The Quaternary Interpolating Scheme for Geometric Design

A novel 4-point interpolating subdivision scheme is presented, whichgenerates the family of limiting curves and its limiting function has support on . It behaves better than classical 4-point binary andternary schemes with the same approximation order in many aspectsthat it has smaller support size, higher smoothness, and is computationallymore efficient. The proposed nonstationary scheme can reproducethe functions of linear spaces spanned by for . Moreover, some examples are illustrated to show thatthe proposed scheme can also reproduce asteroids, cardioids, and conicsections as well.