A Family of 2n-Point Ternary Non-Stationary Interpolating Subdivision Scheme

Abstract

This article offers 2n-point ternary non-stationary interpolating subdivision schemes, with the tension parameter, by using Lagrange identities. By choosing the suitable value of tension parameter, we can get different limit curves according to our own choice. Tightness or looseness of the limit curve depends upon the increment or decline the value of tension parameter. The proposed schemes are the counter part of some existing parametric and non-parametric stationary schemes. The main purpose of this article is to reproduce conics and the proposed schemes reproduce conics very well such that circle, ellipse, parabola and hyperbola. We also establish a deviation error formula which is useful to
calculate the maximum deviation of limit curve from the original limit curve. The presentation and of the proposed schemes are verified by closed and open figures. The given table shows the less deviation of the limit curves by proposed scheme as compare to the existing scheme. Graphical representation of deviation error is also presented and it shows that as the number of control points increases, the deviation error decreases.