How to replicate mathematica's 3d plot look with matplotlib?

Question

I am trying to replicate the plot below done in mathematica using matplotlib in python. As you can see, it is very clean and you immediately know what you're looking at.

This is the python code to generate the plot:

import numpy as np import matplotlib.pyplot as plt from scipy.signal import butter from mpl_toolkits.mplot3d import Axes3D from matplotlib import cm # Butterworth filter order order = 5 # Create a meshgrid for sigma and omega sigma = np.linspace(-1.5, 0.5, 400) omega = np.linspace(-1.5, 1.5, 400) sigma, omega = np.meshgrid(sigma, omega) # Complex frequency (s = sigma + j*omega) s = sigma + 1j * omega # Butterworth filter (analog, so we use s-domain) b, a = butter(order, 1, analog=True) w, h = s, np.polyval(b, s) / np.polyval(a, s) # Calculate the magnitude of the frequency response response = np.abs(h) response[response > 40] = 40 # 3D Plot fig = plt.figure() ax = fig.add_subplot(111, projection='3d') surf = ax.plot_surface(sigma, omega, response, cmap=cm.viridis) ax.set_zlim(0, 40) ax.set_xlabel('Sigma') ax.set_ylabel('Omega') ax.set_zlabel('Magnitude') plt.show()

It looks way less nicer:

What do you like to change in your plot exactly? The angle of view, the transparency of the panes, height or mesh? — Raymond
– Raymond, Commented Dec 9, 2023 at 12:42
The shading so that it is easy to see where exactly the hills start to rise. — Leonhard Euler
– Leonhard Euler, Commented Dec 9, 2023 at 12:49
I am pretty sure you should use a solid color instead of cmap, such as color='orange' and then the shadings will be applied automatically. In fact, shade=True is the default setting. — Raymond
– Raymond, Commented Dec 9, 2023 at 13:43

Raymond · Accepted Answer · 2023-12-09 13:54:20Z

Here I generated some data to show how it works:

import numpy as np import matplotlib.pyplot as plt X = np.linspace(0, 9.42, 500) Y = np.linspace(0, 9.42, 500) X, Y = np.meshgrid(X, Y) Z = -np.sqrt(np.sin(X)**2 + np.cos(Y + X)**2) + X**2/30 fig = plt.figure() ax = fig.add_subplot(111, projection='3d') ax.plot_surface(X, Y, Z, antialiased=False, rstride=5, cstride=5, color='#00c0e7') ax.view_init(45, 80) ax.set_xlabel('X') ax.set_ylabel('Y') plt.show()

Here is your code:

import numpy as np import matplotlib.pyplot as plt from scipy.signal import butter from mpl_toolkits.mplot3d import Axes3D from matplotlib import cm # Butterworth filter order order = 5 # Create a meshgrid for sigma and omega sigma = np.linspace(-1.5, 0.5, 400) omega = np.linspace(-1.5, 1.5, 400) sigma, omega = np.meshgrid(sigma, omega) # Complex frequency (s = sigma + j*omega) s = sigma + 1j * omega # Butterworth filter (analog, so we use s-domain) b, a = butter(order, 1, analog=True) w, h = s, np.polyval(b, s) / np.polyval(a, s) # Calculate the magnitude of the frequency response response = np.abs(h) response[response > 40] = 40 # 3D Plot fig = plt.figure() ax = fig.add_subplot(111, projection='3d') surf = ax.plot_surface(sigma, omega, response, color='#ff7300', antialiased=False, rstride=1, cstride=1) ax.set_zlim(0, 40) ax.set_xlabel('Sigma') ax.set_ylabel('Omega') ax.set_zlabel('Magnitude')

Thanks. But this doesn't look as good as the mathematica one.

MuhammedYunus · Accepted Answer · 2023-12-09 16:14:19Z

Here's one that takes on some of the desired aesthetic.

from matplotlib.colors import LightSource # 3D Plot fig = plt.figure(figsize=(8, 8)) ax = fig.add_subplot(111, projection='3d') ax.view_init(azim=-50, elev=30, roll=0) downsample = 1 lightsource = LightSource(azdeg=50, altdeg=10) #Overlay same plot to help mitigate antialiasing artifacts for _ in range(3): surf = ax.plot_surface( sigma, omega, response, antialiased=True, color='tab:orange', lightsource=lightsource, linewidth=0, alpha=1, rstride=downsample, cstride=downsample, ) # #Alternative using trisurf # for _ in range(3): # surf = ax.plot_trisurf( # sigma.ravel()[::downsample], # omega.ravel()[::downsample], # response.ravel()[::downsample], # color='tab:orange', antialiased=True, # lightsource=lightsource, # linewidth=0, # ) for axis in [ax.xaxis, ax.yaxis, ax.zaxis]: axis.pane.fill = False axis.pane.set_edgecolor('black') ax.grid(False) ax.set_xlabel('σ', fontsize=12) ax.set_ylabel('ω', fontsize=12) ax.set_zlabel('|f(σ, ω)|', fontsize=12) ax.set_title('Butterworth frequency response') ax.set_box_aspect(aspect=None, zoom=0.9) plt.show()

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