A shape preserving C2 non-linear, non-uniform, subdivision scheme with fourth-order accuracy

Yang, Hyoseon; Yoon, Jungho

doi:10.1016/j.acha.2022.03.006

Cited by 6 publications

(4 citation statements)

References 40 publications

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“…These subdivision schemes are quite flexible and can change their nature by tuning the weight function. These weight functions are also called smoothing parameters [1,6,19,21,22].…”

Section: Introductionmentioning

confidence: 99%

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

Gulzar,

Muhammad Javed Iqbal,

Inayatullah Soomro

et al. 2024

VFAST trans. math.

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Making signals better than noise in communication has always been challenging for scientists. Researchers have been working on it in different ways. The computer-aided geometric design is a new research field emerging from the collaboration of computer algorithms and mathematical logic towards curve designing, in which the subdivision schemes used have a key position due to their flexible and smooth behaviour. Using parameters in these schemes allows for increased control over designing. A parameterized framework for generating a wide range of subdivision surfaces with tunable degrees of shape control is presented in the family of schemes. The properties of the proposed family make it suitable for use in isogeometric analysis, computer animation, and geometric modelling. The purpose of this paper is to construct and analyze a family of 4-point ternary subdivision schemes to smooth the curves based on the Laurant polynomial. This family is generated by tuning the weight parameter. The scheme is analysed for its different properties. The scheme has continuity. Visual performance of the subdivision scheme is also provided as an application of this proposed study.

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“…These subdivision schemes are quite flexible and can change their nature by tuning the weight function. These weight functions are also called smoothing parameters [1,6,19,21,22].…”

Section: Introductionmentioning

confidence: 99%

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

Gulzar,

Muhammad Javed Iqbal,

Inayatullah Soomro

et al. 2024

VFAST trans. math.

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show abstract

“…In a result, this SS generates the C 1 limit function with a second approximation order. In 2022, Yang and Yoon formulated a shape-preserving nonlinear SS, which generalized the B-spline of degree 3 [4]. Monotonicity-and convexity-preserving conditions of this SS were extracted, providing an improved approximation order of four while maintaining the same smoothness as the B-spline of degree 3.…”

Section: Introductionmentioning

confidence: 99%

“…Consider the set of initial control points and the limit curve which is generated without satisfying the derived sufcient condition of monotonicity. Figure 1(a) displays the initial control polygon using the monotonic increasing set {(1,1.5), (2,2), (3,4), (4,20.5), (5,21), (6,23), (7,36), (8,38), (9,40)} in which the monotonicity additional condition is not satisfed. Figure 1(b) displays the limit curve generated by the scheme in equation ( 1) for θ � 0.0209 with a blue solid line.…”

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confidence: 99%

“…To highlight the signifcance of the sufcient condition of monotonicity, considering a set of initial control points, the limit curve is generated which preserves the monotonicity of the initial data. Figure 2(a) displays the initial control polygon with the set {(1,1.5), (2,2), (3,4), (4,6), (5,7.5), (6,8.2), (7,10.5), (8,12), (9,14)} in which the control points are increasing monotonically, but the monotonicity additional condition is satisfed. Figure 2(b) displays the limit curve generated by the scheme in equation ( 1) for θ � 0.0209 with blue solid line.…”

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confidence: 99%

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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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Shape preserving rational [3/2] Hermite interpolatory subdivision scheme

Bebarta

Jena

2023

Calcolo

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A shape preserving C2 non-linear, non-uniform, subdivision scheme with fourth-order accuracy

Cited by 6 publications

References 40 publications

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

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

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

Shape preserving rational [3/2] Hermite interpolatory subdivision scheme

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