Convexity preservation of five-point binary subdivision scheme with a parameter

Tan, Jieqing; Yao, Yangang; Cao, Huijuan; Zhang, Li

doi:10.1016/j.amc.2014.07.071

Cited by 16 publications

(9 citation statements)

References 15 publications

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“…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. Others about subdivision were described in [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Four point interpolatory-corner cutting subdivision

Tan

Tong

Zhang

et al. 2015

Applied Mathematics and Computation

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Section: Introductionmentioning

confidence: 99%

Four point interpolatory-corner cutting subdivision

Tan

Tong

Zhang

et al. 2015

Applied Mathematics and Computation

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“…Example 25: Figure 3 shows the interpolatory behaviors of the scheme up to three refinement steps whereas the doted polygon is the initial sketch which is made by six initial control points (x, y) = (5, 0), (10, 0), (20,10), (10,20), (5,20), (−5, 10) denoted by red solid circles. Here we fix the values of parameters as α = 0 and β = −0.05.…”

Section: Numerical and Graphical Analysis Of The Shapesmentioning

confidence: 99%

“…Tan et al [9] presented a 4-point C 3 scheme with two parameters in 2014. In 2014, Tan et al [10] also presented a 5-point scheme with one parameter. Zheng et al [11] introduced a scheme with multi-parameters in 2014.…”

Section: Introductionmentioning

confidence: 99%

A Class of Refinement Schemes With Two Shape Control Parameters

et al. 2020

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A subdivision scheme defines a smooth curve or surface as the limit of a sequence of successive refinements of given polygon or mesh. These schemes take polygons or meshes as inputs and produce smooth curves or surfaces as outputs. In this paper, a class of combine refinement schemes with two shape control parameters is presented. These even and odd rules of these schemes have complexity three and four respectively. The even rule is designed to modify the vertices of the given polygon, whereas the odd rule is designed to insert a new point between every edge of the given polygon. These schemes can produce high order of continuous shapes than existing combine binary and ternary family of schemes. It has been observed that the schemes have interpolating and approximating behaviors depending on the values of parameters. These schemes have an interproximate behavior in the case of non-uniform setting of the parameters. These schemes can be considered as the generalized version of some of the interpolating and B-spline schemes. The theoretical as well as the numerical and graphical analysis of the shapes produced by these schemes are also presented.

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“…Kuijt and van Damme present a local nonlinear interpolatory subdivision scheme which is monotonicity preserving in [9], and Kuijt and van Damme also research a type of shape-preserving 4-point interpolatory subdivision scheme which interpolated nonuniform data in [10]. Tan et al discuss the monotonicity preservation and convexity preservation of the binary subdivision scheme [11,12]. Several subdivision schemes are designed to have their unique properties in [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

A Nonstationary Ternary 4-Point Shape-Preserving Subdivision Scheme

Tan

Tong

2021

Journal of Mathematics

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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.

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Convexity preservation of five-point binary subdivision scheme with a parameter

Cited by 16 publications

References 15 publications

Four point interpolatory-corner cutting subdivision

Four point interpolatory-corner cutting subdivision

A Class of Refinement Schemes With Two Shape Control Parameters

A Nonstationary Ternary 4-Point Shape-Preserving Subdivision Scheme

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