Polar axes in Matplotlib - Mini Project: Build & Apply

Plotting Data on Polar Axes with Matplotlib

📖 Scenario: You are working as a data analyst and need to visualize data that naturally fits a circular layout, like wind directions or angles. Polar plots help show such data clearly.

🎯 Goal: Build a simple polar plot using matplotlib to display data points on a circular graph.

📋 What You'll Learn

Create a list of angles in radians called angles with exact values: 0, π/4, π/2, 3π/4, π

Create a list of radius values called radii with exact values: 1, 2, 3, 4, 5

Create a polar subplot using plt.subplot with projection='polar'

Plot the angles and radii on the polar axes using ax.plot

Display the plot using plt.show()

💡 Why This Matters

🌍 Real World

Polar plots are useful for showing data that depends on angles, such as wind direction, compass bearings, or cyclic phenomena.

💼 Career

Data analysts and scientists often use polar plots to visualize directional data clearly and effectively.

1

Create the data lists for angles and radii

Create a list called angles with these exact values: 0, 0.7853981633974483, 1.5707963267948966, 2.356194490192345, 3.141592653589793 (these are 0, π/4, π/2, 3π/4, π in radians). Also create a list called radii with these exact values: 1, 2, 3, 4, 5.

Matplotlib

# Create the angles list and radii list with exact values
# Your code here

Hint

Use a Python list with the exact floating point values for the angles and integers for radii.

2

Create a polar subplot

Import matplotlib.pyplot as plt. Then create a subplot called ax using plt.subplot with projection='polar'.

Matplotlib

angles = [0, 0.7853981633974483, 1.5707963267948966, 2.356194490192345, 3.141592653589793]
radii = [1, 2, 3, 4, 5]

# Import matplotlib.pyplot as plt and create a polar subplot ax
# Your code here

Hint

Use import matplotlib.pyplot as plt and plt.subplot(projection='polar').

3

Plot the data on the polar axes

Use the ax.plot method to plot the angles and radii lists on the polar subplot.

Matplotlib

import matplotlib.pyplot as plt

angles = [0, 0.7853981633974483, 1.5707963267948966, 2.356194490192345, 3.141592653589793]
radii = [1, 2, 3, 4, 5]

ax = plt.subplot(projection='polar')

# Plot angles and radii on ax
# Your code here

Hint

Use ax.plot(angles, radii) to plot the points on the polar axes.

4

Display the polar plot

Use plt.show() to display the polar plot.

Matplotlib

import matplotlib.pyplot as plt

angles = [0, 0.7853981633974483, 1.5707963267948966, 2.356194490192345, 3.141592653589793]
radii = [1, 2, 3, 4, 5]

ax = plt.subplot(projection='polar')
ax.plot(angles, radii)

# Show the plot
# Your code here

Hint

Call plt.show() to display the figure window with the polar plot.

Practice

1. What does setting projection='polar' do in a matplotlib plot?

easy

A. It creates a 3D plot with depth perspective.

B. It creates a plot with circular axes using angles and radius.

C. It changes the plot background to a polar color scheme.

D. It rotates the plot by 90 degrees.

Solution

1. Step 1: Understand the projection parameter

   The projection argument in matplotlib defines the coordinate system for the plot.

2. Step 2: Identify what 'polar' projection means

   Setting projection='polar' changes the axes to polar coordinates, which use angles and radius instead of x and y.

3. Final Answer:

   It creates a plot with circular axes using angles and radius. -> Option B

4. Quick Check:

   projection='polar' = circular axes [OK]

Hint: Remember: 'polar' means angle + radius axes [OK]

Common Mistakes:

• Confusing polar projection with 3D plotting
• Thinking it changes colors or rotates plot
• Assuming it creates Cartesian axes

2. Which of the following is the correct way to create a polar plot in matplotlib?

easy

A. plt.plot(projection='polar')

B. plt.axis(polar=True)

C. plt.polar()

D. plt.subplot(projection='polar')

Solution

1. Step 1: Recall how to create polar axes

   In matplotlib, plt.subplot(projection='polar') creates a polar subplot.

2. Step 2: Check other options for correctness

   plt.plot() does not accept projection, plt.polar() is deprecated, and plt.axis(polar=True) does not create new axes.

3. Final Answer:

   plt.subplot(projection='polar') -> Option D

4. Quick Check:

   Use subplot with projection='polar' [OK]

Hint: Use plt.subplot(projection='polar') to start polar plots [OK]

Common Mistakes:

• Using plt.plot with projection argument
• Trying deprecated plt.polar() function
• Passing polar=True instead of projection='polar'

3. What will the following code display?

import matplotlib.pyplot as plt
import numpy as np

ax = plt.subplot(projection='polar')
theta = np.linspace(0, 2*np.pi, 100)
r = np.abs(np.sin(3*theta))
ax.plot(theta, r)
plt.show()

medium

A. A polar plot with three 'petals' shaped by sine function.

B. A line plot with sine wave on Cartesian axes.

C. A scatter plot of random points on polar axes.

D. An error because np.abs cannot be used with polar plots.

Solution

1. Step 1: Analyze the data arrays

   theta is angles from 0 to 2π, r is absolute sine of 3 times theta, creating 3 cycles.

2. Step 2: Understand the plot type

   Plotting r vs theta on polar axes draws a 3-petal shape because sine(3θ) repeats 3 times around the circle.

3. Final Answer:

   A polar plot with three 'petals' shaped by sine function. -> Option A

4. Quick Check:

   Polar plot of |sin(3θ)| = 3 petals [OK]

Hint: sin(3θ) on polar plot makes 3 petals [OK]

Common Mistakes:

• Thinking it plots Cartesian sine wave
• Confusing plot type with scatter
• Assuming np.abs causes error

4. Identify the error in this code snippet for a polar plot:

import matplotlib.pyplot as plt
ax = plt.subplot()
ax.plot([0, 1, 2], [0, 1, 0.5])
plt.show()

medium

A. Missing projection='polar' in subplot creation.

B. Plot data lists have different lengths.

C. plt.show() is called before plotting.

D. Using plt.subplot() instead of plt.subplots() causes error.

Solution

1. Step 1: Check subplot creation

   The code uses plt.subplot() without projection='polar', so axes are Cartesian by default.

2. Step 2: Understand impact on polar plotting

   Without polar projection, the plot is not polar. To create polar plot, projection='polar' must be specified.

3. Final Answer:

   Missing projection='polar' in subplot creation. -> Option A

4. Quick Check:

   Polar plot needs projection='polar' [OK]

Hint: Always add projection='polar' for polar axes [OK]

Common Mistakes:

• Assuming plt.subplot() defaults to polar
• Thinking plt.show() order matters here
• Confusing plt.subplot() and plt.subplots()

5. You want to plot wind direction and speed data on a polar plot. Which approach correctly maps wind direction (degrees) to angle and speed to radius in matplotlib?

hard

A. Use wind direction in degrees as theta without conversion; plot with projection='polar'.

B. Use wind direction directly as radius and speed as theta; plot with projection='polar'.

C. Convert wind direction to radians, use as theta; use speed as radius; plot with projection='polar'.

D. Plot wind speed vs wind direction on Cartesian axes with projection='polar'.

Solution

1. Step 1: Understand polar plot axes

   Polar plots use angles in radians for theta and distances for radius.

2. Step 2: Map wind data correctly

   Wind direction in degrees must be converted to radians for theta; wind speed is radius. Plotting with projection='polar' shows correct directional data.

3. Final Answer:

   Convert wind direction to radians, use as theta; use speed as radius; plot with projection='polar'. -> Option C

4. Quick Check:

   Degrees to radians for theta, speed as radius [OK]

Hint: Convert degrees to radians for polar angles [OK]

Common Mistakes:

• Using degrees directly without conversion
• Swapping radius and angle values
• Plotting on Cartesian axes expecting polar behavior