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import pathlib
import meshio
import numpy as np
import pytest
import meshplex
from .helpers import assert_mesh_consistency, compute_all_entities
this_dir = pathlib.Path(__file__).resolve().parent
def test_flip_simple():
# 3 3
# A A
# /|\ / \
# 1/ | \4 1/ 1 \4
# / | \ / \
# 0/ 0 3 \2 ==> 0/___3___\2
# \ | 1 / \ /
# \ | / \ /
# 0\ | /2 0\ 0 /2
# \|/ \ /
# V V
# 1 1
#
points = np.array([[-0.1, 0.0], [0.0, -1.0], [0.1, 0.0], [0.0, 1.1]])
cells = np.array([[0, 1, 3], [1, 2, 3]])
mesh = meshplex.MeshTri(points, cells)
mesh.create_facets()
assert not mesh.is_delaunay
assert mesh.num_delaunay_violations == 1
assert np.array_equal(
mesh.edges["points"], [[0, 1], [0, 3], [1, 2], [1, 3], [2, 3]]
)
assert np.array_equal(mesh.cells("edges"), [[3, 1, 0], [4, 3, 2]])
assert_mesh_consistency(mesh)
# mesh.show()
num_flips = mesh.flip_until_delaunay()
assert num_flips == 1
assert_mesh_consistency(mesh)
assert mesh.num_delaunay_violations == 0
assert np.array_equal(
mesh.edges["points"], [[0, 1], [0, 3], [1, 2], [0, 2], [2, 3]]
)
assert np.array_equal(mesh.cells("points"), [[0, 1, 2], [0, 2, 3]])
assert np.array_equal(mesh.cells("edges"), [[2, 3, 0], [4, 1, 3]])
def test_flip_simple_negative_orientation():
# 3 3
# A A
# /|\ / \
# 1/ | \4 1/ 1 \4
# / | \ / \
# 0/ 0 3 \2 ==> 0/___3___\2
# \ | 1 / \ /
# \ | / \ /
# 0\ | /2 0\ 0 /2
# \|/ \ /
# V V
# 1 1
#
points = np.array([[-0.1, 0.0], [0.0, -1.0], [0.1, 0.0], [0.0, 1.1]])
cells = np.array([[0, 3, 1], [1, 3, 2]])
mesh = meshplex.MeshTri(points, cells)
mesh.create_facets()
assert mesh.num_delaunay_violations == 1
assert np.array_equal(
mesh.edges["points"], [[0, 1], [0, 3], [1, 2], [1, 3], [2, 3]]
)
assert np.array_equal(mesh.cells("edges"), [[3, 0, 1], [4, 2, 3]])
assert_mesh_consistency(mesh)
# mesh.show()
mesh.flip_until_delaunay()
assert_mesh_consistency(mesh)
assert mesh.num_delaunay_violations == 0
assert np.array_equal(
mesh.edges["points"], [[0, 1], [0, 3], [1, 2], [0, 2], [2, 3]]
)
assert np.array_equal(mesh.cells("points"), [[0, 3, 2], [0, 2, 1]])
assert np.array_equal(mesh.cells("edges"), [[4, 3, 1], [2, 0, 3]])
def test_flip_simple_opposite_orientation():
# 3 3
# A A
# /|\ / \
# 1/ | \4 1/ 1 \4
# / | \ / \
# 0/ 0 3 \2 ==> 0/___3___\2
# \ | 1 / \ /
# \ | / \ /
# 0\ | /2 0\ 0 /2
# \|/ \ /
# V V
# 1 1
#
points = np.array([[-0.1, 0.0], [0.0, -1.0], [0.1, 0.0], [0.0, 1.1]])
cells = np.array([[0, 1, 3], [1, 3, 2]])
mesh = meshplex.MeshTri(points, cells)
mesh.create_facets()
assert mesh.num_delaunay_violations == 1
assert np.array_equal(
mesh.edges["points"], [[0, 1], [0, 3], [1, 2], [1, 3], [2, 3]]
)
assert np.array_equal(mesh.cells("edges"), [[3, 1, 0], [4, 2, 3]])
assert_mesh_consistency(mesh)
# mesh.show()
mesh.flip_until_delaunay()
assert_mesh_consistency(mesh)
assert mesh.num_delaunay_violations == 0
assert np.array_equal(
mesh.edges["points"], [[0, 1], [0, 3], [1, 2], [0, 2], [2, 3]]
)
assert np.array_equal(mesh.cells("points"), [[0, 1, 2], [0, 2, 3]])
assert np.array_equal(mesh.cells("edges"), [[2, 3, 0], [4, 1, 3]])
def test_flip_delaunay_near_boundary():
points = np.array([[0.0, +0.0], [0.5, -0.1], [1.0, +0.0], [0.5, +0.1]])
cells = np.array([[0, 1, 2], [0, 2, 3]])
mesh = meshplex.MeshTri(points, cells)
mesh.create_facets()
assert mesh.num_delaunay_violations == 1
assert np.array_equal(mesh.cells("points"), [[0, 1, 2], [0, 2, 3]])
assert np.array_equal(mesh.cells("edges"), [[3, 1, 0], [4, 2, 1]])
mesh.flip_until_delaunay()
assert_mesh_consistency(mesh)
assert mesh.num_delaunay_violations == 0
assert np.array_equal(mesh.cells("points"), [[1, 2, 3], [1, 3, 0]])
assert np.array_equal(mesh.cells("edges"), [[4, 1, 3], [2, 0, 1]])
def test_flip_same_edge_twice():
points = np.array([[0.0, +0.0], [0.5, -0.1], [1.0, +0.0], [0.5, +0.1]])
cells = np.array([[0, 1, 2], [0, 2, 3]])
mesh = meshplex.MeshTri(points, cells)
assert mesh.num_delaunay_violations == 1
mesh.flip_until_delaunay()
assert mesh.num_delaunay_violations == 0
mesh.show(
mark_cells=mesh.is_boundary_cell,
show_point_numbers=True,
show_edge_numbers=True,
show_cell_numbers=True,
)
assert_mesh_consistency(mesh)
new_points = np.array([[0.0, +0.0], [0.1, -0.5], [0.2, +0.0], [0.1, +0.5]])
mesh.points = new_points
assert mesh.num_delaunay_violations == 1
mesh.flip_until_delaunay()
assert mesh.num_delaunay_violations == 0
mesh.show()
# mesh.plot()
def test_flip_two_edges():
alpha = np.array([1.0, 3.0, 5.0, 7.0, 9.0, 11.0]) / 6.0 * np.pi
# Make the mesh slightly asymmetric to get the same flips on every architecture; see
# <https://github.com/nschloe/meshplex/issues/78>.
R = [0.95, 1.0, 0.9, 1.0, 1.2, 1.0]
points = np.array([[r * np.cos(a), r * np.sin(a), 0.0] for a, r in zip(alpha, R)])
cells = np.array([[1, 3, 5], [0, 1, 5], [1, 2, 3], [3, 4, 5]])
mesh = meshplex.MeshTri(points, cells)
assert mesh.num_delaunay_violations == 2
mesh.flip_until_delaunay()
assert mesh.num_delaunay_violations == 0
mesh.show(show_point_numbers=True)
assert np.array_equal(
mesh.cells("points"), [[2, 5, 0], [2, 0, 1], [5, 2, 3], [3, 4, 5]]
)
def test_flip_delaunay_near_boundary_preserve_boundary_count():
# This test is to make sure meshplex preserves the boundary point count.
points = np.array(
[
[+0.0, +0.0],
[+0.5, -0.5],
[+0.5, +0.5],
[+0.0, +0.6],
[-0.5, +0.5],
[-0.5, -0.5],
]
)
cells = np.array([[0, 1, 2], [0, 2, 4], [0, 4, 5], [0, 5, 1], [2, 3, 4]])
mesh = meshplex.MeshTri(points, cells)
mesh.create_facets()
assert mesh.num_delaunay_violations == 1
is_boundary_point_ref = [False, True, True, True, True, True]
assert np.array_equal(mesh.is_boundary_point, is_boundary_point_ref)
mesh.flip_until_delaunay()
assert np.array_equal(mesh.is_boundary_point, is_boundary_point_ref)
def test_flip_orientation():
points = np.array([[0.0, +0.0], [0.5, -0.1], [1.0, +0.0], [0.5, +0.1]])
# preserve positive orientation
cells = np.array([[0, 1, 2], [0, 2, 3]])
mesh = meshplex.MeshTri(points, cells)
assert np.all(mesh.signed_cell_volumes > 0.0)
mesh.flip_until_delaunay()
assert np.all(mesh.signed_cell_volumes > 0.0)
# also preserve negative orientation
cells = np.array([[0, 2, 1], [0, 3, 2]])
mesh = meshplex.MeshTri(points, cells)
assert np.all(mesh.signed_cell_volumes < 0.0)
mesh.flip_until_delaunay()
assert np.all(mesh.signed_cell_volumes < 0.0)
def test_flip_infinite():
"""In rare cases, it can happen that the ce-ratio of an edge is negative (up to
machine precision, -2.13e-15 or something like that), an edge flip is done, and the
ce-ratio of the resulting edge is again negative. The flip_until_delaunay() method
would continue indefinitely. This test replicates such an edge case."""
a = 3.9375644347017862e02
points = np.array([[205.0, a], [185.0, a], [330.0, 380.0], [60.0, 380.0]])
cells = [[0, 1, 2], [1, 2, 3]]
mesh = meshplex.MeshTri(points, cells)
num_flips = mesh.flip_until_delaunay(tol=1.0e-13)
assert num_flips == 0
def test_flip_interior_to_boundary():
# __________ __________
# |\__ A |\__ A
# | \__ /|\ | \__ / \
# | \/ | \ ==> | \/___\
# | __/\ | / | __/\ /
# | __/ \|/ | __/ \ /
# |/________V |/________V
#
points = np.array(
[[0.0, 0.0], [1.0, 0.0], [1.1, 0.5], [1.0, 1.0], [0.0, 1.0], [0.9, 0.5]]
)
cells = np.array([[0, 1, 5], [1, 3, 5], [1, 2, 3], [3, 4, 5], [0, 5, 4]])
mesh = meshplex.MeshTri(points, cells)
compute_all_entities(mesh)
# mesh.show(mark_cells=mesh.is_boundary_cell)
mesh.flip_until_delaunay()
assert_mesh_consistency(mesh)
# mesh.show(mark_cells=mesh.is_boundary_cell)
assert np.all(mesh.is_boundary_cell)
def test_flip_delaunay():
rng = np.random.default_rng(123)
mesh0 = meshio.read(this_dir / ".." / "meshes" / "pacman.vtu")
mesh0.points[:, :2] += 1.0e-1 * rng.random(mesh0.points[:, :2].shape)
mesh0 = meshplex.MeshTri(mesh0.points[:, :2], mesh0.get_cells_type("triangle"))
compute_all_entities(mesh0)
assert np.all(mesh0.signed_cell_volumes > 0)
assert mesh0.num_delaunay_violations == 5
mesh0.flip_until_delaunay()
assert mesh0.num_delaunay_violations == 0
assert_mesh_consistency(mesh0)
# mesh0.show(mark_cells=mesh0.is_boundary_cell)
# We don't need to check for exact equality with a replicated mesh. The order of the
# edges will be different, for example. Just make sure the mesh is consistent.
# mesh1 = meshplex.MeshTri(mesh0.points.copy(), mesh0.cells("points").copy())
# mesh1.create_facets()
# assert_mesh_equality(mesh0, mesh1)
def test_flip_into_existing_edge():
"""For surface meshes, flips can lead to duplicate cells. For context, see
<https://github.com/nschloe/optimesh/issues/71#issuecomment-785699560>.
"""
points = np.array(
[
[0.0, 0.0, 0.0],
[1.0, 0.0, 0.0],
[0.5, 0.3, 0.3],
[0.5, -0.3, 0.3],
]
)
cells = np.array(
[
[1, 2, 0],
[2, 3, 0],
[3, 1, 0],
]
)
mesh = meshplex.MeshTri(points, cells)
with pytest.warns(UserWarning):
n = mesh.flip_until_delaunay()
# no flips performed
assert n == 0
def test_doubled_cell():
# Two congruent cells. One can think of it as a deflated, coarse ball.
points = np.array(
[
[0.0, 0.0],
[1.0, 0.0],
[0.5, 0.4],
]
)
cells = np.array([[0, 1, 2], [0, 1, 2]])
mesh = meshplex.MeshTri(points, cells)
num_flips = mesh.flip_until_delaunay()
assert num_flips == 1
ref = [[2, 0, 2], [2, 2, 1]]
assert np.all(mesh.cells("points") == ref)
def test_negative_after_flip():
points = [[0.0, 0.0], [3.0, 0.0], [1.14960653, 0.03], [1.85039347, 0.03]]
cells = [
[0, 3, 2],
[0, 1, 3],
]
mesh0 = meshplex.MeshTri(points, cells)
with pytest.warns(UserWarning):
mesh0.flip_until_delaunay()
|
