def test_angles():
# 3-4-5 triangle
points = numpy.array([[0.0, 0.0, 0.0], [3.0, 0.0, 0.0], [0.0, 4.0, 0.0]])
cells = numpy.array([[0, 1, 2]])
mesh = meshplex.MeshTri(points, cells)
tol = 1.0e-14
assert near_equal(
mesh.angles,
[[numpy.pi / 2], [numpy.arcsin(4.0 / 5.0)], [numpy.arcsin(3.0 / 5.0)]],
tol,
)
# 30-60-90 triangle
a = 1.0
points = numpy.array(
[[0.0, 0.0, 0.0], [a / 2, 0.0, 0.0], [0.0, a / 2 * numpy.sqrt(3.0), 0.0]]
)
cells = numpy.array([[0, 1, 2]])
mesh = meshplex.MeshTri(points, cells)
ic = mesh.angles / numpy.pi * 180
assert near_equal(ic, [[90], [60], [30]], tol)
return
def test_degenerate_flip():
# almost degenerate
points = [
[0.0, 0.0],
[0.5, -1.0e-5],
[1.0, 0.0],
[0.5, 0.5],
]
cells = [[0, 2, 1], [0, 2, 3]]
mesh = meshplex.MeshTri(points, cells)
num_flips = mesh.flip_until_delaunay()
assert num_flips == 1
ref = np.array([[1, 0, 3], [1, 3, 2]])
assert np.all(mesh.cells("points") == ref)
# make sure the same thing happens if the cell is exactly degenerate
points = [
[0.0, 0.0],
[0.5, 0.0],
[1.0, 0.0],
[0.5, 0.5],
]
cells = [[0, 2, 1], [0, 2, 3]]
mesh = meshplex.MeshTri(points, cells)
num_flips = mesh.flip_until_delaunay()
assert num_flips == 1
ref = np.array([[1, 0, 3], [1, 3, 2]])
assert np.all(mesh.cells("points") == ref)
def test_flip_delaunay():
filename = download_mesh("pacman.msh", "2da8ff96537f844a95a83abb48471b6a")
mesh = meshio.read(filename)
numpy.random.seed(123)
mesh.points[:, :2] += 5.0e-2 * numpy.random.rand(*mesh.points[:, :2].shape)
mesh = meshplex.MeshTri(mesh.points, mesh.cells["triangle"])
assert mesh.num_delaunay_violations() == 16
mesh.flip_until_delaunay()
assert mesh.num_delaunay_violations() == 0
# Assert edges_cells integrity
for cell_gid, edge_gids in enumerate(mesh.cells["edges"]):
for edge_gid in edge_gids:
num_adj_cells, edge_id = mesh._edge_gid_to_edge_list[edge_gid]
assert cell_gid in mesh._edges_cells[num_adj_cells][edge_id]
new_cells = mesh.cells["nodes"].copy()
new_coords = mesh.node_coords.copy()
# Assert that some key values are updated properly
mesh2 = meshplex.MeshTri(new_coords, new_cells)
assert numpy.all(mesh.idx_hierarchy == mesh2.idx_hierarchy)
tol = 1.0e-15
assert near_equal(mesh.half_edge_coords, mesh2.half_edge_coords, tol)
assert near_equal(mesh.cell_volumes, mesh2.cell_volumes, tol)
assert near_equal(mesh.ei_dot_ej, mesh2.ei_dot_ej, tol)
return
def test_flip_delaunay():
mesh = meshio.read(this_dir / "meshes" / "pacman.vtk")
numpy.random.seed(123)
mesh.points[:, :2] += 5.0e-2 * numpy.random.rand(*mesh.points[:, :2].shape)
mesh = meshplex.MeshTri(mesh.points, mesh.get_cells_type("triangle"))
assert mesh.num_delaunay_violations() == 16
mesh.flip_until_delaunay()
assert mesh.num_delaunay_violations() == 0
# Assert edges_cells integrity
for cell_gid, edge_gids in enumerate(mesh.cells["edges"]):
for edge_gid in edge_gids:
num_adj_cells, edge_id = mesh._edge_gid_to_edge_list[edge_gid]
assert cell_gid in mesh._edges_cells[num_adj_cells][edge_id]
new_cells = mesh.cells["nodes"].copy()
new_coords = mesh.node_coords.copy()
# Assert that some key values are updated properly
mesh2 = meshplex.MeshTri(new_coords, new_cells)
assert numpy.all(mesh.idx_hierarchy == mesh2.idx_hierarchy)
tol = 1.0e-15
assert near_equal(mesh.half_edge_coords, mesh2.half_edge_coords, tol)
assert near_equal(mesh.cell_volumes, mesh2.cell_volumes, tol)
assert near_equal(mesh.ei_dot_ej, mesh2.ei_dot_ej, tol)
def test_set_points():
points = np.array([[0.0, 0.0], [1.0, 0.0], [0.0, 1.0]])
cells = np.array([[0, 1, 2]])
mesh = meshplex.MeshTri(points, cells)
mesh.set_points([0.1, 0.1], [0])
ref = mesh.cell_volumes.copy()
mesh2 = meshplex.MeshTri(mesh.points, mesh.cells("points"))
assert np.all(np.abs(ref - mesh2.cell_volumes) < 1.0e-10)
def setup(n):
radius = 1.0
k = np.arange(n)
boundary_pts = radius * np.column_stack(
[np.cos(2 * np.pi * k / n),
np.sin(2 * np.pi * k / n)])
# Compute the number of interior points such that all triangles can be somewhat
# equilateral.
edge_length = 2 * np.pi * radius / n
domain_area = np.pi - n * (radius**2 / 2 *
(edge_length - np.sin(edge_length)))
cell_area = np.sqrt(3) / 4 * edge_length**2
target_num_cells = domain_area / cell_area
# Euler:
# 2 * num_points - num_boundary_edges - 2 = num_cells
# <=>
# num_interior_points ~= 0.5 * (num_cells + num_boundary_edges) + 1 - num_boundary_points
m = int(0.5 * (target_num_cells + n) + 1 - n)
# generate random points in circle;
# <https://mathworld.wolfram.com/DiskPointPicking.html>
for seed in range(0, 255):
np.random.seed(seed)
r = np.random.rand(m)
alpha = 2 * np.pi * np.random.rand(m)
interior_pts = np.column_stack(
[np.sqrt(r) * np.cos(alpha),
np.sqrt(r) * np.sin(alpha)])
pts = np.concatenate([boundary_pts, interior_pts])
tri = Delaunay(pts)
# Make sure there are exactly `n` boundary points
mesh0 = meshplex.MeshTri(pts, tri.simplices)
mesh1 = meshplex.MeshTri(pts, tri.simplices)
if np.sum(mesh0.is_boundary_point) == n:
break
mesh0.create_edges()
mesh1.create_edges()
num_interior_edges = np.sum(mesh0.is_interior_edge)
idx = random.sample(range(num_interior_edges), n // 10)
print(num_interior_edges, len(idx), len(idx) / num_interior_edges)
# # move interior points a little bit such that we have edges to flip
# max_step = np.min(mesh.cell_inradius) / 2
# mesh.points = mesh.points + max_step * np.random.rand(*mesh.points.shape)
# print(mesh.num_delaunay_violations)
return mesh0, mesh1, idx
def test_update_point_coordinates():
mesh = meshio.read(this_dir / ".." / "meshes" / "pacman.vtu")
assert np.all(np.abs(mesh.points[:, 2]) < 1.0e-15)
mesh1 = meshplex.MeshTri(mesh.points, mesh.get_cells_type("triangle"))
np.random.seed(123)
X2 = mesh.points + 1.0e-2 * np.random.rand(*mesh.points.shape)
mesh2 = meshplex.MeshTri(X2, mesh.get_cells_type("triangle"))
mesh1.points = X2
tol = 1.0e-12
assert is_near_equal(mesh1.cell_volumes, mesh2.cell_volumes, tol)
def test_degenerate_small2(h):
points = numpy.array([[0, 0, 0], [1, 0, 0], [0.5, h, 0.0], [0.5, -h, 0.0]])
cells = numpy.array([[0, 1, 2], [0, 1, 3]])
mesh = meshplex.MeshTri(points, cells)
tol = 1.0e-11
# ce_ratios
alpha = h - 1.0 / (4 * h)
beta = 1.0 / (4 * h)
assert near_equal(mesh.ce_ratios_per_interior_edge, [alpha], tol)
alpha2 = (h - 1.0 / (4 * h)) / 2
assert near_equal(mesh.ce_ratios,
[[beta, beta], [beta, beta], [alpha2, alpha2]], tol)
# control volumes
alpha1 = 0.125 * (3 * h - 1.0 / (4 * h))
alpha2 = 0.125 * (h + 1.0 / (4 * h))
assert near_equal(mesh.control_volumes, [alpha1, alpha1, alpha2, alpha2],
tol)
# circumcenters
assert near_equal(mesh.cell_circumcenters,
[[0.5, -12.495, 0.0], [0.5, +12.495, 0.0]], tol)
# cell volumes
assert near_equal(mesh.cell_volumes, [0.5 * h, 0.5 * h], tol)
assert mesh.num_delaunay_violations() == 1
return
def get_disk_mesh(k):
import meshzoo
points, cells = meshzoo.disk(6, k + 1)
out = meshplex.MeshTri(points, cells)
# out.show()
return out
def test_jacobian():
from test_ginzburg_landau import GinzburgLandau
a = 10.0
n = 10
points, cells = meshzoo.rectangle(-a / 2, a / 2, -a / 2, a / 2, n, n)
mesh = meshplex.MeshTri(points, cells)
gl = GinzburgLandau(mesh)
glr = GinzburgLandauReal(mesh)
n = points.shape[0]
numpy.random.seed(123)
for _ in range(10):
psi = numpy.random.rand(n) + 1j * numpy.random.rand(n)
mu = numpy.random.rand(1)[0]
jac0 = gl.jacobian(psi, mu)
jac1 = glr.jacobian(to_real(psi), mu)
for _ in range(10):
phi = numpy.random.rand(n) + 1j * numpy.random.rand(n)
out0 = (jac0 * phi) * mesh.control_volumes
out1 = to_complex(jac1 * to_real(phi))
assert numpy.all(numpy.abs(out0 - out1) < 1.0e-12)
def test_jacobian():
from test_ginzburg_landau import GinzburgLandau
a = 10.0
n = 10
points, cells = meshzoo.rectangle_tri((-a / 2, -a / 2), (a / 2, a / 2), n)
# add column with zeros for magnetic potential
points = np.column_stack([points, np.zeros(points.shape[0])])
mesh = meshplex.MeshTri(points, cells)
gl = GinzburgLandau(mesh)
glr = GinzburgLandauReal(mesh)
n = points.shape[0]
np.random.seed(123)
for _ in range(10):
psi = np.random.rand(n) + 1j * np.random.rand(n)
mu = np.random.rand(1)[0]
jac0 = gl.jacobian(psi, mu)
jac1 = glr.jacobian(to_real(psi), mu)
for _ in range(10):
phi = np.random.rand(n) + 1j * np.random.rand(n)
out0 = (jac0 * phi) * mesh.control_volumes
out1 = to_complex(jac1 * to_real(phi))
assert np.all(np.abs(out0 - out1) < 1.0e-12)
def gosplElev(coords, cells, elev, gmesh, visvtk=False):
Gmesh = meshplex.MeshTri(coords, cells)
s = Gmesh.idx_hierarchy.shape
a = np.sort(Gmesh.idx_hierarchy.reshape(s[0], -1).T)
if meshplex.__version__ >= "0.16.0":
Gmesh.edges = {"points": np.unique(a, axis=0)}
ngbNbs, ngbID = definegtin(len(coords), Gmesh.cells("points"),
Gmesh.edges["points"])
elif meshplex.__version__ >= "0.14.0":
Gmesh.edges = {"points": np.unique(a, axis=0)}
ngbNbs, ngbID = definegtin(len(coords), Gmesh.cells["points"],
Gmesh.edges["points"])
else:
Gmesh.edges = {"nodes": np.unique(a, axis=0)}
ngbNbs, ngbID = definegtin(len(coords), Gmesh.cells["nodes"],
Gmesh.edges["nodes"])
np.savez_compressed(gmesh,
v=coords,
c=cells,
n=ngbID[:, :8].astype(int),
z=elev)
if visvtk:
paleovtk = gmesh + ".vtk"
vis_mesh = meshio.Mesh(coords, {"triangle": cells},
point_data={"z": elev})
meshio.write(paleovtk, vis_mesh)
print("Writing VTK file {}".format(paleovtk))
return
def run_SeismicMesh(ef, HMIN=75.0):
bbox = (-12000, 0.0, 0.0, 67000.0)
rectangle = Rectangle(bbox)
t1 = time.time()
points, cells = generate_mesh(
domain=rectangle,
edge_length=ef,
h0=HMIN,
max_iter=25,
delta_t=0.3,
)
points, cells = geometry.delete_boundary_entities(points,
cells,
dim=2,
min_qual=0.10)
elapsed = time.time() - t1
# meshio.write_points_cells(
# "BP2004_sm.vtk",
# points,
# [("triangle", cells)],
# file_format="vtk",
# )
plex = meshplex.MeshTri(points, cells)
quality = numpy.abs(plex.cell_quality)
num_cells = len(cells)
num_vertices = len(points)
return quality, elapsed, num_vertices, num_cells
def test_update_node_coordinates():
mesh = meshio.read(this_dir / "meshes" / "pacman.vtk")
assert numpy.all(numpy.abs(mesh.points[:, 2]) < 1.0e-15)
mesh1 = meshplex.MeshTri(mesh.points, mesh.get_cells_type("triangle"))
numpy.random.seed(123)
X2 = mesh.points + 1.0e-2 * numpy.random.rand(*mesh.points.shape)
mesh2 = meshplex.MeshTri(X2, mesh.get_cells_type("triangle"))
mesh1.node_coords = X2
mesh1.update_values()
tol = 1.0e-12
assert near_equal(mesh1.ei_dot_ej, mesh2.ei_dot_ej, tol)
assert near_equal(mesh1.cell_volumes, mesh2.cell_volumes, tol)
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_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():
class EnergyEdgeKernel:
def __init__(self):
self.subdomains = [None]
return
def eval(self, mesh, cell_mask):
edge_ce_ratio = mesh.ce_ratios[..., cell_mask]
beta = 1.0
return numpy.array([
[edge_ce_ratio, -edge_ce_ratio * numpy.exp(1j * beta)],
[-edge_ce_ratio * numpy.exp(-1j * beta), edge_ce_ratio],
])
vertices, cells = meshzoo.rectangle(0.0, 2.0, 0.0, 1.0, 101, 51)
mesh = meshplex.MeshTri(vertices, cells)
matrix = pyfvm.get_fvm_matrix(mesh, [EnergyEdgeKernel()], [], [], [])
rhs = mesh.control_volumes.copy()
sa = pyamg.smoothed_aggregation_solver(matrix, smooth="energy")
u = sa.solve(rhs, tol=1e-10)
# Cannot write complex data ot VTU; split real and imaginary parts first.
# <http://stackoverflow.com/a/38902227/353337>
mesh.write("out.vtk", point_data={"u": u.view("(2,)float")})
return
def test_flip_same_edge_twice():
points = numpy.array([[0.0, +0.0, 0.0], [0.5, -0.1, 0.0], [1.0, +0.0, 0.0],
[0.5, +0.1, 0.0]])
cells = numpy.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
# Assert edges_cells integrity
for cell_gid, edge_gids in enumerate(mesh.cells["edges"]):
for edge_gid in edge_gids:
num_adj_cells, edge_id = mesh._edge_gid_to_edge_list[edge_gid]
assert cell_gid in mesh._edges_cells[num_adj_cells][edge_id]
new_points = numpy.array([[0.0, +0.0, 0.0], [0.1, -0.5, 0.0],
[0.2, +0.0, 0.0], [0.1, +0.5, 0.0]])
mesh.node_coords = new_points
mesh.update_values()
assert mesh.num_delaunay_violations() == 1
mesh.flip_until_delaunay()
assert mesh.num_delaunay_violations() == 0
mesh.show()
return
def test_flip_delaunay_near_boundary_preserve_boundary_count():
# This test is to make sure meshplex preserves the boundary node count.
points = numpy.array([
[+0.0, +0.0, 0.0],
[+0.5, -0.5, 0.0],
[+0.5, +0.5, 0.0],
[+0.0, +0.6, 0.0],
[-0.5, +0.5, 0.0],
[-0.5, -0.5, 0.0],
])
cells = numpy.array([[0, 1, 2], [0, 2, 4], [0, 4, 5], [0, 5, 1], [2, 3,
4]])
mesh = meshplex.MeshTri(points, cells)
mesh.create_edges()
assert mesh.num_delaunay_violations() == 1
mesh.mark_boundary()
is_boundary_node_ref = [False, True, True, True, True, True]
assert numpy.array_equal(mesh.is_boundary_node, is_boundary_node_ref)
mesh.flip_until_delaunay()
mesh.mark_boundary()
assert numpy.array_equal(mesh.is_boundary_node, is_boundary_node_ref)
return
def test_shell():
points = numpy.array(
[
[+0.0, +0.0, +1.0],
[+1.0, +0.0, +0.0],
[+0.0, +1.0, +0.0],
[-1.0, +0.0, +0.0],
[+0.0, -1.0, +0.0],
]
)
cells = numpy.array([[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 1, 4]])
mesh = meshplex.MeshTri(points, cells)
tol = 1.0e-14
ce_ratios = 0.5 / numpy.sqrt(3.0) * numpy.ones((4, 3))
assert near_equal(mesh.ce_ratios.T, ce_ratios, tol)
cv = numpy.array([2.0, 1.0, 1.0, 1.0, 1.0]) / numpy.sqrt(3.0)
assert near_equal(mesh.control_volumes, cv, tol)
cell_vols = numpy.sqrt(3.0) / 2.0 * numpy.ones(4)
assert near_equal(mesh.cell_volumes, cell_vols, tol)
assert mesh.num_delaunay_violations() == 0
return
def test():
class D1(Subdomain):
def is_inside(self, x):
return x[1] < 0.5
is_boundary_only = True
class Poisson:
def apply(self, u):
return (integrate(lambda x: -n_dot_grad(u(x)), dS) +
integrate(lambda x: 3.0, dGamma) -
integrate(lambda x: 1.0, dV))
def dirichlet(self, u):
return [(u, D1())]
vertices, cells = meshzoo.rectangle(0.0, 1.0, 0.0, 1.0, 51, 51)
mesh = meshplex.MeshTri(vertices, cells)
matrix, rhs = pyfvm.discretize_linear(Poisson(), mesh)
u = linalg.spsolve(matrix, rhs)
mesh.write("out.vtk", point_data={"u": u})
return
def test():
class Bratu:
def apply(self, u):
return integrate(lambda x: -n_dot_grad(u(x)), dS) - integrate(
lambda x: 2.0 * exp(u(x)), dV)
def dirichlet(self, u):
return [(u, Boundary())]
vertices, cells = meshzoo.rectangle(0.0, 2.0, 0.0, 1.0, 101, 51)
mesh = meshplex.MeshTri(vertices, cells)
f, jac_u = pyfvm.discretize(Bratu(), mesh)
def jacobian_solver(u0, rhs):
from scipy.sparse import linalg
jac = jac_u.get_linear_operator(u0)
return linalg.spsolve(jac, rhs)
u0 = numpy.zeros(len(vertices))
u = pyfvm.newton(lambda u: f.eval(u), jacobian_solver, u0)
# import scipy.optimize
# u = scipy.optimize.newton_krylov(f_eval, u0)
mesh.write("out.vtk", point_data={"u": u})
return
def run_gmsh(ef, HMIN=75.0):
with pygmsh.geo.Geometry() as geom:
geom.add_polygon([
[-12e3, 0.0],
[-12e3, 67e3],
[0.0, 67e3],
[0.0, 0.0],
])
geom.set_mesh_size_callback(lambda dim, tag, x, y, z:
(ef.eval([x, y])))
gmsh.option.setNumber("Mesh.Algorithm", 5)
gmsh.option.setNumber("Mesh.CharacteristicLengthExtendFromBoundary", 0)
t1 = time.time()
mesh = geom.generate_mesh()
elapsed = time.time() - t1
points = mesh.points
cells = mesh.cells[1].data
num_cells = len(cells)
num_vertices = len(points)
plex = meshplex.MeshTri(points, cells)
quality = numpy.abs(plex.cell_quality)
# mesh.write("BP2004_gmsh.vtk")
return quality, elapsed, num_vertices, num_cells
def compute(fun, h):
tic = time.time()
points, cells = fun(h)
toc = time.time()
if cells.shape[1] == 3:
mesh = meshplex.MeshTri(points, cells)
else:
assert cells.shape[1] == 4
mesh = meshplex.MeshTetra(points, cells)
if fun.__name__ == "sphere" or numpy.min(mesh.q_radius_ratio) < 1.0e-5:
num_poisson_steps = numpy.nan
else:
poisson_tol = 1.0e-10
# num_poisson_steps = get_poisson_steps_dolfin(points, cells, poisson_tol)
num_poisson_steps = get_poisson_steps_scikitfem(points, cells, poisson_tol)
return {
"time": toc - tic,
# convert to python float types to JSON compatibility
"quality_min": float(numpy.min(mesh.q_radius_ratio)),
"quality_avg": float(numpy.average(mesh.q_radius_ratio)),
"energy": energy(mesh),
"num_nodes": mesh.points.shape[0],
"num_poisson_steps": num_poisson_steps,
}
def test_regular_tri_order():
points = numpy.array([[0.0, 1.0, 0.0], [0.0, 0.0, 0.0], [1.0, 0.0, 0.0]])
cells = numpy.array([[0, 1, 2]])
mesh = meshplex.MeshTri(points, cells)
assert all((mesh.cells["nodes"] == [0, 1, 2]).flat)
tol = 1.0e-14
# ce_ratios
assert near_equal(mesh.ce_ratios.T, [0.5, 0.0, 0.5], tol)
# control volumes
assert near_equal(mesh.control_volumes, [0.125, 0.25, 0.125], tol)
# cell volumes
assert near_equal(mesh.cell_volumes, [0.5], tol)
# circumcenters
assert near_equal(mesh.cell_circumcenters, [0.5, 0.5, 0.0], tol)
# centroids
assert near_equal(
mesh.control_volume_centroids,
[[1.0 / 6.0, 2.0 / 3.0, 0.0], [0.25, 0.25, 0.0],
[2.0 / 3.0, 1.0 / 6.0, 0.0]],
tol,
)
assert mesh.num_delaunay_violations() == 0
return
def test_regular_tri2(a):
points = (numpy.array([
[-0.5, -0.5 * numpy.sqrt(3.0), 0],
[-0.5, +0.5 * numpy.sqrt(3.0), 0],
[1, 0, 0],
]) / numpy.sqrt(3) * a)
cells = numpy.array([[0, 1, 2]])
mesh = meshplex.MeshTri(points, cells)
tol = 1.0e-14
# ce_ratios
val = 0.5 / numpy.sqrt(3.0)
assert near_equal(mesh.ce_ratios, [val, val, val], tol)
# control volumes
vol = numpy.sqrt(3.0) / 4 * a**2
assert near_equal(mesh.control_volumes, [vol / 3.0, vol / 3.0, vol / 3.0],
tol)
# cell volumes
assert near_equal(mesh.cell_volumes, [vol], tol)
# circumcenters
assert near_equal(mesh.cell_circumcenters, [0.0, 0.0, 0.0], tol)
return
def run_SeismicMesh(ef, HMIN=75.0):
bbox = (-12000.0, 0.0, 0.0, 67000.0)
rectangle = Rectangle(bbox)
t1 = time.time()
points, cells = generate_mesh(
domain=rectangle,
edge_length=ef,
verbose=0,
max_iter=25,
)
elapsed = time.time() - t1
# import meshio
# meshio.write_points_cells(
# "BP2004_sm" + str(HMIN) + ".vtk",
# points,
# [("triangle", cells)],
# file_format="vtk",
# )
plex = meshplex.MeshTri(points, cells)
quality = numpy.abs(plex.cell_quality)
num_cells = len(cells)
num_vertices = len(points)
return quality, elapsed, num_vertices, num_cells
def test_degenerate_small0b(h):
points = numpy.array([[0, 0, 0], [1, 0, 0], [0.5, h, 0.0]])
cells = numpy.array([[0, 1, 2]])
mesh = meshplex.MeshTri(points, cells)
tol = 1.0e-14
# edge lengths
el = numpy.sqrt(0.5**2 + h**2)
assert near_equal(mesh.edge_lengths.T, [el, el, 1.0], tol)
# ce_ratios
ce0 = 0.5 / h * (h**2 - 0.25)
ce12 = 0.25 / h
assert near_equal(mesh.ce_ratios.T, [ce12, ce12, ce0], tol)
# control volumes
cv12 = 0.25 * (1.0**2 * ce0 + (0.25 + h**2) * ce12)
cv0 = 0.5 * (0.25 + h**2) * ce12
assert near_equal(mesh.control_volumes, [cv12, cv12, cv0], tol)
# cell volumes
assert near_equal(mesh.cell_volumes, [0.5 * h], tol)
# circumcenters
assert near_equal(mesh.cell_circumcenters, [0.5, 0.375, 0.0], tol)
assert mesh.num_delaunay_violations() == 0
return
def run_SeismicMesh(HMIN=0.01):
bbox = (-1.0, 1.0, -1.0, 1.0)
disk = SeismicMesh.geometry.Disk([0, 0], 1)
def fh(x):
return numpy.array([HMIN] * len(x))
t1 = time.time()
points, cells = SeismicMesh.generate_mesh(
bbox=bbox,
h0=HMIN,
domain=disk,
edge_length=fh,
max_iter=25,
delta_t=0.3,
)
elapsed = time.time() - t1
# meshio.write_points_cells(
# "SeismicMesh_circle.vtk",
# points,
# [("triangle", cells)],
# )
plex = meshplex.MeshTri(points, cells)
quality = numpy.abs(plex.cell_quality)
num_cells = len(cells)
num_vertices = len(points)
return quality, elapsed, num_vertices, num_cells
def circle_random2(n, radius, seed=0):
"""Boundary points are random, too."""
# generate random points in circle; <https://mathworld.wolfram.com/DiskPointPicking.html>
np.random.seed(seed)
r = np.random.rand(n)
alpha = 2 * np.pi * np.random.rand(n)
pts = np.column_stack([np.sqrt(r) * np.cos(alpha), np.sqrt(r) * np.sin(alpha)])
tri = Delaunay(pts)
# Make sure there are exactly `n` boundary points
mesh = meshplex.MeshTri(pts, tri.simplices)
# inflate the mesh such that the boundary points average around the radius
boundary_pts = pts[mesh.is_boundary_point]
dist = np.sqrt(np.einsum("ij,ij->i", boundary_pts, boundary_pts))
avg_dist = np.sum(dist) / len(dist)
mesh.points = pts / avg_dist
# boundary_pts = pts[mesh.is_boundary_point]
# dist = np.sqrt(np.einsum("ij,ij->i", boundary_pts, boundary_pts))
# avg_dist = np.sum(dist) / len(dist)
# print(avg_dist)
# now move all boundary points to the circle
# bpts = pts[mesh.is_boundary_point]
# pts[mesh.is_boundary_point] = (
# bpts.T / np.sqrt(np.einsum("ij,ij->i", bpts, bpts))
# ).T
# bpts = pts[mesh.is_boundary_point]
# print(np.sqrt(np.einsum("ij,ij->i", bpts, bpts)))
# mesh = meshplex.MeshTri(pts, tri.simplices)
# mesh.show()
return pts, tri.simplices
