Convexity Preservation of the Ternary 6-point Interpolating Subdivision Scheme

Iqbal, Mudassar; Karim, Samsul Ariffin Abdul; Shafie, Afza; Sarfraz, Muhammad

doi:10.1007/978-3-030-79606-8_1

Cited by 3 publications

(3 citation statements)

References 26 publications

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“…By introducing local pushback operation, a brand-new interproximate subdivision framework is established which bridges the gap between interpolating schemes and approximating ones [17]. Convexity preservation of the ternary 6-point interpolating subdivision scheme has been presented in [18]. Te aim of this paper is to determine the convexity and monotonicity preservation of C 3 ternary four-point stationary SS developed by Siddiqi and Rehan [19].…”

Section: Introductionmentioning

confidence: 99%

Convexity and Monotonicity Preservation of Ternary 4-Point Approximating Subdivision Scheme

Akram,

Ullah Khan,

Gobithaasan

et al. 2023

Journal of Mathematics

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This work discusses a ternary 4-point approximation subdivision technique with two properties, namely, convexity and monotonicity preservation. The fundamental contribution of this research article is to extract the conditions that assure the suggested subdivision scheme’s convexity and monotonicity. The methodology for extracting these conditions is explained in two theorems. These theorems prove that if the initial data is strictly convex and monotone and the derived conditions are satisfied, then the limiting curve generated by the proposed subdivision scheme will also be convex and monotone. To show the graphical simulations of results, 2D graphs are plotted. Curvature plots are also drawn to fully comprehend the derived conditions. The entire discourse is backed up by convincing examples.

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Section: Introductionmentioning

confidence: 99%

Convexity and Monotonicity Preservation of Ternary 4-Point Approximating Subdivision Scheme

Akram,

Ullah Khan,

Gobithaasan

et al. 2023

Journal of Mathematics

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“…Zouaoui et al [11] examined the design and analysis of certain novel n-point families for ternary subdivision schemes. Iqbal et al [12] discussed the influence of a geometric characteristic on curve sketching using the tension parameter. Amat et al [13] suggested that the 4-point ternary non-linear non-interpolatory subdivision scheme may eliminate the Gibbs phenomenon.…”

Section: Introductionmentioning

confidence: 99%

“…For certain parameter ranges, the order of continuity of the proposed 3-point binary(11) and 5-point binary(12) schemes.…”

mentioning

confidence: 99%

The Generalized Classes of Linear Symmetric Subdivision Schemes Free from Gibbs Oscillations and Artifacts in the Fitting of Data

Karim,

Mustafa,

Tariq

et al. 2023

Symmetry

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This paper presents the advanced classes of linear symmetric subdivision schemes for the fitting of data and the creation of geometric shapes. These schemes are derived from the B-spline and Lagrange’s blending functions. The important characteristics of the derived schemes, including continuity, support, and the impact of parameters on the magnitude of the artifact and Gibbs oscillations are discussed. Schemes additionally generalize various subdivision schemes. Linear symmetric subdivision schemes can produce Gibbs oscillations when the initial data is taken from discontinuous functions. Additionally, these schemes may generate unwanted artifacts in the limit curve that do not exist in the original polygon. One solution is to use non-linear schemes, but this approach increases the computational complexity of the scheme. An alternative approach is proposed that involves modifying the linear symmetric schemes by introducing parameters into the linear rules. The suitable values of these parameters reduce or eliminate Gibbs oscillations and artifacts while still using linear symmetric schemes. Our approach provides a balance between reducing or eliminating Gibbs oscillations and artifacts while maintaining computational efficiency.

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Fractal and Convexity Analysis of the Quaternary Four-Point Scheme and Its Applications

Yao¹,

Ashraf²,

Ghaffar³

et al. 2023

Fractals

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The main objective of this research is to analyze some geometrical properties of a quaternary four-point interpolatory subdivision scheme ([Formula: see text]-scheme) with a shape parameter and then find the precise range of the shape parameter of the [Formula: see text]-scheme to generate fractal and convexity of limit curves. That allows the curve to change easily and be more flexible without altering its control points. Therefore, by taking the various values of tension parameters, the curve still preserves its characteristics and geometrical configuration. These geometric modeling examples show that our techniques can be easily performed, and they can also provide us with an alternative strong strategy for the modeling of complex figures.

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Convexity Preservation of the Ternary 6-point Interpolating Subdivision Scheme

Cited by 3 publications

References 26 publications

Convexity and Monotonicity Preservation of Ternary 4-Point Approximating Subdivision Scheme

Convexity and Monotonicity Preservation of Ternary 4-Point Approximating Subdivision Scheme

The Generalized Classes of Linear Symmetric Subdivision Schemes Free from Gibbs Oscillations and Artifacts in the Fitting of Data

Fractal and Convexity Analysis of the Quaternary Four-Point Scheme and Its Applications

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