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import time
import numpy as np
def uniform_sphere(size=None):
"""
Generate random points isotropically distributed across the unit sphere.
Args:
- size: int, *optional*
Number of points to generate. If no size is specified, a single
point is returned.
source: Weisstein, Eric W. "Sphere Point Picking." Mathworld.
"""
t0 = time.time()
theta, u = np.random.uniform(0.0, 2*np.pi, size), \
np.random.uniform(-1.0, 1.0, size)
c = np.sqrt(1-u**2)
x = c*np.cos(theta)
y = c*np.sin(theta)
z = u
points = np.empty((x.size, 3))
points[:,0] = x
points[:,1] = y
points[:,2] = z
if size is None:
return points[0]
else:
return points
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