from mpl_toolkits.mplot3d import Axes3D

from matplotlib import cm

import matplotlib.pyplot as plt

import numpy as np

n_angles = 36

n_radii = 8

# An array of radii

# Does not include radius r=0, this is to eliminate duplicate points

radii = np.linspace(0.125, 1.0, n_radii)

# An array of angles

angles = np.linspace(0, 2*np.pi, n_angles, endpoint=False)

# Repeat all angles for each radius

angles = np.repeat(angles[...,np.newaxis], n_radii, axis=1)

# Convert polar (radii, angles) coords to cartesian (x, y) coords

# (0, 0) is added here. There are no duplicate points in the (x, y) plane

x = np.append(0, (radii*np.cos(angles)).flatten())

y = np.append(0, (radii*np.sin(angles)).flatten())

# Pringle surface

z = np.sin(-x*y)

fig = plt.figure()

ax = fig.gca(projection='3d')

ax.plot_trisurf(x, y, z, cmap=cm.jet, linewidth=0.2)

plt.show()