def test_scalar_contour_direction():
""" Test the direction of scalar_contour and the field direction
generated by the scalar contour
"""
mesh, scalars = setup_contour_input()
N = 10
polys, vals = contour.scalar_contour(mesh,
scalars,
N_contours=N,
return_values=True)
compare_contour_direction_to_rotated_gradient(mesh, scalars, polys[-1])
test_point = np.array([[0, 0, 1]])
compare_magnetic_field_directions(mesh, scalars, polys, test_point)
CU1 = coil.U_coupling(points) CU2 = shieldcoil.U_coupling(points) B1 = CB1 @ coil.s B2 = CB2 @ shieldcoil.s U1 = CU1 @ coil.s U2 = CU2 @ shieldcoil.s #%% # Now, plot the field streamlines and scalar potential from bfieldtools.contour import scalar_contour cc1 = scalar_contour(mesh1, mesh1.vertices[:, 2], contours=[-0.001]) cc2 = scalar_contour(mesh2, mesh2.vertices[:, 2], contours=[-0.001]) cx10 = cc1[0][:, 1] cy10 = cc1[0][:, 0] cx20 = cc2[0][:, 1] cy20 = cc2[0][:, 0] cx11 = np.vstack(cc1[1:])[:, 1] cy11 = np.vstack(cc1[1:])[:, 0] cx21 = np.vstack(cc2[1:])[:, 1] cy21 = np.vstack(cc2[1:])[:, 0] B = (B1.T + B2.T)[:2].reshape(2, x.shape[0], y.shape[0]) lw = np.sqrt(B[0]**2 + B[1]**2) lw = 2 * np.log(lw / np.max(lw) * np.e + 1.1)
coil.s, prob = optimize_streamfunctions(
coil,
[target_spec, stray_spec],
objective=(0, 1),
solver="MOSEK",
solver_opts={"mosek_params": {
mosek.iparam.num_threads: 8
}},
)
#%%
# Plot coil windings and target points
N_contours = 6
loops = scalar_contour(coil.mesh, coil.s.vert, N_contours=N_contours)
if PLOT:
f = mlab.figure(None,
bgcolor=(1, 1, 1),
fgcolor=(0.5, 0.5, 0.5),
size=(650, 750))
mlab.clf()
plot_3d_current_loops(loops, colors="auto", figure=f)
# B_target = coil.B_coupling(target_points) @ coil.s
# mlab.quiver3d(*target_points.T, *B_target.T, mode="arrow", scale_factor=1)
f.scene.isometric_view()
s1 = StreamFunction(I1inner, coil1) s2 = StreamFunction(I2inner, coil2) # s = mlab.triangular_mesh(*mesh1.vertices.T, mesh1.faces, scalars=I1) # s.enable_contours=True # s = mlab.triangular_mesh(*mesh2.vertices.T, mesh2.faces, scalars=I2) # s.enable_contours=True B1 = CB1 @ s1 B2 = CB2 @ s2 U1 = CU1 @ s1 U2 = CU2 @ s2 #%% Plot cc1 = scalar_contour(mesh1, mesh1.vertices[:, 2], contours=[-0.001]) cc2 = scalar_contour(mesh2, mesh2.vertices[:, 2], contours=[-0.001]) cx10 = cc1[0][:, 1] cy10 = cc1[0][:, 0] cx20 = cc2[0][:, 1] cy20 = cc2[0][:, 0] cx11 = cc1[1][:, 1] cy11 = cc1[1][:, 0] cx21 = cc2[1][:, 1] cy21 = cc2[1][:, 0] B = (B1.T + B2.T)[:2].reshape(2, x.shape[0], y.shape[0]) lw = np.sqrt(B[0]**2 + B[1]**2) lw = 2 * np.log(lw / np.max(lw) * np.e + 1.1)
[target_spec] + induction_spec,
objective="minimum_inductive_energy",
solver="MOSEK",
solver_opts={"mosek_params": {
mosek.iparam.num_threads: 8
}},
)
from bfieldtools.mesh_conductor import StreamFunction
shield.induced_s = StreamFunction(shield.M_coupling @ coil.s, shield)
#%%
# Plot coil windings and target points
loops = scalar_contour(coil.mesh, coil.s.vert, N_contours=6)
# loops = [simplify_contour(loop, min_edge=1e-2, angle_threshold=2e-2, smooth=True) for loop in loops]
# loops = [loop for loop in loops if loop is not None]
if PLOT:
f = mlab.figure(None,
bgcolor=(1, 1, 1),
fgcolor=(0.5, 0.5, 0.5),
size=(600, 500))
mlab.clf()
plot_3d_current_loops(loops, colors="auto", figure=f, tube_radius=0.005)
B_target = coil.B_coupling(target_points) @ coil.s
import mosek
coil.s, coil.prob = optimize_streamfunctions(
coil,
[target_spec],
objective="minimum_inductive_energy",
solver="MOSEK",
solver_opts={"mosek_params": {
mosek.iparam.num_threads: 8
}},
)
#%%
# Plot coil windings and target points
loops = scalar_contour(coil.mesh, coil.s.vert, N_contours=10)
f = mlab.figure(None,
bgcolor=(1, 1, 1),
fgcolor=(0.5, 0.5, 0.5),
size=(800, 800))
mlab.clf()
plot_3d_current_loops(loops, colors="auto", figure=f)
B_target = coil.B_coupling(target_points) @ coil.s
mlab.quiver3d(*target_points.T, *B_target.T, mode="arrow", scale_factor=0.75)
f.scene.isometric_view()
f.scene.camera.zoom(0.95)
bb = np.zeros(M.shape[1])
bb[: M11.shape[1]] = bi
I = np.linalg.solve(M, bb)
I1 = I[: M11.shape[1]]
I2 = I[M11.shape[1] :]
B1 = CB1 @ I1
B2 = CB2 @ I2
U1 = CU1 @ I1
U2 = CU2 @ I2
# Plot
# Extract the cross-sections of the plane and the surfaces
cc1 = scalar_contour(mesh1, mesh1.vertices[:, 2], contours=[-0.001])[0]
cc2 = scalar_contour(mesh2, mesh2.vertices[:, 2], contours=[-0.001])[0]
B = (B1.T + B2.T)[:2].reshape(2, x.shape[0], y.shape[0])
lw = np.sqrt(B[0] ** 2 + B[1] ** 2)
lw = 2 * lw / np.max(lw)
xx = np.linspace(-1, 1, 16)
# seed_points = 0.51*np.array([xx, -np.sqrt(1-xx**2)])
# seed_points = np.hstack([seed_points, (0.51*np.array([xx, np.sqrt(1-xx**2)]))])
seed_points = np.array([cc1[:, 0], cc1[:, 1]]) * 1.01
# plt.streamplot(x,y, B[1], B[0], density=2, linewidth=lw, color='k',
# start_points=seed_points.T, integration_direction='both')
U = (U1 + U2).reshape(x.shape[0], y.shape[0])
U /= np.max(U)
plt.figure()
plt.contourf(X, Y, U.T, cmap="seismic", levels=40)
-0.28276020498745635,
0.33658483701858727,
0.898196701154387,
]
scene.scene.camera.clipping_range = [16.139073445910277, 116.31572537292347]
scene.scene.camera.compute_view_plane_normal()
scene.scene.render()
#%%
U2_shield = shield.U_coupling(points)
U2_prim = coil.U_coupling(points)
#%%
from bfieldtools.contour import scalar_contour
cc1 = scalar_contour(planemesh, planemesh.vertices[:, 2], contours=[-0.1])
cc1 = np.vstack(cc1)
cc1a = cc1[:cc1.shape[0] // 2]
cc1b = cc1[cc1.shape[0] // 2:]
cc2 = scalar_contour(shieldmesh, shieldmesh.vertices[:, 2], contours=[-0.1])
cc2 = np.vstack(cc2)
cc2a = cc1[:cc2.shape[0] // 2]
cc2b = cc1[cc2.shape[0] // 2:]
import matplotlib.pyplot as plt
import matplotlib.colors as colors
def truncate_colormap(cmap, minval=0.0, maxval=1.0, n=256):
new_cmap = colors.LinearSegmentedColormap.from_list(
"trunc({n},{a:.2f},{b:.2f})".format(n=cmap.name, a=minval, b=maxval),