vtkFlyingEdges3D.cxx 45.6 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"

#include <math.h>

vtkStandardNewMacro(vtkFlyingEdges3D);

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

// This templated class implements the heart of the algorithm.
// vtkFlyingEdges3D populates the information in this class and
// then invokes ContourImage() to actually initiate execution.
template <class T>
class vtkFlyingEdges3DAlgorithm
{
public:
  // Edge case table values.
  static const unsigned char Below = 0; //below isovalue
  static const unsigned char Above = 1; //above isovalue
  static const unsigned char LeftAbove = 1; //left vertex is above isovalue
  static const unsigned char RightAbove = 2; //right vertex is above isovalue
  static const unsigned char BothAbove = 3; //entire edge is above isovalue

  // Dealing with boundary situations when processing volumes.
  static const unsigned char Interior = 0;
  static const unsigned char MinBoundary = 1;
  static const unsigned char MaxBoundary = 2;

  // 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.
  vtkIdType Dims[3];
  double   *Origin;
  double   *Spacing;
  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.
  void ProcessXEdge(double value, T* inPtr, vtkIdType row, vtkIdType slice); //PASS 1
  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.
  void ComputeGradient(unsigned char loc, vtkIdType ijk[3], T *s, float g[3])
    {
      if ( loc == Interior )
        {
        g[0] = ( *(s+this->Inc0) - *(s-this->Inc0) / this->Spacing[0] );
        g[1] = ( *(s+this->Inc1) - *(s-this->Inc1) / this->Spacing[1] );
        g[2] = ( *(s+this->Inc2) - *(s-this->Inc2) / this->Spacing[2] );
        }
      else
        {
        this->ComputeBoundaryGradient(ijk,s,g);
        }
    }

  // Interpolate along a voxel axes edge.
  void InterpolateAxesEdge(double value, unsigned char loc, T *s0, float x0[3],
                           T* s1, float x1[3], vtkIdType vId, vtkIdType ijk[3],
                           float g0[3])
    {
      double t = (value - *s0) / (*s1 - *s0);
      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]);
      if ( this->NeedGradients )
        {
        float gTmp[3], g1[3];
        this->ComputeGradient(loc,ijk,s1,g1);

        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.
  void ComputeBoundaryGradient(vtkIdType ijk[3], T *s, float g[3]);

  // 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).
  void InterpolateEdge(double value, vtkIdType ijk[3], T *s, float x[3],
                       unsigned char edgeNum, unsigned char edgeUses[12],
                       vtkIdType *eIds);

  // Produce the output points on the voxel axes for this voxel cell.
  void GeneratePoints(double value, unsigned char loc, vtkIdType ijk[3], T *sPtr,
                      float x[3], unsigned char *edgeUses, vtkIdType *eIds);

  // 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];
    }
};

//----------------------------------------------------------------------------
// 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),
                            NewPoints(NULL),NewTris(NULL),NewGradients(NULL),
                            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;
            for ( edge = triCase->edges; edge[0] > -1; edge += 3 )
              {// build new case table
              *edgeCase++ = this->EdgeMap[edge[0]];
              *edgeCase++ = this->EdgeMap[edge[1]];
              *edgeCase++ = this->EdgeMap[edge[2]];
              }
            }
          }//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>::
ComputeBoundaryGradient(vtkIdType ijk[3], T *s, float g[3])
{
  if ( ijk[0] == 0 )
    {
    g[0] = (*(s+this->Inc0) - *s) / this->Spacing[0];
    }
  else if ( ijk[0] >= (this->Dims[0]-1) )
    {
    g[0] = (*s - *(s-this->Inc0)) / this->Spacing[0];
    }
  else
    {
    g[0] = 0.5 * ( (*(s+this->Inc0) - *(s-this->Inc0)) / this->Spacing[0] );
    }

  if ( ijk[1] == 0 )
    {
    g[1] = (*(s+this->Inc1) - *s) / this->Spacing[1];
    }
  else if ( ijk[1] >= (this->Dims[1]-1) )
    {
    g[1] = (*s - *(s-this->Inc1)) / this->Spacing[1];
    }
  else
    {
    g[1] = 0.5 * ( (*(s+this->Inc1) - *(s-this->Inc1)) / this->Spacing[1] );
    }

  if ( ijk[2] == 0 )
    {
    g[2] = (*(s+this->Inc2) - *s) / this->Spacing[2];
    }
  else if ( ijk[2] >= (this->Dims[2]-1) )
    {
    g[2] = (*s - *(s-this->Inc2)) / this->Spacing[2];
    }
  else
    {
    g[2] = 0.5 * ( (*(s+this->Inc2) - *(s-this->Inc2)) / this->Spacing[2] );
    }
}

//----------------------------------------------------------------------------
// Interpolate a new point along a boundary edge. Make sure to consider
// proximity to boundary when computing gradients, etc.
template <class T> void vtkFlyingEdges3DAlgorithm<T>::
InterpolateEdge(double value, vtkIdType ijk[3], T *s, float x[3],
                unsigned char edgeNum, unsigned char edgeUses[12],
                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];
  T *s0, *s1;
  float x0[3], x1[3];
  vtkIdType ijk0[3], ijk1[3], vId=eIds[edgeNum];
  int i;

  const unsigned char *offsets = this->VertOffsets[vertMap[0]];
  s0 = s + offsets[0]*this->Inc0 + offsets[1]*this->Inc1 + offsets[2]*this->Inc2;
  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]];
  s1 = s + offsets[0]*this->Inc0 + offsets[1]*this->Inc1 + offsets[2]*this->Inc2;
  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]);
  if ( this->NeedGradients )
    {
    float gTmp[3], g0[3], g1[3];
    this->ComputeBoundaryGradient(ijk0,s0,g0);
    this->ComputeBoundaryGradient(ijk1,s1,g1);

    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>::
GeneratePoints(double value, unsigned char loc, vtkIdType ijk[3], T *sPtr,
               float x[3], unsigned char *edgeUses, vtkIdType *eIds)
{
  // Create a slightly faster path for voxel axes interior to the volume.
  float g0[3], x1[3];
  vtkIdType offset[3];
  if ( this->NeedGradients )
    {
    this->ComputeGradient(loc,ijk,sPtr,g0);
    }
  if ( edgeUses[0] ) //x axes edge
    {
    x1[0] = x[0] + this->Spacing[0]; offset[0] = ijk[0] + 1;
    x1[1] = x[1]; offset[1] = 0;
    x1[2] = x[2]; offset[2] = 0;
    this->InterpolateAxesEdge(value, loc, sPtr, x, sPtr+this->Inc0,
                              x1, eIds[0], offset, g0);
    }
  if ( edgeUses[4] ) //y axes edge
    {
    x1[0] = x[0]; offset[0] = 0;
    x1[1] = x[1] + this->Spacing[1]; offset[1] = ijk[1] + 1;
    x1[2] = x[2]; offset[2] = 0;
    this->InterpolateAxesEdge(value, loc, sPtr, x, sPtr+this->Inc1,
                              x1, eIds[4], offset, g0);
    }
  if ( edgeUses[8] ) //z axes edge
    {
    x1[0] = x[0]; offset[0] = 0;
    x1[1] = x[1]; offset[1] = 0;
    x1[2] = x[2] + this->Spacing[2]; offset[2] = ijk[2] + 1;
    this->InterpolateAxesEdge(value, loc, sPtr, x, sPtr+this->Inc2,
                              x1, eIds[8], offset, g0);
    }

  // Otherwise do more general gyrations. 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 are handled by the default:
  // case and are expected.)
  switch (loc) //location is one of 27 regions in the volume
    {
    case 2: case 6: case 18:
    case 22: case 26: //+x & +x -y & +x -z & +x -y -z +x +y -z
      this->InterpolateEdge(value, ijk, sPtr, x, 5, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, x, 9, edgeUses, eIds);
      break;
    case 8: case 24: case 25: //+y & +y -z & +y -x -z
      this->InterpolateEdge(value, ijk, sPtr, x, 1, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, x, 10, edgeUses, eIds);
      break;
    case 10://+x +y
      this->InterpolateEdge(value, ijk, sPtr, x, 1, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, x, 5, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, x, 9, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, x, 10, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, x, 11, edgeUses, eIds);
      break;
    case 32: case 33: case 36: case 37: //+z & -x +z & -y +z & -x -y +z
      this->InterpolateEdge(value, ijk, sPtr, x, 2, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, x, 6, edgeUses, eIds);
      break;
    case 34: case 38: //+x +z & +x -y +z
      this->InterpolateEdge(value, ijk, sPtr, x, 2, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, x, 5, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, x, 9, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, x, 6, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, x, 7, edgeUses, eIds);
      break;
    case 9: case 40: case 41: //-x +y & +y +z & -x + y + z
      this->InterpolateEdge(value, ijk, sPtr, x, 1, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, x, 2, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, x, 3, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, x, 6, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, x, 10, edgeUses, eIds);
      break;
    case 42: //+x +y +z happens no more than once per volume
      this->InterpolateEdge(value, ijk, sPtr, x, 1, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, x, 2, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, x, 3, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, x, 5, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, x, 9, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, x, 10, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, x, 11, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, x, 6, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, x, 7, edgeUses, eIds);
      break;
    default: //interior, or -x,-y,-z boundary
      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>::
ProcessXEdge(double value, T* inPtr, vtkIdType row, vtkIdType slice)
{
  vtkIdType nxcells=this->Dims[0]-1;
  vtkIdType minInt=nxcells, maxInt = 0;
  vtkIdType *edgeMetaData;
  unsigned char edgeCase;
  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);
  for (vtkIdType i=0; i < nxcells; ++i, ++ePtr)
    {
    s0 = s1;
    s1 = static_cast<double>(*(inPtr + (i+1)*this->Inc0));

    edgeCase  = ( s0 < value ? vtkFlyingEdges3DAlgorithm::Below :
                  vtkFlyingEdges3DAlgorithm::LeftAbove );
    edgeCase |= ( s1 < value ? vtkFlyingEdges3DAlgorithm::Below :
                  vtkFlyingEdges3DAlgorithm::RightAbove );

    this->SetXEdge(ePtr, edgeCase);

    // if edge intersects contour
    if ( edgeCase == vtkFlyingEdges3DAlgorithm::LeftAbove ||
         edgeCase == vtkFlyingEdges3DAlgorithm::RightAbove )
      {
      edgeMetaData[0]++; //increment number of intersections along x-edge
      minInt = ( i < minInt ? i : minInt);
      maxInt = i + 1;
      }//if contour interacts with this x-edge
    }//for all x-cell edges along this x-edge

  // 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
}

//----------------------------------------------------------------------------
// PASS 3: Process the x-row cells to generate output primitives, including
// point coordinates and triangles. This is the third pass of the algorithm.
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;

  // Update scalars along this x-row if necessary
  vtkIdType numNewPts = eMD[1][0] - eMD[0][0];
  if ( this->NewScalars && numNewPts > 0 )
    {
    T TValue = static_cast<T>(value);
    std::fill_n(this->NewScalars+eMD[0][0], numNewPts, TValue);
    }

  // 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
  unsigned char *edgeUses, numTris;
  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
  // possibly interpolate attribute data.
  float x[3];
  x[1] = this->Origin[1] + row*this->Spacing[1];
  x[2] = this->Origin[2] + slice*this->Spacing[2];
  T *sPtr;
  vtkIdType ijk[3]; ijk[1] = row; ijk[2] = slice;
  for (i=xL; i < xR; ++i)
    {
    if ( (numTris=this->GetNumberOfPrimitives(eCase)) > 0 )
      {
      // Start by generating triangles for this case
      this->GenerateTris(eCase,numTris,eIds,triId);

      // Now generate point(s) along voxel axes if needed. Remember to take
      // boundary into account.
      loc = yzLoc | (i < 1 ? MinBoundary :
          (i >= (this->Dims[0]-2) ? MaxBoundary : Interior));
      if ( this->CaseIncludesAxes(eCase) || loc != Interior )
        {
        ijk[0] = i;
        sPtr = rowPtr + i*this->Inc0;
        x[0] = this->Origin[0] + i*this->Spacing[0];
        edgeUses = this->GetEdgeUses(eCase);
        this->GeneratePoints(value, loc, ijk, sPtr, x, edgeUses, eIds);
        }

      this->AdvanceVoxelIds(eCase,eIds);
      }

    // advance along voxel row
    ePtr[0]++; ePtr[1]++; ePtr[2]++; ePtr[3]++;
    eCase = GetEdgeCase(ePtr);
    } //for all non-trimmed cells along this x-edge
}

//----------------------------------------------------------------------------
// Contouring filter specialized for 3D volumes. This templated function
// interfaces the vtkFlyingEdges3D class with the templated algorithm
// class. It also invokes the three passes of the Flying Edges algorithm.
template <class T>
void ContourImage(vtkFlyingEdges3D *self, vtkImageData *input, int extent[6],
                  vtkIdType *incs, T *scalars, vtkPoints *newPts,
                  vtkCellArray *newTris, vtkDataArray *newScalars,
                  vtkFloatArray *newNormals, vtkFloatArray *newGradients)
{
  double value, *values = self->GetValues();
  int numContours = self->GetNumberOfContours();
  T *rowPtr, *slicePtr;
  vtkIdType vidx, row, slice, *eMD, zInc;
  vtkIdType numOutXPts, numOutYPts, numOutZPts, numOutTris;
  vtkIdType numXPts=0, numYPts=0, numZPts=0, numTris=0;
  vtkIdType startXPts, startYPts, startZPts, startTris;
  startXPts = startYPts = startZPts = startTris = 0;

  // This may be subvolume of the total 3D image. Capture information for
  // subsequent processing.
  vtkFlyingEdges3DAlgorithm<T> algo;
  algo.Origin = input->GetOrigin();
  algo.Spacing = input->GetSpacing();
  algo.Min0 = extent[0];
  algo.Max0 = extent[1];
  algo.Inc0 = incs[0];
  algo.Min1 = extent[2];
  algo.Max1 = extent[3];
  algo.Inc1 = incs[1];
  algo.Min2 = extent[4];
  algo.Max2 = extent[5];
  algo.Inc2 = incs[2];

  // Now allocate working arrays. The XCases array tracks x-edge cases.
  algo.Dims[0] = algo.Max0 - algo.Min0 + 1;
  algo.Dims[1] = algo.Max1 - algo.Min1 + 1;
  algo.Dims[2] = algo.Max2 - algo.Min2 + 1;
  algo.SliceOffset = (algo.Dims[0]-1) * algo.Dims[1];
  algo.XCases = new unsigned char [(algo.Dims[0]-1)*algo.Dims[1]*algo.Dims[2]];

  // Also allocate the characterization (metadata) array for the x edges.
  // This array tracks the number of x-, y- and z- intersections on the voxel
  // axes along an x-edge; as well as the number of the output triangles, and
  // the xMin_i and xMax_i (minimum index of first intersection, maximum
  // index of intersection for the ith x-row, the so-called trim edges used
  // for computational trimming).
  algo.EdgeMetaData = new vtkIdType [algo.Dims[1]*algo.Dims[2]*6];

  // Loop across each contour value. This encompasses all three passes.
  for (vidx = 0; vidx < numContours; vidx++)
    {
    value = values[vidx];

    // PASS 1: Traverse all x-rows building edge cases and counting number of
    // intersections (i.e., accumulate information necessary for later output
    // memory allocation, e.g., the number of output points along the x-rows
    // are counted).
    for (slicePtr=scalars, slice=0; slice < algo.Dims[2]; ++slice)
      {
      rowPtr = slicePtr;
      for ( row=0; row < algo.Dims[1]; ++row)
        {
        algo.ProcessXEdge(value, rowPtr, row, slice);
        rowPtr += algo.Inc1;
        }//for all rows
      slicePtr += algo.Inc2;
      }//for all slices

    // PASS 2: Traverse all voxel x-rows and process voxel y&z edges.  The
    // result is a count of the number of y- and z-intersections, as well as
    // the number of triangles generated along these voxel rows.
    for (slicePtr=scalars, slice=0; slice < (algo.Dims[2]-1); ++slice)
      {
      rowPtr = slicePtr;
      for ( row=0; row < (algo.Dims[1]-1); ++row)
        {
        algo.ProcessYZEdges(row, slice);
        }//for all rows
      slicePtr += algo.Inc2;
      }//for all slices

    // PASS 3: Now allocate and generate output. First we have to update the
    // edge meta data to partition the output into separate pieces so
    // independent threads can write without collisions. Once allocation is
    // complete, the volume is processed on a voxel row by row basis to
    // produce output points and triangles, and interpolate point attribute
    // data (as necessary).
    numOutXPts = startXPts;
    numOutYPts = startYPts;
    numOutZPts = startZPts;
    numOutTris = startTris;

    // Count number of points and tris generate along each cell row
    for (slice=0; slice < algo.Dims[2]; ++slice)
      {
      zInc = slice * algo.Dims[1];
      for (row=0; row < algo.Dims[1]; ++row)
        {
        eMD = algo.EdgeMetaData + (zInc+row)*6;
        numXPts = eMD[0];
        numYPts = eMD[1];
        numZPts = eMD[2];
        numTris = eMD[3];
        eMD[0] = numOutXPts + numOutYPts + numOutZPts;
        eMD[1] = eMD[0] + numXPts;
        eMD[2] = eMD[1] + numYPts;
        eMD[3] = numOutTris;
        numOutXPts += numXPts;
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