direct_surface_3d_movie.py

import random, math, pylab, mpl_toolkits.mplot3d

x_list, y_list, z_list = [],[],[]
nsamples = 1000

for sample in range(nsamples):
    x, y, z = random.gauss(0.0, 1.0), random.gauss(0.0, 1.0), random.gauss(0.0, 1.0)
    radius = math.sqrt(x ** 2 + y ** 2 + z ** 2)
    x_list.append(x / radius)
    y_list.append(y / radius)
    z_list.append(z / radius)

# Graphics output
fig = pylab.figure()
ax = fig.gca(projection="3d")
ax.set_aspect("auto")
pylab.plot(x_list, y_list, z_list, ".")
pylab.title("Uniform sampling of the sphere surface")
ax.set_xlabel("$x$", fontsize=14)
ax.set_ylabel("$y$", fontsize=14)
ax.set_zlabel("$z$", fontsize=14)
pylab.savefig("images/direct_surface_3d_movie.png")
#pylab.show()