Subdivision surfaces generated by subdividing general control meshes with the butterfly subdivision method are theoretically smooth. However

the surfaces are not visually smooth

because they are not fairing. Fairing the subdivision surfaces directly with traditional fairing methods has to store the huge volume data of subdivision results with approximation error introduced. In this paper

a new mesh fairing method is presented to address such problem. The subdivision result is faired through moving the vertices of the initial control mesh other than the vertices of the subdivision surface. With simple constraints

the method can fair the subdivision surface while decreasing the approximation error between the subdivision surface and the real 3D geometrical model. Moreover

this method can reduce the volume of data to be stored since it only needs to store the updated initial control mesh. To generate fairing subdivision surface

one just needs to subdivide the initial control mesh with simple subdivision rules.