A new class of odd-point ternary non-stationary approximating schemes

Abstract

In this paper, we establish new family of odd-point ternary non-stationary approximating subdivision schemes by introducing the \(sine\) function in the Lagrange identities. It is to be observed that the limiting conic sections, generated by the proposed schemes compare to the existing non-stationary approximating schemes, have less deviation from being an exact conic sections. Moreover, proposed family of 3-point ternary schemes with fewer initial control points produces better limiting conic sections than other existing schemes. Furthermore, the proposed family of schemes is non-stationary counterpart of the stationary scheme of Hassan and Dodgson (Ternary and three-point univariate subdivision schemes. Nashboro Press, Brentwood, 2003), Lian (Appl Appl Math 3:176–187, 2008), Siddiqi and Rehan (Int J Comput Math 87:1709–1715, 2009), Siddiqi and Rehan (Appl Math Comput 216:970–982, 2010), Mustafa et al. (Am J Comput Math 1:111–118, 2011), Aslam et al. (J Appl Math 2011:13, 2011) and Conti and Romani (J Math Anal Appl 407:443–456, 2013).