Shape preservation of 4-point interpolating non-stationary subdivision scheme

A new class of 2m-point non-stationary subdivision schemes (SSs) is presented, including some of their important properties, such as continuity, curvature, torsion monotonicity, and convexity preservation. The multivariate analysis of subdivision schemes is extended to a class of non-stationary schemes which are asymptotically equivalent to converging stationary or non-stationary schemes. A comparison between the proposed schemes, their stationary counterparts and some existing non-stationary schemes has been depicted through examples. It is observed that the proposed SSs give better approximation and more effective results.

show abstract

“…and ≤ λ, which implies 1 λ ≥ Γ j+1 < λ. Therefore, by mathematical induction, we have 1 λ ≥ Γ j < λ, ∀j ≥ 0, j ∈ Z, completing the proof.…”

Section: Theorem 19 Consider the Control Points {Qmentioning

confidence: 98%

“…In 2009, Cai [6] discussed the convexity preservation of 4-point ternary stationary SSs. Recently, in 2017, Wang and Li [33] proposed a family of convexity preserving SSs and Akram et al [1] deduced the shape preserving properties of binary 4-point non-stationary interpolating SSs.…”

Section: Introductionmentioning

confidence: 99%

A new class of 2m-point binary non-stationary subdivision schemes

et al. 2019

View full text Add to dashboard Cite

show abstract

“…In 2009, Cai [21] discuss the convexity preservation of 4-point ternary stationary subdivision scheme. Recently, in 2017, Wang and Li [22] proposed a family of convexity preserving subdivision schemes and Akram et al [23] deduced the shape preserving properties of binary 4-point non-stationary interpolating subdivision schemes.…”

Section: Literature Reviewmentioning

confidence: 99%

Shape Preservation of Tension Controlled Ternary 4-point Non-Stationary Interpolating Subdivision Scheme

Pervez¹,

Shah²

2018

Preprint

View full text Add to dashboard Cite

The aim of this work is to analyze and investigate the shape preserving properties of ternary 4-point non-stationary interpolating subdivision schemes constructed by Beccari et al. [1] with a tension parameter !k+1 which can reproducing exponential. Moreover, the conditions on the initial control points are developed that allow user to generate shape preserving limit curves after a nite number of subdivision steps and generalize these results in limiting case. Signicance of derived conditions are illustrated through graphs and the whole discussion is followed by examples.

show abstract

“…In 2018, Zhang et al [19] proposed a new combined approximating and interpolating ternary four-point SS with multiple parameters. For more details about the generalizations of SSSs, readers can refer to [18,[20][21][22][23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

A New Class of 2q-Point Nonstationary Subdivision Schemes and Their Applications

et al. 2019

View full text Add to dashboard Cite

The main objective of this study is to introduce a new class of 2 q -point approximating nonstationary subdivision schemes (ANSSs) by applying Lagrange-like interpolant. The theory of asymptotic equivalence is applied to find the continuity of the ANSSs. These schemes can be nicely generalized to contain local shape parameters that allow the user to locally adjust the shape of the limit curve/surface. Moreover, many existing approximating stationary subdivision schemes (ASSSs) can be obtained as nonstationary counterparts of the proposed ANSSs.

show abstract

Shape preservation of 4-point interpolating non-stationary subdivision scheme

Cited by 14 publications

References 9 publications

A new class of 2m-point binary non-stationary subdivision schemes

A new class of 2m-point binary non-stationary subdivision schemes

Shape Preservation of Tension Controlled Ternary 4-point Non-Stationary Interpolating Subdivision Scheme

A New Class of 2q-Point Nonstationary Subdivision Schemes and Their Applications

Contact Info

Product

Resources

About