import numpy as np

def uniform_sphere(size=None, dtype=np.double):
    """
    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. 
    """

    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)

    if size is None:
        return np.array([c*np.cos(theta), c*np.sin(theta), u])

    points = np.empty((size, 3), dtype)

    points[:,0] = c*np.cos(theta)
    points[:,1] = c*np.sin(theta)
    points[:,2] = u

    return points