Plotting a parametric 3D surface

In the previous recipe, we used plot_surface() to plot a scalar field: that is, a function of the f(x, y) = z form. However, matplotlib is able to plot a generic, parametric 3D surface. Let's demonstrate this by plotting a torus, which is a fairly simple parametric surface.

How to do it...

We are going to use plot_surface() again to display a torus, using the following code:

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

# Generate torus mesh
angle = np.linspace(0, 2 * np.pi, 32)
theta, phi = np.meshgrid(angle, angle)
r, R = .25, 1.
X = (R + r * np.cos(phi)) * np.cos(theta)
Y = (R + r * np.cos(phi)) * np.sin(theta)
Z = r * np.sin(phi)

# Display the mesh
fig = plt.figure()
ax = fig.gca(projection = '3d')
ax.set_xlim3d(-1, 1)
ax.set_ylim3d(-1, 1)
ax.set_zlim3d(-1, 1)
ax.plot_surface(X, Y, Z, color = 'w', rstride = 1, cstride = 1)
plt.show()

The preceding code will display our torus as follows:

How it works...

A torus...