Size of tidal factor over (Tropical, Perigee, Nodal) Brillouin zones

lattice_spheres_3d.py

import matplotlib.pyplot as plt
import numpy as np

# Data as multiline string (X, Y, Z, Diameter)
data = """
1 0 0 0.212566
1 0 1 0.504368
0 2 2 0.514627
0 -2 2 0.089845
0 0 2 0.135412
2 0 1 0.51246
2 0 0 0.413257
2 0 2 0.248128
1 -1 0 0.201939
2 -2 0 0.076616
0 0 1 0.448228
2 2 2 0.249092
1 1 0 0.223009
0 2 0 0.106861
2 -1 1 0.075938
0 2 1 0.094287
1 -1 1 0.068607
1 -1 1 0.174236
0 1 1 0.316888
1 1 1 0.331479
0 1 -1 0.233693
0 -1 0 1
0 -2 1 0.344451
1 -1 2 0.305368
0 -2 1 0.150287
2 2 1 0.101558
1 2 1 0.2333
2 -2 1 0.14823
1 -2 1 0.07895
"""

# Parse the data
lines = data.strip().split('\n')
X, Y, Z, D = [], [], [], []
for line in lines:
    xi, yi, zi, di = map(float, line.split())
    X.append(xi)
    Y.append(yi)
    Z.append(zi)
    D.append(di)

X = np.array(X)
Y = np.array(Y)
Z = np.array(Z)
D = np.array(D)

fig = plt.figure(figsize=(10, 8))
ax = fig.add_subplot(111, projection='3d')

# Plot spheres at each (X, Y, Z) location with given diameter D
for xi, yi, zi, di in zip(X, Y, Z, D):
    # Sphere parameterization
    u, v = np.mgrid[0:2*np.pi:24j, 0:np.pi:12j]
    r = di / 2.0  # Convert diameter to radius
    xs = xi + r * np.cos(u) * np.sin(v)
    ys = yi + r * np.sin(u) * np.sin(v)
    zs = zi + r * np.cos(v)
    ax.plot_surface(xs, ys, zs, color=plt.cm.viridis(di / D.max()), alpha=0.7, linewidth=0, shade=True)
    # Draw line from origin to center of sphere
    ax.plot([0, xi], [0, yi], [0, zi], color='k', linewidth=0.8, linestyle='-')

# Set grid, labels, and limits
ax.set_xlabel('Tropical')
ax.set_ylabel('Perigee')
ax.set_zlabel('Nodal')
ax.set_title('3D Integer Grid: Spheres with Given Diameters and Origin Lines')
ax.set_xticks(np.unique(X))
ax.set_yticks(np.unique(Y))
ax.set_zticks(np.unique(Z))
ax.set_box_aspect([1, 1, 1])

margin = 1
ax.set_xlim(X.min()-margin, X.max()+margin)
ax.set_ylim(Y.min()-margin, Y.max()+margin)
ax.set_zlim(Z.min()-margin, Z.max()+margin)

plt.tight_layout()
plt.show()