// @(#)root/geom:$Name:  $:$Id: TGeoMatrix.cxx,v 1.20 2004/02/10 08:56:20 brun Exp $
// Author: Andrei Gheata   25/10/01

/*************************************************************************
 * Copyright (C) 1995-2000, Rene Brun and Fons Rademakers.               *
 * All rights reserved.                                                  *
 *                                                                       *
 * For the licensing terms see $ROOTSYS/LICENSE.                         *
 * For the list of contributors see $ROOTSYS/README/CREDITS.             *
 *************************************************************************/
// Author : Andrei Gheata - Wed 24 Oct 2001 09:46:13 AM CEST

////////////////////////////////////////////////////////////////////////////////
// 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.
//
//Begin_Html
/*
<img src="gif/t_transf.jpg">
*/
//End_Html
//
// 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.
//  
//     

#include "TObjArray.h"

#include "TGeoManager.h"
#include "TGeoMatrix.h"

TGeoIdentity *gGeoIdentity = 0;
const Int_t kN3 = 3*sizeof(Double_t);
const Int_t kN9 = 9*sizeof(Double_t);

// statics and globals

ClassImp(TGeoMatrix)
ClassImp(TGeoTranslation)
ClassImp(TGeoRotation)
ClassImp(TGeoScale)
ClassImp(TGeoCombiTrans)
ClassImp(TGeoGenTrans)
ClassImp(TGeoIdentity)

//-----------------------------------------------------------------------------
TGeoMatrix::TGeoMatrix()
{
// dummy constructor
}
//-----------------------------------------------------------------------------
TGeoMatrix::TGeoMatrix(const char *name)
           :TNamed(name, "")
{
// Constructor
}
//-----------------------------------------------------------------------------
TGeoMatrix::~TGeoMatrix()
{
// Destructor
   if (IsRegistered() && gGeoManager) {
      if (gGeoManager->GetListOfVolumes()) {
         gGeoManager->GetListOfMatrices()->Remove(this);
         Error("dtor", "a registered matrix was removed !!!");
      }
   }
}
//-----------------------------------------------------------------------------
TGeoMatrix &TGeoMatrix::operator*(const TGeoMatrix &right) const
{
// Multiplication
   static TGeoHMatrix h;
   h = *this;
   h.Multiply(&right);
   return h;
}
//-----------------------------------------------------------------------------
Bool_t TGeoMatrix::IsRotAboutZ() const
{
// Returns true if no rotation or the rotation is about Z axis
   if (IsIdentity()) return kTRUE;
   const Double_t *rot = GetRotationMatrix();
   if (TMath::Abs(rot[6])>1E-9) return kFALSE;
   if (TMath::Abs(rot[7])>1E-9) return kFALSE;
   if ((1.-TMath::Abs(rot[8]))>1E-9) return kFALSE;
   return kTRUE;
}   
//-----------------------------------------------------------------------------
Int_t TGeoMatrix::GetByteCount() const
{
// Get total size in bytes of this
   Int_t count = 4+28+strlen(GetName())+strlen(GetTitle()); // fId + TNamed
   if (IsTranslation()) count += 12;
   if (IsScale()) count += 12;
   if (IsCombi() || IsGeneral()) count += 4 + 36;
   return count;
}
//-----------------------------------------------------------------------------
void TGeoMatrix::GetHomogenousMatrix(Double_t *hmat) const
{
// 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.
   Double_t *hmatrix = hmat;
   const Double_t *mat = GetRotationMatrix();
   for (Int_t i=0; i<3; i++) {
      memcpy(hmatrix, mat, kN3);
      mat     += 3;
      hmatrix += 3;
      *hmatrix = 0.0;
      hmatrix++; 
   }
   memcpy(hmatrix, GetTranslation(), kN3);
   hmatrix = hmat;
   if (IsScale()) {
      for (Int_t i=0; i<3; i++) {
         *hmatrix *= GetScale()[i];
         hmatrix  += 5;
      }
   }
}
//-----------------------------------------------------------------------------
void TGeoMatrix::LocalToMaster(const Double_t *local, Double_t *master) const
{
// convert a point by multiplying its column vector (x, y, z, 1) to matrix inverse
  if (IsIdentity()) {
     memcpy(master, local, kN3);
     return;
  }   
  const Double_t *tr = GetTranslation();
  const Double_t *rot = GetRotationMatrix();
  for (Int_t i=0; i<3; i++) {
      master[i] = tr[i] 
                 + local[0]*rot[3*i]
                 + local[1]*rot[3*i+1]
                 + local[2]*rot[3*i+2];
   }
}
//-----------------------------------------------------------------------------
void TGeoMatrix::LocalToMasterVect(const Double_t *local, Double_t *master) const
{
// convert a vector by multiplying its column vector (x, y, z, 1) to matrix inverse
  if (IsIdentity()) {
     memcpy(master, local, kN3);
     return;
  }   
  const Double_t *rot = GetRotationMatrix();
  for (Int_t i=0; i<3; i++) {
      master[i] = local[0]*rot[3*i]
                 + local[1]*rot[3*i+1]
                 + local[2]*rot[3*i+2];
   }
}
//-----------------------------------------------------------------------------
void TGeoMatrix::LocalToMasterBomb(const Double_t *local, Double_t *master) const
{
// convert a point by multiplying its column vector (x, y, z, 1) to matrix inverse
  if (IsIdentity()) {
     memcpy(master, local, kN3);
     return;
  }   
  const Double_t *tr = GetTranslation();
  Double_t bombtr[3];
  gGeoManager->BombTranslation(tr, &bombtr[0]);
  const Double_t *rot = GetRotationMatrix();
  for (Int_t i=0; i<3; i++) {
      master[i] = bombtr[i] 
                 + local[0]*rot[3*i]
                 + local[1]*rot[3*i+1]
                 + local[2]*rot[3*i+2];
   }
}
//-----------------------------------------------------------------------------
void TGeoMatrix::MasterToLocal(const Double_t *master, Double_t *local) const
{
// convert a point by multiplying its column vector (x, y, z, 1) to matrix
  if (IsIdentity()) {
     memcpy(local, master, kN3);
     return;
  }   
  const Double_t *tr  = GetTranslation();
  const Double_t *rot = GetRotationMatrix();
  Double_t mt0  = master[0]-tr[0];
  Double_t mt1  = master[1]-tr[1];
  Double_t mt2  = master[2]-tr[2];
  local[0] = mt0*rot[0] + mt1*rot[3] + mt2*rot[6];
  local[1] = mt0*rot[1] + mt1*rot[4] + mt2*rot[7];
  local[2] = mt0*rot[2] + mt1*rot[5] + mt2*rot[8];
}
//-----------------------------------------------------------------------------
void TGeoMatrix::MasterToLocalVect(const Double_t *master, Double_t *local) const
{
// convert a point by multiplying its column vector (x, y, z, 1) to matrix
  if (IsIdentity()) {
     memcpy(local, master, kN3);
     return;
  }   
  const Double_t *rot = GetRotationMatrix();
  for (Int_t i=0; i<3; i++) {
     local[i] =  master[0]*rot[i]
               + master[1]*rot[i+3]
               + master[2]*rot[i+6];
  }
}
//-----------------------------------------------------------------------------
void TGeoMatrix::MasterToLocalBomb(const Double_t *master, Double_t *local) const
{
// convert a point by multiplying its column vector (x, y, z, 1) to matrix
  if (IsIdentity()) {
     memcpy(local, master, kN3);
     return;
  }   
  const Double_t *tr = GetTranslation();
  Double_t bombtr[3];
  gGeoManager->UnbombTranslation(tr, &bombtr[0]);
  const Double_t *rot = GetRotationMatrix();
    for (Int_t i=0; i<3; i++) {
       local[i] =  (master[0]-bombtr[0])*rot[i]
                 + (master[1]-bombtr[1])*rot[i+3]
                 + (master[2]-bombtr[2])*rot[i+6];
   }
}
//-----------------------------------------------------------------------------
void TGeoMatrix::Print(Option_t *) const
{
// print the matrix in 4x4 format
   const Double_t *rot = GetRotationMatrix();
   const Double_t *tr  = GetTranslation();
   const Double_t *sc  = GetScale();
   printf("matrix %s - translation : %i  rotation : %i  scale : %i\n", GetName(),(Int_t)IsTranslation(),
          (Int_t)IsRotation(), (Int_t)IsScale());
   printf(" %g %g %g %g\n", rot[0], rot[1], rot[2], (Double_t)0); 
   printf(" %g %g %g %g\n", rot[3], rot[4], rot[5], (Double_t)0); 
   printf(" %g %g %g %g\n", rot[6], rot[7], rot[8], (Double_t)0); 

   printf(" %g %g %g %g\n", tr[0], tr[1], tr[2], (Double_t)1);
   if (IsScale()) printf("Scale : %g %g %g\n", sc[0], sc[1], sc[2]);
}

//-----------------------------------------------------------------------------
void TGeoMatrix::RegisterYourself()
{
   if (!IsRegistered() && gGeoManager) {
      gGeoManager->RegisterMatrix(this); 
      SetBit(kGeoRegistered);
   }   
}

//-----------------------------------------------------------------------------
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 :
//   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.
   if (!gGeoManager) return;
   if (strlen(GetName())) return;
   char type = 'n';
   if (IsTranslation()) type = 't'; 
   if (IsRotation()) type = 'r';
   if (IsScale()) type = 's';
   if (IsCombi()) type = 'c';
   if (IsGeneral()) type = 'g';
   TObjArray *matrices = gGeoManager->GetListOfMatrices();
   Int_t index = 0;
   if (matrices) index =matrices->GetEntriesFast() - 1;
   Int_t digits = 1;
   Int_t num = 10;
   while ((Int_t)(index/num)) {
      digits++;
      num *= 10;
   }
   char *name = new char[digits+2];
   sprintf(name, "%c%i", type, index);
   SetName(name);
}
//-----------------------------------------------------------------------------
TGeoTranslation::TGeoTranslation()
{
// Default constructor
   SetBit(kGeoTranslation);
   for (Int_t i=0; i<3; i++) fTranslation[i] = 0;
}

//-----------------------------------------------------------------------------
TGeoTranslation::TGeoTranslation(const TGeoTranslation &other)
                :TGeoMatrix()
{
// Copy ctor.
   SetBit(kGeoTranslation);
   const Double_t *transl = other.GetTranslation();
   memcpy(fTranslation, transl, kN3);
   SetName(other.GetName());
}

//-----------------------------------------------------------------------------
TGeoTranslation::TGeoTranslation(Double_t dx, Double_t dy, Double_t dz)
                :TGeoMatrix("")
{
// Default constructor defining the translation
   SetBit(kGeoTranslation);
   SetDefaultName();
   SetTranslation(dx, dy, dz);
}
//-----------------------------------------------------------------------------
TGeoTranslation::TGeoTranslation(const char *name, Double_t dx, Double_t dy, Double_t dz)
                :TGeoMatrix(name)
{
// Default constructor defining the translation
   SetBit(kGeoTranslation);
   SetTranslation(dx, dy, dz);
}
//-----------------------------------------------------------------------------
TGeoMatrix& TGeoTranslation::Inverse() const
{
// Return a temporary inverse of this.
   static TGeoHMatrix h;
   h = *this;
   Double_t tr[3];
   tr[0] = -fTranslation[0];
   tr[1] = -fTranslation[1];
   tr[2] = -fTranslation[2];
   h.SetTranslation(tr);
   return h;
}   

//-----------------------------------------------------------------------------
void TGeoTranslation::Add(const TGeoTranslation *other)
{
// Adding a translation to this one
   const Double_t *trans = other->GetTranslation();
   for (Int_t i=0; i<3; i++) 
      fTranslation[i] += trans[i];
}
//-----------------------------------------------------------------------------
void TGeoTranslation::Subtract(const TGeoTranslation *other)
{
// Subtracting a translation from this one
   const Double_t *trans = other->GetTranslation();
   for (Int_t i=0; i<3; i++) 
      fTranslation[i] -= trans[i];
}
//-----------------------------------------------------------------------------
void TGeoTranslation::SetTranslation(Double_t dx, Double_t dy, Double_t dz)
{
// Set translation components
   fTranslation[0] = dx;
   fTranslation[1] = dy;
   fTranslation[2] = dz;
}
//-----------------------------------------------------------------------------
void TGeoTranslation::LocalToMaster(const Double_t *local, Double_t *master) const
{
// convert a point by multiplying its column vector (x, y, z, 1) to matrix inverse
  const Double_t *tr = GetTranslation();
  for (Int_t i=0; i<3; i++) 
      master[i] = tr[i] + local[i]; 
}
//-----------------------------------------------------------------------------
void TGeoTranslation::LocalToMasterVect(const Double_t *local, Double_t *master) const
{
// convert a vector to MARS
   memcpy(master, local, kN3);
}
//-----------------------------------------------------------------------------
void TGeoTranslation::LocalToMasterBomb(const Double_t *local, Double_t *master) const
{
// convert a point by multiplying its column vector (x, y, z, 1) to matrix inverse
  const Double_t *tr = GetTranslation();
  Double_t bombtr[3];
  gGeoManager->BombTranslation(tr, &bombtr[0]);
  for (Int_t i=0; i<3; i++) 
      master[i] = bombtr[i] + local[i]; 
}
//-----------------------------------------------------------------------------
void TGeoTranslation::MasterToLocal(const Double_t *master, Double_t *local) const
{
// convert a point by multiplying its column vector (x, y, z, 1) to matrix
  const Double_t *tr = GetTranslation();
    for (Int_t i=0; i<3; i++) 
       local[i] =  master[i]-tr[i];
}
//-----------------------------------------------------------------------------
void TGeoTranslation::MasterToLocalVect(const Double_t *master, Double_t *local) const
{
// convert a vector from MARS to local
   memcpy(local, master, kN3);
}
//-----------------------------------------------------------------------------
void TGeoTranslation::MasterToLocalBomb(const Double_t *master, Double_t *local) const
{
// convert a point by multiplying its column vector (x, y, z, 1) to matrix
  const Double_t *tr = GetTranslation();
  Double_t bombtr[3];
  gGeoManager->UnbombTranslation(tr, &bombtr[0]);
    for (Int_t i=0; i<3; i++) 
       local[i] =  master[i]-bombtr[i];
}
//-----------------------------------------------------------------------------
TGeoRotation::TGeoRotation()
{
// Default constructor.
   SetBit(kGeoRotation);
   for (Int_t i=0; i<9; i++) {
      if (i%4) fRotationMatrix[i] = 0;
      else fRotationMatrix[i] = 1.0;
   }
}

//-----------------------------------------------------------------------------
TGeoRotation::TGeoRotation(const TGeoRotation &other)
             :TGeoMatrix()
{
// Copy ctor.
   SetBit(kGeoRotation);
   SetRotation(other);
   SetName(other.GetName());
}   

//-----------------------------------------------------------------------------
TGeoRotation::TGeoRotation(const char *name)
             :TGeoMatrix(name)
{
// Named rotation constructor
   for (Int_t i=0; i<9; i++) {
      if (i%4) fRotationMatrix[i] = 0;
      else fRotationMatrix[i] = 1.0;
   }
   SetBit(kGeoRotation);
   SetDefaultName();
}
//-----------------------------------------------------------------------------
TGeoRotation::TGeoRotation(const char *name, Double_t phi, Double_t theta, Double_t psi)
             :TGeoMatrix(name)
{
// 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.
   SetBit(kGeoRotation);
   SetAngles(phi, theta, psi);
   CheckMatrix();
   SetDefaultName();
}
//-----------------------------------------------------------------------------
TGeoRotation::TGeoRotation(const char *name, Double_t theta1, Double_t phi1, Double_t theta2, Double_t phi2,
                           Double_t theta3, Double_t phi3)
             :TGeoMatrix(name)
{
// 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);
   SetAngles(theta1, phi1, theta2, phi2, theta3, phi3);
   CheckMatrix();
   SetDefaultName();
}
//-----------------------------------------------------------------------------
TGeoMatrix& TGeoRotation::Inverse() const
{
// Return a temporary inverse of this.
   static TGeoHMatrix h;
   h = *this;
   Double_t newrot[9];
   newrot[0] = fRotationMatrix[0];
   newrot[1] = fRotationMatrix[3];
   newrot[2] = fRotationMatrix[6];
   newrot[3] = fRotationMatrix[1];
   newrot[4] = fRotationMatrix[4];
   newrot[5] = fRotationMatrix[7];
   newrot[6] = fRotationMatrix[2];
   newrot[7] = fRotationMatrix[5];
   newrot[8] = fRotationMatrix[8];
   h.SetRotation(newrot);
   return h;
}   
//-----------------------------------------------------------------------------
Bool_t TGeoRotation::IsValid() const
{
// Perform orthogonality test for rotation.
   const Double_t *r = fRotationMatrix;
   Double_t cij;
   for (Int_t i=0; i<2; i++) {
      for (Int_t j=i+1; j<3; j++) {
         // check columns
         cij = TMath::Abs(r[i]*r[j]+r[i+3]*r[j+3]+r[i+6]*r[j+6]);
         if (cij>1E-4) return kFALSE;
         // check rows
         cij = TMath::Abs(r[3*i]*r[3*j]+r[3*i+1]*r[3*j+1]+r[3*i+2]*r[3*j+2]);
         if (cij>1E-4) return kFALSE;
      }
   }
   return kTRUE;   
}
//-----------------------------------------------------------------------------
void TGeoRotation::Clear(Option_t *)
{
// reset data members to 0
   memset(&fRotationMatrix[0], 0, kN9);
}
//-----------------------------------------------------------------------------
void TGeoRotation::FastRotZ(Double_t *sincos)
{
   fRotationMatrix[0] = sincos[1];
   fRotationMatrix[1] = -sincos[0];
   fRotationMatrix[3] = sincos[0];
   fRotationMatrix[4] = sincos[1];
}
//-----------------------------------------------------------------------------
Double_t TGeoRotation::GetPhiRotation() const
{
//--- Returns rotation angle about Z axis in degrees.
   Double_t phi = 180.*TMath::ATan2(fRotationMatrix[1], fRotationMatrix[0])/TMath::Pi();
   return phi;
}   
//-----------------------------------------------------------------------------
void TGeoRotation::LocalToMaster(const Double_t *local, Double_t *master) const
{
// convert a point by multiplying its column vector (x, y, z, 1) to matrix inverse
  const Double_t *rot = GetRotationMatrix();
  for (Int_t i=0; i<3; i++) {
      master[i] = local[0]*rot[3*i]
                + local[1]*rot[3*i+1]
                + local[2]*rot[3*i+2];
   }
}
//-----------------------------------------------------------------------------
void TGeoRotation::MasterToLocal(const Double_t *master, Double_t *local) const
{
// convert a point by multiplying its column vector (x, y, z, 1) to matrix
  const Double_t *rot = GetRotationMatrix();
    for (Int_t i=0; i<3; i++) {
       local[i] =  master[0]*rot[i]
                 + master[1]*rot[i+3]
                 + master[2]*rot[i+6];
   }
}

//-----------------------------------------------------------------------------
void TGeoRotation::RotateX(Double_t angle)
{
// Rotate about X axis with angle expressed in degrees.
   Double_t phi = angle*TMath::DegToRad();
   Double_t c = TMath::Cos(phi);
   Double_t s = TMath::Sin(phi);
   Double_t v[3];
   Int_t j;
   for (Int_t i=0; i<3; i++) {
      j = 3*i;
      v[0] = fRotationMatrix[j];
      v[1] = c*fRotationMatrix[j+1]+s*fRotationMatrix[j+2];
      v[2] = -s*fRotationMatrix[j+1]+c*fRotationMatrix[j+2];
      memcpy(&fRotationMatrix[j], v, kN3);
   }   
}

//-----------------------------------------------------------------------------
void TGeoRotation::RotateY(Double_t angle)
{
// Rotate about Y axis with angle expressed in degrees.
   Double_t phi = angle*TMath::DegToRad();
   Double_t c = TMath::Cos(phi);
   Double_t s = TMath::Sin(phi);
   Double_t v[3];
   Int_t j;
   for (Int_t i=0; i<3; i++) {
      j = 3*i;
      v[0] = c*fRotationMatrix[j]-s*fRotationMatrix[j+2];
      v[1] = fRotationMatrix[j+1];
      v[2] = s*fRotationMatrix[j]+c*fRotationMatrix[j+2];
      memcpy(&fRotationMatrix[j], v, kN3);
   }   
}

//-----------------------------------------------------------------------------
void TGeoRotation::RotateZ(Double_t angle)
{
// Rotate about Z axis with angle expressed in degrees.
   Double_t phi = angle*TMath::DegToRad();
   Double_t c = TMath::Cos(phi);
   Double_t s = TMath::Sin(phi);
   Double_t v[3];
   Int_t j;
   for (Int_t i=0; i<3; i++) {
      j = 3*i;
      v[0] = c*fRotationMatrix[j]+s*fRotationMatrix[j+1];
      v[1] = -s*fRotationMatrix[j]+c*fRotationMatrix[j+1];
      v[2] = fRotationMatrix[j+2];
      memcpy(&fRotationMatrix[j], v, kN3);
   }   
}

//-----------------------------------------------------------------------------
void TGeoRotation::SetRotation(const TGeoRotation &other)
{
// Copy rotation elements from other rotation matrix.
   const Double_t *rot = other.GetRotationMatrix();
   memcpy(fRotationMatrix, rot, kN9);
}

//-----------------------------------------------------------------------------
void TGeoRotation::SetAngles(Double_t phi, Double_t theta, Double_t psi)
{
// Set matrix elements according to Euler angles
   Double_t degrad = TMath::Pi()/180.;
   Double_t sinphi = TMath::Sin(degrad*phi);
   Double_t cosphi = TMath::Cos(degrad*phi);
   Double_t sinthe = TMath::Sin(degrad*theta);
   Double_t costhe = TMath::Cos(degrad*theta);
   Double_t sinpsi = TMath::Sin(degrad*psi);
   Double_t cospsi = TMath::Cos(degrad*psi);

   fRotationMatrix[0] =  cospsi*cosphi - costhe*sinphi*sinpsi;
   fRotationMatrix[1] = -sinpsi*cosphi - costhe*sinphi*cospsi;
   fRotationMatrix[2] =  sinthe*sinphi;
   fRotationMatrix[3] =  cospsi*sinphi + costhe*cosphi*sinpsi;
   fRotationMatrix[4] = -sinpsi*sinphi + costhe*cosphi*cospsi;
   fRotationMatrix[5] = -sinthe*cosphi;
   fRotationMatrix[6] =  sinpsi*sinthe;
   fRotationMatrix[7] =  cospsi*sinthe;
   fRotationMatrix[8] =  costhe;

   if (!IsValid()) Error("SetAngles", "invalid rotation (Euler angles : phi=%f theta=%f psi=%f)",phi,theta,psi);
}
//-----------------------------------------------------------------------------
void TGeoRotation::SetAngles(Double_t theta1, Double_t phi1, Double_t theta2, Double_t phi2,
                             Double_t theta3, Double_t phi3)
{
// Set matrix elements in the GEANT3 way
   Double_t degrad = TMath::Pi()/180.;
   fRotationMatrix[0] = TMath::Cos(degrad*phi1)*TMath::Sin(degrad*theta1);
   fRotationMatrix[3] = TMath::Sin(degrad*phi1)*TMath::Sin(degrad*theta1);
   fRotationMatrix[6] = TMath::Cos(degrad*theta1);
   fRotationMatrix[1] = TMath::Cos(degrad*phi2)*TMath::Sin(degrad*theta2);
   fRotationMatrix[4] = TMath::Sin(degrad*phi2)*TMath::Sin(degrad*theta2);
   fRotationMatrix[7] = TMath::Cos(degrad*theta2);
   fRotationMatrix[2] = TMath::Cos(degrad*phi3)*TMath::Sin(degrad*theta3);
   fRotationMatrix[5] = TMath::Sin(degrad*phi3)*TMath::Sin(degrad*theta3);
   fRotationMatrix[8] = TMath::Cos(degrad*theta3);
   // do the trick to eliminate most of the floating point errors
   for (Int_t i=0; i<9; i++) {
      if (TMath::Abs(fRotationMatrix[i])<1E-15) fRotationMatrix[i] = 0;
      if (TMath::Abs(fRotationMatrix[i]-1)<1E-15) fRotationMatrix[i] = 1;
      if (TMath::Abs(fRotationMatrix[i]+1)<1E-15) fRotationMatrix[i] = -1;
   }   
   if (!IsValid()) Error("SetAngles", "invalid rotation (G3 angles, th1=%f phi1=%f, th2=%f ph2=%f, th3=%f phi3=%f)",
                          theta1,phi1,theta2,phi2,theta3,phi3);
}

//-----------------------------------------------------------------------------
void TGeoRotation::GetAngles(Double_t &theta1, Double_t &phi1, Double_t &theta2, Double_t &phi2,
                             Double_t &theta3, Double_t &phi3) const
{
// Retreive rotation angles
   Double_t raddeg = 180./TMath::Pi();
   theta1 = raddeg*TMath::ACos(fRotationMatrix[6]);
   theta2 = raddeg*TMath::ACos(fRotationMatrix[7]);
   theta3 = raddeg*TMath::ACos(fRotationMatrix[8]);
   if (TMath::Abs(fRotationMatrix[0])<1E-6 && TMath::Abs(fRotationMatrix[3])<1E-6) phi1=0.;
   else phi1 = raddeg*TMath::ATan2(fRotationMatrix[3],fRotationMatrix[0]);
   if (phi1<0) phi1+=360.;
   if (TMath::Abs(fRotationMatrix[1])<1E-6 && TMath::Abs(fRotationMatrix[4])<1E-6) phi2=0.;
   else phi2 = raddeg*TMath::ATan2(fRotationMatrix[4],fRotationMatrix[1]);
   if (phi2<0) phi2+=360.;
   if (TMath::Abs(fRotationMatrix[2])<1E-6 && TMath::Abs(fRotationMatrix[5])<1E-6) phi3=0.;
   else phi3 = raddeg*TMath::ATan2(fRotationMatrix[5],fRotationMatrix[2]);
   if (phi3<0) phi3+=360.;
}

//-----------------------------------------------------------------------------
Double_t TGeoRotation::Determinant() const
{
// computes determinant of the rotation matrix
   Double_t 
   det = fRotationMatrix[0]*fRotationMatrix[4]*fRotationMatrix[8] + 
         fRotationMatrix[3]*fRotationMatrix[7]*fRotationMatrix[1] +
         fRotationMatrix[6]*fRotationMatrix[1]*fRotationMatrix[5] - 
         fRotationMatrix[2]*fRotationMatrix[4]*fRotationMatrix[6] -
         fRotationMatrix[5]*fRotationMatrix[7]*fRotationMatrix[0] - 
         fRotationMatrix[7]*fRotationMatrix[1]*fRotationMatrix[3];
   return det;
}
//-----------------------------------------------------------------------------
void TGeoRotation::CheckMatrix()
{
   // performes an orthogonality check and finds if the matrix is a reflection
//   Warning("CheckMatrix", "orthogonality check not performed yet");
   if (Determinant() < 0) {
      SetBit(kGeoReflection);
//      printf("matrix %s is reflection/n", GetName());
   }
}
//-----------------------------------------------------------------------------
void TGeoRotation::GetInverse(Double_t *invmat) const
{
// Get the inverse rotation matrix (which is simply the transpose)
   if (!invmat) {
      Error("GetInverse", "no place to store the inverse matrix");
   }
   for (Int_t i=0; i<3; i++) {
      for (Int_t j=0; i<3; i++) {   
         invmat[3*i+j] = fRotationMatrix[3*j+i];
      }
   }
}
//-----------------------------------------------------------------------------
void TGeoRotation::MultiplyBy(TGeoRotation *rot, Bool_t after)
{
   const Double_t *matleft, *matright;
   Double_t  newmat[9] = {0};
   if (after) {
      matleft  = &fRotationMatrix[0];
      matright = rot->GetRotationMatrix();
   } else {
      matleft  = rot->GetRotationMatrix();
      matright = &fRotationMatrix[0];
   }
   for (Int_t i=0; i<3; i++) {
      for (Int_t j=0; j<3; j++) { 
         for (Int_t k=0; k<3; k++) {
            newmat[3*i+j] += matleft[3*i+k] * matright[3*k+j];
         }
      }
   }
   memcpy(&fRotationMatrix[0], &newmat[0], kN9);
}
//-----------------------------------------------------------------------------
TGeoScale::TGeoScale()
{
// default constructor
   SetBit(kGeoScale);
   for (Int_t i=0; i<3; i++) fScale[i] = 0;
}
//-----------------------------------------------------------------------------
TGeoScale::TGeoScale(const TGeoScale &other)
          :TGeoMatrix()
{
// Copy constructor
   SetBit(kGeoScale);
   const Double_t *scl =  other.GetScale();
   memcpy(fScale, scl, kN3);
   SetName(other.GetName());
}   

//-----------------------------------------------------------------------------
TGeoScale::TGeoScale(Double_t sx, Double_t sy, Double_t sz)
          :TGeoMatrix("")
{
// default constructor
   SetBit(kGeoScale);
   SetDefaultName();
   SetScale(sx, sy, sz);
}
//-----------------------------------------------------------------------------
TGeoScale::TGeoScale(const char *name, Double_t sx, Double_t sy, Double_t sz)
          :TGeoMatrix(name)
{
// default constructor
   SetBit(kGeoScale);
   SetScale(sx, sy, sz);
}
//-----------------------------------------------------------------------------
TGeoScale::~TGeoScale()
{
// destructor
}
//-----------------------------------------------------------------------------
TGeoMatrix& TGeoScale::Inverse() const
{
// Return a temporary inverse of this.
   static TGeoHMatrix h;
   h = *this;
   Double_t scale[3];
   scale[0] = 1./fScale[0];
   scale[1] = 1./fScale[1];
   scale[2] = 1./fScale[2];
   h.SetScale(scale);
   return h;
}   
//-----------------------------------------------------------------------------
void TGeoScale::SetScale(Double_t sx, Double_t sy, Double_t sz)
{
// scale setter
   fScale[0] = sx;
   fScale[1] = sy;
   fScale[2] = sz;
   if (!(Normalize())) {
      Error("ctor", "Invalid scale");
      return;
   }
}
//-----------------------------------------------------------------------------
Bool_t TGeoScale::Normalize()
{
// A scale transformation should be normalized by sx*sy*sz factor
   Double_t normfactor = fScale[0]*fScale[1]*fScale[2];
   if (normfactor <= 1E-5) return kFALSE;
   for (Int_t i=0; i<3; i++)
      fScale[i] /= normfactor;
   return kTRUE;
}
//-----------------------------------------------------------------------------
TGeoCombiTrans::TGeoCombiTrans()
{
// dummy ctor
   SetBit(kGeoCombiTrans);
   for (Int_t i=0; i<3; i++) fTranslation[i] = 0.0;
   fRotation = 0;
}
//-----------------------------------------------------------------------------
TGeoCombiTrans::TGeoCombiTrans(const TGeoCombiTrans &other)
               :TGeoMatrix()
{
// Copy ctor
   SetBit(kGeoCombiTrans);
   const Double_t *trans = other.GetTranslation();
   const TGeoRotation rot = *other.GetRotation();
   memcpy(fTranslation, trans, kN3);
   fRotation = new TGeoRotation(rot); 
   SetName(other.GetName());
}   
//-----------------------------------------------------------------------------
TGeoCombiTrans::TGeoCombiTrans(const TGeoTranslation &tr, const TGeoRotation &rot)
{
   SetBit(kGeoCombiTrans);
   const Double_t *trans = tr.GetTranslation();
   memcpy(fTranslation, trans, kN3);
   fRotation = new TGeoRotation(rot);
}   

//-----------------------------------------------------------------------------
TGeoCombiTrans::TGeoCombiTrans(const char *name)
               :TGeoMatrix(name)
{
// ctor
   SetBit(kGeoCombiTrans);
   SetDefaultName();
   for (Int_t i=0; i<3; i++) fTranslation[i] = 0.0;
   fRotation = new TGeoRotation("");
}

//-----------------------------------------------------------------------------
TGeoCombiTrans::TGeoCombiTrans(Double_t dx, Double_t dy, Double_t dz, TGeoRotation *rot)
               :TGeoMatrix("")
{
// ctor
   SetBit(kGeoCombiTrans);
   SetDefaultName();
   SetTranslation(dx, dy, dz);
   fRotation = 0;
   SetRotation(rot);
}
//-----------------------------------------------------------------------------
TGeoCombiTrans::TGeoCombiTrans(const char *name, Double_t dx, Double_t dy, Double_t dz, TGeoRotation *rot)
               :TGeoMatrix(name)
{
// ctor
   SetBit(kGeoCombiTrans);
   SetTranslation(dx, dy, dz);
   fRotation = 0;
   SetRotation(rot);
}
//-----------------------------------------------------------------------------
TGeoCombiTrans::~TGeoCombiTrans()
{
// destructor
   if (fRotation) delete fRotation;
}
//-----------------------------------------------------------------------------
TGeoMatrix& TGeoCombiTrans::Inverse() const
{
// Return a temporary inverse of this.
   static TGeoHMatrix h;
   h = *this;
   Double_t tr[3];
   Double_t newrot[9];
   const Double_t *rot = GetRotationMatrix();
   tr[0] = -fTranslation[0];
   tr[1] = -fTranslation[1];
   tr[2] = -fTranslation[2];
   h.SetTranslation(tr);
   newrot[0] = rot[0];
   newrot[1] = rot[3];
   newrot[2] = rot[6];
   newrot[3] = rot[1];
   newrot[4] = rot[4];
   newrot[5] = rot[7];
   newrot[6] = rot[2];
   newrot[7] = rot[5];
   newrot[8] = rot[8];
   h.SetRotation(newrot);
   return h;
}   
//-----------------------------------------------------------------------------
void TGeoCombiTrans::RegisterYourself()
{
   if (!IsRegistered() && gGeoManager) {
      gGeoManager->RegisterMatrix(this); 
      SetBit(kGeoRegistered);
//      if (fRotation) fRotation->RegisterYourself();
   }
   if (!gGeoManager) 
      Warning("RegisterYourself", "cannot register without geometry");
}
//-----------------------------------------------------------------------------
void TGeoCombiTrans::RotateX(Double_t angle)
{
// Combine this with a rotation about X axis. Current rotation must be not NULL.
   if (!fRotation) {
      Warning("RotateX", "cannot rotate since original rotation is not defined");
      return;
   }
   fRotation->RotateX(angle);
   if (fTranslation[0]==0 && fTranslation[1]==0 && fTranslation[2]==0) return;
   Double_t phi = angle*TMath::DegToRad();
   Double_t c = TMath::Cos(phi);
   Double_t s = TMath::Sin(phi);
   Double_t tr[3];
   tr[0] = fTranslation[0];
   tr[1] = c*fTranslation[1]+s*fTranslation[2];
   tr[2] = -s*fTranslation[1]+c*fTranslation[2];
   SetTranslation(tr);
}   

//-----------------------------------------------------------------------------
void TGeoCombiTrans::RotateY(Double_t angle)
{
// Combine this with a rotation about Y axis. Current rotation must be not NULL.
   if (!fRotation) {
      Warning("RotateY", "cannot rotate since original rotation is not defined");
      return;
   }
   fRotation->RotateY(angle);
   if (fTranslation[0]==0 && fTranslation[1]==0 && fTranslation[2]==0) return;
   Double_t phi = angle*TMath::DegToRad();
   Double_t c = TMath::Cos(phi);
   Double_t s = TMath::Sin(phi);
   Double_t tr[3];
   tr[0] = c*fTranslation[0]-s*fTranslation[2];
   tr[1] = fTranslation[1];
   tr[2] = s*fTranslation[0]+c*fTranslation[2];
   SetTranslation(tr);
}   

//-----------------------------------------------------------------------------
void TGeoCombiTrans::RotateZ(Double_t angle)
{
// Combine this with a rotation about Z axis. Current rotation must be not NULL.
   if (!fRotation) {
      Warning("RotateZ", "cannot rotate since original rotation is not defined");
      return;
   }
   fRotation->RotateZ(angle);
   if (fTranslation[0]==0 && fTranslation[1]==0 && fTranslation[2]==0) return;
   Double_t phi = angle*TMath::DegToRad();
   Double_t c = TMath::Cos(phi);
   Double_t s = TMath::Sin(phi);
   Double_t tr[3];
   tr[0] = c*fTranslation[0]+s*fTranslation[1];
   tr[1] = -s*fTranslation[0]+c*fTranslation[1];
   tr[2] = fTranslation[2];
   SetTranslation(tr);
}   

//-----------------------------------------------------------------------------
void TGeoCombiTrans::SetRotation(TGeoRotation *rot)
{
// Copy the rotation from another one.
   if (!fRotation) fRotation = new TGeoRotation();
   const TGeoRotation r = *rot;
   fRotation->SetRotation(r);
}

//-----------------------------------------------------------------------------
void TGeoCombiTrans::SetRotation(const TGeoRotation &rot)
{
// Copy the rotation from another one.
   if (!fRotation) fRotation = new TGeoRotation();
   fRotation->SetRotation(rot); 
}

//-----------------------------------------------------------------------------
void TGeoCombiTrans::SetTranslation(const TGeoTranslation &tr)
{
// copy the translation component
   const Double_t *trans = tr.GetTranslation();
   memcpy(fTranslation, trans, kN3);
}   

//-----------------------------------------------------------------------------
void TGeoCombiTrans::SetTranslation(Double_t dx, Double_t dy, Double_t dz)
{
// set the translation component
   fTranslation[0] = dx;
   fTranslation[1] = dy;
   fTranslation[2] = dz;
}
//-----------------------------------------------------------------------------
void TGeoCombiTrans::SetTranslation(Double_t *vect)
{
// set the translation component
   fTranslation[0] = vect[0];
   fTranslation[1] = vect[1];
   fTranslation[2] = vect[2];
}
//-----------------------------------------------------------------------------
const Double_t *TGeoCombiTrans::GetRotationMatrix() const
{
// get the rotation array
   if (!fRotation) return kIdentityMatrix;
   return fRotation->GetRotationMatrix();
}
//-----------------------------------------------------------------------------
TGeoGenTrans::TGeoGenTrans()
{
// dummy ctor
   SetBit(kGeoGenTrans);
   for (Int_t i=0; i<3; i++) fTranslation[i] = 0.0;
   for (Int_t j=0; j<3; j++) fScale[j] = 1.0;
   fRotation = 0;
}
//-----------------------------------------------------------------------------
TGeoGenTrans::TGeoGenTrans(const char *name)
             :TGeoCombiTrans(name)
{
// ctor
   SetBit(kGeoGenTrans);
   for (Int_t i=0; i<3; i++) fTranslation[i] = 0.0;
   for (Int_t j=0; j<3; j++) fScale[j] = 1.0;
   fRotation = 0;
}
//-----------------------------------------------------------------------------
TGeoGenTrans::TGeoGenTrans(Double_t dx, Double_t dy, Double_t dz,
                           Double_t sx, Double_t sy, Double_t sz, TGeoRotation *rot)
             :TGeoCombiTrans("")
{
// ctor
   SetBit(kGeoGenTrans);
   SetDefaultName();
   SetTranslation(dx, dy, dz);
   SetScale(sx, sy, sz);
   SetRotation(rot);
}
//-----------------------------------------------------------------------------
TGeoGenTrans::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
   SetBit(kGeoGenTrans);
   SetTranslation(dx, dy, dz);
   SetScale(sx, sy, sz);
   SetRotation(rot);
}
//-----------------------------------------------------------------------------
TGeoGenTrans::~TGeoGenTrans()
{
// destructor
}
//-----------------------------------------------------------------------------
void TGeoGenTrans::Clear(Option_t *)
{
// clear the fields of this transformation
   memset(&fTranslation[0], 0, kN3);
   memset(&fScale[0], 0, kN3);
   if (fRotation) fRotation->Clear();
}
//-----------------------------------------------------------------------------
void TGeoGenTrans::SetScale(Double_t sx, Double_t sy, Double_t sz)
{
// set the scale
   fScale[0] = sx;
   fScale[1] = sy;
   fScale[2] = sz;
   if (!(Normalize())) {
      Error("ctor", "Invalid scale");
      return;
   }
}
//-----------------------------------------------------------------------------
TGeoMatrix& TGeoGenTrans::Inverse() const
{
// Return a temporary inverse of this.
   Error("Inverse", "not implemented");
   static TGeoHMatrix h;
   h = *this;
   return h;
}   
//-----------------------------------------------------------------------------
Bool_t TGeoGenTrans::Normalize()
{
// A scale transformation should be normalized by sx*sy*sz factor
   Double_t normfactor = fScale[0]*fScale[1]*fScale[2];
   if (normfactor <= 1E-5) return kFALSE;
   for (Int_t i=0; i<3; i++)
      fScale[i] /= normfactor;
   return kTRUE;
}

//-----------------------------------------------------------------------------
TGeoIdentity::TGeoIdentity()
{
// dummy ctor
   if (!gGeoIdentity) gGeoIdentity = this;
   RegisterYourself();
}
//-----------------------------------------------------------------------------
TGeoIdentity::TGeoIdentity(const char *name)
             :TGeoMatrix(name)
{
// ctor
   if (!gGeoIdentity) gGeoIdentity = this;
   RegisterYourself();
}
//-----------------------------------------------------------------------------
TGeoMatrix &TGeoIdentity::Inverse() const
{
// Return a temporary inverse of this.
   return *gGeoIdentity;
}
   
/*************************************************************************
 * TGeoHMatrix - Matrix class used for computing global transformations  *
 *     Should NOT be used for node definition. An instance of this class *
 *     is generally used to pile-up local transformations starting from  *
 *     the top level physical node, down to the current node.            *
 *************************************************************************/

ClassImp(TGeoHMatrix)
   
//-----------------------------------------------------------------------------
TGeoHMatrix::TGeoHMatrix()
{
// dummy ctor
   memset(&fTranslation[0], 0, kN3);
   memcpy(fRotationMatrix,kIdentityMatrix,kN9);
   memcpy(fScale,kUnitScale,kN3);
}
//-----------------------------------------------------------------------------
TGeoHMatrix::TGeoHMatrix(const char* name)
            :TGeoMatrix(name)
{
// ctor
   memset(&fTranslation[0], 0, kN3);
   SetRotation(&kIdentityMatrix[0]);
   SetScale(&kUnitScale[0]);
}
//-----------------------------------------------------------------------------
TGeoHMatrix::TGeoHMatrix(const TGeoMatrix &matrix)
{
   // assignment
   if (matrix.IsTranslation()) {
      SetBit(kGeoTranslation);
      SetTranslation(matrix.GetTranslation());
   } else {
      memset(&fTranslation[0], 0, kN3);   
   }
   if (matrix.IsRotation()) {
      SetBit(kGeoRotation);
      memcpy(fRotationMatrix,matrix.GetRotationMatrix(),kN9);
   } else {
      memcpy(fRotationMatrix,kIdentityMatrix,kN9);   
   }
   if (matrix.IsScale()) {
      SetBit(kGeoScale);
      memcpy(fScale,matrix.GetScale(),kN3);
   } else {
      memcpy(fScale,kUnitScale,kN3);   
   }
}
//-----------------------------------------------------------------------------
TGeoHMatrix::~TGeoHMatrix()
{
// destructor
}
//-----------------------------------------------------------------------------
TGeoHMatrix &TGeoHMatrix::operator=(const TGeoMatrix *matrix)
{
   // assignment
   if (matrix == this) return *this;
   Clear();
   if (matrix->IsIdentity()) return *this;
   if (matrix->IsTranslation()) {
      SetBit(kGeoTranslation);
      memcpy(fTranslation,matrix->GetTranslation(),kN3);
   }
   if (matrix->IsRotation()) {
      SetBit(kGeoRotation);
      memcpy(fRotationMatrix,matrix->GetRotationMatrix(),kN9);
   }
   if (matrix->IsScale()) {
      SetBit(kGeoScale);
      memcpy(fScale,matrix->GetScale(),kN3);
   }
   return *this;
}
//-----------------------------------------------------------------------------
TGeoHMatrix &TGeoHMatrix::operator=(const TGeoMatrix &matrix)
{
   // assignment
   if (&matrix == this) return *this;
   if (matrix.IsIdentity()) return *this;
   if (matrix.IsTranslation()) {
      SetBit(kGeoTranslation);
      memcpy(fTranslation,matrix.GetTranslation(),kN3);
   } else {
      memcpy(fTranslation,kNullVector,kN3);
   }   
   if (matrix.IsRotation()) {
      SetBit(kGeoRotation);
      memcpy(fRotationMatrix,matrix.GetRotationMatrix(),kN9);
   } else {
      memcpy(fRotationMatrix,kIdentityMatrix,kN9);
   }   
   if (matrix.IsScale()) {
      SetBit(kGeoScale);
      memcpy(fScale,matrix.GetScale(),kN3);
   } else {
      memcpy(fScale,kUnitScale,kN3);
   }   
   return *this;
}

//-----------------------------------------------------------------------------
void TGeoHMatrix::Clear(Option_t *)
{
// clear the data for this matrix
   if (IsIdentity()) return;
   if (IsTranslation()) {
      ResetBit(kGeoTranslation);
      memcpy(fTranslation,kNullVector,kN3);
   }
   if (IsRotation()) {
      ResetBit(kGeoRotation);
      memcpy(fRotationMatrix,kIdentityMatrix,kN9);
   }
   if (IsScale()) {      
      ResetBit(kGeoScale);
      memcpy(fScale,kUnitScale,kN3);
   }
}
//-----------------------------------------------------------------------------
TGeoMatrix& TGeoHMatrix::Inverse() const
{
// Return a temporary inverse of this.
   static TGeoHMatrix h;
   h = *this;
   if (IsTranslation()) {
      Double_t tr[3];
      tr[0] = -fTranslation[0];
      tr[1] = -fTranslation[1];
      tr[2] = -fTranslation[2];
      h.SetTranslation(tr);
   }
   if (IsRotation()) {
      Double_t newrot[9];
      newrot[0] = fRotationMatrix[0];
      newrot[1] = fRotationMatrix[3];
      newrot[2] = fRotationMatrix[6];
      newrot[3] = fRotationMatrix[1];
      newrot[4] = fRotationMatrix[4];
      newrot[5] = fRotationMatrix[7];
      newrot[6] = fRotationMatrix[2];
      newrot[7] = fRotationMatrix[5];
      newrot[8] = fRotationMatrix[8];
      h.SetRotation(newrot);
   }
   if (IsScale()) {
      Double_t sc[3];
      sc[0] = 1./fScale[0];
      sc[1] = 1./fScale[1];
      sc[2] = 1./fScale[2]; 
      h.SetScale(sc);  
   }
   return h;
}   

//-----------------------------------------------------------------------------
void TGeoHMatrix::Multiply(const TGeoMatrix *right)
{
// multiply to the right with an other transformation
   // if right is identity matrix, just return
   if (right == gGeoIdentity) return;
   const Double_t *r_tra = right->GetTranslation();
   const Double_t *r_rot = right->GetRotationMatrix();
   const Double_t *r_scl = right->GetScale();
   if (IsIdentity()) {
      if (right->IsRotation()) {
         SetBit(kGeoRotation);
         memcpy(fRotationMatrix,r_rot,kN9);
      }
      if (right->IsScale()) {
         SetBit(kGeoScale);
         memcpy(fScale,r_scl,kN3);
      }
      if (right->IsTranslation()) {
         SetBit(kGeoTranslation);
         memcpy(fTranslation,r_tra,kN3);
      }
      return;
   }
   Int_t i, j;
   Double_t new_rot[9]; 

   if (right->IsRotation())    SetBit(kGeoRotation);
   if (right->IsScale())       SetBit(kGeoScale);
   if (right->IsTranslation()) SetBit(kGeoTranslation);

   // new translation
   if (IsTranslation()) { 
      for (i=0; i<3; i++) {
         fTranslation[i] += fRotationMatrix[3*i]*r_tra[0]
                         + fRotationMatrix[3*i+1]*r_tra[1]
                         + fRotationMatrix[3*i+2]*r_tra[2];
      }
   }
   if (IsRotation()) {
      // new rotation
      for (i=0; i<3; i++) {
         for (j=0; j<3; j++) {
               new_rot[3*i+j] = fRotationMatrix[3*i]*r_rot[j] +
                                fRotationMatrix[3*i+1]*r_rot[3+j] +
                                fRotationMatrix[3*i+2]*r_rot[6+j];
         }
      }
      memcpy(fRotationMatrix,new_rot,kN9);
   }
   // new scale
   if (IsScale()) {
      for (i=0; i<3; i++) fScale[i] *= r_scl[i];
   }
}
 
//-----------------------------------------------------------------------------
void TGeoHMatrix::MultiplyLeft(const TGeoMatrix *left)
{
// multiply to the left with an other transformation
   // if right is identity matrix, just return
   if (left == gGeoIdentity) return;
   const Double_t *l_tra = left->GetTranslation();
   const Double_t *l_rot = left->GetRotationMatrix();
   const Double_t *l_scl = left->GetScale();
   if (IsIdentity()) {
      if (left->IsRotation()) {
         SetBit(kGeoRotation);
         memcpy(fRotationMatrix,l_rot,kN9);
      }
      if (left->IsScale()) {
         SetBit(kGeoScale);
         memcpy(fScale,l_scl,kN3);
      }
      if (left->IsTranslation()) {
         SetBit(kGeoTranslation);
         memcpy(fTranslation,l_tra,kN3);
      }
      return;
   }
   Int_t i, j;
   Double_t new_tra[3]; 
   Double_t new_rot[9]; 

   if (left->IsRotation())    SetBit(kGeoRotation);
   if (left->IsScale())       SetBit(kGeoScale);
   if (left->IsTranslation()) SetBit(kGeoTranslation);

   // new translation
   if (IsTranslation()) {  
      for (i=0; i<3; i++) {
         new_tra[i] = l_tra[i]
                      + l_rot[3*i]*  fTranslation[0]
                      + l_rot[3*i+1]*fTranslation[1]
                      + l_rot[3*i+2]*fTranslation[2];
      }
      memcpy(fTranslation,new_tra,kN3);
   }
   if (IsRotation()) {
      // new rotation
      for (i=0; i<3; i++) {
         for (j=0; j<3; j++) {
               new_rot[3*i+j] = l_rot[3*i]*fRotationMatrix[j] +
                                l_rot[3*i+1]*fRotationMatrix[3+j] +
                                l_rot[3*i+2]*fRotationMatrix[6+j];
         }
      }
      memcpy(fRotationMatrix,new_rot,kN9);
   }
   // new scale
   if (IsScale()) {
      for (i=0; i<3; i++) fScale[i] *= l_scl[i];
   }
}
//-----------------------------------------------------------------------------
void TGeoHMatrix::RotateX(Double_t angle)
{
// Rotate about X axis with angle expressed in degrees.
   Double_t phi = angle*TMath::DegToRad();
   Double_t c = TMath::Cos(phi);
   Double_t s = TMath::Sin(phi);
   Double_t v[3];
   Int_t j;
   for (Int_t i=0; i<3; i++) {
      j = 3*i;
      v[0] = fRotationMatrix[j];
      v[1] = c*fRotationMatrix[j+1]+s*fRotationMatrix[j+2];
      v[2] = -s*fRotationMatrix[j+1]+c*fRotationMatrix[j+2];
      memcpy(&fRotationMatrix[j], v, kN3);
   }   
   SetBit(kGeoRotation);
   v[0] = fTranslation[0];
   v[1] = c*fTranslation[1]+s*fTranslation[2];
   v[2] = -s*fTranslation[1]+c*fTranslation[2];
   memcpy(fTranslation,v,kN3);
}

//-----------------------------------------------------------------------------
void TGeoHMatrix::RotateY(Double_t angle)
{
// Rotate about Y axis with angle expressed in degrees.
   Double_t phi = angle*TMath::DegToRad();
   Double_t c = TMath::Cos(phi);
   Double_t s = TMath::Sin(phi);
   Double_t v[3];
   Int_t j;
   for (Int_t i=0; i<3; i++) {
      j = 3*i;
      v[0] = c*fRotationMatrix[j]-s*fRotationMatrix[j+2];
      v[1] = fRotationMatrix[j+1];
      v[2] = s*fRotationMatrix[j]+c*fRotationMatrix[j+2];
      memcpy(&fRotationMatrix[j], v, kN3);
   }   
   SetBit(kGeoRotation);
   v[0] = c*fTranslation[0]-s*fTranslation[2];
   v[1] = fTranslation[1];
   v[2] = s*fTranslation[0]+c*fTranslation[2];
   memcpy(fTranslation,v,kN3);
}

//-----------------------------------------------------------------------------
void TGeoHMatrix::RotateZ(Double_t angle)
{
// Rotate about Z axis with angle expressed in degrees.
   Double_t phi = angle*TMath::DegToRad();
   Double_t c = TMath::Cos(phi);
   Double_t s = TMath::Sin(phi);
   Double_t v[3];
   Int_t j;
   for (Int_t i=0; i<3; i++) {
      j = 3*i;
      v[0] = c*fRotationMatrix[j]+s*fRotationMatrix[j+1];
      v[1] = -s*fRotationMatrix[j]+c*fRotationMatrix[j+1];
      v[2] = fRotationMatrix[j+2];
      memcpy(&fRotationMatrix[j], v, kN3);
   }   
   SetBit(kGeoRotation);
   v[0] = c*fTranslation[0]+s*fTranslation[1];
   v[1] = -s*fTranslation[0]+c*fTranslation[1];
   v[2] = fTranslation[2];
   memcpy(fTranslation,v,kN3);
}
