# class TVector3: public TObject

The Physics Vector package
-*                    ==========================
-* The Physics Vector package consists of five classes:
-*   - TVector2
-*   - TVector3
-*   - TRotation
-*   - TLorentzVector
-*   - TLorentzRotation
-* It is a combination of CLHEPs Vector package written by
-* Leif Lonnblad, Andreas Nilsson and Evgueni Tcherniaev
-* and a ROOT package written by Pasha Murat.
-* for CLHEP see:  http://wwwinfo.cern.ch/asd/lhc++/clhep/
*

## TVector3

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

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 v2(1);     // v2 = (1,0,0)
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 memberfunctions SetX(), SetY(), SetZ() and SetXYZ() allow to set the components:

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

### Noncartesian 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 noncartesian 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.

## Function Members (Methods)

public:
 TVector3(const Double_t*) TVector3(const Float_t*) TVector3(const TVector3&) TVector3(Double_t x = 0.0, Double_t y = 0.0, Double_t z = 0.0) virtual ~TVector3() void TObject::AbstractMethod(const char* method) const Double_t Angle(const TVector3&) const virtual void TObject::AppendPad(Option_t* option = "") virtual void TObject::Browse(TBrowser* b) static TClass* Class() static TClass* TObject::Class() virtual const char* TObject::ClassName() const virtual void TObject::Clear(Option_t* = "") virtual TObject* TObject::Clone(const char* newname = "") const virtual Int_t TObject::Compare(const TObject* obj) const virtual void TObject::Copy(TObject& object) const Double_t CosTheta() const TVector3 Cross(const TVector3& p) const virtual void TObject::Delete(Option_t* option = "")MENU Double_t DeltaPhi(const TVector3& v) const Double_t DeltaR(const TVector3&) const virtual Int_t TObject::DistancetoPrimitive(Int_t px, Int_t py) Double_t Dot(const TVector3& p) const virtual void TObject::Draw(Option_t* option = "") virtual void TObject::DrawClass() constMENU virtual TObject* TObject::DrawClone(Option_t* option = "") constMENU Double_t DrEtaPhi(const TVector3& v) const virtual void TObject::Dump() constMENU virtual void TObject::Error(const char* method, const char* msgfmt) const Double_t Eta() const TVector2 EtaPhiVector() const virtual void TObject::Execute(const char* method, const char* params, Int_t* error = 0) virtual void TObject::Execute(TMethod* method, TObjArray* params, Int_t* error = 0) virtual void TObject::ExecuteEvent(Int_t event, Int_t px, Int_t py) virtual void TObject::Fatal(const char* method, const char* msgfmt) const virtual TObject* TObject::FindObject(const char* name) const virtual TObject* TObject::FindObject(const TObject* obj) const virtual Option_t* TObject::GetDrawOption() const static Long_t TObject::GetDtorOnly() virtual const char* TObject::GetIconName() const virtual const char* TObject::GetName() const virtual char* TObject::GetObjectInfo(Int_t px, Int_t py) const static Bool_t TObject::GetObjectStat() virtual Option_t* TObject::GetOption() const virtual const char* TObject::GetTitle() const virtual UInt_t TObject::GetUniqueID() const void GetXYZ(Double_t* carray) const void GetXYZ(Float_t* carray) const virtual Bool_t TObject::HandleTimer(TTimer* timer) virtual ULong_t TObject::Hash() const virtual void TObject::Info(const char* method, const char* msgfmt) const virtual Bool_t TObject::InheritsFrom(const char* classname) const virtual Bool_t TObject::InheritsFrom(const TClass* cl) const virtual void TObject::Inspect() constMENU void TObject::InvertBit(UInt_t f) virtual TClass* IsA() const virtual TClass* TObject::IsA() const virtual Bool_t TObject::IsEqual(const TObject* obj) const virtual Bool_t TObject::IsFolder() const Bool_t TObject::IsOnHeap() const virtual Bool_t TObject::IsSortable() const Bool_t TObject::IsZombie() const virtual void TObject::ls(Option_t* option = "") const Double_t Mag() const Double_t Mag2() const void TObject::MayNotUse(const char* method) const virtual Bool_t TObject::Notify() static void TObject::operator delete(void* ptr) static void TObject::operator delete(void* ptr, void* vp) static void TObject::operator delete[](void* ptr) static void TObject::operator delete[](void* ptr, void* vp) void* TObject::operator new(size_t sz) void* TObject::operator new(size_t sz, void* vp) void* TObject::operator new[](size_t sz) void* TObject::operator new[](size_t sz, void* vp) Bool_t operator!=(const TVector3& v) const Double_t operator()(int) const Double_t& operator()(int) TVector3& operator*=(Double_t a) TVector3& operator*=(const TRotation&) TVector3& operator+=(const TVector3& p) TVector3 operator-() const TVector3& operator-=(const TVector3& p) TVector3& operator=(const TVector3& p) TObject& TObject::operator=(const TObject& rhs) Bool_t operator==(const TVector3& v) const Double_t operator[](int i) const Double_t& operator[](int i) TVector3 Orthogonal() const virtual void TObject::Paint(Option_t* option = "") Double_t Perp() const Double_t Perp(const TVector3&) const Double_t Perp2() const Double_t Perp2(const TVector3& p) const Double_t Phi() const virtual void TObject::Pop() virtual void Print(Option_t* option = "") const Double_t PseudoRapidity() const Double_t Pt() const Double_t Pt(const TVector3& p) const Double_t Px() const Double_t Py() const Double_t Pz() const virtual Int_t TObject::Read(const char* name) virtual void TObject::RecursiveRemove(TObject* obj) void TObject::ResetBit(UInt_t f) void Rotate(Double_t, const TVector3&) void RotateUz(const TVector3&) void RotateX(Double_t) void RotateY(Double_t) void RotateZ(Double_t) virtual void TObject::SaveAs(const char* filename = "", Option_t* option = "") constMENU virtual void TObject::SavePrimitive(basic_ostream >& out, Option_t* option = "") void TObject::SetBit(UInt_t f) void TObject::SetBit(UInt_t f, Bool_t set) virtual void TObject::SetDrawOption(Option_t* option = "")MENU static void TObject::SetDtorOnly(void* obj) void SetMag(Double_t ma) void SetMagThetaPhi(Double_t mag, Double_t theta, Double_t phi) static void TObject::SetObjectStat(Bool_t stat) void SetPerp(Double_t r) void SetPhi(Double_t) void SetPtEtaPhi(Double_t pt, Double_t eta, Double_t phi) void SetPtThetaPhi(Double_t pt, Double_t theta, Double_t phi) void SetTheta(Double_t) virtual void TObject::SetUniqueID(UInt_t uid) void SetX(Double_t xx) void SetXYZ(Double_t xx, Double_t yy, Double_t zz) void SetY(Double_t yy) void SetZ(Double_t zz) virtual void ShowMembers(TMemberInspector& insp, char* parent) virtual void TObject::ShowMembers(TMemberInspector& insp, char* parent) virtual void Streamer(TBuffer& b) virtual void TObject::Streamer(TBuffer& b) void StreamerNVirtual(TBuffer& b) void TObject::StreamerNVirtual(TBuffer& b) virtual void TObject::SysError(const char* method, const char* msgfmt) const Bool_t TObject::TestBit(UInt_t f) const Int_t TObject::TestBits(UInt_t f) const Double_t Theta() const TVector3& Transform(const TRotation&) TVector3 Unit() const virtual void TObject::UseCurrentStyle() virtual void TObject::Warning(const char* method, const char* msgfmt) const virtual Int_t TObject::Write(const char* name = 0, Int_t option = 0, Int_t bufsize = 0) virtual Int_t TObject::Write(const char* name = 0, Int_t option = 0, Int_t bufsize = 0) const 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
protected:
 virtual void TObject::DoError(int level, const char* location, const char* fmt, va_list va) const void TObject::MakeZombie()

## Data Members

private:
 enum TObject::EStatusBits { kCanDelete kMustCleanup kObjInCanvas kIsReferenced kHasUUID kCannotPick kNoContextMenu kInvalidObject }; enum TObject::[unnamed] { kIsOnHeap kNotDeleted kZombie kBitMask kSingleKey kOverwrite kWriteDelete };
private:
 Double_t fX Double_t fY Double_t fZ

## Function documentation

TVector3(const TVector3 & p)
{}
TVector3(Double_t x = 0.0, Double_t y = 0.0, Double_t z = 0.0)
{}
TVector3(const Double_t * x0)
{}
TVector3(const Float_t * x0)
{}

{}
TVector3 & Transform(const TRotation& )
transform this vector with a TRotation
Double_t Angle(const TVector3& ) const
return the angle w.r.t. another 3-vector
Double_t Mag() const
return the magnitude (rho in spherical coordinate system)
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 Phi() const
return the  azimuth angle. returns phi from -pi to pi
Double_t Theta() const
return the polar angle
TVector3 Unit() const
return unit vector parallel to this.
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 Rotate(Double_t , const TVector3& )
rotate vector
void RotateUz(const TVector3& )
NewUzVector must be normalized !
Double_t PseudoRapidity() const
Double_t m = Mag();
return 0.5*log( (m+fZ)/(m-fZ) );
guard against Pt=0
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 SetPhi(Double_t )
Set phi keeping mag and theta constant (BaBar).
Double_t DeltaR(const TVector3& ) const
return deltaR with respect to v
void SetMagThetaPhi(Double_t mag, Double_t theta, Double_t phi)
setter with mag, theta, phi
void Streamer(TBuffer& b)
Stream an object of class TVector3.
void Print(Option_t* option = "") const
print vector parameters
Double_t & operator[](int i)
{ return operator()(i); }
Double_t operator[](int i)
{ return operator()(i); }
Double_t x() const
{ return fX; }
Double_t y() const
{ return fY; }
Double_t z() const
{ return fZ; }
Double_t X() const
{ return fX; }
Double_t Y() const
{ return fY; }
Double_t Z() const
{ return fZ; }
Double_t Px() const
{ return fX; }
Double_t Py() const
{ return fY; }
Double_t Pz() const
{ return fZ; }
void SetX(Double_t xx)
{ fX = xx; }
void SetY(Double_t yy)
{ fY = yy; }
void SetZ(Double_t zz)
{ fZ = zz; }
void SetXYZ(Double_t xx, Double_t yy, Double_t zz)
void GetXYZ(Double_t *carray)
void GetXYZ(Float_t *carray)
Double_t Dot(const TVector3& p) const
TVector3 Cross(const TVector3& p) const
Double_t Mag2() const
{ return fX*fX + fY*fY + fZ*fZ; }
TVector3 Orthogonal() const
Double_t Perp2() const
{ return fX*fX + fY*fY; }
Double_t Pt() const
{ return Perp(); }
Double_t Perp2(const TVector3& p) const
Double_t Pt(const TVector3& p) const
Double_t CosTheta() const
void SetMag(Double_t ma)
void SetPerp(Double_t r)
Double_t DeltaPhi(const TVector3& v) const
Double_t Eta() const
Double_t DrEtaPhi(const TVector3& v) const
TVector2 EtaPhiVector() const
TVector2 XYvector() const