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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def filter_humphrey(mesh, alpha=0.1, beta=0.5, iterations=10, laplacian_operator=None):
 """ Smooth a mesh in-place using laplacian smoothing and Humphrey filtering. Articles "Improved Laplacian Smoothing of Noisy Surface Meshes" J. Vollmer, R. Mencl, and H. Muller Parameters mesh : trimesh.Trimesh Mesh to be smoothed in place alpha : float Controls shrinkage, range is 0.0 - 1.0 If 0.0, not considered If 1.0, no smoothing beta : float Controls how aggressive smoothing is If 0.0, no smoothing If 1.0, full aggressiveness iterations : int Number of passes to run filter laplacian_operator : None or scipy.sparse.coo.coo_matrix Sparse matrix laplacian operator Will be autogenerated if None """

    # if the laplacian operator was not passed create it here
    if laplacian_operator is None:
        laplacian_operator = laplacian_calculation(mesh)

    # get mesh vertices as vanilla numpy array
    vertices = mesh.vertices.copy().view(np.ndarray)
    # save original unmodified vertices
    original = vertices.copy()

    # run through iterations of filter
    for _index in range(iterations):
        vert_q = vertices.copy()
        vertices = laplacian_operator.dot(vertices)
        vert_b = vertices - (alpha * original + (1.0 - alpha) * vert_q)
        vertices -= (beta * vert_b + (1.0 - beta) *
                     laplacian_operator.dot(vert_b))

    # assign modified vertices back to mesh
    mesh.vertices = vertices
    return mesh