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
|
"""Unit tests for the IntersectionConstruction class"""
# Copyright (C) 2014 Anders Logg and August Johansson
#
# This file is part of DOLFIN.
#
# DOLFIN is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# DOLFIN 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 Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with DOLFIN. If not, see <http://www.gnu.org/licenses/>.
import pytest
import numpy as np
from dolfin import *
from dolfin_utils.test import skip_in_parallel
def triangulation_to_mesh_2d(triangulation):
editor = MeshEditor()
mesh = Mesh()
editor.open(mesh, 2, 2)
num_cells = len(triangulation) // 6
num_vertices = len(triangulation) // 2
editor.init_cells(num_cells)
editor.init_vertices(num_vertices)
for i in range(num_cells):
editor.add_cell(i, np.array( (3*i, 3*i + 1, 3*i + 2), dtype='uint') )
for i in range(num_vertices):
editor.add_vertex(i, np.array( (triangulation[2*i], triangulation[2*i + 1]), dtype='float'))
editor.close()
return mesh
def triangulation_to_mesh_2d_3d(triangulation):
editor = MeshEditor()
mesh = Mesh()
editor.open(mesh,2,3)
num_cells = len(triangulation) // 9
num_vertices = len(triangulation) // 3
editor.init_cells(num_cells)
editor.init_vertices(num_vertices)
for i in range(num_cells):
editor.add_cell(i, np.array( (3*i, 3*i+1, 3*i+2), dtype='uint'))
for i in range(num_vertices):
editor.add_vertex(i, np.array( (triangulation[3*i], triangulation[3*i+1], triangulation[3*i+2]), dtype='float') )
editor.close()
return mesh
def triangulation_to_mesh_3d(triangulation):
editor = MeshEditor()
mesh = Mesh()
editor.open(mesh,3,3)
num_cells = len(triangulation) // 12
num_vertices = len(triangulation) // 3
editor.init_cells(num_cells)
editor.init_vertices(num_vertices)
for i in range(num_cells):
editor.add_cell(i, np.array( (4*i, 4*i+1, 4*i+2, 4*i+3), dtype='uint'))
for i in range(num_vertices):
editor.add_vertex(i, np.array( (triangulation[3*i], triangulation[3*i+1], triangulation[3*i+2]), dtype='float'))
editor.close()
return mesh
@skip_in_parallel
@pytest.mark.skipif(True, reason="Missing swig typemap")
def test_triangulate_intersection_2d():
# Create two meshes of the unit square
mesh_0 = UnitSquareMesh(1, 1)
mesh_1 = UnitSquareMesh(1, 1)
# Translate second mesh randomly
#dx = Point(np.random.rand(),np.random.rand())
dx = Point(0.278498, 0.546881)
mesh_1.translate(dx)
# Exact volume of intersection
exactvolume = (1 - abs(dx[0]))*(1 - abs(dx[1]))
# Compute triangulation volume
volume = 0
for c0 in cells(mesh_0):
for c1 in cells(mesh_1):
intersection = c0.intersection(c1)
if len(intersection) >= 3 :
triangulation = cpp.geometry.ConvexTriangulation.triangulate(intersection, 2, 2)
tmesh = triangulation_to_mesh_2d(triangulation)
for t in cells(tmesh):
volume += t.volume()
errorstring = "translation=" + str(dx[0]) + str(" ") + str(dx[1])
assert round(volume - exactvolume, 7) == 0, errorstring
@skip_in_parallel
@pytest.mark.skipif(True, reason="Not implemented in 3D")
def test_triangulate_intersection_2d_3d():
# Note: this test will fail if the triangle mesh is aligned
# with the tetrahedron mesh
# Create a unit cube
mesh_0 = UnitCubeMesh(1,1,1)
# Create a 3D surface mesh
editor = MeshEditor()
mesh_1 = Mesh()
editor.open(mesh_1,2,3)
editor.init_cells(2)
editor.init_vertices(4)
# Add cells
editor.add_cell(0, np.array( (0,1,2), dtype='uint'))
editor.add_cell(1, np.array( (1,2,3), dtype='uint'))
# Add vertices
editor.add_vertex(0, np.array( (0, 0, 0.5), dtype='float'))
editor.add_vertex(1, np.array( (1, 0, 0.5), dtype='float'))
editor.add_vertex(2, np.array( (0, 1, 0.5), dtype='float'))
editor.add_vertex(3, np.array( (1, 1, 0.5), dtype='float'))
editor.close()
# Rotate the triangle mesh around y axis
angle = 23.46354
mesh_1.rotate(angle,1)
# Exact area
exact_volume = 1
# Compute triangulation
volume = 0
for c0 in cells(mesh_0):
for c1 in cells(mesh_1):
intersection = c0.intersection(c1)
triangulation = cpp.geometry.ConvexTriangulation.triangulate(intersection, 3, 2)
if (triangulation.size>0):
tmesh = triangulation_to_mesh_2d_3d(triangulation)
for t in cells(tmesh):
volume += t.volume()
errorstring = "rotation angle = " + str(angle)
assert round(volume - exact_volume, 7) == 0, errorstring
@skip_in_parallel
@pytest.mark.skipif(True, reason="Missing swig typemap for call to ConvexTriangulation")
def test_triangulate_intersection_3d():
# Create two meshes of the unit cube
mesh_0 = UnitCubeMesh(1, 1, 1)
mesh_1 = UnitCubeMesh(1, 1, 1)
# Translate second mesh
# dx = Point(np.random.rand(),np.random.rand(),np.random.rand())
dx = Point(0.913375, 0.632359, 0.097540)
mesh_1.translate(dx)
exactvolume = (1 - abs(dx[0]))*(1 - abs(dx[1]))*(1 - abs(dx[2]))
# Compute triangulation
volume = 0
for c0 in cells(mesh_0):
for c1 in cells(mesh_1):
intersection = c0.intersection(c1)
triangulation = cpp.geometry.ConvexTriangulation.triangulate(intersection, 3, 3)
if (triangulation.size>0):
tmesh = triangulation_to_mesh_3d(triangulation)
for t in cells(tmesh):
volume += t.volume()
errorstring = "translation="
errorstring += str(dx[0])+" "+str(dx[1])+" "+str(dx[2])
assert round(volume - exactvolume, 7) == 0, errorstring
def test_triangle_triangle_2d_trivial() :
" These two triangles intersect in a common edge"
res = cpp.geometry.IntersectionConstruction.intersection_triangle_triangle_2d(Point(0.0, 0.0),
Point(1.0, 0.0),
Point(0.5, 1.0),
Point(0.5, 0.5),
Point(1.0, 1.5),
Point(0.0, 1.5))
assert len(res) == 4
def test_triangle_triangle_2d() :
" These two triangles intersect in a common edge"
res = cpp.geometry.IntersectionConstruction.intersection_triangle_triangle_2d(Point(0.4960412972015322, 0.3953317542541379),
Point(0.5, 0.3997044273055517),
Point(0.5, 0.4060889538943557),
Point(0.4960412972015322, 0.3953317542541379),
Point(0.5, 0.4060889538943557),
Point(.5, .5))
for p in res:
print(p[0], p[1])
assert len(res) == 2
@skip_in_parallel
def test_parallel_segments_2d():
" These two segments should be parallel and the intersection computed accordingly"
p0 = Point(0, 0)
p1 = Point(1, 0)
q0 = Point(0.4, 0)
q1 = Point(1.4, 0)
intersection = cpp.geometry.IntersectionConstruction.intersection_segment_segment_2d(p0, p1, q0, q1)
assert len(intersection) == 2
def test_equal_segments_2d():
" These two segments are equal and the intersection computed accordingly"
p0 = Point(DOLFIN_PI / 7., 9. / DOLFIN_PI)
p1 = Point(9. / DOLFIN_PI, DOLFIN_PI / 7.)
q0 = Point(DOLFIN_PI / 7., 9. / DOLFIN_PI)
q1 = Point(9. / DOLFIN_PI, DOLFIN_PI / 7.)
intersection = cpp.geometry.IntersectionConstruction.intersection_segment_segment_2d(p0, p1, q0, q1)
assert len(intersection) == 2
@skip_in_parallel
def test_triangle_segment_2D_1():
"The intersection of a specific triangle and a specific segment"
p0 = Point(1e-30, 0)
p1 = Point(1, 2)
p2 = Point(2, 1)
q0 = Point(1, 0)
q1 = Point(0, 0)
intersection = cpp.geometry.IntersectionConstruction.intersection_triangle_segment_2d(p0, p1, p2, q0, q1)
assert len(intersection) == 1
intersection = cpp.geometry.IntersectionConstruction.intersection_triangle_segment_2d(p0, p1, p2, q1, q0)
assert len(intersection) == 1
def compare_with_cgal(p0, p1, q0, q1, cgal):
intersection = cpp.geometry.IntersectionConstruction.intersection_segment_segment_2d(p0, p1, q0, q1)
#for p in intersection:
# print(*p)
return abs(intersection[0][0] - cgal[0]) < DOLFIN_EPS and \
abs(intersection[0][1] - cgal[1]) < DOLFIN_EPS
@skip_in_parallel
@pytest.mark.skipif(True, reason="This is a case where the intersection currently fails")
def test_segment_segment_1():
"Case that fails CGAL comparison. We get a different intersection point but still correct area."
p0 = Point(-0.50000000000000710543,-0.50000000000000710543)
p1 = Point(0.99999999999999955591,-2)
q0 = Point(0.9142135623730932581,-1.9142135623730944793)
q1 = Point(-0.29289321881346941367,-0.70710678118654635149)
# The intersection should according to CGAL be
cgal = Point(0.91066799144849319703, -1.9106679914484945293)
assert compare_with_cgal(p0, p1, q0, q1, cgal)
@skip_in_parallel
@pytest.mark.skipif(True, reason="This is a case where the intersection currently fails")
def test_segment_segment_2():
"Case that fails CGAL comparison. We get a different intersection point but still correct area."
p0 = Point(0.70710678118654746172,-0.70710678118654746172)
p1 = Point(0.70710678118654612945,0.70710678118654612945)
q0 = Point(0.70710678118654612945,0.70710678118654113344)
q1 = Point(0.70710678118654657354,0.2928932188134645842)
cgal = Point(0.70710678118654612945, 0.7071067811865050512)
assert compare_with_cgal(p0, p1, q0, q1, cgal)
@skip_in_parallel
#@pytest.mark.skipif(True, reason="This test needs to be updated")
def test_segment_segment_3():
"Case that fails CGAL comparison. We get a different intersection point but still correct area."
p0 = Point(0.70710678118654746172,-0.70710678118654746172)
p1 = Point(0.70710678118654612945,0.70710678118654612945)
q0 = Point(0.70710678118654757274,-0.097631072937819973756)
q1 = Point(0.70710678118654257673,-0.1601886205085209236)
cgal = Point(0.70710678118654679558, -0.10611057050352221132)
assert compare_with_cgal(p0, p1, q0, q1, cgal)
@skip_in_parallel
@pytest.mark.skipif(True, reason="This is a case where the intersection currently fails")
def test_segment_segment_4():
"Case that fails CGAL comparison. We get a different intersection point but still correct area."
p0 = Point(0.70710678118654746172,-0.70710678118654746172)
p1 = Point(3.5527136788005009294e-14,3.5527136788005009294e-14)
q0 = Point(0.35355339059326984508,-0.35355339059327078877)
q1 = Point(0.70710678118655057034,-0.70710678118654701763)
cgal = Point(0.67572340116162599166, -0.67572340116162288304)
assert compare_with_cgal(p0, p1, q0, q1, cgal)
@skip_in_parallel
def test_segment_segment_5():
"Case that failed CGAL comparison but passed when scaling the numerator in x = p0 + o / d * v"
p0 = Point(1.1429047494274684563e-12,0.5)
p1 = Point(0.42146018366139809119,0.9214601836602551721)
q0 = Point(0.34292036732279607136,0.8429203673205103442)
q1 = Point(0.3429203673205103442,0.8429203673205103442)
cgal = Point(0.3429203673216533188,0.8429203673205103442)
assert compare_with_cgal(p0, p1, q0, q1, cgal)
@skip_in_parallel
def test_segment_segment_6():
"Test that demonstrates, among other things, that we must check the orientation for p0, p1 in intersection_segment_segment_2d"
p0 = Point(0.045342566799435518599,0.41358248517265505662);
p1 = Point(0.045342566799434436131,0.41358248517265394639);
q0 = Point(1.8601965322712701917e-16,0.5);
q1 = Point(1.873501354054951662e-16,0.3499999999999999778);
intersection = cpp.geometry.IntersectionConstruction.intersection_segment_segment_2d(p0, p1, q0, q1)
assert len(intersection) == 0
|
