ROOT 6.10/09 Reference Guide |
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:
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 embedding 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:
Translation: Inverse translation:
Scale: Inverse scale:
where:
rij
are the 3x3 rotation matrix components,tx
, ty
, tz
are the translation componentssx
, sy
, sz
are arbitrary scale constants on each 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.
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.
These allow correct conversion also for reflections.
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 :
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.
Represent a (dx,dy,dz) translation. Data members: Double_t fTranslation[3]. Translations can be added/subtracted.
Represent a pure rotation. Data members: Double_t fRotationMatrix[3*3]. Rotations can be defined either by Euler angles, either, by GEANT3 angles :
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.
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.
Represent a scale shrinking/enlargement. Data members :Double_t fScale[3]. Not fully implemented yet.
Represent a rotation followed by a translation. Data members: Double_t fTranslation[3], TGeoRotation *fRotation.
Combined transformations including a scale. Not implemented.
A generic singleton matrix representing a identity transformation NOTE: identified by the global variable gGeoIdentity.
Definition at line 38 of file TGeoMatrix.h.
Public Types | |
enum | EGeoTransfTypes { kGeoIdentity = 0, kGeoShared = BIT(14), kGeoTranslation = BIT(17), kGeoRotation = BIT(18), kGeoScale = BIT(19), kGeoReflection = BIT(20), kGeoRegistered = BIT(21), kGeoSavePrimitive = BIT(22), kGeoMatrixOwned = BIT(23), kGeoCombiTrans = kGeoTranslation | kGeoRotation, kGeoGenTrans = kGeoTranslation | kGeoRotation | kGeoScale } |
Public Types inherited from TObject | |
enum | { kIsOnHeap = 0x01000000, kNotDeleted = 0x02000000, kZombie = 0x04000000, kBitMask = 0x00ffffff } |
enum | { kSingleKey = BIT(0), kOverwrite = BIT(1), kWriteDelete = BIT(2) } |
enum | EStatusBits { kCanDelete = BIT(0), kMustCleanup = BIT(3), kObjInCanvas = BIT(3), kIsReferenced = BIT(4), kHasUUID = BIT(5), kCannotPick = BIT(6), kNoContextMenu = BIT(8), kInvalidObject = BIT(13) } |
Public Member Functions | |
TGeoMatrix () | |
dummy constructor More... | |
TGeoMatrix (const char *name) | |
Constructor. More... | |
virtual | ~TGeoMatrix () |
Destructor. More... | |
virtual Int_t | GetByteCount () const |
Get total size in bytes of this. More... | |
void | GetHomogenousMatrix (Double_t *hmat) const |
The homogenous matrix associated with the transformation is used for piling up's and visualization. More... | |
char * | GetPointerName () const |
Provide a pointer name containing uid. More... | |
virtual const Double_t * | GetRotationMatrix () const =0 |
virtual const Double_t * | GetScale () const =0 |
virtual const Double_t * | GetTranslation () const =0 |
virtual TGeoMatrix & | Inverse () const =0 |
Bool_t | IsCombi () const |
Bool_t | IsGeneral () const |
Bool_t | IsIdentity () const |
Bool_t | IsReflection () const |
Bool_t | IsRegistered () const |
Bool_t | IsRotAboutZ () const |
Returns true if no rotation or the rotation is about Z axis. More... | |
Bool_t | IsRotation () const |
Bool_t | IsScale () const |
Bool_t | IsShared () const |
Bool_t | IsTranslation () const |
virtual void | LocalToMaster (const Double_t *local, Double_t *master) const |
convert a point by multiplying its column vector (x, y, z, 1) to matrix inverse More... | |
virtual void | LocalToMasterBomb (const Double_t *local, Double_t *master) const |
convert a point by multiplying its column vector (x, y, z, 1) to matrix inverse More... | |
virtual void | LocalToMasterVect (const Double_t *local, Double_t *master) const |
convert a vector by multiplying its column vector (x, y, z, 1) to matrix inverse More... | |
virtual TGeoMatrix * | MakeClone () const =0 |
virtual void | MasterToLocal (const Double_t *master, Double_t *local) const |
convert a point by multiplying its column vector (x, y, z, 1) to matrix More... | |
virtual void | MasterToLocalBomb (const Double_t *master, Double_t *local) const |
convert a point by multiplying its column vector (x, y, z, 1) to matrix More... | |
virtual void | MasterToLocalVect (const Double_t *master, Double_t *local) const |
convert a point by multiplying its column vector (x, y, z, 1) to matrix More... | |
TGeoMatrix & | operator* (const TGeoMatrix &right) const |
Multiplication. More... | |
TGeoMatrix & | operator= (const TGeoMatrix &matrix) |
Assignment operator. More... | |
Bool_t | operator== (const TGeoMatrix &other) const |
Is-equal operator. More... | |
void | Print (Option_t *option="") const |
print the matrix in 4x4 format More... | |
virtual void | ReflectX (Bool_t leftside, Bool_t rotonly=kFALSE) |
Multiply by a reflection respect to YZ. More... | |
virtual void | ReflectY (Bool_t leftside, Bool_t rotonly=kFALSE) |
Multiply by a reflection respect to ZX. More... | |
virtual void | ReflectZ (Bool_t leftside, Bool_t rotonly=kFALSE) |
Multiply by a reflection respect to XY. More... | |
virtual void | RegisterYourself () |
Register the matrix in the current manager, which will become the owner. More... | |
virtual void | RotateX (Double_t) |
virtual void | RotateY (Double_t) |
virtual void | RotateZ (Double_t) |
void | SetDefaultName () |
If no name was supplied in the ctor, the type of transformation is checked. More... | |
virtual void | SetDx (Double_t) |
virtual void | SetDy (Double_t) |
virtual void | SetDz (Double_t) |
void | SetShared (Bool_t flag=kTRUE) |
Public Member Functions inherited from TNamed | |
TNamed () | |
TNamed (const char *name, const char *title) | |
TNamed (const TString &name, const TString &title) | |
TNamed (const TNamed &named) | |
TNamed copy ctor. More... | |
virtual | ~TNamed () |
virtual void | Clear (Option_t *option="") |
Set name and title to empty strings (""). More... | |
virtual TObject * | Clone (const char *newname="") const |
Make a clone of an object using the Streamer facility. More... | |
virtual Int_t | Compare (const TObject *obj) const |
Compare two TNamed objects. More... | |
virtual void | Copy (TObject &named) const |
Copy this to obj. More... | |
virtual void | FillBuffer (char *&buffer) |
Encode TNamed into output buffer. More... | |
virtual const char * | GetName () const |
Returns name of object. More... | |
virtual const char * | GetTitle () const |
Returns title of object. More... | |
virtual ULong_t | Hash () const |
Return hash value for this object. More... | |
virtual Bool_t | IsSortable () const |
virtual void | ls (Option_t *option="") const |
List TNamed name and title. More... | |
TNamed & | operator= (const TNamed &rhs) |
TNamed assignment operator. More... | |
virtual void | SetName (const char *name) |
Set the name of the TNamed. More... | |
virtual void | SetNameTitle (const char *name, const char *title) |
Set all the TNamed parameters (name and title). More... | |
virtual void | SetTitle (const char *title="") |
Set the title of the TNamed. More... | |
virtual Int_t | Sizeof () const |
Return size of the TNamed part of the TObject. More... | |
Public Member Functions inherited from TObject | |
TObject () | |
TObject constructor. More... | |
TObject (const TObject &object) | |
TObject copy ctor. More... | |
virtual | ~TObject () |
TObject destructor. More... | |
void | AbstractMethod (const char *method) const |
Use this method to implement an "abstract" method that you don't want to leave purely abstract. More... | |
virtual void | AppendPad (Option_t *option="") |
Append graphics object to current pad. More... | |
virtual void | Browse (TBrowser *b) |
Browse object. May be overridden for another default action. More... | |
virtual const char * | ClassName () const |
Returns name of class to which the object belongs. More... | |
virtual void | Delete (Option_t *option="") |
Delete this object. More... | |
virtual Int_t | DistancetoPrimitive (Int_t px, Int_t py) |
Computes distance from point (px,py) to the object. More... | |
virtual void | Draw (Option_t *option="") |
Default Draw method for all objects. More... | |
virtual void | DrawClass () const |
Draw class inheritance tree of the class to which this object belongs. More... | |
virtual TObject * | DrawClone (Option_t *option="") const |
Draw a clone of this object in the current selected pad for instance with: gROOT->SetSelectedPad(gPad) . More... | |
virtual void | Dump () const |
Dump contents of object on stdout. More... | |
virtual void | Error (const char *method, const char *msgfmt,...) const |
Issue error message. More... | |
virtual void | Execute (const char *method, const char *params, Int_t *error=0) |
Execute method on this object with the given parameter string, e.g. More... | |
virtual void | Execute (TMethod *method, TObjArray *params, Int_t *error=0) |
Execute method on this object with parameters stored in the TObjArray. More... | |
virtual void | ExecuteEvent (Int_t event, Int_t px, Int_t py) |
Execute action corresponding to an event at (px,py). More... | |
virtual void | Fatal (const char *method, const char *msgfmt,...) const |
Issue fatal error message. More... | |
virtual TObject * | FindObject (const char *name) const |
Must be redefined in derived classes. More... | |
virtual TObject * | FindObject (const TObject *obj) const |
Must be redefined in derived classes. More... | |
virtual Option_t * | GetDrawOption () const |
Get option used by the graphics system to draw this object. More... | |
virtual const char * | GetIconName () const |
Returns mime type name of object. More... | |
virtual char * | GetObjectInfo (Int_t px, Int_t py) const |
Returns string containing info about the object at position (px,py). More... | |
virtual Option_t * | GetOption () const |
virtual UInt_t | GetUniqueID () const |
Return the unique object id. More... | |
virtual Bool_t | HandleTimer (TTimer *timer) |
Execute action in response of a timer timing out. More... | |
virtual void | Info (const char *method, const char *msgfmt,...) const |
Issue info message. More... | |
virtual Bool_t | InheritsFrom (const char *classname) const |
Returns kTRUE if object inherits from class "classname". More... | |
virtual Bool_t | InheritsFrom (const TClass *cl) const |
Returns kTRUE if object inherits from TClass cl. More... | |
virtual void | Inspect () const |
Dump contents of this object in a graphics canvas. More... | |
void | InvertBit (UInt_t f) |
virtual Bool_t | IsEqual (const TObject *obj) const |
Default equal comparison (objects are equal if they have the same address in memory). More... | |
virtual Bool_t | IsFolder () const |
Returns kTRUE in case object contains browsable objects (like containers or lists of other objects). More... | |
Bool_t | IsOnHeap () const |
Bool_t | IsZombie () const |
void | MayNotUse (const char *method) const |
Use this method to signal that a method (defined in a base class) may not be called in a derived class (in principle against good design since a child class should not provide less functionality than its parent, however, sometimes it is necessary). More... | |
virtual Bool_t | Notify () |
This method must be overridden to handle object notification. More... | |
void | Obsolete (const char *method, const char *asOfVers, const char *removedFromVers) const |
Use this method to declare a method obsolete. More... | |
void | operator delete (void *ptr) |
Operator delete. More... | |
void | operator delete[] (void *ptr) |
Operator delete []. More... | |
void * | operator new (size_t sz) |
void * | operator new (size_t sz, void *vp) |
void * | operator new[] (size_t sz) |
void * | operator new[] (size_t sz, void *vp) |
TObject & | operator= (const TObject &rhs) |
TObject assignment operator. More... | |
virtual void | Paint (Option_t *option="") |
This method must be overridden if a class wants to paint itself. More... | |
virtual void | Pop () |
Pop on object drawn in a pad to the top of the display list. More... | |
virtual Int_t | Read (const char *name) |
Read contents of object with specified name from the current directory. More... | |
virtual void | RecursiveRemove (TObject *obj) |
Recursively remove this object from a list. More... | |
void | ResetBit (UInt_t f) |
virtual void | SaveAs (const char *filename="", Option_t *option="") const |
Save this object in the file specified by filename. More... | |
virtual void | SavePrimitive (std::ostream &out, Option_t *option="") |
Save a primitive as a C++ statement(s) on output stream "out". More... | |
void | SetBit (UInt_t f, Bool_t set) |
Set or unset the user status bits as specified in f. More... | |
void | SetBit (UInt_t f) |
virtual void | SetDrawOption (Option_t *option="") |
Set drawing option for object. More... | |
virtual void | SetUniqueID (UInt_t uid) |
Set the unique object id. More... | |
virtual void | SysError (const char *method, const char *msgfmt,...) const |
Issue system error message. More... | |
Bool_t | TestBit (UInt_t f) const |
Int_t | TestBits (UInt_t f) const |
virtual void | UseCurrentStyle () |
Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked. More... | |
virtual void | Warning (const char *method, const char *msgfmt,...) const |
Issue warning message. More... | |
virtual Int_t | Write (const char *name=0, Int_t option=0, Int_t bufsize=0) |
Write this object to the current directory. More... | |
virtual Int_t | Write (const char *name=0, Int_t option=0, Int_t bufsize=0) const |
Write this object to the current directory. More... | |
Static Public Member Functions | |
static void | Normalize (Double_t *vect) |
Normalize a vector. More... | |
Static Public Member Functions inherited from TObject | |
static Long_t | GetDtorOnly () |
Return destructor only flag. More... | |
static Bool_t | GetObjectStat () |
Get status of object stat flag. More... | |
static void | SetDtorOnly (void *obj) |
Set destructor only flag. More... | |
static void | SetObjectStat (Bool_t stat) |
Turn on/off tracking of objects in the TObjectTable. More... | |
Protected Member Functions | |
TGeoMatrix (const TGeoMatrix &other) | |
copy constructor More... | |
Protected Member Functions inherited from TObject | |
virtual void | DoError (int level, const char *location, const char *fmt, va_list va) const |
Interface to ErrorHandler (protected). More... | |
void | MakeZombie () |
Additional Inherited Members | |
Protected Attributes inherited from TNamed | |
TString | fName |
TString | fTitle |
#include <TGeoMatrix.h>
Enumerator | |
---|---|
kGeoIdentity | |
kGeoShared | |
kGeoTranslation | |
kGeoRotation | |
kGeoScale | |
kGeoReflection | |
kGeoRegistered | |
kGeoSavePrimitive | |
kGeoMatrixOwned | |
kGeoCombiTrans | |
kGeoGenTrans |
Definition at line 41 of file TGeoMatrix.h.
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protected |
copy constructor
Definition at line 238 of file TGeoMatrix.cxx.
TGeoMatrix::TGeoMatrix | ( | ) |
dummy constructor
Definition at line 231 of file TGeoMatrix.cxx.
TGeoMatrix::TGeoMatrix | ( | const char * | name | ) |
Constructor.
Definition at line 247 of file TGeoMatrix.cxx.
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virtual |
Destructor.
Definition at line 255 of file TGeoMatrix.cxx.
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virtual |
Get total size in bytes of this.
Definition at line 332 of file TGeoMatrix.cxx.
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
where Rij is the rotation matrix, (sx, sy, sz) is the scale transformation and (dx, dy, dz) is the translation.
Definition at line 364 of file TGeoMatrix.cxx.
char * TGeoMatrix::GetPointerName | ( | ) | const |
Provide a pointer name containing uid.
Definition at line 344 of file TGeoMatrix.cxx.
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pure virtual |
Implemented in TGeoHMatrix, TGeoIdentity, TGeoCombiTrans, TGeoScale, TGeoRotation, and TGeoTranslation.
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pure virtual |
Implemented in TGeoHMatrix, TGeoIdentity, TGeoGenTrans, TGeoCombiTrans, TGeoScale, TGeoRotation, and TGeoTranslation.
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pure virtual |
Implemented in TGeoHMatrix, TGeoIdentity, TGeoCombiTrans, TGeoScale, TGeoRotation, and TGeoTranslation.
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pure virtual |
Implemented in TGeoHMatrix, TGeoIdentity, TGeoGenTrans, TGeoCombiTrans, TGeoScale, TGeoRotation, and TGeoTranslation.
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inline |
Definition at line 81 of file TGeoMatrix.h.
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inline |
Definition at line 83 of file TGeoMatrix.h.
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inline |
Definition at line 75 of file TGeoMatrix.h.
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inline |
Definition at line 78 of file TGeoMatrix.h.
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inline |
Definition at line 85 of file TGeoMatrix.h.
Bool_t TGeoMatrix::IsRotAboutZ | ( | ) | const |
Returns true if no rotation or the rotation is about Z axis.
Definition at line 319 of file TGeoMatrix.cxx.
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inline |
Definition at line 77 of file TGeoMatrix.h.
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inline |
Definition at line 79 of file TGeoMatrix.h.
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inline |
Definition at line 80 of file TGeoMatrix.h.
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inline |
Definition at line 76 of file TGeoMatrix.h.
convert a point by multiplying its column vector (x, y, z, 1) to matrix inverse
Reimplemented in TGeoIdentity, TGeoScale, TGeoRotation, and TGeoTranslation.
Definition at line 389 of file TGeoMatrix.cxx.
convert a point by multiplying its column vector (x, y, z, 1) to matrix inverse
Reimplemented in TGeoIdentity, TGeoRotation, and TGeoTranslation.
Definition at line 430 of file TGeoMatrix.cxx.
convert a vector by multiplying its column vector (x, y, z, 1) to matrix inverse
Reimplemented in TGeoIdentity, TGeoScale, TGeoRotation, and TGeoTranslation.
Definition at line 413 of file TGeoMatrix.cxx.
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pure virtual |
Implemented in TGeoHMatrix, TGeoIdentity, TGeoGenTrans, TGeoCombiTrans, TGeoScale, TGeoRotation, and TGeoTranslation.
convert a point by multiplying its column vector (x, y, z, 1) to matrix
Reimplemented in TGeoIdentity, TGeoScale, TGeoRotation, and TGeoTranslation.
Definition at line 456 of file TGeoMatrix.cxx.
convert a point by multiplying its column vector (x, y, z, 1) to matrix
Reimplemented in TGeoIdentity, TGeoRotation, and TGeoTranslation.
Definition at line 498 of file TGeoMatrix.cxx.
convert a point by multiplying its column vector (x, y, z, 1) to matrix
Reimplemented in TGeoIdentity, TGeoScale, TGeoRotation, and TGeoTranslation.
Definition at line 481 of file TGeoMatrix.cxx.
Normalize a vector.
Definition at line 523 of file TGeoMatrix.cxx.
TGeoMatrix & TGeoMatrix::operator* | ( | const TGeoMatrix & | right | ) | const |
Multiplication.
Definition at line 280 of file TGeoMatrix.cxx.
TGeoMatrix & TGeoMatrix::operator= | ( | const TGeoMatrix & | matrix | ) |
Assignment operator.
Definition at line 268 of file TGeoMatrix.cxx.
Bool_t TGeoMatrix::operator== | ( | const TGeoMatrix & | other | ) | const |
Is-equal operator.
Definition at line 291 of file TGeoMatrix.cxx.
print the matrix in 4x4 format
Reimplemented from TNamed.
Definition at line 536 of file TGeoMatrix.cxx.
Multiply by a reflection respect to YZ.
Reimplemented in TGeoHMatrix, TGeoCombiTrans, TGeoScale, and TGeoRotation.
Definition at line 554 of file TGeoMatrix.cxx.
Multiply by a reflection respect to ZX.
Reimplemented in TGeoHMatrix, TGeoCombiTrans, TGeoScale, and TGeoRotation.
Definition at line 561 of file TGeoMatrix.cxx.
Multiply by a reflection respect to XY.
Reimplemented in TGeoHMatrix, TGeoCombiTrans, TGeoScale, and TGeoRotation.
Definition at line 568 of file TGeoMatrix.cxx.
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virtual |
Register the matrix in the current manager, which will become the owner.
Reimplemented in TGeoCombiTrans.
Definition at line 575 of file TGeoMatrix.cxx.
Reimplemented in TGeoHMatrix, TGeoCombiTrans, TGeoRotation, and TGeoTranslation.
Definition at line 104 of file TGeoMatrix.h.
Reimplemented in TGeoHMatrix, TGeoCombiTrans, TGeoRotation, and TGeoTranslation.
Definition at line 105 of file TGeoMatrix.h.
Reimplemented in TGeoHMatrix, TGeoCombiTrans, TGeoRotation, and TGeoTranslation.
Definition at line 106 of file TGeoMatrix.h.
void TGeoMatrix::SetDefaultName | ( | ) |
If no name was supplied in the ctor, the type of transformation is checked.
A letter will be prepended to the name :
Definition at line 598 of file TGeoMatrix.cxx.
Reimplemented in TGeoHMatrix, TGeoCombiTrans, and TGeoTranslation.
Definition at line 112 of file TGeoMatrix.h.
Reimplemented in TGeoHMatrix, TGeoCombiTrans, and TGeoTranslation.
Definition at line 113 of file TGeoMatrix.h.
Reimplemented in TGeoHMatrix, TGeoCombiTrans, and TGeoTranslation.
Definition at line 114 of file TGeoMatrix.h.
Definition at line 115 of file TGeoMatrix.h.