TVector3 Class Reference

Attention

TVector3 is a legacy class. It is slower and worse for serialization than the recommended superior alternative ROOT::Math::XYZVector.

More details can be found in the documentation of the Physics Vectors package.

TVector3 is a general three vector class, which can be used for the description of different vectors in 3D.

Declaration / Access to the components

TVector3 has been implemented as a vector of three Double_t variables, representing the cartesian coordinates. By default all components are initialized to zero:

TVector3 v1;        // v1 = (0,0,0)
TVector3 v3(1,2,3); // v3 = (1,2,3)
TVector3 v4(v2);    // v4 = v2

It is also possible (but not recommended) to initialize a TVector3 with a Double_t or Float_t C array.

You can get the basic components either by name or by index using operator():

xx = v1.X(); or xx = v1(0);
yy = v1.Y();    yy = v1(1);
zz = v1.Z();    zz = v1(2);

The member functions SetX(), SetY(), SetZ() and SetXYZ() allow to set the components:

v1.SetX(1.); v1.SetY(2.); v1.SetZ(3.);
v1.SetXYZ(1.,2.,3.);

Non-cartesian coordinates

To get information on the TVector3 in spherical (rho,phi,theta) or cylindrical (z,r,theta) coordinates, the

the member functions Mag() (=magnitude=rho in spherical coordinates), Mag2(), Theta(), CosTheta(), Phi(), Perp() (the transverse component=r in cylindrical coordinates), Perp2() can be used:

Double_t m = v.Mag();       // get magnitude (=rho=Sqrt(x*x+y*y+z*z)))
Double_t m2 = v.Mag2();     // get magnitude squared
Double_t t = v.Theta();     // get polar angle
Double_t ct = v.CosTheta(); // get cos of theta
Double_t p = v.Phi();       // get azimuth angle
Double_t pp = v.Perp();     // get transverse component
Double_t pp2= v.Perp2();    // get transvers component squared

It is also possible to get the transverse component with respect to another vector:

Double_t ppv1 = v.Perp(v1);
Double_t pp2v1 = v.Perp2(v1);

The pseudo-rapidity ( eta=-ln (tan (theta/2)) ) can be obtained by Eta() or PseudoRapidity():

Double_t eta = v.PseudoRapidity();

There are set functions to change one of the non-cartesian coordinates:

v.SetTheta(.5); // keeping rho and phi
v.SetPhi(.8);   // keeping rho and theta
v.SetMag(10.);  // keeping theta and phi
v.SetPerp(3.);  // keeping z and phi

Arithmetic / Comparison

The TVector3 class provides the operators to add, subtract, scale and compare vectors:

v3  = -v1;
v1  = v2+v3;
v1 += v3;
v1  = v1 - v3
v1 -= v3;
v1 *= 10;
v1  = 5*v2;
if (v1==v2) {...}
if (v1!=v2) {...}

Related Vectors

v2 = v1.Unit(); // get unit vector parallel to v1
v2 = v1.Orthogonal(); // get vector orthogonal to v1

Scalar and vector products

s = v1.Dot(v2);   // scalar product
s = v1 * v2;      // scalar product
v = v1.Cross(v2); // vector product

Angle between two vectors

Double_t a = v1.Angle(v2);

Rotations

Rotation around axes

v.RotateX(.5);
v.RotateY(TMath::Pi());
v.RotateZ(angle);

Rotation around a vector

v1.Rotate(TMath::Pi()/4, v2); // rotation around v2

Rotation by TRotation

TVector3 objects can be rotated by objects of the TRotation class using the Transform() member functions,

the operator *= or the operator * of the TRotation class:

TRotation m;
...
v1.transform(m);
v1  = m*v1;
v1 *= m; // Attention v1 = m*v1

Transformation from rotated frame

TVector3 direction = v.Unit()
v1.RotateUz(direction); // direction must be TVector3 of unit length

transforms v1 from the rotated frame (z' parallel to direction, x' in the theta plane and y' in the xy plane as well as perpendicular to the theta plane) to the (x,y,z) frame.

Definition at line 22 of file TVector3.h.

Public Types
typedef Double_t	Scalar
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 )) }

Public Member Functions
	TVector3 ()
	Constructors.
	TVector3 (const Double_t *)
	TVector3 (const Float_t *)
	TVector3 (const TVector3 &) noexcept
	TVector3 (Double_t x, Double_t y, Double_t z)
	~TVector3 () override=default
Double_t	Angle (const TVector3 &) const
	Return the angle w.r.t. another 3-vector.
Double_t	CosTheta () const
TVector3	Cross (const TVector3 &) const
Double_t	DeltaPhi (const TVector3 &) const
Double_t	DeltaR (const TVector3 &) const
	Return deltaR with respect to v.
Double_t	Dot (const TVector3 &) const
Double_t	DrEtaPhi (const TVector3 &) const
Double_t	Eta () const
TVector2	EtaPhiVector () const
void	GetXYZ (Double_t *carray) const
void	GetXYZ (Float_t *carray) const
TClass *	IsA () const override
Double_t	Mag () const
Double_t	Mag2 () const
Bool_t	operator!= (const TVector3 &) const
Double_t &	operator() (int)
Double_t	operator() (int) const
TVector3 &	operator*= (const TRotation &)
	Multiplication operator.
TVector3 &	operator*= (Double_t)
TVector3 &	operator+= (const TVector3 &)
TVector3	operator- () const
TVector3 &	operator-= (const TVector3 &)
TVector3 &	operator= (const TVector3 &)
Bool_t	operator== (const TVector3 &) const
Double_t &	operator[] (int)
Double_t	operator[] (int) const
TVector3	Orthogonal () const
Double_t	Perp () const
	Return the transverse component (R in cylindrical coordinate system)
Double_t	Perp (const TVector3 &) const
	Return the transverse component (R in cylindrical coordinate system)
Double_t	Perp2 () const
Double_t	Perp2 (const TVector3 &) const
Double_t	Phi () const
	Return the azimuth angle. Returns phi from -pi to pi.
void	Print (Option_t *option="") const override
	Print vector parameters.
Double_t	PseudoRapidity () const
	Double_t m = Mag(); return 0.5*log( (m+fZ)/(m-fZ) ); guard against Pt=0.
Double_t	Pt () const
Double_t	Pt (const TVector3 &) const
Double_t	Px () const
Double_t	Py () const
Double_t	Pz () const
void	Rotate (Double_t, const TVector3 &)
	Rotate vector.
void	RotateUz (const TVector3 &)
	Express the coordinates of this vector in a new reference frame S' whose z' axis will lie in the direction of NewUzVector (expressed in frame S).
void	RotateX (Double_t)
	Rotate vector around X.
void	RotateY (Double_t)
	Rotate vector around Y.
void	RotateZ (Double_t)
	Rotate vector around Z.
void	SetMag (Double_t)
void	SetMagThetaPhi (Double_t mag, Double_t theta, Double_t phi)
	Setter with mag, theta, phi.
void	SetPerp (Double_t)
void	SetPhi (Double_t)
	Set phi keeping mag and theta constant (BaBar).
void	SetPtEtaPhi (Double_t pt, Double_t eta, Double_t phi)
	Set Pt, Eta and Phi.
void	SetPtThetaPhi (Double_t pt, Double_t theta, Double_t phi)
	Set Pt, Theta and Phi.
void	SetTheta (Double_t)
	Set theta keeping mag and phi constant (BaBar).
void	SetX (Double_t)
void	SetXYZ (Double_t x, Double_t y, Double_t z)
void	SetY (Double_t)
void	SetZ (Double_t)
constexpr std::size_t	size () const
	The length is always 3. For compatibility with the standard library.
void	Streamer (TBuffer &) override
	Stream an object of class TVector3.
void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)
Double_t	Theta () const
	Return the polar angle.
TVector3 &	Transform (const TRotation &)
	Transform this vector with a TRotation.
TVector3	Unit () const
	Return unit vector parallel to this.
Double_t	x () const
Double_t	X () const
TVector2	XYvector () const
Double_t	y () const
Double_t	Y () const
Double_t	z () const
Double_t	Z () const
Public Member Functions inherited from TObject
	TObject ()
	TObject constructor.
	TObject (const TObject &object) noexcept
	TObject copy ctor.
virtual	~TObject ()
	TObject destructor.
void	AbstractMethod (const char *method) const
	Call this function within a function that you don't want to define as purely virtual, in order not to force all users deriving from that class to implement that maybe (on their side) unused function; but at the same time, emit a run-time warning if they try to call it, telling that it is not implemented in the derived class: action must thus be taken on the user side to override it.
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	Copy (TObject &object) const
	Copy this to obj.
virtual void	Delete (Option_t *option="")
	Delete this object.
virtual Int_t	DistancetoPrimitive (Int_t px, Int_t py)
	Computes distance from point (px,py) to the object.
virtual void	Draw (Option_t *option="")
	Default Draw method for all objects.
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	ExecuteEvent (Int_t event, Int_t px, Int_t py)
	Execute action corresponding to an event at (px,py).
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 Option_t *	GetOption () const
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
virtual void	ls (Option_t *option="") const
	The ls function lists the contents of a class on stdout.
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 (the base implementation is no-op).
void	Obsolete (const char *method, const char *asOfVers, const char *removedFromVers) const
	Use this method to declare a method obsolete.
void	operator delete (void *, size_t)
	Operator delete for sized deallocation.
void	operator delete (void *ptr)
	Operator delete.
void	operator delete (void *ptr, void *vp)
	Only called by placement new when throwing an exception.
void	operator delete[] (void *, size_t)
	Operator delete [] for sized deallocation.
void	operator delete[] (void *ptr)
	Operator delete [].
void	operator delete[] (void *ptr, void *vp)
	Only called by placement new[] when throwing an exception.
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) noexcept
	TObject assignment operator.
virtual void	Paint (Option_t *option="")
	This method must be overridden if a class wants to paint itself.
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.
virtual void	SavePrimitive (std::ostream &out, Option_t *option="")
	Save a primitive as a C++ statement(s) on output stream "out".
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.

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 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.

Private Attributes
Double_t	fX
Double_t	fY
Double_t	fZ

Friends
class	TLorentzVector

Additional Inherited Members
Protected Types inherited from TObject
enum	{ kOnlyPrepStep = (1ULL << ( 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).
void	MakeZombie ()
Static Protected Member Functions inherited from TObject
static void	SavePrimitiveConstructor (std::ostream &out, TClass *cl, const char *variable_name, const char *constructor_agrs="", Bool_t empty_line=kTRUE)
	Save object constructor in the output stream "out".
static void	SavePrimitiveDraw (std::ostream &out, const char *variable_name, Option_t *option=nullptr)
	Save invocation of primitive Draw() method Skipped if option contains "nodraw" string.
static TString	SavePrimitiveVector (std::ostream &out, const char *prefix, Int_t len, Double_t *arr, Bool_t empty_line=kFALSE)
	Save array in the output stream "out" as vector.

#include <TVector3.h>

Inheritance diagram for TVector3:

Member Typedef Documentation

Scalar

typedef Double_t TVector3::Scalar

Definition at line 26 of file TVector3.h.

Constructor & Destructor Documentation

TVector3() [1/5]

TVector3::TVector3 ( )

inline

Constructors.

Definition at line 250 of file TVector3.h.

TVector3() [2/5]

TVector3::TVector3 ( Double_t x, Double_t y, Double_t z )

inline

Definition at line 256 of file TVector3.h.

TVector3() [3/5]

TVector3::TVector3 ( const Double_t * x0 )

inline

Definition at line 259 of file TVector3.h.

TVector3() [4/5]

TVector3::TVector3 ( const Float_t * x0 )

inline

Definition at line 262 of file TVector3.h.

TVector3() [5/5]

TVector3::TVector3 ( const TVector3 & p )

inlinenoexcept

Definition at line 253 of file TVector3.h.

~TVector3()

TVector3::~TVector3 ( )

overridedefault

Member Function Documentation

Angle()

Double_t TVector3::Angle

(

const TVector3 &

q

)

const

Return the angle w.r.t. another 3-vector.

Definition at line 202 of file TVector3.cxx.

Class()

static TClass * TVector3::Class ( )

static

Returns

TClass describing this class

Class_Name()

static const char * TVector3::Class_Name ( )

static

Returns

Name of this class

Class_Version()

static constexpr Version_t TVector3::Class_Version ( )

inlinestaticconstexpr

Returns

Version of this class

Definition at line 191 of file TVector3.h.

CosTheta()

Double_t TVector3::CosTheta ( ) const

inline

Definition at line 374 of file TVector3.h.

Cross()

TVector3 TVector3::Cross ( const TVector3 & p ) const

inline

Definition at line 338 of file TVector3.h.

DeclFileName()

static const char * TVector3::DeclFileName ( )

inlinestatic

Returns

Name of the file containing the class declaration

Definition at line 191 of file TVector3.h.

DeltaPhi()

Double_t TVector3::DeltaPhi ( const TVector3 & v ) const

inline

Definition at line 399 of file TVector3.h.

DeltaR()

Double_t TVector3::DeltaR

(

const TVector3 &

v

)

const

Return deltaR with respect to v.

Definition at line 397 of file TVector3.cxx.

Dot()

Double_t TVector3::Dot ( const TVector3 & p ) const

inline

Definition at line 334 of file TVector3.h.

DrEtaPhi()

Double_t TVector3::DrEtaPhi ( const TVector3 & v ) const

inline

Definition at line 407 of file TVector3.h.

Eta()

Double_t TVector3::Eta ( ) const

inline

Definition at line 403 of file TVector3.h.

EtaPhiVector()

TVector2 TVector3::EtaPhiVector ( ) const

inline

Definition at line 412 of file TVector3.h.

GetXYZ() [1/2]

void TVector3::GetXYZ ( Double_t * carray ) const

inline

Definition at line 236 of file TVector3.h.

GetXYZ() [2/2]

void TVector3::GetXYZ ( Float_t * carray ) const

inline

Definition at line 242 of file TVector3.h.

IsA()

TClass * TVector3::IsA ( ) const

inlineoverridevirtual

Returns

TClass describing current object

Reimplemented from TObject.

Definition at line 191 of file TVector3.h.

Mag()

Double_t TVector3::Mag ( ) const

inline

Definition at line 89 of file TVector3.h.

Mag2()

Double_t TVector3::Mag2 ( ) const

inline

Definition at line 342 of file TVector3.h.

operator!=()

Bool_t TVector3::operator!= ( const TVector3 & v ) const

inline

Definition at line 305 of file TVector3.h.

operator()() [1/2]

Double_t & TVector3::operator() ( int i )

inline

Definition at line 280 of file TVector3.h.

operator()() [2/2]

Double_t TVector3::operator() ( int i ) const

inline

Definition at line 266 of file TVector3.h.

operator*=() [1/2]

TVector3 & TVector3::operator*=

(

const TRotation &

m

)

Multiplication operator.

Definition at line 188 of file TVector3.cxx.

operator*=() [2/2]

TVector3 & TVector3::operator*= ( Double_t a )

inline

Definition at line 327 of file TVector3.h.

operator+=()

TVector3 & TVector3::operator+= ( const TVector3 & p )

inline

Definition at line 309 of file TVector3.h.

operator-()

TVector3 TVector3::operator- ( ) const

inline

Definition at line 323 of file TVector3.h.

operator-=()

TVector3 & TVector3::operator-= ( const TVector3 & p )

inline

Definition at line 316 of file TVector3.h.

operator=()

TVector3 & TVector3::operator= ( const TVector3 & p )

inline

Definition at line 294 of file TVector3.h.

operator==()

Bool_t TVector3::operator== ( const TVector3 & v ) const

inline

Definition at line 301 of file TVector3.h.

operator[]() [1/2]

Double_t & TVector3::operator[] ( int i )

inline

Definition at line 213 of file TVector3.h.

operator[]() [2/2]

Double_t TVector3::operator[] ( int i ) const

inline

Definition at line 214 of file TVector3.h.

Orthogonal()

TVector3 TVector3::Orthogonal ( ) const

inline

Definition at line 345 of file TVector3.h.

Perp() [1/2]

Double_t TVector3::Perp

(

)

const

Return the transverse component (R in cylindrical coordinate system)

Definition at line 218 of file TVector3.cxx.

Perp() [2/2]

Double_t TVector3::Perp

(

const TVector3 &

p

)

const

Return the transverse component (R in cylindrical coordinate system)

Definition at line 227 of file TVector3.cxx.

Perp2() [1/2]

Double_t TVector3::Perp2 ( ) const

inline

Definition at line 356 of file TVector3.h.

Perp2() [2/2]

Double_t TVector3::Perp2 ( const TVector3 & p ) const

inline

Definition at line 361 of file TVector3.h.

Phi()

Double_t TVector3::Phi

(

)

const

Return the azimuth angle. Returns phi from -pi to pi.

Definition at line 235 of file TVector3.cxx.

Print()

void TVector3::Print ( Option_t * option = "" ) const

overridevirtual

Print vector parameters.

Reimplemented from TObject.

Definition at line 485 of file TVector3.cxx.

PseudoRapidity()

Double_t TVector3::PseudoRapidity

(

)

const

Double_t m = Mag(); return 0.5*log( (m+fZ)/(m-fZ) ); guard against Pt=0.

Definition at line 345 of file TVector3.cxx.

Pt() [1/2]

Double_t TVector3::Pt ( ) const

inline

Definition at line 359 of file TVector3.h.

Pt() [2/2]

Double_t TVector3::Pt ( const TVector3 & p ) const

inline

Definition at line 370 of file TVector3.h.

Px()

Double_t TVector3::Px ( ) const

inline

Definition at line 222 of file TVector3.h.

Py()

Double_t TVector3::Py ( ) const

inline

Definition at line 223 of file TVector3.h.

Pz()

Double_t TVector3::Pz ( ) const

inline

Definition at line 224 of file TVector3.h.

Rotate()

void TVector3::Rotate	(	Double_t	angle,
		const TVector3 &	axis )

Rotate vector.

Definition at line 295 of file TVector3.cxx.

RotateUz()

void TVector3::RotateUz

(

const TVector3 &

NewUzVector

)

Express the coordinates of this vector in a new reference frame S' whose z' axis will lie in the direction of NewUzVector (expressed in frame S).

Note

NewUzVector must be normalized !

\[ R = \left( \begin{array}{ccc} u1*u3/up & -u2/up & u1 \\ u2*u3/up & u1/up & u2 \\ -up & 0 & u3 \end{array} \right) \]

The columns of the applied rotation matrix represent the coordinates of unit vectors of the new axes in the original coordinate system. The z' axis i.e. third column is NewUzVector=(u1,u2,u3). The y' axis i.e. second column is the cross product of the old and new Z axes: (0,0,1)x(u1,u2,u3) = (-u2,u1,0), which after normalisation becomes (-u2/up,u1/up,0) with up=sqrt(u1*u1+u2*u2). The x' axis i.e. first column is the cross product of new y' and z' axes: (-u2/up,u1/up,0)x(u1,u2,u3) = (u1*u3/up,u2*u3/up,-up). In the special case that z' is parallel to z, the vector is left untouched; if it's antiparallel, the sign of the x and z vector coordinates is inverted.

This function originates from CLHEP / Geant4.

See also

https://proj-clhep.web.cern.ch/proj-clhep/doc/CLHEP_1_7/UserGuide/VectorDefs/node49.html#eq:rotUz

Note

If you want to transform your frame using the "shortest" rotation path and avoid Gimbal-lock artefacts, use instead TVector3::Rotate(Double_t angle,const TVector3& axis), where axis=(u2/up, -u1/up, 0) andangle=-arccos(u3), beingaxis the normalized cross-product of(u1,u2,u3)and(0,0,1)`.

Definition at line 324 of file TVector3.cxx.

RotateX()

void TVector3::RotateX

(

Double_t

angle

)

Rotate vector around X.

Definition at line 262 of file TVector3.cxx.

RotateY()

void TVector3::RotateY

(

Double_t

angle

)

Rotate vector around Y.

Definition at line 273 of file TVector3.cxx.

RotateZ()

void TVector3::RotateZ

(

Double_t

angle

)

Rotate vector around Z.

Definition at line 284 of file TVector3.cxx.

SetMag()

void TVector3::SetMag ( Double_t ma )

inline

Definition at line 379 of file TVector3.h.

SetMagThetaPhi()

void TVector3::SetMagThetaPhi	(	Double_t	mag,
		Double_t	theta,
		Double_t	phi )

Setter with mag, theta, phi.

Definition at line 407 of file TVector3.cxx.

SetPerp()

void TVector3::SetPerp ( Double_t r )

inline

Definition at line 391 of file TVector3.h.

SetPhi()

void TVector3::SetPhi

(

Double_t

ph

)

Set phi keeping mag and theta constant (BaBar).

Definition at line 387 of file TVector3.cxx.

SetPtEtaPhi()

void TVector3::SetPtEtaPhi	(	Double_t	pt,
		Double_t	eta,
		Double_t	phi )

Set Pt, Eta and Phi.

Definition at line 357 of file TVector3.cxx.

SetPtThetaPhi()

void TVector3::SetPtThetaPhi	(	Double_t	pt,
		Double_t	theta,
		Double_t	phi )

Set Pt, Theta and Phi.

Definition at line 365 of file TVector3.cxx.

SetTheta()

void TVector3::SetTheta

(

Double_t

th

)

Set theta keeping mag and phi constant (BaBar).

Definition at line 375 of file TVector3.cxx.

SetX()

void TVector3::SetX ( Double_t xx )

inline

Definition at line 226 of file TVector3.h.

SetXYZ()

void TVector3::SetXYZ ( Double_t x, Double_t y, Double_t z )

inline

Definition at line 230 of file TVector3.h.

SetY()

void TVector3::SetY ( Double_t yy )

inline

Definition at line 227 of file TVector3.h.

SetZ()

void TVector3::SetZ ( Double_t zz )

inline

Definition at line 228 of file TVector3.h.

size()

constexpr std::size_t TVector3::size ( ) const

inlineconstexpr

The length is always 3. For compatibility with the standard library.

Definition at line 44 of file TVector3.h.

Streamer()

void TVector3::Streamer ( TBuffer & R__b )

overridevirtual

Stream an object of class TVector3.

Reimplemented from TObject.

Definition at line 418 of file TVector3.cxx.

StreamerNVirtual()

void TVector3::StreamerNVirtual ( TBuffer & ClassDef_StreamerNVirtual_b )

inline

Definition at line 191 of file TVector3.h.

Theta()

Double_t TVector3::Theta

(

)

const

Return the polar angle.

Definition at line 243 of file TVector3.cxx.

Transform()

TVector3 & TVector3::Transform

(

const TRotation &

m

)

Transform this vector with a TRotation.

Definition at line 195 of file TVector3.cxx.

Unit()

TVector3 TVector3::Unit

(

)

const

Return unit vector parallel to this.

Definition at line 251 of file TVector3.cxx.

x()

Double_t TVector3::x ( ) const

inline

Definition at line 216 of file TVector3.h.

X()

Double_t TVector3::X ( ) const

inline

Definition at line 219 of file TVector3.h.

XYvector()

TVector2 TVector3::XYvector ( ) const

inline

Definition at line 416 of file TVector3.h.

y()

Double_t TVector3::y ( ) const

inline

Definition at line 217 of file TVector3.h.

Y()

Double_t TVector3::Y ( ) const

inline

Definition at line 220 of file TVector3.h.

z()

Double_t TVector3::z ( ) const

inline

Definition at line 218 of file TVector3.h.

Z()

Double_t TVector3::Z ( ) const

inline

Definition at line 221 of file TVector3.h.

Friends And Related Symbol Documentation

TLorentzVector

friend class TLorentzVector

friend

Definition at line 194 of file TVector3.h.

Member Data Documentation

fX

Double_t TVector3::fX

private

Definition at line 188 of file TVector3.h.

fY

Double_t TVector3::fY

private

Definition at line 188 of file TVector3.h.

fZ

Double_t TVector3::fZ

private

Definition at line 188 of file TVector3.h.

Libraries for TVector3:

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

• math/physics/inc/TVector3.h
• math/physics/src/TVector3.cxx