How to Set Axis in Polar Coordinates in Matplotlib ?

Introduction

This guide demonstrates how to configure and manipulate axes in polar coordinates using Matplotlib, a popular Python plotting library. We’ll cover the basics of setting up a polar plot, adjusting axis ticks, plotting points and functions, and even visualizing a Fraunhofer diffraction pattern.

Table of contents

Introduction
Setting Up Axis in Polar Coordinates
Formatting Polar Axis Ticks
Plotting a Point in Polar Coordinates
Plotting a Function in Polar Coordinates
Plotting a Surface: Fraunhofer Diffraction Pattern
References

Setting Up Axis in Polar Coordinates

To configure a plot in polar coordinates, you need to set the projection='polar' when creating the axis. Here's a simple example:

import matplotlib.pyplot as plt

fig = plt.figure()
ax = fig.add_subplot(111, projection='polar')

plt.savefig("polar_coordinates_01.png", bbox_inches='tight')
plt.show()

How to Set Axis in Polar Coordinates in Matplotlib ?

In this example, we create a figure and define an axis with a polar projection. The plot is then saved and displayed.

Formatting Polar Axis Ticks

You can modify the ticks on both the radial (r) and angular (theta) axes using set_xticks and set_yticks. This is particularly useful if you need customized labeling for your plot.

import matplotlib.pyplot as plt
import numpy as np

fig = plt.figure()
ax = fig.add_subplot(111, projection='polar')

# Set custom theta ticks (in radians)
ax.set_xticks(np.arange(0, 2.0 * np.pi, np.pi / 6))

# Set radial limits and custom ticks
ax.set_ylim(0, 4)
ax.set_yticks(np.arange(0, 4, 1))

plt.savefig("polar_coordinates_02.png", bbox_inches='tight')
plt.show()

In this case, the angular ticks are set to divide the full circle (2π radians) into 12 parts, and the radial axis is limited to a range of 0 to 4.

Plotting a Point in Polar Coordinates

To plot a single point, you need to specify its radius r and angle theta (in radians). You can use numpy.deg2rad() to convert degrees to radians if needed.

import matplotlib.pyplot as plt
import numpy as np

r = 2.0
theta = np.deg2rad(60.0)  # Convert 60 degrees to radians

fig = plt.figure()
ax = fig.add_subplot(111, projection='polar')

# Plot a point at (r, theta)
ax.scatter(theta, r)

# Format the axis
ax.set_xticks(np.arange(0, 2.0 * np.pi, np.pi / 6))
ax.set_ylim(0, 4)
ax.set_yticks(np.arange(0, 4, 1))

plt.savefig("polar_coordinates_03.png", bbox_inches='tight')
plt.show()

Here, a single point at a radius of 2.0 units and an angle of 60 degrees is plotted.

Plotting a Function in Polar Coordinates

You can also plot functions in polar coordinates, where theta represents the angular coordinate and r the radial coordinate.

import matplotlib.pyplot as plt
import numpy as np

r = np.arange(0, 6, 0.01)
theta = 2 * np.pi * r  # A spiral function

fig = plt.figure()
ax = fig.add_subplot(111, projection='polar')

# Plot the function
ax.plot(theta, r)

# Format the axis
ax.set_xticks(np.arange(0, 2.0 * np.pi, np.pi / 6))
ax.set_ylim(0, 4)
ax.set_yticks(np.arange(0, 4, 1))

plt.savefig("polar_coordinates_04.png", bbox_inches='tight')
plt.show()

In this example, we plot a spiral function where the radial distance increases as theta increases.

Plotting a Surface: Fraunhofer Diffraction Pattern

Here’s an advanced example of plotting a Fraunhofer diffraction pattern from a dataset, visualizing the intensity distribution in polar coordinates. (FraunhoferHexagonalAperture_Data.txt)

#!/usr/bin/env python

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.cm as cm
from matplotlib import ticker

# Load the dataset
r, theta, refl = np.loadtxt("FraunhoferHexagonalAperture_Data.txt", unpack=True)

# Reshape the reflection data for contouring
refl = np.reshape(refl, (360, -1))

# Generate grid for polar plot
azimuths = np.radians(np.linspace(0, 360, 360))
zeniths = np.arange(0.00000000001, 30, 0.1)
r, theta = np.meshgrid(zeniths, azimuths)

# Create the polar plot
fig, ax = plt.subplots(subplot_kw=dict(projection='polar'))

# Define contour levels for diffraction intensity
contour_levels = [0.0000000001, 0.000000001, 0.00000001, 0.0000001,
                  0.000001, 0.00001, 0.0001, 0.001, 0.01, 0.1, 1.0]

# Plot the filled contours
CS = ax.contourf(theta, r, refl, contour_levels, cmap=cm.gist_earth_r, locator=ticker.LogLocator())

# Add colorbar
cbar = plt.colorbar(CS)
cbar.set_label(r"Fraunhofer Diffracted Intensity $I/I_0$")

plt.savefig('FraunhoferHexagonalAperture.png')
plt.show()

In this plot, we visualize the intensity of a Fraunhofer diffraction pattern, with contours representing different intensity levels.

References

Link	Site
Wikipedia: Polar Coordinates	wikipedia
Matplotlib Documentation: Scatter Plot on Polar Axis	matplotlib.org
Matplotlib Example: Polar Demo	matplotlib.org/
Matplotlib API: Polar Plots	matplotlib.org/
Stack Overflow: Set Axis Limit in Polar Plot	stackoverflow.com
Matplotlib: Transoffset Example	matplotlib.org

Hi, I'm Ben, the Founder of moonbooks.org. I work as a research scientist specializing in Earth satellite remote sensing, particularly focusing on Fire detection using VIIRS and ABI sensors. My areas of expertise include Python, Machine Learning, and Open Science. Feel free to reach out if you notice any errors on the site. I am constantly striving to enhance it. Thank you!