擅长:python、mysql、java
<p>基于<a href="http://mathworld.wolfram.com/SpherePointPicking.html" rel="noreferrer">the last approach on this page</a>,您可以简单地从三个标准正态分布生成一个由独立样本组成的向量,然后对该向量进行规范化,使其大小为1:</p>
<pre><code>import numpy as np
def sample_spherical(npoints, ndim=3):
vec = np.random.randn(ndim, npoints)
vec /= np.linalg.norm(vec, axis=0)
return vec
</code></pre>
<p>例如:</p>
<pre><code>from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import axes3d
phi = np.linspace(0, np.pi, 20)
theta = np.linspace(0, 2 * np.pi, 40)
x = np.outer(np.sin(theta), np.cos(phi))
y = np.outer(np.sin(theta), np.sin(phi))
z = np.outer(np.cos(theta), np.ones_like(phi))
xi, yi, zi = sample_spherical(100)
fig, ax = plt.subplots(1, 1, subplot_kw={'projection':'3d', 'aspect':'equal'})
ax.plot_wireframe(x, y, z, color='k', rstride=1, cstride=1)
ax.scatter(xi, yi, zi, s=100, c='r', zorder=10)
</code></pre>
<p><a href="https://i.stack.imgur.com/4vpfj.png" rel="noreferrer"><img src="https://i.stack.imgur.com/4vpfj.png" alt="enter image description here"/></a></p>
<p>同样的方法也推广到单位圆(<code>ndim=2</code>)或高维单位超球表面上的均匀分布点的提取。</p>