test_marching_cubes.py 29.2 KB
Newer Older
1
# Copyright (c) Meta Platforms, Inc. and affiliates.
Patrick Labatut's avatar
Patrick Labatut committed
2
3
4
5
6
# All rights reserved.
#
# This source code is licensed under the BSD-style license found in the
# LICENSE file in the root directory of this source tree.

7
8
9
10
11
12
13
import os
import pickle
import unittest

import torch
from pytorch3d.ops.marching_cubes import marching_cubes_naive

Jeremy Reizenstein's avatar
Jeremy Reizenstein committed
14
15
from .common_testing import get_tests_dir, TestCaseMixin

16
17

USE_SCIKIT = False
18
DATA_DIR = get_tests_dir() / "data"
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34


def convert_to_local(verts, volume_dim):
    return (2 * verts) / (volume_dim - 1) - 1


class TestCubeConfiguration(TestCaseMixin, unittest.TestCase):

    # Test single cubes. Each case corresponds to the corresponding
    # cube vertex configuration in each case here (0-indexed):
    # https://en.wikipedia.org/wiki/Marching_cubes#/media/File:MarchingCubes.svg

    def test_empty_volume(self):  # case 0
        volume_data = torch.ones(1, 2, 2, 2)  # (B, W, H, D)
        verts, faces = marching_cubes_naive(volume_data, return_local_coords=False)

35
36
        expected_verts = torch.tensor([[]])
        expected_faces = torch.tensor([[]], dtype=torch.int64)
37
38
39
40
41
42
43
44
45
46
47
48
        self.assertClose(verts, expected_verts)
        self.assertClose(faces, expected_faces)

    def test_case1(self):  # case 1
        volume_data = torch.ones(1, 2, 2, 2)  # (B, W, H, D)
        volume_data[0, 0, 0, 0] = 0
        volume_data = volume_data.permute(0, 3, 2, 1)  # (B, D, H, W)
        verts, faces = marching_cubes_naive(volume_data, return_local_coords=False)
        expected_verts = torch.tensor(
            [
                [0.5, 0, 0],
                [0, 0.5, 0],
49
                [0, 0, 0.5],
50
51
52
            ]
        )

53
        expected_faces = torch.tensor([[0, 1, 2]])
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

        verts, faces = marching_cubes_naive(volume_data, return_local_coords=True)
        expected_verts = convert_to_local(expected_verts, 2)
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

    def test_case2(self):
        volume_data = torch.ones(1, 2, 2, 2)  # (B, W, H, D)
        volume_data[0, 0:2, 0, 0] = 0
        volume_data = volume_data.permute(0, 3, 2, 1)  # (B, D, H, W)
        verts, faces = marching_cubes_naive(volume_data, return_local_coords=False)

        expected_verts = torch.tensor(
            [
                [1.0000, 0.0000, 0.5000],
71
                [0.0000, 0.5000, 0.0000],
72
73
74
75
                [0.0000, 0.0000, 0.5000],
                [1.0000, 0.5000, 0.0000],
            ]
        )
76
        expected_faces = torch.tensor([[0, 1, 2], [3, 1, 0]])
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

        verts, faces = marching_cubes_naive(volume_data, return_local_coords=True)
        expected_verts = convert_to_local(expected_verts, 2)
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

    def test_case3(self):
        volume_data = torch.ones(1, 2, 2, 2)  # (B, W, H, D)
        volume_data[0, 0, 0, 0] = 0
        volume_data[0, 1, 1, 0] = 0
        volume_data = volume_data.permute(0, 3, 2, 1)  # (B, D, H, W)
        verts, faces = marching_cubes_naive(volume_data, return_local_coords=False)

        expected_verts = torch.tensor(
            [
94
                [1.0000, 0.5000, 0.0000],
95
96
                [1.0000, 1.0000, 0.5000],
                [0.5000, 1.0000, 0.0000],
97
                [0.5000, 0.0000, 0.0000],
98
                [0.0000, 0.5000, 0.0000],
99
                [0.0000, 0.0000, 0.5000],
100
101
            ]
        )
102
        expected_faces = torch.tensor([[0, 1, 2], [3, 4, 5]])
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

        verts, faces = marching_cubes_naive(volume_data, return_local_coords=True)
        expected_verts = convert_to_local(expected_verts, 2)
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

    def test_case4(self):
        volume_data = torch.ones(1, 2, 2, 2)  # (B, W, H, D)
        volume_data[0, 1, 0, 0] = 0
        volume_data[0, 1, 0, 1] = 0
        volume_data[0, 0, 0, 1] = 0
        volume_data = volume_data.permute(0, 3, 2, 1)  # (B, D, H, W)
        verts, faces = marching_cubes_naive(volume_data, return_local_coords=False)

        expected_verts = torch.tensor(
            [
                [0.0000, 0.0000, 0.5000],
122
123
                [1.0000, 0.5000, 0.0000],
                [0.5000, 0.0000, 0.0000],
124
125
126
127
                [0.0000, 0.5000, 1.0000],
                [1.0000, 0.5000, 1.0000],
            ]
        )
128
        expected_faces = torch.tensor([[0, 1, 2], [0, 3, 1], [3, 4, 1]])
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

        verts, faces = marching_cubes_naive(volume_data, return_local_coords=True)
        expected_verts = convert_to_local(expected_verts, 2)
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

    def test_case5(self):
        volume_data = torch.ones(1, 2, 2, 2)  # (B, W, H, D)
        volume_data[0, 0:2, 0, 0:2] = 0
        volume_data = volume_data.permute(0, 3, 2, 1)  # (B, D, H, W)
        verts, faces = marching_cubes_naive(volume_data, return_local_coords=False)

        expected_verts = torch.tensor(
            [
                [1.0000, 0.5000, 0.0000],
                [0.0000, 0.5000, 0.0000],
147
148
                [1.0000, 0.5000, 1.0000],
                [0.0000, 0.5000, 1.0000],
149
150
151
            ]
        )

152
        expected_faces = torch.tensor([[0, 1, 2], [2, 1, 3]])
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

        verts, faces = marching_cubes_naive(volume_data, return_local_coords=True)
        expected_verts = convert_to_local(expected_verts, 2)
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

    def test_case6(self):
        volume_data = torch.ones(1, 2, 2, 2)  # (B, W, H, D)
        volume_data[0, 1, 0, 0] = 0
        volume_data[0, 1, 0, 1] = 0
        volume_data[0, 0, 0, 1] = 0
        volume_data[0, 0, 1, 0] = 0
        volume_data = volume_data.permute(0, 3, 2, 1)  # (B, D, H, W)
        verts, faces = marching_cubes_naive(volume_data, return_local_coords=False)

        expected_verts = torch.tensor(
            [
                [0.5000, 1.0000, 0.0000],
                [0.0000, 1.0000, 0.5000],
174
175
176
                [0.0000, 0.5000, 0.0000],
                [1.0000, 0.5000, 0.0000],
                [0.5000, 0.0000, 0.0000],
177
178
                [0.0000, 0.5000, 1.0000],
                [1.0000, 0.5000, 1.0000],
179
                [0.0000, 0.0000, 0.5000],
180
181
            ]
        )
182
        expected_faces = torch.tensor([[0, 1, 2], [3, 4, 5], [3, 5, 6], [5, 4, 7]])
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202

        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

        verts, faces = marching_cubes_naive(volume_data, return_local_coords=True)
        expected_verts = convert_to_local(expected_verts, 2)
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

    def test_case7(self):
        volume_data = torch.ones(1, 2, 2, 2)  # (B, W, H, D)
        volume_data[0, 0, 0, 0] = 0
        volume_data[0, 1, 0, 1] = 0
        volume_data[0, 1, 1, 0] = 0
        volume_data[0, 0, 1, 1] = 0
        volume_data = volume_data.permute(0, 3, 2, 1)  # (B, D, H, W)
        verts, faces = marching_cubes_naive(volume_data, return_local_coords=False)

        expected_verts = torch.tensor(
            [
203
204
205
                [0.5000, 1.0000, 1.0000],
                [0.0000, 0.5000, 1.0000],
                [0.0000, 1.0000, 0.5000],
206
                [1.0000, 0.0000, 0.5000],
207
208
                [0.5000, 0.0000, 1.0000],
                [1.0000, 0.5000, 1.0000],
209
                [0.5000, 0.0000, 0.0000],
210
                [0.0000, 0.5000, 0.0000],
211
212
213
                [0.0000, 0.0000, 0.5000],
                [0.5000, 1.0000, 0.0000],
                [1.0000, 0.5000, 0.0000],
214
                [1.0000, 1.0000, 0.5000],
215
216
217
            ]
        )

218
        expected_faces = torch.tensor([[0, 1, 2], [3, 4, 5], [6, 7, 8], [9, 10, 11]])
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239

        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

        verts, faces = marching_cubes_naive(volume_data, return_local_coords=True)
        expected_verts = convert_to_local(expected_verts, 2)
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

    def test_case8(self):
        volume_data = torch.ones(1, 2, 2, 2)  # (B, W, H, D)
        volume_data[0, 0, 0, 0] = 0
        volume_data[0, 0, 0, 1] = 0
        volume_data[0, 1, 0, 1] = 0
        volume_data[0, 0, 1, 1] = 0
        volume_data = volume_data.permute(0, 3, 2, 1)  # (B, D, H, W)
        verts, faces = marching_cubes_naive(volume_data, return_local_coords=False)

        expected_verts = torch.tensor(
            [
                [1.0000, 0.5000, 1.0000],
240
241
242
                [0.0000, 1.0000, 0.5000],
                [0.5000, 1.0000, 1.0000],
                [1.0000, 0.0000, 0.5000],
243
                [0.0000, 0.5000, 0.0000],
244
                [0.5000, 0.0000, 0.0000],
245
246
            ]
        )
247
        expected_faces = torch.tensor([[0, 1, 2], [3, 1, 0], [3, 4, 1], [3, 5, 4]])
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

        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

        verts, faces = marching_cubes_naive(volume_data, return_local_coords=True)
        expected_verts = convert_to_local(expected_verts, 2)
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

    def test_case9(self):
        volume_data = torch.ones(1, 2, 2, 2)  # (B, W, H, D)
        volume_data[0, 1, 0, 0] = 0
        volume_data[0, 0, 0, 1] = 0
        volume_data[0, 1, 0, 1] = 0
        volume_data[0, 0, 1, 1] = 0
        volume_data = volume_data.permute(0, 3, 2, 1)  # (B, D, H, W)
        verts, faces = marching_cubes_naive(volume_data, return_local_coords=False)

        expected_verts = torch.tensor(
            [
                [0.5000, 0.0000, 0.0000],
                [0.0000, 0.0000, 0.5000],
                [0.0000, 1.0000, 0.5000],
                [1.0000, 0.5000, 1.0000],
                [1.0000, 0.5000, 0.0000],
273
                [0.5000, 1.0000, 1.0000],
274
275
            ]
        )
276
        expected_faces = torch.tensor([[0, 1, 2], [0, 2, 3], [0, 3, 4], [5, 3, 2]])
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295

        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

        verts, faces = marching_cubes_naive(volume_data, return_local_coords=True)
        expected_verts = convert_to_local(expected_verts, 2)
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

    def test_case10(self):
        volume_data = torch.ones(1, 2, 2, 2)  # (B, W, H, D)
        volume_data[0, 0, 0, 0] = 0
        volume_data[0, 1, 1, 1] = 0
        volume_data = volume_data.permute(0, 3, 2, 1)  # (B, D, H, W)
        verts, faces = marching_cubes_naive(volume_data, return_local_coords=False)

        expected_verts = torch.tensor(
            [
                [0.5000, 0.0000, 0.0000],
296
                [0.0000, 0.5000, 0.0000],
297
298
299
                [0.0000, 0.0000, 0.5000],
                [1.0000, 1.0000, 0.5000],
                [1.0000, 0.5000, 1.0000],
300
                [0.5000, 1.0000, 1.0000],
301
302
303
            ]
        )

304
        expected_faces = torch.tensor([[0, 1, 2], [3, 4, 5]])
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324

        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

        verts, faces = marching_cubes_naive(volume_data, return_local_coords=True)
        expected_verts = convert_to_local(expected_verts, 2)
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

    def test_case11(self):
        volume_data = torch.ones(1, 2, 2, 2)  # (B, W, H, D)
        volume_data[0, 0, 0, 0] = 0
        volume_data[0, 1, 0, 0] = 0
        volume_data[0, 1, 1, 1] = 0
        volume_data = volume_data.permute(0, 3, 2, 1)  # (B, D, H, W)
        verts, faces = marching_cubes_naive(volume_data, return_local_coords=False)

        expected_verts = torch.tensor(
            [
                [1.0000, 0.0000, 0.5000],
325
                [0.0000, 0.5000, 0.0000],
326
                [0.0000, 0.0000, 0.5000],
327
                [1.0000, 0.5000, 0.0000],
328
329
                [1.0000, 1.0000, 0.5000],
                [1.0000, 0.5000, 1.0000],
330
                [0.5000, 1.0000, 1.0000],
331
332
333
            ]
        )

334
        expected_faces = torch.tensor([[0, 1, 2], [0, 3, 1], [4, 5, 6]])
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354

        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

        verts, faces = marching_cubes_naive(volume_data, return_local_coords=True)
        expected_verts = convert_to_local(expected_verts, 2)
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

    def test_case12(self):
        volume_data = torch.ones(1, 2, 2, 2)  # (B, W, H, D)
        volume_data[0, 1, 0, 0] = 0
        volume_data[0, 0, 1, 0] = 0
        volume_data[0, 1, 1, 1] = 0
        volume_data = volume_data.permute(0, 3, 2, 1)  # (B, D, H, W)
        verts, faces = marching_cubes_naive(volume_data, return_local_coords=False)

        expected_verts = torch.tensor(
            [
                [1.0000, 0.0000, 0.5000],
355
                [1.0000, 0.5000, 0.0000],
356
357
358
                [0.5000, 0.0000, 0.0000],
                [1.0000, 1.0000, 0.5000],
                [1.0000, 0.5000, 1.0000],
359
                [0.5000, 1.0000, 1.0000],
360
                [0.0000, 0.5000, 0.0000],
361
362
                [0.5000, 1.0000, 0.0000],
                [0.0000, 1.0000, 0.5000],
363
364
365
            ]
        )

366
        expected_faces = torch.tensor([[0, 1, 2], [3, 4, 5], [6, 7, 8]])
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387

        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

        verts, faces = marching_cubes_naive(volume_data, return_local_coords=True)
        expected_verts = convert_to_local(expected_verts, 2)
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

    def test_case13(self):
        volume_data = torch.ones(1, 2, 2, 2)  # (B, W, H, D)
        volume_data[0, 0, 0, 0] = 0
        volume_data[0, 0, 1, 0] = 0
        volume_data[0, 1, 0, 1] = 0
        volume_data[0, 1, 1, 1] = 0
        volume_data = volume_data.permute(0, 3, 2, 1)  # (B, D, H, W)
        verts, faces = marching_cubes_naive(volume_data, return_local_coords=False)

        expected_verts = torch.tensor(
            [
                [1.0000, 0.0000, 0.5000],
388
                [0.5000, 0.0000, 1.0000],
389
                [1.0000, 1.0000, 0.5000],
390
391
392
                [0.5000, 1.0000, 1.0000],
                [0.0000, 0.0000, 0.5000],
                [0.5000, 0.0000, 0.0000],
393
394
395
396
397
                [0.5000, 1.0000, 0.0000],
                [0.0000, 1.0000, 0.5000],
            ]
        )

398
        expected_faces = torch.tensor([[0, 1, 2], [2, 1, 3], [4, 5, 6], [4, 6, 7]])
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420

        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

        verts, faces = marching_cubes_naive(volume_data, return_local_coords=True)
        expected_verts = convert_to_local(expected_verts, 2)
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

    def test_case14(self):
        volume_data = torch.ones(1, 2, 2, 2)  # (B, W, H, D)
        volume_data[0, 0, 0, 0] = 0
        volume_data[0, 0, 0, 1] = 0
        volume_data[0, 1, 0, 1] = 0
        volume_data[0, 1, 1, 1] = 0
        volume_data = volume_data.permute(0, 3, 2, 1)  # (B, D, H, W)
        verts, faces = marching_cubes_naive(volume_data, return_local_coords=False)

        expected_verts = torch.tensor(
            [
                [0.5000, 0.0000, 0.0000],
                [0.0000, 0.5000, 0.0000],
421
422
423
424
                [0.0000, 0.5000, 1.0000],
                [1.0000, 1.0000, 0.5000],
                [1.0000, 0.0000, 0.5000],
                [0.5000, 1.0000, 1.0000],
425
426
427
            ]
        )

428
        expected_faces = torch.tensor([[0, 1, 2], [0, 2, 3], [0, 3, 4], [3, 2, 5]])
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447

        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

        verts, faces = marching_cubes_naive(volume_data, return_local_coords=True)
        expected_verts = convert_to_local(expected_verts, 2)
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)


class TestMarchingCubes(TestCaseMixin, unittest.TestCase):
    def test_single_point(self):
        volume_data = torch.zeros(1, 3, 3, 3)  # (B, W, H, D)
        volume_data[0, 1, 1, 1] = 1
        volume_data = volume_data.permute(0, 3, 2, 1)  # (B, D, H, W)
        verts, faces = marching_cubes_naive(volume_data, return_local_coords=False)

        expected_verts = torch.tensor(
            [
448
449
450
451
452
453
                [1.0000, 0.5000, 1.0000],
                [1.0000, 1.0000, 0.5000],
                [0.5000, 1.0000, 1.0000],
                [1.5000, 1.0000, 1.0000],
                [1.0000, 1.5000, 1.0000],
                [1.0000, 1.0000, 1.5000],
454
455
456
457
            ]
        )
        expected_faces = torch.tensor(
            [
458
459
460
461
462
463
464
                [0, 1, 2],
                [1, 0, 3],
                [1, 4, 2],
                [1, 3, 4],
                [0, 2, 5],
                [3, 0, 5],
                [2, 4, 5],
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
                [3, 5, 4],
            ]
        )
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

        verts, faces = marching_cubes_naive(volume_data, return_local_coords=True)
        expected_verts = convert_to_local(expected_verts, 3)
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)
        self.assertTrue(verts[0].ge(-1).all() and verts[0].le(1).all())

    def test_cube(self):
        volume_data = torch.zeros(1, 5, 5, 5)  # (B, W, H, D)
        volume_data[0, 1, 1, 1] = 1
        volume_data[0, 1, 1, 2] = 1
        volume_data[0, 2, 1, 1] = 1
        volume_data[0, 2, 1, 2] = 1
        volume_data[0, 1, 2, 1] = 1
        volume_data[0, 1, 2, 2] = 1
        volume_data[0, 2, 2, 1] = 1
        volume_data[0, 2, 2, 2] = 1
        volume_data = volume_data.permute(0, 3, 2, 1)  # (B, D, H, W)
        verts, faces = marching_cubes_naive(volume_data, 0.9, return_local_coords=False)

        expected_verts = torch.tensor(
            [
                [1.0000, 0.9000, 1.0000],
493
494
                [1.0000, 1.0000, 0.9000],
                [0.9000, 1.0000, 1.0000],
495
                [2.0000, 0.9000, 1.0000],
496
497
498
499
                [2.0000, 1.0000, 0.9000],
                [2.1000, 1.0000, 1.0000],
                [1.0000, 2.0000, 0.9000],
                [0.9000, 2.0000, 1.0000],
500
                [2.0000, 2.0000, 0.9000],
501
502
                [2.1000, 2.0000, 1.0000],
                [1.0000, 2.1000, 1.0000],
503
                [2.0000, 2.1000, 1.0000],
504
505
506
                [1.0000, 0.9000, 2.0000],
                [0.9000, 1.0000, 2.0000],
                [2.0000, 0.9000, 2.0000],
507
                [2.1000, 1.0000, 2.0000],
508
                [0.9000, 2.0000, 2.0000],
509
                [2.1000, 2.0000, 2.0000],
510
511
512
513
514
515
                [1.0000, 2.1000, 2.0000],
                [2.0000, 2.1000, 2.0000],
                [1.0000, 1.0000, 2.1000],
                [2.0000, 1.0000, 2.1000],
                [1.0000, 2.0000, 2.1000],
                [2.0000, 2.0000, 2.1000],
516
517
518
519
520
            ]
        )

        expected_faces = torch.tensor(
            [
521
522
523
524
525
526
527
528
529
530
                [0, 1, 2],
                [0, 3, 4],
                [1, 0, 4],
                [4, 3, 5],
                [1, 6, 7],
                [2, 1, 7],
                [4, 8, 1],
                [1, 8, 6],
                [8, 4, 5],
                [9, 8, 5],
531
                [6, 10, 7],
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
                [6, 8, 11],
                [10, 6, 11],
                [8, 9, 11],
                [12, 0, 2],
                [13, 12, 2],
                [3, 0, 14],
                [14, 0, 12],
                [15, 5, 3],
                [14, 15, 3],
                [2, 7, 13],
                [7, 16, 13],
                [5, 15, 9],
                [9, 15, 17],
                [10, 18, 16],
                [7, 10, 16],
                [11, 19, 10],
                [19, 18, 10],
549
550
                [9, 17, 19],
                [11, 9, 19],
551
552
553
                [12, 13, 20],
                [14, 12, 20],
                [21, 14, 20],
554
                [15, 14, 21],
555
556
                [13, 16, 22],
                [20, 13, 22],
557
                [21, 20, 23],
558
                [20, 22, 23],
559
560
                [17, 15, 21],
                [23, 17, 21],
561
                [16, 18, 22],
562
563
564
565
566
567
568
                [23, 22, 18],
                [19, 23, 18],
                [17, 23, 19],
            ]
        )
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)
569

570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
        verts, faces = marching_cubes_naive(volume_data, 0.9, return_local_coords=True)
        expected_verts = convert_to_local(expected_verts, 5)
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

        # Check all values are in the range [-1, 1]
        self.assertTrue(verts[0].ge(-1).all() and verts[0].le(1).all())

    def test_cube_no_duplicate_verts(self):
        volume_data = torch.zeros(1, 5, 5, 5)  # (B, W, H, D)
        volume_data[0, 1, 1, 1] = 1
        volume_data[0, 1, 1, 2] = 1
        volume_data[0, 2, 1, 1] = 1
        volume_data[0, 2, 1, 2] = 1
        volume_data[0, 1, 2, 1] = 1
        volume_data[0, 1, 2, 2] = 1
        volume_data[0, 2, 2, 1] = 1
        volume_data[0, 2, 2, 2] = 1
        volume_data = volume_data.permute(0, 3, 2, 1)  # (B, D, H, W)
        verts, faces = marching_cubes_naive(volume_data, 1, return_local_coords=False)

        expected_verts = torch.tensor(
            [
593
594
595
596
597
                [2.0, 1.0, 1.0],
                [2.0, 2.0, 1.0],
                [1.0, 1.0, 1.0],
                [1.0, 2.0, 1.0],
                [2.0, 1.0, 1.0],
598
                [1.0, 1.0, 1.0],
599
                [2.0, 1.0, 2.0],
600
                [1.0, 1.0, 2.0],
601
                [1.0, 1.0, 1.0],
602
                [1.0, 2.0, 1.0],
603
                [1.0, 1.0, 2.0],
604
605
606
607
608
                [1.0, 2.0, 2.0],
                [2.0, 1.0, 1.0],
                [2.0, 1.0, 2.0],
                [2.0, 2.0, 1.0],
                [2.0, 2.0, 2.0],
609
610
611
612
613
614
615
616
                [2.0, 2.0, 1.0],
                [2.0, 2.0, 2.0],
                [1.0, 2.0, 1.0],
                [1.0, 2.0, 2.0],
                [2.0, 1.0, 2.0],
                [1.0, 1.0, 2.0],
                [2.0, 2.0, 2.0],
                [1.0, 2.0, 2.0],
617
618
619
620
621
            ]
        )

        expected_faces = torch.tensor(
            [
622
623
624
625
626
627
628
629
630
631
632
633
                [0, 1, 2],
                [2, 1, 3],
                [4, 5, 6],
                [6, 5, 7],
                [8, 9, 10],
                [9, 11, 10],
                [12, 13, 14],
                [14, 13, 15],
                [16, 17, 18],
                [17, 19, 18],
                [20, 21, 22],
                [21, 23, 22],
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
            ]
        )
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

        verts, faces = marching_cubes_naive(volume_data, 1, return_local_coords=True)
        expected_verts = convert_to_local(expected_verts, 5)
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

        # Check all values are in the range [-1, 1]
        self.assertTrue(verts[0].ge(-1).all() and verts[0].le(1).all())

    def test_sphere(self):
        # (B, W, H, D)
        volume = torch.Tensor(
            [
                [
                    [(x - 10) ** 2 + (y - 10) ** 2 + (z - 10) ** 2 for z in range(20)]
                    for y in range(20)
                ]
                for x in range(20)
            ]
        ).unsqueeze(0)
        volume = volume.permute(0, 3, 2, 1)  # (B, D, H, W)
        verts, faces = marching_cubes_naive(
            volume, isolevel=64, return_local_coords=False
        )

        data_filename = "test_marching_cubes_data/sphere_level64.pickle"
        filename = os.path.join(DATA_DIR, data_filename)
        with open(filename, "rb") as file:
            verts_and_faces = pickle.load(file)
667
668
        expected_verts = verts_and_faces["verts"]
        expected_faces = verts_and_faces["faces"]
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

        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

        verts, faces = marching_cubes_naive(
            volume, isolevel=64, return_local_coords=True
        )

        expected_verts = convert_to_local(expected_verts, 20)
        self.assertClose(verts[0], expected_verts)
        self.assertClose(faces[0], expected_faces)

        # Check all values are in the range [-1, 1]
        self.assertTrue(verts[0].ge(-1).all() and verts[0].le(1).all())

    # Uses skimage.draw.ellipsoid
    def test_double_ellipsoid(self):
        if USE_SCIKIT:
            import numpy as np
            from skimage.draw import ellipsoid

            ellip_base = ellipsoid(6, 10, 16, levelset=True)
            ellip_double = np.concatenate(
                (ellip_base[:-1, ...], ellip_base[2:, ...]), axis=0
            )
            volume = torch.Tensor(ellip_double).unsqueeze(0)
            volume = volume.permute(0, 3, 2, 1)  # (B, D, H, W)
            verts, faces = marching_cubes_naive(volume, isolevel=0.001)

            data_filename = "test_marching_cubes_data/double_ellipsoid.pickle"
            filename = os.path.join(DATA_DIR, data_filename)
            with open(filename, "rb") as file:
                verts_and_faces = pickle.load(file)
            expected_verts = verts_and_faces["verts"]
            expected_faces = verts_and_faces["faces"]

705
706
            self.assertClose(verts[0], expected_verts)
            self.assertClose(faces[0], expected_faces)
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775

    def test_cube_surface_area(self):
        if USE_SCIKIT:
            from skimage.measure import marching_cubes_classic, mesh_surface_area

            volume_data = torch.zeros(1, 5, 5, 5)
            volume_data[0, 1, 1, 1] = 1
            volume_data[0, 1, 1, 2] = 1
            volume_data[0, 2, 1, 1] = 1
            volume_data[0, 2, 1, 2] = 1
            volume_data[0, 1, 2, 1] = 1
            volume_data[0, 1, 2, 2] = 1
            volume_data[0, 2, 2, 1] = 1
            volume_data[0, 2, 2, 2] = 1
            volume_data = volume_data.permute(0, 3, 2, 1)  # (B, D, H, W)
            verts, faces = marching_cubes_naive(volume_data, return_local_coords=False)
            verts_sci, faces_sci = marching_cubes_classic(volume_data[0])

            surf = mesh_surface_area(verts[0], faces[0])
            surf_sci = mesh_surface_area(verts_sci, faces_sci)

            self.assertClose(surf, surf_sci)

    def test_sphere_surface_area(self):
        if USE_SCIKIT:
            from skimage.measure import marching_cubes_classic, mesh_surface_area

            # (B, W, H, D)
            volume = torch.Tensor(
                [
                    [
                        [
                            (x - 10) ** 2 + (y - 10) ** 2 + (z - 10) ** 2
                            for z in range(20)
                        ]
                        for y in range(20)
                    ]
                    for x in range(20)
                ]
            ).unsqueeze(0)
            volume = volume.permute(0, 3, 2, 1)  # (B, D, H, W)
            verts, faces = marching_cubes_naive(volume, isolevel=64)
            verts_sci, faces_sci = marching_cubes_classic(volume[0], level=64)

            surf = mesh_surface_area(verts[0], faces[0])
            surf_sci = mesh_surface_area(verts_sci, faces_sci)

            self.assertClose(surf, surf_sci)

    def test_double_ellipsoid_surface_area(self):
        if USE_SCIKIT:
            import numpy as np
            from skimage.draw import ellipsoid
            from skimage.measure import marching_cubes_classic, mesh_surface_area

            ellip_base = ellipsoid(6, 10, 16, levelset=True)
            ellip_double = np.concatenate(
                (ellip_base[:-1, ...], ellip_base[2:, ...]), axis=0
            )
            volume = torch.Tensor(ellip_double).unsqueeze(0)
            volume = volume.permute(0, 3, 2, 1)  # (B, D, H, W)
            verts, faces = marching_cubes_naive(volume, isolevel=0)
            verts_sci, faces_sci = marching_cubes_classic(volume[0], level=0)

            surf = mesh_surface_area(verts[0], faces[0])
            surf_sci = mesh_surface_area(verts_sci, faces_sci)

            self.assertClose(surf, surf_sci)

776
777
778
779
780
781
782
783
    def test_ball_example(self):
        N = 15
        axis_tensor = torch.arange(0, N)
        X, Y, Z = torch.meshgrid(axis_tensor, axis_tensor, axis_tensor, indexing="ij")
        u = (X - 15) ** 2 + (Y - 15) ** 2 + (Z - 15) ** 2 - 8**2
        u = u[None].float()
        verts, faces = marching_cubes_naive(u, 0, return_local_coords=False)

784
    @staticmethod
785
    def marching_cubes_with_init(algo_type: str, batch_size: int, V: int):
786
787
788
789
        device = torch.device("cuda:0")
        volume_data = torch.rand(
            (batch_size, V, V, V), dtype=torch.float32, device=device
        )
790
791
792
        algo_table = {
            "naive": marching_cubes_naive,
        }
793
794

        def convert():
795
            algo_table[algo_type](volume_data, return_local_coords=False)
796
797
798
            torch.cuda.synchronize()

        return convert