method, const char *msgfmt,...) const
	Issue info message.
virtual Bool_t	InheritsFrom (const char *classname) const
	Returns kTRUE if object inherits from class "classname".
virtual Bool_t	InheritsFrom (const TClass *cl) const
	Returns kTRUE if object inherits from TClass cl.
virtual void	Inspect () const
	Dump contents of this object in a graphics canvas.
void	InvertBit (UInt_t f)
Bool_t	IsDestructed () const
	IsDestructed.
virtual Bool_t	IsEqual (const TObject *obj) const
	Default equal comparison (objects are equal if they have the same address in memory).
virtual Bool_t	IsFolder () const
	Returns kTRUE in case object contains browsable objects (like containers or lists of other objects).
R__ALWAYS_INLINE Bool_t	IsOnHeap () const
virtual Bool_t	IsSortable () const
R__ALWAYS_INLINE Bool_t	IsZombie () const
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).
virtual Bool_t	Notify ()
	This method must be overridden to handle object notification.
void	Obsolete (const char *method, const char *asOfVers, const char *removedFromVers) const
	Use this method to declare a method obsolete.
void	operator delete (void *ptr)
	Operator delete.
void	operator delete[] (void *ptr)
	Operator delete [].
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.
virtual void	Pop ()
	Pop on object drawn in a pad to the top of the display list.
virtual Int_t	Read (const char *name)
	Read contents of object with specified name from the current directory.
virtual void	RecursiveRemove (TObject *obj)
	Recursively remove this object from a list.
void	ResetBit (UInt_t f)
virtual void	SaveAs (const char *filename="", Option_t *option="") const
	Save this object in the file specified by filename.
void	SetBit (UInt_t f)
void	SetBit (UInt_t f, Bool_t set)
	Set or unset the user status bits as specified in f.
virtual void	SetDrawOption (Option_t *option="")
	Set drawing option for object.
virtual void	SetUniqueID (UInt_t uid)
	Set the unique object id.
void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)
virtual void	SysError (const char *method, const char *msgfmt,...) const
	Issue system error message.
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.
virtual void	Warning (const char *method, const char *msgfmt,...) const
	Issue warning message.
virtual Int_t	Write (const char *name=nullptr, Int_t option=0, Int_t bufsize=0)
	Write this object to the current directory.
virtual Int_t	Write (const char *name=nullptr, Int_t option=0, Int_t bufsize=0) const
	Write this object to the current directory.
Public Member Functions inherited from TAttLine
	TAttLine ()
	AttLine default constructor.
	TAttLine (Color_t lcolor, Style_t lstyle, Width_t lwidth)
	AttLine normal constructor.
virtual	~TAttLine ()
	AttLine destructor.
void	Copy (TAttLine &attline) const
	Copy this line attributes to a new TAttLine.
Int_t	DistancetoLine (Int_t px, Int_t py, Double_t xp1, Double_t yp1, Double_t xp2, Double_t yp2)
	Compute distance from point px,py to a line.
virtual Color_t	GetLineColor () const
	Return the line color.
virtual Style_t	GetLineStyle () const
	Return the line style.
virtual Width_t	GetLineWidth () const
	Return the line width.
virtual void	Modify ()
	Change current line attributes if necessary.
virtual void	ResetAttLine (Option_t *option="")
	Reset this line attributes to default values.
virtual void	SaveLineAttributes (std::ostream &out, const char *name, Int_t coldef=1, Int_t stydef=1, Int_t widdef=1)
	Save line attributes as C++ statement(s) on output stream out.
virtual void	SetLineAttributes ()
	Invoke the DialogCanvas Line attributes.
virtual void	SetLineColor (Color_t lcolor)
	Set the line color.
virtual void	SetLineColorAlpha (Color_t lcolor, Float_t lalpha)
	Set a transparent line color.
virtual void	SetLineStyle (Style_t lstyle)
	Set the line style.
virtual void	SetLineWidth (Width_t lwidth)
	Set the line width.
void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)
Public Member Functions inherited from TAtt3D
	TAtt3D ()
virtual	~TAtt3D ()
virtual void	Sizeof3D () const
	Set total size of this 3D object (used by X3D interface).
void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

Static Public Member Functions
static TClass *	Class ()
static const char *	Class_Name ()
static constexpr Version_t	Class_Version ()
static const char *	DeclFileName ()
Static Public Member Functions inherited from TPolyLine3D
static TClass *	Class ()
static const char *	Class_Name ()
static constexpr Version_t	Class_Version ()
static const char *	DeclFileName ()
static void	DrawOutlineCube (TList *outline, Double_t *rmin, Double_t *rmax)
	Draw cube outline with 3d polylines.
Static Public Member Functions inherited from TObject
static TClass *	Class ()
static const char *	Class_Name ()
static constexpr Version_t	Class_Version ()
static const char *	DeclFileName ()
static Longptr_t	GetDtorOnly ()
	Return destructor only flag.
static Bool_t	GetObjectStat ()
	Get status of object stat flag.
static void	SetDtorOnly (void *obj)
	Set destructor only flag.
static void	SetObjectStat (Bool_t stat)
	Turn on/off tracking of objects in the TObjectTable.
Static Public Member Functions inherited from TAttLine
static TClass *	Class ()
static const char *	Class_Name ()
static constexpr Version_t	Class_Version ()
static const char *	DeclFileName ()
Static Public Member Functions inherited from TAtt3D
static TClass *	Class ()
static const char *	Class_Name ()
static constexpr Version_t	Class_Version ()
static const char *	DeclFileName ()

Protected Member Functions
Double_t	FindClosestPhase (Double_t phi0, Double_t cosine)
	Finds the closest phase to phi0 that gives cos(phase) = cosine.
THelix &	operator= (const THelix &)
	assignment operator
void	SetRotMatrix ()
	Set the rotational matrix according to the helix axis.
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).
void	MakeZombie ()

Protected Attributes
Double_t	fAxis [3]
Double_t	fPhi0
Double_t	fRange [2]
TRotMatrix *	fRotMat
Double_t	fVt
Double_t	fVz
Double_t	fW
Double_t	fX0
Double_t	fY0
Double_t	fZ0
Protected Attributes inherited from TPolyLine3D
Int_t	fLastPoint {-1}
	The index of the last filled point.
Int_t	fN {0}
	Number of points.
TString	fOption
	options
Float_t *	fP {nullptr}
	[3*fN] Array of 3-D coordinates (x,y,z)
Protected Attributes inherited from TAttLine
Color_t	fLineColor
	Line color.
Style_t	fLineStyle
	Line style.
Width_t	fLineWidth
	Line width.

Static Protected Attributes
static Int_t	fgMinNSeg =5

Additional Inherited Members
Public Types inherited from TObject
enum	{   kIsOnHeap = 0x01000000 , kNotDeleted = 0x02000000 , kZombie = 0x04000000 , kInconsistent = 0x08000000 ,   kBitMask = 0x00ffffff }
enum	{ kSingleKey = (1ULL << ( 0 )) , kOverwrite = (1ULL << ( 1 )) , kWriteDelete = (1ULL << ( 2 )) }
enum	EDeprecatedStatusBits { kObjInCanvas = (1ULL << ( 3 )) }
enum	EStatusBits {   kCanDelete = (1ULL << ( 0 )) , kMustCleanup = (1ULL << ( 3 )) , kIsReferenced = (1ULL << ( 4 )) , kHasUUID = (1ULL << ( 5 )) ,   kCannotPick = (1ULL << ( 6 )) , kNoContextMenu = (1ULL << ( 8 )) , kInvalidObject = (1ULL << ( 13 )) }
Protected Types inherited from TObject
enum	{ kOnlyPrepStep = (1ULL << ( 3 )) }

#include <THelix.h>

Inheritance diagram for THelix:

Constructor & Destructor Documentation

THelix() [1/4]

THelix::THelix

(

)

Helix default constructor.

Definition at line 121 of file THelix.cxx.

THelix() [2/4]

THelix::THelix	(	Double_t	x,
		Double_t	y,
		Double_t	z,
		Double_t	vx,
		Double_t	vy,
		Double_t	vz,
		Double_t	w
	)

Helix normal constructor.

Definition at line 134 of file THelix.cxx.

THelix() [3/4]

THelix::THelix	(	Double_t const *	xyz,
		Double_t const *	v,
		Double_t	w,
		Double_t const *	range = nullptr,
		EHelixRangeType	rtype = kHelixZ,
		Double_t const *	axis = nullptr
	)

Helix normal constructor.

Definition at line 156 of file THelix.cxx.

THelix() [4/4]

THelix::THelix

(

const THelix &

helix

)

Helix copy constructor.

Definition at line 236 of file THelix.cxx.

~THelix()

THelix::~THelix ( )

virtual

Helix destructor.

Definition at line 227 of file THelix.cxx.

Member Function Documentation

Class()

static TClass * THelix::Class ( )

static

Returns

TClass describing this class

Class_Name()

static const char * THelix::Class_Name ( )

static

Returns

Name of this class

Class_Version()

static constexpr Version_t THelix::Class_Version ( )

inlinestaticconstexpr

Returns

Version of this class

Definition at line 69 of file THelix.h.

Copy()

void THelix::Copy ( TObject &  helix ) const

virtual

Copy this helix to obj.

Reimplemented from TObject.

Definition at line 246 of file THelix.cxx.

DeclFileName()

static const char * THelix::DeclFileName ( )

inlinestatic

Returns

Name of the file containing the class declaration

Definition at line 69 of file THelix.h.

Draw()

void THelix::Draw ( Option_t *  option = "" )

virtual

Draw this helix with its current attributes.

Reimplemented from TObject.

Definition at line 281 of file THelix.cxx.

FindClosestPhase()

Double_t THelix::FindClosestPhase ( Double_t  phi0, Double_t  cosine  )

protected

Finds the closest phase to phi0 that gives cos(phase) = cosine.

Definition at line 598 of file THelix.cxx.

GetOption()

Option_t * THelix::GetOption ( ) const

inlinevirtual

Reimplemented from TObject.

Definition at line 57 of file THelix.h.

IsA()

virtual TClass * THelix::IsA ( ) const

inlinevirtual

Returns

TClass describing current object

Reimplemented from TObject.

Definition at line 69 of file THelix.h.

operator=()

THelix & THelix::operator= ( const THelix &  hx )

protected

assignment operator

Definition at line 203 of file THelix.cxx.

Print()

void THelix::Print ( Option_t *  option = "" ) const

virtual

Dump this helix with its attributes.

Reimplemented from TObject.

Definition at line 290 of file THelix.cxx.

SavePrimitive()

void THelix::SavePrimitive ( std::ostream &  out, Option_t *  option = ""  )

virtual

Save primitive as a C++ statement(s) on output stream out.

Reimplemented from TObject.

Definition at line 299 of file THelix.cxx.

SetAxis() [1/2]

void THelix::SetAxis ( Double_t const *  axis )

virtual

Set a new axis for the helix. This will make a new rotation matrix.

Definition at line 323 of file THelix.cxx.

SetAxis() [2/2]

void THelix::SetAxis ( Double_t  x, Double_t  y, Double_t  z  )

virtual

Set axis.

Definition at line 348 of file THelix.cxx.

SetHelix()

void THelix::SetHelix	(	Double_t const *	xyz,
		Double_t const *	v,
		Double_t	w,
		Double_t const *	range = nullptr,
		EHelixRangeType	type = kUnchanged,
		Double_t const *	axis = nullptr
	)

Set all helix parameters.

Definition at line 83 of file THelix.cxx.

SetOption()

virtual void THelix::SetOption ( Option_t *  option = "" )

inlinevirtual

Reimplemented from TPolyLine3D.

Definition at line 60 of file THelix.h.

SetRange() [1/2]

void THelix::SetRange ( Double_t *  range, EHelixRangeType  rtype = kHelixZ  )

virtual

Set a new range for the helix. This will remake the polyline.

Definition at line 358 of file THelix.cxx.

SetRange() [2/2]

void THelix::SetRange ( Double_t  r1, Double_t  r2, EHelixRangeType  rtype = kHelixZ  )

virtual

Set range.

Definition at line 551 of file THelix.cxx.

SetRotMatrix()

void THelix::SetRotMatrix ( )

protected

Set the rotational matrix according to the helix axis.

Definition at line 569 of file THelix.cxx.

Streamer()

void THelix::Streamer ( TBuffer &  R__b )

virtual

Stream an object of class THelix.

Reimplemented from TObject.

Definition at line 621 of file THelix.cxx.

StreamerNVirtual()

void THelix::StreamerNVirtual ( TBuffer &  ClassDef_StreamerNVirtual_b )

inline

Definition at line 69 of file THelix.h.

Member Data Documentation

fAxis

Double_t THelix::fAxis[3]

protected

Definition at line 33 of file THelix.h.

fgMinNSeg

Int_t THelix::fgMinNSeg =5

staticprotected

Definition at line 42 of file THelix.h.

fPhi0

Double_t THelix::fPhi0

protected

Definition at line 30 of file THelix.h.

fRange

Double_t THelix::fRange[2]

protected

Definition at line 35 of file THelix.h.

fRotMat

TRotMatrix* THelix::fRotMat

protected

Definition at line 34 of file THelix.h.

fVt

Double_t THelix::fVt

protected

Definition at line 29 of file THelix.h.

fVz

Double_t THelix::fVz

protected

Definition at line 31 of file THelix.h.

fW

Double_t THelix::fW

protected

Definition at line 32 of file THelix.h.

fX0

Double_t THelix::fX0

protected

Definition at line 26 of file THelix.h.

fY0

Double_t THelix::fY0

protected

Definition at line 27 of file THelix.h.

fZ0

Double_t THelix::fZ0

protected

Definition at line 28 of file THelix.h.

Libraries for THelix:

---

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

• graf3d/g3d/inc/THelix.h
• graf3d/g3d/src/THelix.cxx