( 2 n - 1 ) -Point Ternary Approximating and Interpolating Subdivision Schemes

Abstract

We present an explicit formula which unifies the mask of $(2n-1)$-point ternary interpolating as well as approximating subdivision schemes. We observe that the odd point ternary interpolating and approximating schemes introduced by Lian (2009), Siddiqi and Rehan (2010, 2009) and Hassan and Dodgson (2003) are special cases of our proposed masks/schemes. Moreover, schemes introduced by Zheng et al. (2009) can easily be generated by our proposed masks. It is also proved from comparison that $(2n-1)$-point schemes are better than $2n$-scheme in the sense of computational cost, support and error bounds.