A New Paradigm to Design a Class of Combined Ternary Subdivision Schemes

Abstract

Subdivision schemes play a vital role in curve modeling. The curves produced by the class of 2 n + 2 -point ternary scheme (Deslauriers and Dubuc (1989)) interpolate the given data while the curves produced by a class of 2 n + 2 -point ternary B-spline schemes approximate the given data. In this research, we merge these two classes to introduce a consolidated and unified class of combined subdivision schemes with two shape control parameters in order to grow versatility for overseeing valuable necessities. However, the proposed class of subdivision schemes gives optimal smoothness in the final shapes, yet we can increase its smoothness by using a proposed general formula in form of its Laurent polynomial. The theoretical analysis of the class of subdivision schemes is done by using various mathematical tools and using their coding in the Maple environment. The graphical analysis of the class of schemes is done in the Maple environment by writing the codes based on the recursive mathematical expressions of the class of subdivision schemes.

Geometric Modelling of a Family of 4-Point Ternary Approximating Subdivision Scheme U_φ with Visual Performance

“…A generalized symbol for the construction of a family of ternary approximating subdivision schemes is proposed. In the construction of this proposed 4-point ternary approximating SDS, the smoothing and refining operators used in [20] are given in equation ( 1) and (2).…”

“…A "combined" subdivision system, described by the authors as a linear combination of two distinct ternary subdivision schemes, is presented. To develop a new scheme with improved properties, the advantages of the two basic systems have to be combined [20]. A novel polynomialbased quaternary subdivision system that can represent a range of curves and surface shapes is presented by Mustafa et al and is controlled by two parameters.…”

A Family of Integer-Point Ternary Parametric Subdivision Schemes

“…ey also discussed the shape preserving properties of the proposed subdivision scheme. Tariq et al [14] presented a unified class of combined subdivision schemes with two-shape control parameters in order to grow versatility for overseeing valuable necessities. Hameed et al [15] presented a new method to construct a family of (2N + 2)-point binary subdivision schemes with one tension parameter.…”