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.);
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
v3 = -v1;
v1 = v2+v3;
v1 += v3;
v1 = v1 - v3
v1 -= v3;
v1 *= 10;
v1 = 5*v2;
if(v1==v2) {...}
if(v1!=v2) {...}
TRotation m;
...
v1.transform(m);
v1 = m*v1;
v1 *= m; // Attention v1 = m*v1
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. END_HTML // #include "TVector3.h" #include "TRotation.h" #include "TMath.h" #include "TClass.h" ClassImp(TVector3) //______________________________________________________________________________ TVector3::TVector3(const TVector3 & p) : TObject(p), fX(p.fX), fY(p.fY), fZ(p.fZ) {} TVector3::TVector3(Double_t xx, Double_t yy, Double_t zz) : fX(xx), fY(yy), fZ(zz) {} TVector3::TVector3(const Double_t * x0) : fX(x0[0]), fY(x0[1]), fZ(x0[2]) {} TVector3::TVector3(const Float_t * x0) : fX(x0[0]), fY(x0[1]), fZ(x0[2]) {} TVector3::~TVector3() {} //______________________________________________________________________________ Double_t TVector3::operator () (int i) const { //dereferencing operator const switch(i) { case 0: return fX; case 1: return fY; case 2: return fZ; default: Error("operator()(i)", "bad index (%d) returning 0",i); } return 0.; } //______________________________________________________________________________ Double_t & TVector3::operator () (int i) { //dereferencing operator switch(i) { case 0: return fX; case 1: return fY; case 2: return fZ; default: Error("operator()(i)", "bad index (%d) returning &fX",i); } return fX; } //______________________________________________________________________________ TVector3 & TVector3::operator *= (const TRotation & m){ //multiplication operator return *this = m * (*this); } //______________________________________________________________________________ TVector3 & TVector3::Transform(const TRotation & m) { //transform this vector with a TRotation return *this = m * (*this); } //______________________________________________________________________________ Double_t TVector3::Angle(const TVector3 & q) const { // return the angle w.r.t. another 3-vector Double_t ptot2 = Mag2()*q.Mag2(); if(ptot2 <= 0) { return 0.0; } else { Double_t arg = Dot(q)/TMath::Sqrt(ptot2); if(arg > 1.0) arg = 1.0; if(arg < -1.0) arg = -1.0; return TMath::ACos(arg); } } //______________________________________________________________________________ Double_t TVector3::Mag() const { // return the magnitude (rho in spherical coordinate system) return TMath::Sqrt(Mag2()); } //______________________________________________________________________________ Double_t TVector3::Perp() const { //return the transverse component (R in cylindrical coordinate system) return TMath::Sqrt(Perp2()); } //______________________________________________________________________________ Double_t TVector3::Perp(const TVector3 & p) const { //return the transverse component (R in cylindrical coordinate system) return TMath::Sqrt(Perp2(p)); } //______________________________________________________________________________ Double_t TVector3::Phi() const { //return the azimuth angle. returns phi from -pi to pi return fX == 0.0 && fY == 0.0 ? 0.0 : TMath::ATan2(fY,fX); } //______________________________________________________________________________ Double_t TVector3::Theta() const { //return the polar angle return fX == 0.0 && fY == 0.0 && fZ == 0.0 ? 0.0 : TMath::ATan2(Perp(),fZ); } //______________________________________________________________________________ TVector3 TVector3::Unit() const { // return unit vector parallel to this. Double_t tot = Mag2(); TVector3 p(fX,fY,fZ); return tot > 0.0 ? p *= (1.0/TMath::Sqrt(tot)) : p; } //______________________________________________________________________________ void TVector3::RotateX(Double_t angle) { //rotate vector around X Double_t s = TMath::Sin(angle); Double_t c = TMath::Cos(angle); Double_t yy = fY; fY = c*yy - s*fZ; fZ = s*yy + c*fZ; } //______________________________________________________________________________ void TVector3::RotateY(Double_t angle) { //rotate vector around Y Double_t s = TMath::Sin(angle); Double_t c = TMath::Cos(angle); Double_t zz = fZ; fZ = c*zz - s*fX; fX = s*zz + c*fX; } //______________________________________________________________________________ void TVector3::RotateZ(Double_t angle) { //rotate vector around Z Double_t s = TMath::Sin(angle); Double_t c = TMath::Cos(angle); Double_t xx = fX; fX = c*xx - s*fY; fY = s*xx + c*fY; } //______________________________________________________________________________ void TVector3::Rotate(Double_t angle, const TVector3 & axis){ //rotate vector TRotation trans; trans.Rotate(angle, axis); operator*=(trans); } //______________________________________________________________________________ void TVector3::RotateUz(const TVector3& NewUzVector) { // NewUzVector must be normalized ! Double_t u1 = NewUzVector.fX; Double_t u2 = NewUzVector.fY; Double_t u3 = NewUzVector.fZ; Double_t up = u1*u1 + u2*u2; if (up) { up = TMath::Sqrt(up); Double_t px = fX, py = fY, pz = fZ; fX = (u1*u3*px - u2*py + u1*up*pz)/up; fY = (u2*u3*px + u1*py + u2*up*pz)/up; fZ = (u3*u3*px - px + u3*up*pz)/up; } else if (u3 < 0.) { fX = -fX; fZ = -fZ; } // phi=0 teta=pi else {}; } //______________________________________________________________________________ Double_t TVector3::PseudoRapidity() const { //Double_t m = Mag(); //return 0.5*log( (m+fZ)/(m-fZ) ); // guard against Pt=0 double cosTheta = CosTheta(); if (cosTheta*cosTheta < 1) return -0.5* TMath::Log( (1.0-cosTheta)/(1.0+cosTheta) ); Warning("PseudoRapidity","transvers momentum = 0! return +/- 10e10"); if (fZ > 0) return 10e10; else return -10e10; } //______________________________________________________________________________ void TVector3::SetPtEtaPhi(Double_t pt, Double_t eta, Double_t phi) { //set Pt, Eta and Phi Double_t apt = TMath::Abs(pt); SetXYZ(apt*TMath::Cos(phi), apt*TMath::Sin(phi), apt/TMath::Tan(2.0*TMath::ATan(TMath::Exp(-eta))) ); } //______________________________________________________________________________ void TVector3::SetPtThetaPhi(Double_t pt, Double_t theta, Double_t phi) { //set Pt, Theta and Phi fX = pt * TMath::Cos(phi); fY = pt * TMath::Sin(phi); Double_t tanTheta = TMath::Tan(theta); fZ = tanTheta ? pt / tanTheta : 0; } //______________________________________________________________________________ void TVector3::SetTheta(Double_t th) { // Set theta keeping mag and phi constant (BaBar). Double_t ma = Mag(); Double_t ph = Phi(); SetX(ma*TMath::Sin(th)*TMath::Cos(ph)); SetY(ma*TMath::Sin(th)*TMath::Sin(ph)); SetZ(ma*TMath::Cos(th)); } //______________________________________________________________________________ void TVector3::SetPhi(Double_t ph) { // Set phi keeping mag and theta constant (BaBar). Double_t xy = Perp(); SetX(xy*TMath::Cos(ph)); SetY(xy*TMath::Sin(ph)); } //______________________________________________________________________________ Double_t TVector3::DeltaR(const TVector3 & v) const { //return deltaR with respect to v Double_t deta = Eta()-v.Eta(); Double_t dphi = TVector2::Phi_mpi_pi(Phi()-v.Phi()); return TMath::Sqrt( deta*deta+dphi*dphi ); } //______________________________________________________________________________ void TVector3::SetMagThetaPhi(Double_t mag, Double_t theta, Double_t phi) { //setter with mag, theta, phi Double_t amag = TMath::Abs(mag); fX = amag * TMath::Sin(theta) * TMath::Cos(phi); fY = amag * TMath::Sin(theta) * TMath::Sin(phi); fZ = amag * TMath::Cos(theta); } //______________________________________________________________________________ void TVector3::Streamer(TBuffer &R__b) { // Stream an object of class TVector3. if (R__b.IsReading()) { UInt_t R__s, R__c; Version_t R__v = R__b.ReadVersion(&R__s, &R__c); if (R__v > 2) { R__b.ReadClassBuffer(TVector3::Class(), this, R__v, R__s, R__c); return; } //====process old versions before automatic schema evolution if (R__v < 2) TObject::Streamer(R__b); R__b >> fX; R__b >> fY; R__b >> fZ; R__b.CheckByteCount(R__s, R__c, TVector3::IsA()); //====end of old versions } else { R__b.WriteClassBuffer(TVector3::Class(),this); } } TVector3 operator + (const TVector3 & a, const TVector3 & b) { return TVector3(a.X() + b.X(), a.Y() + b.Y(), a.Z() + b.Z()); } TVector3 operator - (const TVector3 & a, const TVector3 & b) { return TVector3(a.X() - b.X(), a.Y() - b.Y(), a.Z() - b.Z()); } TVector3 operator * (const TVector3 & p, Double_t a) { return TVector3(a*p.X(), a*p.Y(), a*p.Z()); } TVector3 operator * (Double_t a, const TVector3 & p) { return TVector3(a*p.X(), a*p.Y(), a*p.Z()); } Double_t operator * (const TVector3 & a, const TVector3 & b) { return a.Dot(b); } TVector3 operator * (const TMatrix & m, const TVector3 & v ) { return TVector3( m(0,0)*v.X()+m(0,1)*v.Y()+m(0,2)*v.Z(), m(1,0)*v.X()+m(1,1)*v.Y()+m(1,2)*v.Z(), m(2,0)*v.X()+m(2,1)*v.Y()+m(2,2)*v.Z()); } //const TVector3 kXHat(1.0, 0.0, 0.0); //const TVector3 kYHat(0.0, 1.0, 0.0); //const TVector3 kZHat(0.0, 0.0, 1.0); void TVector3::Print(Option_t*)const { //print vector parameters Printf("%s %s (x,y,z)=(%f,%f,%f) (rho,theta,phi)=(%f,%f,%f)",GetName(),GetTitle(),X(),Y(),Z(), Mag(),Theta()*TMath::RadToDeg(),Phi()*TMath::RadToDeg()); }