def test_volume_quadrilateralR3(coordinates):
mesh = Mesh(MPI.comm_world, CellType.quadrilateral,
numpy.array(coordinates, dtype=numpy.float64),
numpy.array([[0, 1, 2, 3]], dtype=numpy.int32), [],
cpp.mesh.GhostMode.none)
mesh.create_connectivity_all()
assert cpp.mesh.volume_entities(mesh, [0], mesh.topology.dim) == 1.0
def test_volume_quadrilateral_coplanarity_check_2(scaling):
with pytest.raises(RuntimeError) as error:
# Unit square cell scaled down by 'scaling' and the first vertex
# is distorted so that the vertices are clearly non coplanar
mesh = Mesh(
MPI.comm_world, CellType.quadrilateral,
numpy.array([[1.0, 0.5, 0.6], [0.0, scaling, 0.0],
[0.0, 0.0, scaling], [0.0, 1.0, 1.0]],
dtype=numpy.float64),
numpy.array([[0, 1, 2, 3]], dtype=numpy.int32), [],
cpp.mesh.GhostMode.none)
mesh.create_connectivity_all()
cpp.mesh.volume_entities(mesh, [0], mesh.topology.dim)
assert "Not coplanar" in str(error.value)
def unit_cell(cell_type, random_order=True):
if cell_type == CellType.interval:
points = np.array([[0.], [1.]])
if cell_type == CellType.triangle:
# Define equilateral triangle with area 1
root = 3**0.25 # 4th root of 3
points = np.array([[0., 0.], [2 / root, 0.], [1 / root, root]])
elif cell_type == CellType.tetrahedron:
# Define regular tetrahedron with volume 1
s = 2**0.5 * 3**(1 / 3) # side length
points = np.array([[0., 0., 0.], [s, 0., 0.],
[s / 2, s * np.sqrt(3) / 2, 0.],
[s / 2, s / 2 / np.sqrt(3), s * np.sqrt(2 / 3)]])
elif cell_type == CellType.quadrilateral:
# Define unit quadrilateral (area 1)
points = np.array([[0., 0.], [1., 0.], [0., 1.], [1., 1.]])
elif cell_type == CellType.hexahedron:
# Define unit hexahedron (volume 1)
points = np.array([[0., 0., 0.], [1., 0., 0.], [0., 1., 0.],
[1., 1., 0.], [0., 0., 1.], [1., 0., 1.],
[0., 1., 1.], [1., 1., 1.]])
num_points = len(points)
# Randomly number the points and create the mesh
order = list(range(num_points))
if random_order:
shuffle(order)
ordered_points = np.zeros(points.shape)
for i, j in enumerate(order):
ordered_points[j] = points[i]
cells = np.array([order])
mesh = Mesh(MPI.comm_world, cell_type, ordered_points, cells, [],
cpp.mesh.GhostMode.none)
mesh.geometry.coord_mapping = fem.create_coordinate_map(mesh)
mesh.create_connectivity_all()
return mesh
def two_unit_cells(cell_type,
agree=False,
random_order=True,
return_order=False):
if cell_type == CellType.interval:
points = np.array([[0.], [1.], [-1.]])
if agree:
cells = [[0, 1], [2, 0]]
else:
cells = [[0, 1], [0, 2]]
if cell_type == CellType.triangle:
# Define equilateral triangles with area 1
root = 3**0.25 # 4th root of 3
points = np.array([[0., 0.], [2 / root, 0.], [1 / root, root],
[1 / root, -root]])
if agree:
cells = [[0, 1, 2], [0, 3, 1]]
else:
cells = [[0, 1, 2], [1, 0, 3]]
elif cell_type == CellType.tetrahedron:
# Define regular tetrahedra with volume 1
s = 2**0.5 * 3**(1 / 3) # side length
points = np.array([[0., 0., 0.], [s, 0., 0.],
[s / 2, s * np.sqrt(3) / 2, 0.],
[s / 2, s / 2 / np.sqrt(3), s * np.sqrt(2 / 3)],
[s / 2, s / 2 / np.sqrt(3), -s * np.sqrt(2 / 3)]])
if agree:
cells = [[0, 1, 2, 3], [0, 1, 4, 2]]
else:
cells = [[0, 1, 2, 3], [0, 2, 1, 4]]
elif cell_type == CellType.quadrilateral:
# Define unit quadrilaterals (area 1)
points = np.array([[0., 0.], [1., 0.], [0., 1.], [1., 1.], [0., -1.],
[1., -1.]])
if agree:
cells = [[0, 1, 2, 3], [4, 5, 0, 1]]
else:
cells = [[0, 1, 2, 3], [5, 1, 4, 0]]
elif cell_type == CellType.hexahedron:
# Define unit hexahedra (volume 1)
points = np.array([[0., 0., 0.], [1., 0., 0.], [0., 1., 0.],
[1., 1., 0.], [0., 0., 1.], [1., 0., 1.],
[0., 1., 1.], [1., 1., 1.], [0., 0., -1.],
[1., 0., -1.], [0., 1., -1.], [1., 1., -1.]])
if agree:
cells = [[0, 1, 2, 3, 4, 5, 6, 7], [8, 9, 10, 11, 0, 1, 2, 3]]
else:
cells = [[0, 1, 2, 3, 4, 5, 6, 7], [9, 11, 8, 10, 1, 3, 0, 2]]
num_points = len(points)
# Randomly number the points and create the mesh
order = list(range(num_points))
if random_order:
shuffle(order)
ordered_points = np.zeros(points.shape)
for i, j in enumerate(order):
ordered_points[j] = points[i]
ordered_cells = np.array([[order[i] for i in c] for c in cells])
mesh = Mesh(MPI.comm_world, cell_type, ordered_points, ordered_cells, [],
cpp.mesh.GhostMode.none)
mesh.geometry.coord_mapping = fem.create_coordinate_map(mesh)
mesh.create_connectivity_all()
if return_order:
return mesh, order
return mesh
