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