def test(irad=0.05,
orad=0.6):
'''Torus, rotated in space.
'''
geom = pygmsh.built_in.Geometry()
R = pygmsh.rotation_matrix([1., 0., 0.], np.pi / 2)
geom.add_torus(
irad=irad, orad=orad, lcar=0.03,
x0=[0.0, 0.0, -1.0],
R=R
)
R = pygmsh.rotation_matrix([0., 1., 0.], np.pi / 2)
geom.add_torus(
irad=irad, orad=orad, lcar=0.03,
x0=[0.0, 0.0, 1.0],
variant='extrude_circle'
)
ref = 2 * 2 * np.pi ** 2 * orad * irad ** 2
points, cells, _, _, _ = pygmsh.generate_mesh(geom)
assert np.isclose(compute_volume(points, cells), ref,
rtol=5e-2)
return points, cells
def generate():
geom = pg.Geometry()
# internal radius of torus
irad = 0.15
# external radius of torus
orad = 0.27
#
Z_pos = (irad+orad) * np.r_[
np.ones(8),
-np.ones(8),
np.ones(8),
-np.ones(8)
]
Alpha = np.r_[
np.arange(8) * np.pi/4.0,
np.arange(8) * np.pi/4.0 + np.pi/16.0,
np.arange(8) * np.pi/4.0,
np.arange(8) * np.pi/4.0 + np.pi/16.0
]
A1 = (irad+orad) / np.tan(np.pi/8.0) * \
np.r_[
1.6*np.ones(8),
1.6*np.ones(8),
1.9*np.ones(8),
1.9*np.ones(8)
]
for alpha, a1, z in zip(Alpha, A1, Z_pos):
# Rotate torus to the y-z-plane.
R1 = pg.rotation_matrix([0.0, 1.0, 0.0], 0.5*np.pi)
R2 = pg.rotation_matrix([0.0, 0.0, 1.0], alpha)
x0 = np.array([a1, 0.0, 0.0])
x1 = np.array([0.0, 0.0, z])
# First rotate to y-z-plane, then move out to a1, rotate by angle
# alpha, move up by z.
#
# xnew = R2*(R1*x+x0) + x1
#
geom.add_torus(
irad=irad,
orad=orad,
lcar=0.1,
R=np.dot(R2, R1),
x0=np.dot(R2, x0) + x1
)
geom.add_box(
-1.0, 1.0,
-1.0, 1.0,
-1.0, 1.0,
lcar=0.3
)
return geom.get_code()
def generate():
geom = pg.Geometry()
# internal radius of torus
irad = 0.15
# external radius of torus
orad = 0.27
#
Z_pos = (irad+orad) * np.r_[
np.ones(8),
-np.ones(8),
np.ones(8),
-np.ones(8)
]
Alpha = np.r_[
np.arange(8) * np.pi/4.0,
np.arange(8) * np.pi/4.0 + np.pi/16.0,
np.arange(8) * np.pi/4.0,
np.arange(8) * np.pi/4.0 + np.pi/16.0
]
A1 = (irad+orad) / np.tan(np.pi/8.0) * \
np.r_[
1.6*np.ones(8),
1.6*np.ones(8),
1.9*np.ones(8),
1.9*np.ones(8)
]
for alpha, a1, z in zip(Alpha, A1, Z_pos):
# Rotate torus to the y-z-plane.
R1 = pg.rotation_matrix([0.0, 1.0, 0.0], 0.5*np.pi)
R2 = pg.rotation_matrix([0.0, 0.0, 1.0], alpha)
x0 = np.array([a1, 0.0, 0.0])
x1 = np.array([0.0, 0.0, z])
# First rotate to y-z-plane, then move out to a1, rotate by angle
# alpha, move up by z.
#
# xnew = R2*(R1*x+x0) + x1
#
geom.add_torus(
irad=irad,
orad=orad,
lcar=0.1,
R=np.dot(R2, R1),
x0=np.dot(R2, x0) + x1
)
geom.add_box(
-1.0, 1.0,
-1.0, 1.0,
-1.0, 1.0,
lcar=0.3
)
return geom
def test():
geom = pygmsh.built_in.Geometry()
# internal radius of torus
irad = 0.15
# external radius of torus
orad = 0.27
Z_pos = (irad + orad) * np.concatenate(
[+np.ones(8), -np.ones(8), +np.ones(8), -np.ones(8)])
Alpha = np.concatenate([
np.arange(8) * np.pi / 4.0,
np.arange(8) * np.pi / 4.0 + np.pi / 16.0,
np.arange(8) * np.pi / 4.0,
np.arange(8) * np.pi / 4.0 + np.pi / 16.0
])
# pylint: disable=no-member
A1 = (irad+orad) / np.tan(np.pi/8.0) * \
np.concatenate([
1.6*np.ones(8),
1.6*np.ones(8),
1.9*np.ones(8),
1.9*np.ones(8)
])
for alpha, a1, z in zip(Alpha, A1, Z_pos):
# Rotate torus to the y-z-plane.
R1 = pygmsh.rotation_matrix([0.0, 1.0, 0.0], 0.5 * np.pi)
R2 = pygmsh.rotation_matrix([0.0, 0.0, 1.0], alpha)
x0 = np.array([a1, 0.0, 0.0])
x1 = np.array([0.0, 0.0, z])
# First rotate to y-z-plane, then move out to a1, rotate by angle
# alpha, move up by z.
#
# xnew = R2*(R1*x+x0) + x1
#
geom.add_torus(irad=irad,
orad=orad,
lcar=0.1,
R=np.dot(R2, R1),
x0=np.dot(R2, x0) + x1)
geom.add_box(-1.0, 1.0, -1.0, 1.0, -1.0, 1.0, lcar=0.3)
ref = 15.276653079300184
points, cells, _, _, _ = pygmsh.generate_mesh(geom)
assert abs(compute_volume(points, cells) - ref) < 1.0e-2 * ref
return points, cells
def test():
geom = pygmsh.built_in.Geometry()
# internal radius of torus
irad = 0.15
# external radius of torus
orad = 0.27
Z_pos = (irad + orad) * np.concatenate(
[+np.ones(8), -np.ones(8), +np.ones(8), -np.ones(8)]
)
Alpha = np.concatenate(
[
np.arange(8) * np.pi / 4.0,
np.arange(8) * np.pi / 4.0 + np.pi / 16.0,
np.arange(8) * np.pi / 4.0,
np.arange(8) * np.pi / 4.0 + np.pi / 16.0,
]
)
A1 = (
(irad + orad)
/ np.tan(np.pi / 8.0)
* np.concatenate(
[1.6 * np.ones(8), 1.6 * np.ones(8), 1.9 * np.ones(8), 1.9 * np.ones(8)]
)
)
for alpha, a1, z in zip(Alpha, A1, Z_pos):
# Rotate torus to the y-z-plane.
R1 = pygmsh.rotation_matrix([0.0, 1.0, 0.0], 0.5 * np.pi)
R2 = pygmsh.rotation_matrix([0.0, 0.0, 1.0], alpha)
x0 = np.array([a1, 0.0, 0.0])
x1 = np.array([0.0, 0.0, z])
# First rotate to y-z-plane, then move out to a1, rotate by angle
# alpha, move up by z.
#
# xnew = R2*(R1*x+x0) + x1
#
geom.add_torus(
irad=irad, orad=orad, lcar=0.1, R=np.dot(R2, R1), x0=np.dot(R2, x0) + x1
)
geom.add_box(-1.0, 1.0, -1.0, 1.0, -1.0, 1.0, lcar=0.3)
ref = len(A1) * 2 * np.pi ** 2 * orad * irad ** 2 + 2.0 ** 3
mesh = pygmsh.generate_mesh(geom)
assert np.isclose(compute_volume(mesh), ref, rtol=2e-2)
return mesh
def generate():
'''Pipe with double-ring enclosure, rotated in space.
'''
geom = pg.Geometry()
R = pg.rotation_matrix([1, 0, 0], np.pi/6.0)
geom.add_pipe(
inner_radius=0.3,
outer_radius=0.4,
length=1.0,
R=R,
lcar=0.04
)
# x0 = np.array([0, 0, 0.3])
# geom.add_torus(
# irad=0.05, orad=0.6, lcar=0.1,
# R=R,
# x0=np.dot(R, x0)
# )
# x0 = np.array([0, 0, -0.3])
# geom.add_torus(
# irad=0.05, orad=0.6, lcar=0.1,
# R=R,
# x0=np.dot(R, x0)
# )
return geom
def test():
"""Pipe with double-ring enclosure, rotated in space."""
with pygmsh.geo.Geometry() as geom:
sqrt2on2 = 0.5 * np.sqrt(2.0)
R = pygmsh.rotation_matrix([sqrt2on2, sqrt2on2, 0], np.pi / 6.0)
geom.add_pipe(inner_radius=0.3,
outer_radius=0.4,
length=1.0,
R=R,
mesh_size=0.04)
R = np.array([[0.0, 0.0, 1.0], [0.0, 1.0, 0.0], [1.0, 0.0, 0.0]])
geom.add_pipe(
inner_radius=0.3,
outer_radius=0.4,
length=1.0,
mesh_size=0.04,
R=R,
variant="circle_extrusion",
)
mesh = geom.generate_mesh()
ref = 0.43988203517453256
assert abs(compute_volume(mesh) - ref) < 1.0e-2 * ref
return mesh
def generate():
'''Pipe with double-ring enclosure, rotated in space.
'''
geom = pg.Geometry()
R = pg.rotation_matrix([1, 1, 0], np.pi/6.0)
geom.add_pipe(
inner_radius=0.3,
outer_radius=0.4,
length=1.0,
R=R,
lcar=0.04
)
R = np.array([
[0.0, 0.0, 1.0],
[0.0, 1.0, 0.0],
[1.0, 0.0, 0.0]
])
geom.add_pipe(
inner_radius=0.3,
outer_radius=0.4,
length=1.0,
lcar=0.04,
R=R,
variant='circle_extrusion'
)
return geom
def test():
'''Pipe with double-ring enclosure, rotated in space.
'''
geom = pygmsh.built_in.Geometry()
sqrt2on2 = 0.5*np.sqrt(2.)
R = pygmsh.rotation_matrix([sqrt2on2, sqrt2on2, 0], np.pi/6.0)
geom.add_pipe(
inner_radius=0.3,
outer_radius=0.4,
length=1.0,
R=R,
lcar=0.04
)
R = np.array([
[0.0, 0.0, 1.0],
[0.0, 1.0, 0.0],
[1.0, 0.0, 0.0]
])
geom.add_pipe(
inner_radius=0.3,
outer_radius=0.4,
length=1.0,
lcar=0.04,
R=R,
variant='circle_extrusion'
)
ref = 0.43988203517453256
points, cells, _, _, _ = pygmsh.generate_mesh(geom)
assert abs(compute_volume(points, cells) - ref) < 1.0e-2 * ref
return points, cells
def generate():
'''Pipe with double-ring enclosure, rotated in space.
'''
geom = pg.Geometry()
R = pg.rotation_matrix([1, 0, 0], np.pi/6.0)
geom.add_pipe(
inner_radius=0.3,
outer_radius=0.4,
length=1.0,
R=R,
lcar=0.04
)
# x0 = np.array([0, 0, 0.3])
# geom.add_torus(
# irad=0.05, orad=0.6, lcar=0.1,
# R=R,
# x0=np.dot(R, x0)
# )
# x0 = np.array([0, 0, -0.3])
# geom.add_torus(
# irad=0.05, orad=0.6, lcar=0.1,
# R=R,
# x0=np.dot(R, x0)
# )
return geom.get_code()
def generate():
'''Pipe with double-ring enclosure, rotated in space.
'''
geom = pg.Geometry()
R = pg.rotation_matrix([1, 1, 0], np.pi/6.0)
geom.add_pipe(
inner_radius=0.3,
outer_radius=0.4,
length=1.0,
R=R,
lcar=0.04
)
R = np.array([
[0.0, 0.0, 1.0],
[0.0, 1.0, 0.0],
[1.0, 0.0, 0.0]
])
geom.add_pipe(
inner_radius=0.3,
outer_radius=0.4,
length=1.0,
lcar=0.04,
R=R,
variant='circle_extrusion'
)
return geom, 0.5317080205627609
def test(irad=0.05, orad=0.6):
"""Torus, rotated in space.
"""
geom = pygmsh.built_in.Geometry()
R = pygmsh.rotation_matrix([1.0, 0.0, 0.0], np.pi / 2)
geom.add_torus(irad=irad, orad=orad, lcar=0.03, x0=[0.0, 0.0, -1.0], R=R)
R = pygmsh.rotation_matrix([0.0, 1.0, 0.0], np.pi / 2)
geom.add_torus(
irad=irad, orad=orad, lcar=0.03, x0=[0.0, 0.0, 1.0], variant="extrude_circle"
)
ref = 2 * 2 * np.pi ** 2 * orad * irad ** 2
mesh = pygmsh.generate_mesh(geom)
assert np.isclose(compute_volume(mesh), ref, rtol=5e-2)
return mesh
def test():
geom = pygmsh.built_in.Geometry()
# internal radius of torus
irad = 0.15
# external radius of torus
orad = 0.27
Z_pos = (irad + orad) * np.concatenate(
[+np.ones(8), -np.ones(8), +np.ones(8), -np.ones(8)])
Alpha = np.concatenate([
np.arange(8) * np.pi / 4.0,
np.arange(8) * np.pi / 4.0 + np.pi / 16.0,
np.arange(8) * np.pi / 4.0,
np.arange(8) * np.pi / 4.0 + np.pi / 16.0,
])
A1 = ((irad + orad) / np.tan(np.pi / 8.0) * np.concatenate([
1.6 * np.ones(8), 1.6 * np.ones(8), 1.9 * np.ones(8), 1.9 * np.ones(8)
]))
for alpha, a1, z in zip(Alpha, A1, Z_pos):
# Rotate torus to the y-z-plane.
R1 = pygmsh.rotation_matrix([0.0, 1.0, 0.0], 0.5 * np.pi)
R2 = pygmsh.rotation_matrix([0.0, 0.0, 1.0], alpha)
x0 = np.array([a1, 0.0, 0.0])
x1 = np.array([0.0, 0.0, z])
# First rotate to y-z-plane, then move out to a1, rotate by angle
# alpha, move up by z.
#
# xnew = R2*(R1*x+x0) + x1
#
geom.add_torus(irad=irad,
orad=orad,
lcar=0.1,
R=np.dot(R2, R1),
x0=np.dot(R2, x0) + x1)
geom.add_box(-1.0, 1.0, -1.0, 1.0, -1.0, 1.0, lcar=0.3)
ref = len(A1) * 2 * np.pi**2 * orad * irad**2 + 2.0**3
mesh = pygmsh.generate_mesh(geom)
assert np.isclose(compute_volume(mesh), ref, rtol=2e-2)
return mesh
def test(radius=1.0):
with pygmsh.geo.Geometry() as geom:
R = [
pygmsh.rotation_matrix(np.eye(1, 3, d)[0], theta)
for d, theta in enumerate(np.pi / np.array([2.0, 3.0, 5]))
]
geom.add_circle([7.0, 11.0, 13.0], radius, 0.1, R[0] @ R[1] @ R[2])
ref = np.pi * radius ** 2
mesh = geom.generate_mesh()
assert np.isclose(compute_volume(mesh), ref, rtol=1e-2)
return mesh
def test(radius=1.0):
geom = pygmsh.built_in.Geometry()
R = [
pygmsh.rotation_matrix(np.eye(1, 3, d)[0], theta)
for d, theta in enumerate(np.pi / np.array([2.0, 3.0, 5]))
]
geom.add_circle([7.0, 11.0, 13.0], radius, 0.1, R[0] @ R[1] @ R[2])
ref = np.pi * radius**2
points, cells, _, _, _ = pygmsh.generate_mesh(geom)
assert np.isclose(compute_volume(points, cells), ref, rtol=1e-2)
return points, cells
def test(radius=1.0):
geom = pygmsh.built_in.Geometry()
R = [
pygmsh.rotation_matrix(np.eye(1, 3, d)[0], theta)
for d, theta in enumerate(np.pi / np.array([2.0, 3.0, 5]))
]
geom.add_circle([7.0, 11.0, 13.0], radius, 0.1, R[0] @ R[1] @ R[2])
ref = np.pi * radius ** 2
mesh = pygmsh.generate_mesh(geom)
assert np.isclose(compute_volume(mesh), ref, rtol=1e-2)
return mesh
def test(irad=0.05, orad=0.6):
"""Torus, rotated in space."""
with pygmsh.geo.Geometry() as geom:
R = pygmsh.rotation_matrix([1.0, 0.0, 0.0], np.pi / 2)
geom.add_torus(irad=irad,
orad=orad,
mesh_size=0.03,
x0=[0.0, 0.0, -1.0],
R=R)
mesh = geom.generate_mesh()
ref = 2 * np.pi**2 * orad * irad**2
assert np.isclose(compute_volume(mesh), ref, rtol=5e-2)
return mesh
def generate():
'''Pipe with double-ring enclosure, rotated in space.
'''
geom = pg.Geometry()
sqrt2on2 = 0.5 * np.sqrt(2.)
R = pg.rotation_matrix([sqrt2on2, sqrt2on2, 0], np.pi / 6.0)
geom.add_pipe(inner_radius=0.3,
outer_radius=0.4,
length=1.0,
R=R,
lcar=0.04)
R = np.array([[0.0, 0.0, 1.0], [0.0, 1.0, 0.0], [1.0, 0.0, 0.0]])
geom.add_pipe(inner_radius=0.3,
outer_radius=0.4,
length=1.0,
lcar=0.04,
R=R,
variant='circle_extrusion')
return geom, 0.43988203517453256
def test():
"""Pipe with double-ring enclosure, rotated in space.
"""
geom = pygmsh.built_in.Geometry()
sqrt2on2 = 0.5 * np.sqrt(2.0)
R = pygmsh.rotation_matrix([sqrt2on2, sqrt2on2, 0], np.pi / 6.0)
geom.add_pipe(inner_radius=0.3, outer_radius=0.4, length=1.0, R=R, lcar=0.04)
R = np.array([[0.0, 0.0, 1.0], [0.0, 1.0, 0.0], [1.0, 0.0, 0.0]])
geom.add_pipe(
inner_radius=0.3,
outer_radius=0.4,
length=1.0,
lcar=0.04,
R=R,
variant="circle_extrusion",
)
ref = 0.43988203517453256
mesh = pygmsh.generate_mesh(geom)
assert abs(compute_volume(mesh) - ref) < 1.0e-2 * ref
return mesh
