user423805 user423805 - 1 year ago 193
Python Question

Plotting A Hyperboloid

Teacher in class gave this formula

w = x**2 + y**2 - z**2

and showed its 3d graphic in class seen below. How do I plot this using Matplotlib (minus the intersecting plane)? I guess first a specific value for w needs to be selected, for example 10, otherwise 3d plotting would not be possible. Then should I convert to polar coordinates because of the z**2 in the formula? I tried this and failed. Any help would be appreciated. Also, does this shape have a name?

enter image description here

Answer Source

Got it. Found some good stuff here, and following the formulas presented, I have the Python code below.

from __future__ import division

from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np

fig = plt.figure(figsize=plt.figaspect(1))  # Square figure
ax = fig.add_subplot(111, projection='3d')


a = 1
b = 1
c = 1

x = a*np.cosh(u)*np.cos(v)
y = b*np.cosh(u)*np.sin(v)
z = c*np.sinh(u)

ax.plot_surface(x, y, z,  rstride=4, cstride=4, color='b')
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