Three dimensions

Deposit a 3D cloud of markers, gather back from it, and look at it in slices and lines.

The same calls work in 1D, 2D and 3D: scatter with $(3, N)$ positions, evaluate with one coordinate fixed for a plane, two for a line. Here a cloud with a hollow core is deposited, smoothed and cut through its centre.

Python source

"""Three dimensions

Deposit a 3D cloud of markers, gather back from it, and look at it in slices and lines.

The same calls work in 1D, 2D and 3D: `scatter` with $(3, N)$ positions, `evaluate`
with one coordinate fixed for a plane, two for a line. Here a cloud with a hollow core is
deposited, smoothed and cut through its centre.
"""

import matplotlib.pyplot as plt
import numpy as np
import plasma_plots  # noqa: F401

from mpifield import Field

rng = np.random.default_rng(10)
count = 200_000
direction = rng.normal(size=(3, count))
direction /= np.linalg.norm(direction, axis=0)
positions = direction * (0.5 + 0.08 * rng.normal(size=count))  # a spherical shell

density = Field(
    ndim=3, lower_bound=(-1.0,) * 3, upper_bound=(1.0,) * 3, num_gridpoints=41
)
density.scatter(positions, np.ones((1, count)))
density.smooth_binomial(passes=2)
gathered = density.gather(positions)
print(f"mean density seen by the markers: {gathered.mean():.1f} per node")

fig, (left, right) = plt.subplots(1, 2, figsize=(11, 4.5), layout="constrained")
density.plot(ax=left, z=0.0, name="density", equal_aspect=True)
density.plot(ax=right, y=0.25, name="density", equal_aspect=True)
density.plot(y=0.0, z=0.0, name="density")
plt.show()

Plots