import datetime
import numpy
import pytest
from freesurfer_surface import setlocale, Vertex, Triangle, LineSegment, \
Annotation, Surface, PolygonalCircuit
from conftest import ANNOTATION_FILE_PATH, SURFACE_FILE_PATH
# pylint: disable=protected-access
def test_read_triangular():
surface = Surface.read_triangular(SURFACE_FILE_PATH)
assert surface.creator == b'fabianpeter'
assert surface.creation_datetime \
== datetime.datetime(2019, 5, 9, 22, 37, 41)
assert len(surface.vertices) == 155622
assert len(surface.triangles) == 311240
assert not surface.using_old_real_ras
assert surface.volume_geometry_info == (
b'valid = 1 # volume info valid\n',
b'filename = ../mri/filled-pretess255.mgz\n',
b'volume = 256 256 256\n',
b'voxelsize = 1.000000000000000e+00 1.000000000000000e+00 1.000000000000000e+00\n',
b'xras = -1.000000000000000e+00 0.000000000000000e+00 1.862645149230957e-09\n',
b'yras = 0.000000000000000e+00 -6.655682227574289e-09 -1.000000000000000e+00\n',
b'zras = 0.000000000000000e+00 1.000000000000000e+00 -8.300048648379743e-09\n',
b'cras = -2.773597717285156e+00 1.566547393798828e+01 -7.504364013671875e+00\n')
assert surface.command_lines == [
b'mris_remove_intersection ../surf/lh.orig ../surf/lh.orig'
b' ProgramVersion: $Name: stable6 $'
b' TimeStamp: 2019/05/09-17:42:36-GMT'
b' BuildTimeStamp: Jan 18 2017 16:38:58'
b' CVS: $Id: mris_remove_intersection.c,v 1.6 2011/03/02 00:04:32 nicks Exp $'
b' User: fabianpeter'
b' Machine: host12345'
b' Platform: Linux'
b' PlatformVersion: 4.15.0-46-generic'
b' CompilerName: GCC'
b' CompilerVersion: 40400'
b' ',
b'mris_make_surfaces -orig_white white.preaparc -orig_pial white.preaparc'
b' -aseg ../mri/aseg.presurf -mgz -T1 brain.finalsurfs'
b' fabian20190509 lh ProgramVersion: $Name: $'
b' TimeStamp: 2019/05/09-20:27:28-GMT'
b' BuildTimeStamp: Jan 18 2017 16:38:58'
b' CVS: $Id: mris_make_surfaces.c,v 1.164.2.4 2016/12/13 22:26:32 zkaufman Exp $'
b' User: fabianpeter'
b' Machine: host12345'
b' Platform: Linux'
b' PlatformVersion: 4.15.0-46-generic'
b' CompilerName: GCC'
b' CompilerVersion: 40400'
b' ']
def test_read_triangular_locale():
with setlocale('de_AT.utf8'):
surface = Surface.read_triangular(SURFACE_FILE_PATH)
assert surface.creation_datetime \
== datetime.datetime(2019, 5, 9, 22, 37, 41)
@pytest.mark.parametrize(('creation_datetime', 'expected_str'), [
(datetime.datetime(2019, 5, 9, 22, 37, 41), b'Thu May 9 22:37:41 2019'),
(datetime.datetime(2019, 4, 24, 23, 29, 22), b'Wed Apr 24 23:29:22 2019'),
])
def test_triangular_strftime(creation_datetime, expected_str):
# pylint: disable=protected-access
assert expected_str == Surface._triangular_strftime(creation_datetime)
def test_read_write_triangular_same(tmpdir):
surface = Surface.read_triangular(SURFACE_FILE_PATH)
output_path = tmpdir.join('surface').strpath
surface.write_triangular(output_path,
creation_datetime=surface.creation_datetime)
with open(output_path, 'rb') as output_file:
with open(SURFACE_FILE_PATH, 'rb') as expected_file:
assert expected_file.read() == output_file.read()
def test_read_write_datetime(tmpdir):
surface = Surface.read_triangular(SURFACE_FILE_PATH)
original_creation_datetime = surface.creation_datetime
output_path = tmpdir.join('surface').strpath
surface.write_triangular(output_path)
assert original_creation_datetime == surface.creation_datetime
new_surface = Surface.read_triangular(output_path)
assert new_surface.creation_datetime > original_creation_datetime
assert datetime.datetime.now() > new_surface.creation_datetime
assert (datetime.datetime.now() - new_surface.creation_datetime) \
< datetime.timedelta(seconds=20)
def test_write_read_triangular_same(tmpdir):
expected_surface = Surface()
expected_surface.creator = b'pytest'
expected_surface.creation_datetime = datetime.datetime.now().replace(microsecond=0)
expected_surface.vertices = [Vertex(0.0, 0.0, 0.0),
Vertex(1.0, 2.0, 3.0),
Vertex(2.0, 4.0, 6.0),
Vertex(3.0, 5.0, 7.0)]
expected_surface.triangles = [Triangle((0, 1, 2)),
Triangle((0, 1, 3)),
Triangle((3, 2, 1))]
expected_surface.using_old_real_ras = False
expected_surface.volume_geometry_info = tuple(b'?\n' for _ in range(8))
expected_surface.command_lines = [b'?', b'!']
output_path = tmpdir.join('surface').strpath
expected_surface.write_triangular(output_path,
creation_datetime=expected_surface.creation_datetime)
resulted_surface = Surface.read_triangular(output_path)
assert numpy.array_equal(expected_surface.vertices,
resulted_surface.vertices)
expected_surface.vertices = resulted_surface.vertices = []
assert vars(expected_surface) == vars(resulted_surface)
def test_write_triangular_same_locale(tmpdir):
surface = Surface()
surface.creator = b'pytest'
surface.volume_geometry_info = tuple(b'?' for _ in range(8))
creation_datetime = datetime.datetime(2018, 12, 31, 21, 42)
output_path = tmpdir.join('surface').strpath
with setlocale('de_AT.utf8'):
surface.write_triangular(output_path,
creation_datetime=creation_datetime)
resulted_surface = Surface.read_triangular(output_path)
assert resulted_surface.creation_datetime == creation_datetime
with open(output_path, 'rb') as output_file:
assert output_file.read().split(b' on ')[1] \
.startswith(b'Mon Dec 31 21:42:00 2018\n')
def test_load_annotation():
surface = Surface.read_triangular(SURFACE_FILE_PATH)
assert not surface.annotation
surface.load_annotation_file(ANNOTATION_FILE_PATH)
assert isinstance(surface.annotation, Annotation)
assert len(surface.annotation.vertex_label_index) == 155622
assert surface.annotation.vertex_label_index[0] == 5
def test_add_vertex():
surface = Surface()
assert not surface.vertices
assert surface.add_vertex(Vertex(1.0, 1.5, 2.0)) == 0
assert len(surface.vertices) == 1
assert surface.vertices[0].anterior == pytest.approx(1.5)
assert surface.add_vertex(Vertex(-3.0, 0.0, 4.0)) == 1
assert len(surface.vertices) == 2
assert surface.vertices[1].right == pytest.approx(-3.0)
@pytest.mark.parametrize('vertices_coords', [
((0, 0, 0), (2, 4, 0), (2, 4, 3)),
((0, 0, 0), (2, 4, 0), (2, 4, 3), (0, 0, 3)),
((1, 1, 0), (3, 5, 0), (3, 5, 3), (1, 1, 3)),
((1, 1, 7), (3, 5, 7), (3, 5, 3), (1, 1, 3)),
((1, 1, 1), (3, 5, 7), (3, 5, 9), (1, 1, 3)),
((3, 5, 7), (1, 1, 1), (1, 1, 3)),
((3, 5, 7), (1, 1, 1), (1, 1, 3), (3, 5, 9)),
])
def test_add_rectangle(vertices_coords):
surface = Surface()
for vertex_coords in vertices_coords:
surface.add_vertex(Vertex(*(float(c) for c in vertex_coords)))
surface.add_rectangle(range(len(vertices_coords)))
assert len(surface.vertices) == 4
assert len(surface.triangles) == 2
assert surface.triangles[0].vertex_indices == (0, 1, 2)
assert surface.triangles[1].vertex_indices == (2, 3, 0)
@pytest.mark.parametrize(('vertices_coords', 'expected_extra_vertex_coords'), [
(((0, 0, 0), (2, 4, 0), (2, 4, 3)), (0, 0, 3)),
(((1, 1, 0), (3, 5, 0), (3, 5, 3)), (1, 1, 3)),
(((1, 1, 7), (3, 5, 7), (3, 5, 3)), (1, 1, 3)),
(((1, 1, 1), (3, 5, 7), (3, 5, 9)), (1, 1, 3)),
(((3, 5, 7), (1, 1, 1), (1, 1, 3)), (3, 5, 9)),
])
def test_add_rectangle_3(vertices_coords, expected_extra_vertex_coords):
surface = Surface()
for vertex_coords in vertices_coords:
surface.add_vertex(Vertex(*(float(c) for c in vertex_coords)))
surface.add_rectangle(range(3))
assert tuple(surface.vertices[3]) \
== pytest.approx(expected_extra_vertex_coords)
def test__triangle_count_by_adjacent_vertex_indices_empty():
surface = Surface()
assert surface._triangle_count_by_adjacent_vertex_indices() == {}
def test__triangle_count_by_adjacent_vertex_indices_none():
surface = Surface()
surface.vertices.append(Vertex(1, 0, 0))
surface.vertices.append(Vertex(2, 0, 0))
surface.vertices.append(Vertex(3, 0, 0))
assert surface._triangle_count_by_adjacent_vertex_indices() \
== {0: {}, 1: {}, 2: {}}
def test__triangle_count_by_adjacent_vertex_indices_single():
surface = Surface()
surface.triangles.append(Triangle([surface.add_vertex(Vertex(i, 0, 0))
for i in range(3)]))
assert surface._triangle_count_by_adjacent_vertex_indices() \
== {0: {1: 1, 2: 1},
1: {0: 1, 2: 1},
2: {0: 1, 1: 1}}
def test__triangle_count_by_adjacent_vertex_indices_multiple():
surface = Surface()
for i in range(5):
surface.add_vertex(Vertex(i, 0, 0))
surface.triangles.append(Triangle((0, 1, 2)))
surface.triangles.append(Triangle((3, 1, 2)))
assert surface._triangle_count_by_adjacent_vertex_indices() \
== {0: {1: 1, 2: 1},
1: {0: 1, 2: 2, 3: 1},
2: {0: 1, 1: 2, 3: 1},
3: {1: 1, 2: 1},
4: {}}
surface.triangles.append(Triangle((3, 4, 2)))
assert surface._triangle_count_by_adjacent_vertex_indices() \
== {0: {1: 1, 2: 1},
1: {0: 1, 2: 2, 3: 1},
2: {0: 1, 1: 2, 3: 2, 4: 1},
3: {1: 1, 2: 2, 4: 1},
4: {2: 1, 3: 1}}
surface.triangles.append(Triangle((3, 0, 2)))
assert surface._triangle_count_by_adjacent_vertex_indices() \
== {0: {1: 1, 2: 2, 3: 1},
1: {0: 1, 2: 2, 3: 1},
2: {0: 2, 1: 2, 3: 3, 4: 1},
3: {0: 1, 1: 1, 2: 3, 4: 1},
4: {2: 1, 3: 1}}
def test__triangle_count_by_adjacent_vertex_indices_real():
surface = Surface.read_triangular(SURFACE_FILE_PATH)
counts = surface._triangle_count_by_adjacent_vertex_indices()
assert len(counts) == len(surface.vertices)
assert all(counts.values())
assert all(count == 2
for vertex_counts in counts.values()
for count in vertex_counts.values())
assert sum(count for vertex_counts in counts.values()
for count in vertex_counts.values()) \
== len(surface.triangles) * 6
def test_find_borders_none():
surface = Surface.read_triangular(SURFACE_FILE_PATH)
assert not list(surface.find_borders())
def test_find_borders_single():
surface = Surface.read_triangular(SURFACE_FILE_PATH)
single_index = surface.add_vertex(Vertex(0, 21, 42))
borders = list(surface.find_borders())
assert len(borders) == 1
assert borders[0] == PolygonalCircuit((single_index,))
def test_find_borders_singles():
surface = Surface.read_triangular(SURFACE_FILE_PATH)
single_indices = [surface.add_vertex(Vertex(i, 21, 42))
for i in range(3)]
borders = set(surface.find_borders())
assert len(borders) == 3
assert PolygonalCircuit((single_indices[0],)) in borders
assert PolygonalCircuit((single_indices[1],)) in borders
assert PolygonalCircuit((single_indices[2],)) in borders
def test_find_borders_single_triangle_simple():
surface = Surface()
vertex_indices = [surface.add_vertex(Vertex(i, 21, 42))
for i in range(3)]
surface.triangles.append(Triangle(vertex_indices))
borders = set(surface.find_borders())
assert len(borders) == 1
assert PolygonalCircuit(vertex_indices) in borders
def test_find_borders_single_triangle_real():
surface = Surface.read_triangular(SURFACE_FILE_PATH)
vertex_indices = [surface.add_vertex(Vertex(i, 21, 42))
for i in range(3)]
surface.triangles.append(Triangle(vertex_indices))
borders = set(surface.find_borders())
assert len(borders) == 1
assert PolygonalCircuit(vertex_indices) in borders
def test_find_borders_remove_triangle():
surface = Surface.read_triangular(SURFACE_FILE_PATH)
triangle = surface.triangles.pop()
borders = set(surface.find_borders())
assert len(borders) == 1
assert triangle in borders
def test_find_borders_remove_non_adjacent_triangles():
surface = Surface.read_triangular(SURFACE_FILE_PATH)
triangles = [surface.triangles.pop(),
surface.triangles.pop()]
borders = set(surface.find_borders())
assert len(borders) == 2
assert triangles[0] in borders
assert triangles[1] in borders
def test_find_borders_remove_adjacent_triangles():
surface = Surface.read_triangular(SURFACE_FILE_PATH)
triangles = [surface.triangles.pop(),
surface.triangles.pop()]
triangles.append(surface.triangles.pop(270682))
assert triangles[1] == Triangle((136141, 136142, 137076))
assert triangles[2] == Triangle((136141, 136142, 135263))
borders = set(surface.find_borders())
assert len(borders) == 2
assert triangles[0] in borders
assert PolygonalCircuit((137076, 136141, 135263, 136142)) in borders
surface.triangles.pop(270682)
borders = set(surface.find_borders())
assert len(borders) == 2
assert triangles[0] in borders
assert PolygonalCircuit((137076, 136141, 135263, 135264, 136142)) in borders
surface.triangles.pop(274320)
borders = set(surface.find_borders())
assert len(borders) == 2
assert PolygonalCircuit((136143, 138007, 138008, 137078)) in borders
assert PolygonalCircuit((137076, 136141, 135263, 135264, 136142)) in borders
def test__get_vertex_label_index():
surface = Surface.read_triangular(SURFACE_FILE_PATH)
surface.load_annotation_file(ANNOTATION_FILE_PATH)
# pylint: disable=protected-access
assert surface._get_vertex_label_index(64290) == 22
assert surface._get_vertex_label_index(72160) == 22
assert surface._get_vertex_label_index(84028) == 24
assert surface._get_vertex_label_index(97356) == 24
assert surface._get_vertex_label_index(123173) == 27
assert surface._get_vertex_label_index(140727) == 27
assert surface._get_vertex_label_index(93859) == 28
assert surface._get_vertex_label_index(78572) == 0
assert surface._get_vertex_label_index(120377) == 0
vertex_index = surface.add_vertex(Vertex(0.0, 21.0, 42.0))
assert surface._get_vertex_label_index(vertex_index) is None
del surface.annotation.vertex_label_index[140727]
assert surface._get_vertex_label_index(140727) is None
def test__find_label_border_segments():
surface = Surface.read_triangular(SURFACE_FILE_PATH)
surface.load_annotation_file(ANNOTATION_FILE_PATH)
precentral_label, = filter(lambda l: l.name == 'precentral',
surface.annotation.labels.values())
# pylint: disable=protected-access
border_segments = set(
surface._find_label_border_segments(precentral_label))
assert len(border_segments) == 417
assert LineSegment((33450, 32065)) in border_segments
assert LineSegment((33454, 33450)) in border_segments
for border_vertex_index in [33450, 33454, 32065]:
assert surface.annotation.vertex_label_index[border_vertex_index] == precentral_label.index
for other_vertex_index in [32064, 33449, 33455, 33449, 33455]:
assert LineSegment((other_vertex_index, border_vertex_index)) \
not in border_segments
assert LineSegment((border_vertex_index, other_vertex_index)) \
not in border_segments
def test__find_label_border_segments_incomplete_annotation():
surface = Surface.read_triangular(SURFACE_FILE_PATH)
surface.load_annotation_file(ANNOTATION_FILE_PATH)
precentral_label, = filter(lambda l: l.name == 'precentral',
surface.annotation.labels.values())
# pylint: disable=protected-access
assert surface._find_label_border_segments(precentral_label)
surface.triangles.append(Triangle([
surface.add_vertex(Vertex(0.0, 21.0 * factor, 42.0 * factor))
for factor in range(3)
]))
border_segments = set(
surface._find_label_border_segments(precentral_label))
assert len(border_segments) == 417
def test_find_label_border_polygonal_chains():
surface = Surface.read_triangular(SURFACE_FILE_PATH)
surface.load_annotation_file(ANNOTATION_FILE_PATH)
precentral_label, = filter(lambda l: l.name == 'precentral',
surface.annotation.labels.values())
border_chain, = surface.find_label_border_polygonal_chains(precentral_label)
vertex_indices = list(border_chain.vertex_indices)
assert len(vertex_indices) == 418
min_index = vertex_indices.index(min(vertex_indices))
vertex_indices_normalized = vertex_indices[min_index:] + vertex_indices[:min_index]
assert vertex_indices_normalized[:4] == [32065, 32072, 32073, 32080]
assert vertex_indices_normalized[-4:] == [36281, 34870, 33454, 33450]
def test__unused_vertices():
surface = Surface()
assert not surface._unused_vertices()
for i in range(4):
surface.add_vertex(Vertex(i, i, i))
assert surface._unused_vertices() == {0, 1, 2, 3}
surface.triangles.append(Triangle((0, 2, 3)))
assert surface._unused_vertices() == {1}
surface.triangles.append(Triangle((0, 3, 1)))
assert not surface._unused_vertices()
del surface.triangles[0]
assert surface._unused_vertices() == {2}
def test__unused_vertices_real():
surface = Surface.read_triangular(SURFACE_FILE_PATH)
assert not surface._unused_vertices()
surface.triangles = list(filter(lambda t: 42 not in t.vertex_indices,
surface.triangles))
assert surface._unused_vertices() == {42}
def test_remove_unused_vertices_all():
surface = Surface()
for i in range(5):
surface.add_vertex(Vertex(i, i, i))
assert len(surface.vertices) == 5
surface.remove_unused_vertices()
assert not surface.vertices
surface.remove_unused_vertices()
assert not surface.vertices
def test_remove_unused_vertices_almost_all():
surface = Surface()
for i in range(5):
surface.add_vertex(Vertex(i, i, i))
assert len(surface.vertices) == 5
surface.triangles.append(Triangle((0, 2, 3)))
surface.remove_unused_vertices()
assert len(surface.vertices) == 3
assert surface.vertices[0] == pytest.approx(Vertex(0, 0, 0))
assert surface.vertices[1] == pytest.approx(Vertex(2, 2, 2))
assert surface.vertices[2] == pytest.approx(Vertex(3, 3, 3))
assert len(surface.triangles) == 1
assert surface.triangles[0] == Triangle((0, 1, 2))
del surface.triangles[0]
surface.remove_unused_vertices()
assert not surface.vertices
def test_remove_unused_vertices_some():
surface = Surface()
for i in range(9):
surface.add_vertex(Vertex(i, i, i))
surface.triangles.append(Triangle((0, 2, 3)))
surface.triangles.append(Triangle((3, 4, 5)))
surface.triangles.append(Triangle((3, 2, 5)))
surface.triangles.append(Triangle((3, 2, 8)))
surface.remove_unused_vertices()
assert len(surface.vertices) == 6
assert surface.vertices[0] == pytest.approx(Vertex(0, 0, 0))
assert surface.vertices[1] == pytest.approx(Vertex(2, 2, 2))
assert surface.vertices[2] == pytest.approx(Vertex(3, 3, 3))
assert surface.vertices[3] == pytest.approx(Vertex(4, 4, 4))
assert surface.vertices[4] == pytest.approx(Vertex(5, 5, 5))
assert surface.vertices[5] == pytest.approx(Vertex(8, 8, 8))
assert len(surface.triangles) == 4
assert surface.triangles[0] == Triangle((0, 1, 2))
assert surface.triangles[1] == Triangle((2, 3, 4))
assert surface.triangles[2] == Triangle((2, 1, 4))
assert surface.triangles[3] == Triangle((2, 1, 5))
surface.remove_unused_vertices()
assert len(surface.triangles) == 4
def test_remove_unused_vertices_none():
surface = Surface.read_triangular(SURFACE_FILE_PATH)
assert len(surface.vertices) == 155622
assert len(surface.triangles) == 311240
surface.remove_unused_vertices()
assert len(surface.vertices) == 155622
assert len(surface.triangles) == 311240
def test_remove_unused_vertices_single():
surface = Surface.read_triangular(SURFACE_FILE_PATH)
assert len(surface.vertices) == 155622
assert len(surface.triangles) == 311240
assert surface.triangles[-1] == Triangle((136143, 138007, 137078))
surface.triangles = list(filter(lambda t: 42 not in t.vertex_indices,
surface.triangles))
assert surface._unused_vertices() == {42}
surface.remove_unused_vertices()
assert len(surface.vertices) == 155622 - 1
assert len(surface.triangles) == 311240 - 7
assert surface.triangles[-1] == Triangle((136142, 138006, 137077))
assert all(vertex_index < len(surface.vertices)
for triangle in surface.triangles
for vertex_index in triangle.vertex_indices)
def test__triangles_vertex_indices():
surface = Surface()
for i in range(5):
surface.add_vertex(Vertex(i, i, i))
surface.triangles.append(Triangle((0, 1, 2)))
surface.triangles.append(Triangle((3, 1, 2)))
surface.triangles.append(Triangle((3, 1, 4)))
surface.triangles.append(Triangle((5, 1, 4)))
assert (surface._triangles_vertex_indices()
== [[0, 1, 2], [3, 1, 2], [3, 1, 4], [5, 1, 4]]).all()
def test_select_vertices():
surface = Surface()
for i in range(4):
surface.add_vertex(Vertex(i, i, i))
assert (surface.select_vertices([2, 1]) \
== [surface.vertices[2], surface.vertices[1]]).all()
assert (surface.select_vertices((3, 2)) \
== [surface.vertices[3], surface.vertices[2]]).all()
assert (surface.select_vertices((3, 2)) \
== [[3, 3, 3], [2, 2, 2]]).all()
assert (surface.select_vertices(filter(lambda i: i % 2 == 1, range(4))) \
== [[1, 1, 1], [3, 3, 3]]).all()
def test__triangles_vertex_coords():
surface = Surface()
for i in range(6):
surface.add_vertex(Vertex(i, i, i))
surface.triangles.append(Triangle((0, 1, 2)))
surface.triangles.append(Triangle((3, 1, 2)))
surface.triangles.append(Triangle((3, 1, 4)))
surface.triangles.append(Triangle((5, 1, 4)))
assert (surface._triangles_vertex_coords()
== [[[0, 0, 0], [1, 1, 1], [2, 2, 2]],
[[3, 3, 3], [1, 1, 1], [2, 2, 2]],
[[3, 3, 3], [1, 1, 1], [4, 4, 4]],
[[5, 5, 5], [1, 1, 1], [4, 4, 4]]]).all()
assert (surface._triangles_vertex_coords().transpose(1, 0, 2)
== [[[0, 0, 0], [3, 3, 3], [3, 3, 3], [5, 5, 5]],
[[1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1]],
[[2, 2, 2], [2, 2, 2], [4, 4, 4], [4, 4, 4]]]).all()
def test__triangles_point_normal():
surface = Surface()
surface.add_vertex(Vertex(0, 0, 0))
surface.add_vertex(Vertex(2, 0, 0))
surface.add_vertex(Vertex(0, 2, 0))
surface.add_vertex(Vertex(0, 0, 2))
surface.add_vertex(Vertex(0, 1, 3))
surface.triangles.append(Triangle((0, 1, 2)))
surface.triangles.append(Triangle((0, 1, 3)))
surface.triangles.append(Triangle((2, 1, 3)))
surface.triangles.append(Triangle((0, 3, 4)))
surface.triangles.append(Triangle((0, 1, 4)))
surface.triangles.append(Triangle((1, 4, 0)))
surface.triangles.append(Triangle((4, 0, 1)))
surface.triangles.append(Triangle((4, 1, 0)))
surface.triangles.append(Triangle((4, 1, 2)))
normal_vectors, constants = surface._triangles_point_normal()
assert (normal_vectors == [[0, 0, 4],
[0, -4, 0],
[-4, -4, -4],
[-2, 0, 0],
[0, -6, 2],
[0, -6, 2],
[0, -6, 2],
[0, 6, -2],
[6, 6, 2]]).all()
assert (constants == [0, 0, -8, 0, 0, 0, 0, 0, 12]).all()
for triangle, normal_vector, constant \
in zip(surface.triangles, normal_vectors, constants):
vertices = [surface.vertices[i] for i in triangle.vertex_indices]
for vertex in vertices:
assert numpy.inner(normal_vector, vertex) \
== pytest.approx(constant)