def test_cuboids_intersection():
c0 = pygalmesh.Cuboid([0, 0, -0.5], [3, 3, 0.5])
c1 = pygalmesh.Cuboid([1, 1, -2], [2, 2, 2])
u = pygalmesh.Intersection([c0, c1])
# In CGAL, feature edges must not intersect, and that's a problem here: The
# intersection edges of the cuboids share eight points with the edges of
# the tall and skinny cuboid.
# eps = 1.0e-2
# extra_features = [
# [[1.0, 1.0 + eps, 0.5], [1.0, 2.0 - eps, 0.5]],
# [[1.0 + eps, 2.0, 0.5], [2.0 - eps, 2.0, 0.5]],
# [[2.0, 2.0 - eps, 0.5], [2.0, 1.0 + eps, 0.5]],
# [[2.0 - eps, 1.0, 0.5], [1.0 + eps, 1.0, 0.5]],
# ]
mesh = pygalmesh.generate_mesh(u, cell_size=0.1, edge_size=0.1, verbose=False)
# filter the vertices that belong to cells
verts = mesh.points[numpy.unique(mesh.cells["tetra"])]
tol = 1.0e-2
assert abs(max(verts[:, 0]) - 2.0) < tol
assert abs(min(verts[:, 0]) - 1.0) < tol
assert abs(max(verts[:, 1]) - 2.0) < tol
assert abs(min(verts[:, 1]) - 1.0) < tol
assert abs(max(verts[:, 2]) - 0.5) < 0.05
assert abs(min(verts[:, 2]) + 0.5) < 0.05
vol = sum(helpers.compute_volumes(mesh.points, mesh.cells["tetra"]))
assert abs(vol - 1.0) < 0.05
return
def test_cuboids_union():
c0 = pygalmesh.Cuboid([0, 0, -0.5], [3, 3, 0.5])
c1 = pygalmesh.Cuboid([1, 1, -2], [2, 2, 2])
u = pygalmesh.Union([c0, c1])
pygalmesh.generate_mesh(u,
'out.mesh',
cell_size=0.2,
edge_size=0.2,
verbose=False)
vertices, cells, _, _, _ = meshio.read('out.mesh')
# filter the vertices that belong to cells
verts = vertices[numpy.unique(cells['tetra'])]
tol = 1.0e-2
assert abs(max(verts[:, 0]) - 3.0) < tol
assert abs(min(verts[:, 0]) - 0.0) < tol
assert abs(max(verts[:, 1]) - 3.0) < tol
assert abs(min(verts[:, 1]) - 0.0) < tol
assert abs(max(verts[:, 2]) - 2.0) < tol
assert abs(min(verts[:, 2]) + 2.0) < tol
vol = sum(compute_volumes(vertices, cells['tetra']))
assert abs(vol - 12.0) < 0.1
return
def l_shape_3d(h):
b0 = pygalmesh.Cuboid([-1.0, -1.0, -1.0], [1.0, 1.0, 1.0])
b1 = pygalmesh.Cuboid([0.0, 0.0, 0.0], [1.1, 1.1, 1.1])
u = pygalmesh.Difference(b0, b1)
mesh = pygalmesh.generate_mesh(
u,
max_edge_size_at_feature_edges=h,
max_cell_circumradius=h,
verbose=False,
# TODO sharpen the intersection edges and avoid
# [1] 591479 segmentation fault (core dumped) python3 pygalmesh_examples.py
# feature_edges=[
# [[1.0, 0.0, z] for z in numpy.linspace(0.0, 1.0, int(1.0 / h))]
# ]
)
mesh.remove_lower_dimensional_cells()
mesh.remove_orphaned_nodes()
return mesh.points, mesh.get_cells_type("tetra")
def test_halfspace():
c = pygalmesh.Cuboid([0, 0, 0], [1, 1, 1])
s = pygalmesh.HalfSpace([1.0, 2.0, 3.0], 1.0, 2.0)
u = pygalmesh.Intersection([c, s])
mesh = pygalmesh.generate_mesh(u, cell_size=0.2, edge_size=0.2, verbose=False)
vol = sum(helpers.compute_volumes(mesh.points, mesh.cells["tetra"]))
assert abs(vol - 1 / 750) < 1.0e-3
return
def test_rotation():
s0 = pygalmesh.Rotate(
pygalmesh.Cuboid([0, 0, 0], [1, 2, 3]), [1.0, 0.0, 0.0], numpy.pi / 12.0
)
mesh = pygalmesh.generate_mesh(s0, cell_size=0.1, edge_size=0.1, verbose=False)
tol = 1.0e-2
vol = sum(helpers.compute_volumes(mesh.points, mesh.cells["tetra"]))
assert abs(vol - 6.0) < tol
return
def test_cuboids_union():
c0 = pygalmesh.Cuboid([0, 0, -0.5], [3, 3, 0.5])
c1 = pygalmesh.Cuboid([1, 1, -2], [2, 2, 2])
u = pygalmesh.Union([c0, c1])
mesh = pygalmesh.generate_mesh(u, cell_size=0.2, edge_size=0.2, verbose=False)
# filter the vertices that belong to cells
verts = mesh.points[numpy.unique(mesh.cells["tetra"])]
tol = 1.0e-2
assert abs(max(verts[:, 0]) - 3.0) < tol
assert abs(min(verts[:, 0]) - 0.0) < tol
assert abs(max(verts[:, 1]) - 3.0) < tol
assert abs(min(verts[:, 1]) - 0.0) < tol
assert abs(max(verts[:, 2]) - 2.0) < tol
assert abs(min(verts[:, 2]) + 2.0) < tol
vol = sum(helpers.compute_volumes(mesh.points, mesh.cells["tetra"]))
assert abs(vol - 12.0) < 0.1
return
def test_translation():
s0 = pygalmesh.Translate(pygalmesh.Cuboid([0, 0, 0], [1, 2, 3]), [1.0, 0.0, 0.0])
mesh = pygalmesh.generate_mesh(s0, cell_size=0.1, edge_size=0.1, verbose=False)
tol = 1.0e-2
assert abs(max(mesh.points[:, 0]) - 2.0) < tol
assert abs(min(mesh.points[:, 0]) - 1.0) < tol
assert abs(max(mesh.points[:, 1]) - 2.0) < tol
assert abs(min(mesh.points[:, 1]) + 0.0) < tol
assert abs(max(mesh.points[:, 2]) - 3.0) < tol
assert abs(min(mesh.points[:, 2]) + 0.0) < tol
vol = sum(helpers.compute_volumes(mesh.points, mesh.cells["tetra"]))
assert abs(vol - 6.0) < tol
return
def test_cuboid():
s0 = pygalmesh.Cuboid([0, 0, 0], [1, 2, 3])
mesh = pygalmesh.generate_mesh(s0, edge_size=0.1, verbose=False)
tol = 1.0e-3
assert abs(max(mesh.points[:, 0]) - 1.0) < tol
assert abs(min(mesh.points[:, 0]) + 0.0) < tol
assert abs(max(mesh.points[:, 1]) - 2.0) < tol
assert abs(min(mesh.points[:, 1]) + 0.0) < tol
assert abs(max(mesh.points[:, 2]) - 3.0) < tol
assert abs(min(mesh.points[:, 2]) + 0.0) < tol
vol = sum(
helpers.compute_volumes(mesh.points, mesh.get_cells_type("tetra")))
assert abs(vol - 6.0) < tol
def test_scaling():
alpha = 1.3
s = pygalmesh.Scale(pygalmesh.Cuboid([0, 0, 0], [1, 2, 3]), alpha)
mesh = pygalmesh.generate_mesh(s, cell_size=0.2, edge_size=0.1, verbose=False)
tol = 1.0e-2
assert abs(max(mesh.points[:, 0]) - 1 * alpha) < tol
assert abs(min(mesh.points[:, 0]) + 0.0) < tol
assert abs(max(mesh.points[:, 1]) - 2 * alpha) < tol
assert abs(min(mesh.points[:, 1]) + 0.0) < tol
assert abs(max(mesh.points[:, 2]) - 3 * alpha) < tol
assert abs(min(mesh.points[:, 2]) + 0.0) < tol
vol = sum(helpers.compute_volumes(mesh.points, mesh.cells["tetra"]))
assert abs(vol - 6.0 * alpha ** 3) < tol
return
def box_with_refinement(h):
s = pygalmesh.Cuboid([-1.0, -1.0, -1.0], [1.0, 1.0, 1.0])
def edge_length(x):
return h + 0.1 * numpy.sqrt(x[0]**2 + x[1]**2 + x[2]**2)
mesh = pygalmesh.generate_mesh(
s,
max_edge_size_at_feature_edges=h,
# The actual factor sqrt(3 / 8) leads to cells too small in comparison with
# cells near the feature edges. Again, just take edge_size.
max_cell_circumradius=edge_length,
verbose=False,
)
return mesh.points, mesh.get_cells_type("tetra")
def test_halfspace():
c = pygalmesh.Cuboid([0, 0, 0], [1, 1, 1])
s = pygalmesh.HalfSpace([1.0, 2.0, 3.0], 1.0, 2.0)
u = pygalmesh.Intersection([c, s])
pygalmesh.generate_mesh(u,
'out.mesh',
cell_size=0.2,
edge_size=0.2,
verbose=False)
vertices, cells, _, _, _ = meshio.read('out.mesh')
vol = sum(compute_volumes(vertices, cells['tetra']))
assert abs(vol - 1 / 750) < 1.0e-3
return
def test_rotation():
s0 = pygalmesh.Rotate(pygalmesh.Cuboid([0, 0, 0], [1, 2, 3]),
[1.0, 0.0, 0.0], numpy.pi / 12.0)
pygalmesh.generate_mesh(s0,
'out.mesh',
cell_size=0.1,
edge_size=0.1,
verbose=False)
vertices, cells, _, _, _ = meshio.read('out.mesh')
tol = 1.0e-3
vol = sum(compute_volumes(vertices, cells['tetra']))
assert abs(vol - 6.0) < tol
return
def test_cuboid():
s0 = pygalmesh.Cuboid([0, 0, 0], [1, 2, 3])
pygalmesh.generate_mesh(s0, "out.mesh", edge_size=0.1, verbose=False)
mesh = meshio.read("out.mesh")
tol = 1.0e-3
assert abs(max(mesh.points[:, 0]) - 1.0) < tol
assert abs(min(mesh.points[:, 0]) + 0.0) < tol
assert abs(max(mesh.points[:, 1]) - 2.0) < tol
assert abs(min(mesh.points[:, 1]) + 0.0) < tol
assert abs(max(mesh.points[:, 2]) - 3.0) < tol
assert abs(min(mesh.points[:, 2]) + 0.0) < tol
vol = sum(compute_volumes(mesh.points, mesh.cells["tetra"]))
assert abs(vol - 6.0) < tol
return
def test_stretch():
alpha = 2.0
s = pygalmesh.Stretch(pygalmesh.Cuboid([0, 0, 0], [1, 2, 3]), [alpha, 0.0, 0.0])
mesh = pygalmesh.generate_mesh(s, cell_size=0.2, edge_size=0.2, verbose=False)
tol = 1.0e-2
assert abs(max(mesh.points[:, 0]) - alpha) < tol
assert abs(min(mesh.points[:, 0]) + 0.0) < tol
assert abs(max(mesh.points[:, 1]) - 2.0) < tol
assert abs(min(mesh.points[:, 1]) + 0.0) < tol
assert abs(max(mesh.points[:, 2]) - 3.0) < tol
assert abs(min(mesh.points[:, 2]) + 0.0) < tol
vol = sum(helpers.compute_volumes(mesh.points, mesh.cells["tetra"]))
assert abs(vol - 12.0) < tol
return
def test_cuboid():
s0 = pygalmesh.Cuboid([0, 0, 0], [1, 2, 3])
pygalmesh.generate_mesh(s0, 'out.mesh', edge_size=0.1, verbose=False)
vertices, cells, _, _, _ = meshio.read('out.mesh')
tol = 1.0e-3
assert abs(max(vertices[:, 0]) - 1.0) < tol
assert abs(min(vertices[:, 0]) + 0.0) < tol
assert abs(max(vertices[:, 1]) - 2.0) < tol
assert abs(min(vertices[:, 1]) + 0.0) < tol
assert abs(max(vertices[:, 2]) - 3.0) < tol
assert abs(min(vertices[:, 2]) + 0.0) < tol
vol = sum(compute_volumes(vertices, cells['tetra']))
assert abs(vol - 6.0) < tol
return
def test_scaling():
alpha = 1.3
s = pygalmesh.Scale(pygalmesh.Cuboid([0, 0, 0], [1, 2, 3]), alpha)
pygalmesh.generate_mesh(s,
'out.mesh',
cell_size=0.2,
edge_size=0.1,
verbose=False)
vertices, cells, _, _, _ = meshio.read('out.mesh')
tol = 1.0e-3
assert abs(max(vertices[:, 0]) - 1 * alpha) < tol
assert abs(min(vertices[:, 0]) + 0.0) < tol
assert abs(max(vertices[:, 1]) - 2 * alpha) < tol
assert abs(min(vertices[:, 1]) + 0.0) < tol
assert abs(max(vertices[:, 2]) - 3 * alpha) < tol
assert abs(min(vertices[:, 2]) + 0.0) < tol
vol = sum(compute_volumes(vertices, cells['tetra']))
assert abs(vol - 6.0 * alpha**3) < tol
return
def run_cgal(ef, HMIN=75.0):
print("generating a mesh with cgal...")
t1 = time.time()
mesh = pygalmesh.generate_mesh(
pygalmesh.Cuboid([-4200.0, 0.0, 0.0], [0.0, 13520.0, 13520.0]),
facet_angle=30,
cell_radius_edge_ratio=2.0,
cell_size=lambda x: ef.eval(x) / 1.1,
edge_size=HMIN,
)
elapsed = time.time() - t1
# mesh.write("cgal_EAGE.vtk")
plex = meshplex.MeshTetra(mesh.points, mesh.cells[1][1])
angles = plex.q_min_sin_dihedral_angles
quality = plex.q_radius_ratio
num_cells = len(mesh.cells[1][1])
num_vertices = len(mesh.points)
return angles, quality, elapsed, num_vertices, num_cells
def test_stretch():
alpha = 2.0
s = pygalmesh.Stretch(pygalmesh.Cuboid([0, 0, 0], [1, 2, 3]),
[alpha, 0.0, 0.0])
pygalmesh.generate_mesh(s,
'out.mesh',
cell_size=0.2,
edge_size=0.2,
verbose=False)
vertices, cells, _, _, _ = meshio.read('out.mesh')
tol = 1.0e-3
assert abs(max(vertices[:, 0]) - alpha) < tol
assert abs(min(vertices[:, 0]) + 0.0) < tol
assert abs(max(vertices[:, 1]) - 2.0) < tol
assert abs(min(vertices[:, 1]) + 0.0) < tol
assert abs(max(vertices[:, 2]) - 3.0) < tol
assert abs(min(vertices[:, 2]) + 0.0) < tol
vol = sum(compute_volumes(vertices, cells['tetra']))
assert abs(vol - 12.0) < tol
return
