TGeoRotation

class TGeoRotation : public TGeoMatrix

    protected:

      void CheckMatrix()

    public:

                              TGeoRotation()
                              TGeoRotation(const TGeoRotation& other)
                              TGeoRotation(const TGeoMatrix& other)
                              TGeoRotation(const char* name)
                              TGeoRotation(const char* name, Double_t alpha, Double_t beta, Double_t gamma)
                              TGeoRotation(const char* name, Double_t theta1, Double_t phi1, Double_t theta2, Double_t phi2, Double_t theta3, Double_t phi3)
                      virtual ~TGeoRotation()
               static TClass* Class()
                 virtual void Clear(Option_t* option = "")
                     Double_t Determinant() const
                         void FastRotZ(Double_t* sincos)
                         void GetAngles(Double_t& theta1, Double_t& phi1, Double_t& theta2, Double_t& phi2, Double_t& theta3, Double_t& phi3) const
                         void GetInverse(Double_t* invmat) const
                     Double_t GetPhiRotation() const
      virtual const Double_t* GetRotationMatrix() const
      virtual const Double_t* GetScale() const
      virtual const Double_t* GetTranslation() const
          virtual TGeoMatrix& Inverse() const
              virtual TClass* IsA() const
                       Bool_t IsValid() const
                 virtual void LocalToMaster(const Double_t* local, Double_t* master) const
                 virtual void LocalToMasterBomb(const Double_t* local, Double_t* master) const
                 virtual void LocalToMasterVect(const Double_t* local, Double_t* master) const
                 virtual void MasterToLocal(const Double_t* master, Double_t* local) const
                 virtual void MasterToLocalBomb(const Double_t* master, Double_t* local) const
                 virtual void MasterToLocalVect(const Double_t* master, Double_t* local) const
                         void MultiplyBy(TGeoRotation* rot, Bool_t after = kTRUE)
                TGeoRotation& operator=(const TGeoMatrix& matrix)
                TGeoRotation& operator=(const TGeoRotation& other)
                 virtual void RotateX(Double_t angle)
                 virtual void RotateY(Double_t angle)
                 virtual void RotateZ(Double_t angle)
                 virtual void SavePrimitive(ofstream& out, Option_t* option)
                         void SetAngles(Double_t alpha, Double_t beta, Double_t gamma)
                         void SetAngles(Double_t theta1, Double_t phi1, Double_t theta2, Double_t phi2, Double_t theta3, Double_t phi3)
                         void SetMatrix(const Double_t* rot)
                         void SetRotation(const TGeoMatrix& other)
                 virtual void ShowMembers(TMemberInspector& insp, char* parent)
                 virtual void Streamer(TBuffer& b)
                         void StreamerNVirtual(TBuffer& b)

Data Members

    protected:

      Double_t fRotationMatrix[9]  rotation matrix

Class Description

 Geometrical transformation package.

   All geometrical transformations handled by the modeller are provided as a
 built-in package. This was designed to minimize memory requirements and
 optimize performance of point/vector master-to-local and local-to-master
 computation. We need to have in mind that a transformation in TGeo has 2
 major use-cases. The first one is for defining the placement of a volume
 with respect to its container reference frame. This frame will be called
 'master' and the frame of the positioned volume - 'local'. If T is a
 transformation used for positioning volume daughters, then:

          MASTER = T * LOCAL

   Therefore a local-to-master conversion will be performed by using T, while
 a master-to-local by using its inverse. The second use case is the computation
 of the global transformation of a given object in the geometry. Since the
 geometry is built as 'volumes-inside-volumes', this global transformation
 represent the pile-up of all local transformations in the corresponding
 branch. The conversion from the global reference frame and the given object
 is also called master-to-local, but it is handled by the manager class.
   A general homogenous transformation is defined as a 4x4 matrix embeeding
 a rotation, a translation and a scale. The advantage of this description
 is that each basic transformation can be represented as a homogenous matrix,
 composition being performed as simple matrix multiplication.
   Rotation:                      Inverse rotation:
         r11  r12  r13   0              r11  r21  r31   0
         r21  r22  r23   0              r12  r22  r32   0
         r31  r32  r33   0              r13  r23  r33   0
          0    0    0    1               0    0    0    1

   Translation:                   Inverse translation:
          1    0    0    tx               1    0    0   -tx
          0    1    0    ty               0    1    0   -ty
          0    0    1    tz               0    0    1   -tz
          0    0    0    1                0    0    0   1

   Scale:                         Inverse scale:
          sx   0    0    0              1/sx  0    0    0
          0    sy   0    0               0   1/sy  0    0
          0    0    sz   0               0    0   1/sz  0
          0    0    0    1               0    0    0    1

  where: rij are the 3x3 rotation matrix components,
         tx, ty, tz are the translation components
         sx, sy, sz are arbitrary scale constants on the eacks axis,

   The disadvantage in using this approach is that computation for 4x4 matrices
 is expensive. Even combining two translation would become a multiplication
 of their corresponding matrices, which is quite an undesired effect. On the
 other hand, it is not a good idea to store a translation as a block of 16
 numbers. We have therefore chosen to implement each basic transformation type
 as a class deriving from the same basic abstract class and handling its specific
 data and point/vector transformation algorithms.

 The base class TGeoMatrix defines abstract metods for:

 - translation, rotation and scale getters. Every derived class stores only
   its specific data, e.g. a translation stores an array of 3 doubles and a
   rotation an array of 9. However, asking which is the rotation array of a
   TGeoTranslation through the base TGeoMatrix interface is a legal operation.
   The answer in this case is a pointer to a global constant array representing
   an identity rotation.
      Double_t *TGeoMatrix::GetTranslation()
      Double_t *TGeoMatrix::GetRotation()
      Double_t *TGeoMatrix::GetScale()

 - MasterToLocal() and LocalToMaster() point and vector transformations :
      void      TGeoMatrix::MasterToLocal(const Double_t *master, Double_t *local)
      void      TGeoMatrix::LocalToMaster(const Double_t *local, Double_t *master)
      void      TGeoMatrix::MasterToLocalVect(const Double_t *master, Double_t *local)
      void      TGeoMatrix::LocalToMasterVect(const Double_t *local, Double_t *master)
   These allow correct conversion also for reflections.
 - Transformation type getters :
      Bool_t    TGeoMatrix::IsIdentity()
      Bool_t    TGeoMatrix::IsTranslation()
      Bool_t    TGeoMatrix::IsRotation()
      Bool_t    TGeoMatrix::IsScale()
      Bool_t    TGeoMatrix::IsCombi() (translation + rotation)
      Bool_t    TGeoMatrix::IsGeneral() (translation + rotation + scale)

   Combinations of basic transformations are represented by specific classes
 deriving from TGeoMatrix. In order to define a matrix as a combination of several
 others, a special class TGeoHMatrix is provided. Here is an example of matrix
 creation :

 Matrix creation example:

   root[0] TGeoRotation r1,r2;
           r1.SetAngles(90,0,30);        // rotation defined by Euler angles
           r2.SetAngles(90,90,90,180,0,0); // rotation defined by GEANT3 angles
           TGeoTranslation t1(-10,10,0);
           TGeoTranslation t2(10,-10,5);
           TGeoCombiTrans c1(t1,r1);
           TGeoCombiTrans c2(t2,r2);
           TGeoHMatrix h = c1 * c2; // composition is done via TGeoHMatrix class
   root[7] TGeoHMatrix *ph = new TGeoHMatrix(hm); // this is the one we want to
                                                // use for positioning a volume
   root[8] ph->Print();
           ...
           pVolume->AddNode(pVolDaughter,id,ph) // now ph is owned by the manager

 Rule for matrix creation:
  - unless explicitly used for positioning nodes (TGeoVolume::AddNode()) all
 matrices deletion have to be managed by users. Matrices passed to geometry
 have to be created by using new() operator and their deletion is done by
 TGeoManager class.

 Available geometrical transformations

   1. TGeoTranslation - represent a (dx,dy,dz) translation. Data members:
 Double_t fTranslation[3]. Translations can be added/subtracted.
         TGeoTranslation t1;
         t1->SetTranslation(-5,10,4);
         TGeoTranslation *t2 = new TGeoTranslation(4,3,10);
         t2->Subtract(&t1);

   2. Rotations - represent a pure rotation. Data members: Double_t fRotationMatrix[3*3].
 Rotations can be defined either by Euler angles, either, by GEANT3 angles :
         TGeoRotation *r1 = new TGeoRotation();
         r1->SetAngles(phi, theta, psi); // all angles in degrees
      This represent the composition of : first a rotation about Z axis with
      angle phi, then a rotation with theta about the rotated X axis, and
      finally a rotation with psi about the new Z axis.

         r1->SetAngles(th1,phi1, th2,phi2, th3,phi3)
      This is a rotation defined in GEANT3 style. Theta and phi are the spherical
      angles of each axis of the rotated coordinate system with respect to the
      initial one. This construction allows definition of malformed rotations,
      e.g. not orthogonal. A check is performed and an error message is issued
      in this case.

      Specific utilities : determinant, inverse.

   3. Scale transformations - represent a scale shrinking/enlargement. Data
      members :Double_t fScale[3]. Not fully implemented yet.

   4. Combined transformations - represent a rotation folowed by a translation.
      Data members: Double_t fTranslation[3], TGeoRotation *fRotation.
         TGeoRotation *rot = new TGeoRotation("rot",10,20,30);
         TGeoTranslation trans;
         ...
         TGeoCombiTrans *c1 = new TGeoCombiTrans(trans, rot);
         TGeoCombiTrans *c2 = new TGeoCombiTrans("somename",10,20,30,rot)

   5. TGeoGenTrans - combined transformations including a scale. Not implemented.
   6. TGeoIdentity - a generic singleton matrix representing a identity transformation
       NOTE: identified by the global variable gGeoIdentity.

 Default constructor.

 Copy ctor.

 Copy ctor.

 Named rotation constructor

 Default rotation constructor with Euler angles. Phi is the rotation angle about
 Z axis  and is done first, theta is the rotation about new Y and is done
 second, psi is the rotation angle about new Z and is done third. All angles are in
 degrees.

 Rotation constructor a la GEANT3. Angles theta(i), phi(i) are the polar and azimuthal
 angles of the (i) axis of the rotated system with respect to the initial non-rotated
 system.
   Example : the identity matrix (no rotation) is composed by
      theta1=90, phi1=0, theta2=90, phi2=90, theta3=0, phi3=0
   SetBit(kGeoRotation);

 Return a temporary inverse of this.

 Perform orthogonality test for rotation.

 reset data members

--- Returns rotation angle about Z axis in degrees.

 convert a point by multiplying its column vector (x, y, z, 1) to matrix inverse

 convert a point by multiplying its column vector (x, y, z, 1) to matrix

 Rotate about X axis of the master frame with angle expressed in degrees.

 Rotate about Y axis of the master frame with angle expressed in degrees.

 Rotate about Z axis of the master frame with angle expressed in degrees.

 Save a primitive as a C++ statement(s) on output stream "out".

 Copy rotation elements from other rotation matrix.

 Set matrix elements according to Euler angles

 Set matrix elements in the GEANT3 way

 Retreive rotation angles

 computes determinant of the rotation matrix

 performes an orthogonality check and finds if the matrix is a reflection
   Warning("CheckMatrix", "orthogonality check not performed yet");

 Get the inverse rotation matrix (which is simply the transpose)

Inline Functions

                   void ~TGeoRotation()
          TGeoRotation& operator=(const TGeoMatrix& matrix)
          TGeoRotation& operator=(const TGeoRotation& other)
                   void LocalToMasterVect(const Double_t* local, Double_t* master) const
                   void MasterToLocalVect(const Double_t* master, Double_t* local) const
                   void LocalToMasterBomb(const Double_t* local, Double_t* master) const
                   void MasterToLocalBomb(const Double_t* master, Double_t* local) const
                   void SetMatrix(const Double_t* rot)
        const Double_t* GetTranslation() const
        const Double_t* GetRotationMatrix() const
        const Double_t* GetScale() const
                TClass* Class()
                TClass* IsA() const
                   void ShowMembers(TMemberInspector& insp, char* parent)
                   void Streamer(TBuffer& b)
                   void StreamerNVirtual(TBuffer& b)