iProjectorIncrementalSiddon.cc

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/*
This file is part of CASToR.

    CASToR is free software: you can redistribute it and/or modify it under the
    terms of the GNU General Public License as published by the Free Software
    Foundation, either version 3 of the License, or (at your option) any later
    version.

    CASToR is distributed in the hope that it will be useful, but WITHOUT ANY
    WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
    FOR A PARTICULAR PURPOSE.  See the GNU General Public License for more
    details.

    You should have received a copy of the GNU General Public License along with
    CASToR (in file GNU_GPL.TXT). If not, see <http://www.gnu.org/licenses/>.

Copyright 2017-2019 all CASToR contributors listed below:

    --> Didier BENOIT, Claude COMTAT, Marina FILIPOVIC, Thibaut MERLIN, Mael MILLARDET, Simon STUTE, Valentin VIELZEUF

This is CASToR version 3.0.
*/

#include "iProjectorIncrementalSiddon.hh"
#include "sOutputManager.hh"
#ifdef _WIN32
// Avoid compilation errors due to mix up between std::min()/max() and
// min max macros
#undef min
#undef max
#endif

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iProjectorIncrementalSiddon::iProjectorIncrementalSiddon() : vProjector()
{
  // This projector is compatible with SPECT attenuation correction because
  // all voxels contributing to a given line are ordered from point 1 (focal)
  // to point 2 (scanner). Note that there can be some aliasing problem with
  // this incremental method, but which will depend on the voxel size and number.
  // However, these problems are quite negligible and pretty uncommon. So we still
  // say that this projector is compatible.
  m_compatibleWithSPECTAttenuationCorrection = true;
  // This projector is compatible with compression as it works only with the
  // cartesian coordinates of 2 end points of a line
  m_compatibleWithCompression = true;
}

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iProjectorIncrementalSiddon::~iProjectorIncrementalSiddon()
{
}

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int iProjectorIncrementalSiddon::ReadConfigurationFile(const string& a_configurationFile)
{
  // No options for incremental siddon
  ;
  // Normal end
  return 0;
}

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int iProjectorIncrementalSiddon::ReadOptionsList(const string& a_optionsList)
{
  // No options for incremental siddon
  ;
  // Normal end
  return 0;
}

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void iProjectorIncrementalSiddon::ShowHelpSpecific()
{
  cout << "This projector is a simple line projector that computes the exact path length of a line through the voxels." << endl;
  cout << "It is basically an incremental version of the original algorithm proposed by R. L. Siddon (see the classicSiddon projector)." << endl;
  cout << "It is implemented from the following published paper:" << endl;
  cout << "F. Jacobs et al, \"A fast algorithm to calculate the exact radiological path through a pixel or voxel space\", J. Comput. Inf. Technol., vol. 6, pp. 89-94, 1998." << endl;
}

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int iProjectorIncrementalSiddon::CheckSpecificParameters()
{
  // Nothing to check for this projector
  ;
  // Normal end
  return 0;
}

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int iProjectorIncrementalSiddon::InitializeSpecific()
{
  // Verbose
  if (m_verbose>=2) Cout("iProjectorIncrementalSiddon::InitializeSpecific() -> Use incremental Siddon projector" << endl);
  // Normal end
  return 0;
}

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INTNB iProjectorIncrementalSiddon::EstimateMaxNumberOfVoxelsPerLine()
{
  // Find the maximum number of voxels along a given dimension
  INTNB max_nb_voxels_in_dimension = mp_ImageDimensionsAndQuantification->GetNbVoxX();
  if (mp_ImageDimensionsAndQuantification->GetNbVoxY()>max_nb_voxels_in_dimension) max_nb_voxels_in_dimension = mp_ImageDimensionsAndQuantification->GetNbVoxY();
  if (mp_ImageDimensionsAndQuantification->GetNbVoxZ()>max_nb_voxels_in_dimension) max_nb_voxels_in_dimension = mp_ImageDimensionsAndQuantification->GetNbVoxZ();
  // We should have at most 4 voxels in a given plane, so multiply by 4
  // (note: this is not true however it ensures no overflow and is already quite optimized for RAM usage !)
  max_nb_voxels_in_dimension *= 4;
  // Return the value
  return max_nb_voxels_in_dimension;
}

// =====================================================================
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int iProjectorIncrementalSiddon::ProjectWithoutTOF(int a_direction, oProjectionLine* ap_ProjectionLine )
{
  #ifdef CASTOR_DEBUG
  if (!m_initialized)
  {
    Cerr("***** iProjectorIncrementalSiddon::ProjectWithoutTOF() -> Called while not initialized !" << endl);
    Exit(EXIT_DEBUG);
  }
  #endif

  #ifdef CASTOR_VERBOSE
  if (m_verbose>=10)
  {
    string direction = "";
    if (a_direction==FORWARD) direction = "forward";
    else direction = "backward";
    Cout("iProjectorIncrementalSiddon::Project without TOF -> Project line '" << ap_ProjectionLine << "' in " << direction << " direction" << endl);
  }
  #endif

  // Get event positions
  FLTNB* event1Float = ap_ProjectionLine->GetPosition1();
  FLTNB* event2Float = ap_ProjectionLine->GetPosition2();
  HPFLTNB event1[3] = { event1Float[0], event1Float[1], event1Float[2] };
  HPFLTNB event2[3] = { event2Float[0], event2Float[1], event2Float[2] };

  // **************************************
  // STEP 1: LOR length calculation
  // **************************************
  HPFLTNB length_LOR = ap_ProjectionLine->GetLength();

  // **************************************
  // STEP 2: Compute entrance voxel indexes
  // **************************************
  HPFLTNB alphaFirst[] = { 0.0, 0.0, 0.0 };
  HPFLTNB alphaLast[] = { 0.0, 0.0, 0.0 };

  HPFLTNB alphaMin = 0.0f, alphaMax = 1.0f;
  HPFLTNB delta_pos[] = {
    event2[ 0 ] - event1[ 0 ],
    event2[ 1 ] - event1[ 1 ],
    event2[ 2 ] - event1[ 2 ]
  };

  // Computation of alphaMin et alphaMax values (entrance and exit point of the ray)
  for( int i = 0; i < 3; ++i )
  {
    if( delta_pos[ i ] != 0.0 )
    {
      alphaFirst[i] = (-mp_halfFOV[i] - event1[i]) / (delta_pos[ i ]);
      alphaLast[i]  = ( mp_halfFOV[i] - event1[i]) / (delta_pos[ i ]);
      alphaMin = (std::max)(alphaMin,(std::min)(alphaFirst[i],alphaLast[i]));
      alphaMax = (std::min)(alphaMax,(std::max)(alphaFirst[i],alphaLast[i]));
    }
  }

  // if alphaMax is less than or equal to alphaMin no intersection
  // and return an empty buffer
  if( alphaMax <= alphaMin ) return 0;

  // Now we have to find the indices of the particular plane
  // (iMin,iMax), (jMin,jMax), (kMin,kMax)
  int iMin = 0, iMax = 0;
  int jMin = 0, jMax = 0;
  int kMin = 0, kMax = 0;

  // For the X-axis
  if( delta_pos[ 0 ] > 0.0f )
  {
    iMin = ::ceil( ( mp_nbVox[ 0 ] + 1 ) - ( mp_halfFOV[ 0 ] - alphaMin * delta_pos[ 0 ] - event1[ 0 ] ) / mp_sizeVox[0] );
    iMax = ::floor( 1 + ( event1[ 0 ] + alphaMax * delta_pos[ 0 ] - (-mp_halfFOV[ 0 ]) ) / mp_sizeVox[0] );
  }
  else if( delta_pos[ 0 ] < 0.0f )
  {
    iMin = ::ceil( ( mp_nbVox[ 0 ] + 1 ) - ( mp_halfFOV[ 0 ] - alphaMax * delta_pos[ 0 ] - event1[ 0 ] ) / mp_sizeVox[0] );
    iMax = ::floor( 1 + ( event1[ 0 ] + alphaMin * delta_pos[ 0 ] - (-mp_halfFOV[ 0 ]) ) / mp_sizeVox[0] );
  }
  if( delta_pos[ 0 ] == 0 )
  {
    iMin = 1, iMax = 0;
  }

  // For the Y-axis
  if( delta_pos[ 1 ] > 0 )
  {
    jMin = ::ceil( ( mp_nbVox[ 1 ] + 1 ) - ( mp_halfFOV[ 1 ] - alphaMin * delta_pos[ 1 ] - event1[ 1 ] ) / mp_sizeVox[1] );
    jMax = ::floor( 1 + ( event1[ 1 ] + alphaMax * delta_pos[ 1 ] - (-mp_halfFOV[ 1 ]) ) / mp_sizeVox[1] );
  }
  else if( delta_pos[ 1 ] < 0 )
  {
    jMin = ::ceil( ( mp_nbVox[ 1 ] + 1 ) - ( mp_halfFOV[ 1 ] - alphaMax * delta_pos[ 1 ] - event1[ 1 ] ) / mp_sizeVox[1] );
    jMax = ::floor( 1 + ( event1[ 1 ] + alphaMin * delta_pos[ 1 ] - (-mp_halfFOV[ 1 ]) ) / mp_sizeVox[1] );
  }
  else if( delta_pos[ 1 ] == 0 )
  {
    jMin = 1, jMax = 0;
  }

  // For the Z-axis
  if( delta_pos[ 2 ] > 0 )
  {
    kMin = ::ceil( ( mp_nbVox[ 2 ] + 1 ) - ( mp_halfFOV[ 2 ] - alphaMin * delta_pos[ 2 ] - event1[ 2 ] ) / mp_sizeVox[2] );
    kMax = ::floor( 1 + ( event1[ 2 ] + alphaMax * delta_pos[ 2 ] - (-mp_halfFOV[ 2 ]) ) / mp_sizeVox[2] );
  }
  else if( delta_pos[ 2 ] < 0 )
  {
    kMin = ::ceil( ( mp_nbVox[ 2 ] + 1 ) - ( mp_halfFOV[ 2 ] - alphaMax * delta_pos[ 2 ] - event1[ 2 ] ) / mp_sizeVox[2] );
    kMax = ::floor( 1 + ( event1[ 2 ] + alphaMin * delta_pos[ 2 ] - (-mp_halfFOV[ 2 ]) ) / mp_sizeVox[2] );
  }
  else if( delta_pos[ 2 ] == 0 )
  {
    kMin = 1, kMax = 0;
  }

  // Computing the last term n number of intersection
  INTNB n = ( iMax - iMin + 1 ) + ( jMax - jMin + 1 )
    + ( kMax - kMin + 1 );

  // Array storing the first alpha in X, Y and Z
  HPFLTNB alpha_XYZ[ 3 ] = { 1.0f, 1.0f, 1.0f };

  // Computing the first alpha in X
  if( delta_pos[ 0 ] > 0 )
    alpha_XYZ[ 0 ] = ( ( (-mp_halfFOV[ 0 ]) + ( iMin - 1 ) * mp_sizeVox[0] ) - event1[ 0 ] ) / delta_pos[ 0 ];
  else if( delta_pos[ 0 ] < 0 )
    alpha_XYZ[ 0 ] = ( ( (-mp_halfFOV[ 0 ]) + ( iMax - 1 ) * mp_sizeVox[0] ) - event1[ 0 ] ) / delta_pos[ 0 ];

  // Computing the first alpha in Y
  if( delta_pos[ 1 ] > 0 )
    alpha_XYZ[ 1 ] = ( ( (-mp_halfFOV[ 1 ]) + ( jMin - 1 ) * mp_sizeVox[1] ) - event1[ 1 ] ) / delta_pos[ 1 ];
  else if( delta_pos[ 1 ] < 0 )
    alpha_XYZ[ 1 ] = ( ( (-mp_halfFOV[ 1 ]) + ( jMax - 1 ) * mp_sizeVox[1] ) - event1[ 1 ] ) / delta_pos[ 1 ];

  // Computing the first alpha in Z
  if( delta_pos[ 2 ] > 0 )
    alpha_XYZ[ 2 ] = ( ( (-mp_halfFOV[ 2 ]) + ( kMin - 1 ) * mp_sizeVox[2] ) - event1[ 2 ] ) / delta_pos[ 2 ];
  else if( delta_pos[ 2 ] < 0 )
    alpha_XYZ[ 2 ] = ( ( (-mp_halfFOV[ 2 ]) + ( kMax - 1 ) * mp_sizeVox[2] ) - event1[ 2 ] ) / delta_pos[ 2 ];

  // Computing the alpha updating
  HPFLTNB alpha_u[ 3 ] = {
    mp_sizeVox[0] / std::fabs( delta_pos[ 0 ] ),
    mp_sizeVox[1] / std::fabs( delta_pos[ 1 ] ),
    mp_sizeVox[2] / std::fabs( delta_pos[ 2 ] )
  };

  // Computing the index updating 
  INTNB index_u[ 3 ] = {
    (delta_pos[ 0 ] < 0) ? -1 : 1,
    (delta_pos[ 1 ] < 0) ? -1 : 1,
    (delta_pos[ 2 ] < 0) ? -1 : 1
  };

  // Check which alpha is the min/max and increment
  if( alpha_XYZ[ 0 ] == alphaMin ) alpha_XYZ[ 0 ] += alpha_u[ 0 ];
  if( alpha_XYZ[ 1 ] == alphaMin ) alpha_XYZ[ 1 ] += alpha_u[ 1 ];
  if( alpha_XYZ[ 2 ] == alphaMin ) alpha_XYZ[ 2 ] += alpha_u[ 2 ];

  // Computing the minimum value in the alpha_XYZ buffer
  HPFLTNB const min_alpha_XYZ = (std::min)( alpha_XYZ[ 0 ],
    (std::min)( alpha_XYZ[ 1 ], alpha_XYZ[ 2 ] ) );

  // Computing the first index of intersection
  HPFLTNB alphaMid = ( min_alpha_XYZ + alphaMin ) / 2.0f;
  INTNB index_ijk[ 3 ] = {
    1 + (int)( ( event1[ 0 ] + alphaMid * delta_pos[ 0 ] - (-mp_halfFOV[ 0 ]) ) / mp_sizeVox[0] ),
    1 + (int)( ( event1[ 1 ] + alphaMid * delta_pos[ 1 ] - (-mp_halfFOV[ 1 ]) ) / mp_sizeVox[1] ),
    1 + (int)( ( event1[ 2 ] + alphaMid * delta_pos[ 2 ] - (-mp_halfFOV[ 2 ]) ) / mp_sizeVox[2] )
  };

  INTNB const w = mp_nbVox[ 0 ];
  INTNB const wh = w * mp_nbVox[ 1 ];

  // Loop over the number of plane to cross
  HPFLTNB alpha_c = alphaMin;
  FLTNB coeff = 0.0f;
  INTNB numVox = 0;

  for( int nP = 0; nP < n - 1; ++nP )
  {
    if( ( alpha_XYZ[ 0 ] <= alpha_XYZ[ 1 ] )
     && ( alpha_XYZ[ 0 ] <= alpha_XYZ[ 2 ] ) )
    {
      // Storing values
      if( ( alpha_XYZ[ 0 ] >= alphaMin )
       && ( index_ijk[ 0 ] - 1 >= 0 )
       && ( index_ijk[ 0 ] - 1 <= mp_nbVox[ 0 ] - 1 )
       && ( index_ijk[ 1 ] - 1 >= 0 )
       && ( index_ijk[ 1 ] - 1 <= mp_nbVox[ 1 ] - 1 )
       && ( index_ijk[ 2 ] - 1 >= 0 )
       && ( index_ijk[ 2 ] - 1 <= mp_nbVox[ 2 ] - 1 ) )
      {
        coeff = ( alpha_XYZ[ 0 ] - alpha_c ) * length_LOR;
        numVox = ( index_ijk[ 0 ] - 1 ) + ( ( index_ijk[ 1 ] - 1 ) ) * w + ( ( index_ijk[ 2 ] - 1 ) ) * wh;
        // if this voxel is masked, do nothing
        if (!m_hasMask || mp_mask[numVox]) ap_ProjectionLine->AddVoxel(a_direction, numVox, coeff);
      }
      // Increment values
      alpha_c = alpha_XYZ[ 0 ];
      alpha_XYZ[ 0 ] += alpha_u[ 0 ];
      index_ijk[ 0 ] += index_u[ 0 ];
    }
    else if( ( alpha_XYZ[ 1 ] < alpha_XYZ[ 0 ] )
          && ( alpha_XYZ[ 1 ] <= alpha_XYZ[ 2 ] ) )
    {
      // Storing values
      if( ( alpha_XYZ[ 1 ] >= alphaMin )
       && ( index_ijk[ 0 ] - 1 >= 0 )
       && ( index_ijk[ 0 ] - 1 <= mp_nbVox[ 0 ] - 1 )
       && ( index_ijk[ 1 ] - 1 >= 0 )
       && ( index_ijk[ 1 ] - 1 <= mp_nbVox[ 1 ] - 1 )
       && ( index_ijk[ 2 ] - 1 >= 0 )
       && ( index_ijk[ 2 ] - 1 <= mp_nbVox[ 2 ] - 1 ) )
      {
        coeff = ( alpha_XYZ[ 1 ] - alpha_c ) * length_LOR;
        numVox = ( index_ijk[ 0 ] - 1 ) + ( ( index_ijk[ 1 ] - 1 ) ) * w + ( ( index_ijk[ 2 ] - 1 ) ) * wh;
        // if this voxel is masked, do nothing
        if (!m_hasMask || mp_mask[numVox]) ap_ProjectionLine->AddVoxel(a_direction, numVox, coeff);
      }
      // Increment values
      alpha_c = alpha_XYZ[ 1 ];
      alpha_XYZ[ 1 ] += alpha_u[ 1 ];
      index_ijk[ 1 ] += index_u[ 1 ];
    }
    else if( ( alpha_XYZ[ 2 ] < alpha_XYZ[ 0 ] )
          && ( alpha_XYZ[ 2 ] < alpha_XYZ[ 1 ] ) )
    {
      // Storing values
      if( ( alpha_XYZ[ 2 ] >= alphaMin )
       && ( index_ijk[ 0 ] - 1 >= 0 )
       && ( index_ijk[ 0 ] - 1 <= mp_nbVox[ 0 ] - 1 )
       && ( index_ijk[ 1 ] - 1 >= 0 )
       && ( index_ijk[ 1 ] - 1 <= mp_nbVox[ 1 ] - 1 )
       && ( index_ijk[ 2 ] - 1 >= 0 )
       && ( index_ijk[ 2 ] - 1 <= mp_nbVox[ 2 ] - 1 ) )
      {
        coeff = ( alpha_XYZ[ 2 ] - alpha_c ) * length_LOR;
        numVox = ( index_ijk[ 0 ] - 1 ) + ( ( index_ijk[ 1 ] - 1 ) ) * w + ( ( index_ijk[ 2 ] - 1 ) ) * wh;
        // if this voxel is masked, do nothing
        if (!m_hasMask || mp_mask[numVox]) ap_ProjectionLine->AddVoxel(a_direction, numVox, coeff);
      }
      // Increment values
      alpha_c = alpha_XYZ[ 2 ];
      alpha_XYZ[ 2 ] += alpha_u[ 2 ];
      index_ijk[ 2 ] += index_u[ 2 ];
    }
  }

  return 0;
}

// =====================================================================
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// =====================================================================

int iProjectorIncrementalSiddon::ProjectTOFListmode(int a_direction, oProjectionLine* ap_ProjectionLine)
{
  #ifdef CASTOR_DEBUG
  if (!m_initialized)
  {
    Cerr("***** iProjectorIncrementalSiddon::ProjectTOFListmode() -> Called while not initialized !" << endl);
    Exit(EXIT_DEBUG);
  }
  #endif

  #ifdef CASTOR_VERBOSE
  if (m_verbose>=10)
  {
    string direction = "";
    if (a_direction==FORWARD) direction = "forward";
    else direction = "backward";
    Cout("iProjectorIncrementalSiddon::Project with TOF position -> Project line '" << ap_ProjectionLine << "' in " << direction << " direction" << endl);
  }
  #endif

  // Simpler way now, hopefully it works
  FLTNB* event1Float = ap_ProjectionLine->GetPosition1();
  FLTNB* event2Float = ap_ProjectionLine->GetPosition2();
  HPFLTNB event1[3] = { event1Float[0], event1Float[1], event1Float[2] };
  HPFLTNB event2[3] = { event2Float[0], event2Float[1], event2Float[2] };

  // **************************************
  // STEP 1: LOR length calculation
  // **************************************
  HPFLTNB length_LOR = ap_ProjectionLine->GetLength();

  // **************************************
  // STEP 2: Compute entrance voxel indexes
  // **************************************
  HPFLTNB alphaFirst[] = { 0.0, 0.0, 0.0 };
  HPFLTNB alphaLast[] = { 0.0, 0.0, 0.0 };

  HPFLTNB alphaMin = 0.0f, alphaMax = 1.0f;
  HPFLTNB delta_pos[] = {
    event2[ 0 ] - event1[ 0 ],
    event2[ 1 ] - event1[ 1 ],
    event2[ 2 ] - event1[ 2 ]
  };

  // Get TOF info
  HPFLTNB tof_measurement = ap_ProjectionLine->GetTOFMeasurementInPs();

  // convert delta time into delta length
  HPFLTNB tof_delta = tof_measurement * SPEED_OF_LIGHT_IN_MM_PER_PS * 0.5;

  // TOF Gaussian standard deviation and truncation
  HPFLTNB tof_sigma = m_TOFResolutionInMm / TWO_SQRT_TWO_LN_2;
  HPFLTNB tof_sigma_sqrt2 = sqrt(2.)*tof_sigma;
  HPFLTNB tof_half_span = 0.;

  if (m_TOFWeightingFcnPrecomputedFlag) tof_half_span = ((HPFLTNB)m_TOFWeightingFcnNbSamples)/(2.*m_TOFPrecomputedSamplingFactor);
  else if (m_TOFBinProperProcessingFlag) tof_half_span = tof_sigma * m_TOFNbSigmas + 0.5 * m_TOFBinSizeInMm;
  else tof_half_span = tof_sigma * m_TOFNbSigmas;

  // distance between the first event1 and the TOF measurement
  HPFLTNB lor_tof_center = length_LOR * 0.5 + tof_delta;

  // index along each axis of the first voxel falling inside the truncated TOF distribution centered at the TOF measurement
  HPFLTNB tof_edge_low[] = {0,0,0};
  // index along each axis of the last voxel falling inside the truncated TOF distribution centered at the TOF measurement
  HPFLTNB tof_edge_high[] = {0,0,0};
  HPFLTNB tof_center;
  INTNB tof_index_low[] = {0,0,0};
  INTNB tof_index_high[] = {0,0,0};

  // low/high voxel edges (in absolute coordinates) for truncated TOF
  for (int ax=0;ax<3;ax++)
  {
    // absolute coordinate along each axis of the center of the TOF distribution
    tof_center = event1[ax] +  lor_tof_center * delta_pos[ax] / length_LOR;

    // absolute coordinate along each axis of the lowest voxel edge spanned by the TOF distribution, limited by the lowest FOV edge
    tof_edge_low[ax] = tof_center - tof_half_span * fabs(delta_pos[ax]) / length_LOR;
    tof_index_low[ax] = max( (INTNB)::floor( (tof_edge_low[ax] - (-mp_halfFOV[ax])) / mp_sizeVox[ax] ), (INTNB)0);
    // if low TOF edge above the highest FOV edge, return empty line
    if (tof_index_low[ax]>mp_nbVox[ax]-1) return 0;
    tof_edge_low[ax] = (HPFLTNB)tof_index_low[ax] *  mp_sizeVox[ax] - mp_halfFOV[ax];

    // absolute coordinate along each axis of the highest voxel edge spanned by the TOF distribution, limited by the highest FOV edge
    tof_edge_high[ax] = tof_center + tof_half_span * fabs(delta_pos[ax]) / length_LOR;
    tof_index_high[ax] = min( (INTNB)::floor( (tof_edge_high[ax] - (-mp_halfFOV[ax])) / mp_sizeVox[ax] ), mp_nbVox[ax]-1);
    // if high TOF edge below the lowest FOV edge, return empty line
    if (tof_index_high[ax]<0) return 0;
    tof_edge_high[ax] = (HPFLTNB)(tof_index_high[ax]+1) * mp_sizeVox[ax] - mp_halfFOV[ax];
  }

  // Computation of alphaMin et alphaMax values entrance and exit point of the ray at voxel grid (edges),
  // with respect to the truncated TOF distribution centered at the TOF measurement,
  // limited by the FOV, absolute normalized distance from event1
  for( int i = 0; i < 3; ++i )
  {
    if( delta_pos[ i ] != 0.0 )
    {
      alphaFirst[i] = (-mp_halfFOV[i] - event1[i]) / (delta_pos[ i ]);
      alphaLast[i]  = ( mp_halfFOV[i] - event1[i]) / (delta_pos[ i ]);
      alphaMin = (std::max)(alphaMin,(std::min)(alphaFirst[i],alphaLast[i]));
      alphaMax = (std::min)(alphaMax,(std::max)(alphaFirst[i],alphaLast[i]));
    }
  }

  // if alphaMax is less than or equal to alphaMin no intersection
  // and return an empty buffer
  if( alphaMax <= alphaMin ) return 0;

  // Now we have to find the indices of the particular plane
  // (iMin,iMax), (jMin,jMax), (kMin,kMax)
  int iMin = 0, iMax = 0;
  int jMin = 0, jMax = 0;
  int kMin = 0, kMax = 0;

  // For the X-axis
  if( delta_pos[ 0 ] > 0.0f )
  {
    iMin = ::ceil( ( mp_nbVox[ 0 ] + 1 ) - ( mp_halfFOV[ 0 ] - alphaMin * delta_pos[ 0 ] - event1[ 0 ] ) / mp_sizeVox[0] );
    iMax = ::floor( 1 + ( event1[ 0 ] + alphaMax * delta_pos[ 0 ] - (-mp_halfFOV[ 0 ]) ) / mp_sizeVox[0] );
  }
  else if( delta_pos[ 0 ] < 0.0f )
  {
    iMin = ::ceil( ( mp_nbVox[ 0 ] + 1 ) - ( mp_halfFOV[ 0 ] - alphaMax * delta_pos[ 0 ] - event1[ 0 ] ) / mp_sizeVox[0] );
    iMax = ::floor( 1 + ( event1[ 0 ] + alphaMin * delta_pos[ 0 ] - (-mp_halfFOV[ 0 ]) ) / mp_sizeVox[0] );
  }
  if( delta_pos[ 0 ] == 0 )
  {
    iMin = 1, iMax = 0;
  }

  // For the Y-axis
  if( delta_pos[ 1 ] > 0 )
  {
    jMin = ::ceil( ( mp_nbVox[ 1 ] + 1 ) - ( mp_halfFOV[ 1 ] - alphaMin * delta_pos[ 1 ] - event1[ 1 ] ) / mp_sizeVox[1] );
    jMax = ::floor( 1 + ( event1[ 1 ] + alphaMax * delta_pos[ 1 ] - (-mp_halfFOV[ 1 ]) ) / mp_sizeVox[1] );
  }
  else if( delta_pos[ 1 ] < 0 )
  {
    jMin = ::ceil( ( mp_nbVox[ 1 ] + 1 ) - ( mp_halfFOV[ 1 ] - alphaMax * delta_pos[ 1 ] - event1[ 1 ] ) / mp_sizeVox[1] );
    jMax = ::floor( 1 + ( event1[ 1 ] + alphaMin * delta_pos[ 1 ] - (-mp_halfFOV[ 1 ]) ) / mp_sizeVox[1] );
  }
  else if( delta_pos[ 1 ] == 0 )
  {
    jMin = 1, jMax = 0;
  }

  // For the Z-axis
  if( delta_pos[ 2 ] > 0 )
  {
    kMin = ::ceil( ( mp_nbVox[ 2 ] + 1 ) - ( mp_halfFOV[ 2 ] - alphaMin * delta_pos[ 2 ] - event1[ 2 ] ) / mp_sizeVox[2] );
    kMax = ::floor( 1 + ( event1[ 2 ] + alphaMax * delta_pos[ 2 ] - (-mp_halfFOV[ 2 ]) ) / mp_sizeVox[2] );
  }
  else if( delta_pos[ 2 ] < 0 )
  {
    kMin = ::ceil( ( mp_nbVox[ 2 ] + 1 ) - ( mp_halfFOV[ 2 ] - alphaMax * delta_pos[ 2 ] - event1[ 2 ] ) / mp_sizeVox[2] );
    kMax = ::floor( 1 + ( event1[ 2 ] + alphaMin * delta_pos[ 2 ] - (-mp_halfFOV[ 2 ]) ) / mp_sizeVox[2] );
  }
  else if( delta_pos[ 2 ] == 0 )
  {
    kMin = 1, kMax = 0;
  }

  // Computing the last term n number of intersection
  INTNB n = ( iMax - iMin + 1 ) + ( jMax - jMin + 1 )
    + ( kMax - kMin + 1 );

  // Array storing the first alpha in X, Y and Z
  HPFLTNB alpha_XYZ[ 3 ] = { 1.0f, 1.0f, 1.0f };

  // Computing the first alpha in X
  if( delta_pos[ 0 ] > 0 )
    alpha_XYZ[ 0 ] = ( ( (-mp_halfFOV[ 0 ]) + ( iMin - 1 ) * mp_sizeVox[0] ) - event1[ 0 ] ) / delta_pos[ 0 ];
  else if( delta_pos[ 0 ] < 0 )
    alpha_XYZ[ 0 ] = ( ( (-mp_halfFOV[ 0 ]) + ( iMax - 1 ) * mp_sizeVox[0] ) - event1[ 0 ] ) / delta_pos[ 0 ];

  // Computing the first alpha in Y
  if( delta_pos[ 1 ] > 0 )
    alpha_XYZ[ 1 ] = ( ( (-mp_halfFOV[ 1 ]) + ( jMin - 1 ) * mp_sizeVox[1] ) - event1[ 1 ] ) / delta_pos[ 1 ];
  else if( delta_pos[ 1 ] < 0 )
    alpha_XYZ[ 1 ] = ( ( (-mp_halfFOV[ 1 ]) + ( jMax - 1 ) * mp_sizeVox[1] ) - event1[ 1 ] ) / delta_pos[ 1 ];

  // Computing the first alpha in Z
  if( delta_pos[ 2 ] > 0 )
    alpha_XYZ[ 2 ] = ( ( (-mp_halfFOV[ 2 ]) + ( kMin - 1 ) * mp_sizeVox[2] ) - event1[ 2 ] ) / delta_pos[ 2 ];
  else if( delta_pos[ 2 ] < 0 )
    alpha_XYZ[ 2 ] = ( ( (-mp_halfFOV[ 2 ]) + ( kMax - 1 ) * mp_sizeVox[2] ) - event1[ 2 ] ) / delta_pos[ 2 ];

  // Computing the alpha updating
  HPFLTNB alpha_u[ 3 ] = {
    mp_sizeVox[0] / std::fabs( delta_pos[ 0 ] ),
    mp_sizeVox[1] / std::fabs( delta_pos[ 1 ] ),
    mp_sizeVox[2] / std::fabs( delta_pos[ 2 ] )
  };

  // Computing the index updating
  INTNB index_u[ 3 ] = {
    (delta_pos[ 0 ] < 0) ? -1 : 1,
    (delta_pos[ 1 ] < 0) ? -1 : 1,
    (delta_pos[ 2 ] < 0) ? -1 : 1
  };
 
  // Check which alpha is the min/max and increment
  if( alpha_XYZ[ 0 ] == alphaMin ) alpha_XYZ[ 0 ] += alpha_u[ 0 ];
  if( alpha_XYZ[ 1 ] == alphaMin ) alpha_XYZ[ 1 ] += alpha_u[ 1 ];
  if( alpha_XYZ[ 2 ] == alphaMin ) alpha_XYZ[ 2 ] += alpha_u[ 2 ];

  // Computing the minimum value in the alpha_XYZ buffer
  HPFLTNB const min_alpha_XYZ = (std::min)( alpha_XYZ[ 0 ], (std::min)( alpha_XYZ[ 1 ], alpha_XYZ[ 2 ] ) );

  // Computing the first index of intersection
  HPFLTNB alphaMid = ( min_alpha_XYZ + alphaMin ) / 2.0f;
  INTNB index_ijk[ 3 ] = {
    1 + (INTNB)( ( event1[ 0 ] + alphaMid * delta_pos[ 0 ] - (-mp_halfFOV[ 0 ]) ) / mp_sizeVox[0] ),
    1 + (INTNB)( ( event1[ 1 ] + alphaMid * delta_pos[ 1 ] - (-mp_halfFOV[ 1 ]) ) / mp_sizeVox[1] ),
    1 + (INTNB)( ( event1[ 2 ] + alphaMid * delta_pos[ 2 ] - (-mp_halfFOV[ 2 ]) ) / mp_sizeVox[2] )
  };

  INTNB const w = mp_nbVox[ 0 ];
  INTNB const wh = w * mp_nbVox[ 1 ];

  //HPFLTNB previous_edge_erf = 0.;
  //HPFLTNB next_edge_erf = 0.;
  //bool previous_edge_erf_initialized = false;

  // Loop over the number of plane to cross
  HPFLTNB alpha_c = alphaMin;
  FLTNB coeff = 0.0f;
  INTNB numVox = 0;
  for( int nP = 0; nP < n - 1; ++nP )
  {
    if( ( alpha_XYZ[ 0 ] <= alpha_XYZ[ 1 ] )
     && ( alpha_XYZ[ 0 ] <= alpha_XYZ[ 2 ] ) )
    {
      // Storing values
      if( ( alpha_XYZ[ 0 ] >= alphaMin )
       && ( index_ijk[ 0 ] - 1 >= tof_index_low[0] )
       && ( index_ijk[ 0 ] - 1 <= tof_index_high[0] )
       && ( index_ijk[ 1 ] - 1 >= tof_index_low[1] )
       && ( index_ijk[ 1 ] - 1 <= tof_index_high[1] )
       && ( index_ijk[ 2 ] - 1 >= tof_index_low[2] )
       && ( index_ijk[ 2 ] - 1 <= tof_index_high[2]  ) )
      {
        //if (!previous_edge_erf_initialized)
        //{
          //previous_edge_erf = erf( (length_LOR *alpha_c - lor_tof_center) / tof_sigma_sqrt2 );
          //previous_edge_erf_initialized = true;
        //}

        numVox = ( index_ijk[ 0 ] - 1 ) + ( ( index_ijk[ 1 ] - 1 ) ) * w + ( ( index_ijk[ 2 ] - 1 ) ) * wh;

        // voxel center
        alphaMid = ( alpha_XYZ[ 0 ] + alpha_c ) * 0.5;

        // non TOF projection coefficient
        coeff = ( alpha_XYZ[ 0 ] - alpha_c ) * length_LOR;

        if (m_TOFWeightingFcnPrecomputedFlag)
        {
          // fetch the value of the precomputed TOF weighting function (centered at the TOF measurement)
          // nearest to the projection of the voxel center onto the LOR
          INTNB temp = m_TOFWeightingFcnNbSamples/2 + (INTNB)round( (alphaMid * length_LOR - lor_tof_center) * m_TOFPrecomputedSamplingFactor );
          // multiply the non TOF projection coefficient with the TOF weight
          if (temp>=0 && temp<m_TOFWeightingFcnNbSamples) coeff *= mp_TOFWeightingFcn[temp];
          else coeff = 0.;
        }
        else
        {
          if (m_TOFBinProperProcessingFlag)
          {
            // integration between the edges of the current quantization TOF bin (centered at the TOF measurement)
            // of the Gaussian centered at the projection of the voxel center onto the LOR
            // normalized by the size of the bin so that the integral of the final TOF weighting function remains 1
            HPFLTNB temp_erf = std::min(tof_half_span, std::max(-tof_half_span, lor_tof_center - m_TOFBinSizeInMm/2. - alphaMid * length_LOR));
            HPFLTNB prev_erf = erf(temp_erf/tof_sigma_sqrt2);
            temp_erf = std::min(tof_half_span, std::max(-tof_half_span, lor_tof_center + m_TOFBinSizeInMm/2. - alphaMid * length_LOR));
            HPFLTNB new_erf = erf(temp_erf/tof_sigma_sqrt2);
            // multiply the non TOF projection coefficient with the TOF weight
            coeff *= 0.5 * fabs(new_erf - prev_erf) / m_TOFBinSizeInMm;
          }
          else
          {
            //next_edge_erf = erf( (length_LOR * alpha_XYZ[ 0 ] - lor_tof_center) / tof_sigma_sqrt2 );
            //coeff = 0.5 * std::fabs(previous_edge_erf - next_edge_erf) ;
            //previous_edge_erf = next_edge_erf;

            // TOF weight = value of the normalized Gaussian (centered at the TOF measurement)
            // at the projection of the voxel center onto the LOR
            HPFLTNB temp =  (alphaMid * length_LOR - lor_tof_center)  / tof_sigma;
            // multiply the non TOF projection coefficient with the TOF weight
            coeff *=  exp(- 0.5 * temp * temp ) * m_TOFGaussianNormCoef;
          }
        }

        if (!m_hasMask || mp_mask[numVox])  ap_ProjectionLine->AddVoxel(a_direction, numVox, coeff);
      }

      // Increment values
      alpha_c = alpha_XYZ[ 0 ];
      alpha_XYZ[ 0 ] += alpha_u[ 0 ];
      index_ijk[ 0 ] += index_u[ 0 ];
    }
    else if( ( alpha_XYZ[ 1 ] < alpha_XYZ[ 0 ] )
          && ( alpha_XYZ[ 1 ] <= alpha_XYZ[ 2 ] ) )
    {
      // Storing values
      if( ( alpha_XYZ[ 1 ] >= alphaMin )
       && ( index_ijk[ 0 ] - 1 >= tof_index_low[0] )
       && ( index_ijk[ 0 ] - 1 <= tof_index_high[0] )
       && ( index_ijk[ 1 ] - 1 >= tof_index_low[1] )
       && ( index_ijk[ 1 ] - 1 <= tof_index_high[1] )
       && ( index_ijk[ 2 ] - 1 >= tof_index_low[2] )
       && ( index_ijk[ 2 ] - 1 <= tof_index_high[2]  ) )
      {
        //if (!previous_edge_erf_initialized)
        //{
          //previous_edge_erf = erf( (length_LOR *alpha_c - lor_tof_center) / tof_sigma_sqrt2 );
          //previous_edge_erf_initialized = true;
        //}

        numVox = ( index_ijk[ 0 ] - 1 ) + ( ( index_ijk[ 1 ] - 1 ) ) * w + ( ( index_ijk[ 2 ] - 1 ) ) * wh;

        alphaMid = ( alpha_XYZ[ 1 ]  + alpha_c ) / 2.;

        // non TOF projection coefficient
        coeff = ( alpha_XYZ[ 1 ] - alpha_c ) * length_LOR;

        if (m_TOFWeightingFcnPrecomputedFlag)
        {
          // fetch the value of the precomputed TOF weighting function (centered at the TOF measurement)
          // nearest to the projection of the voxel center onto the LOR
          INTNB temp = m_TOFWeightingFcnNbSamples/2 + (INTNB)round( (alphaMid * length_LOR - lor_tof_center) * m_TOFPrecomputedSamplingFactor );
          // multiply the non TOF projection coefficient with the TOF weight
          if (temp>=0 && temp<m_TOFWeightingFcnNbSamples) coeff *= mp_TOFWeightingFcn[temp];
          else coeff=0.;
        }
        else
        {
          if (m_TOFBinProperProcessingFlag)
          {
            // integration between the edges of the current quantization TOF bin (centered at the TOF measurement)
            // of the Gaussian centered at the projection of the voxel center onto the LOR
            // normalized by the size of the bin so that the integral of the final TOF weighting function remains 1
            HPFLTNB temp_erf = std::min(tof_half_span, std::max(-tof_half_span, lor_tof_center - m_TOFBinSizeInMm/2. - alphaMid * length_LOR));
            HPFLTNB prev_erf = erf(temp_erf/tof_sigma_sqrt2);
            temp_erf = std::min(tof_half_span, std::max(-tof_half_span, lor_tof_center + m_TOFBinSizeInMm/2. - alphaMid * length_LOR));
            HPFLTNB new_erf = erf(temp_erf/tof_sigma_sqrt2);
            // multiply the non TOF projection coefficient with the TOF weight
            coeff *= 0.5 * fabs(new_erf - prev_erf) / m_TOFBinSizeInMm;
          }
          else
          {
            //next_edge_erf = erf( (length_LOR * alpha_XYZ[ 1 ] - lor_tof_center) / tof_sigma_sqrt2 );
            //coeff = 0.5 * std::fabs(previous_edge_erf - next_edge_erf) ;
            //previous_edge_erf = next_edge_erf;

            // TOF weight = value of the normalized Gaussian (centered at the TOF measurement)
            // at the projection of the voxel center onto the LOR
            HPFLTNB temp = (alphaMid * length_LOR - lor_tof_center) / tof_sigma;
            // multiply the non TOF projection coefficient with the TOF weight
            coeff *=  exp(- 0.5 * temp * temp ) * m_TOFGaussianNormCoef;
          }
        }

        // if the voxel is not masked 
        if (!m_hasMask || mp_mask[numVox]) ap_ProjectionLine->AddVoxel(a_direction, numVox, coeff);
      }

      // Increment values
      alpha_c = alpha_XYZ[ 1 ];
      alpha_XYZ[ 1 ] += alpha_u[ 1 ];
      index_ijk[ 1 ] += index_u[ 1 ];
    }
    else if( ( alpha_XYZ[ 2 ] < alpha_XYZ[ 0 ] )
          && ( alpha_XYZ[ 2 ] < alpha_XYZ[ 1 ] ) )
    {
      // Storing values
      if( ( alpha_XYZ[ 2 ] >= alphaMin )
       && ( index_ijk[ 0 ] - 1 >= tof_index_low[0] )
       && ( index_ijk[ 0 ] - 1 <= tof_index_high[0] )
       && ( index_ijk[ 1 ] - 1 >= tof_index_low[1] )
       && ( index_ijk[ 1 ] - 1 <= tof_index_high[1] )
       && ( index_ijk[ 2 ] - 1 >= tof_index_low[2] )
       && ( index_ijk[ 2 ] - 1 <= tof_index_high[2]  ) )
      {
        //if (!previous_edge_erf_initialized)
        //{
          //previous_edge_erf = erf( (length_LOR *alpha_c - lor_tof_center) / tof_sigma_sqrt2 );
          //previous_edge_erf_initialized = true;
        //}

        numVox = ( index_ijk[ 0 ] - 1 ) + ( ( index_ijk[ 1 ] - 1 ) ) * w + ( ( index_ijk[ 2 ] - 1 ) ) * wh;

        alphaMid = ( alpha_XYZ[ 2 ]  + alpha_c ) / 2.;

        // non TOF projection coefficient
        coeff = ( alpha_XYZ[ 2 ] - alpha_c ) * length_LOR;

        if (m_TOFWeightingFcnPrecomputedFlag)
        {
          // fetch the value of the precomputed TOF weighting function (centered at the TOF measurement)
          // nearest to the projection of the voxel center onto the LOR
          INTNB temp = m_TOFWeightingFcnNbSamples/2 + (INTNB)round( (alphaMid * length_LOR - lor_tof_center) * m_TOFPrecomputedSamplingFactor );
          // multiply the non TOF projection coefficient with the TOF weight
          if (temp>=0 && temp<m_TOFWeightingFcnNbSamples) coeff *= mp_TOFWeightingFcn[temp];
          else coeff = 0.;
        }
        else
        {
          if (m_TOFBinProperProcessingFlag)
          {
            // integration between the edges of the current quantization TOF bin (centered at the TOF measurement)
            // of the Gaussian centered at the projection of the voxel center onto the LOR
            // normalized by the size of the bin so that the integral of the final TOF weighting function remains 1
            HPFLTNB temp_erf = std::min(tof_half_span, std::max(-tof_half_span, lor_tof_center - m_TOFBinSizeInMm/2. - alphaMid * length_LOR));
            HPFLTNB prev_erf = erf(temp_erf/tof_sigma_sqrt2);
            temp_erf = std::min(tof_half_span, std::max(-tof_half_span, lor_tof_center + m_TOFBinSizeInMm/2. - alphaMid * length_LOR));
            HPFLTNB new_erf = erf(temp_erf/tof_sigma_sqrt2);
            // multiply the non TOF projection coefficient with the TOF weight
            coeff *= 0.5 * fabs(new_erf - prev_erf) / m_TOFBinSizeInMm;
          }
          else
          {
            //next_edge_erf = erf( (length_LOR * alpha_XYZ[ 2 ] - lor_tof_center) / tof_sigma_sqrt2 );
            //coeff = 0.5 * std::fabs(previous_edge_erf - next_edge_erf) ;
            //previous_edge_erf = next_edge_erf;

            // TOF weight = value of the normalized Gaussian (centered at the TOF measurement)
            // at the projection of the voxel center onto the LOR
            HPFLTNB temp = (alphaMid * length_LOR - lor_tof_center) / tof_sigma;
            // multiply the non TOF projection coefficient with the TOF weight
            coeff *=  exp(- 0.5 * temp * temp ) * m_TOFGaussianNormCoef;
          }
        }

        // if the voxel is not masked 
        if (!m_hasMask || mp_mask[numVox]) ap_ProjectionLine->AddVoxel(a_direction, numVox, coeff);
      }

      // Increment values
      alpha_c = alpha_XYZ[ 2 ];
      alpha_XYZ[ 2 ] += alpha_u[ 2 ];
      index_ijk[ 2 ] += index_u[ 2 ];
    }
  }

  return 0;
}

// =====================================================================
// ---------------------------------------------------------------------
// ---------------------------------------------------------------------
// =====================================================================

int iProjectorIncrementalSiddon::ProjectTOFHistogram(int a_direction, oProjectionLine* ap_ProjectionLine)
{
  #ifdef CASTOR_DEBUG
  if (!m_initialized)
  {
    Cerr("***** iProjectorIncrementalSiddon::ProjectTOFHistogram() -> Called while not initialized !" << endl);
    Exit(EXIT_DEBUG);
  }
  #endif

  #ifdef CASTOR_VERBOSE
  if (m_verbose>=10)
  {
    string direction = "";
    if (a_direction==FORWARD) direction = "forward";
    else direction = "backward";
    Cout("iProjectorIncrementalSiddon::Project with TOF bins -> Project line '" << ap_ProjectionLine << "' in " << direction << " direction" << endl);
  }
  #endif

  // Simpler way now, hopefully it works
  FLTNB* event1Float = ap_ProjectionLine->GetPosition1();
  FLTNB* event2Float = ap_ProjectionLine->GetPosition2();
  HPFLTNB event1[3] = { event1Float[0], event1Float[1], event1Float[2] };
  HPFLTNB event2[3] = { event2Float[0], event2Float[1], event2Float[2] };

  // **************************************
  // STEP 1: LOR length calculation
  // **************************************
  HPFLTNB length_LOR = ap_ProjectionLine->GetLength();
  HPFLTNB length_LOR_half = length_LOR * 0.5;
  
  // **************************************
  // STEP 2: Compute entrance voxel indexes
  // **************************************
  HPFLTNB alphaFirst[] = { 0.0, 0.0, 0.0 };
  HPFLTNB alphaLast[] = { 0.0, 0.0, 0.0 };

  HPFLTNB alphaMin = 0.0f, alphaMax = 1.0f;
  HPFLTNB delta_pos[] = {
    event2[ 0 ] - event1[ 0 ],
    event2[ 1 ] - event1[ 1 ],
    event2[ 2 ] - event1[ 2 ]
  };

  // Get TOF info
  INTNB tof_nb_bins = ap_ProjectionLine->GetNbTOFBins();
  INTNB tof_half_nb_bins = tof_nb_bins/2;

  // TOF Gaussian standard deviation and truncation
  HPFLTNB tof_sigma = m_TOFResolutionInMm / TWO_SQRT_TWO_LN_2;
  HPFLTNB tof_sigma_sqrt2 = sqrt(2.)*tof_sigma;
  HPFLTNB tof_half_span = 0.;
  if (m_TOFWeightingFcnPrecomputedFlag) tof_half_span = ((HPFLTNB)m_TOFWeightingFcnNbSamples)/(2.*m_TOFPrecomputedSamplingFactor);
  else tof_half_span = tof_sigma * m_TOFNbSigmas;

  // if integration of the Gaussian over the TOF bin, need for help variables to save calls to erf
  HPFLTNB prev_erf = 0., new_erf = 0.;

  // minimum and maximum TOF bins
  INTNB tof_bin_last = tof_half_nb_bins;
  INTNB tof_bin_first = -tof_half_nb_bins;

  // distance between the first event1 and the center of a TOF bin along the LOR
  HPFLTNB lor_tof_center = 0.;
  // the sum of all TOF bin weights for a voxel
  //HPFLTNB tof_norm_coef = 0.;

  // the first and the last relevant TOF bins for a voxel
  INTNB tof_bin_first_for_voxel = 0, tof_bin_last_for_voxel = 0;

  // Computation of alphaMin et alphaMax values (entrance and exit point of the ray)
  for( int i = 0; i < 3; ++i )
  {
    if( delta_pos[ i ] != 0.0 )
    {
      alphaFirst[i] = (-mp_halfFOV[i] - event1[i]) / (delta_pos[ i ]);
      alphaLast[i]  = ( mp_halfFOV[i] - event1[i]) / (delta_pos[ i ]);
      alphaMin = (std::max)(alphaMin,(std::min)(alphaFirst[i],alphaLast[i]));
      alphaMax = (std::min)(alphaMax,(std::max)(alphaFirst[i],alphaLast[i]));
    }
  }

  // if alphaMax is less than or equal to alphaMin no intersection
  // and return an empty buffer
  if( alphaMax <= alphaMin ) return 0;

  // temporary storage for TOF bin weights
  // allocation after potential returns
  HPFLTNB* tof_weights_temp = new HPFLTNB[tof_nb_bins];
  for (INTNB tof_bin=0; tof_bin<tof_nb_bins; tof_bin++) tof_weights_temp[tof_bin] = 0.;

  // Now we have to find the indices of the particular plane
  // (iMin,iMax), (jMin,jMax), (kMin,kMax)
  int iMin = 0, iMax = 0;
  int jMin = 0, jMax = 0;
  int kMin = 0, kMax = 0;

  // For the X-axis
  if( delta_pos[ 0 ] > 0.0f )
  {
    iMin = ::ceil( ( mp_nbVox[ 0 ] + 1 ) - ( mp_halfFOV[ 0 ] - alphaMin * delta_pos[ 0 ] - event1[ 0 ] ) / mp_sizeVox[0] );
    iMax = ::floor( 1 + ( event1[ 0 ] + alphaMax * delta_pos[ 0 ] - (-mp_halfFOV[ 0 ]) ) / mp_sizeVox[0] );
  }
  else if( delta_pos[ 0 ] < 0.0f )
  {
    iMin = ::ceil( ( mp_nbVox[ 0 ] + 1 ) - ( mp_halfFOV[ 0 ] - alphaMax * delta_pos[ 0 ] - event1[ 0 ] ) / mp_sizeVox[0] );
    iMax = ::floor( 1 + ( event1[ 0 ] + alphaMin * delta_pos[ 0 ] - (-mp_halfFOV[ 0 ]) ) / mp_sizeVox[0] );
  }
  if( delta_pos[ 0 ] == 0 )
  {
    iMin = 1, iMax = 0;
  }

  // For the Y-axis
  if( delta_pos[ 1 ] > 0 )
  {
    jMin = ::ceil( ( mp_nbVox[ 1 ] + 1 ) - ( mp_halfFOV[ 1 ] - alphaMin * delta_pos[ 1 ] - event1[ 1 ] ) / mp_sizeVox[1] );
    jMax = ::floor( 1 + ( event1[ 1 ] + alphaMax * delta_pos[ 1 ] - (-mp_halfFOV[ 1 ]) ) / mp_sizeVox[1] );
  }
  else if( delta_pos[ 1 ] < 0 )
  {
    jMin = ::ceil( ( mp_nbVox[ 1 ] + 1 ) - ( mp_halfFOV[ 1 ] - alphaMax * delta_pos[ 1 ] - event1[ 1 ] ) / mp_sizeVox[1] );
    jMax = ::floor( 1 + ( event1[ 1 ] + alphaMin * delta_pos[ 1 ] - (-mp_halfFOV[ 1 ]) ) / mp_sizeVox[1] );
  }
  else if( delta_pos[ 1 ] == 0 )
  {
    jMin = 1, jMax = 0;
  }

  // For the Z-axis
  if( delta_pos[ 2 ] > 0 )
  {
    kMin = ::ceil( ( mp_nbVox[ 2 ] + 1 ) - ( mp_halfFOV[ 2 ] - alphaMin * delta_pos[ 2 ] - event1[ 2 ] ) / mp_sizeVox[2] );
    kMax = ::floor( 1 + ( event1[ 2 ] + alphaMax * delta_pos[ 2 ] - (-mp_halfFOV[ 2 ]) ) / mp_sizeVox[2] );
  }
  else if( delta_pos[ 2 ] < 0 )
  {
    kMin = ::ceil( ( mp_nbVox[ 2 ] + 1 ) - ( mp_halfFOV[ 2 ] - alphaMax * delta_pos[ 2 ] - event1[ 2 ] ) / mp_sizeVox[2] );
    kMax = ::floor( 1 + ( event1[ 2 ] + alphaMin * delta_pos[ 2 ] - (-mp_halfFOV[ 2 ]) ) / mp_sizeVox[2] );
  }
  else if( delta_pos[ 2 ] == 0 )
  {
    kMin = 1, kMax = 0;
  }

  // Computing the last term n number of intersection
  INTNB n = ( iMax - iMin + 1 ) + ( jMax - jMin + 1 )
    + ( kMax - kMin + 1 );

  // Array storing the first alpha in X, Y and Z
  HPFLTNB alpha_XYZ[ 3 ] = { 1.0f, 1.0f, 1.0f };

  // Computing the first alpha in X
  if( delta_pos[ 0 ] > 0 )
    alpha_XYZ[ 0 ] = ( ( (-mp_halfFOV[ 0 ]) + ( iMin - 1 ) * mp_sizeVox[0] ) - event1[ 0 ] ) / delta_pos[ 0 ];
  else if( delta_pos[ 0 ] < 0 )
    alpha_XYZ[ 0 ] = ( ( (-mp_halfFOV[ 0 ]) + ( iMax - 1 ) * mp_sizeVox[0] ) - event1[ 0 ] ) / delta_pos[ 0 ];

  // Computing the first alpha in Y
  if( delta_pos[ 1 ] > 0 )
    alpha_XYZ[ 1 ] = ( ( (-mp_halfFOV[ 1 ]) + ( jMin - 1 ) * mp_sizeVox[1] ) - event1[ 1 ] ) / delta_pos[ 1 ];
  else if( delta_pos[ 1 ] < 0 )
    alpha_XYZ[ 1 ] = ( ( (-mp_halfFOV[ 1 ]) + ( jMax - 1 ) * mp_sizeVox[1] ) - event1[ 1 ] ) / delta_pos[ 1 ];

  // Computing the first alpha in Z
  if( delta_pos[ 2 ] > 0 )
    alpha_XYZ[ 2 ] = ( ( (-mp_halfFOV[ 2 ]) + ( kMin - 1 ) * mp_sizeVox[2] ) - event1[ 2 ] ) / delta_pos[ 2 ];
  else if( delta_pos[ 2 ] < 0 )
    alpha_XYZ[ 2 ] = ( ( (-mp_halfFOV[ 2 ]) + ( kMax - 1 ) * mp_sizeVox[2] ) - event1[ 2 ] ) / delta_pos[ 2 ];

  // Computing the alpha updating
  HPFLTNB alpha_u[ 3 ] = {
    mp_sizeVox[0] / std::fabs( delta_pos[ 0 ] ),
    mp_sizeVox[1] / std::fabs( delta_pos[ 1 ] ),
    mp_sizeVox[2] / std::fabs( delta_pos[ 2 ] )
  };

  // Computing the index updating
  INTNB index_u[ 3 ] = {
    (delta_pos[ 0 ] < 0) ? -1 : 1,
    (delta_pos[ 1 ] < 0) ? -1 : 1,
    (delta_pos[ 2 ] < 0) ? -1 : 1
  };

  // Check which alpha is the min/max and increment
  if( alpha_XYZ[ 0 ] == alphaMin ) alpha_XYZ[ 0 ] += alpha_u[ 0 ];
  if( alpha_XYZ[ 1 ] == alphaMin ) alpha_XYZ[ 1 ] += alpha_u[ 1 ];
  if( alpha_XYZ[ 2 ] == alphaMin ) alpha_XYZ[ 2 ] += alpha_u[ 2 ];

  // Computing the minimum value in the alpha_XYZ buffer
  HPFLTNB const min_alpha_XYZ = (std::min)( alpha_XYZ[ 0 ], (std::min)( alpha_XYZ[ 1 ], alpha_XYZ[ 2 ] ) );

  // Computing the first index of intersection
  HPFLTNB alphaMid = ( min_alpha_XYZ + alphaMin ) / 2.0f;
  INTNB index_ijk[ 3 ] = {
    1 + (INTNB)( ( event1[ 0 ] + alphaMid * delta_pos[ 0 ] - (-mp_halfFOV[ 0 ]) ) / mp_sizeVox[0] ),
    1 + (INTNB)( ( event1[ 1 ] + alphaMid * delta_pos[ 1 ] - (-mp_halfFOV[ 1 ]) ) / mp_sizeVox[1] ),
    1 + (INTNB)( ( event1[ 2 ] + alphaMid * delta_pos[ 2 ] - (-mp_halfFOV[ 2 ]) ) / mp_sizeVox[2] )
  };

  INTNB const w = mp_nbVox[ 0 ];
  INTNB const wh = w * mp_nbVox[ 1 ];

  // Loop over the number of plane to cross
  HPFLTNB alpha_c = alphaMin;
  FLTNB coeff = 0.0f;
  INTNB numVox = 0;

  for( int nP = 0; nP < n - 1; ++nP )
  {
    if( ( alpha_XYZ[ 0 ] <= alpha_XYZ[ 1 ] )
     && ( alpha_XYZ[ 0 ] <= alpha_XYZ[ 2 ] ) )
    {
      // Storing values
      if( ( alpha_XYZ[ 0 ] >= alphaMin )
       && ( index_ijk[ 0 ] - 1 >= 0 )
       && ( index_ijk[ 0 ] - 1 <= mp_nbVox[ 0 ] - 1 )
       && ( index_ijk[ 1 ] - 1 >= 0 )
       && ( index_ijk[ 1 ] - 1 <= mp_nbVox[ 1 ] - 1 )
       && ( index_ijk[ 2 ] - 1 >= 0 )
       && ( index_ijk[ 2 ] - 1 <= mp_nbVox[ 2 ] - 1 ) )
      {
        numVox = ( index_ijk[ 0 ] - 1 ) + ( ( index_ijk[ 1 ] - 1 ) ) * w + ( ( index_ijk[ 2 ] - 1 ) ) * wh;
        
        // if this voxel is masked, do nothing
        if (!m_hasMask || mp_mask[numVox])
        {
          coeff = ( alpha_XYZ[ 0 ] - alpha_c ) * length_LOR;

          alphaMid = ( alpha_XYZ[ 0 ] + alpha_c ) * 0.5;

          // compute the first and the last relevant TOF bin for this voxel
          if (!m_TOFWeightingFcnPrecomputedFlag && m_TOFBinProperProcessingFlag)
          {
            // taking the TOF bins reached by the truncated Gaussian centered at the voxel center projection
            tof_bin_first_for_voxel = max(tof_bin_first , (INTNB)(floor( (alphaMid * length_LOR - tof_half_span - length_LOR_half - m_TOFBinSizeInMm/2.) / m_TOFBinSizeInMm )));
            tof_bin_last_for_voxel = min(tof_bin_last , (INTNB)(ceil( (alphaMid * length_LOR + tof_half_span - length_LOR_half + m_TOFBinSizeInMm/2.) / m_TOFBinSizeInMm )));
          }
          else
          {
            // taking the TOF bins whose TOF weighting function, centered at the bin center, reaches the voxel center projection 
            tof_bin_first_for_voxel = max(tof_bin_first , (INTNB)(ceil( (alphaMid * length_LOR - tof_half_span - length_LOR_half ) / m_TOFBinSizeInMm )));
            tof_bin_last_for_voxel = min(tof_bin_last , (INTNB)(floor( (alphaMid * length_LOR + tof_half_span - length_LOR_half) / m_TOFBinSizeInMm )));
          }

          lor_tof_center = length_LOR_half + tof_bin_first_for_voxel * m_TOFBinSizeInMm;

          // shift tof bin indices from -/+ to 0:nbBins range
          tof_bin_first_for_voxel += tof_half_nb_bins;
          tof_bin_last_for_voxel += tof_half_nb_bins;

          // initialization of help variables for reducing calls to erf
          if (!m_TOFWeightingFcnPrecomputedFlag && m_TOFBinProperProcessingFlag)
          {
            // bound the integration to the Gaussian truncation
            HPFLTNB temp = std::min(tof_half_span,std::max(-tof_half_span, lor_tof_center - m_TOFBinSizeInMm/2. - alphaMid * length_LOR));
            prev_erf = erf(temp/tof_sigma_sqrt2);
          }

          // compute TOF bin weights for the current voxel for all relevant TOF bins
          //tof_norm_coef = 0.;
          for (INTNB tof_bin=tof_bin_first_for_voxel; tof_bin<=tof_bin_last_for_voxel; tof_bin++)
          {
            if (m_TOFWeightingFcnPrecomputedFlag)
            {
              // fetch the value of the precomputed TOF weighting function (centered at the TOF bin center)
              // nearest to the projection of the voxel center onto the LOR
              INTNB temp = m_TOFWeightingFcnNbSamples/2 + (INTNB)round( ( alphaMid * length_LOR - lor_tof_center) * m_TOFPrecomputedSamplingFactor);
              if (temp>=0 && temp<m_TOFWeightingFcnNbSamples) tof_weights_temp[tof_bin] = mp_TOFWeightingFcn[temp];
              // add the weight to the sum for normalization
              //tof_norm_coef += tof_weights_temp[tof_bin];
              // update TOF bin center along the LOR for the next TOF bin
              lor_tof_center += m_TOFBinSizeInMm;
            }
            else
            {
              if (m_TOFBinProperProcessingFlag)
              {
                // integration between the edges of the current TOF bin of the Gaussian centered at the projection of the voxel center onto the LOR
                // reuse of integration from the previous bin to save calls to erf
                // bound the integration to the Gaussian truncation
                HPFLTNB temp = std::min(tof_half_span, std::max(-tof_half_span, lor_tof_center + m_TOFBinSizeInMm/2. - alphaMid * length_LOR));
                new_erf = erf(temp/tof_sigma_sqrt2);
                tof_weights_temp[tof_bin] = 0.5 * fabs(new_erf - prev_erf);
                // add the weight to the sum
               // tof_norm_coef += tof_weights_temp[tof_bin];
                prev_erf = new_erf;
                // update TOF bin center along the LOR for the next TOF bin
                lor_tof_center += m_TOFBinSizeInMm;
              }
              else
              {
                // TOF weight = TOF bin size * value of the normalized Gaussian (centered at the TOF bin center) at the projection of the voxel center onto the LOR
                HPFLTNB temp = ( alphaMid * length_LOR - lor_tof_center) / tof_sigma;
                // save the weight temporarily
                tof_weights_temp[tof_bin] = exp(- 0.5 * temp * temp ) * m_TOFGaussianNormCoef * m_TOFBinSizeInMm;
                // add the weight to the sum
                //tof_norm_coef += tof_weights_temp[tof_bin];
                // update TOF center along the LOR for the next TOF bin
                lor_tof_center += m_TOFBinSizeInMm;
              }
            }
          }
/*
          if (tof_norm_coef>0.)
          {
            // first normalize TOF bin weights so that they sum to 1
            for (INTNB tof_bin=tof_bin_first_for_voxel; tof_bin<=tof_bin_last_for_voxel; tof_bin++) tof_weights_temp[tof_bin] /= tof_norm_coef;
          }
*/
          // write the final TOF bin weighted projection coefficients for the current voxel
          ap_ProjectionLine->AddVoxelAllTOFBins(a_direction, numVox, coeff, tof_weights_temp, tof_bin_first_for_voxel, tof_bin_last_for_voxel);

        }
      }
      // Increment values
      alpha_c = alpha_XYZ[ 0 ];
      alpha_XYZ[ 0 ] += alpha_u[ 0 ];
      index_ijk[ 0 ] += index_u[ 0 ];
    }
    else if( ( alpha_XYZ[ 1 ] < alpha_XYZ[ 0 ] )
          && ( alpha_XYZ[ 1 ] <= alpha_XYZ[ 2 ] ) )
    {
      // Storing values
      if( ( alpha_XYZ[ 1 ] >= alphaMin )
       && ( index_ijk[ 0 ] - 1 >= 0 )
       && ( index_ijk[ 0 ] - 1 <= mp_nbVox[ 0 ] - 1 )
       && ( index_ijk[ 1 ] - 1 >= 0 )
       && ( index_ijk[ 1 ] - 1 <= mp_nbVox[ 1 ] - 1 )
       && ( index_ijk[ 2 ] - 1 >= 0 )
       && ( index_ijk[ 2 ] - 1 <= mp_nbVox[ 2 ] - 1 ) )
      {
        numVox = ( index_ijk[ 0 ] - 1 ) + ( ( index_ijk[ 1 ] - 1 ) ) * w + ( ( index_ijk[ 2 ] - 1 ) ) * wh;

        // if this voxel is masked, do nothing
        if (!m_hasMask || mp_mask[numVox])
        {
          coeff = ( alpha_XYZ[ 1 ] - alpha_c ) * length_LOR;

          alphaMid = ( alpha_XYZ[ 1 ] + alpha_c ) * 0.5;

          // compute the first and the last relevant TOF bin for this voxel
          if (!m_TOFWeightingFcnPrecomputedFlag && m_TOFBinProperProcessingFlag)
          {
            // taking the TOF bins reached by the truncated Gaussian centered at the voxel center projection
            tof_bin_first_for_voxel = max(tof_bin_first , (INTNB)(floor( (alphaMid * length_LOR - tof_half_span - length_LOR_half - m_TOFBinSizeInMm/2.) / m_TOFBinSizeInMm )));
            tof_bin_last_for_voxel = min(tof_bin_last , (INTNB)(ceil( (alphaMid * length_LOR + tof_half_span - length_LOR_half + m_TOFBinSizeInMm/2.) / m_TOFBinSizeInMm )));
          }
          else
          {
            // taking the TOF bins whose TOF weighting function, centered at the bin center, reaches the voxel center projection 
            tof_bin_first_for_voxel = max(tof_bin_first , (INTNB)(ceil( (alphaMid * length_LOR - tof_half_span - length_LOR_half ) / m_TOFBinSizeInMm )));
            tof_bin_last_for_voxel = min(tof_bin_last , (INTNB)(floor( (alphaMid * length_LOR + tof_half_span - length_LOR_half) / m_TOFBinSizeInMm )));
          }
          
          lor_tof_center = length_LOR_half + tof_bin_first_for_voxel * m_TOFBinSizeInMm;

          // shift tof bin indices from -/+ to 0:nbBins range
          tof_bin_first_for_voxel += tof_half_nb_bins;
          tof_bin_last_for_voxel += tof_half_nb_bins;

          // initialization of help variables for reducing calls to erf
          if (!m_TOFWeightingFcnPrecomputedFlag && m_TOFBinProperProcessingFlag)
          {
            // bound the integration to the Gaussian truncation
            HPFLTNB temp = std::min(tof_half_span,std::max(-tof_half_span, lor_tof_center - m_TOFBinSizeInMm/2. - alphaMid * length_LOR));
            prev_erf = erf(temp/tof_sigma_sqrt2);
          }

          // compute TOF bin weights for the current voxel for all relevant TOF bins
          //tof_norm_coef = 0.;
          for (INTNB tof_bin=tof_bin_first_for_voxel; tof_bin<=tof_bin_last_for_voxel; tof_bin++)
          {
            if (m_TOFWeightingFcnPrecomputedFlag)
            {
              // fetch the value of the precomputed TOF weighting function (centered at the TOF bin center)
              // nearest to the projection of the voxel center onto the LOR
              INTNB temp = m_TOFWeightingFcnNbSamples/2 + (INTNB)round( ( alphaMid * length_LOR - lor_tof_center) * m_TOFPrecomputedSamplingFactor );
              if (temp>=0 && temp<m_TOFWeightingFcnNbSamples) tof_weights_temp[tof_bin] = mp_TOFWeightingFcn[temp];
              // add the weight to the sum
              //tof_norm_coef += tof_weights_temp[tof_bin];
              // update TOF center along the LOR for the next TOF bin
              lor_tof_center += m_TOFBinSizeInMm;
            }
            else
            {
              if (m_TOFBinProperProcessingFlag)
              {
                // integration between the edges of the current TOF bin of the Gaussian centered at the projection of the voxel center onto the LOR
                // reuse of integration from the previous bin to save calls to erf
                // bound the integration to the Gaussian truncation
                HPFLTNB temp = std::min(tof_half_span, std::max(-tof_half_span, lor_tof_center + m_TOFBinSizeInMm/2. - alphaMid * length_LOR));
                new_erf = erf(temp/tof_sigma_sqrt2);
                tof_weights_temp[tof_bin] = 0.5 * fabs(new_erf - prev_erf);
                // add the weight to the sum for normalization
                //tof_norm_coef += tof_weights_temp[tof_bin];
                prev_erf = new_erf;
                // update TOF center along the LOR for the next TOF bin
                lor_tof_center += m_TOFBinSizeInMm;
              }
              else
              {
                // TOF weight = TOF bin size * value of the normalized Gaussian (centered at the TOF bin center) at the projection of the voxel center onto the LOR
                HPFLTNB temp = ( alphaMid * length_LOR - lor_tof_center) / tof_sigma;
                // save the weight temporarily
                tof_weights_temp[tof_bin] = exp(- 0.5 * temp * temp ) * m_TOFGaussianNormCoef * m_TOFBinSizeInMm;
                // add the weight to the sum for normalization
                //tof_norm_coef += tof_weights_temp[tof_bin];
                // update TOF center along the LOR for the next TOF bin
                lor_tof_center += m_TOFBinSizeInMm;
              } 
            }
          }
/*
          if (tof_norm_coef>0.)
          {
            // first normalize TOF bin weights so that they sum to 1
            for (INTNB tof_bin=tof_bin_first_for_voxel; tof_bin<=tof_bin_last_for_voxel; tof_bin++) tof_weights_temp[tof_bin] /= tof_norm_coef;
          }
*/
          // write the final TOF bin weighted projection coefficients for the current voxel
          ap_ProjectionLine->AddVoxelAllTOFBins(a_direction, numVox, coeff, tof_weights_temp, tof_bin_first_for_voxel, tof_bin_last_for_voxel);
        }
      }

      // Increment values
      alpha_c = alpha_XYZ[ 1 ];
      alpha_XYZ[ 1 ] += alpha_u[ 1 ];
      index_ijk[ 1 ] += index_u[ 1 ];
    }
    else if( ( alpha_XYZ[ 2 ] < alpha_XYZ[ 0 ] )
          && ( alpha_XYZ[ 2 ] < alpha_XYZ[ 1 ] ) )
    {
      // Storing values
      if( ( alpha_XYZ[ 2 ] >= alphaMin )
       && ( index_ijk[ 0 ] - 1 >= 0 )
       && ( index_ijk[ 0 ] - 1 <= mp_nbVox[ 0 ] - 1 )
       && ( index_ijk[ 1 ] - 1 >= 0 )
       && ( index_ijk[ 1 ] - 1 <= mp_nbVox[ 1 ] - 1 )
       && ( index_ijk[ 2 ] - 1 >= 0 )
       && ( index_ijk[ 2 ] - 1 <= mp_nbVox[ 2 ] - 1 ) )
      {
        numVox = ( index_ijk[ 0 ] - 1 ) + ( ( index_ijk[ 1 ] - 1 ) ) * w + ( ( index_ijk[ 2 ] - 1 ) ) * wh;

        // if this voxel is masked, do nothing
        if (!m_hasMask || mp_mask[numVox])
        {
          coeff = ( alpha_XYZ[ 2 ] - alpha_c ) * length_LOR;

          alphaMid = ( alpha_XYZ[ 2 ] + alpha_c ) * 0.5;

          // compute the first and the last relevant TOF bin for this voxel
          if (!m_TOFWeightingFcnPrecomputedFlag && m_TOFBinProperProcessingFlag)
          {
            // taking the TOF bins reached by the truncated Gaussian centered at the voxel center projection
            tof_bin_first_for_voxel = max(tof_bin_first , (INTNB)(floor( (alphaMid * length_LOR - tof_half_span - length_LOR_half - m_TOFBinSizeInMm/2.) / m_TOFBinSizeInMm )));
            tof_bin_last_for_voxel = min(tof_bin_last , (INTNB)(ceil( (alphaMid * length_LOR + tof_half_span - length_LOR_half + m_TOFBinSizeInMm/2.) / m_TOFBinSizeInMm )));
          }
          else
          {
            // taking the TOF bins whose TOF weighting function, centered at the bin center, reaches the voxel center projection 
            tof_bin_first_for_voxel = max(tof_bin_first , (INTNB)(ceil( (alphaMid * length_LOR - tof_half_span - length_LOR_half ) / m_TOFBinSizeInMm )));
            tof_bin_last_for_voxel = min(tof_bin_last , (INTNB)(floor( (alphaMid * length_LOR + tof_half_span - length_LOR_half) / m_TOFBinSizeInMm )));
          }

          lor_tof_center = length_LOR_half + tof_bin_first_for_voxel * m_TOFBinSizeInMm;

          // shift tof bin indices from -/+ to 0:nbBins range
          tof_bin_first_for_voxel += tof_half_nb_bins;
          tof_bin_last_for_voxel += tof_half_nb_bins;


          // initialization of help variables for reducing calls to erf
          if (!m_TOFWeightingFcnPrecomputedFlag && m_TOFBinProperProcessingFlag)
          {
            // bound the integration to the Gaussian truncation
            HPFLTNB temp = std::min(tof_half_span,std::max(-tof_half_span, lor_tof_center - m_TOFBinSizeInMm/2. - alphaMid * length_LOR));
            prev_erf = erf(temp/tof_sigma_sqrt2);
          }

          // compute TOF bin weights for the current voxel for all relevant TOF bins
          //tof_norm_coef = 0.;
          for (INTNB tof_bin=tof_bin_first_for_voxel; tof_bin<=tof_bin_last_for_voxel; tof_bin++)
          {
            if (m_TOFWeightingFcnPrecomputedFlag)
            {
              // fetch the value of the precomputed TOF weighting function (centered at the TOF bin center)
              // nearest to the projection of the voxel center onto the LOR
              INTNB temp = m_TOFWeightingFcnNbSamples/2 + (INTNB)round( ( alphaMid * length_LOR - lor_tof_center) * m_TOFPrecomputedSamplingFactor );
              if (temp>=0 && temp<m_TOFWeightingFcnNbSamples) tof_weights_temp[tof_bin] = mp_TOFWeightingFcn[temp];
              // add the weight to the sum
              //tof_norm_coef += tof_weights_temp[tof_bin];
              // update TOF bin center along the LOR for the next TOF bin
              lor_tof_center += m_TOFBinSizeInMm;
            }
            else
            {
              if (m_TOFBinProperProcessingFlag)
              {
                // integration between the edges of the current TOF bin of the Gaussian centered at the projection of the voxel center onto the LOR
                // reuse of integration from the previous bin to save calls to erf
                // bound the integration to the Gaussian truncation
                HPFLTNB temp = std::min(tof_half_span, std::max(-tof_half_span, lor_tof_center + m_TOFBinSizeInMm/2. - alphaMid * length_LOR));
                new_erf = erf(temp/tof_sigma_sqrt2);
                tof_weights_temp[tof_bin] = 0.5 * fabs(new_erf - prev_erf);
                // add the weight to the sum
                //tof_norm_coef += tof_weights_temp[tof_bin];
                prev_erf = new_erf;
                // update TOF center along the LOR for the next TOF bin
                lor_tof_center += m_TOFBinSizeInMm;
              }
              else
              {
                // TOF weight = TOF bin size * value of the normalized Gaussian (centered at the TOF bin center) at the projection of the voxel center onto the LOR
                HPFLTNB temp = ( alphaMid * length_LOR - lor_tof_center) / tof_sigma;
                tof_weights_temp[tof_bin] = exp(- 0.5 * temp * temp ) * m_TOFGaussianNormCoef * m_TOFBinSizeInMm;
                // add the weight to the sum
                //tof_norm_coef += tof_weights_temp[tof_bin];
                // update TOF center along the LOR for the next TOF bin
                lor_tof_center += m_TOFBinSizeInMm;
              }
            }
          }
/*
          if (tof_norm_coef>0.)
          {
            // first normalize TOF bin weights so that they sum to 1
            for (INTNB tof_bin=tof_bin_first_for_voxel; tof_bin<=tof_bin_last_for_voxel; tof_bin++) tof_weights_temp[tof_bin] /= tof_norm_coef;
          }
*/
          // write the final TOF bin weighted projection coefficients for the current voxel
          ap_ProjectionLine->AddVoxelAllTOFBins(a_direction, numVox, coeff, tof_weights_temp, tof_bin_first_for_voxel, tof_bin_last_for_voxel);
        }
      }

      // Increment values
      alpha_c = alpha_XYZ[ 2 ];
      alpha_XYZ[ 2 ] += alpha_u[ 2 ];
      index_ijk[ 2 ] += index_u[ 2 ];
    }
  }

  delete[] tof_weights_temp;

  return 0;
}

// =====================================================================
// ---------------------------------------------------------------------
// ---------------------------------------------------------------------
// =====================================================================