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
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
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
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
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
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
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
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
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
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
426
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
484
485
486
487
488
489
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
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
|
/****************************************************************************
* VCGLib o o *
* Visual and Computer Graphics Library o o *
* _ O _ *
* Copyright(C) 2004-2016 \/)\/ *
* Visual Computing Lab /\/| *
* ISTI - Italian National Research Council | *
* \ *
* All rights reserved. *
* *
* This program is free software; you can redistribute it and/or modify *
* it under the terms of the GNU General Public License as published by *
* the Free Software Foundation; either version 2 of the License, or *
* (at your option) any later version. *
* *
* This program is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
* GNU General Public License (http://www.gnu.org/licenses/gpl.txt) *
* for more details. *
* *
****************************************************************************/
/***************************************************************************/
#ifndef __VCG_MARCHING_CUBES
#define __VCG_MARCHING_CUBES
#include "mc_lookup_table.h"
namespace vcg
{
namespace tri
{
// Doxygen documentation
/** \addtogroup trimesh */
/*@{*/
/*
* Cube description:
* 3 ________ 2 _____2__
* /| /| / | /|
* / | / | 11/ 3 10/ |
* 7 /_______ / | /__6_|__ / |1
* | | |6 | | | | |
* | 0|__|_____|1 | |__|__0__|
* | / | / 7 8/ 5 /
* | / | / | / | /9
* |/_______|/ |/___4___|/
* 4 5
*/
//! This class implements the Marching Cubes algorithm.
/*!
* The implementation is enough generic: this class works only on one volume cell for each
* call to <CODE>ProcessCell</CODE>. Using the field value at the cell corners, it adds to the
* mesh the triangles set approximating the surface that cross that cell. The ambiguities
* are resolved using an enhanced topologically controlled lookup table.
* @param TRIMESH_TYPE (Template parameter) the mesh type that will be constructed
* @param WALKER_TYPE (Template parameter) the class that implement the traversal ordering of the volume
**/
template<class TRIMESH_TYPE, class WALKER_TYPE>
class MarchingCubes
{
public:
enum Dimension {X, Y, Z};
typedef typename vcg::tri::Allocator< TRIMESH_TYPE > AllocatorType;
typedef typename TRIMESH_TYPE::ScalarType ScalarType;
typedef typename TRIMESH_TYPE::VertexType VertexType;
typedef typename TRIMESH_TYPE::VertexPointer VertexPointer;
typedef typename TRIMESH_TYPE::VertexIterator VertexIterator;
typedef typename TRIMESH_TYPE::FaceType FaceType;
typedef typename TRIMESH_TYPE::FacePointer FacePointer;
typedef typename TRIMESH_TYPE::FaceIterator FaceIterator;
typedef typename TRIMESH_TYPE::CoordType CoordType;
typedef typename TRIMESH_TYPE::CoordType* CoordPointer;
/*!
* Constructor
* \param mesh the mesh that will be constructed
* \param walker the class implementing the traversal policy
*/
MarchingCubes(TRIMESH_TYPE &mesh, WALKER_TYPE &walker)
{
_mesh = &mesh;
_walker = &walker;
};
/*!
* Execute the initialiazation.
* This method must be executed before the first call to <CODE>ApplyMC</CODE>
*/
void Initialize()
{
_mesh->Clear();
}; // end of Initialize()
/*!
*
* This method must be executed after the last call to <CODE>ApplyMC</CODE>
*/
void Finalize()
{
_mesh = NULL;
_walker = NULL;
}; // end of Finalize()
/*!
* Apply the <I>marching cubes</I> algorithm to the volume cell identified by the two points <CODE>min</CODE> and <CODE>max</CODE>.
* All the three coordinates of the first point must be smaller than the respectives three coordinatas of the second point.
* \param min the first point
* \param max the second point
*/
void ProcessCell(const vcg::Point3i &min, const vcg::Point3i &max)
{
_case = _subconfig = _config = -1;
assert(min[0]<max[0] && min[1]<max[1] && min[2]<max[2]);
_corners[0].X()=min.X(); _corners[0].Y()=min.Y(); _corners[0].Z()=min.Z();
_corners[1].X()=max.X(); _corners[1].Y()=min.Y(); _corners[1].Z()=min.Z();
_corners[2].X()=max.X(); _corners[2].Y()=max.Y(); _corners[2].Z()=min.Z();
_corners[3].X()=min.X(); _corners[3].Y()=max.Y(); _corners[3].Z()=min.Z();
_corners[4].X()=min.X(); _corners[4].Y()=min.Y(); _corners[4].Z()=max.Z();
_corners[5].X()=max.X(); _corners[5].Y()=min.Y(); _corners[5].Z()=max.Z();
_corners[6].X()=max.X(); _corners[6].Y()=max.Y(); _corners[6].Z()=max.Z();
_corners[7].X()=min.X(); _corners[7].Y()=max.Y(); _corners[7].Z()=max.Z();
for (int i=0; i<8; i++)
_field[i] = _walker->V( _corners[i].X(), _corners[i].Y(), _corners[i].Z() );
unsigned char cubetype = 0;
for (int i=0; i<8; i++)
if (_field[i]>0) cubetype += 1<<i;
_case = MCLookUpTable::Cases(cubetype, 0); //_case = cases[cubetype][0];
_config = MCLookUpTable::Cases(cubetype, 1); //_config = cases[cubetype][1];
_subconfig = 0;
VertexPointer v12 = NULL;
switch( _case )
{
case 0 : { break ; }
case 1 : { AddTriangles( MCLookUpTable::Tiling1(_config), 1 ); break; } //case 1 : { AddTriangles( tiling1[_config], 1 ); break; }
case 2 : { AddTriangles( MCLookUpTable::Tiling2(_config), 2 ); break; } //case 2 : { AddTriangles( tiling2[_config], 2 ); break; }
case 3 :
{
//if( TestFace( test3[_config]) ) AddTriangles( tiling3_2[_config], 4 ) ; // 3.2
if( TestFace( MCLookUpTable::Test3(_config)) )
AddTriangles( MCLookUpTable::Tiling3_2(_config), 4 ) ; // 3.2
else
AddTriangles( MCLookUpTable::Tiling3_1(_config), 2 ) ; // 3.1
break ;
}
case 4 :
{
//if( TestInterior( test4[_config]) ) AddTriangles( tiling4_1[_config], 2 ) ; // 4.1.1
if( TestInterior( MCLookUpTable::Test4(_config) ) )
AddTriangles( MCLookUpTable::Tiling4_1(_config), 2 ) ; // 4.1.1
else
AddTriangles( MCLookUpTable::Tiling4_2(_config), 6 ) ; // 4.1.2
break ;
}
case 5 : { AddTriangles( MCLookUpTable::Tiling5(_config), 3 ); break; }
case 6 :
{
//if( TestFace( test6[_config][0]) )
if( TestFace( MCLookUpTable::Test6(_config, 0)) )
AddTriangles( MCLookUpTable::Tiling6_2(_config), 5 ) ; // 6.2
else
{
if( TestInterior( MCLookUpTable::Test6(_config, 1)) )
AddTriangles( MCLookUpTable::Tiling6_1_1(_config), 3 ) ; // 6.1.1
else
AddTriangles( MCLookUpTable::Tiling6_1_2(_config), 7 ) ; // 6.1.2
}
break ;
}
case 7 :
{
//if( TestFace( test7[_config][0] ) ) _subconfig += 1 ;
//if( TestFace( test7[_config][1] ) ) _subconfig += 2 ;
//if( TestFace( test7[_config][2] ) ) _subconfig += 4 ;
if( TestFace( MCLookUpTable::Test7(_config, 0) ) ) _subconfig += 1 ;
if( TestFace( MCLookUpTable::Test7(_config, 1) ) ) _subconfig += 2 ;
if( TestFace( MCLookUpTable::Test7(_config, 2) ) ) _subconfig += 4 ;
switch( _subconfig )
{
case 0 : { AddTriangles( MCLookUpTable::Tiling7_1(_config), 3 ) ; break; }
case 1 : { AddTriangles( MCLookUpTable::Tiling7_2(_config,0), 5 ) ; break; }
case 2 : { AddTriangles( MCLookUpTable::Tiling7_2(_config,1), 5 ) ; break; }
case 3 : { ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling7_3(_config,0), 9, v12 ) ; break ; }
case 4 : { AddTriangles( MCLookUpTable::Tiling7_2(_config, 2), 5 ) ; break ;}
case 5 : { ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling7_3(_config,1), 9, v12 ) ; break ; }
case 6 : { ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling7_3(_config,2), 9, v12 ) ; break ; }
case 7 :
{
if( TestInterior( MCLookUpTable::Test7(_config, 3) ) )
AddTriangles( MCLookUpTable::Tiling7_4_2(_config), 9 ) ;
else
AddTriangles( MCLookUpTable::Tiling7_4_1(_config), 5 ) ;
break ;
}
};
break ;
} // end of case 7
case 8 : { AddTriangles( MCLookUpTable::Tiling8(_config), 2 ) ; break ;}
case 9 : { AddTriangles( MCLookUpTable::Tiling9(_config), 4 ) ; break ;}
case 10 :
{
if( TestFace( MCLookUpTable::Test10(_config, 0)) ) //if( TestFace( test10[_config][0]) )
{
if( TestFace( MCLookUpTable::Test10(_config,1) ) )
AddTriangles( MCLookUpTable::Tiling10_1_1_(_config), 4 ) ; // 10.1.1
else
{
ComputeCVertex(v12);
AddTriangles( MCLookUpTable::Tiling10_2(_config), 8, v12 ) ; // 10.2
}
}
else
{
if( TestFace( MCLookUpTable::Test10(_config, 1) ) )
{
ComputeCVertex(v12) ;
AddTriangles( MCLookUpTable::Tiling10_2_(_config), 8, v12 ) ; // 10.2
}
else
{
if( TestInterior( MCLookUpTable::Test10(_config, 2) ) )
AddTriangles( MCLookUpTable::Tiling10_1_1(_config), 4 ) ; // 10.1.1
else
AddTriangles( MCLookUpTable::Tiling10_1_2(_config), 8 ) ; // 10.1.2
}
}
break ;
} // end of case 10
case 11 : { AddTriangles( MCLookUpTable::Tiling11(_config), 4 ) ; break ; }
case 12 :
{
if( TestFace( MCLookUpTable::Test12(_config, 0) ) ) //if( TestFace( test12[_config][0]) )
{
if( TestFace( MCLookUpTable::Test12(_config, 1) ) )
AddTriangles( MCLookUpTable::Tiling12_1_1_(_config), 4 ) ; // 12.1.1
else
{
ComputeCVertex(v12) ;
AddTriangles( MCLookUpTable::Tiling12_2(_config), 8, v12 ) ; // 12.2
}
}
else
{
if( TestFace( MCLookUpTable::Test12(_config, 1) ) )
{
ComputeCVertex(v12) ;
AddTriangles( MCLookUpTable::Tiling12_2_(_config), 8, v12 ) ; // 12.2
}
else
{
if( TestInterior( MCLookUpTable::Test12(_config, 2) ) )
AddTriangles( MCLookUpTable::Tiling12_1_1(_config), 4 ) ; // 12.1.1
else
AddTriangles( MCLookUpTable::Tiling12_1_2(_config), 8 ) ; // 12.1.2
}
}
break ;
} // end of case 12
case 13 :
{
//if( TestFace( test13[_config][0] ) ) _subconfig += 1 ;
//if( TestFace( test13[_config][1] ) ) _subconfig += 2 ;
//if( TestFace( test13[_config][2] ) ) _subconfig += 4 ;
//if( TestFace( test13[_config][3] ) ) _subconfig += 8 ;
//if( TestFace( test13[_config][4] ) ) _subconfig += 16 ;
//if( TestFace( test13[_config][5] ) ) _subconfig += 32 ;
if( TestFace( MCLookUpTable::Test13(_config, 0) ) ) _subconfig += 1 ;
if( TestFace( MCLookUpTable::Test13(_config, 1) ) ) _subconfig += 2 ;
if( TestFace( MCLookUpTable::Test13(_config, 2) ) ) _subconfig += 4 ;
if( TestFace( MCLookUpTable::Test13(_config, 3) ) ) _subconfig += 8 ;
if( TestFace( MCLookUpTable::Test13(_config, 4) ) ) _subconfig += 16 ;
if( TestFace( MCLookUpTable::Test13(_config, 5) ) ) _subconfig += 32 ;
switch( MCLookUpTable::Subconfig13(_subconfig) ) //switch( subconfig13[_subconfig] )
{
case 0 : { /* 13.1 */ AddTriangles( MCLookUpTable::Tiling13_1(_config) , 4 ) ; break ; }
case 1 : { /* 13.2 */ AddTriangles( MCLookUpTable::Tiling13_2(_config, 0), 6 ) ; break ; }
case 2 : { /* 13.2 */ AddTriangles( MCLookUpTable::Tiling13_2(_config, 1), 6 ) ; break ; }
case 3 : { /* 13.2 */ AddTriangles( MCLookUpTable::Tiling13_2(_config, 2), 6 ) ; break ; }
case 4 : { /* 13.2 */ AddTriangles( MCLookUpTable::Tiling13_2(_config, 3), 6 ) ; break ; }
case 5 : { /* 13.2 */ AddTriangles( MCLookUpTable::Tiling13_2(_config, 4), 6 ) ; break ; }
case 6 : { /* 13.2 */ AddTriangles( MCLookUpTable::Tiling13_2(_config, 5), 6 ) ; break ; }
case 7 : { /* 13.3 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_3(_config, 0), 10, v12 ) ; break ; }
case 8 : { /* 13.3 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_3(_config, 1), 10, v12 ) ; break ; }
case 9 : { /* 13.3 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_3(_config, 2), 10, v12 ) ; break ; }
case 10 : { /* 13.3 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_3(_config, 3), 10, v12 ) ; break ; }
case 11 : { /* 13.3 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_3(_config, 4), 10, v12 ) ; break ; }
case 12 : { /* 13.3 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_3(_config, 5), 10, v12 ) ; break ; }
case 13 : { /* 13.3 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_3(_config, 6), 10, v12 ) ; break ; }
case 14 : { /* 13.3 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_3(_config, 7), 10, v12 ) ; break ; }
case 15 : { /* 13.3 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_3(_config, 8), 10, v12 ) ; break ; }
case 16 : { /* 13.3 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_3(_config, 9), 10, v12 ) ; break ; }
case 17 : { /* 13.3 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_3(_config,10), 10, v12 ) ; break ; }
case 18 : { /* 13.3 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_3(_config,11), 10, v12 ) ; break ; }
case 19 : { /* 13.4 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_4(_config, 0), 12, v12 ) ; break ; }
case 20 : { /* 13.4 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_4(_config, 1), 12, v12 ) ; break ; }
case 21 : { /* 13.4 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_4(_config, 2), 12, v12 ) ; break ; }
case 22 : { /* 13.4 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_4(_config, 3), 12, v12 ) ; break ; }
case 23 :
{ /* 13.5 */
_subconfig = 0 ;
if( TestInterior( MCLookUpTable::Test13(_config, 6) ) )
AddTriangles( MCLookUpTable::Tiling13_5_1(_config, 0), 6 ) ;
else
AddTriangles( MCLookUpTable::Tiling13_5_2(_config, 0), 10 ) ;
break ;
}
case 24 :
{ /* 13.5 */
_subconfig = 1 ;
if( TestInterior( MCLookUpTable::Test13(_config, 6) ) )
AddTriangles( MCLookUpTable::Tiling13_5_1(_config, 1), 6 ) ;
else
AddTriangles( MCLookUpTable::Tiling13_5_2(_config, 1), 10 ) ;
break ;
}
case 25 :
{/* 13.5 */
_subconfig = 2 ;
if( TestInterior( MCLookUpTable::Test13(_config, 6) ) )
AddTriangles( MCLookUpTable::Tiling13_5_1(_config, 2), 6 ) ;
else
AddTriangles( MCLookUpTable::Tiling13_5_2(_config, 2), 10 ) ;
break ;
}
case 26 :
{/* 13.5 */
_subconfig = 3 ;
if( TestInterior( MCLookUpTable::Test13(_config, 6) ) )
AddTriangles( MCLookUpTable::Tiling13_5_1(_config, 3), 6 ) ;
else
AddTriangles( MCLookUpTable::Tiling13_5_2(_config, 3), 10 ) ;
break ;
}
case 27 : { /* 13.3 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_3_(_config, 0), 10, v12 ) ; break ; }
case 28 : { /* 13.3 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_3_(_config, 1), 10, v12 ) ; break ; }
case 29 : { /* 13.3 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_3_(_config, 2), 10, v12 ) ; break ; }
case 30 : { /* 13.3 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_3_(_config, 3), 10, v12 ) ; break ; }
case 31 : { /* 13.3 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_3_(_config, 4), 10, v12 ) ; break ; }
case 32 : { /* 13.3 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_3_(_config, 5), 10, v12 ) ; break ; }
case 33 : { /* 13.3 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_3_(_config, 6), 10, v12 ) ; break ; }
case 34 : { /* 13.3 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_3_(_config, 7), 10, v12 ) ; break ; }
case 35 : { /* 13.3 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_3_(_config, 8), 10, v12 ) ; break ; }
case 36 : { /* 13.3 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_3_(_config, 9), 10, v12 ) ; break ; }
case 37 : { /* 13.3 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_3_(_config,10), 10, v12 ) ; break ; }
case 38 : { /* 13.3 */ ComputeCVertex(v12); AddTriangles( MCLookUpTable::Tiling13_3_(_config,11), 10, v12 ) ; break ; }
case 39 : { /* 13.2 */ AddTriangles( MCLookUpTable::Tiling13_2_(_config,0), 6 ) ; break ; }
case 40 : { /* 13.2 */ AddTriangles( MCLookUpTable::Tiling13_2_(_config,1), 6 ) ; break ; }
case 41 : { /* 13.2 */ AddTriangles( MCLookUpTable::Tiling13_2_(_config,2), 6 ) ; break ; }
case 42 : { /* 13.2 */ AddTriangles( MCLookUpTable::Tiling13_2_(_config,3), 6 ) ; break ; }
case 43 : { /* 13.2 */ AddTriangles( MCLookUpTable::Tiling13_2_(_config,4), 6 ) ; break ; }
case 44 : { /* 13.2 */ AddTriangles( MCLookUpTable::Tiling13_2_(_config,5), 6 ) ; break ; }
case 45 : { /* 13.1 */ AddTriangles( MCLookUpTable::Tiling13_1_(_config) , 4 ) ; break ; }
default : { /*Impossible case 13*/ assert(false); }
}
break ;
} // end of case 13
case 14 : { AddTriangles( MCLookUpTable::Tiling14(_config), 4 ) ; }
break ;
} //end of switch (_case)
}; // end of ApplyMC
private:
/*!
*/
WALKER_TYPE *_walker;
/*!
*/
TRIMESH_TYPE *_mesh;
/*!
* The field value at the cell corners
*/
ScalarType _field[8];
/*!
* Array of the 8 corners of the volume cell being processed
*/
vcg::Point3i _corners[8];
/*!
* Case of the volume cell being processed
*/
unsigned char _case;
/*!
* Configuration of the volume cell being processed
*/
unsigned char _config;
/*!
* Subconfiguration of the volume cell being processed
*/
unsigned char _subconfig;
/*!
* Tests if the components of the tesselation of the cube should be connected
* by the interior of an ambiguous face
*/
inline bool TestFace(signed char face)
{
ScalarType A,B,C,D ;
switch( face )
{
case -1 : case 1 : A = _field[0] ; B = _field[4] ; C = _field[5] ; D = _field[1] ; break ;
case -2 : case 2 : A = _field[1] ; B = _field[5] ; C = _field[6] ; D = _field[2] ; break ;
case -3 : case 3 : A = _field[2] ; B = _field[6] ; C = _field[7] ; D = _field[3] ; break ;
case -4 : case 4 : A = _field[3] ; B = _field[7] ; C = _field[4] ; D = _field[0] ; break ;
case -5 : case 5 : A = _field[0] ; B = _field[3] ; C = _field[2] ; D = _field[1] ; break ;
case -6 : case 6 : A = _field[4] ; B = _field[7] ; C = _field[6] ; D = _field[5] ; break ;
default : assert(false); // Invalid face code
};
return face * A * ( A*C - B*D ) >= 0 ; // face and A invert signs
} // end of TestFace
/*!
* Tests if the components of the tesselation of the cube should be connected
* through the interior of the cube
*/
inline bool TestInterior(signed char s)
{
ScalarType t, At=0, Bt=0, Ct=0, Dt=0, a, b ;
char test = 0 ;
char edge = -1 ; // reference edge of the triangulation
switch( _case )
{
case 4 :
case 10 :
{
a = (_field[4]-_field[0])*(_field[6]-_field[2]) - (_field[7]-_field[3])*(_field[5]-_field[1]);
b = _field[2]*(_field[4]-_field[0])+_field[0]*(_field[6]-_field[2])-_field[1]*(_field[7]-_field[3])-_field[3]*(_field[5]-_field[1]);
t = - b / (2*a) ;
if( t<0 || t>1 )
return s>0 ;
At = _field[0] + ( _field[4] - _field[0] ) * t ;
Bt = _field[3] + ( _field[7] - _field[3] ) * t ;
Ct = _field[2] + ( _field[6] - _field[2] ) * t ;
Dt = _field[1] + ( _field[5] - _field[1] ) * t ;
break ;
}
case 6 :
case 7 :
case 12 :
case 13 :
switch( _case )
{
case 6 : edge = MCLookUpTable::Test6 (_config, 2) ; break ;
case 7 : edge = MCLookUpTable::Test7 (_config, 4) ; break ;
case 12 : edge = MCLookUpTable::Test12(_config, 3) ; break ;
case 13 : edge = MCLookUpTable::Tiling13_5_1(_config, _subconfig)[0] ; break ;
}
switch( edge )
{
case 0 :
t = _field[0] / ( _field[0] - _field[1] ) ;
At = 0 ;
Bt = _field[3] + ( _field[2] - _field[3] ) * t ;
Ct = _field[7] + ( _field[6] - _field[7] ) * t ;
Dt = _field[4] + ( _field[5] - _field[4] ) * t ;
break ;
case 1 :
t = _field[1] / ( _field[1] - _field[2] ) ;
At = 0 ;
Bt = _field[0] + ( _field[3] - _field[0] ) * t ;
Ct = _field[4] + ( _field[7] - _field[4] ) * t ;
Dt = _field[5] + ( _field[6] - _field[5] ) * t ;
break ;
case 2 :
t = _field[2] / ( _field[2] - _field[3] ) ;
At = 0 ;
Bt = _field[1] + ( _field[0] - _field[1] ) * t ;
Ct = _field[5] + ( _field[4] - _field[5] ) * t ;
Dt = _field[6] + ( _field[7] - _field[6] ) * t ;
break ;
case 3 :
t = _field[3] / ( _field[3] - _field[0] ) ;
At = 0 ;
Bt = _field[2] + ( _field[1] - _field[2] ) * t ;
Ct = _field[6] + ( _field[5] - _field[6] ) * t ;
Dt = _field[7] + ( _field[4] - _field[7] ) * t ;
break ;
case 4 :
t = _field[4] / ( _field[4] - _field[5] ) ;
At = 0 ;
Bt = _field[7] + ( _field[6] - _field[7] ) * t ;
Ct = _field[3] + ( _field[2] - _field[3] ) * t ;
Dt = _field[0] + ( _field[1] - _field[0] ) * t ;
break ;
case 5 :
t = _field[5] / ( _field[5] - _field[6] ) ;
At = 0 ;
Bt = _field[4] + ( _field[7] - _field[4] ) * t ;
Ct = _field[0] + ( _field[3] - _field[0] ) * t ;
Dt = _field[1] + ( _field[2] - _field[1] ) * t ;
break ;
case 6 :
t = _field[6] / ( _field[6] - _field[7] ) ;
At = 0 ;
Bt = _field[5] + ( _field[4] - _field[5] ) * t ;
Ct = _field[1] + ( _field[0] - _field[1] ) * t ;
Dt = _field[2] + ( _field[3] - _field[2] ) * t ;
break ;
case 7 :
t = _field[7] / ( _field[7] - _field[4] ) ;
At = 0 ;
Bt = _field[6] + ( _field[5] - _field[6] ) * t ;
Ct = _field[2] + ( _field[1] - _field[2] ) * t ;
Dt = _field[3] + ( _field[0] - _field[3] ) * t ;
break ;
case 8 :
t = _field[0] / ( _field[0] - _field[4] ) ;
At = 0 ;
Bt = _field[3] + ( _field[7] - _field[3] ) * t ;
Ct = _field[2] + ( _field[6] - _field[2] ) * t ;
Dt = _field[1] + ( _field[5] - _field[1] ) * t ;
break ;
case 9 :
t = _field[1] / ( _field[1] - _field[5] ) ;
At = 0 ;
Bt = _field[0] + ( _field[4] - _field[0] ) * t ;
Ct = _field[3] + ( _field[7] - _field[3] ) * t ;
Dt = _field[2] + ( _field[6] - _field[2] ) * t ;
break ;
case 10 :
t = _field[2] / ( _field[2] - _field[6] ) ;
At = 0 ;
Bt = _field[1] + ( _field[5] - _field[1] ) * t ;
Ct = _field[0] + ( _field[4] - _field[0] ) * t ;
Dt = _field[3] + ( _field[7] - _field[3] ) * t ;
break ;
case 11 :
t = _field[3] / ( _field[3] - _field[7] ) ;
At = 0 ;
Bt = _field[2] + ( _field[6] - _field[2] ) * t ;
Ct = _field[1] + ( _field[5] - _field[1] ) * t ;
Dt = _field[0] + ( _field[4] - _field[0] ) * t ;
break ;
default: { assert(false); /* Invalid edge */ break ; }
}
break ;
default : assert(false); /* Invalid ambiguous case */ break;
}
if( At >= 0 ) test ++ ;
if( Bt >= 0 ) test += 2 ;
if( Ct >= 0 ) test += 4 ;
if( Dt >= 0 ) test += 8 ;
switch( test )
{
case 0 : return s>0 ;
case 1 : return s>0 ;
case 2 : return s>0 ;
case 3 : return s>0 ;
case 4 : return s>0 ;
case 5 : if( At * Ct < Bt * Dt ) return s>0 ; break ;
case 6 : return s>0 ;
case 7 : return s<0 ;
case 8 : return s>0 ;
case 9 : return s>0 ;
case 10 : if( At * Ct >= Bt * Dt ) return s>0 ; break ;
case 11 : return s<0 ;
case 12 : return s>0 ;
case 13 : return s<0 ;
case 14 : return s<0 ;
case 15 : return s<0 ;
}
return s<0 ;
} //end of TestInterior
/*!
* Adds a vertex inside the current cube
* \param v The pointer to the new vertex along the edge
*/
inline void ComputeCVertex(VertexPointer &v12)
{
v12 = &*AllocatorType::AddVertices(*_mesh, 1);
v12->P() = CoordType(0.0, 0.0, 0.0);
unsigned int count = 0;
VertexPointer v = NULL;
if (_walker->Exist(_corners[0], _corners[1], v) )
{
count++;
v12->P() += v->P();
}
if (_walker->Exist(_corners[1], _corners[2], v) )
{
count++;
v12->P() += v->P();
}
if (_walker->Exist(_corners[3], _corners[2], v) )
{
count++;
v12->P() += v->P();
}
if (_walker->Exist(_corners[0], _corners[3], v) )
{
count++;
v12->P() += v->P();
}
if (_walker->Exist(_corners[4], _corners[5], v) )
{
count++;
v12->P() += v->P();
}
if (_walker->Exist(_corners[5], _corners[6], v) )
{
count++;
v12->P() += v->P();
}
if (_walker->Exist(_corners[7], _corners[6], v) )
{
count++;
v12->P() += v->P();
}
if (_walker->Exist(_corners[4], _corners[7], v) )
{
count++;
v12->P() += v->P();
}
if (_walker->Exist(_corners[0], _corners[4], v) )
{
count++;
v12->P() += v->P();
}
if (_walker->Exist(_corners[1], _corners[5], v) )
{
count++;
v12->P() += v->P();
}
if (_walker->Exist(_corners[2], _corners[6], v) )
{
count++;
v12->P() += v->P();
}
if (_walker->Exist(_corners[3], _corners[7], v) )
{
count++;
v12->P() += v->P();
}
v12->P() /= (float) count;
} // end of AddCVertex
/*!
* Adds new triangles to the mesh
* \param vertices_list The list of vertex indices
* \param n The number of triangles that will be added to the mesh
* \param v12 The pointer to the vertex inside the current cell
*/
inline void AddTriangles(const char *vertices_list, char n, VertexPointer v12=NULL)
{
VertexPointer vp = NULL;
size_t face_idx = _mesh->face.size();
size_t v12_idx = -1;
size_t vertices_idx[3];
if (v12 != NULL) v12_idx = v12 - &_mesh->vert[0];
AllocatorType::AddFaces(*_mesh, (int) n);
for (int trig=0; trig<3*n; face_idx++ )
{
vp = NULL;
memset(vertices_idx, -1, 3*sizeof(size_t));
for (int vert=0; vert<3; vert++, trig++) //ok
{
switch ( vertices_list[trig] )
{
case 0: { _walker->GetXIntercept(_corners[0], _corners[1], vp); vertices_idx[vert] = tri::Index(*_mesh,vp); break; }
case 1: { _walker->GetYIntercept(_corners[1], _corners[2], vp); vertices_idx[vert] = tri::Index(*_mesh,vp); break; }
case 2: { _walker->GetXIntercept(_corners[3], _corners[2], vp); vertices_idx[vert] = tri::Index(*_mesh,vp); break; }
case 3: { _walker->GetYIntercept(_corners[0], _corners[3], vp); vertices_idx[vert] = tri::Index(*_mesh,vp); break; }
case 4: { _walker->GetXIntercept(_corners[4], _corners[5], vp); vertices_idx[vert] = tri::Index(*_mesh,vp); break; }
case 5: { _walker->GetYIntercept(_corners[5], _corners[6], vp); vertices_idx[vert] = tri::Index(*_mesh,vp); break; }
case 6: { _walker->GetXIntercept(_corners[7], _corners[6], vp); vertices_idx[vert] = tri::Index(*_mesh,vp); break; }
case 7: { _walker->GetYIntercept(_corners[4], _corners[7], vp); vertices_idx[vert] = tri::Index(*_mesh,vp); break; }
case 8: { _walker->GetZIntercept(_corners[0], _corners[4], vp); vertices_idx[vert] = tri::Index(*_mesh,vp); break; }
case 9: { _walker->GetZIntercept(_corners[1], _corners[5], vp); vertices_idx[vert] = tri::Index(*_mesh,vp); break; }
case 10: { _walker->GetZIntercept(_corners[2], _corners[6], vp); vertices_idx[vert] = tri::Index(*_mesh,vp); break; }
case 11: { _walker->GetZIntercept(_corners[3], _corners[7], vp); vertices_idx[vert] = tri::Index(*_mesh,vp); break; }
case 12: { assert(v12 != NULL); vertices_idx[vert] = v12_idx; break; }
default: { assert(false); /* Invalid edge identifier */ }
} // end of switch
// Note that vp can be zero if we are in case 12 and that vertices_idx is surely >0 so the following assert has to be corrected as below.
// assert((vp - &_mesh->vert[0])>=0 && vertices_idx[vert]<_mesh->vert.size());
assert(vertices_idx[vert]<_mesh->vert.size());
} // end for (int vert=0 ...)
_mesh->face[face_idx].V(0) = &_mesh->vert[vertices_idx[0]];
_mesh->face[face_idx].V(1) = &_mesh->vert[vertices_idx[1]];
_mesh->face[face_idx].V(2) = &_mesh->vert[vertices_idx[2]];
} // end for (int trig=0...)
} // end of AddTriangles
}; // end of class MarchingCubes
/*! @} */
//end of Doxygen documentation
} // end of namespace tri
} // end of namespace vcg
#endif //__VCG_MARCHING_CUBES
|
