Create Polar Contour Plot

Question

I am trying to recreate the contour plot shown below in Matplotlib, using the following code to generate the data:

theta = np.arange(math.radians(0), math.radians(361),0.01).tolist() # initialise theta values
g4 = []
for i in theta:
    v = ((2**(1-1)) * (1 + (1*math.cos(i)))**1) # equation to generate the data
g4.append(v)

fig, ax = plt.subplots(subplot_kw={'projection': 'polar'})
ax.scatter(theta, g4, c=g4, cmap='viridis')

So far, I have been able to generate a scatter plot using this data which looks as follows:

However I am completely unsure of how to convert my data into the correct form to produce the required scatter plot, I have tried:

ax.contourf(theta, g4, g4)

But I get TypeError: Input z must be 2D, not 1D

Answer 1

Based on the answer here, you could do:

azimuths = np.radians(np.linspace(0, 360, 50))
zeniths = np.linspace(0, 4, 50)

r, theta = np.meshgrid(zeniths, azimuths)

f = 1 + np.cos(theta)  # your function is essentially this

fig, ax = plt.subplots(subplot_kw={'projection': 'polar'})

ax.contourf(theta, r, f)

which produces:

This obviously doesn't look like the example plot that you show, but that's because your function is only a function of theta and not of r. So, it is therefore constant in the radial direction for any value of theta.

To get something similar to the example plot, you could add the r variable in to the function, e.g.:

azimuths = np.radians(np.linspace(0, 360, 250))
zeniths = np.linspace(0, 4, 250)

r, theta = np.meshgrid(zeniths, azimuths)

# function that also depends on r
f = 1 + np.cos(theta) - (0.35 * r)**2

fig, ax = plt.subplots(subplot_kw={'projection': 'polar'})

f[f <= 0] = np.inf  # mask out values that are negative

ax.grid()
ax.pcolormesh(theta, r, f, cmap="viridis_r")  # plot function
ax.grid(True)
ax.contour(theta, r, f, levels=10, colors="k", linewidths=0.25)  # add contours
ax.set_rticks([0, 1, 2, 3, 4]);  # set radial tick values