Python matplotlib polar coordinate is not plotting as it is supposed to be

Question

I am plotting from a CSV file that contains Cartesian coordinates and I want to change it to Polar coordinates, then plot using the Polar coordinates.

Here is the code

import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
import seaborn as sns

df = pd.read_csv('test_for_plotting.csv',index_col = 0)

x_temp = df['x'].values
y_temp = df['y'].values

df['radius'] =  np.sqrt( np.power(x_temp,2) + np.power(y_temp,2) )
df['theta'] = np.arctan2(y_temp,x_temp)
df['degrees'] = np.degrees(df['theta'].values)
df['radians'] = np.radians(df['degrees'].values)

ax = plt.axes(polar = True)
ax.set_aspect('equal')
ax.axis("off")

sns.set(rc={'axes.facecolor':'white', 'figure.facecolor':'white','figure.figsize':(10,10)})
# sns.scatterplot(data = df, x = 'x',y = 'y', s= 1,alpha = 0.1, color = 'black',ax = ax)
sns.scatterplot(data = df, x = 'radians',y = 'radius', s= 1,alpha = 0.1, color = 'black',ax = ax)

plt.tight_layout()
plt.show()

Here is the dataset

If you run this command using polar = False and use this line to plot sns.scatterplot(data = df, x = 'x',y = 'y', s= 1,alpha = 0.1, color = 'black',ax = ax) it will result in this picture

now after setting polar = True and run this line to plot sns.scatterplot(data = df, x = 'radians',y = 'radius', s= 1,alpha = 0.1, color = 'black',ax = ax) It is supposed to give you this

But it is not working as if you run the actual code the shape in the Polar format is the same as Cartesian which does not make sense and it does not match the picture I showed you for polar (If you are wondering where did I get the second picture from, I plotted it using R)

I would appreciate your help and insights and thanks in advance!

Answer 1

For a polar plot, the "x-axis" represents the angle in radians. So, you need to switch x and y, and convert the angles to radians (I also added ax=ax, as the axes was created explicitly):

import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
import seaborn as sns

data = {'radius': [0, 0.5, 1, 1.5, 2, 2.5], 'degrees': [0, 25, 75, 155, 245, 335]}

df_temp = pd.DataFrame(data)
ax = plt.axes(polar=True)
sns.scatterplot(x=np.radians(df_temp['degrees']), y=df_temp['radius'].to_numpy(),
                s=100, alpha=1, color='black', ax=ax)
for deg, y in zip(df_temp['degrees'], df_temp['radius']):
    x = np.radians(deg)
    ax.axvline(x, color='skyblue', ls=':')
    ax.text(x, y, f'  {deg}', color='crimson')
ax.set_rlabel_position(-15)  # Move radial labels away from plotted dots
plt.tight_layout()
plt.show()

About your new question: if you have an xy plot, and you convert these xy values to polar coordinates, and then plot these on a polar plot, you'll get again the same plot.

After some more testing with the data, I decided to create the plot directly with matplotlib, as seaborn makes some changes that don't have exactly equal effects across seaborn and matplotlib versions.

What seems to be happening in R:

• The angles (given by "x") are spread out to fill the range (0,2 pi). This either requires a rescaling of x, or change how the x-values are mapped to angles. One way to get this, is subtracting the minimum. And with that result divide by the new maximum and multiply by 2 pi.
• The 0 of the angles it at the top, and the angles go clockwise.

The following code should create the plot with Python. You might want to experiment with alpha and with s in the scatter plot options. (Default the scatter dots get an outline, which often isn't desired when working with very small dots, and can be removed by lw=0.)

ax = plt.axes(polar=True)
ax.set_aspect('equal')
ax.axis('off')
x_temp = df['x'].to_numpy()
y_temp = df['y'].to_numpy()
x_temp -= x_temp.min()
x_temp = x_temp / x_temp.max() * 2 * np.pi
ax.scatter(x=x_temp, y=y_temp, s=0.05, alpha=1, color='black', lw=0)
ax.set_rlim(y_temp.min(), y_temp.max())
ax.set_theta_zero_location("N")  # set zero at the north (top)
ax.set_theta_direction(-1) # go clockwise
plt.show()

At the left the resulting image, at the right using the y-values for coloring (ax.scatter(..., c=y_temp, s=0.05, alpha=1, cmap='plasma_r', lw=0)):