class AliITSgeomMatrix: public TObject

 The Default constructor for the AliITSgeomMatrix class. By Default
 the angles of rotations are set to zero, meaning that the rotation
 matrix is the unit matrix. The translation vector is also set to
 zero as are the module id number. The detector type is set to -1
 (an undefined value). The full rotation matrix is kept so that
 the evaluation  of a coordinate transformation can be done
 quickly and with a minimum of CPU overhead. The basic coordinate
 systems are the ALICE global coordinate system and the detector
 local coordinate system. In general this structure is not limited
 to just those two coordinate systems.

 Inputs:
    none.
 Outputs:
    none.
 Return:
    A default constructes AliITSgeomMatrix class.

 fShapeIndex was)
 The standard Copy constructor. This make a full / proper copy of
 this class.
 Inputs:
    AliITSgeomMatrix &source   The source of this copy
 Outputs:
    none.
 Return:
    A copy constructes AliITSgeomMatrix class.

 The standard = operator. This make a full / proper copy of
 this class.
 The standard Copy constructor. This make a full / proper copy of
 this class.
 Inputs:
    AliITSgeomMatrix &source   The source of this copy
 Outputs:
    none.
 Return:
    A copy of the source AliITSgeomMatrix class.

 This is a constructor for the AliITSgeomMatrix class. The matrix is
 defined by 3 standard rotation angles [radians], and the translation
 vector tran [cm]. In addition the layer, ladder, and detector number
 for this particular module and the type of module must be given.
 The full rotation matrix is kept so that the evaluation
 of a coordinate transformation can be done quickly and with a minimum
 of CPU overhead. The basic coordinate systems are the ALICE global
 coordinate system and the detector local coordinate system. In general
 this structure is not limited to just those two coordinate systems.

 Inputs:
    Int_t idt        The detector index value
    Int_t id[3]      The layer, ladder, and detector numbers
    Double_t rot[3]  The 3 Cartician rotaion angles [radians]
    Double_t tran[3] The 3 Cartician translation distnaces
 Outputs:
    none.
 Return:
    A properly inilized AliITSgeomMatrix class.

 This is a constructor for the AliITSgeomMatrix class. The
 rotation matrix is given as one of the inputs, and the
 translation vector tran [cm]. In  addition the layer, ladder,
 and detector number for this particular module and the type of
 module must be given. The full rotation matrix is kept so that
 the evaluation of a coordinate transformation can be done quickly
 and with a minimum of CPU overhead. The basic coordinate systems
 are the ALICE global coordinate system and the detector local
 coordinate system. In general this structure is not limited to just
 those two coordinate systems.

 Inputs:
    Int_t idt          The detector index value
    Int_t id[3]        The layer, ladder, and detector numbers
    Double_t rot[3][3] The 3x3 Cartician rotaion matrix
    Double_t tran[3]   The 3 Cartician translation distnaces
 Outputs:
    none.
 Return:
    A properly inilized AliITSgeomMatrix class.

 This function returns the 6 GEANT 3.21 rotation angles [degrees] in
 the array ang which must be at least [6] long.
 Inputs:
   none.
 Outputs:
   Double_t ang[6]  The 6 Geant3.21 rotation angles. [degrees]
 Return:
   noting

 Given the 6 GEANT 3.21 rotation angles [degree], this will compute and
 set the rotations matrix and 3 standard rotation angles [radians].
 These angles and rotation matrix are overwrite the existing values in
 this class.
 Inputs:
   Double_t ang[6]  The 6 Geant3.21 rotation angles. [degrees]
 Outputs:
   none.
 Return:
   noting

 This is a constructor for the AliITSgeomMatrix class. The matrix
 is defined by the 6 GEANT 3.21 rotation angles [degrees], and
 the translation vector tran [cm]. In addition the layer, ladder,
 and detector number for this particular module and the type of
 module must be given. The full rotation matrix is kept so that
 the evaluation  of a coordinate transformation can be done
 quickly and with a minimum of CPU overhead. The basic coordinate
 systems are the ALICE global coordinate system and the detector
 local coordinate system. In general this structure is not limited
 to just those two coordinate systems.

 Inputs:
    Double_t rotd[6]  The 6 Geant 3.21 rotation angles [degrees]
    Int_t idt         The module Id number
    Int_t id[3]       The layer, ladder and detector number
    Double_t tran[3]  The translation vector

 Computes the angles from the rotation matrix up to a phase of
 180 degrees. The matrix used in AliITSgeomMatrix::MatrixFromAngle()
 and  its inverse AliITSgeomMatrix::AngleFromMatrix() are defined in
 the following ways, R = Rz*Ry*Rx (M=R*L+T) where
     1   0   0       Cy  0 +Sy       Cz -Sz  0
 Rx= 0   Cx -Sx  Ry=  0  1   0   Rz=+Sz  Cz  0
     0  +Sx  Cx     -Sy  0  Cy        0   0  1
 The choice of the since of S, comes from the choice between
 the rotation of the object or the coordinate system (view). I think
 that this choice is the first, the rotation of the object.
 Inputs:
   none
 Outputs:
   none
 Return:
   none

 Computes the Rotation matrix from the angles [radians] kept in this
 class. The matrix used in AliITSgeomMatrix::MatrixFromAngle() and
 its inverse AliITSgeomMatrix::AngleFromMatrix() are defined in
 the following ways, R = Rz*Ry*Rx (M=R*L+T) where
     1   0   0       Cy  0 +Sy       Cz -Sz  0
 Rx= 0   Cx -Sx  Ry=  0  1   0   Rz=+Sz  Cz  0
     0  +Sx  Cx     -Sy  0  Cy        0   0  1
 The choice of the since of S, comes from the choice between
 the rotation of the object or the coordinate system (view). I think
 that this choice is the first, the rotation of the object.
 Inputs:
   none
 Outputs:
   none
 Return:
   none

 Computes the Rotation matrix from the Euler angles [radians],
 Chi-convention, kept in this class. The matrix used in
 AliITSgeomMatrix::SetEulerAnglesChi and
 its inverse AliITSgeomMatrix::GetEulerAnglesChi() are defined in
 the following ways, R = Rb*Rc*Rd (M=R*L+T) where
     C2 +S2  0       1  0    0       C0 +S0  0
 Rb=-S2  C2  0  Rc=  0  C1 +S1   Rd=-S0  C0  0
     0   0   1       0 -S1  C1       0   0   1
 This form is taken from Wolfram Research's Geometry>
 Transformations>Rotations web page (also should be
 found in their book).
 Inputs:
   Double_t ang[3] The three Euler Angles Phi, Theta, Psi
 Outputs:
   none
 Return:
   none

 Returns the local coordinates given the global coordinates [cm].
 Inputs:
   Double_t g[3]   The position represented in the ALICE
                   global coordinate system
 Outputs:
   Double_t l[3]  The poistion represented in the local
                  detector coordiante system
 Return:
   none

 Returns the global coordinates given the local coordinates [cm].
 Inputs:
   Double_t l[3]   The poistion represented in the detector
                   local coordinate system
 Outputs:
   Double_t g[3]   The poistion represented in the ALICE
                   Global coordinate system
 Return:
   none.

 Returns the local coordinates of the momentum given the global
 coordinates of the momentum. It transforms just like GtoLPosition
 except that the translation vector is zero.
 Inputs:
   Double_t g[3] The momentum represented in the ALICE global
                 coordinate system
 Outputs:
   Double_t l[3] the momentum represented in the detector
                 local coordinate system
 Return:
   none.

 Returns the Global coordinates of the momentum given the local
 coordinates of the momentum. It transforms just like LtoGPosition
 except that the translation vector is zero.
 Inputs:
   Double_t l[3] the momentum represented in the detector
                 local coordinate system
 Outputs:
   Double_t g[3] The momentum represented in the ALICE global
                 coordinate system
 Return:
   none.

 Given an Uncertainty matrix in Global coordinates it is
 rotated so that  its representation in local coordinates can
 be returned. There is no effect due to the translation vector
 or its uncertainty.
 Inputs:
   Double_t g[3][3] The error matrix represented in the ALICE global
                    coordinate system
 Outputs:
   Double_t l[3][3] the error matrix represented in the detector
                    local coordinate system
 Return:
   none.

 Given an Uncertainty matrix in Local coordinates it is rotated so that
 its representation in global coordinates can be returned. There is no
 effect due to the translation vector or its uncertainty.
 Inputs:
   Double_t l[3][3] the error matrix represented in the detector
                    local coordinate system
 Outputs:
   Double_t g[3][3] The error matrix represented in the ALICE global
                    coordinate system
 Return:
   none.

 A slightly different coordinate system is used when tracking.
 This coordinate system is only relevant when the geometry represents
 the cylindrical ALICE ITS geometry. For tracking the Z axis is left
 alone but X -> -Y and Y -> X such that X always points out of the
 ITS Cylinder for every layer including layer 1 (where the detector
 are mounted upside down).

 Inputs:
   Double_t g[3]   The position represented in the ALICE
                   global coordinate system
 Outputs:
   Double_t l[3]  The poistion represented in the local
                  detector coordiante system
 Return:
   none

 A slightly different coordinate system is used when tracking.
 This coordinate system is only relevant when the geometry represents
 the cylindrical ALICE ITS geometry. For tracking the Z axis is left
 alone but X -> -Y and Y -> X such that X always points out of the
 ITS Cylinder for every layer including layer 1 (where the detector
 are mounted upside down).

 Inputs:
   Double_t l[3]   The poistion represented in the detector
                   local coordinate system
 Outputs:
   Double_t g[3]   The poistion represented in the ALICE
                   Global coordinate system
 Return:
   none.

 A slightly different coordinate system is used when tracking.
 This coordinate system is only relevant when the geometry represents
 the cylindrical ALICE ITS geometry. For tracking the Z axis is left
 alone but X -> -Y and Y -> X such that X always points out of the
 ITS Cylinder for every layer including layer 1 (where the detector
 are mounted upside down).

 Inputs:
   Double_t g[3] The momentum represented in the ALICE global
                 coordinate system
 Outputs:
   Double_t l[3] the momentum represented in the detector
                 local coordinate system
 Return:
   none.

 A slightly different coordinate system is used when tracking.
 This coordinate system is only relevant when the geometry represents
 the cylindrical ALICE ITS geometry. For tracking the Z axis is left
 alone but X -> -Y and Y -> X such that X always points out of the
 ITS Cylinder for every layer including layer 1 (where the detector
 are mounted upside down).

 Inputs:
   Double_t l[3] the momentum represented in the detector
                 local coordinate system
 Outputs:
   Double_t g[3] The momentum represented in the ALICE global
                 coordinate system
 Return:
   none.

 A slightly different coordinate system is used when tracking.
 This coordinate system is only relevant when the geometry represents
 the cylindrical ALICE ITS geometry. For tracking the Z axis is left
 alone but X -> -Y and Y -> X such that X always points out of the
 ITS Cylinder for every layer including layer 1 (where the detector
 are mounted upside down).

 Inputs:
   Double_t g[3][3] The error matrix represented in the ALICE global
                    coordinate system
 Outputs:
   Double_t l[3][3] the error matrix represented in the detector
                    local coordinate system
 Return:

 A slightly different coordinate system is used when tracking.
 This coordinate system is only relevant when the geometry represents
 the cylindrical ALICE ITS geometry. For tracking the Z axis is left
 alone but X -> -Y and Y -> X such that X always points out of the
 ITS Cylinder for every layer including layer 1 (where the detector
 are mounted upside down).

 Inputs:
   Double_t l[3][3] the error matrix represented in the detector
                    local coordinate system
 Outputs:
   Double_t g[3][3] The error matrix represented in the ALICE global
                    coordinate system
 Return:
   none.

 Standard output format for this class but it includes variable
 names and formatting that makes it easer to read.
 Inputs:
    ostream *os   The output stream to print the title on
 Outputs:
    none.
 Return:
    none.

  output format used by Print.
 Inputs:
    ostream *os   The output stream to print the comments on
 Outputs:
    none.
 Return:
    none.

 Standard output format for this class.
 Inputs:
    ostream *os   The output stream to print the class data on
 Outputs:
    none.
 Return:
    none.

 Standard input format for this class.
 Inputs:
    istream *is   The input stream to read on
 Outputs:
    none.
 Return:
    none.

 Stream an object of class AliITSgeomMatrix.
 Inputs:
     TBuffer &R__b   The output buffer to stream data on.
 Outputs:
    none.
 Return:
    none.

 Sets the translation vector and computes fCylR and fCylPhi.
 Inputs:
   Double_t trans[3]   The translation vector to be used
 Outputs:
   none.
 Return:
   none.

 This class is used as part of the documentation of this class
 Inputs:
   none.
 Outputs:
   none.
 Return:
   A pointer to a new TPolyLine3D object showing the 3 line
   segments that make up the this local axis in the global
   reference system.

 This class is used as part of the documentation of this class
 Inputs:
   none.
 Outputs:
   none.
 Return:
   A pointer to a new TPolyLine3D object showing the 3 line
   segments that make up the this local axis in the global
   reference system.

 Creates a node inside of the node mother out of the shape shape
 in the position, with respect to mother, indecated by "this". If axis
 is ture, it will insert an axis within this node/shape.
 Inputs:
   Char_t *nodeName  This name of this node
   Char_t *nodeTitle This node title
   TNode  *mother    The node this node will be inside of/with respect to
   TShape *shape     The shape of this node
   Bool_t axis       If ture, a set of x,y,z axis will be included
 Outputs:
   none.
 Return:
   A pointer to "this" node.

 make figures to help document this class
 Inputs:
   none.
 Outputs:
   none.
 Return:
   none.

 Prints a line describing the output format of the function Print.

 Prints out the content of this class in ASCII format.

 Reads in the content of this class in the format of Print

 Returns the geometry path corresponding to this transformation

 Sets the geometry path

 Given the rotation angles [radians] it fills frot and computes
 the rotation matrix fm.

 sets the rotation matrix and computes the rotation angles [radians]

 Sets the detector index value

 Sets the detector layer, ladder, detector (id) values.

 Returns the rotation angles [radians]

 Returns the translation vector [cm]

 Returns the translation vector in cylindrical
 coordinates [cm,radians]

 Returns the values of the rotation matrix

 Returns the detector index value.

 returns the modules index layer, ladder, detector

 return the x,y,z components (global) of the normalized normal
 vector which helps to define the plane the detector is a part of

 Computes the distance squared [cm^2] between a point t[3] and
 this module/detector