vtkFlyingEdges3D.cxx 50.5 KB
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/*=========================================================================

  Program:   Visualization Toolkit
  Module:    vtkFlyingEdges3D.cxx

  Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
  All rights reserved.
  See Copyright.txt or http://www.kitware.com/Copyright.htm for details.

     This software is distributed WITHOUT ANY WARRANTY; without even
     the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
     PURPOSE.  See the above copyright notice for more information.

=========================================================================*/
#include "vtkFlyingEdges3D.h"

#include "vtkMath.h"
#include "vtkImageData.h"
#include "vtkCellArray.h"
#include "vtkInformation.h"
#include "vtkInformationIntegerVectorKey.h"
#include "vtkInformationVector.h"
#include "vtkObjectFactory.h"
#include "vtkPointData.h"
#include "vtkPolyData.h"
#include "vtkFloatArray.h"
#include "vtkStreamingDemandDrivenPipeline.h"
#include "vtkMarchingCubesTriangleCases.h"
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#include "vtkSMPTools.h"
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#include <math.h>

vtkStandardNewMacro(vtkFlyingEdges3D);

//----------------------------------------------------------------------------

// This templated class implements the heart of the algorithm.
// vtkFlyingEdges3D populates the information in this class and
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// then invokes Contour() to actually initiate execution.
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template <class T>
class vtkFlyingEdges3DAlgorithm
{
public:
  // Edge case table values.
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  enum {
    Below = 0, //below isovalue
    Above = 1, //above isovalue
    LeftAbove = 1, //left vertex is above isovalue
    RightAbove = 2, //right vertex is above isovalue
    BothAbove = 3 //entire edge is above isovalue
  };
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  // Dealing with boundary situations when processing volumes.
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  enum {
    Interior = 0,
    MinBoundary = 1,
    MaxBoundary = 2
  } vtkBoundarySituations;
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  // Edge-based case table to generate output triangle primitives. It is
  // equivalent to the vertex-based Marching Cubes case table but provides
  // several computational advantages (parallel separability, more efficient
  // computation). This table is built from the MC case table when the class
  // is instantiated.
  unsigned char EdgeCases[256][16];

  // A table to map old edge ids (as defined from vtkMarchingCubesCases) into
  // the edge-based case table. This is so that the existing Marching Cubes
  // case tables can be reused.
  static const unsigned char EdgeMap[12];

  // A table that lists voxel point ids as a function of edge ids (edge ids
  // for edge-based case table).
  static const unsigned char VertMap[12][2];

  // A table describing vertex offsets (in index space) from the cube axes
  // origin for each of the eight vertices of a voxel.
  static const unsigned char VertOffsets[8][3];

  // This table is used to accelerate the generation of output triangles and
  // points. The EdgeUses array, a function of the voxel case number,
  // indicates which voxel edges intersect with the contour (i.e., require
  // interpolation). This array is filled in at instantiation during the case
  // table generation process.
  unsigned char EdgeUses[256][12];

  // Flags indicate whether a particular case requires voxel axes to be
  // processed. A cheap acceleration structure computed from the case
  // tables at the point of instantiation.
  unsigned char IncludesAxes[256];

  // Algorithm-derived data. XCases tracks the x-row edge cases. The
  // EdgeMetaData tracks information needed for parallel partitioning,
  // and to enable generation of the output primitives without using
  // a point locator.
  unsigned char *XCases;
  vtkIdType *EdgeMetaData;

  // Internal variables used by the various algorithm methods. Interfaces VTK
  // image data in a form more convenient to the algorithm.
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  T        *Scalars;
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  vtkIdType Dims[3];
  double   *Origin;
  double   *Spacing;
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  vtkIdType NumberOfEdges;
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  vtkIdType SliceOffset;
  int Min0;
  int Max0;
  int Inc0;
  int Min1;
  int Max1;
  int Inc1;
  int Min2;
  int Max2;
  int Inc2;

  // Output data. Threads write to partitioned memory.
  T         *NewScalars;
  vtkIdType *NewTris;
  float     *NewPoints;
  float     *NewGradients;
  float     *NewNormals;
  unsigned char NeedGradients;

  // Setup algorithm
  vtkFlyingEdges3DAlgorithm();

  // The three main passes of the algorithm.
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  void ProcessXEdge(double value, T const * const inPtr, vtkIdType row, vtkIdType slice); //PASS 1
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  void ProcessYZEdges(vtkIdType row, vtkIdType slice); //PASS 2
  void GenerateOutput(double value, T* inPtr, vtkIdType row, vtkIdType slice);//PASS 3

  // Place holder for now in case fancy bit fiddling is needed later.
  void SetXEdge(unsigned char *ePtr, unsigned char edgeCase)
    {*ePtr = edgeCase;}

  // Given the four x-edge cases defining this voxel, return the voxel case
  // number.
  unsigned char GetEdgeCase(unsigned char *ePtr[4])
    {
    return (*(ePtr[0]) | ((*(ePtr[1]))<<2) | ((*(ePtr[2]))<<4) | ((*(ePtr[3]))<<6));
    }

  // Return the number of contouring primitives for a particular edge case number.
  unsigned char GetNumberOfPrimitives(unsigned char eCase)
    { return this->EdgeCases[eCase][0]; }

  // Return an array indicating which voxel edges intersect the contour.
  unsigned char *GetEdgeUses(unsigned char eCase)
    { return this->EdgeUses[eCase]; }

  // Indicate whether voxel axes need processing for this case.
  unsigned char CaseIncludesAxes(unsigned char eCase)
    { return this->IncludesAxes[eCase]; }

  // Count edge intersections near volume boundaries.
  void CountBoundaryYZInts(unsigned char loc, unsigned char *edgeCases,
                           vtkIdType *eMD[4]);

  // Produce the output triangles for this voxel cell.
  void GenerateTris(unsigned char eCase, unsigned char numTris, vtkIdType *eIds,
                    vtkIdType &triId)
    {
      vtkIdType *tri;
      const unsigned char *edges = this->EdgeCases[eCase] + 1;
      for (int i=0; i < numTris; ++i, edges+=3)
        {
        tri = this->NewTris + 4*triId++;
        tri[0] = 3;
        tri[1] = eIds[edges[0]];
        tri[2] = eIds[edges[1]];
        tri[3] = eIds[edges[2]];
        }
    }

  // Compute gradient on interior point.
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  void ComputeGradient(unsigned char loc, vtkIdType ijk[3],
                       T const * const s0_start, T const * const s0_end,
                       T const * const s1_start, T const * const s1_end,
                       T const * const s2_start, T const * const s2_end,
                       float g[3])
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    {
      if ( loc == Interior )
        {
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        g[0] = 0.5*( (*s0_start - *s0_end) / this->Spacing[0] );
        g[1] = 0.5*( (*s1_start - *s1_end) / this->Spacing[1] );
        g[2] = 0.5*( (*s2_start - *s2_end) / this->Spacing[2] );
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        }
      else
        {
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        this->ComputeBoundaryGradient(ijk,
                                      s0_start, s0_end,
                                      s1_start, s1_end,
                                      s2_start, s2_end,
                                      g);
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        }
    }

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  // Interpolate along a voxel axes edge.
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  void InterpolateAxesEdge(double t, unsigned char loc,
                           float x0[3],
                           T const * const s,
                           const int incs[3],
                           float x1[3],
                           vtkIdType vId,
                           vtkIdType ijk[3],
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                           float g0[3])
    {
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      float *x = this->NewPoints + 3*vId;
      x[0] = x0[0] + t*(x1[0]-x0[0]);
      x[1] = x0[1] + t*(x1[1]-x0[1]);
      x[2] = x0[2] + t*(x1[2]-x0[2]);
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      if ( this->NeedGradients )
        {
        float gTmp[3], g1[3];
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        this->ComputeGradient(loc,ijk,
                              s + incs[0], s - incs[0],
                              s + incs[1], s - incs[1],
                              s + incs[2], s - incs[2],
                              g1);
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        float *g = ( this->NewGradients ? this->NewGradients + 3*vId : gTmp );
        g[0] = g0[0] + t*(g1[0]-g0[0]);
        g[1] = g0[1] + t*(g1[1]-g0[1]);
        g[2] = g0[2] + t*(g1[2]-g0[2]);

        if ( this->NewNormals )
          {
          float *n = this->NewNormals + 3*vId;
          n[0] = -g[0];
          n[1] = -g[1];
          n[2] = -g[2];
          vtkMath::Normalize(n);
          }
        }//if normals or gradients required
    }

  // Compute the gradient on a point which may be on the boundary of the volume.
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  void ComputeBoundaryGradient(vtkIdType ijk[3],
                               T const * const s0_start, T const * const s0_end,
                               T const * const s1_start, T const * const s1_end,
                               T const * const s2_start, T const * const s2_end,
                               float g[3]);
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  // Interpolate along an arbitrary edge, typically one that may be on the
  // volume boundary. This means careful computation of stuff requiring
  // neighborhood information (e.g., gradients).
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  void InterpolateEdge(double value, vtkIdType ijk[3],
                       T const * const s, const int incs[3],
                       float x[3],
                       unsigned char edgeNum,
                       unsigned char const* const edgeUses,
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                       vtkIdType *eIds);

  // Produce the output points on the voxel axes for this voxel cell.
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  void GeneratePoints(double value, unsigned char loc, vtkIdType ijk[3],
                      T const * const sPtr, const int incs[3],
                      float x[3], unsigned char const * const edgeUses,
                      vtkIdType *eIds);
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  // Helper function to set up the point ids on voxel edges.
  unsigned char InitVoxelIds(unsigned char *ePtr[4], vtkIdType *eMD[4],
                             vtkIdType *eIds)
    {
      unsigned char eCase = GetEdgeCase(ePtr);
      eIds[0] = eMD[0][0]; //x-edges
      eIds[1] = eMD[1][0];
      eIds[2] = eMD[2][0];
      eIds[3] = eMD[3][0];
      eIds[4] = eMD[0][1]; //y-edges
      eIds[5] = eIds[4] + this->EdgeUses[eCase][4];
      eIds[6] = eMD[2][1];
      eIds[7] = eIds[6] + this->EdgeUses[eCase][6];
      eIds[8] = eMD[0][2]; //z-edges
      eIds[9] = eIds[8] + this->EdgeUses[eCase][8];
      eIds[10] = eMD[1][2];
      eIds[11] = eIds[10] + this->EdgeUses[eCase][10];
      return eCase;
    }

  // Helper function to advance the point ids along voxel rows.
  void AdvanceVoxelIds(unsigned char eCase, vtkIdType *eIds)
    {
      eIds[0] += this->EdgeUses[eCase][0]; //x-edges
      eIds[1] += this->EdgeUses[eCase][1];
      eIds[2] += this->EdgeUses[eCase][2];
      eIds[3] += this->EdgeUses[eCase][3];
      eIds[4] += this->EdgeUses[eCase][4]; //y-edges
      eIds[5] = eIds[4] + this->EdgeUses[eCase][5];
      eIds[6] += this->EdgeUses[eCase][6];
      eIds[7] = eIds[6] + this->EdgeUses[eCase][7];
      eIds[8] += this->EdgeUses[eCase][8]; //z-edges
      eIds[9] = eIds[8] + this->EdgeUses[eCase][9];
      eIds[10] += this->EdgeUses[eCase][10];
      eIds[11] = eIds[10] + this->EdgeUses[eCase][11];
    }
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  // Threading integration via SMPTools
  template <class TT> class Pass1
    {
    public:
      vtkFlyingEdges3DAlgorithm<TT> *Algo;
      double Value;
      Pass1(vtkFlyingEdges3DAlgorithm<TT> *algo, double value)
        {this->Algo = algo; this->Value = value;}
      void  operator()(vtkIdType slice, vtkIdType end)
        {
        vtkIdType row;
        TT *rowPtr, *slicePtr = this->Algo->Scalars + slice*this->Algo->Inc2;
        for ( ; slice < end; ++slice )
          {
          for (row=0, rowPtr=slicePtr; row < this->Algo->Dims[1]; ++row)
            {
            this->Algo->ProcessXEdge(this->Value, rowPtr, row, slice);
            rowPtr += this->Algo->Inc1;
            }//for all rows in this slice
          slicePtr += this->Algo->Inc2;
          }//for all slices in this batch
        }
    };
  template <class TT> class Pass2
    {
    public:
      Pass2(vtkFlyingEdges3DAlgorithm<TT> *algo)
        {this->Algo = algo;}
      vtkFlyingEdges3DAlgorithm<TT> *Algo;
      void  operator()(vtkIdType slice, vtkIdType end)
        {
        for ( ; slice < end; ++slice)
          {
          for ( vtkIdType row=0; row < (this->Algo->Dims[1]-1); ++row)
            {
            this->Algo->ProcessYZEdges(row, slice);
            }//for all rows in this slice
          }//for all slices in this batch
        }
    };
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  template <class TT> class Pass4
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    {
    public:
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      Pass4(vtkFlyingEdges3DAlgorithm<TT> *algo, double value)
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        {this->Algo = algo; this->Value = value;}
      vtkFlyingEdges3DAlgorithm<TT> *Algo;
      double Value;
      void  operator()(vtkIdType slice, vtkIdType end)
        {
        vtkIdType row;
        vtkIdType *eMD0 = this->Algo->EdgeMetaData + slice*6*this->Algo->Dims[1];
        vtkIdType *eMD1 = eMD0 + 6*this->Algo->Dims[1];
        TT *rowPtr, *slicePtr = this->Algo->Scalars + slice*this->Algo->Inc2;
        for ( ; slice < end; ++slice )
          {
          // It's possible to skip entire slices if there is nothing to generate
          if ( eMD1[3] > eMD0[3] ) //there are triangle primitives!
            {
            for (row=0, rowPtr=slicePtr; row < this->Algo->Dims[1]-1; ++row)
              {
              this->Algo->GenerateOutput(this->Value, rowPtr, row, slice);
              rowPtr += this->Algo->Inc1;
              }//for all rows in this slice
            }//if there are triangles
          slicePtr += this->Algo->Inc2;
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          eMD0 = eMD1;
          eMD1 = eMD0 + 6*this->Algo->Dims[1];
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          }//for all slices in this batch
        }
    };

  // Interface between VTK and templated functions
  static void Contour(vtkFlyingEdges3D *self, vtkImageData *input,
                      int extent[6], vtkIdType *incs, T *scalars,
                      vtkPoints *newPts, vtkCellArray *newTris,
                      vtkDataArray *newScalars,vtkFloatArray *newNormals,
                      vtkFloatArray *newGradients);
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};

//----------------------------------------------------------------------------
// Map MC edges numbering to use the saner FlyingEdges edge numbering scheme.
template <class T> const unsigned char vtkFlyingEdges3DAlgorithm<T>::
EdgeMap[12] = {0,5,1,4,2,7,3,6,8,9,10,11};

//----------------------------------------------------------------------------
// Map MC edges numbering to use the saner FlyingEdges edge numbering scheme.
template <class T> const unsigned char vtkFlyingEdges3DAlgorithm<T>::
VertMap[12][2] = {{0,1}, {2,3}, {4,5}, {6,7}, {0,2}, {1,3}, {4,6}, {5,7},
                  {0,4}, {1,5}, {2,6}, {3,7}};

//----------------------------------------------------------------------------
// The offsets of each vertex (in index space) from the voxel axes origin.
template <class T> const unsigned char vtkFlyingEdges3DAlgorithm<T>::
VertOffsets[8][3] = {{0,0,0}, {1,0,0}, {0,1,0}, {1,1,0},
                     {0,0,1}, {1,0,1}, {0,1,1}, {1,1,1}};

//----------------------------------------------------------------------------
// Instantiate and initialize key data members. Mostly we build the
// edge-based case table, and associated acceleration structures, from the
// marching cubes case table. Some of this code is borrowed shamelessly from
// vtkVoxel::Contour() method.
template <class T> vtkFlyingEdges3DAlgorithm<T>::
vtkFlyingEdges3DAlgorithm():XCases(NULL),EdgeMetaData(NULL),NewScalars(NULL),
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                            NewTris(NULL),NewPoints(NULL),NewGradients(NULL),
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                            NewNormals(NULL)
{
  int i, j, k, l, ii, eCase, index, numTris;
  static int vertMap[8] = {0,1,3,2,4,5,7,6};
  static int CASE_MASK[8] = {1,2,4,8,16,32,64,128};
  EDGE_LIST *edge;
  vtkMarchingCubesTriangleCases *triCase;
  unsigned char *edgeCase;

  // Initialize cases, increments, and edge intersection flags
  for (eCase=0; eCase<256; ++eCase)
    {
    for (j=0; j<16; ++j)
      {
      this->EdgeCases[eCase][j] = 0;
      }
    for (j=0; j<12; ++j)
      {
      this->EdgeUses[eCase][j] = 0;
      }
    this->IncludesAxes[eCase] = 0;
    }

  // The voxel, edge-based case table is a function of the four x-edge cases
  // that define the voxel. Here we convert the existing MC vertex-based case
  // table into a x-edge case table. Note that the four x-edges are ordered
  // (0->3): x, x+y, x+z, x+y+z; the four y-edges are ordered (4->7): y, y+x,
  // y+z, y+x+z; and the four z-edges are ordered (8->11): z, z+x, z+y,
  // z+x+y.
  for (l=0; l<4; ++l)
    {
    for (k=0; k<4; ++k)
      {
      for (j=0; j<4; ++j)
        {
        for (i=0; i<4; ++i)
          {
          //yes we could just count to (0->255) but where's the fun in that?
          eCase = i | (j<<2) | (k<<4) | (l<<6);
          for ( ii=0, index = 0; ii < 8; ++ii)
            {
            if ( eCase & (1<<vertMap[ii]) ) //map into ancient MC table
              {
              index |= CASE_MASK[ii];
              }
            }
          //Now build case table
          triCase = vtkMarchingCubesTriangleCases::GetCases() + index;
          edge = triCase->edges;
          for ( numTris=0, edge=triCase->edges; edge[0] > -1; edge += 3 )
            {//count the number of triangles
            numTris++;
            }
          if ( numTris > 0 )
            {
            edgeCase = this->EdgeCases[eCase];
            *edgeCase++ = numTris;
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            for ( edge = triCase->edges; edge[0] > -1; edge += 3, edgeCase+=3 )
              {
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              // Build new case table.
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              edgeCase[0] = this->EdgeMap[edge[0]];
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              edgeCase[1] = this->EdgeMap[edge[1]];
              edgeCase[2] = this->EdgeMap[edge[2]];
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              }
            }
          }//x-edges
        }//x+y-edges
      }//x+z-edges
    }//x+y+z-edges

  // Okay now build the acceleration structure. This is used to generate
  // output points and triangles when processing a voxel x-row as well as to
  // perform other topological reasoning. This structure is a function of the
  // particular case number.
  for (eCase=0; eCase < 256; ++eCase)
    {
    edgeCase = this->EdgeCases[eCase];
    numTris = *edgeCase++;

    // Mark edges that are used by this case.
    for (i=0; i < numTris*3; ++i) //just loop over all edges
      {
      this->EdgeUses[eCase][edgeCase[i]] = 1;
      }

    this->IncludesAxes[eCase] = this->EdgeUses[eCase][0] |
      this->EdgeUses[eCase][4] | this->EdgeUses[eCase][8];

    }//for all cases
}

//----------------------------------------------------------------------------
// Count intersections along voxel axes. When traversing the volume across
// x-edges, the voxel axes on the boundary may be undefined near boundaries
// (because there are no fully-formed cells). Thus the voxel axes on the
// boundary are treated specially.
template <class T> void vtkFlyingEdges3DAlgorithm<T>::
CountBoundaryYZInts(unsigned char loc, unsigned char *edgeUses,
                    vtkIdType *eMD[4])
{
  switch (loc)
    {
    case 2: //+x boundary
      eMD[0][1] += edgeUses[5];
      eMD[0][2] += edgeUses[9];
      break;
    case 8: //+y
      eMD[1][2] += edgeUses[10];
      break;
    case 10://+x +y
      eMD[0][1] += edgeUses[5];
      eMD[0][2] += edgeUses[9];
      eMD[1][2] += edgeUses[10];
      eMD[1][2] += edgeUses[11];
      break;
    case 32://+z
      eMD[2][1] += edgeUses[6];
      break;
    case 34: //+x +z
      eMD[0][1] += edgeUses[5];
      eMD[0][2] += edgeUses[9];
      eMD[2][1] += edgeUses[6];
      eMD[2][1] += edgeUses[7];
      break;
    case 40: //+y +z
      eMD[2][1] += edgeUses[6];
      eMD[1][2] += edgeUses[10];
      break;
    case 42: //+x +y +z happens no more than once per volume
      eMD[0][1] += edgeUses[5];
      eMD[0][2] += edgeUses[9];
      eMD[1][2] += edgeUses[10];
      eMD[1][2] += edgeUses[11];
      eMD[2][1] += edgeUses[6];
      eMD[2][1] += edgeUses[7];
      break;
    default: //uh-oh shouldn't happen
      break;
    }
}

//----------------------------------------------------------------------------
// Compute the gradient when the point may be near the boundary of the
// volume.
template <class T> void vtkFlyingEdges3DAlgorithm<T>::
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ComputeBoundaryGradient(vtkIdType ijk[3],
                        T const * const s0_start, T const * const s0_end,
                        T const * const s1_start, T const * const s1_end,
                        T const * const s2_start, T const * const s2_end,
                        float g[3])
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{
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  const T* s = s0_start - this->Inc0;

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  if ( ijk[0] == 0 )
    {
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    g[0] = (*s0_start - *s) / this->Spacing[0];
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    }
  else if ( ijk[0] >= (this->Dims[0]-1) )
    {
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    g[0] = (*s - *s0_end) / this->Spacing[0];
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    }
  else
    {
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    g[0] = 0.5 * ( (*s0_start - *s0_end) / this->Spacing[0] );
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    }

  if ( ijk[1] == 0 )
    {
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    g[1] = (*s1_start - *s) / this->Spacing[1];
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    }
  else if ( ijk[1] >= (this->Dims[1]-1) )
    {
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    g[1] = (*s - *s1_end) / this->Spacing[1];
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    }
  else
    {
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    g[1] = 0.5 * ( (*s1_start - *s1_end) / this->Spacing[1] );
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    }

  if ( ijk[2] == 0 )
    {
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    g[2] = (*s2_start - *s) / this->Spacing[2];
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    }
  else if ( ijk[2] >= (this->Dims[2]-1) )
    {
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    g[2] = (*s - *s2_end) / this->Spacing[2];
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    }
  else
    {
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    g[2] = 0.5 * ( (*s2_start - *s2_end) / this->Spacing[2] );
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    }
}

//----------------------------------------------------------------------------
// Interpolate a new point along a boundary edge. Make sure to consider
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// proximity to the boundary when computing gradients, etc.
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template <class T> void vtkFlyingEdges3DAlgorithm<T>::
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InterpolateEdge(double value, vtkIdType ijk[3],
                T const * const s,
                const int incs[3],
                float x[3],
                unsigned char edgeNum,
                unsigned char const * const edgeUses,
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                vtkIdType *eIds)
{
  // if this edge is not used then get out
  if ( ! edgeUses[edgeNum] )
    {
    return;
    }

  // build the edge information
  const unsigned char *vertMap = this->VertMap[edgeNum];
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  float x0[3], x1[3];
  vtkIdType ijk0[3], ijk1[3], vId=eIds[edgeNum];
  int i;

  const unsigned char *offsets = this->VertOffsets[vertMap[0]];
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  T const * const s0 = s + offsets[0]*incs[0] +
                           offsets[1]*incs[1] +
                           offsets[2]*incs[2];
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  for (i=0; i<3; ++i)
    {
    ijk0[i] = ijk[i] + offsets[i];
    x0[i] = x[i] + offsets[i]*this->Spacing[i];
    }

  offsets = this->VertOffsets[vertMap[1]];
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  T const * const s1 = s + offsets[0]*incs[0] +
                           offsets[1]*incs[1] +
                           offsets[2]*incs[2];
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  for (i=0; i<3; ++i)
    {
    ijk1[i] = ijk[i] + offsets[i];
    x1[i] = x[i] + offsets[i]*this->Spacing[i];
    }

  // Okay interpolate
  double t = (value - *s0) / (*s1 - *s0);
  float *xPtr = this->NewPoints + 3*vId;
  xPtr[0] = x0[0] + t*(x1[0]-x0[0]);
  xPtr[1] = x0[1] + t*(x1[1]-x0[1]);
  xPtr[2] = x0[2] + t*(x1[2]-x0[2]);
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  if ( this->NeedGradients )
    {
    float gTmp[3], g0[3], g1[3];
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    this->ComputeBoundaryGradient(ijk0,
                                  s0+incs[0], s0-incs[0],
                                  s0+incs[1], s0-incs[1],
                                  s0+incs[2], s0-incs[2],
                                  g0);
    this->ComputeBoundaryGradient(ijk1,
                                  s1+incs[0], s1-incs[0],
                                  s1+incs[1], s1-incs[1],
                                  s1+incs[2], s1-incs[2],
                                  g1);
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    float *g = ( this->NewGradients ? this->NewGradients + 3*vId : gTmp );
    g[0] = g0[0] + t*(g1[0]-g0[0]);
    g[1] = g0[1] + t*(g1[1]-g0[1]);
    g[2] = g0[2] + t*(g1[2]-g0[2]);

    if ( this->NewNormals )
      {
      float *n = this->NewNormals + 3*vId;
      n[0] = -g[0];
      n[1] = -g[1];
      n[2] = -g[2];
      vtkMath::Normalize(n);
      }
    }//if normals or gradients required
}

//----------------------------------------------------------------------------
// Generate the output points and optionally normals, gradients and
// interpolate attributes.
template <class T> void vtkFlyingEdges3DAlgorithm<T>::
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GeneratePoints(double value, unsigned char loc, vtkIdType ijk[3],
               T const * const sPtr, const int incs[3],
               float x[3],
               unsigned char const * const edgeUses,
               vtkIdType *eIds)
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{
  // Create a slightly faster path for voxel axes interior to the volume.
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  float g0[3];
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  if ( this->NeedGradients )
    {
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    this->ComputeGradient(loc,ijk,
                          sPtr + incs[0], sPtr - incs[0],
                          sPtr + incs[1], sPtr - incs[1],
                          sPtr + incs[2], sPtr - incs[2],
                          g0);
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    }
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  // Interpolate the cell axes edges
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  for(int i=0; i < 3; ++i)
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    {
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    if(edgeUses[i*4])
      {
      //edgesUses[0] == x axes edge
      //edgesUses[4] == y axes edge
      //edgesUses[8] == z axes edge
      float x1[3] = {x[0], x[1], x[2] }; x1[i] += this->Spacing[i];
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      vtkIdType ijk1[3] = { ijk[0], ijk[1], ijk[2] }; ++ijk1[i];
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      T const * const sPtr2 = (sPtr+incs[i]);
      double t = (value - *sPtr) / (*sPtr2 - *sPtr);
      this->InterpolateAxesEdge(t, loc, x, sPtr2, incs, x1, eIds[i*4], ijk1, g0);
      }
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    }

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  // On the boundary cells special work has to be done to cover the partial
  // cell axes. These are boundary situations where the voxel axes is not
  // fully formed. These situations occur on the +x,+y,+z volume
  // boundaries. (The other cases fall through the default: case which is
  // expected.)
  //
  // Note that loc is one of 27 regions in the volume, with (0,1,2)
  // indicating (interior, min, max) along coordinate axes.
  switch (loc)
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    {
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    case 2: case 6: case 18: case 22: //+x
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      this->InterpolateEdge(value, ijk, sPtr, incs, x, 5, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 9, edgeUses, eIds);
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      break;
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    case 8: case 9: case 24: case 25: //+y
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      this->InterpolateEdge(value, ijk, sPtr, incs, x, 1, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 10, edgeUses, eIds);
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      break;
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    case 32: case 33: case 36: case 37: //+z
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 2, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 6, edgeUses, eIds);
      break;
    case 10: case 26: //+x +y
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      this->InterpolateEdge(value, ijk, sPtr, incs, x, 1, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 5, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 9, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 10, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 11, edgeUses, eIds);
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      break;
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    case 34: case 38: //+x +z
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      this->InterpolateEdge(value, ijk, sPtr, incs, x, 2, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 5, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 9, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 6, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 7, edgeUses, eIds);
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      break;
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    case 40: case 41: //+y +z
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      this->InterpolateEdge(value, ijk, sPtr, incs, x, 1, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 2, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 3, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 6, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 10, edgeUses, eIds);
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      break;
    case 42: //+x +y +z happens no more than once per volume
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      this->InterpolateEdge(value, ijk, sPtr, incs, x, 1, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 2, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 3, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 5, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 9, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 10, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 11, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 6, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 7, edgeUses, eIds);
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      break;
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    default: //interior, or -x,-y,-z boundaries
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      return;
    }
}

//----------------------------------------------------------------------------
// PASS 1: Process a single volume x-row (and all of the voxel edges that
// compose the row). Determine the x-edges case classification, count the
// number of x-edge intersections, and figure out where intersections along
// the x-row begins and ends (i.e., gather information for computational
// trimming).
template <class T> void vtkFlyingEdges3DAlgorithm<T>::
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ProcessXEdge(double value, T const* const inPtr, vtkIdType row, vtkIdType slice)
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{
  vtkIdType nxcells=this->Dims[0]-1;
  vtkIdType minInt=nxcells, maxInt = 0;
  vtkIdType *edgeMetaData;
  unsigned char *ePtr = this->XCases + slice*this->SliceOffset + row*nxcells;
  double s0, s1 = static_cast<double>(*inPtr);

  //run along the entire x-edge computing edge cases
  edgeMetaData = this->EdgeMetaData + (slice*this->Dims[1] + row)*6;
  std::fill_n(edgeMetaData, 6, 0);
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  vtkIdType sum = 0;

  //pull this out help reduce false sharing
  vtkIdType inc0 = this->Inc0;

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  for (vtkIdType i=0; i < nxcells; ++i, ++ePtr)
    {
    s0 = s1;
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    s1 = static_cast<double>(*(inPtr + (i+1)*inc0));
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    unsigned char edgeCase = vtkFlyingEdges3DAlgorithm::Below;
    if (s0 >= value)
      {
      edgeCase = vtkFlyingEdges3DAlgorithm::LeftAbove;
      }
    if( s1 >= value)
      {
      edgeCase |= vtkFlyingEdges3DAlgorithm::RightAbove;
      }
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    this->SetXEdge(ePtr, edgeCase);

    // if edge intersects contour
    if ( edgeCase == vtkFlyingEdges3DAlgorithm::LeftAbove ||
         edgeCase == vtkFlyingEdges3DAlgorithm::RightAbove )
      {
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      ++sum; //increment number of intersections along x-edge
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      minInt = ( i < minInt ? i : minInt);
      maxInt = i + 1;
      }//if contour interacts with this x-edge
    }//for all x-cell edges along this x-edge

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  edgeMetaData[0] += sum; //write back the number of intersections along x-edge

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  // The beginning and ending of intersections along the edge is used for
  // computational trimming.
  edgeMetaData[4] = minInt; //where intersections start along x edge
  edgeMetaData[5] = maxInt; //where intersections end along x edge
}

//----------------------------------------------------------------------------
// PASS 2: Process a single x-row of voxels. Count the number of y- and
// z-intersections by topological reasoning from x-edge cases. Determine the
// number of primitives (i.e., triangles) generated from this row. Use
// computational trimming to reduce work. Note *ePtr[4] is four pointers to
// four x-edge rows that bound the voxel x-row and which contain edge case
// information.
template <class T> void vtkFlyingEdges3DAlgorithm<T>::
ProcessYZEdges(vtkIdType row, vtkIdType slice)
{
  // Grab the four edge cases bounding this voxel x-row.
  unsigned char *ePtr[4], ec0, ec1, ec2, ec3;
  ePtr[0] = this->XCases + slice*this->SliceOffset + row*(this->Dims[0]-1);
  ePtr[1] = ePtr[0] + this->Dims[0]-1;
  ePtr[2] = ePtr[0] + this->SliceOffset;
  ePtr[3] = ePtr[2] + this->Dims[0]-1;

  // Grab the edge meta data surrounding the voxel row.
  vtkIdType *eMD[4];
  eMD[0] = this->EdgeMetaData + (slice*this->Dims[1] + row)*6; //this x-edge
  eMD[1] = eMD[0] + 6; //x-edge in +y direction
  eMD[2] = eMD[0] + this->Dims[1]*6; //x-edge in +z direction
  eMD[3] = eMD[2] + 6; //x-edge in +y+z direction

  // Determine whether this row of x-cells needs processing. If there are no
  // x-edge intersections, and the state of the four bounding x-edges is the
  // same, then there is no need for processing.
  if ( (eMD[0][0] | eMD[1][0] | eMD[2][0] | eMD[3][0]) == 0 ) //any x-ints?
    {
    if ( *(ePtr[0]) == *(ePtr[1]) &&  *(ePtr[1]) == *(ePtr[2]) &&
         *(ePtr[2]) == *(ePtr[3]) )
      {
      return; //there are no y- or z-ints, thus no contour, skip voxel row
      }
    }

  // Determine proximity to the boundary of volume. This information is used
  // to count edge intersections in boundary situations.
  unsigned char loc, yLoc, zLoc, yzLoc;
  yLoc = (row >= (this->Dims[1]-2) ? MaxBoundary : Interior);
  zLoc = (slice >= (this->Dims[2]-2) ? MaxBoundary : Interior);
  yzLoc = (yLoc << 2) | (zLoc << 4);

  // The trim edges may need adjustment if the contour travels between rows
  // of x-edges (without intersecting these x-edges). This means checking
  // whether the trim faces at (xL,xR) made up of the y-z edges intersect the
  // contour. Basically just an intersection operation. Determine the voxel
  // row trim edges, need to check all four x-edges.
  vtkIdType xL=eMD[0][4], xR=eMD[0][5];
  vtkIdType i;
  for (i=1; i < 4; ++i)
    {
    xL = ( eMD[i][4] < xL ? eMD[i][4] : xL);
    xR = ( eMD[i][5] > xR ? eMD[i][5] : xR);
    }

  if ( xL > 0 ) //if trimmed in the -x direction
    {
    ec0 = *(ePtr[0]+xL); ec1 = *(ePtr[1]+xL);
    ec2 = *(ePtr[2]+xL); ec3 = *(ePtr[3]+xL);
    if ( (ec0 & 0x1) != (ec1 & 0x1) || (ec1 & 0x1) != (ec2 & 0x1) ||
         (ec2 & 0x1) != (ec3 & 0x1) )
      {
      xL = eMD[0][4] = 0; //reset left trim
      }
    }

  if ( xR < (this->Dims[0]-1) ) //if trimmed in the +x direction
    {
    ec0 = *(ePtr[0]+xR); ec1 = *(ePtr[1]+xR);
    ec2 = *(ePtr[2]+xR); ec3 = *(ePtr[3]+xR);
    if ( (ec0 & 0x2) != (ec1 & 0x2) || (ec1 & 0x2) != (ec2 & 0x2) ||
         (ec2 & 0x2) != (ec3 & 0x2) )
      {
      xR = eMD[0][5] = this->Dims[0]-1; //reset right trim
      }
    }

  // Okay run along the x-voxels and count the number of y- and
  // z-intersections. Here we are just checking y,z edges that make up the
  // voxel axes. Also check the number of primitives generated.
  unsigned char *edgeUses, eCase, numTris;
  ePtr[0] += xL; ePtr[1] += xL; ePtr[2] += xL; ePtr[3] += xL;
  for (i=xL; i < xR; ++i) //run along the trimmed x-voxels
    {
    eCase = this->GetEdgeCase(ePtr);
    if ( (numTris=this->GetNumberOfPrimitives(eCase)) > 0 )
      {
      // Okay let's increment the triangle count.
      eMD[0][3] += numTris;

      // Count the number of y- and z-points to be generated. Pass# 1 counted
      // the number of x-intersections along the x-edges. Now we count all
      // intersections on the y- and z-voxel axes.
      edgeUses = this->GetEdgeUses(eCase);
      eMD[0][1] += edgeUses[4]; //y-voxel axes edge always counted
      eMD[0][2] += edgeUses[8]; //z-voxel axes edge always counted
      loc = yzLoc | (i >= (this->Dims[0]-2) ? MaxBoundary : Interior);
      if ( loc != 0 )
        {
        this->CountBoundaryYZInts(loc,edgeUses,eMD);
        }
      }//if cell contains contour

    // advance the four pointers along voxel row
    ePtr[0]++; ePtr[1]++; ePtr[2]++; ePtr[3]++;
    }//for all voxels along this x-edge
}

//----------------------------------------------------------------------------
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// PASS 4: Process the x-row cells to generate output primitives, including
// point coordinates and triangles. This is the fourth and final pass of the
// algorithm.
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template <class T> void vtkFlyingEdges3DAlgorithm<T>::
GenerateOutput(double value, T* rowPtr, vtkIdType row, vtkIdType slice)
{
  // Grab the edge meta data surrounding the voxel row.
  vtkIdType *eMD[4];
  eMD[0] = this->EdgeMetaData + (slice*this->Dims[1] + row)*6; //this x-edge
  eMD[1] = eMD[0] + 6; //x-edge in +y direction
  eMD[2] = eMD[0] + this->Dims[1]*6; //x-edge in +z direction
  eMD[3] = eMD[2] + 6; //x-edge in +y+z direction

  // Return if there is nothing to do (i.e., no triangles to generate)
  if ( eMD[0][3] == eMD[1][3] )
    {
    return;
    }

  // Get the voxel row trim edges and prepare to generate. Find the voxel row
  // trim edges, need to check all four x-edges to compute row trim edge.
  vtkIdType xL=eMD[0][4], xR=eMD[0][5];
  vtkIdType i;
  for (i=1; i < 4; ++i)
    {
    xL = ( eMD[i][4] < xL ? eMD[i][4] : xL);
    xR = ( eMD[i][5] > xR ? eMD[i][5] : xR);
    }

  // Grab the four edge cases bounding this voxel x-row. Begin at left trim edge.
  unsigned char *ePtr[4];
  ePtr[0] = this->XCases + slice*this->SliceOffset + row*(this->Dims[0]-1) + xL;
  ePtr[1] = ePtr[0] + this->Dims[0]-1;
  ePtr[2] = ePtr[0] + this->SliceOffset;
  ePtr[3] = ePtr[2] + this->Dims[0]-1;

  // Traverse all voxels in this row, those containing the contour are
  // further identified for processing, meaning generating points and
  // triangles. Begin by setting up point ids on voxel edges.
  vtkIdType triId = eMD[0][3];
  vtkIdType eIds[12]; //the ids of generated points
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  unsigned char eCase = this->InitVoxelIds(ePtr,eMD,eIds);

  // Determine the proximity to the boundary of volume. This information is
  // used to generate edge intersections.
  unsigned char loc, yLoc, zLoc, yzLoc;
  yLoc = (row < 1 ? MinBoundary :
          (row >= (this->Dims[1]-2) ? MaxBoundary : Interior));
  zLoc = (slice < 1 ? MinBoundary :
          (slice >= (this->Dims[2]-2) ? MaxBoundary : Interior));
  yzLoc = (yLoc << 2) | (zLoc << 4);

  // Run along voxels in x-row direction and generate output primitives. Note
  // that active voxel axes edges are interpolated to produce points and
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