def rect_with_refinement(h):
return dmsh.generate(
dmsh.Rectangle(-1.0, 1.0, -1.0, 1.0),
edge_size=lambda x: h + 0.1 * numpy.sqrt(x[0]**2 + x[1]**2),
tol=1.0e-10,
max_steps=max_steps,
)
def test(show=False):
geo = dmsh.Translation(dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0), [1.0, 1.0])
X, cells = dmsh.generate(geo, 0.1, show=show)
ref_norms = [1.7525e+03, 5.5677441324948013e+01, 3.0]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-12)
return
def test(show=False):
geo = dmsh.Rotation(dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0), 0.1 * numpy.pi)
X, cells = dmsh.generate(geo, 0.1, show=show, tol=1.0e-10)
ref_norms = [9.5457720168192884e+02, 3.1356929329612782e+01, 2.2111300269652543e+00]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-12)
return X, cells
def drawPlot(it, ax, geo):
edge_size = 0.25
X, cells = dmsh.generate(geo, edge_size, show=False, max_steps=it, verbose=False)
eps = 1.0e-10
is_inside = geo.dist(X.T) < eps
x, y, z = geo._get_xyz()
ax.contour(x, y, z, levels=[0.0], colors="k")
ax.plot(X[is_inside, 0], X[is_inside, 1], ".")
ax.triplot(X[:, 0], X[:, 1], cells)
pts = []
for x, y in zip(X[:, 0], X[:, 1]):
pts.append((float("{:.5f}".format(x)), float("{:.5f}".format(y))))
triangles = []
for cell in cells:
tria = [pts[cell[0]], pts[cell[1]], pts[cell[2]]]
triangles.append(tria)
res = 0
for tria in triangles:
erg = F3.main(tria[0][0], tria[0][1], tria[1][0], tria[1][1], tria[2][0], tria[2][1])
res += erg
print("\n\n\nIteration #" + str(it) + ": " + '{:.4f}'.format(res))
print("Number of triangles: " + str(len(triangles)))
# Format
ax.axis("square")
ax.title.set_text("Steps: " + str(it) + " | " + str(len(triangles)) + " triangles | " + " size: " + '{:.2f}'.format(res))
def test_rectangle(show=False):
geo = dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0)
X, cells = dmsh.generate(geo, 0.1, show=show)
ref_norms = [9.7542898028694776e02, 3.1710503119308623e01, 2.0]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-12)
return X, cells
def get_mesh(area, contour):
"""
get the points resulting from meshing
Parameters:
----------
area: int, area of small zones
contour:list of tuples containing contour points coordinates
Return:
------
points: numpy.array, coordinates of the points forming the vertices of the mesh
"""
contour = np.array(contour) / 100
esize = area
geo = dmsh.Polygon(contour)
vertices, cells = dmsh.generate(geo, esize)
vertices = (vertices * 100).astype(int)
points = []
for cell in cells:
i, j, k = cell[0], cell[1], cell[2]
point = (vertices[i] + vertices[j] + vertices[k]) / 3
points.append(point.astype(int))
points = np.vstack((points))
return points, vertices, cells
def test(show=False):
geo = dmsh.Scaling(dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0), 2.0)
X, cells = dmsh.generate(geo, 0.1, show=show, tol=1.0e-5)
ref_norms = [7.7120645429243405e03, 1.2509238632152577e02, 4.0]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-12)
return X, cells
def test(show=True):
geo = dmsh.Stretch(dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0), [1.0, 1.0])
X, cells = dmsh.generate(geo, 0.2, show=show, tol=1.0e-3)
ref_norms = [4.3338293115124242e02, 2.3621770543834902e01, 2.6213203435596428e00]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-12)
return X, cells
def test(show=False):
geo = dmsh.Scaling(dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0), 2.0)
X, cells = dmsh.generate(geo, 0.1, show=show, tol=1.0e-5, max_steps=100)
ref_norms = [7.6829959173892494e03, 1.2466061090733828e02, 4.0000000000000000e00]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-7)
return X, cells
def polygonTriangulation(borderPoints, edge_size):
"""
De una lista de puntos de borde crea una triangulacion de tamaño edge_size
del poligono determinado por esos puntos
"""
points, cells = dmsh.generate(dmsh.Polygon(borderPoints), edge_size)
return Triangulation(points, cells)
def test(show=False):
geo = dmsh.Translation(dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0), [1.0, 1.0])
X, cells = dmsh.generate(geo, 0.1, show=show, max_steps=100)
ref_norms = [
1.7524999999999998e03, 5.5612899955332637e01, 3.0000000000000000e00
]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-7)
def test(show=False):
# should both work
geo = [1.0, 1.0] + dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0)
geo = dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0) + [1.0, 1.0]
X, _ = dmsh.generate(geo, 0.1, show=show, max_steps=100)
ref_norms = [1.7524999999999998e03, 5.5612899955332637e01, 3.0000000000000000e00]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-7)
def test_union(show=False):
geo = dmsh.Union(
[dmsh.Circle([-0.5, 0.0], 1.0),
dmsh.Circle([+0.5, 0.0], 1.0)])
X, cells = dmsh.generate(geo, 0.15, show=show, tol=1.0e-10)
ref_norms = [3.0088043884612756e+02, 1.5785099320497183e+01, 1.5]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-12)
return X, cells
def test(show=True):
geo = dmsh.Stretch(dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0), [1.0, 1.0])
X, cells = dmsh.generate(geo, 0.3, show=show, tol=1.0e-3)
ref_norms = [
1.9391178579025609e02, 1.5890693098212086e01, 2.6213203435596428e00
]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-2)
return X, cells
def test(show=False):
geo = dmsh.Rotation(dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0), 0.1 * np.pi)
X, cells = dmsh.generate(geo, 0.1, show=show, tol=1.0e-10, max_steps=100)
ref_norms = [
9.4730152857365385e02, 3.1160562530932285e01, 2.2111300269652543e00
]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-10)
return X, cells
def test_circle(show=True):
geo = dmsh.Circle([0.0, 0.0], 1.0)
X, cells = dmsh.generate(geo, 0.1, show=show)
ref_norms = [
3.2795193920779542e02, 1.4263721858241993e01, 1.0000000000000000e00
]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-12)
return X, cells
def _set_TUB(self, mesh_size):
geo = dmsh.Polygon([[1 / 3, 1 / 3], [1, 0], [0.5, 0.5]])
points, triangles = dmsh.generate(geo, mesh_size)
self._centroids = np.empty((len(triangles), 2))
for i, triangle in enumerate(triangles):
self._centroids[i] = np.mean(points[triangle], axis=0)
tri = Triangulation(points[:, 0], points[:, 1], triangles)
self._trifinder = tri.get_trifinder()
def test_rectangle(show=False):
geo = dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0)
X, cells = dmsh.generate(geo, 0.1, show=show, max_steps=100)
ref_norms = [
9.7172325705673779e02, 3.1615286239175994e01, 2.0000000000000000e00
]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-10)
return X, cells
def test(show=False):
geo = dmsh.Rotation(dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0), 0.1 * numpy.pi)
X, cells = dmsh.generate(geo, 0.1, show=show, tol=1.0e-10)
ref_norms = [
9.5352192763033452e02, 3.1344318120314945e01, 2.2111300269652543e00
]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-10)
return X, cells
def test(show=False):
geo = dmsh.Stretch(dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0), [1.0, 1.0])
X, cells = dmsh.generate(geo, 0.3, show=show, tol=1.0e-3, max_steps=100)
ref_norms = [
1.9006907971528796e02, 1.5666202908904914e01, 2.6213203435596428e00
]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-2)
return X, cells
def test_circle(radius, ref_norms, show=False):
geo = dmsh.Circle([0.0, 0.0], 1.0)
X, cells = dmsh.generate(geo, radius, show=show)
# make sure the origin is part of the mesh
assert numpy.sum(numpy.einsum("ij,ij->i", X, X) < 1.0e-10) == 1
assert_norm_equality(X.flatten(), ref_norms, 1.0e-5)
return X, cells
def sartenTriangulation(size, edge_size):
"""
Triangulación de silueta de una sartén de cocina
"""
c = dmsh.Circle([0, 0], size)
r = dmsh.Rectangle(-2.5*size, -size*0.9, -size/8, size/8)
geo = dmsh.Union([c, r])
points, cells = dmsh.generate(geo, edge_size)
return Triangulation(points, cells)
def test_union(show=False):
geo = dmsh.Union([
dmsh.Rectangle(-1.0, +0.5, -1.0, +0.5),
dmsh.Rectangle(-0.5, +1.0, -0.5, +1.0)
])
X, cells = dmsh.generate(geo, 0.15, show=show, tol=1.0e-10)
ref_norms = [1.7868961429998612e+02, 1.1117047580567053e+01, 1.0]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-12)
return X, cells
def test_pacman(show=False):
geo = dmsh.Difference(
dmsh.Circle([0.0, 0.0], 1.0),
dmsh.Polygon([[0.0, 0.0], [1.5, 0.4], [1.5, -0.4]]),
)
X, cells = dmsh.generate(geo, 0.1, show=show, tol=1.0e-10)
ref_norms = [3.0385105041432689e02, 1.3644964912810719e01, 1.0]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-10)
return X, cells
def test_difference(show=False):
geo = dmsh.Difference(dmsh.Circle([-0.5, 0.0], 1.0),
dmsh.Circle([+0.5, 0.0], 1.0))
X, cells = dmsh.generate(geo, 0.1, show=show)
geo.plot()
ref_norms = [2.9445555e02, 1.58563569e01, 1.499999914e00]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-7)
return X, cells
def test_difference(show=False):
geo = dmsh.Difference(dmsh.Circle([-0.5, 0.0], 1.0),
dmsh.Circle([+0.5, 0.0], 1.0))
X, cells = dmsh.generate(geo, 0.1, show=show)
ref_norms = [
2.9445552442961758e+02, 1.5856356670813716e+01, 1.4999999157880513e+00
]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-9)
return X, cells
def test_circle(radius, ref_norms, show=False):
geo = dmsh.Circle([0.0, 0.0], 1.0)
X, cells = dmsh.generate(geo, radius, show=show, max_steps=100)
meshplex.MeshTri(X, cells).show()
# make sure the origin is part of the mesh
assert np.sum(np.einsum("ij,ij->i", X, X) < 1.0e-6) == 1
assert_norm_equality(X.flatten(), ref_norms, 1.0e-5)
return X, cells
def test_union_rectangles(show=False):
geo = dmsh.Rectangle(-1.0, +0.5, -1.0, +0.5) | dmsh.Rectangle(
-0.5, +1.0, -0.5, +1.0)
X, cells = dmsh.generate(geo, 0.15, show=show, tol=1.0e-5, max_steps=100)
ref_norms = [
1.8417796811774514e02, 1.1277323166424049e01, 1.0000000000000000e00
]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-10)
return X, cells
def test_ellipse(show=False):
geo = dmsh.Ellipse([0.0, 0.0], 2.0, 1.0)
X, cells = dmsh.generate(geo, 0.2, show=show)
geo.plot()
ref_norms = [
2.5108886251367960e02, 1.5652935519539316e01, 1.9890059982474428e00
]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-12)
return X, cells
def test_ellipse(show=False):
geo = dmsh.Ellipse([0.0, 0.0], 2.0, 1.0)
X, cells = dmsh.generate(geo, 0.2, show=show)
geo.plot()
ref_norms = [
2.5108941453435716e02, 1.5652963447587933e01, 1.9890264390440919e00
]
assert_norm_equality(X.flatten(), ref_norms, 2.0e-2)
return X, cells
