Approximating subdivision for quadrilateral nets with 4-valence topology

In the paper, a new approximating subdivision scheme is presented for quadrilateral nets with 4-valence topology which generates the limit surface of C¹ in the limit at the regular face and quasi-tangent plane continuous at the irregular region. The main advantage of the scheme comparing with other algorithms is limit surfaces generated by the scheme can hold the shape of initial control polyhedra better than others. So, the criterion satisfies important requirements for practical applications in computer graphics and engineering.