在python中使用极坐标图进行笛卡尔缩放

Question

I am trying to plot some data in polar coordinates (I am currently using the polar projection):

The code I am using is the following:

import matplotlib.pyplot as plt
import numpy as np

# Create radial and angular array
r = np.linspace(1.0,10,11)
t = np.linspace(0.0,0.5*np.pi,101)

# Define the quantity that I want to plot
z = np.zeros((len(t),len(r)))
for yval in range(len(r)):
  z[:,yval] = np.cos(16.0*t)/r[yval]

#Create the figure
f = plt.figure(figsize=(13,8))
ax = plt.subplot(111, projection='polar')
ax.set_rorigin(-1)

#Plot the data
pcm = ax.pcolormesh(t,r,z.T,cmap = 'hot',shading='gouraud')
ax.set_xlim([0.0,0.5*np.pi])
ax.set_ylim([1.0,10.0])

#Add colorbar and show
bar = f.colorbar(pcm)
plt.show()

So far I have no problem, but I would like to zoom on a particular region of this plot. However, when I set the axes range the axes is still polar, therefore I cannot zoom on a "cartesian" region of the domain (ie a square box).

A possible option would be to transform the data into cartesian coordinates, but when I do it I lose a lot of resolution in the inner part of the domain, which is something that I should absolutely avoid.

How can I select a rectangular zone of a plot in polar coordinates without transforming by hand the data? And in case I have to switch to cartesian coordinates, is there any matplotlib or python function that does it while taking care of the resolution in the inner regions of the domain? Thanks in advance

Answer 1

You can create an X, Y mesh yourself that is has a higher resolution on the inner part of the domain and use that with ax.pcolormesh()

# Create radial and angular array
r = np.linspace(1.0,10,11)
t = np.linspace(0.0,0.5*np.pi,101)

# Define the quantity that I want to plot
z = np.zeros((len(t),len(r)))
for yval in range(len(r)):
    z[:,yval] = np.cos(16.0*t)/r[yval]


#Create the figure, bigger figsize to make the resulting plot square
f = plt.figure(figsize=(13,10))
ax = plt.subplot(111) # Drop back to XY coordinates


# Generate the XY corners of the colormesh
X = np.array([[ri*np.cos(j) for j in t] for ri in r])
Y = np.array([[ri*np.sin(j) for j in t] for ri in r])

#Plot the data
pcm = ax.pcolormesh(X,Y,z.T,cmap = 'hot',shading='gouraud')

#Add colorbar and show
bar = f.colorbar(pcm)
plt.show()

The figure from the question

The figure generated by code above