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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_taubin(mesh, lamb=0.5, nu=0.5, iterations=10, laplacian_operator=None):
 """ Smooth a mesh in-place using laplacian smoothing and taubin 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. lamb : float Controls shrinkage, range is 0.0 - 1.0 nu : float Controls dilation, range is 0.0 - 1.0 Nu shall be between 0.0 < 1.0/lambda - 1.0/nu < 0.1 iterations : int Number of passes to run the 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)

    # run through multiple passes of the filter
    for index in range(iterations):
        # do a sparse dot product on the vertices
        dot = laplacian_operator.dot(vertices) - vertices
        # alternate shrinkage and dilation
        if index % 2 == 0:
            vertices += lamb * dot
        else:
            vertices -= nu * dot

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