Analysis of Geometric Properties of Ternary Four-Point Rational Interpolating Subdivision Scheme

This paper uses the continued fraction technique to construct a nonstationary 4-point ternary interpolatory subdivision scheme, which provides the user with a tension parameter that effectively handles cusps compared with a stationary 4-point ternary interpolatory subdivision scheme. Then, the continuous nonstationary 4-point ternary scheme is analyzed, and the limit curve is at least C 2 -continuous. Furthermore, the monotonicity preservation and convexity preservation are proved.

Section: Introductionmentioning

confidence: 99%

A Nonstationary Ternary 4-Point Shape-Preserving Subdivision Scheme

Tan

Tong

2021

“…ey also analyzed degree of smoothness of a family of ternary 3point and 4-point subdivision schemes which are C 1 and C 3 continuity, respectively. Ashraf et al [11,12] presented and analyzed the geometrical properties of the 4-point ternary interpolating subdivision scheme.…”

Section: Introductionmentioning

confidence: 99%

A Family of Integer-Point Ternary Parametric Subdivision Schemes

Mustafa

Asghar

Ali

et al. 2021

New subdivision schemes are always required for the generation of smooth curves and surfaces. The purpose of this paper is to present a general formula for family of parametric ternary subdivision schemes based on the Laurent polynomial method. The different complexity subdivision schemes are obtained by substituting the different values of the parameter. The important properties of the proposed family of subdivision schemes are also presented. The continuity of the proposed family is C 2 m . Comparison shows that the proposed family of subdivision schemes has higher degree of polynomial generation, degree of polynomial reproduction, and continuity compared with the exiting subdivision schemes. Maple software is used for mathematical calculations and plotting of graphs.

“…ey discuss the shape preserving properties of the subdivision scheme. Ashraf et al [6,7] presented and analyzed the geometrical properties of four point interpolating subdivision schemes. Hameed et al [8] presented a 4-point subdivision scheme for regular curves and surfaces design.…”

Section: Introductionmentioning

confidence: 99%

The Family of Multiparameter Quaternary Subdivision Schemes

Mustafa

Asghar

Ali

et al. 2021

In the field of subdivision, the smoothness increases as the arity of schemes increases. The family of high arity schemes gives high smoothness comparative to low arity schemes. In this paper, we propose a simple and generalized formula for a family of multiparameter quaternary subdivision schemes. The conditions for convergence of subdivision schemes are also presented. Moreover, we derive subdivision schemes after substituting the different values of parameters. We also analyzed the important properties of the proposed family of subdivision schemes. After comparison with existing schemes, we analyze that the proposed family of subdivision schemes gives better smoothness and approximation compared with the existing subdivision schemes.