TGeoMatrix

class TGeoMatrix : public TNamed

    public:

                      virtual ~TGeoMatrix()
               static TClass* Class()
                virtual Int_t GetByteCount() const
                         void GetHomogenousMatrix(Double_t* hmat) 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 IsCombi() const
                       Bool_t IsGeneral() const
                       Bool_t IsIdentity() const
                       Bool_t IsReflection() const
                       Bool_t IsRegistered() const
                       Bool_t IsRotAboutZ() const
                       Bool_t IsRotation() const
                       Bool_t IsScale() const
                       Bool_t IsTranslation() 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
                  TGeoMatrix& operator*(const TGeoMatrix& right) const
                  TGeoMatrix& operator=(const TGeoMatrix& matrix)
                       Bool_t operator==(const TGeoMatrix& other) const
                 virtual void Print(Option_t* option) const
                 virtual void RegisterYourself()
                 virtual void RotateX(Double_t)
                 virtual void RotateY(Double_t)
                 virtual void RotateZ(Double_t)
                         void SetDefaultName()
                 virtual void ShowMembers(TMemberInspector& insp, char* parent)
                 virtual void Streamer(TBuffer& b)
                         void StreamerNVirtual(TBuffer& b)

Data Members

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    0               1    0    0    0
          0    1    0    0               0    1    0    0
          0    0    1    0               0    0    1    0
          tx   ty   tz   1              -tx  -ty  -tz   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.

 Destructor

 Returns true if no rotation or the rotation is about Z axis

 Get total size in bytes of this

 The homogenous matrix associated with the transformation is used for
 piling up's and visualization. A homogenous matrix is a 4*4 array
 containing the translation, the rotation and the scale components

          | R00*sx  R01    R02    dx |
          | R10    R11*sy  R12    dy |
          | R20     R21   R22*sz  dz |
          |  0       0      0      1 |

   where Rij is the rotation matrix, (sx, sy, sz) is the scale
 transformation and (dx, dy, dz) is the translation.

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

 convert a vector 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 inverse

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

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

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

 print the matrix in 4x4 format

 If no name was supplied in the ctor, the type of transformation is checked.
 A letter will be prepended to the name :
   t - translation
   r - rotation
   s - scale
   c - combi (translation + rotation)
   g - general (tr+rot+scale)
 The index of the transformation in gGeoManager list of transformations will
 be appended.

Inline Functions

            TGeoMatrix& operator=(const TGeoMatrix& matrix)
            TGeoMatrix& operator*(const TGeoMatrix& right) const
                 Bool_t operator==(const TGeoMatrix& other) const
                 Bool_t IsIdentity() const
                 Bool_t IsTranslation() const
                 Bool_t IsRotation() const
                 Bool_t IsReflection() const
                 Bool_t IsScale() const
                 Bool_t IsCombi() const
                 Bool_t IsGeneral() const
                 Bool_t IsRegistered() const
        const Double_t* GetTranslation() const
        const Double_t* GetRotationMatrix() const
        const Double_t* GetScale() const
            TGeoMatrix& Inverse() const
                   void RotateX(Double_t)
                   void RotateY(Double_t)
                   void RotateZ(Double_t)
                TClass* Class()
                TClass* IsA() const
                   void ShowMembers(TMemberInspector& insp, char* parent)
                   void Streamer(TBuffer& b)
                   void StreamerNVirtual(TBuffer& b)