create an ellipsoid with a hole vertically through the center. the hole should be continuous. the output should be similar to a torus in matlab

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

# Define the parameters of the ellipsoid
a, b, c = 4, 2, 3  # Axes lengths of the ellipsoid
center = np.array([0, 0, 0])  # Center point of the ellipsoid

# Generate points on the ellipsoid surface
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(-np.pi/2, np.pi/2, 50)
x = a * np.outer(np.cos(u), np.cos(v))
y = b * np.outer(np.sin(u), np.cos(v))
z = c * np.outer(np.ones(np.size(u)), np.sin(v))

# Define the parameters of the hole
radius = 1.5  # Radius of the hole
hole_height = 2  # Height of the hole

# Generate points on the cylinder surface for the hole
theta = np.linspace(0, 2 * np.pi, 100)
y_hole = radius * np.cos(theta)
z_hole = hole_height * np.sin(theta)

# Subtract the cylinder from the ellipsoid to create the hole
for i in range(len(z)):
    for j in range(len(x)):
        if np.sqrt(y[j]**2 + z[i]**2) <= radius:
            x[j, i] = 0
            y[j, i] = 0
            z[j, i] = 0

# Plot the ellipsoid with the hole
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(x, y, z, color='blue')

ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
plt.show()
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