Figure 1: Stream function example

An example stream function (red–blue colormap) and its rotated gradient, i.e. the surface current density (arrows; green colormap) on a surface mesh with a hole in it. The surface normal is oriented up towards the reader.

Static Scene

Interactive Scene

Calculating surface harmonics expansion...
Computing the laplacian matrix...
Computing the mass matrix...

import pyvista as pv
from bfieldtools._example_plots import mesh_actor
from bfieldtools._example_plots import vector_glyphs

pv.set_plot_theme("document")


from bfieldtools.mesh_conductor import MeshConductor, StreamFunction
from bfieldtools import resources
from bfieldtools.mesh_calculus import gradient
import numpy as np

SAVE = False
SAVE_DIR = "./Streamfunction gradient/"


c = MeshConductor(
    mesh_file=resources.files("bfieldtools", "example_meshes/curved_surf_w_hole.stl"),
    process=True,
    basis_name="suh",
    N_suh=10,
    fix_normals=True,
)


T_x = 1.5 * np.pi / 2
T_z = -1.02 * np.pi
rotmat = np.array(
    [
        [np.cos(T_z), -np.sin(T_z), 0, 0],
        [np.sin(T_z), np.cos(T_z), 0, 0],
        [0, 0, 1, 0],
        [0, 0, 0, 1],
    ]
) @ np.array(
    [
        [1, 0, 0, 0],
        [0, np.cos(T_x), -np.sin(T_x), 0],
        [0, np.sin(T_x), np.cos(T_x), 0],
        [0, 0, 0, 1],
    ]
)


c.mesh.apply_transform(rotmat)

s = np.zeros((c.basis.shape[1],))
s[2] += 1
# s[63] += 2

s = StreamFunction(s, c)


plotter = f = pv.Plotter(window_size=(800, 700))
plotter = s.plot(figure=f, ncolors=256)
plotter = c.plot_mesh(style="wireframe", figure=f)


j = gradient(s.vert, c.mesh, rotated=True)

Len = np.log(np.linalg.norm(j, axis=0))

vectors = plotter.add_mesh(
    vector_glyphs(*c.mesh.triangles_center.T, *j, mode="arrow", scalars=Len),
    cmap="Greens",
    show_scalar_bar=False,
)

f.view_xy()

#
mesh_actor(vectors).mapper.lookup_table.n_values = 8
plotter.add_scalar_bar(title="Current density", n_labels=0)
f.camera.position = [-0.3696892487983681, 0.2840788710848503, 3.701830880912346]
f.camera.focal_point = [-0.3696892487983681, 0.2840788710848503, 0.8575533408480627]
f.camera.view_angle = 30.0
f.camera.up = [0.0, 1.0, 0.0]
f.camera.clipping_range = [2.5164461179149695, 3.263810326333801]
f.render()

if SAVE:
    f.screenshot(SAVE_DIR + "streamfunction_gradient.png", scale=4)

# Display the assembled scene (Sphinx-Gallery captures it during docs builds).
if "plotter" in globals() and not plotter._closed:
    plotter.show()