Pixel Field (Quiver Plot)

Added in version 5.2: Pixel Vector Field

The Sensor object with its pixel attribute can be conveniently used to visualize vector fields "B", "H", "M", or "J" as quiver plots. Detailed documentation is available in the styles-pixel-vectorfield section. This notebook provides practical examples and explanations of relevant parameters for effective usage.

Example 1: Transparent Magnet

A simple example using pixel field functionality, combined with magnet transparency, displays the B field on a surface passing through the magnet.

Show code cell source

Hide code cell source

import numpy as np
import magpylib as magpy

# Define a magnet with opacity
magnet = magpy.magnet.Cuboid(
    polarization=(1, 1, 0),
    dimension=(4e-3, 4e-3, 2e-3),
    style_opacity=0.5,
)

# Create a grid of pixel positions in the xy-plane
xy_grid = np.mgrid[-4e-3:4e-3:15j, -4e-3:4e-3:15j, 0:0:1j].T[0]

# Create a sensor with pixel array and pixel field style
sens = magpy.Sensor(
    pixel=xy_grid,
    style_pixel_field_source="B",
    style_pixel_field_sizescaling="log",
)

# Display the sensor and magnet using the Plotly backend
magpy.show([sens, magnet], backend="plotly")

Example 2: Complex Pixel Grids

Sensor pixels are not restricted to any specific grid structure and can be positioned freely to represent curved surfaces, lines, or individual points of interest.

The following example demonstrates visualization of the magnetic field of a magnetic pole wheel, evaluated along curved surfaces and lines, using different color maps and arrow shapes.

Show code cell source

Hide code cell source

from numpy import pi, sin, cos, linspace
import magpylib as magpy

# Create a pole wheel magnet composed of 12 alternating cylinder segments
pole_wheel = magpy.Collection()
for i in range(12):
    zone = magpy.magnet.CylinderSegment(
        dimension=(1.8, 2, 1, -15, 15),
        polarization=((-1)**i, 0, 0),
    ).rotate_from_angax(30*i, axis="z")
    pole_wheel.add(zone)

# Sensor 1: Disc inside the wheel
ts = linspace(0.8, 1.6, 950, endpoint=False)
pixel_line = [(t*cos(100*t), t*sin(100*t), 0) for t in ts]

sensor1 = magpy.Sensor(
    pixel=pixel_line,
    style_pixel_field_source="H",
)

# Sensor 2: Curved surface (vertical cylinder segment)
z_values = linspace(-1, 1, 10)
ang2 = linspace(-9*pi/8, -2*pi/8, 30)
pixel_grid2 = [[(3.5*cos(a), 3.5*sin(a), z) for a in ang2] for z in z_values]

sensor2 = magpy.Sensor(
    pixel=pixel_grid2,
    style_pixel_field={
        "source": "H",
        "sizescaling": "uniform",
        "colormap": "Blues",
        "symbol": "arrow3d",
    }
)

# Sensor 3: Curved surface (horizontal annular sector)
r_values = linspace(3, 4, 5)
ang3 = linspace(-pi/8, 6*pi/8, 30)
pixel_grid3 = [[(r*cos(a), r*sin(a), 0) for a in ang3] for r in r_values]

sensor3 = magpy.Sensor(
    pixel=pixel_grid3,
    style_pixel_field={
        "source": "H",
        "sizescaling": "log",
        "colormap": "Plasma",
        "symbol": "arrow3d",
    }
)

# Display sensors and magnets using Plotly backend
magpy.show(
    [sensor1, sensor2, sensor3, pole_wheel],
    backend="plotly",
    style_arrows_x_show=False,
    style_arrows_y_show=False,
    style_arrows_z_show=False,
)

Example 3: Pixel Field Animation

Pixel fields can be combined with animation to create spectacular visualizations, such as displaying the magnetic field of rotating magnets.

Show code cell source

Hide code cell source

import numpy as np
import magpylib as magpy

# Create a cuboid magnet with vertical polarization
magnet = magpy.magnet.Cuboid(
    polarization=(0, 0, 1),
    dimension=(1, 3, 1)
)

# Apply a rotation to the Cuboid that generates a path with 51 steps
magnet.rotate_from_angax(
    angle=np.linspace(0, 360, 51),
    axis="y",
    start=0
)

# Create a sensor with pixel grid in the xy-plane at z=1
pixel_grid = np.mgrid[-2:2:12j, -2:2:12j, 1:1:1j].T[0]
sensor = magpy.Sensor(pixel=pixel_grid)

# Display as animation in the Plotly backend
magpy.show(
    magnet,
    sensor,
    animation=True,
    style_pixel_field_symbol="arrow3d",
    style_pixel_field_source="B",
    backend="plotly",
)