How to show Cartesian system in polar plot in python?

Question

Here I tried to add the polar plot on top of the Cartesian grid,but what I got instead was 2 separate figures(one polar another Cartesian),I want this polar figure to be embedded in the Cartesian plot. Also I have used some of the code previously available as I am new to matplotlib.

from pylab import *
import matplotlib.pyplot as plt
x = [0,10,-3,-10]
y = [0,10,1,-10]
color=['w','w','w','w']

fig = plt.figure()
ax1 = fig.add_subplot(111)

scatter(x,y, s=100 ,marker='.', c=color,edgecolor='w')

circle1=plt.Circle((0,0),5,color='r',fill=False)
circle_min=plt.Circle((0,0),4.5,color='g',fill=False)
circle_max=plt.Circle((0,0),5.445,color='b',fill=False)
fig = plt.gcf()


fig.gca().add_artist(circle1)
fig.gca().add_artist(circle_min)
fig.gca().add_artist(circle_max)

left,right = ax1.get_xlim()
low,high = ax1.get_ylim()
arrow( left, 0, right -left, 0, length_includes_head = True, head_width = 0.15 )
arrow( 0, low, 0, high-low, length_includes_head = True, head_width = 0.15 )


grid()

fig = plt.figure()
ax2 = fig.add_subplot(111)

scatter(x,y, s=100 ,marker='.', c=color,edgecolor='w')

circle2=plt.Circle((0,0),5,color='r',fill=False)
circle_min=plt.Circle((0,0),4.5,color='g',fill=False)
circle_max=plt.Circle((0,0),5.445,color='b',fill=False)
fig = plt.gcf()


fig.gca().add_artist(circle2)
fig.gca().add_artist(circle_min)
fig.gca().add_artist(circle_max)

left,right = ax2.get_xlim()
low,high = ax2.get_ylim()
arrow( left, 0, right -left, 0, length_includes_head = True, head_width = 0.15 )
arrow( 0, low, 0, high-low, length_includes_head = True, head_width = 0.15 )

import numpy as np
import matplotlib.pyplot as plt


theta = np.linspace(-np.pi, np.pi, 100)  
r1 = 1 - np.sin(3*theta)
r2 = 1 + np.cos(theta)


ax = plt.subplot(111, polar=True,      # add subplot in polar coordinates 
                 axisbg='Azure')       # background colour

ax.set_rmax(2.2)                       # r maximum value
ax.grid(True)                          # add the grid

ax.plot(theta, r1,
        color='Tomato',                # line colour
        ls='--',                       # line style
        lw=3,                          # line width
        label='a 3-fold curve')        # label

ax.plot(theta, r2, 
        color='purple',
        linewidth=3,
        ls = '-',
        label = 'a cardioid')


ax.legend(loc="lower right")           # legend location

titlefont = {
        'family' : 'serif',
        'color'  : 'black',
        'weight' : 'bold',
        'size'   : 16,
        }

ax.set_title("A plot in polar coordinates", # title
             va='bottom',                   # some space below the title
             fontdict = titlefont           # set the font properties
             )



grid()

show()



#I am getting a separate Cartesian image + a polar image while what I need   is both the things in a single image

Answer 1

I am not used to matplotlib but I reduced your code to his minimum to better understand it and make it look less redudant. look at what I get:

import pylab
import matplotlib.pyplot as plt
import numpy as np
#########################################
x = [0,10,-3,-10]
y = [0,10,1,-10]
color=['w','w','w','w']
theta = np.linspace(-np.pi, np.pi, 100)  
#########################################
pylab.scatter(x,y, s=100 ,marker='.', c=color,edgecolor='w')

plt.gcf().gca().add_artist(plt.Circle((0,0),5,color='r',fill=False))
plt.gcf().gca().add_artist(plt.Circle((0,0),4.5,color='g',fill=False))
plt.gcf().gca().add_artist(plt.Circle((0,0),5.445,color='b',fill=False))

plt.figure().add_subplot(111)
ax = plt.subplot(111, polar=True,axisbg='Azure')
ax.plot(theta, 1 - np.sin(3*theta),color='Tomato',ls='--',lw=3,label='a 3-fold curve')
ax.plot(theta, 1 + np.cos(theta),color='purple',linewidth=3,ls = '-',label = 'a cardioid')

pylab.show()

it is nearly the same result...

Answer 2

import matplotlib.pyplot as plt
import numpy as np
#########################################
color=['w','w','w','w']
theta = np.linspace(-np.pi, np.pi, 100)  
fig = plt.figure()# initializing the figure
rect = [0.1, 0.1, 0.8, 0.8]# setting the axis limits in [left, bottom, width, height]
ax_carthesian  = fig.add_axes(rect)# the carthesian axis:
ax_polar = fig.add_axes(rect, polar=True, frameon=False)# the polar axis:
#########################################

ax_carthesian.add_artist(plt.Circle((0.5,0.5),5/15,color='r',fill=False))
ax_carthesian.add_artist(plt.Circle((0.5,0.5),4.5/15,color='g',fill=False))
ax_carthesian.add_artist(plt.Circle((0.5,0.5),5.445/15,color='b',fill=False))

ax_polar.plot(theta, 1 - np.sin(3*theta),   color='Tomato',ls='--',lw=1,        label='a 3-fold curve')
ax_polar.plot(theta, 1 + np.cos(theta),     color='purple',linewidth=1,ls = '-',label = 'a cardioid')


plt.show()