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Integrals testingΒΆ
import pyvista as pv
from bfieldtools._example_plots import triangle_mesh, vector_glyphs, polyline
pv.set_plot_theme("document")
import numpy as np
import matplotlib.pyplot as plt
import trimesh
Test potential shape slightly above the surface %%
x = np.sin(np.pi / 6)
y = np.cos(np.pi / 6)
points = (
np.array(
[
[0, 0, 0],
[1, 0, 0],
[x, y, 0],
[-x, y, 0],
[-1, 0, 0],
[-x, -y, 0],
[x, -y, 0],
]
)
* 2
)
tris = np.array([[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [0, 5, 6], [0, 6, 1]])
mesh = trimesh.Trimesh(points, tris)
scalars = np.zeros(7)
scalars[0] = 1
Linear dipole density %%
# Sign ok
points = np.array([[0.1, 1, 1], [0.1, 1, -1], [0.1, -1, -1], [0.1, -1, 1]]) * 2
# points = np.roll(points, 2, 1)
tris = np.array([[0, 1, 2], [2, 3, 0]])
mesh2 = trimesh.Trimesh(points, tris)
for ii in range(7):
mesh2 = mesh2.subdivide()
from bfieldtools.legacy.integrals import triangle_potential_dipole_linear as t1
from bfieldtools.integrals import triangle_potential_dipole_linear as t2
RR = mesh2.vertices[:, None, None, :] - mesh.vertices[None, mesh.faces]
p1 = t1(RR, mesh.face_normals, mesh.area_faces, planar=False)
p2 = t2(RR, mesh.face_normals, mesh.area_faces)
assert np.allclose(p1, p2)
plotter = pv.Plotter(window_size=(800, 800))
plotter.add_mesh(
triangle_mesh(*mesh2.vertices.T, mesh2.faces),
scalars=p1[:, :, 0].sum(axis=1),
show_scalar_bar=False,
)
plotter.add_scalar_bar()
plotter.add_mesh(
triangle_mesh(*mesh.vertices.T, mesh.faces),
style="wireframe",
show_scalar_bar=False,
)
plotter.add_mesh(
vector_glyphs(*mesh.triangles_center.T, *mesh.face_normals.T), show_scalar_bar=False
)
plotter = pv.Plotter(window_size=(800, 800))
plotter.add_mesh(
triangle_mesh(*mesh2.vertices.T, mesh2.faces),
scalars=p2[:, :, 0].sum(axis=1),
show_scalar_bar=False,
)
plotter.add_scalar_bar()
plotter.add_mesh(
triangle_mesh(*mesh.vertices.T, mesh.faces),
style="wireframe",
show_scalar_bar=False,
)
plotter.add_mesh(
vector_glyphs(*mesh.triangles_center.T, *mesh.face_normals.T), show_scalar_bar=False
)
plotter = pv.Plotter(window_size=(800, 800))
plotter.add_mesh(
triangle_mesh(*mesh2.vertices.T, mesh2.faces),
scalars=(p1 - p2)[:, :, 0].sum(axis=1),
show_scalar_bar=False,
)
plotter.add_scalar_bar()
<vtkmodules.vtkRenderingAnnotation.vtkScalarBarActor(0x55979b3a6e80) at 0x7f127a987280>
points = np.zeros((100, 3))
points[:, 2] = np.linspace(-1, 1, 100)
from bfieldtools.legacy.integrals import omega as omega1
from bfieldtools.integrals import omega as omega2
RR = points[:, None, None, :] - mesh.vertices[None, mesh.faces]
o1 = omega1(RR).sum(axis=1)
o2 = omega2(RR).sum(axis=1)
assert np.allclose(o1, -o2)
plt.plot(o1)
plt.plot(o2)
plotter.add_mesh(
polyline(*points.T, points[:, 2]).tube(radius=0.01),
cmap="seismic",
show_scalar_bar=False,
)
plotter.add_mesh(
vector_glyphs(*mesh.triangles_center.T, *mesh.face_normals.T), show_scalar_bar=False
)
Actor (0x7f127a986b00)
Center: (0.0, 0.0, 0.07637625932693481)
Pickable: True
Position: (0.0, 0.0, 0.0)
Scale: (1.0, 1.0, 1.0)
Visible: True
X Bounds -1.015E+00, 1.015E+00
Y Bounds -1.170E+00, 1.170E+00
Z Bounds -1.035E-18, 1.528E-01
User matrix: Identity
Has mapper: True
Property (0x7f127b8c9240)
Ambient: 0.0
Ambient color: Color(name='light_blue', hex='#add8e6ff', opacity=255)
Anisotropy: 0.0
Color: Color(name='light_blue', hex='#add8e6ff', opacity=255)
Culling: "none"
Diffuse: 1.0
Diffuse color: Color(name='light_blue', hex='#add8e6ff', opacity=255)
Edge color: Color(name='black', hex='#000000ff', opacity=255)
Edge opacity: 1.0
Interpolation: InterpolationType.FLAT
Lighting: True
Line width: 1.0
Metallic: 0.0
Opacity: 1.0
Point size: 5.0
Render lines as tubes: False
Render points as spheres: False
Roughness: 0.5
Show edges: False
Specular: 0.0
Specular color: Color(name='light_blue', hex='#add8e6ff', opacity=255)
Specular power: 100.0
Style: "Surface"
DataSetMapper (0x7f127a8ef4c0)
Scalar visibility: True
Scalar range: (1.0, 1.0)
Interpolate before mapping: True
Scalar map mode: point
Color mode: map
Attached dataset:
PolyData (0x7f1298b98220)
N Cells: 258
N Points: 606
N Strips: 0
X Bounds: -1.015e+00, 1.015e+00
Y Bounds: -1.170e+00, 1.170e+00
Z Bounds: -1.035e-18, 1.528e-01
N Arrays: 2
Plot x_i
from bfieldtools.integrals import x_distance
RR = mesh2.vertices[:, None, None, :] - mesh.vertices[None, mesh.faces]
xdist = x_distance(RR, mesh.face_normals)
plotter.add_mesh(
triangle_mesh(*mesh2.vertices.T, mesh2.faces),
scalars=xdist[:, 1, 0],
cmap="seismic",
clim=[-1, 1],
show_scalar_bar=False,
)
plotter.add_scalar_bar()
plotter.add_mesh(
triangle_mesh(*mesh.vertices.T, mesh.faces),
style="wireframe",
show_scalar_bar=False,
)
plotter.add_mesh(
vector_glyphs(*mesh.triangles_center.T, *mesh.face_normals.T), show_scalar_bar=False
)
Actor (0x7f127b6a5ae0)
Center: (0.0, 0.0, 0.07637625932693481)
Pickable: True
Position: (0.0, 0.0, 0.0)
Scale: (1.0, 1.0, 1.0)
Visible: True
X Bounds -1.015E+00, 1.015E+00
Y Bounds -1.170E+00, 1.170E+00
Z Bounds -1.035E-18, 1.528E-01
User matrix: Identity
Has mapper: True
Property (0x7f127b14fee0)
Ambient: 0.0
Ambient color: Color(name='light_blue', hex='#add8e6ff', opacity=255)
Anisotropy: 0.0
Color: Color(name='light_blue', hex='#add8e6ff', opacity=255)
Culling: "none"
Diffuse: 1.0
Diffuse color: Color(name='light_blue', hex='#add8e6ff', opacity=255)
Edge color: Color(name='black', hex='#000000ff', opacity=255)
Edge opacity: 1.0
Interpolation: InterpolationType.FLAT
Lighting: True
Line width: 1.0
Metallic: 0.0
Opacity: 1.0
Point size: 5.0
Render lines as tubes: False
Render points as spheres: False
Roughness: 0.5
Show edges: False
Specular: 0.0
Specular color: Color(name='light_blue', hex='#add8e6ff', opacity=255)
Specular power: 100.0
Style: "Surface"
DataSetMapper (0x7f127b14d300)
Scalar visibility: True
Scalar range: (1.0, 1.0)
Interpolate before mapping: True
Scalar map mode: point
Color mode: map
Attached dataset:
PolyData (0x7f127b14efe0)
N Cells: 258
N Points: 606
N Strips: 0
X Bounds: -1.015e+00, 1.015e+00
Y Bounds: -1.170e+00, 1.170e+00
Z Bounds: -1.035e-18, 1.528e-01
N Arrays: 2
Uniform charge density
from bfieldtools.legacy.integrals import triangle_potential_uniform as u1
from bfieldtools.integrals import triangle_potential_uniform as u2
RR = mesh2.vertices[:, None, None, :] - mesh.vertices[None, mesh.faces]
p1 = u1(RR, mesh.face_normals, planar=False)
p2 = u2(RR, mesh.face_normals, planar=False)
assert np.allclose(p1, p2)
plotter = pv.Plotter()
plotter.add_mesh(
triangle_mesh(*mesh2.vertices.T, mesh2.faces),
scalars=p1.sum(axis=1),
show_scalar_bar=False,
)
plotter.add_scalar_bar()
plotter.add_mesh(
triangle_mesh(*mesh.vertices.T, mesh.faces),
style="wireframe",
show_scalar_bar=False,
)
plotter.add_mesh(
vector_glyphs(*mesh.triangles_center.T, *mesh.face_normals.T), show_scalar_bar=False
)
plotter = pv.Plotter()
plotter.add_mesh(
triangle_mesh(*mesh2.vertices.T, mesh2.faces),
scalars=p2.sum(axis=1),
show_scalar_bar=False,
)
plotter.add_scalar_bar()
plotter.add_mesh(
triangle_mesh(*mesh.vertices.T, mesh.faces),
style="wireframe",
show_scalar_bar=False,
)
plotter.add_mesh(
vector_glyphs(*mesh.triangles_center.T, *mesh.face_normals.T), show_scalar_bar=False
)
Actor (0x7f12798f96c0)
Center: (0.0, 0.0, 0.07637625932693481)
Pickable: True
Position: (0.0, 0.0, 0.0)
Scale: (1.0, 1.0, 1.0)
Visible: True
X Bounds -1.015E+00, 1.015E+00
Y Bounds -1.170E+00, 1.170E+00
Z Bounds -1.035E-18, 1.528E-01
User matrix: Identity
Has mapper: True
Property (0x7f12995eeda0)
Ambient: 0.0
Ambient color: Color(name='light_blue', hex='#add8e6ff', opacity=255)
Anisotropy: 0.0
Color: Color(name='light_blue', hex='#add8e6ff', opacity=255)
Culling: "none"
Diffuse: 1.0
Diffuse color: Color(name='light_blue', hex='#add8e6ff', opacity=255)
Edge color: Color(name='black', hex='#000000ff', opacity=255)
Edge opacity: 1.0
Interpolation: InterpolationType.FLAT
Lighting: True
Line width: 1.0
Metallic: 0.0
Opacity: 1.0
Point size: 5.0
Render lines as tubes: False
Render points as spheres: False
Roughness: 0.5
Show edges: False
Specular: 0.0
Specular color: Color(name='light_blue', hex='#add8e6ff', opacity=255)
Specular power: 100.0
Style: "Surface"
DataSetMapper (0x7f12995eeda0)
Scalar visibility: True
Scalar range: (1.0, 1.0)
Interpolate before mapping: True
Scalar map mode: point
Color mode: map
Attached dataset:
PolyData (0x7f127b8cb280)
N Cells: 258
N Points: 606
N Strips: 0
X Bounds: -1.015e+00, 1.015e+00
Y Bounds: -1.170e+00, 1.170e+00
Z Bounds: -1.035e-18, 1.528e-01
N Arrays: 2
from bfieldtools.integrals import d_distance
RR = mesh2.vertices[:, None, None, :] - mesh.vertices[None, mesh.faces]
ddist = d_distance(RR, mesh.face_normals)
plotter = pv.Plotter()
plotter.add_mesh(
triangle_mesh(*mesh2.vertices.T, mesh2.faces),
scalars=ddist[:, 0],
cmap="seismic",
clim=[-1, 1],
show_scalar_bar=False,
)
plotter.add_scalar_bar()
plotter.add_mesh(
triangle_mesh(*mesh.vertices.T, mesh.faces),
style="wireframe",
show_scalar_bar=False,
)
plotter.add_mesh(
vector_glyphs(*mesh.triangles_center.T, *mesh.face_normals.T), show_scalar_bar=False
)
Actor (0x7f127ca30f40)
Center: (0.0, 0.0, 0.07637625932693481)
Pickable: True
Position: (0.0, 0.0, 0.0)
Scale: (1.0, 1.0, 1.0)
Visible: True
X Bounds -1.015E+00, 1.015E+00
Y Bounds -1.170E+00, 1.170E+00
Z Bounds -1.035E-18, 1.528E-01
User matrix: Identity
Has mapper: True
Property (0x7f127ca30ca0)
Ambient: 0.0
Ambient color: Color(name='light_blue', hex='#add8e6ff', opacity=255)
Anisotropy: 0.0
Color: Color(name='light_blue', hex='#add8e6ff', opacity=255)
Culling: "none"
Diffuse: 1.0
Diffuse color: Color(name='light_blue', hex='#add8e6ff', opacity=255)
Edge color: Color(name='black', hex='#000000ff', opacity=255)
Edge opacity: 1.0
Interpolation: InterpolationType.FLAT
Lighting: True
Line width: 1.0
Metallic: 0.0
Opacity: 1.0
Point size: 5.0
Render lines as tubes: False
Render points as spheres: False
Roughness: 0.5
Show edges: False
Specular: 0.0
Specular color: Color(name='light_blue', hex='#add8e6ff', opacity=255)
Specular power: 100.0
Style: "Surface"
DataSetMapper (0x7f127ca30ca0)
Scalar visibility: True
Scalar range: (1.0, 1.0)
Interpolate before mapping: True
Scalar map mode: point
Color mode: map
Attached dataset:
PolyData (0x7f12798fb280)
N Cells: 258
N Points: 606
N Strips: 0
X Bounds: -1.015e+00, 1.015e+00
Y Bounds: -1.170e+00, 1.170e+00
Z Bounds: -1.035e-18, 1.528e-01
N Arrays: 2
from bfieldtools.legacy.mesh_magnetics import (
magnetic_field_coupling_analytic as magnetic_field_coupling_analytic_old,
)
from bfieldtools.mesh_magnetics import magnetic_field_coupling_analytic
b1 = magnetic_field_coupling_analytic_old(mesh, mesh2.vertices)
b2 = magnetic_field_coupling_analytic(mesh, mesh2.vertices)
assert np.allclose(b1, b2)
plotter = pv.Plotter()
plotter.add_mesh(
vector_glyphs(*mesh2.vertices.T, *b1[:, :, 0].T), show_scalar_bar=False
)
plotter.add_mesh(
vector_glyphs(*mesh2.vertices.T, *b2[:, :, 0].T), show_scalar_bar=False
)
Computing magnetic field coupling matrix analytically, 7 vertices by 16641 target points... took 0.09 seconds.
Computing magnetic field coupling matrix analytically, 7 vertices by 16641 target points... took 0.08 seconds.
Actor (0x7f127ca323e0)
Center: (0.2029091864824295, 0.0, 0.0028907060623168945)
Pickable: True
Position: (0.0, 0.0, 0.0)
Scale: (1.0, 1.0, 1.0)
Visible: True
X Bounds 1.637E-01, 2.421E-01
Y Bounds -2.008E+00, 2.008E+00
Z Bounds -2.000E+00, 2.006E+00
User matrix: Identity
Has mapper: True
Property (0x7f12a9726020)
Ambient: 0.0
Ambient color: Color(name='light_blue', hex='#add8e6ff', opacity=255)
Anisotropy: 0.0
Color: Color(name='light_blue', hex='#add8e6ff', opacity=255)
Culling: "none"
Diffuse: 1.0
Diffuse color: Color(name='light_blue', hex='#add8e6ff', opacity=255)
Edge color: Color(name='black', hex='#000000ff', opacity=255)
Edge opacity: 1.0
Interpolation: InterpolationType.FLAT
Lighting: True
Line width: 1.0
Metallic: 0.0
Opacity: 1.0
Point size: 5.0
Render lines as tubes: False
Render points as spheres: False
Roughness: 0.5
Show edges: False
Specular: 0.0
Specular color: Color(name='light_blue', hex='#add8e6ff', opacity=255)
Specular power: 100.0
Style: "Surface"
DataSetMapper (0x7f12a9726020)
Scalar visibility: True
Scalar range: (2.268676801975289e-08, 2.3241000235429965e-06)
Interpolate before mapping: True
Scalar map mode: point
Color mode: map
Attached dataset:
PolyData (0x7f127ca33ee0)
N Cells: 715563
N Points: 1680741
N Strips: 0
X Bounds: 1.637e-01, 2.421e-01
Y Bounds: -2.008e+00, 2.008e+00
Z Bounds: -2.000e+00, 2.006e+00
N Arrays: 2
Gammma
from bfieldtools.legacy.integrals import gamma0 as g1
from bfieldtools.integrals import gamma0 as g2
# RR = mesh2.vertices[:, None, None, :] - mesh.vertices[None, mesh.faces]
t = np.linspace(-1.5, 1.5)
points = (
t[:, None] * mesh.vertices[mesh.faces][0][0]
+ (1 - t)[:, None] * mesh.vertices[mesh.faces][0][1]
)
R = points[:, None, None, :] - mesh.vertices[None, mesh.faces]
p1 = g1(R, symmetrize=True)
p2 = g2(R, symmetrize=True)
assert np.allclose(p1, p2)
plt.figure()
plt.plot(p1[:, 0, :])
plt.figure()
plt.plot(p2[:, 0, :])
# Display the assembled scene (Sphinx-Gallery captures it during docs builds).
if "plotter" in globals() and not plotter._closed:
plotter.show()
Total running time of the script: (0 minutes 12.061 seconds)