Generate smooth wire sphere with specific number of concentric

I would like to generate in python a wire sphere with specific number of concentric circles, (3 horizontal and 22 vertical).

How can I do this? I have tried some code in here but to make the sphere look nice it is necessary to use a large number, e.g., 200. I need this to generate a 6-member ring sugar puckering diagram.

I would also be nice if at each intercepting point between the circles there would be a point. I tried some python code but the wire sphere is not smooth

Solution

There are a few ways to go about this. The first is using ax.plot_wireframe(...) but that doesn't look very visually appealing with such a small number of horizontal circles. Another (better) method is plotting each circle individually in a for loop. This is the method I have included below.

Note that I still used np.mgrid(...) even for the better method. This will give you arrays of (x,y,z) coordinates which can be used to access intersection points.

Example Output

Code

# %matplotlib notebook # uncomment if you use jupyter notebook
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt
# creating figure
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z')
# parameters to describe your sphere
numVertCircles = 22
numHorizCircles = 3
radius = 10
theta = np.linspace(0, 2 * np.pi, 201)
# generating data for vertical circles
xy = radius*np.cos(theta)
z = radius*np.sin(theta)
# generating data for horizontal circles
u1, v1 = np.mgrid[0:2*np.pi:numVertCircles*1j, 0:np.pi:(numHorizCircles+2)*1j]
x1 = radius*np.cos(u1)*np.sin(v1)
y1 = radius*np.sin(u1)*np.sin(v1)
z1 = radius*np.cos(v1)
horizRadii = np.amax(x1,axis=0) # array of radii (1 per horizontal circle)
uniqueZs = np.unique(z1) # array of z vals (1 per horizontal circle)
# plotting vertical circles
for i in range(numVertCircles):
phi = i*np.pi/numVertCircles
ax.plot(xy*np.sin(phi), xy*np.cos(phi), z, color ='#15B05E')
# plotting horizontal circles
for j in range(numHorizCircles):
ax.plot(np.cos(theta)*horizRadii[j+1], 
np.sin(theta)*horizRadii[j+1], 
np.full(201,uniqueZs[j+1]), color ='#15B05E')
# showing the intesection points
# NOTE: There are a bunch of overlapping points at the poles of the sphere
ax.scatter(x1.flatten(),y1.flatten(),z1.flatten(), color='red')
plt.show()
plt.savefig('wireFrameSphere.png', bbox_inches='tight', pad_inches=0.1)