def METHOD_NAME(mesh, points, radius):
    """
    Return the discrete gaussian curvature measure of a sphere
    centered at a point as detailed in 'Restricted Delaunay
    triangulations and normal cycle'- Cohen-Steiner and Morvan.
    This is the sum of the vertex defects at all vertices
    within the radius for each point.
    Parameters
    ----------
    points : (n, 3) float
      Points in space
    radius : float ,
      The sphere radius, which can be zero if vertices
      passed are points.
    Returns
    --------
    gaussian_curvature:  (n,) float
      Discrete gaussian curvature measure.
    """
    points = np.asanyarray(points, dtype=np.float64)
    if not util.is_shape(points, (-1, 3)):
        raise ValueError('points must be (n,3)!')
    nearest = mesh.kdtree.query_ball_point(points, radius)
    gauss_curv = [mesh.vertex_defects[vertices].sum() for vertices in nearest]
    return np.asarray(gauss_curv)