球函数及其应用（球谐函数可视化）

import matplotlib.pyplot as plt from matplotlib import cm, colors from mpl_toolkits.mplot3d import Axes3D import numpy as np from scipy.special import sph_harm phi = np.linspace(0, np.pi, 100) theta = np.linspace(0, 2*np.pi, 100) phi, theta = np.meshgrid(phi, theta) # The Cartesian coordinates of the unit sphere x = np.sin(phi) * np.cos(theta) y = np.sin(phi) * np.sin(theta) z = np.cos(phi) m, l = 2, 3 # Calculate the spherical harmonic Y(l,m) and normalize to [0,1] fcolors = sph_harm(m, l, theta, phi).real fmax, fmin = fcolors.max(), fcolors.min() fcolors = (fcolors - fmin)/(fmax - fmin) # Set the aspect ratio to 1 so our sphere looks spherical fig = plt.figure(figsize=plt.figaspect(1.)) ax = fig.add_subplot(111, projection='3d') ax.plot_surface(x, y, z, rstride=1, cstride=1, facecolors=cm.seismic(fcolors)) # Turn off the axis planes ax.set_axis_off() plt.show()