mesh3D.py 39.7 KB
Newer Older
1
2
3
4
5
6
7
8
9
10
11
#!/usr/bin/env
# encoding: utf-8
"""
Author:     Daniel Boeckenhoff
Mail:       daniel.boeckenhoff@ipp.mpg.de

part of tfields library
"""
import numpy as np
import sympy
import tfields
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
12
13

# obj imports
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
14
from tfields.lib.decorators import cached_property
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
15
16
import logging
import os
17
18


19
20
21
22
23
24
25
26
27
28
29
30
31
def _dist_from_plane(point, plane):
    return plane['normal'].dot(point) + plane['d']


def _segment_plane_intersection(p0, p1, plane):
    """
    Returns:
        points, direction
    """
    distance0 = _dist_from_plane(p0, plane)
    distance1 = _dist_from_plane(p1, plane)
    p0OnPlane = abs(distance0) < np.finfo(float).eps
    p1OnPlane = abs(distance1) < np.finfo(float).eps
32
    points = []
33
34
    direction = 0
    if p0OnPlane:
35
        points.append(p0)
36
37

    if p1OnPlane:
38
        points.append(p1)
39
    # remove duplicate points
40
41
    if len(points) > 1:
        points = np.unique(points, axis=0)
42
    if p0OnPlane and p1OnPlane:
43
        return points, direction
44
45

    if distance0 * distance1 > np.finfo(float).eps:
46
        return points, direction
47
48
49

    direction = np.sign(distance0)
    if abs(distance0) < np.finfo(float).eps:
50
        return points, direction
51
    elif abs(distance1) < np.finfo(float).eps:
52
        return points, direction
53
54
55
    if abs(distance0 - distance1) > np.finfo(float).eps:
        t = distance0 / (distance0 - distance1)
    else:
56
        return points, direction
57

58
    points.append(p0 + t * (p1 - p0))
59
    # remove duplicate points
60
61
62
    if len(points) > 1:
        points = np.unique(points, axis=0)
    return points, direction
63
64
65
66
67
68
69


def _intersect(triangle, plane, vertices_rejected):
    """
    Intersect a triangle with a plane. Give the info, which side of the
    triangle is rejected by passing the mask vertices_rejected
    Returns:
70
71
72
73
74
75
76
77
78
        list of list. The inner list is of length 3 and refers to the points of
        new triangles. The reference is done with varying types:
            int: reference to triangle index
            complex: reference to duplicate point. This only happens in case
                two triangles are returned. Then only in the second triangle
            iterable: new vertex

    TODO:
        align norm vectors with previous face
79
80
81
82
83
84
85
86
    """
    nTrue = vertices_rejected.count(True)
    lonely_bool = True if nTrue == 1 else False
    index = vertices_rejected.index(lonely_bool)
    s0, d0 = _segment_plane_intersection(triangle[0], triangle[1], plane)
    s1, d1 = _segment_plane_intersection(triangle[1], triangle[2], plane)
    s2, d2 = _segment_plane_intersection(triangle[2], triangle[0], plane)

87
88
89
    single_index = index
    couple_indices = [j for j in range(3)
                      if not vertices_rejected[j] == lonely_bool]
90
91
92
93
94
95

    # TODO handle special cases. For now triangles with at least two points on plane are excluded
    new_points = None

    if len(s0) == 2:
        # both points on plane
96
        return new_points
97
98
    if len(s1) == 2:
        # both points on plane
99
        return new_points
100
101
    if len(s2) == 2:
        # both points on plane
102
        return new_points
103
    if lonely_bool:
104
        # two new triangles
105
        if len(s0) == 1 and len(s1) == 1:
106
107
            new_points = [[couple_indices[0], s0[0], couple_indices[1]],
                          [couple_indices[1], complex(1), s1[0]]]
108
        elif len(s1) == 1 and len(s2) == 1:
109
110
            new_points = [[couple_indices[0], couple_indices[1], s1[0]],
                          [couple_indices[0], complex(2), s2[0]]]
111
        elif len(s0) == 1 and len(s2) == 1:
112
113
            new_points = [[couple_indices[0], couple_indices[1], s0[0]],
                          [couple_indices[1], s2[0], complex(2)]]
114
115

    else:
116
        # one new triangle
117
        if len(s0) == 1 and len(s1) == 1:
118
            new_points = [[single_index, s1[0], s0[0]]]
119
        elif len(s1) == 1 and len(s2) == 1:
120
            new_points = [[single_index, s2[0], s1[0]]]
121
        elif len(s0) == 1 and len(s2) == 1:
122
123
            new_points = [[single_index, s0[0], s2[0]]]
    return new_points
124
125


126
127
128
129
130
131
def scalars_to_fields(scalars):
    scalars = np.array(scalars)
    if len(scalars.shape) == 1:
        return [tfields.Tensors(scalars)]
    return [tfields.Tensors(fs) for fs in scalars]

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
132

133
134
135
def fields_to_scalars(fields):
    return np.array(fields)

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
136

137
def faces_to_maps(faces, *fields):
138
    return [tfields.TensorFields(faces, *fields, dtype=int, dim=3)]
139

140

141
def maps_to_faces(maps):
142
143
144
145
146
    if len(maps) == 0:
        return np.array([])
    elif len(maps) > 1:
        raise NotImplementedError("Multiple maps")
    return np.array(maps[0])
147
148


149
150
151
152
153
class Mesh3D(tfields.TensorMaps):
    # pylint: disable=R0904
    """
    Points3D child used as vertices combined with faces to build a geometrical mesh of triangles
    Examples:
154
155
        >>> import tfields
        >>> import numpy as np
156
        >>> m = tfields.Mesh3D([[1,2,3], [3,3,3], [0,0,0], [5,6,7]], faces=[[0, 1, 2], [1, 2, 3]])
157
158
159
160
161
        >>> m.equal([[1, 2, 3],
        ...          [3, 3, 3],
        ...          [0, 0, 0],
        ...          [5, 6, 7]])
        True
162
        >>> np.array_equal(m.faces, [[0, 1, 2], [1, 2, 3]])
163
        True
164
165

        conversion to points only
166
167
168
169
170
        >>> tfields.Points3D(m).equal([[1, 2, 3],
        ...                            [3, 3, 3],
        ...                            [0, 0, 0],
        ...                            [5, 6, 7]])
        True
171
172
173
174
175
176

        Empty instances
        >>> m = tfields.Mesh3D([]);

        going from Mesh3D to Triangles3D instance is easy and will be cached.
        >>> m = tfields.Mesh3D([[1,0,0], [0,1,0], [0,0,0]], faces=[[0, 1, 2]]);
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
177
        >>> assert m.triangles().equal(tfields.Triangles3D([[ 1.,  0.,  0.],
178
179
        ...                                               [ 0.,  1.,  0.],
        ...                                               [ 0.,  0.,  0.]]))
180
181

        a list of scalars is assigned to each face
182
183
184
        >>> mScalar = tfields.Mesh3D([[1,0,0], [0,1,0], [0,0,0]], faces=[[0, 1, 2]], faceScalars=[.5]);
        >>> np.array_equal(mScalar.faceScalars, [[ 0.5]])
        True
185
186

        adding together two meshes:
187
188
189
190
191
192
193
194
195
196
        >>> m2 = tfields.Mesh3D([[1,0,0],[2,0,0],[0,3,0]],
        ...                     faces=[[0,1,2]], faceScalars=[.7])
        >>> msum = tfields.Mesh3D.merged(mScalar, m2)
        >>> msum.equal([[ 1.,  0.,  0.],
        ...             [ 0.,  1.,  0.],
        ...             [ 0.,  0.,  0.],
        ...             [ 1.,  0.,  0.],
        ...             [ 2.,  0.,  0.],
        ...             [ 0.,  3.,  0.]])
        True
197
        >>> assert np.array_equal(msum.faces, [[0, 1, 2], [3, 4, 5]])
198
199
200
201

        Saving and reading
        >>> from tempfile import NamedTemporaryFile
        >>> outFile = NamedTemporaryFile(suffix='.npz')
202
        >>> m.save(outFile.name)
203
        >>> _ = outFile.seek(0)
204
        >>> m1 = tfields.Mesh3D.load(outFile.name)
205
206
        >>> bool(np.all(m == m1))
        True
207
        >>> assert np.array_equal(m1.faces, np.array([[0, 1, 2]]))
208
209

    """
210
    def __new__(cls, tensors, *fields, **kwargs):
211
212
        if not issubclass(type(tensors), Mesh3D):
            kwargs['dim'] = 3
213
214
215
        faces = kwargs.pop('faces', None)
        faceScalars = kwargs.pop('faceScalars', [])
        maps = kwargs.pop('maps', None)
216
        if maps is not None and faces is not None:
217
218
219
            raise ValueError("Conflicting options maps and faces")
        if maps is not None:
            kwargs['maps'] = maps
220
        if len(faceScalars) > 0:
221
222
223
224
225
226
227
228
229
230
231
232
233
            map_fields = scalars_to_fields(faceScalars)
        else:
            map_fields = []
        if faces is not None:
            kwargs['maps'] = faces_to_maps(faces,
                                           *map_fields)
        obj = super(Mesh3D, cls).__new__(cls, tensors, *fields, **kwargs)
        if len(obj.maps) > 1:
            raise ValueError("Mesh3D only allows one map")
        if obj.maps and obj.maps[0].dim != 3:
            raise ValueError("Face dimension should be 3")
        return obj

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
    def _save_obj(self, path, **kwargs):
        """
        Save obj as wavefront/.obj file
        """
        obj = kwargs.pop('object', None)
        group = kwargs.pop('group', None)

        cmap = kwargs.pop('cmap', 'viridis')
        map_index = kwargs.pop('map_index', None)

        path = path.replace('.obj', '')
        directory, name = os.path.split(path)

        if not (self.faceScalars.size == 0 or map_index is None):
            scalars = self.maps[0].fields[map_index]
            min_scalar = scalars[~np.isnan(scalars)].min()
            max_scalar = scalars[~np.isnan(scalars)].max()
            vmin = kwargs.pop('vmin', min_scalar)
            vmax = kwargs.pop('vmax', max_scalar)
            if vmin == vmax:
                if vmin == 0.:
                    vmax = 1.
                else:
                    vmin = 0.
Daniel Boeckenhoff's avatar
dunno    
Daniel Boeckenhoff committed
258
259
            import matplotlib.colors as colors
            import matplotlib.pyplot as plt
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
260
261
262
263
264
265
            norm = colors.Normalize(vmin, vmax)
            color_map = plt.get_cmap(cmap)
        else:
            # switch for not coloring the triangles and thus not producing the materials
            norm = None

Daniel Boeckenhoff's avatar
dunno    
Daniel Boeckenhoff committed
266
267
268
        if len(kwargs) != 0:
            raise ValueError("Unused arguments.")

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
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
        if norm is not None:
            mat_name = name + '_frame_{0}.mat'.format(map_index)
            scalars[np.isnan(scalars)] = min_scalar - 1
            sorted_scalars = scalars[scalars.argsort()]
            sorted_scalars[sorted_scalars == min_scalar - 1] = np.nan
            sorted_faces = self.faces[scalars.argsort()]
            scalar_set = np.unique(sorted_scalars)
            scalar_set[scalar_set == min_scalar - 1] = np.nan
            mat_path = os.path.join(directory, mat_name)
            with open(mat_path, 'w') as mf:
                for s in scalar_set:
                    if np.isnan(s):
                        mf.write("newmtl nan")
                        mf.write("Kd 0 0 0\n\n")
                    else:
                        mf.write("newmtl mtl_{0}\n".format(s))
                        mf.write("Kd {c[0]} {c[1]} {c[2]}\n\n".format(c=color_map(norm(s))))
        else:
            sorted_faces = self.faces

        # writing of the obj file
        with open(path + '.obj', 'w') as f:
            f.write("# File saved with tfields Mesh3D._save_obj method\n\n")
            if norm is not None:
                f.write("mtllib ./{0}\n\n".format(mat_name))
            if obj is not None:
                f.write("o {0}\n".format(obj))
            if group is not None:
                f.write("g {0}\n".format(group))
            for vertex in self:
                f.write("v {v[0]} {v[1]} {v[2]}\n".format(v=vertex))

            last_scalar = None
            for i, face in enumerate(sorted_faces + 1):
                if norm is not None:
                    if not last_scalar == sorted_scalars[i]:
                        last_scalar = sorted_scalars[i]
                        f.write("usemtl mtl_{0}\n".format(last_scalar))
                f.write("f {f[0]} {f[1]} {f[2]}\n".format(f=face))

    @classmethod
    def _load_obj(cls, path, *group_names):
        """
        Factory method
        Given a path to a obj/wavefront file, construct the object
        """
        import csv
        log = logging.getLogger()

        with open(path, mode='r') as f:
            reader = csv.reader(f, delimiter=' ')
            groups = []
            group = None
            vertex_no = 1
            for line in reader:
                if not line:
                    continue
                if line[0] == '#':
                    continue
                if line[0] == 'g':
                    if group:
                        groups.append(group)
                    group = dict(name=line[1], vertices={}, faces=[])
                elif line[0] == 'v':
                    if not group:
                        log.warning("No group specified. I invent one myself.")
                        group = dict(name='Group', vertices={}, faces=[])
                    vertex = list(map(float, line[1:4]))
                    group['vertices'][vertex_no] = vertex
                    vertex_no += 1
                elif line[0] == 'f':
                    face = []
                    for v in line[1:]:
                        w = v.split('/')
                        face.append(int(w[0]))
                    group['faces'].append(face)

        vertices = []
        for g in groups[:]:
            vertices.extend(g['vertices'].values())

        if len(group_names) != 0:
            groups = [g for g in groups if g['name'] in group_names]

        faces = []
        for g in groups:
            faces.extend(g['faces'])
        faces = np.add(np.array(faces), -1).tolist()

        """
        Building the class from retrieved vertices and faces
        """
        if len(vertices) == 0:
            return cls([])
        faceLenghts = [len(face) for face in faces]
        for i in reversed(range(len(faceLenghts))):
            length = faceLenghts[i]
            if length == 3:
                continue
            if length == 4:
                log.warning("Given a Rectangle. I will split it but "
                            "sometimes the order is different.")
                faces.insert(i + 1, faces[i][2:] + faces[i][:1])
                faces[i] = faces[i][:3]
            else:
                raise NotImplementedError()
        mesh = cls(vertices, faces=faces)
        if group_names:
            mesh = mesh.cleaned()
        return mesh

380
381
    @classmethod
    def plane(cls, *base_vectors, **kwargs):
382
383
384
385
386
387
388
        """
        Alternative constructor for creating a plane from
        Args:
            *base_vectors: see grid constructors in core. One base_vector has to
                be one-dimensional
            **kwargs: forwarded to __new__
        """
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
389
        vertices = tfields.Tensors.grid(*base_vectors, **kwargs)
390
391
392

        base_vectors = tfields.grid.ensure_complex(*base_vectors)
        base_vectors = tfields.grid.to_base_vectors(*base_vectors)
393
394
395
396
397
398
399
        fix_coord = None
        for coord in range(3):
            if len(base_vectors[coord]) > 1:
                continue
            if len(base_vectors[coord]) == 0:
                continue
            fix_coord = coord
400
401
        if fix_coord is None:
            raise ValueError("Describe a plane with one variable fiexed")
402
403
404
405
406
407
408
409
410
411
412
413
414
415

        var_coords = list(range(3))
        var_coords.pop(var_coords.index(fix_coord))

        faces = []
        base0, base1 = base_vectors[var_coords[0]], base_vectors[var_coords[1]]
        for i1 in range(len(base1) - 1):
            for i0 in range(len(base0) - 1):
                idx_top_left = len(base1) * (i0 + 0) + (i1 + 0)
                idx_top_right = len(base1) * (i0 + 0) + (i1 + 1)
                idx_bot_left = len(base1) * (i0 + 1) + (i1 + 0)
                idx_bot_right = len(base1) * (i0 + 1) + (i1 + 1)
                faces.append([idx_top_left, idx_top_right, idx_bot_left])
                faces.append([idx_top_right, idx_bot_left, idx_bot_right])
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
416
        inst = cls.__new__(cls, vertices, faces=faces)
417
418
419
420
        return inst

    @classmethod
    def grid(cls, *base_vectors, **kwargs):
421
422
        """
        Construct 'cuboid' along base_vectors
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
423
424
425
426
427
428
429
430
431
432
433
434
        Examples:
            Building symmetric geometries were never as easy:

            Approximated sphere with radius 1, translated in y by 2 units
            >>> sphere = tfields.Mesh3D.grid((1, 1, 1),
            ...                              (-np.pi, np.pi, 12),
            ...                              (-np.pi / 2, np.pi / 2, 12),
            ...                              coord_sys='spherical')
            >>> sphere.transform('cartesian')
            >>> sphere[:, 1] += 2

            Oktaeder
Daniel Boeckenhoff's avatar
dunno    
Daniel Boeckenhoff committed
435
436
437
438
            >>> oktaeder = tfields.Mesh3D.grid((1, 1, 1),
            ...                                (-np.pi, np.pi, 5),
            ...                                (-np.pi / 2, np.pi / 2, 3),
            ...                                coord_sys='spherical')
439
            >>> oktaeder.transform('cartesian')
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
440
441
442
443
444
445
446
447
448
449
450

            Cube with edge length of 2 units
            >>> cube = tfields.Mesh3D.grid((-1, 1, 2),
            ...                            (-1, 1, 2),
            ...                            (-5, -3, 2))

            Cylinder 
            >>> cylinder = tfields.Mesh3D.grid((1, 1, 1),
            ...                                (-np.pi, np.pi, 12),
            ...                                (-5, 3, 12),
            ...                                coord_sys='cylinder')
451
            >>> cylinder.transform('cartesian')
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
452

453
        """
454
455
456
        if not len(base_vectors) == 3:
            raise AttributeError("3 base_vectors vectors required")

457
458
459
        base_vectors = tfields.grid.ensure_complex(*base_vectors)
        base_vectors = tfields.grid.to_base_vectors(*base_vectors)

460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
        indices = [0, -1]
        coords = range(3)
        baseLengthsAbove1 = [len(b) > 1 for b in base_vectors]
        # if one plane is given: rearrange indices and coords
        if not all(baseLengthsAbove1):
            indices = [0]
            for i, b in enumerate(baseLengthsAbove1):
                if not b:
                    coords = [i]
                    break

        base_vectors = list(base_vectors)
        planes = []
        for ind in indices:
            for coord in coords:
                basePart = base_vectors[:]
                basePart[coord] = np.array([base_vectors[coord][ind]],
                                           dtype=float)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
478
                planes.append(cls.plane(*basePart, **kwargs))
479
480
481
        inst = cls.merged(*planes, **kwargs)
        return inst

482
483
484
485
486
487
488
489
490
491
492
493
494
    @property
    def faces(self):
        return maps_to_faces(self.maps)

    @faces.setter
    def faces(self, faces):
        self.maps = faces_to_maps(faces)

    @property
    def faceScalars(self):
        return fields_to_scalars(self.maps[0].fields)

    @faceScalars.setter
495
496
    def faceScalars(self, scalars):
        self.maps[0].fields = scalars_to_fields(scalars)
497

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
498
499
    @cached_property()
    def _triangles(self):
500
501
502
503
504
505
        """
        with the decorator, this should be handled like an attribute though it is a function

        """
        if self.faces.size == 0:
            return tfields.Triangles3D([])
506
507
508
509
        tris = tfields.Tensors.merged(*[self[mp.flatten()] for mp in self.maps])
        map_fields = [mp.fields for mp in self.maps]
        fields = [tfields.Tensors.merged(*fields) for fields in zip(*map_fields)]
        return tfields.Triangles3D(tris, *fields)
510

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
511
    def triangles(self):
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
512
513
514
515
516
517
518
519
        """
        Cached method to retrieve the triangles, belonging to this mesh
        Examples:
            >>> import tfields
            >>> mesh = tfields.Mesh3D.grid((0, 1, 3), (1, 2, 3), (2, 3, 3))
            >>> assert mesh.triangles() is mesh.triangles()

        """
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
520
521
522
523
524
525
526
        return self._triangles

    def centroids(self):
        return self.triangles().centroids()

    @cached_property()
    def _planes(self):
527
528
        if self.faces.size == 0:
            return tfields.Planes3D([])
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
529
530
531
532
        return tfields.Planes3D(self.centroids(), self.triangles().norms())

    def planes(self):
        return self._planes
533

534
    def nfaces(self):
535
536
        return self.faces.shape[0]

537
    def in_faces(self, points, delta, assign_multiple=False):
538
539
        """
        Check whether points lie within triangles with Barycentric Technique
540
        see Triangles3D.in_triangles
541
        """
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
542
        masks = self.triangles().in_triangles(points, delta,
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
543
                                              assign_multiple=assign_multiple)
544
545
        return masks

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
546
    def removeFaces(self, face_delete_mask):
547
        """
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
548
        Remove faces where face_delete_mask is True
549
        """
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
550
551
552
        face_delete_mask = np.array(face_delete_mask, dtype=bool)
        self.faces = self.faces[~face_delete_mask]
        self.faceScalars = self.faceScalars[~face_delete_mask]
553

554
    def template(self, sub_mesh):
555
        """
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
556
        'Manual' way to build a template that can be used with self.cut
557
        Returns:
558
559
            Mesh3D: template (see cut), can be used as template to retrieve
                sub_mesh from self instance
560
        Examples:
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
561
562
            >>> mp = tfields.TensorFields([[0,1,2],[2,3,0],[3,2,5],[5,4,3]],
            ...                           [1, 2, 3, 4])
563
            >>> m = tfields.Mesh3D([[0,0,0], [1,0,0], [1,1,0], [0,1,0], [0,2,0], [1,2,0]],
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
564
            ...                     maps=[mp])
565
            >>> from sympy.abc import y
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
566
567
568
            >>> m_cut = m.cut(y < 1.5, at_intersection='split')
            >>> template = m.template(m_cut)
            >>> assert m_cut.equal(m.cut(template))
569

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
570
571
        TODO:
            fields template not yet implemented
572
        """
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
573
574
        face_indices = np.arange(self.maps[0].shape[0])
        cents = tfields.Tensors(sub_mesh.centroids())
575
        mask = self.in_faces(cents, delta=None)
576
        inst = sub_mesh.copy()
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
577
578
579
580
581
582
583
584
585
586
587
        if inst.maps:
            scalars = []
            for face_mask in mask:
                scalars.append(face_indices[face_mask][0])
            inst.maps[0].fields = [tfields.Tensors(scalars, dim=1)]
        else:
            inst.maps = [tfields.TensorFields([],
                                              tfields.Tensors([], dim=1),
                                              dim=3,
                                              dtype=int)
                        ]
588
589
        return inst

590
    def _cut_sympy(self, expression, at_intersection="remove", _in_recursion=False):
591
        """
592
        Partition the mesh with the cuts given and return the template
593
594

        """
595
596
597
598
599
        eps = 0.000000001
        # direct return if self is empty
        if len(self) == 0:
            return self.copy(), self.copy()

600
601
602
603
604
605
606
607
608
609
610
        inst = self.copy()

        '''
        add the indices of the vertices and maps to the fields. They will be
        removed afterwards
        '''
        if not _in_recursion:
            inst.fields.append(tfields.Tensors(np.arange(len(inst))))
            for mp in inst.maps:
                mp.fields.append(tfields.Tensors(np.arange(len(mp))))

611
        # mask for points that do not fulfill the cut expression
612
        mask = inst.evalf(expression)
613
        # remove the points
614

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
615
        if not any(~mask):
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
616
617
618
619
            # no vertex is valid
            inst = inst[mask]
        elif all(~mask):
            # all vertices are valid
620
            inst = inst[mask]
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
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
        elif at_intersection == 'keep':
            expression_parts = tfields.lib.symbolics.split_expression(expression)
            if len(expression_parts) > 1:
                new_mesh = inst.copy()
                for exprPart in expression_parts:
                    inst, _ = inst._cut_sympy(exprPart,
                                              at_intersection=at_intersection,
                                              _in_recursion=True)
            elif len(expression_parts) == 1:
                face_delete_indices = set([])
                for i, face in enumerate(inst.maps[0]):
                    """
                    vertices_rejected is a mask for each face that is True, where
                    a Point is on the rejected side of the plane
                    """
                    vertices_rejected = [~mask[f] for f in face]
                    if all(vertices_rejected):
                        # delete face
                        face_delete_indices.add(i)
                mask = np.full(len(inst.maps[0]), True, dtype=bool)
                for face_idx in range(len(inst.maps[0])):
                    if face_idx in face_delete_indices:
                        mask[face_idx] = False
                inst.maps[0] = inst.maps[0][mask]
            else:
                raise ValueError("Sympy expression is not splitable.")
            inst = inst.cleaned()
648
649
        elif at_intersection == 'split' or at_intersection == 'splitRough':
            '''
650
            add vertices and faces that are at the border of the cuts
651
            '''
652
            expression_parts = tfields.lib.symbolics.split_expression(expression)
653
            if len(expression_parts) > 1:
654
                new_mesh = inst.copy()
655
656
657
658
659
660
661
662
                if at_intersection == 'splitRough':
                    """
                    the following is, to speed up the process. Problem is, that
                    triangles can exist, where all points lie outside the cut,
                    but part of the area
                    still overlaps with the cut.
                    These are at the intersection line between two cuts.
                    """
663
664
                    faceIntersMask = np.full((inst.faces.shape[0]), False, dtype=bool)
                    for i, face in enumerate(inst.faces):
665
666
                        vertices_rejected = [-mask[f] for f in face]
                        face_on_edge = any(vertices_rejected) and not all(vertices_rejected)
667
                        if face_on_edge:
668
                            faceIntersMask[i] = True
669
                    new_mesh.removeFaces(-faceIntersMask)
670

671
                for exprPart in expression_parts:
672
673
674
                    inst, _ = inst._cut_sympy(exprPart,
                                              at_intersection='split',
                                              _in_recursion=True)
675
            elif len(expression_parts) == 1:
676
                # TODO maps[0] -> smthng like inst.get_map(dim=3)
677
678
679
                points = [sympy.symbols('x0, y0, z0'),
                          sympy.symbols('x1, y1, z1'),
                          sympy.symbols('x2, y2, z2')]
680
                plane_sympy = tfields.lib.symbolics.to_plane(expression)
681
682
683
                norm_sympy = np.array(plane_sympy.normal_vector).astype(float)
                d = -norm_sympy.dot(np.array(plane_sympy.p1).astype(float))
                plane = {'normal': norm_sympy, 'd': d}
684

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
685
                norm_vectors = inst.triangles().norms()
686
687
                new_points = np.empty((0, 3))
                new_faces = np.empty((0, 3))
688
                new_fields = [tfields.Tensors(np.empty((0,) + field.shape[1:]),
689
                                              coord_sys=field.coord_sys)
690
691
                              for field in inst.fields]
                new_map_fields = [[] for field in inst.maps[0].fields]
692
                new_norm_vectors = []
693
                newScalarMap = []
694
                n_new = 0
695

696
697
698
699
700
701
702
                vertices = np.array(inst)
                faces = np.array(inst.maps[0])
                fields = [np.array(field) for field in inst.fields]
                faces_fields = [np.array(field) for field in inst.maps[0].fields]

                face_delete_indices = set([])
                for i, face in enumerate(inst.maps[0]):
703
                    """
704
                    vertices_rejected is a mask for each face that is True, where
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
705
                    a point is on the rejected side of the plane
706
                    """
707
                    vertices_rejected = [~mask[f] for f in face]
708
709
710
711
712
                    if any(vertices_rejected):
                        # delete face
                        face_delete_indices.add(i)
                    if any(vertices_rejected) and not all(vertices_rejected):
                        # face on edge
713
                        nTrue = vertices_rejected.count(True)
714
                        lonely_bool = True if nTrue == 1 else False
715

Daniel Boeckenhoff's avatar
dunno    
Daniel Boeckenhoff committed
716
                        triangle_points = [vertices[f] for f in face]
717
                        """
718
                        Add the intersection points and faces
719
                        """
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
720
                        intersection = _intersect(triangle_points, plane, vertices_rejected)
721
                        last_idx = len(vertices) - 1
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
722
                        for tri_list in intersection:
723
                            new_face = []
724
725
726
                            for item in tri_list:
                                if isinstance(item, int):
                                    # reference to old vertex
727
                                    new_face.append(face[item])
728
729
730
                                elif isinstance(item, complex):
                                    # reference to new vertex that has been
                                    # concatenated already
731
                                    new_face.append(last_idx + int(item.imag))
732
733
                                else:
                                    # new vertex
734
                                    new_face.append(len(vertices))
735
                                    vertices = np.append(vertices,
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
736
                                                         [[float(x) for x in item]],
737
738
739
740
741
                                                         axis=0)
                                    fields = [np.append(field,
                                                        np.full((1,) + field.shape[1:], np.nan),
                                                        axis=0)
                                              for field in fields]
742
                            faces = np.append(faces, [new_face], axis=0)
743
                            faces_fields = [np.append(field,
744
                                                      [field[i]],
745
746
747
748
749
                                                      axis=0)
                                            for field in faces_fields]
                            faces_fields[-1][-1] = i

                face_map = tfields.TensorFields(faces, *faces_fields,
750
                                                dtype=int,
751
                                                coord_sys=inst.maps[0].coord_sys)
752
753
754
                inst = tfields.Mesh3D(vertices,
                                      *fields,
                                      maps=[face_map] + inst.maps[1:],
755
                                      coord_sys=inst.coord_sys)
756
757
758
759
760
                mask = np.full(len(inst.maps[0]), True, dtype=bool)
                for face_idx in range(len(inst.maps[0])):
                    if face_idx in face_delete_indices:
                        mask[face_idx] = False
                inst.maps[0] = inst.maps[0][mask]
761
            else:
762
                raise ValueError("Sympy expression is not splitable.")
763
            inst = inst.cleaned()
764
        elif at_intersection == 'remove':
765
            inst = inst[mask]
766
        else:
767
768
            raise AttributeError("No at_intersection method called {at_intersection} "
                                 "implemented".format(**locals()))
769
770
771
772
773
774
775
776
777
778
779
780
781

        if _in_recursion:
            template = None
        else:
            template_field = inst.fields.pop(-1)
            template_maps = []
            for mp in inst.maps:
                t_mp = tfields.TensorFields(tfields.Tensors(mp),
                                            mp.fields.pop(-1))
                template_maps.append(t_mp)
            template = tfields.Mesh3D(tfields.Tensors(inst),
                                      template_field,
                                      maps=template_maps)
782
        return inst, template
783
784

    def _cut_template(self, template):
785
786
787
788
789
790
791
792
        """
        Args:
            template (tfields.Mesh3D)

        Examples:
            >>> import tfields
            >>> import numpy as np

793
            Build mesh
794
795
796
            >>> mmap = tfields.TensorFields([[0, 1, 2], [0, 3, 4]],
            ...                             [[42, 21], [-42, -21]])
            >>> m = tfields.Mesh3D([[0]*3, [1]*3, [2]*3, [3]*3, [4]*3],
797
798
            ...                    [0.0, 0.1, 0.2, 0.3, 0.4],
            ...                    [0.0, -0.1, -0.2, -0.3, -0.4],
799
800
            ...                    maps=[mmap])

801
            Build template
802
803
804
            >>> tmap = tfields.TensorFields([[0, 3, 4], [0, 1, 2]],
            ...                             [1, 0])
            >>> t = tfields.Mesh3D([[0]*3, [-1]*3, [-2]*3, [-3]*3, [-4]*3],
805
            ...                    [1, 0, 3, 2, 4],
806
807
            ...                    maps=[tmap])

808
            Use template as instruction to make a fast cut
809
810
811
812
813
814
815
816
817
            >>> res = m._cut_template(t)
            >>> assert np.array_equal(res.fields,
            ...                       [[0.1, 0.0, 0.3, 0.2, 0.4],
            ...                        [-0.1, 0.0, -0.3, -0.2, -0.4]])

            >>> assert np.array_equal(res.maps[0].fields[0],
            ...                       [[-42, -21], [42, 21]])
                                   
        """
818
819
        # Possible Extension (small todo): check: len(field(s)) == len(self/maps)

820
        # Redirect fields
821
        fields = []
822
        if template.fields:
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
            template_field = np.array(template.fields[0])
            if len(self) > 0:
                '''
                if new vertices have been created in the template, it is
                in principle unclear what fields we have to refer to.
                Thus in creating the template, we gave np.nan.
                To make it fast, we replace nan with 0 as a dummy and correct
                the field entries afterwards with np.nan.
                '''
                nan_mask = np.isnan(template_field)
                template_field[nan_mask] = 0  # dummy reference to index 0.
                template_field = template_field.astype(int)
                for field in self.fields:
                    projected_field = field[template_field]
                    projected_field[nan_mask] = np.nan  # correction for nan
                    fields.append(projected_field)
839

840
        # Redirect maps and their fields
841
842
        maps = []
        for mp, template_mp in zip(self.maps, template.maps):
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
843
            mp_fields = []
844
845
846
847
            for field in mp.fields:
                if len(template_mp) == 0 and len(template_mp.fields) == 0:
                    mp_fields.append(field[0:0])  # np.empty
                else:
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
848
                    mp_fields.append(field[template_mp.fields[0].astype(int)])
849
            new_mp = tfields.TensorFields(tfields.Tensors(template_mp),
850
851
852
                                          *mp_fields)
            maps.append(new_mp)

853
854
        inst = tfields.Mesh3D(tfields.Tensors(template),
                              *fields,
855
                              maps=maps)
856
857
        return inst

858
    def cut(self, expression, coord_sys=None, at_intersection=None,
859
            return_template=False):
860
861
862
        """
        cut method for Mesh3D.
        Args:
863
864
865
866
867
868
869
870
871
872
            expression (sympy logical expression | Mesh3D):
                sympy locical expression: Sympy expression that defines planes
                    in 3D
                Mesh3D: A mesh3D will be interpreted as a template, i.e. a
                    fast instruction of how to cut the triangles.
                    It is the second part of the tuple, returned by a previous
                    cut with a sympy locial expression with 'return_template=True'.
                    We use the vertices and maps of the Mesh as the sceleton of
                    the returned mesh. The fields are mapped according to
                    indices in the template.maps[i].fields.
873
            coord_sys (coordinate system to cut in):
874
            at_intersection (str): instruction on what to do, when a cut will intersect a triangle.
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
875
876
877
                Options:    'remove' (Default) - remove the faces that are on the edge
                            'keep' - keep the faces that are on the edge
                            'split' - Create new triangles that make up the old one.
878
879
            return_template (bool): If True: return the template
                            to redo the same cut fast
880
881
        Examples:
            define the cut
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
882
            >>> import numpy as np
883
            >>> import tfields
884
            >>> from sympy.abc import x,y,z
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
885
            >>> cut_expr = x > 1.5
886

887
888
            >>> m = tfields.Mesh3D.grid((0, 3, 4),
            ...                         (0, 3, 4),
889
            ...                         (0, 0, 1))
890
891
892
893
894
895
            >>> m.fields.append(tfields.Tensors(np.linspace(0, len(m) - 1,
            ...                                             len(m))))
            >>> m.maps[0].fields.append(
            ...     tfields.Tensors(np.linspace(0,
            ...                                 len(m.maps[0]) - 1,
            ...                                 len(m.maps[0]))))
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
896
            >>> mNew = m.cut(cut_expr)
897
            >>> len(mNew)
898
            8
899
            >>> mNew.nfaces()
900
901
902
903
            6
            >>> float(mNew[:, 0].min())
            2.0

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
904
905
906
907
908
909
910
911
912
913
            Cutting with the 'keep' option will leave triangles on the edge
            untouched:
            >>> m_keep = m.cut(cut_expr, at_intersection='keep')
            >>> float(m_keep[:, 0].min())
            1.0
            >>> m_keep.nfaces()
            12

            Cutting with the 'split' option will create new triangles on the edge:
            >>> m_split = m.cut(cut_expr, at_intersection='split')
914
            >>> float(m_split[:, 0].min())
915
            1.5
916
            >>> len(m_split)
917
            15
918
            >>> m_split.nfaces()
919
920
            15

921
922
            Cut with 'return_template=True' will return the exact same mesh but
            additionally an instruction to conduct the exact same cut fast (template)
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
923
            >>> m_split_2, template = m.cut(cut_expr, at_intersection='split',
924
            ...                                    return_template=True)
925
926
927
928
929
930
931
932
933
934
            >>> m_split_template = m.cut(template)
            >>> assert m_split.equal(m_split_2, equal_nan=True)
            >>> assert m_split.equal(m_split_template, equal_nan=True)
            >>> assert len(template.fields) == 1
            >>> assert len(m_split.fields) == 1
            >>> assert len(m_split_template.fields) == 1
            >>> assert m_split.fields[0].equal(
            ...     list(range(8, 16)) + [np.nan] * 7, equal_nan=True)
            >>> assert m_split_template.fields[0].equal(
            ...     list(range(8, 16)) + [np.nan] * 7, equal_nan=True)
935
936
937
938
939
940
941
942
943
944
945

            This seems irrelevant at first but Consider, the map field or the
            tensor field changes:
            >>> m_altered_fields = m.copy()
            >>> m_altered_fields[0] += 42
            >>> assert not m_split.equal(m_altered_fields.cut(template))
            >>> assert tfields.Tensors(m_split).equal(m_altered_fields.cut(template))
            >>> assert tfields.Tensors(m_split.maps[0]).equal(m_altered_fields.cut(template).maps[0])


            The cut expression may be a sympy.BooleanFunction:
946
947
            >>> cut_expr_bool_fun = (x > 1.5) & (y < 1.5) & (y >0.2) & (z > -0.5)
            >>> m_split_bool = m.cut(cut_expr_bool_fun, at_intersection='split')
948
949
950

        Returns:
            copy of cut mesh
951
            * optional: template
952
953

        """
954
        with self.tmp_transform(coord_sys or self.coord_sys):
955
            if isinstance(expression, Mesh3D):
956
957
                template = expression
                obj = self._cut_template(template)
958
959
960
961
962
963
            else:
                at_intersection = at_intersection or "remove"
                obj, template = self._cut_sympy(expression, at_intersection=at_intersection)
        if return_template:
            return obj, template
        return obj
964

965
966
967
968
969
970
971
972
973
974
975
976
977
    def disjoint_parts(self, return_template=False):
        mp_description = self.disjoint_map(0)
        parts = self.parts(mp_description)
        if not return_template:
            return parts
        else:
            templates = []
            for i, part in enumerate(parts):
                template = part.copy()
                template.maps[0].fields[0] = tfields.Tensors(mp_description[1][i])
                templates.append(template)
            return parts, templates

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
978
    def plot(self, **kwargs):  # pragma: no cover
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
979
        """
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
980
        Forwarding to plotTools.plot_mesh
Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
        """
        scalars_demanded = any([v in kwargs for v in ['vmin', 'vmax', 'cmap']])
        map_index = kwargs.pop('map_index', None if not scalars_demanded else 0)
        if map_index is not None:
            if not len(self.maps[0]) == 0:
                kwargs['color'] = self.maps[0].fields[map_index]

        dim_defined = False
        if 'axis' in kwargs:
            dim_defined = True
        if 'zAxis' in kwargs:
            if kwargs['zAxis'] is not None:
                kwargs['dim'] = 3
            else:
                kwargs['dim'] = 2
            dim_defined = True
        if 'dim' in kwargs:
            dim_defined = True

        if not dim_defined:
            kwargs['dim'] = 2

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1003
        return tfields.plotting.plot_mesh(self, self.faces, **kwargs)
1004

1005

Daniel Boeckenhoff's avatar
Daniel Boeckenhoff committed
1006
if __name__ == '__main__':  # pragma: no cover
1007
1008
    import doctest

1009
    # doctest.run_docstring_examples(Mesh3D.cut, globals())
1010
    doctest.testmod()