A new four-point shape-preserving <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:math> subdivision scheme

Tan, Jieqing; Zhuang, Xinglong; Zhang, Li

doi:10.1016/j.cagd.2013.12.003

Cited by 19 publications

(16 citation statements)

References 16 publications

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“…For example, Hassan et al [7,8] present a ternary 4-point interpolation scheme and ternary 3-point approximate scheme that generate C 2 continuity limiting curves. Tan et al [9] also present a new four-point shape-preserving C 3 subdivision. Li et al first present interproximate curve subdivision in [10], which combine interpolatory and approximate subdivision.It is expected to improve behavior of the limit curves.…”

Section: Introductionmentioning

confidence: 96%

Four point interpolatory-corner cutting subdivision

Tan

Tong

Zhang

et al. 2015

Applied Mathematics and Computation

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Section: Introductionmentioning

confidence: 96%

Four point interpolatory-corner cutting subdivision

Tan

Tong

Zhang

et al. 2015

Applied Mathematics and Computation

Self Cite

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“…al. [15], which derived the monotonic preservation. Herein, in current study, we examined monotonicity preservation of ternary and quaternary subdivision schemes.…”

Section: Kuijt and Dammementioning

confidence: 99%

A Family of 6-Point n-Ary Interpolating Subdivision Schemes

Bashir

Mustafa

2018

Mehran Univ. res. j. eng. technol.

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We derive three-step algorithm based on divided difference to generate a class of 6-point n-ary interpolating sub-division schemes. In this technique second order divided differences have been calculated at specific position and used to insert new vertices. Interpolating sub-division schemes are more attractive than approximating schemes in computer aided geometric designs because of their interpolation property. Polynomial generation and polynomial reproduction are attractive properties of sub-division schemes.Shape preserving properties are also significant tool in sub-division schemes. Further, some significant properties of ternary and quaternary sub-division schemes have been elaborated such as continuity, degree of polynomial generation, polynomial reproduction and approximation order. Furthermore, shape preserving property that is monotonicity is also derived. Moreover, the visual performance of proposed schemes has also been demonstrated through several examples.

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“…Figures 2 and 3 are produced by using monotone data set presented in Table 1 borrowed by [17]. In Figure 2 (a), curve is generated by using cubic Hermite spline which looses the monotone shape of the data, Figures 2 (b)-(e) are monotone curves obtained by rational cubic function [16], [31], schemes (2.2) and (2.3) at µ = 0.5, respectively. It must be noted that rational cubic function tightly fit the data while schemes (2.2) and (2.3) have relaxed data fitting.…”

Section: Demonstrationmentioning

confidence: 99%

“…Hao et al [14] introduced a linear 6-point binary approximating subdivision scheme which preserves convexity while its support is large. Tan et al [31] presented only a binary four point subdivision scheme which preserve monotonicity and convexity of the limit curve. Owing to this we have evaluated monotonicity, convexity, and concavity preservation of our proposed ternary and quaternary schemes.…”

Section: Introductionmentioning

confidence: 99%

A class of shape preserving 5-point n-ary approximating schemes

Bashir¹,

Mustafa²,

Agarwal³

2018

J. Math. Computer Sci.

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A new class of shape preserving relaxed 5-point n-ary approximating subdivision schemes is presented. Further, the conditions on the initial data assuring monotonicity, convexity and concavity preservation of the limit functions are derived. Furthermore, some significant properties of ternary and quaternary subdivision schemes have been elaborated such as continuity, Hölder exponent, polynomial generation, polynomial reproduction, approximation order, and support of basic limit function. Moreover the visual performance of schemes has also been demonstrated through several examples.

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A new four-point shape-preserving C3 subdivision scheme

Cited by 19 publications

References 16 publications

Four point interpolatory-corner cutting subdivision

Four point interpolatory-corner cutting subdivision

A Family of 6-Point n-Ary Interpolating Subdivision Schemes

A class of shape preserving 5-point n-ary approximating schemes

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