Point control of the interpolating curve with a rational cubic spline

Bao, Fangxun; Sun, Qinghua; Duan, Qi

doi:10.1016/j.jvcir.2009.03.003

Cited by 22 publications

(26 citation statements)

References 16 publications

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“…Thus, (5) generalizes the classical rational cubic spline (2). Further, If s i = 0 and the shape parameters α i = β i , the SRFIF reduces to the standard cubic polynomial interpolant.…”

Section: Construction Of Srfifmentioning

confidence: 97%

“…Now we develop a smooth rational spline FIF which is derived from the rational cubic interpolation ϕ(x) defined by (2). Consider the IFS {I × R;…”

Section: Construction Of Srfifmentioning

confidence: 99%

“…In the context of shape preserving and constrained control for curves and surfaces, the rational functions are more effective than the polynomial functions. Many literatures on the rational interpolation have investigated the problem [1,2,10,11,14,15,[19][20][21]. And yet, it is not well explored hitherto in references on the fractal interpolation.…”

Section: Introductionmentioning

confidence: 99%

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Visualization of constrained data by smooth rational fractal interpolation

Liu

Bao

2015

International Journal of Computer Mathematics

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A family of smooth rational spline fractal interpolation function (SRFIF) is presented with the help of classical rational cubic spline. Each SRFIF of the family is identified uniquely by the values of vertical scaling factor s i and shape parameters α i and β i , and the shape of the fractal interpolating curves can be constrained and modified by selecting suitable parameters and vertical scaling factor. In order to meet the needs of practical design, a new method is developed to visualize constrained data in the view of constrained curves. In the special case, the methods of linear constraint and quadratic constraint are discussed. Also, convergence analysis shows that SRFIF gives a good approximation to the original function.

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“…Thus, (5) generalizes the classical rational cubic spline (2). Further, If s i = 0 and the shape parameters α i = β i , the SRFIF reduces to the standard cubic polynomial interpolant.…”

Section: Construction Of Srfifmentioning

confidence: 97%

“…Now we develop a smooth rational spline FIF which is derived from the rational cubic interpolation ϕ(x) defined by (2). Consider the IFS {I × R;…”

Section: Construction Of Srfifmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Visualization of constrained data by smooth rational fractal interpolation

Liu

Bao

2015

International Journal of Computer Mathematics

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“…It can be shown that P 1 .0.3/ D 216333 55000 D 3.9333 by (16). For the given interpolating data, if the design requires P.0.3/ D 3.8, then u D 0.6 by (9).…”

Section: (*) Value Controlmentioning

confidence: 99%

Reconstruction of curves with minimal energy using a blending interpolator

Sun

Bao

Pan³

et al. 2012

Math Methods in App Sciences

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A weighted blending interpolator, a kind of smooth rational spline based only on function values, is constructed using a rational cubic spline and a polynomial spline. In order to meet the needs of practical design, a new control method is employed to control the shape of curves. The advantage of the method is that it can be applied to modify the local shape of an interpolating curve by selecting suitable parameters and weight coefficients simply. Also, when the weight coefficient is in [0,1], the error estimation formula of this interpolator is obtained. Copyright © 2012 John Wiley & Sons, Ltd.

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“…Rational cubic spline curves with G 2 continuity is considered in the work [11]. Weighted rational cubic spline interpolation and its application are considered in the articles [12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%