The Quaternary Interpolating Scheme for Geometric Design

Abstract

A novel 4-point interpolating subdivision scheme is presented, which generates the family of C2 limiting curves and its limiting function has support on [−7/3,7/3]. It behaves better than classical 4-point binary and ternary schemes with the same approximation order in many aspects that it has smaller support size, higher smoothness, and is computationally more efficient. The proposed nonstationary scheme can reproduce the functions of linear spaces spanned by {1,sin(αx),cos(αx)} for 0<α<π/3. Moreover, some examples are illustrated to show that the proposed scheme can also reproduce asteroids, cardioids, and conic sections as well.