均匀球形分布的随机三维单位向量
生成具有均匀球形分布的随机三维单位向量[参考]
import numpy as np
import matplotlib.pyplot as plt
def random_three_vector():
"""
Generates a random 3D unit vector (direction) with a uniform spherical distribution
Algo from http://stackoverflow.com/questions/5408276/python-uniform-spherical-distribution
:return:
"""
phi = np.random.uniform(0,np.pi*2)
costheta = np.random.uniform(-1,1)
theta = np.arccos( costheta )
x = np.sin( theta) * np.cos( phi )
y = np.sin( theta) * np.sin( phi )
z = np.cos( theta )
return (x,y,z)
# Example IPython code to test the uniformity of the distribution
from pylab import scatter
threetups = []
for _ in range(1000):
threetups.append(random_three_vector())
x,y,z = zip(*threetups)
plt.scatter(x, y)
plt.title("Distribution of Random 3D Unit Vectors")
plt.xlabel("X-axis")
plt.ylabel("Y-axis")
plt.show()result:
