TVector3.cxx

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// @(#)root/physics:$Id$
// Author: Pasha Murat, Peter Malzacher   12/02/99
//    Aug 11 1999: added Pt == 0 guard to Eta()
//    Oct  8 1999: changed Warning to Error and
//                 return fX in Double_t & operator()
//    Oct 20 1999: Bug fix: sign in PseudoRapidity
//                 Warning-> Error in Double_t operator()

//______________________________________________________________________________
//*-*-*-*-*-*-*-*-*-*-*-*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/             *
//*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
//BEGIN_HTML <!--
/* -->
<H2>
TVector3</H2>
<TT>TVector3</TT> is a general three vector class, which can be used for
the description of different vectors in 3D.
<H3>
Declaration / Access to the components</H3>
<TT>TVector3</TT> has been implemented as a vector of three <TT>Double_t</TT>
variables, representing the cartesian coordinates. By default all components
are initialized to zero:

<P><TT>&nbsp; TVector3 v1;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; //
v1 = (0,0,0)</TT>
<BR><TT>&nbsp; TVector3 v3(1,2,3); // v3 = (1,2,3)</TT>
<BR><TT>&nbsp; TVector3 v4(v2);&nbsp;&nbsp;&nbsp; // v4 = v2</TT>

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

<P>You can get the basic components either by name or by index using <TT>operator()</TT>:

<P><TT>&nbsp; xx = v1.X();&nbsp;&nbsp;&nbsp; or&nbsp;&nbsp;&nbsp; xx =
v1(0);</TT>
<BR><TT>&nbsp; yy = v1.Y();&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
yy = v1(1);</TT>
<BR><TT>&nbsp; zz = v1.Z();&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
zz = v1(2);</TT>

<P>The memberfunctions <TT>SetX()</TT>, <TT>SetY()</TT>, <TT>SetZ()</TT>
and<TT> SetXYZ()</TT> allow to set the components:

<P><TT>&nbsp; v1.SetX(1.); v1.SetY(2.); v1.SetZ(3.);</TT>
<BR><TT>&nbsp; v1.SetXYZ(1.,2.,3.);</TT>
<BR>&nbsp;
<H3>
Noncartesian coordinates</H3>
To get information on the <TT>TVector3</TT> in spherical (rho,phi,theta)
or cylindrical (z,r,theta) coordinates, the
<BR>the member functions <TT>Mag()</TT> (=magnitude=rho in spherical coordinates),
<TT>Mag2()</TT>, <TT>Theta()</TT>, <TT>CosTheta()</TT>, <TT>Phi()</TT>,
<TT>Perp()</TT> (the transverse component=r in cylindrical coordinates),
<TT>Perp2()</TT> can be used:

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

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

<P><TT>&nbsp; Double_t ppv1 = v.Perp(v1);</TT>
<BR><TT>&nbsp; Double_t pp2v1 = v.Perp2(v1);</TT>

<P>The pseudo-rapidity ( eta=-ln (tan (theta/2)) ) can be obtained by <TT>Eta()</TT>
or <TT>PseudoRapidity()</TT>:
<BR>&nbsp;
<BR><TT>&nbsp; Double_t eta = v.PseudoRapidity();</TT>

<P>There are set functions to change one of the noncartesian coordinates:

<P><TT>&nbsp; v.SetTheta(.5); // keeping rho and phi</TT>
<BR><TT>&nbsp; v.SetPhi(.8);&nbsp;&nbsp; // keeping rho and theta</TT>
<BR><TT>&nbsp; v.SetMag(10.);&nbsp; // keeping theta and phi</TT>
<BR><TT>&nbsp; v.SetPerp(3.);&nbsp; // keeping z and phi</TT>
<BR>&nbsp;
<H3>
Arithmetic / Comparison</H3>
The <TT>TVector3</TT> class provides the operators to add, subtract, scale and compare
vectors:

<P><TT>&nbsp; v3&nbsp; = -v1;</TT>
<BR><TT>&nbsp; v1&nbsp; = v2+v3;</TT>
<BR><TT>&nbsp; v1 += v3;</TT>
<BR><TT>&nbsp; v1&nbsp; = v1 - v3</TT>
<BR><TT>&nbsp; v1 -= v3;</TT>
<BR><TT>&nbsp; v1 *= 10;</TT>
<BR><TT>&nbsp; v1&nbsp; = 5*v2;</TT>

<P><TT>&nbsp; if(v1==v2) {...}</TT>
<BR><TT>&nbsp; if(v1!=v2) {...}</TT>
<BR>&nbsp;
<H3>
Related Vectors</H3>
<TT>&nbsp; v2 = v1.Unit();&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; // get unit
vector parallel to v1</TT>
<BR><TT>&nbsp; v2 = v1.Orthogonal(); // get vector orthogonal to v1</TT>
<H3>
Scalar and vector products</H3>
<TT>&nbsp; s = v1.Dot(v2);&nbsp;&nbsp; // scalar product</TT>
<BR><TT>&nbsp; s = v1 * v2;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; // scalar product</TT>
<BR><TT>&nbsp; v = v1.Cross(v2); // vector product</TT>
<H3>
&nbsp;Angle between two vectors</H3>
<TT>&nbsp; Double_t a = v1.Angle(v2);</TT>
<H3>
Rotations</H3>

<H5>
Rotation around axes</H5>
<TT>&nbsp; v.RotateX(.5);</TT>
<BR><TT>&nbsp; v.RotateY(TMath::Pi());</TT>
<BR><TT>&nbsp; v.RotateZ(angle);</TT>
<H5>
Rotation around a vector</H5>
<TT>&nbsp; v1.Rotate(TMath::Pi()/4, v2); // rotation around v2</TT>
<H5>
Rotation by TRotation</H5>
<TT>TVector3</TT> objects can be rotated by objects of the <TT>TRotation</TT>
class using the <TT>Transform()</TT> member functions,
<BR>the <TT>operator *=</TT> or the <TT>operator *</TT> of the TRotation
class:

<P><TT>&nbsp; TRotation m;</TT>
<BR><TT>&nbsp; ...</TT>
<BR><TT>&nbsp; v1.transform(m);</TT>
<BR><TT>&nbsp; v1 = m*v1;</TT>
<BR><TT>&nbsp; v1 *= m; // Attention v1 = m*v1</TT>
<H5>
Transformation from rotated frame</H5>
<TT>&nbsp; TVector3 direction = v.Unit()</TT>
<BR><TT>&nbsp; v1.RotateUz(direction); // direction must be TVector3 of
unit length</TT>

<P>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.

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// -->END_HTML
//

#include "TVector3.h"

#include "TBuffer.h"
#include "TRotation.h"
#include "TMath.h"
#include "TClass.h"

ClassImp(TVector3)

////////////////////////////////////////////////////////////////////////////////

TVector3::TVector3()
: fX(0.0), fY(0.0), fZ(0.0) {}

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() {}

////////////////////////////////////////////////////////////////////////////////
///dereferencing operator const

Double_t TVector3::operator () (int i) 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.;
}

////////////////////////////////////////////////////////////////////////////////
///dereferencing operator

Double_t & TVector3::operator () (int i) {
   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;
}

////////////////////////////////////////////////////////////////////////////////
///multiplication operator

TVector3 & TVector3::operator *= (const TRotation & m){
   return *this = m * (*this);
}

////////////////////////////////////////////////////////////////////////////////
///transform this vector with a TRotation

TVector3 & TVector3::Transform(const TRotation & m) {
   return *this = m * (*this);
}

////////////////////////////////////////////////////////////////////////////////
/// return the angle w.r.t. another 3-vector

Double_t TVector3::Angle(const TVector3 & q) const
{
   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);
   }
}

////////////////////////////////////////////////////////////////////////////////
/// return the magnitude (rho in spherical coordinate system)

Double_t TVector3::Mag() const
{
   return TMath::Sqrt(Mag2());
}

////////////////////////////////////////////////////////////////////////////////
///return the transverse component  (R in cylindrical coordinate system)

Double_t TVector3::Perp() const
{
   return TMath::Sqrt(Perp2());
}


////////////////////////////////////////////////////////////////////////////////
///return the transverse component (R in cylindrical coordinate system)

Double_t TVector3::Perp(const TVector3 & p) const
{
   return TMath::Sqrt(Perp2(p));
}

////////////////////////////////////////////////////////////////////////////////
///return the  azimuth angle. returns phi from -pi to pi

Double_t TVector3::Phi() const
{
   return fX == 0.0 && fY == 0.0 ? 0.0 : TMath::ATan2(fY,fX);
}

////////////////////////////////////////////////////////////////////////////////
///return the polar angle

Double_t TVector3::Theta() const
{
   return fX == 0.0 && fY == 0.0 && fZ == 0.0 ? 0.0 : TMath::ATan2(Perp(),fZ);
}

////////////////////////////////////////////////////////////////////////////////
/// return unit vector parallel to this.

TVector3 TVector3::Unit() const
{
   Double_t  tot2 = Mag2();
   Double_t tot = (tot2 > 0) ?  1.0/TMath::Sqrt(tot2) : 1.0;
   TVector3 p(fX*tot,fY*tot,fZ*tot);
   return p;
}

////////////////////////////////////////////////////////////////////////////////
///rotate vector around X

void TVector3::RotateX(Double_t angle) {
   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;
}

////////////////////////////////////////////////////////////////////////////////
///rotate vector around Y

void TVector3::RotateY(Double_t angle) {
   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;
}

////////////////////////////////////////////////////////////////////////////////
///rotate vector around Z

void TVector3::RotateZ(Double_t angle) {
   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;
}

////////////////////////////////////////////////////////////////////////////////
///rotate vector

void TVector3::Rotate(Double_t angle, const TVector3 & axis){
   TRotation trans;
   trans.Rotate(angle, axis);
   operator*=(trans);
}

////////////////////////////////////////////////////////////////////////////////
/// NewUzVector must be normalized !

void TVector3::RotateUz(const TVector3& NewUzVector) {
   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 m = Mag();
///return 0.5*log( (m+fZ)/(m-fZ) );
/// guard against Pt=0

Double_t TVector3::PseudoRapidity() const {
   double cosTheta = CosTheta();
   if (cosTheta*cosTheta < 1) return -0.5* TMath::Log( (1.0-cosTheta)/(1.0+cosTheta) );
   if (fZ == 0) return 0;
   Warning("PseudoRapidity","transvers momentum = 0! return +/- 10e10");
   if (fZ > 0) return 10e10;
   else        return -10e10;
}

////////////////////////////////////////////////////////////////////////////////
///set Pt, Eta and Phi

void TVector3::SetPtEtaPhi(Double_t pt, Double_t eta, Double_t 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))) );
}

////////////////////////////////////////////////////////////////////////////////
///set Pt, Theta and Phi

void TVector3::SetPtThetaPhi(Double_t pt, Double_t theta, Double_t phi) {
   fX = pt * TMath::Cos(phi);
   fY = pt * TMath::Sin(phi);
   Double_t tanTheta = TMath::Tan(theta);
   fZ = tanTheta ? pt / tanTheta : 0;
}

////////////////////////////////////////////////////////////////////////////////
/// Set theta keeping mag and phi constant (BaBar).

void TVector3::SetTheta(Double_t th)
{
   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));
}

////////////////////////////////////////////////////////////////////////////////
/// Set phi keeping mag and theta constant (BaBar).

void TVector3::SetPhi(Double_t ph)
{
   Double_t xy   = Perp();
   SetX(xy*TMath::Cos(ph));
   SetY(xy*TMath::Sin(ph));
}

////////////////////////////////////////////////////////////////////////////////
///return deltaR with respect to v

Double_t TVector3::DeltaR(const TVector3 & v) const
{
   Double_t deta = Eta()-v.Eta();
   Double_t dphi = TVector2::Phi_mpi_pi(Phi()-v.Phi());
   return TMath::Sqrt( deta*deta+dphi*dphi );
}

////////////////////////////////////////////////////////////////////////////////
///setter with mag, theta, phi

void TVector3::SetMagThetaPhi(Double_t mag, Double_t theta, Double_t 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);
}

////////////////////////////////////////////////////////////////////////////////
/// Stream an object of class TVector3.

void TVector3::Streamer(TBuffer &R__b)
{
   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());
}