library: libPhysics
#include "TVector3.h"

TVector3

class description - source file - inheritance tree (.pdf)

class TVector3 : public TObject

Inheritance Chart:

TObject

TVector3


    public:

                      TVector3(Double_t x = 0.0, Double_t y = 0.0, Double_t z = 0.0)
                      TVector3(const Double_t*)
                      TVector3(const Float_t*)
                      TVector3(const TVector3&)
             TVector3 operator-() const
             TVector3 Unit() const
             TVector3 Orthogonal() const
             TVector3 Cross(const TVector3& p) const
              virtual ~TVector3()
             Double_t Angle(const TVector3& q) const
       static TClass* Class()
             Double_t CosTheta() const
             Double_t DeltaPhi(const TVector3& v) const
             Double_t DeltaR(const TVector3& v) const
             Double_t Dot(const TVector3& p) const
             Double_t DrEtaPhi(const TVector3& v) const
             Double_t Eta() const
             TVector2 EtaPhiVector() const
                 void GetXYZ(Double_t* carray) const
                 void GetXYZ(Float_t* carray) const
      virtual TClass* IsA() const
             Double_t Mag() const
             Double_t Mag2() const
               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& p)
            TVector3& operator=(const TVector3& p)
               Bool_t operator==(const TVector3& v) const
             Double_t operator[](int i) const
            Double_t& operator[](int i)
             Double_t Perp() const
             Double_t Perp(const TVector3& p) const
             Double_t Perp2() const
             Double_t Perp2(const TVector3& p) const
             Double_t Phi() const
         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
                 void Rotate(Double_t, const TVector3&)
                 void RotateUz(const TVector3&)
                 void RotateX(Double_t)
                 void RotateY(Double_t)
                 void RotateZ(Double_t)
                 void SetMag(Double_t ma)
                 void SetMagThetaPhi(Double_t mag, Double_t theta, Double_t phi)
                 void SetPerp(Double_t r)
                 void SetPhi(Double_t ph)
                 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 th)
                 void SetX(Double_t x)
                 void SetXYZ(Double_t x, Double_t y, Double_t z)
                 void SetY(Double_t y)
                 void SetZ(Double_t z)
         virtual void ShowMembers(TMemberInspector& insp, char* parent)
         virtual void Streamer(TBuffer& b)
                 void StreamerNVirtual(TBuffer& b)
             Double_t Theta() const
            TVector3& Transform(const TRotation&)
             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

Data Members

    private:

      Double_t fX  
      Double_t fY  
      Double_t fZ

Class Description

*-*-*-*-*-*-*-*-*-*-*-*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.

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 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 pseudorapiditiy ( eta=-ln (tan (phi/2)) ) can be get 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.

TVector3(const TVector3 & p) : TObject(p), fX(p.fX), fY(p.fY), fZ(p.fZ)

TVector3(Double_t x, Double_t y, Double_t z) : fX(x), fY(y), fZ(z)

TVector3(const Double_t * x0) : fX(x0[0]), fY(x0[1]), fZ(x0[2])

TVector3(const Float_t * x0) : fX(x0[0]), fY(x0[1]), fZ(x0[2])

~TVector3()

TVector3& Transform(const TRotation & m)

void RotateX(Double_t angle)

void RotateY(Double_t angle)

void RotateZ(Double_t angle)

void Rotate(Double_t angle, const TVector3 & axis)

void RotateUz(const TVector3& NewUzVector)

 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)

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

void Streamer(TBuffer &R__b)

 Stream an object of class TVector3.

void Print(Option_t*)const

Inline Functions

           Double_t operator()(int) const
           Double_t operator[](int i) const
          Double_t& operator()(int)
          Double_t& operator[](int i)
           Double_t x() const
           Double_t y() const
           Double_t z() const
           Double_t X() const
           Double_t Y() const
           Double_t Z() const
           Double_t Px() const
           Double_t Py() const
           Double_t Pz() const
               void SetX(Double_t x)
               void SetY(Double_t y)
               void SetZ(Double_t z)
               void SetXYZ(Double_t x, Double_t y, Double_t z)
               void GetXYZ(Double_t* carray) const
               void GetXYZ(Float_t* carray) const
           Double_t Phi() const
           Double_t Theta() const
           Double_t CosTheta() const
           Double_t Mag2() const
           Double_t Mag() const
               void SetPhi(Double_t ph)
               void SetTheta(Double_t th)
               void SetMag(Double_t ma)
           Double_t Perp2() const
           Double_t Pt() const
           Double_t Perp() const
               void SetPerp(Double_t r)
           Double_t Perp2(const TVector3& p) const
           Double_t Pt(const TVector3& p) const
           Double_t Perp(const TVector3& p) const
           Double_t DeltaPhi(const TVector3& v) const
           Double_t DeltaR(const TVector3& v) const
           Double_t DrEtaPhi(const TVector3& v) const
           TVector2 EtaPhiVector() const
               void SetMagThetaPhi(Double_t mag, Double_t theta, Double_t phi)
          TVector3& operator=(const TVector3& p)
             Bool_t operator==(const TVector3& v) const
             Bool_t operator!=(const TVector3& v) const
          TVector3& operator+=(const TVector3& p)
          TVector3& operator-=(const TVector3& p)
           TVector3 operator-() const
          TVector3& operator*=(Double_t a)
           TVector3 Unit() const
           TVector3 Orthogonal() const
           Double_t Dot(const TVector3& p) const
           TVector3 Cross(const TVector3& p) const
           Double_t Angle(const TVector3& q) const
           Double_t Eta() const
          TVector3& operator*=(const TRotation&)
           TVector2 XYvector() const
            TClass* Class()
            TClass* IsA() const
               void ShowMembers(TMemberInspector& insp, char* parent)
               void StreamerNVirtual(TBuffer& b)

Author: Pasha Murat, Peter Malzacher 12/02/99
Last update: root/physics:$Name: $:$Id: TVector3.cxx,v 1.8 2004/04/29 17:43:59 brun Exp $

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