Polar axes in Matplotlib - Step-by-Step Execution

Concept Flow - Polar axes

Start: Create Figure

↓

Add Polar Axes

↓

Plot Data in Polar Coordinates

↓

Customize: Labels, Limits

↓

Show Plot

↓

End

This flow shows how to create a polar plot step-by-step: start with a figure, add polar axes, plot data using angles and radii, customize, then display.

Execution Sample

Matplotlib

import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(111, polar=True)
ax.plot([0, 1, 2], [1, 2, 3])
plt.show()

This code creates a simple polar plot with three points connected by lines.

Execution Table

Step	Action	Input/Parameters	Result/State
1	Create Figure	None	Figure object created
2	Add subplot with polar=True	111, polar=True	PolarAxesSubplot object added to figure
3	Plot data	theta=[0,1,2], r=[1,2,3]	Data plotted on polar axes
4	Show plot	None	Plot window opens displaying polar plot
5	End	None	Execution complete

💡 Plot displayed and program ends

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4
fig	None	Figure object	Figure object	Figure object	Figure object
ax	None	None	PolarAxesSubplot object	PolarAxesSubplot object with data	PolarAxesSubplot object with data

Key Moments - 3 Insights

Why do we use 'polar=True' when adding a subplot?

Using 'polar=True' tells matplotlib to create polar axes instead of regular Cartesian axes, as shown in execution_table step 2.

What do the two lists passed to ax.plot() represent?

The first list is angles (theta), the second is radius (r). This is clear in execution_table step 3 where theta=[0,1,2] and r=[1,2,3].

Why does plt.show() come last?

plt.show() displays the plot window and pauses execution until closed, as seen in execution_table step 4.

Visual Quiz - 3 Questions

Look at the execution_table, what type of object is 'ax' after step 2?

A Line2D object

B PolarAxes object

C Figure object

D None

💡 Hint

Check the 'Result/State' column in step 2 of execution_table

At which step is the data actually plotted on the polar axes?

A Step 1

B Step 2

C Step 3

D Step 4

💡 Hint

Look for 'Data plotted on polar axes' in execution_table

If we omit 'polar=True' in step 2, what changes in the execution?

A ax becomes a regular Cartesian Axes object

B ax becomes a PolarAxes object anyway

C Plot will show polar coordinates by default

D Code will raise an error

💡 Hint

Recall the purpose of 'polar=True' from key_moments question 1

Concept Snapshot

Polar axes in matplotlib:
- Use fig.add_subplot(111, polar=True) to create polar axes
- Plot with ax.plot(theta, r) where theta=angles, r=radii
- plt.show() displays the plot
- Polar plots use angle-radius coordinates instead of x-y
- Customize with labels, limits on ax

Full Transcript

This visual execution trace shows how to create a polar plot using matplotlib. First, a figure is created. Then, a subplot with polar=True is added to get polar axes. Next, data points are plotted using angles and radii. Finally, plt.show() displays the plot window. Variables 'fig' and 'ax' track the figure and axes objects. Key points include the need for polar=True to get polar axes and understanding that ax.plot() takes angle and radius lists. The quiz tests understanding of object types and execution steps.

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