def test_balls_intersection():
radius = 1.0
displacement = 0.5
s0 = pygalmesh.Ball([displacement, 0, 0], radius)
s1 = pygalmesh.Ball([-displacement, 0, 0], radius)
u = pygalmesh.Intersection([s0, s1])
a = numpy.sqrt(radius ** 2 - displacement ** 2)
edge_size = 0.1
n = int(2 * numpy.pi * a / edge_size)
circ = [
[0.0, a * numpy.cos(i * 2 * numpy.pi / n), a * numpy.sin(i * 2 * numpy.pi / n)]
for i in range(n)
]
circ.append(circ[0])
mesh = pygalmesh.generate_mesh(
u, feature_edges=[circ], cell_size=0.15, edge_size=edge_size, verbose=False
)
assert abs(max(mesh.points[:, 0]) - (radius - displacement)) < 0.02
assert abs(min(mesh.points[:, 0]) + (radius - displacement)) < 0.02
assert abs(max(mesh.points[:, 1]) - a) < 0.02
assert abs(min(mesh.points[:, 1]) + a) < 0.02
assert abs(max(mesh.points[:, 2]) - a) < 0.02
assert abs(min(mesh.points[:, 2]) + a) < 0.02
vol = sum(helpers.compute_volumes(mesh.points, mesh.cells["tetra"]))
h = radius - displacement
ref_vol = 2 * (h * numpy.pi / 6.0 * (3 * a ** 2 + h ** 2))
assert abs(vol - ref_vol) < 0.1
return
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_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_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