library: libGeom #include "TGeoMatrix.h"

# TGeoGenTrans

class description - source file - inheritance tree (.pdf)

## class TGeoGenTrans : public TGeoCombiTrans

| Inheritance Chart:

`TObject`

<-

`TNamed`

<-

`TGeoMatrix`

<-

`TGeoCombiTrans`

<-

`TGeoGenTrans`

        public:

                                  TGeoGenTrans()
                                  TGeoGenTrans(const char* name)
                                  TGeoGenTrans(Double_t dx, Double_t dy, Double_t dz, Double_t sx, Double_t sy, Double_t sz, TGeoRotation* rot)
                                  TGeoGenTrans(const char* name, Double_t dx, Double_t dy, Double_t dz, Double_t sx, Double_t sy, Double_t sz, TGeoRotation* rot)
                                  TGeoGenTrans(const TGeoGenTrans&)
                          virtual ~TGeoGenTrans()
                   static TClass* Class()
                     virtual void Clear(Option_t* option = "")
          virtual const Double_t* GetScale() const
              virtual TGeoMatrix& Inverse() const
                  virtual TClass* IsA() const
                           Bool_t Normalize()
                    TGeoGenTrans& operator=(const TGeoGenTrans&)
                             void SetScale(Double_t sx, Double_t sy, Double_t sz)
                             void SetScale(Double_t* scale)
                     virtual void ShowMembers(TMemberInspector& insp, char* parent)
                     virtual void Streamer(TBuffer& b)
                             void StreamerNVirtual(TBuffer& b)

### Data Members

        protected:

          Double_t fScale[3]  scale (x, y, z)

## 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.

TGeoGenTrans()

     dummy ctor

TGeoGenTrans(const char *name) :TGeoCombiTrans(name)

     ctor

TGeoGenTrans(Double_t dx, Double_t dy, Double_t dz, Double_t sx, Double_t sy, Double_t sz, TGeoRotation *rot) :TGeoCombiTrans("")

     ctor

TGeoGenTrans(const char *name, Double_t dx, Double_t dy, Double_t dz, Double_t sx, Double_t sy, Double_t sz, TGeoRotation *rot) :TGeoCombiTrans(name)

     ctor

~TGeoGenTrans()

     destructor

void Clear(Option_t *)

     clear the fields of this transformation

void SetScale(Double_t sx, Double_t sy, Double_t sz)

     set the scale

TGeoMatrix& Inverse() const

     Return a temporary inverse of this.

Bool_t Normalize()

     A scale transformation should be normalized by sx*sy*sz factor

### Inline Functions

                       void SetScale(Double_t* scale)
            const Double_t* GetScale() const
                    TClass* Class()
                    TClass* IsA() const
                       void ShowMembers(TMemberInspector& insp, char* parent)
                       void Streamer(TBuffer& b)
                       void StreamerNVirtual(TBuffer& b)
               TGeoGenTrans TGeoGenTrans(const TGeoGenTrans&)
              TGeoGenTrans& operator=(const TGeoGenTrans&)

Author: Andrei Gheata 25/10/01
Last update: root/geom:$Name: $:$Id: TGeoMatrix.cxx,v 1.39 2005/04/05 08:54:12 brun Exp $
Copyright (C) 1995-2000, Rene Brun and Fons Rademakers. *