def test_simple_lloyd(mesh, ref1, ref2, refi):
X, cells = mesh()
X, cells = optimesh.lloyd(X, cells, 1.0e-2, 100, fcc_type="boundary", verbosity=2)
# Test if we're dealing with the mesh we expect.
nc = X.flatten()
norm1 = numpy.linalg.norm(nc, ord=1)
norm2 = numpy.linalg.norm(nc, ord=2)
normi = numpy.linalg.norm(nc, ord=numpy.inf)
tol = 1.0e-12
assert abs(norm1 - ref1) < tol * ref1
assert abs(norm2 - ref2) < tol * ref2
assert abs(normi - refi) < tol * refi
return
def _create_mesh(filename):
poly = dmsh.Polygon(
[
[-295.0, 0.0],
[-160.0, 0.0],
[-50.0, 110.0],
[-50.0, 190.0],
[+50.0, 190.0],
[+50.0, 110.0],
[+160.0, 0.0],
[+295.0, 0.0],
[+405.0, 110.0],
[+405.0, 235.0],
[+200.0, 430.0],
[+170.0, 400.0],
[+355.0, 235.0],
[-355.0, 235.0],
[-170.0, 400.0],
[-200.0, 430.0],
[-405.0, 235.0],
[-405.0, 110.0],
]
)
geo = dmsh.Union(
[
poly,
dmsh.Circle([-295.0, 110.0], 110.0),
dmsh.Circle([+295.0, 110.0], 110.0),
dmsh.Circle([-160.0, 110.0], 110.0),
dmsh.Circle([+160.0, 110.0], 110.0),
]
)
X, cells = dmsh.generate(
geo,
35.0,
# show=True
)
X, cells = optimesh.lloyd(X, cells, 1.0e-3, 100)
X = numpy.column_stack([X[:, 0], X[:, 1], numpy.zeros(X.shape[0])])
meshio.write_points_cells(filename, X, {"triangle": cells})
return
def create_logo():
geom = pygmsh.opencascade.Geometry(characteristic_length_min=0.5,
characteristic_length_max=0.5)
container = geom.add_rectangle([0.0, 0.0, 0.0], 10.0, 10.0)
letter_i = geom.add_rectangle([2.0, 2.0, 0.0], 1.0, 4.5)
i_dot = geom.add_disk([2.5, 7.5, 0.0], 0.6)
disk1 = geom.add_disk([6.25, 4.5, 0.0], 2.5)
disk2 = geom.add_disk([6.25, 4.5, 0.0], 1.5)
letter_o = geom.boolean_difference([disk1], [disk2])
geom.boolean_difference([container], [letter_i, i_dot, letter_o])
X, cells, _, _, _ = pygmsh.generate_mesh(geom)
X, cells = optimesh.lloyd(X, cells["triangle"], 1.0e-3, 1000)
return X, cells
diff1 = geom.boolean_difference([r1], [r2])
r22 = geom.add_rectangle([9.0, 10.0, 0.0], 11.0, 11.0)
inter1 = geom.boolean_intersection([diff1, r22])
r3 = geom.add_rectangle([10.0, 19.5, 0.0], 21.0, 21.0, corner_radius=8.0)
r4 = geom.add_rectangle([10.0, 20.5, 0.0], 20.0, 20.0, corner_radius=7.0)
diff2 = geom.boolean_difference([r3], [r4])
r33 = geom.add_rectangle([20.0, 19.0, 0.0], 11.0, 11.0)
inter2 = geom.boolean_intersection([diff2, r33])
geom.boolean_difference(
[rect1, rect2], [disk1, disk2, rect3, rect4, inter1, inter2]
)
mesh = pygmsh.generate_mesh(geom)
ref = 1082.4470502181903
assert abs(compute_volume(mesh) - ref) < 1.0e-2 * ref
return mesh
if __name__ == "__main__":
import optimesh
mesh = test()
points, cells = optimesh.lloyd(mesh.points, mesh.cells["triangle"], 1.0e-5, 10000)
# # from helpers import plot
# # plot("logo.png", points, {"triangle": cells})
import meshio
meshio.write_points_cells("logo.svg", points, {"triangle": cells})
diff1 = geom.boolean_difference([r1], [r2])
r22 = geom.add_rectangle([9.0, 10.0, 0.0], 11.0, 11.0)
inter1 = geom.boolean_intersection([diff1, r22])
r3 = geom.add_rectangle([10.0, 19.5, 0.0], 21.0, 21.0, corner_radius=8.0)
r4 = geom.add_rectangle([10.0, 20.5, 0.0], 20.0, 20.0, corner_radius=7.0)
diff2 = geom.boolean_difference([r3], [r4])
r33 = geom.add_rectangle([20.0, 19.0, 0.0], 11.0, 11.0)
inter2 = geom.boolean_intersection([diff2, r33])
geom.boolean_difference([rect1, rect2],
[disk1, disk2, rect3, rect4, inter1, inter2])
mesh = pygmsh.generate_mesh(geom)
ref = 1082.4470502181903
assert abs(compute_volume(mesh) - ref) < 1.0e-2 * ref
return mesh
if __name__ == "__main__":
import optimesh
mesh = test()
points, cells = optimesh.lloyd(mesh.points, mesh.cells["triangle"], 1.0e-5,
10000)
# # from helpers import plot
# # plot("logo.png", points, {"triangle": cells})
import meshio
meshio.write_points_cells("logo.svg", points, {"triangle": cells})