python_implicit.py

import numpy as np
import matplotlib.pyplot as plt

from mpl_toolkits import mplot3d


theta = np.linspace(0, 8 * np.pi, 120)
w = np.linspace(-0.25, 0.25, 8)
w, theta = np.meshgrid(w, theta)

phi = 0.5 * theta
r = 1 + w * np.cos(phi)

x = np.ravel(r * np.cos(theta))
y = np.ravel(r * np.sin(theta))
z = np.ravel(w * np.sin(phi) + 0.25*phi)

# triangulate in the underlying parametrization
from matplotlib.tri import Triangulation
tri = Triangulation(np.ravel(w), np.ravel(theta))

ax = plt.axes(projection='3d')
ax.plot_trisurf(x, y, z, triangles=tri.triangles,
                cmap='viridis', linewidths=0.2);

# ax.set_xlim(-1, 1); ax.set_ylim(-1, 1); ax.set_zlim(-1, 1);
plt.show()