vtkFlyingEdges3D.cxx 53 KB
Newer Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
/*=========================================================================

  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"
29
#include "vtkArrayListTemplate.h"
30
#include "vtkSMPTools.h"
31

Sean McBride's avatar
Sean McBride committed
32
#include <cmath>
33
34
35
36

vtkStandardNewMacro(vtkFlyingEdges3D);

//----------------------------------------------------------------------------
37
38
39
namespace {
#include "vtkArrayListTemplate.h" // For processing attribute data
}
40
41
42

// This templated class implements the heart of the algorithm.
// vtkFlyingEdges3D populates the information in this class and
43
// then invokes Contour() to actually initiate execution.
44
45
46
47
48
template <class T>
class vtkFlyingEdges3DAlgorithm
{
public:
  // Edge case table values.
Will Schroeder's avatar
Will Schroeder committed
49
  enum EdgeClass {
50
51
52
53
54
55
    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
  };
56
57

  // Dealing with boundary situations when processing volumes.
Will Schroeder's avatar
Will Schroeder committed
58
  enum CellClass {
59
60
61
    Interior = 0,
    MinBoundary = 1,
    MaxBoundary = 2
Will Schroeder's avatar
Will Schroeder committed
62
  };
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104

  // 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.
Will Schroeder's avatar
Will Schroeder committed
105
  T        *Scalars;
106
  vtkIdType Dims[3];
Will Schroeder's avatar
Will Schroeder committed
107
108
  double    Origin[3];
  double    Spacing[3];
Will Schroeder's avatar
Will Schroeder committed
109
  vtkIdType NumberOfEdges;
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
  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;
127
  bool       NeedGradients;
128
129
  bool       InterpolateAttributes;
  ArrayList  Arrays;
130
131
132
133

  // Setup algorithm
  vtkFlyingEdges3DAlgorithm();

Will Schroeder's avatar
Will Schroeder committed
134
135
136
137
138
139
140
141
  // Adjust the origin to the lower-left corner of the volume (if necessary)
  void AdjustOrigin()
    {
    this->Origin[0] = this->Origin[0] + this->Spacing[0]*this->Min0;
    this->Origin[1] = this->Origin[1] + this->Spacing[1]*this->Min1;
    this->Origin[2] = this->Origin[2] + this->Spacing[2]*this->Min2;;
    }

142
  // The three main passes of the algorithm.
Will Schroeder's avatar
Will Schroeder committed
143
  void ProcessXEdge(double value, T const * const inPtr, vtkIdType row, vtkIdType slice); //PASS 1
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
  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.
Will Schroeder's avatar
Will Schroeder committed
191
192
193
194
195
  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])
196
197
198
    {
      if ( loc == Interior )
        {
Will Schroeder's avatar
Will Schroeder committed
199
200
201
        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] );
202
203
204
        }
      else
        {
Will Schroeder's avatar
Will Schroeder committed
205
206
207
208
209
        this->ComputeBoundaryGradient(ijk,
                                      s0_start, s0_end,
                                      s1_start, s1_end,
                                      s2_start, s2_end,
                                      g);
210
211
212
        }
    }

Will Schroeder's avatar
Will Schroeder committed
213

214
  // Interpolate along a voxel axes edge.
Will Schroeder's avatar
Will Schroeder committed
215
216
217
218
219
220
  void InterpolateAxesEdge(double t, unsigned char loc,
                           float x0[3],
                           T const * const s,
                           const int incs[3],
                           float x1[3],
                           vtkIdType vId,
221
222
                           vtkIdType ijk0[3],
                           vtkIdType ijk1[3],
223
224
                           float g0[3])
    {
Will Schroeder's avatar
Will Schroeder committed
225

226
227
228
229
      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]);
230

231
232
233
      if ( this->NeedGradients )
        {
        float gTmp[3], g1[3];
234
        this->ComputeGradient(loc,ijk1,
Will Schroeder's avatar
Will Schroeder committed
235
236
237
238
                              s + incs[0], s - incs[0],
                              s + incs[1], s - incs[1],
                              s + incs[2], s - incs[2],
                              g1);
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253

        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
254
255
256
257
258
259
260

      if ( this->InterpolateAttributes )
        {
        vtkIdType v0=ijk0[0] + ijk0[1]*incs[1] + ijk0[2]*incs[2];
        vtkIdType v1=ijk1[0] + ijk1[1]*incs[1] + ijk1[2]*incs[2];;
        this->Arrays.InterpolateEdge(v0,v1,t,vId);
        }
261
262
263
    }

  // Compute the gradient on a point which may be on the boundary of the volume.
Will Schroeder's avatar
Will Schroeder committed
264
265
266
267
268
  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]);
269
270
271
272

  // 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).
Will Schroeder's avatar
Will Schroeder committed
273
274
275
276
277
  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,
278
279
280
                       vtkIdType *eIds);

  // Produce the output points on the voxel axes for this voxel cell.
Will Schroeder's avatar
Will Schroeder committed
281
282
283
284
  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);
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321

  // 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];
    }
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362

  // 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
        }
    };
363
  template <class TT> class Pass4
364
365
    {
    public:
366
      Pass4(vtkFlyingEdges3DAlgorithm<TT> *algo, double value)
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
        {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;
388
389
          eMD0 = eMD1;
          eMD1 = eMD0 + 6*this->Algo->Dims[1];
390
391
392
393
394
395
396
          }//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,
397
                      vtkPolyData *output, vtkPoints *newPts, vtkCellArray *newTris,
398
399
                      vtkDataArray *newScalars,vtkFloatArray *newNormals,
                      vtkFloatArray *newGradients);
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
};

//----------------------------------------------------------------------------
// 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),
Will Schroeder's avatar
Will Schroeder committed
426
                            NewTris(NULL),NewPoints(NULL),NewGradients(NULL),
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
                            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;
484
485
            for ( edge = triCase->edges; edge[0] > -1; edge += 3, edgeCase+=3 )
              {
486
              // Build new case table.
487
              edgeCase[0] = this->EdgeMap[edge[0]];
488
489
              edgeCase[1] = this->EdgeMap[edge[1]];
              edgeCase[2] = this->EdgeMap[edge[2]];
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
              }
            }
          }//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>::
Will Schroeder's avatar
Will Schroeder committed
572
573
574
575
576
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])
577
{
Will Schroeder's avatar
Will Schroeder committed
578
579
  const T* s = s0_start - this->Inc0;

580
581
  if ( ijk[0] == 0 )
    {
Will Schroeder's avatar
Will Schroeder committed
582
    g[0] = (*s0_start - *s) / this->Spacing[0];
583
584
585
    }
  else if ( ijk[0] >= (this->Dims[0]-1) )
    {
Will Schroeder's avatar
Will Schroeder committed
586
    g[0] = (*s - *s0_end) / this->Spacing[0];
587
588
589
    }
  else
    {
Will Schroeder's avatar
Will Schroeder committed
590
    g[0] = 0.5 * ( (*s0_start - *s0_end) / this->Spacing[0] );
591
592
593
594
    }

  if ( ijk[1] == 0 )
    {
Will Schroeder's avatar
Will Schroeder committed
595
    g[1] = (*s1_start - *s) / this->Spacing[1];
596
597
598
    }
  else if ( ijk[1] >= (this->Dims[1]-1) )
    {
Will Schroeder's avatar
Will Schroeder committed
599
    g[1] = (*s - *s1_end) / this->Spacing[1];
600
601
602
    }
  else
    {
Will Schroeder's avatar
Will Schroeder committed
603
    g[1] = 0.5 * ( (*s1_start - *s1_end) / this->Spacing[1] );
604
605
606
607
    }

  if ( ijk[2] == 0 )
    {
Will Schroeder's avatar
Will Schroeder committed
608
    g[2] = (*s2_start - *s) / this->Spacing[2];
609
610
611
    }
  else if ( ijk[2] >= (this->Dims[2]-1) )
    {
Will Schroeder's avatar
Will Schroeder committed
612
    g[2] = (*s - *s2_end) / this->Spacing[2];
613
614
615
    }
  else
    {
Will Schroeder's avatar
Will Schroeder committed
616
    g[2] = 0.5 * ( (*s2_start - *s2_end) / this->Spacing[2] );
617
618
619
620
621
    }
}

//----------------------------------------------------------------------------
// Interpolate a new point along a boundary edge. Make sure to consider
622
// proximity to the boundary when computing gradients, etc.
623
template <class T> void vtkFlyingEdges3DAlgorithm<T>::
Will Schroeder's avatar
Will Schroeder committed
624
625
626
627
628
629
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,
630
631
632
633
634
635
636
637
638
639
                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];
Will Schroeder's avatar
Will Schroeder committed
640

641
642
643
644
645
  float x0[3], x1[3];
  vtkIdType ijk0[3], ijk1[3], vId=eIds[edgeNum];
  int i;

  const unsigned char *offsets = this->VertOffsets[vertMap[0]];
Will Schroeder's avatar
Will Schroeder committed
646
647
648
  T const * const s0 = s + offsets[0]*incs[0] +
                           offsets[1]*incs[1] +
                           offsets[2]*incs[2];
649
650
651
652
653
654
655
  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]];
Will Schroeder's avatar
Will Schroeder committed
656
657
658
  T const * const s1 = s + offsets[0]*incs[0] +
                           offsets[1]*incs[1] +
                           offsets[2]*incs[2];
659
660
661
662
663
664
665
666
667
668
669
670
  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]);
671

672
673
674
  if ( this->NeedGradients )
    {
    float gTmp[3], g0[3], g1[3];
Will Schroeder's avatar
Will Schroeder committed
675
676
677
678
679
680
681
682
683
684
    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);
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699

    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
700
701
702
703
704
705
706

  if ( this->InterpolateAttributes )
    {
    vtkIdType v0=ijk0[0] + ijk0[1]*incs[1] + ijk0[2]*incs[2];
    vtkIdType v1=ijk1[0] + ijk1[1]*incs[1] + ijk1[2]*incs[2];;
    this->Arrays.InterpolateEdge(v0,v1,t,vId);
    }
707
708
709
710
711
712
}

//----------------------------------------------------------------------------
// Generate the output points and optionally normals, gradients and
// interpolate attributes.
template <class T> void vtkFlyingEdges3DAlgorithm<T>::
Will Schroeder's avatar
Will Schroeder committed
713
714
715
716
717
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)
718
719
{
  // Create a slightly faster path for voxel axes interior to the volume.
Will Schroeder's avatar
Will Schroeder committed
720
  float g0[3];
721
722
  if ( this->NeedGradients )
    {
Will Schroeder's avatar
Will Schroeder committed
723
724
725
726
727
    this->ComputeGradient(loc,ijk,
                          sPtr + incs[0], sPtr - incs[0],
                          sPtr + incs[1], sPtr - incs[1],
                          sPtr + incs[2], sPtr - incs[2],
                          g0);
728
    }
Will Schroeder's avatar
Will Schroeder committed
729

730
  // Interpolate the cell axes edges
Will Schroeder's avatar
Will Schroeder committed
731
  for(int i=0; i < 3; ++i)
732
    {
Will Schroeder's avatar
Will Schroeder committed
733
734
735
736
737
738
    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];
739
      vtkIdType ijk1[3] = { ijk[0], ijk[1], ijk[2] }; ++ijk1[i];
Will Schroeder's avatar
Will Schroeder committed
740
741
742

      T const * const sPtr2 = (sPtr+incs[i]);
      double t = (value - *sPtr) / (*sPtr2 - *sPtr);
743
      this->InterpolateAxesEdge(t, loc, x, sPtr2, incs, x1, eIds[i*4], ijk, ijk1, g0);
Will Schroeder's avatar
Will Schroeder committed
744
      }
745
746
    }

747
748
749
750
751
752
753
754
755
  // 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)
756
    {
757
    case 2: case 6: case 18: case 22: //+x
Will Schroeder's avatar
Will Schroeder committed
758
759
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 5, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 9, edgeUses, eIds);
760
      break;
761
    case 8: case 9: case 24: case 25: //+y
Will Schroeder's avatar
Will Schroeder committed
762
763
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 1, edgeUses, eIds);
      this->InterpolateEdge(value, ijk, sPtr, incs, x, 10, edgeUses, eIds);
764
      break;
765
766
767
768
769
    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
Will Schroeder's avatar
Will Schroeder committed
770
771
772
773
774
      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);
775
      break;
776
    case 34: case 38: //+x +z
Will Schroeder's avatar
Will Schroeder committed
777
778
779
780
781
      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);
782
      break;
783
    case 40: case 41: //+y +z
Will Schroeder's avatar
Will Schroeder committed
784
785
786
787
788
      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);
789
790
      break;
    case 42: //+x +y +z happens no more than once per volume
Will Schroeder's avatar
Will Schroeder committed
791
792
793
794
795
796
797
798
799
      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);
800
      break;
801
    default: //interior, or -x,-y,-z boundaries
802
803
804
805
806
807
808
809
810
811
812
      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>::
Will Schroeder's avatar
Will Schroeder committed
813
ProcessXEdge(double value, T const* const inPtr, vtkIdType row, vtkIdType slice)
814
815
816
817
{
  vtkIdType nxcells=this->Dims[0]-1;
  vtkIdType minInt=nxcells, maxInt = 0;
  vtkIdType *edgeMetaData;
818
  unsigned char edgeCase, *ePtr=this->XCases+slice*this->SliceOffset+row*nxcells;
819
  double s0, s1 = static_cast<double>(*inPtr);
820
  vtkIdType sum = 0;
821
822
823
824

  //run along the entire x-edge computing edge cases
  edgeMetaData = this->EdgeMetaData + (slice*this->Dims[1] + row)*6;
  std::fill_n(edgeMetaData, 6, 0);
Will Schroeder's avatar
Will Schroeder committed
825
826
827
828

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

829
830
831
  for (vtkIdType i=0; i < nxcells; ++i, ++ePtr)
    {
    s0 = s1;
Will Schroeder's avatar
Will Schroeder committed
832
    s1 = static_cast<double>(*(inPtr + (i+1)*inc0));
833

Will Schroeder's avatar
Will Schroeder committed
834
835
836
837
    if (s0 >= value)
      {
      edgeCase = vtkFlyingEdges3DAlgorithm::LeftAbove;
      }
838
839
840
841
    else
      {
      edgeCase = vtkFlyingEdges3DAlgorithm::Below;
      }
Will Schroeder's avatar
Will Schroeder committed
842
843
844
845
    if( s1 >= value)
      {
      edgeCase |= vtkFlyingEdges3DAlgorithm::RightAbove;
      }
846
847
848
849
850
851
852

    this->SetXEdge(ePtr, edgeCase);

    // if edge intersects contour
    if ( edgeCase == vtkFlyingEdges3DAlgorithm::LeftAbove ||
         edgeCase == vtkFlyingEdges3DAlgorithm::RightAbove )
      {
Will Schroeder's avatar
Will Schroeder committed
853
      ++sum; //increment number of intersections along x-edge
854
855
856
857
      if ( i < minInt )
        {
        minInt = i;
        }
858
859
860
861
      maxInt = i + 1;
      }//if contour interacts with this x-edge
    }//for all x-cell edges along this x-edge

Will Schroeder's avatar
Will Schroeder committed
862
863
  edgeMetaData[0] += sum; //write back the number of intersections along x-edge

864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
  // 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.
Will Schroeder's avatar
Will Schroeder committed
881
  unsigned char *ePtr[4], ec0, ec1, ec2, ec3, xInts=1;
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
  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
      }
Will Schroeder's avatar
Will Schroeder committed
904
905
906
907
    else
      {
      xInts = 0; //there are y- or z- edge ints however
      }
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
    }

  // 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;
Will Schroeder's avatar
Will Schroeder committed
924
  if ( xInts )
925
    {
Will Schroeder's avatar
Will Schroeder committed
926
927
928
929
930
    for (i=1; i < 4; ++i)
      {
      xL = ( eMD[i][4] < xL ? eMD[i][4] : xL);
      xR = ( eMD[i][5] > xR ? eMD[i][5] : xR);
      }
931

Will Schroeder's avatar
Will Schroeder committed
932
    if ( xL > 0 ) //if trimmed in the -x direction
933
      {
Will Schroeder's avatar
Will Schroeder committed
934
935
936
937
938
939
940
      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
        }
941
942
      }

Will Schroeder's avatar
Will Schroeder committed
943
    if ( xR < (this->Dims[0]-1) ) //if trimmed in the +x direction
944
      {
Will Schroeder's avatar
Will Schroeder committed
945
946
947
948
949
950
951
      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
        }
952
953
      }
    }
Will Schroeder's avatar
Will Schroeder committed
954
955
956
957
958
  else //contour cuts through without intersecting x-edges, reset trim edges
    {
    xL = eMD[0][4] = 0;
    xR = eMD[0][5] = this->Dims[0]-1;
    }
959
960
961
962
963
964

  // 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;
965
  const vtkIdType dim0Wall = this->Dims[0]-2;
966
967
968
969
970
971
972
973
974
975
976
977
978
979
  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
980
      loc = yzLoc | (i >= dim0Wall ? MaxBoundary : Interior);
981
982
983
984
985
986
987
988
989
990
991
992
      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
}

//----------------------------------------------------------------------------
993
994
995
// 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.
996
997
998
999
1000
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];
For faster browsing, not all history is shown. View entire blame