def test_cylinder():
radius = 1.0
z0 = 0.0
z1 = 1.0
edge_length = 0.1
s0 = pygalmesh.Cylinder(z0, z1, radius, edge_length)
mesh = pygalmesh.generate_mesh(s0,
cell_size=0.1,
edge_size=edge_length,
verbose=False)
tol = 1.0e-1
assert abs(max(mesh.points[:, 0]) - radius) < tol
assert abs(min(mesh.points[:, 0]) + radius) < tol
assert abs(max(mesh.points[:, 1]) - radius) < tol
assert abs(min(mesh.points[:, 1]) + radius) < tol
assert abs(max(mesh.points[:, 2]) - z1) < tol
assert abs(min(mesh.points[:, 2]) + z0) < tol
vol = sum(
helpers.compute_volumes(mesh.points, mesh.get_cells_type("tetra")))
ref_vol = numpy.pi * radius * radius * (z1 - z0)
assert abs(vol - ref_vol) < tol
def test_balls_union():
radius = 1.0
displacement = 0.5
s0 = pygalmesh.Ball([displacement, 0, 0], radius)
s1 = pygalmesh.Ball([-displacement, 0, 0], radius)
u = pygalmesh.Union([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]) - radius) < 0.02
assert abs(min(mesh.points[:, 1]) + radius) < 0.02
assert abs(max(mesh.points[:, 2]) - radius) < 0.02
assert abs(min(mesh.points[:, 2]) + radius) < 0.02
vol = sum(helpers.compute_volumes(mesh.points, mesh.cells["tetra"]))
h = radius - displacement
ref_vol = 2 * (4.0 / 3.0 * numpy.pi * radius**3 - h * numpy.pi / 6.0 *
(3 * a**2 + h**2))
assert abs(vol - ref_vol) < 0.1
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_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 ball(h):
s = pygalmesh.Ball([0, 0, 0], 1.0)
# The circumradius of a regular tetrahedron with the given edge_size is sqrt(3 / 8)
# * edge_size ~= 0.61 * edge_size. Relax it a bit and just use h.
mesh = pygalmesh.generate_mesh(s, max_cell_circumradius=h, verbose=False)
return mesh.points, mesh.get_cells_type("tetra")
def test_custom_function():
class Hyperboloid(pygalmesh.DomainBase):
def __init__(self, edge_size):
super(Hyperboloid, self).__init__()
self.z0 = -1.0
self.z1 = 1.0
self.waist_radius = 0.5
self.edge_size = edge_size
return
def eval(self, x):
if self.z0 < x[2] and x[2] < self.z1:
return x[0]**2 + x[1]**2 - (x[2]**2 + self.waist_radius)**2
return 1.0
def get_bounding_sphere_squared_radius(self):
z_max = max(abs(self.z0), abs(self.z1))
r_max = z_max**2 + self.waist_radius
return r_max * r_max + z_max * z_max
def get_features(self):
radius0 = self.z0**2 + self.waist_radius
n0 = int(2 * numpy.pi * radius0 / self.edge_size)
circ0 = [[
radius0 * numpy.cos((2 * numpy.pi * k) / n0),
radius0 * numpy.sin((2 * numpy.pi * k) / n0), self.z0
] for k in range(n0)]
circ0.append(circ0[0])
radius1 = self.z1**2 + self.waist_radius
n1 = int(2 * numpy.pi * radius1 / self.edge_size)
circ1 = [[
radius1 * numpy.cos((2 * numpy.pi * k) / n1),
radius1 * numpy.sin((2 * numpy.pi * k) / n1), self.z1
] for k in range(n1)]
circ1.append(circ1[0])
return [circ0, circ1]
edge_size = 0.12
d = Hyperboloid(edge_size)
pygalmesh.generate_mesh(d,
'out.mesh',
cell_size=0.1,
edge_size=edge_size,
verbose=False)
vertices, cells, _, _, _ = meshio.read('out.mesh')
# TODO check the reference values
tol = 1.0e-1
assert abs(max(vertices[:, 0]) - 1.4) < tol
assert abs(min(vertices[:, 0]) + 1.4) < tol
assert abs(max(vertices[:, 1]) - 1.4) < tol
assert abs(min(vertices[:, 1]) + 1.4) < tol
assert abs(max(vertices[:, 2]) - 1.0) < tol
assert abs(min(vertices[:, 2]) + 1.0) < tol
vol = sum(compute_volumes(vertices, cells['tetra']))
assert abs(vol - 2 * numpy.pi * 47.0 / 60.0) < 0.15
return
import os
import matplotlib.pyplot as plt
import numpy
import pygalmesh
s = pygalmesh.Ball([0, 0, 0], 1.0)
mesh = pygalmesh.generate_mesh(s, cell_size=3.0e-2, verbose=True)
mesh.cells = {"tetra": mesh.cells["tetra"]}
mesh.point_data = {}
mesh.cell_data = {}
print("num points: {}".format(mesh.points.shape[0]))
formats = {
"vtu": ".vtu",
"vtk": ".vtk",
"gmsh": ".msh",
"abaqus": ".inp",
# "ansys": ".ans",
"cgns": ".cgns",
"dolfin-xml": ".xml",
"mdpa": ".mdpa",
"med": ".med",
"medit": ".mesh",
"moab": ".h5m",
# "obj": ".obj",
# "ply": ".ply",
# "stl": ".stl",
"nastran": ".bdf",
# "off": ".off",