How to produce a revolution of a 2D plot with matplotlib in Python

Question

I have created a 2D plot using matplotlib in Python, an example being this one: It has been produced using 2 lists:

import matplotlib.pyplot as plt
import numpy as np

plt.plot(X, Y) #X and Y are lists, containing the x and y coordinates of points respectively
plt.show()

Now I want to create a revolution of that plot around the Y-axis, and visualizing it in a way that the Y-axis is vertical. How can that be done using matplotlib?

Do you want to create a 3D surface being the revolution of the curve around an axis? Or just rotate the curve? — JohanC, Dec 19 '19 at 08:10
For a 3D surface: https://stackoverflow.com/questions/43586082/how-to-draw-solid-of-revolution-of-a-polynomial-function-about-y-axis — JohanC, Dec 19 '19 at 08:12
I wanted for a 3D surface and the link you provided was useful but I think what William wrote was also pretty useful and very well explained — Ivalin, Dec 19 '19 at 20:20

William Miller · Accepted Answer · 2022-12-31T21:52:54.380

If you have a curve defined as a collection of x and y points in two 1D arrays and you want to revolve them about the y axis you simply need to construct 2D arrays to satisfy matplotlib's Axes3D.plot_surface by taking the outer products, using np.outer(), of x with np.cos(theta) and np.sin(theta) for theta in [0, 2π]. This will give you a collection of cartesian points in xy space, which will represent the circles created by revolving each original point about the z axis. Constructing the z array is a bit tricky because of the shape expected by plot_surface().

Here is a complete example which demonstrates this method and compares it with the original 2D plot

from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np

n = 100

fig = plt.figure(figsize=(12,6))
ax1 = fig.add_subplot(121)
ax2 = fig.add_subplot(122,projection='3d')
y = np.linspace(np.pi/8, np.pi*4/5, n)
x = np.sin(y)
t = np.linspace(0, np.pi*2, n)

xn = np.outer(x, np.cos(t))
yn = np.outer(x, np.sin(t))
zn = np.zeros_like(xn)

for i in range(len(x)):
    zn[i:i+1,:] = np.full_like(zn[0,:], y[i])

ax1.plot(x, y)
ax2.plot_surface(xn, yn, zn)
plt.show()

How to produce a revolution of a 2D plot with matplotlib in Python

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