from __future__ import division
import numpy as np
from numpy import pi, cos, sin, sqrt, outer, ones
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

fig = plt.figure(figsize=(10, 10))
ax = fig.add_subplot(111, projection='3d')
u = np.linspace(0, 2 * pi, 100)
v = np.linspace(0, pi, 100)
one_v = ones(100)


# Sphere
x1 = 10 * outer(cos(u), sin(v))
y1 = 10 * outer(sin(u), sin(v)) + 17
z1 = 10 * outer(one_v, np.cos(v))
ax.plot_surface(x1, y1, z1, rstride=5, cstride=5, cmap='Spectral',
                linewidth=0.5)

# Cylinder
x2 = 6 * outer(cos(u), one_v)
y2 = 6 * outer(sin(u), one_v)
z2 = 20 * outer(one_v, v/pi - 0.5)
ax.plot_surface(x2, y2, z2, rstride=5, cstride=5, cmap='Spectral',
                linewidth=0.5)

# Hyperboloid
v = 2*v/pi - 1
x3 = 6 * outer(cos(u), sqrt(1 + v**2))
y3 = 6 * outer(sin(u), sqrt(1 + v**2)) - 16
z3 = 12 * outer(one_v, v)
ax.plot_surface(x3, y3, z3, rstride=5, cstride=5, cmap='Spectral',
                linewidth=0.5)

# Fix aspect ratio and axes details
ax.set_xlim(-13, 13)
ax.set_ylim(-13, 13)
ax.set_zlim(-13, 13)
ax.view_init(elev=35, azim=-45)
plt.axis('off')
plt.savefig('Gaussian curvature.svg', transparent=True)
plt.show()