TRotation

class description - source file - inheritance tree

class TRotation : public TObject


    protected:

      TRotation TRotation(Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t)

    public:

                    TRotation TRotation()
                    TRotation TRotation(const TRotation&)
                    TRotation operator*(const TRotation&) const
                    TRotation Inverse() const
                         void ~TRotation()
                         void AngleAxis(Double_t&, TVector3&) const
               static TClass* Class()
                   TRotation& Invert()
              virtual TClass* IsA() const
                       Bool_t IsIdentity() const
                       Bool_t operator!=(const TRotation& m) const
                     Double_t operator()(int, int) const
                     TVector3 operator*(const TVector3& p) const
                   TRotation& operator*=(const TRotation& m)
                   TRotation& operator=(const TRotation& m)
                       Bool_t operator==(const TRotation& m) const
      TRotation::TRotationRow operator[](int i) const
                     Double_t PhiX() const
                     Double_t PhiY() const
                     Double_t PhiZ() const
                   TRotation& Rotate(Double_t, const TVector3&)
                   TRotation& Rotate(Double_t psi, const TVector3* p)
                   TRotation& RotateAxes(const TVector3& newX, const TVector3& newY, const TVector3& newZ)
                   TRotation& RotateX(Double_t)
                   TRotation& RotateY(Double_t)
                   TRotation& RotateZ(Double_t)
                 virtual void ShowMembers(TMemberInspector& insp, char* parent)
                 virtual void Streamer(TBuffer& b)
                     Double_t ThetaX() const
                     Double_t ThetaY() const
                     Double_t ThetaZ() const
                   TRotation& Transform(const TRotation& m)
                     Double_t XX() const
                     Double_t XY() const
                     Double_t XZ() const
                     Double_t YX() const
                     Double_t YY() const
                     Double_t YZ() const
                     Double_t ZX() const
                     Double_t ZY() const
                     Double_t ZZ() const

  Data Members

    protected:

      Double_t fxx  
      Double_t fxy  
      Double_t fxz  
      Double_t fyx  
      Double_t fyy  
      Double_t fyz  
      Double_t fzx  
      Double_t fzy  
      Double_t fzz

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/             *
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

/*

TRotation

The TRotation class describes a rotation of objects of the TVector3 class. It is a 3*3 matrix of Double_t:

| xx xy xz |
| yx yy yz |
| zx zy zz |

It describes a socalled active rotation, i.e. rotation of objects inside a static system of coordinates. In case you want to rotate the frame and want to know the coordinates of objects in the rotated system, you should apply the inverse rotation to the objects. If you want to transform coordinates from the rotated frame to the original frame you have to apply the direct transformation.

A rotation around a specified axis means counterclockwise rotation around the positive direction of the axis.

Declaration, Access, Comparisons

TRotation r; // r initialized as identity
TRotation m(r); // m = r

There is no direct way to to set the matrix elements - to ensure that a TRotation object always describes a real rotation. But you can get the values by the member functions XX()..ZZ() or the (,) operator:

Double_t xx = r.XX(); // the same as xx=r(0,0)
xx = r(0,0);

if (r==m) {...} // test for equality
if (r!=m) {..} // test for inequality
if (r.IsIdentity()) {...} // test for identity

Rotation around axes

The following matrices desrcibe counterclockwise rotations around coordinate axes

| 1 0 0 |
Rx(a) = | 1 cos(a) -sin(a) |
| 0 sin(a) cos(a) |

        | cos(a) 0 sin(a) |
Ry(a) = |   0     1    0   |
        | -sin(a) 0 cos(a) |

| cos(a) -sin(a) 0 |
Rz(a) = | cos(a) -sin(a) 0 |
| 0 0 1 |
and are implemented as member functions RotateX(), RotateY() and RotateZ():

r.RotateX(TMath::Pi()); // rotation around the x-axis

Rotation around arbitary axis

The member function Rotate() allows to rotate around an arbitary vector (not neccessary a unit one) and returns the result.

r.Rotate(TMath::Pi()/3,TVector3(3,4,5));

It is possible to find a unit vector and an angle, which describe the same rotation as the current one:

Double_t angle;
TVector3 axis;
r.GetAngleAxis(angle,axis);

Rotation of local axes

Member function RotateAxes() adds a rotation of local axes to the current rotation and returns the result:

TVector3 newX(0,1,0);
TVector3 newY(0,0,1);
TVector3 newZ(1,0,0);
a.RotateAxes(newX,newX,newZ);

Memberfunctions ThetaX(), ThetaY(), ThetaZ(), PhiX(), PhiY(),PhiZ() return azimuth and polar angles of the rotated axes:

Double_t tx,ty,tz,px,py,pz;
tx= a.ThetaX();
...
pz= a.PhiZ();

Inverse rotation

TRotation a,b;
...
b = a.Inverse(); // b is inverse of a, a is unchanged
b = a.Invert(); // invert a and set b = a

Compound Rotations

The operator * has been implemented in a way that follows the mathematical notation of a product of the two matrices which describe the two consecutiv rotations. Therefore the second rotation should be placed first:

r = r2 * r1;

Rotation of TVector3

The TRotation class provides an operator * which allows to express a rotation of a TVector3 analog to the mathematical notation

| x' | | xx xy xz | | x |
| y' | = | yx yy yz | | y |
| z' | | zx zy zz | | z |

e.g.:

TVector3 v(1,1,1);
v = r * v;

You can also use the Transform() member function or the operator *= of the
TVector3 class:

TVector3 v;
TRotation r;
v.Transform(r);
v *= r; //Attention v = r * v

*/

TRotation() : fxx(1.0), fxy(0.0), fxz(0.0), fyx(0.0), fyy(1.0), fyz(0.0), fzx(0.0), fzy(0.0), fzz(1.0)

TRotation(const TRotation & m) : fxx(m.fxx), fxy(m.fxy), fxz(m.fxz), fyx(m.fyx), fyy(m.fyy), fyz(m.fyz), fzx(m.fzx), fzy(m.fzy), fzz(m.fzz)

TRotation(Double_t mxx, Double_t mxy, Double_t mxz, Double_t myx, Double_t myy, Double_t myz, Double_t mzx, Double_t mzy, Double_t mzz) : fxx(mxx), fxy(mxy), fxz(mxz), fyx(myx), fyy(myy), fyz(myz), fzx(mzx), fzy(mzy), fzz(mzz)

Double_t PhiX() const

Double_t PhiY() const

Double_t PhiZ() const

Double_t ThetaX() const

Double_t ThetaY() const

Double_t ThetaZ() const

void AngleAxis(Double_t &angle, TVector3 &axis) const

Inline Functions

                       Double_t XX() const
                       Double_t XY() const
                       Double_t XZ() const
                       Double_t YX() const
                       Double_t YY() const
                       Double_t YZ() const
                       Double_t ZX() const
                       Double_t ZY() const
                       Double_t ZZ() const
        TRotation::TRotationRow operator[](int i) const
                       Double_t operator()(int, int) const
                     TRotation& operator=(const TRotation& m)
                         Bool_t operator==(const TRotation& m) const
                         Bool_t operator!=(const TRotation& m) const
                         Bool_t IsIdentity() const
                       TVector3 operator*(const TVector3& p) const
                      TRotation operator*(const TRotation&) const
                     TRotation& operator*=(const TRotation& m)
                     TRotation& Transform(const TRotation& m)
                      TRotation Inverse() const
                     TRotation& Invert()
                     TRotation& RotateX(Double_t)
                     TRotation& RotateY(Double_t)
                     TRotation& RotateZ(Double_t)
                     TRotation& Rotate(Double_t, const TVector3&)
                     TRotation& Rotate(Double_t psi, const TVector3* p)
                     TRotation& RotateAxes(const TVector3& newX, const TVector3& newY, const TVector3& newZ)
                        TClass* Class()
                        TClass* IsA() const
                           void ShowMembers(TMemberInspector& insp, char* parent)
                           void Streamer(TBuffer& b)
                           void ~TRotation()

Author: Peter Malzacher 19/06/99
Last update: root/physics:$Name: $:$Id: TRotation.cxx,v 1.1.1.1 2000/05/16 17:00:45 rdm Exp $

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