The 4-Point α-Ary Approximating Subdivision Scheme

Abstract

A general formula for 4-point -Ary approximating subdivision scheme for curve designing is introduced for any arity 2  . The new scheme is extension of B-spline of degree 6. Laurent polynomial method is used to investigate the continuity of the scheme. The variety of effects can be achieved in correspondence for different values of parameter. The applications of the proposed scheme are illustrated in comparison with the established subdivision schemes.

Family of a-Ary Univariate Subdivision Schemes Generated by Laurent Polynomial

“…Ghaffar et al [14] proposed a 3-point scheme for any arity. They also presented 4-point, -ary subdivision schemes with tension parameter [15]. Zheng et al [16] presented a family 2 Mathematical Problems in Engineering of integer point binary subdivision schemes with tension parameter.…”

Generalized 5-Point Approximating Subdivision Scheme of Varying Arity

“…Later, Ghaffar et al [18] considered 3-point approximating subdivision schemes and observed that the given approach is more universal and is applied to schemes of arbitrary arity. Ghaffar et al [19] introduced a general formula for 4-point a-ary approximating subdivision scheme for curve designing for any arity a ≥ 2.…”

A New Computational Approach to Estimate the Subdivision Depth of n-Ary Subdivision Scheme

“…Generally, the above techniques do not ensure the computations of subdivision depth unless some strong condition is assumed on the mask of the schemes. The condition for curve case is δ 1 < 1 while for surface case is δ 2 < 1, where δ 1 and δ 2 are defined in ( [13], Equations (5) and (6)). The generalizations of the work of [10], [11] is done by [15]- [17] by using the convolution technique.…”