Group Project 2, Problem 14

import matplotlib
import matplotlib.pyplot as plt
import numpy as np
%matplotlib inline
from mpl_toolkits.mplot3d.axes3d import Axes3D
%matplotlib notebook
import matplotlib.pyplot as plt
import numpy as np

'''Prepare the figure container'''
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

'''Prepare the 2D domain: x from -1 to 1 and y from -1 to 1'''
x,y = np.meshgrid(np.linspace(-1,1,41),np.linspace(-1,1,41))
t = np.linspace(0, 2*np.pi)
X = np.cos(t)
Y = np.sin(t)
z1 = x**2 - y**2

z3 = 2*X**2 - 1

x2=np.linspace(-1,1,40)
z2=np.linspace(-2,2,40)

X2, Z2=np.meshgrid(x2,z2)
Y2=np.sqrt(1-X2**2)

ax.plot_wireframe(X2,Y2,Z2)
ax.plot_wireframe(X2,-Y2,Z2)

'''Plot the surface'''
ax.plot_surface(x,y,z1)

ax.plot(X,Y,z3, color="red")

'''Set all labels, view, and then plot'''
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('f(x,y)')
ax.set_xticks([-1,-0.5,0,0.5,1])
ax.set_yticks([-1,-0.5,0,0.5,1])
ax.set_zticks([-1,-0.5,0,0.5,1])
plt.show()