Abstract:A new scheme for constructing a two steps Catmull-Clark subdivision surface with the vertex normal vector constraint interpolates the vertices of a quadrilateral mesh with arbitrary topology. Firstly, the new mesh is generated by the modified Catmull-Clark subdivision. Secondly, the new mesh is adjusted through vertex normal vector constraints. The two-phase scheme makes the limit surface interpolate all vertices and normal vector in the original mesh by applying the progressive iterative method and the Lagrange multiplier method respectively. The experimental examples are given to show that the method is effective both in interpolating initial control points and normal vector, the limit surface has good modeling effect.