def _shift_nodal_coord(nodal_data, displacements, scale_factor):
    """ Return the nodal coordinates after deformation.

    A helper function for plot_countour.

    Parameter
    ---------
    nodal_data : numpy.array
        the nodal_data from the SolverInput object
    displacements : numpy.array
        the displacements from the BaseSolver object  
    scale_factor : float
        The deformation scale factor assigned in the param.
    
    Return
    ------
    numpy.ndarray
        An array that contains the shifted coordinate by the deformation
    """
    shifted_nodal_coord = nodal_data[:,1:3].copy()
    scaled_disp = displacements * scale_factor
    for i in range(nodal_data.shape[0]):
        shifted_nodal_coord[i, 0] += scaled_disp[2 * i]
        shifted_nodal_coord[i, 1] += scaled_disp[2 * i + 1]
    return shifted_nodal_coord