uniform rotation on sphere

random_uniform_rotation.py

def random_uniform_rotation(size=1):
    """
    Return uniform rotation vectors sampled on a sphere
    Args:
        size : int 
          The number of vectors
    Returns:
        vector: np.ndarray
          The rotation vectors
    """
    u1 = numpy.random.uniform(0, 1, size=size)
    u2 = numpy.random.uniform(0, 1, size=size)
    u3 = numpy.random.uniform(0, 1, size=size)
    theta = numpy.arccos(2 * u1 - 1)
    phi = 2 * pi * u2
    x = numpy.sin(theta) * numpy.cos(phi)
    y = numpy.sin(theta) * numpy.sin(phi)
    z = numpy.cos(theta)
    vectors = numpy.array((x, y, z)).T
    vectors *= 2 * pi * u3.reshape((u3.size, 1))
    return vectors