The construction of λμ-B-spline curves and its application to rotational surfaces

Hu, Gang; Qin, Xinqiang; Ji, Xiaomin; Wei, Guo; Zhang, Suxia

doi:10.1016/j.amc.2015.05.056

Cited by 12 publications

(9 citation statements)

References 17 publications

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“…Specifically, the shape of a Bézier curve is well-determined by its control points after choosing the basis functions [17]. In recent years, in order to improve the performance of Bézier curves, many scholars have constructed some new curves which are similar to the Bézier ones by introducing parameters into basis functions; see [18][19][20][21][22]. These new curves share many basic properties with the Bézier ones.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Approximate Multidegree Reduction ofλ-Bézier Curves

Cao

Zhang

2016

Mathematical Problems in Engineering

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Besides inheriting the properties of classical Bézier curves of degreen, the correspondingλ-Bézier curves have a good performance in adjusting their shapes by changing shape control parameter. In this paper, we derive an approximation algorithm for multidegree reduction ofλ-Bézier curves in theL2-norm. By analysing the properties ofλ-Bézier curves of degreen, a method which can deal with approximatingλ-Bézier curve of degreen+1byλ-Bézier curve of degreem (m≤n)is presented. Then, in unrestricted andC0,C1constraint conditions, the new control points of approximatingλ-Bézier curve can be obtained by solving linear equations, which can minimize the least square error between the approximating curves and the original ones. Finally, several numerical examples of degree reduction are given and the errors are computed in three conditions. The results indicate that the proposed method is effective and easy to implement.

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Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Approximate Multidegree Reduction ofλ-Bézier Curves

Cao

Zhang

2016

Mathematical Problems in Engineering

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“…These curves are shown by blue lines which are generated by setting μ= −1, 0, 1) and λ =1. The corresponding cubic λ-μ B-spline curve of [14] is shown by red lines in both figure 2 and figure 3. Thus the cubic λ-μ B-spline curve can be made closer to the control polygon than the classical cubic B-spline curve with Bernstein basis.…”

Section: Shape Analysis Of the λ-μ B-spline Curvesmentioning

confidence: 99%

“…We define the cubic blending functions with two shape parameters λ and μ (which are the extension of [14]) as follows: …”

Section: The λ-μ Basis Functions With Two Shape Parametersmentioning

confidence: 99%

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Extension of ?-? B-Spline Curves and Its Application in Surface Modelling

2015

IJSR

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An extension of λ-μ B-spline curves with a shape parameter is presented in this paper. Each curve segmet is generated by four consecutive control points. These curves possess most optimal properties of B-spline basis. We can easily obtain different shapes by altering the value of shape parameter. The lower degree of the basis functions provides less computational complexity. The associated λ-μ B-spline surfaces can exactly represent the surfaces of revolution.

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“…In recent years, researchers also paid attention to extension of traditional B-spline methods. But they mainly concentrated on Bezier curves [13], quadratic and cubic uniform B-spline curves [14][15][16][17][18][19]. Uniform B-splines can represent overall continuity closed curves and surfaces.…”

Section: Introductionmentioning

confidence: 99%

Cubic B‐Spline Curves with Shape Parameter and Their Applications

Hou-jun

Xing

et al. 2017

Mathematical Problems in Engineering

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The present studies on the extension of B-spline mainly focus on Bezier methods and uniform B-spline and are confined to the adjustment role of shape parameters to curves. Researchers pay little attention to nonuniform B-spline. This paper discusses deeply the extension of the quasi-uniform B-spline curves. Firstly, by introducing shape parameters in the basis function, the spline curves are defined in matrix form. Secondly, the application of the shape parameter in shape design is analyzed deeply. With shape parameters, we get another means for adjusting the curves. Meanwhile, some examples are given. Thirdly, we discuss the smooth connection between adjacent B-spline segments in detail and present the adjusting methods. Without moving the control points position, through assigning appropriate value to the shape parameter, C 1 continuity of combined spline curves can be realized easily. Results show that the methods are simple and suitable for the engineering application.

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The construction of λμ-B-spline curves and its application to rotational surfaces

Cited by 12 publications

References 17 publications

Approximate Multidegree Reduction ofλ-Bézier Curves

Approximate Multidegree Reduction ofλ-Bézier Curves

Extension of ?-? B-Spline Curves and Its Application in Surface Modelling

Cubic B‐Spline Curves with Shape Parameter and Their Applications

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