Positivity preserving curves using rational cubic Ball interpolant

Tahat, Ayser Nasir Hassan; Piah, Abd Rahni Mt; Yahya, Zainor Ridzuan

doi:10.1063/1.4932425

Cited by 2 publications

(1 citation statement)

References 13 publications

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“…Meng Tian [13] preserved the shape of monotone data by C 1 piecewise rational cubic spline with two shape parameters that can be used to generate the desired monotone curves, but there is no flexibility for the user to refine the curves further if needed so it is unsuitable for interactive curve design. In this paper we will use the same interpolant in [14] to solve the problem of monotonicity. The proposed scheme providing extra freedom for the user to modify the shape of the curve.…”

Section: Introductionmentioning

confidence: 99%

Rational cubic Ball curves for monotone data

Tahat¹,

Piah²,

Yahya³

2016

AIP Conference Proceedings

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Abstract.A problem of monotonicity preserving interpolation is discussed in this presentation. If a given set of data is monotonic, we want the interpolant to also be monotonic. A rational interpolation scheme is developed. This scheme utilizes piecewise rational cubic Ball functions with four shape parameters in its description. Sufficient conditions to preserve the shape inherent in the data are derived. Three parameters will be allowed for a designer to further refine or control the shape of the curve, if desired. The arithmetic mean algorithm is used to approximate the first derivative at each data point. The degree of smoothness is C 1 . A number of numerical examples are presented.

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Section: Introductionmentioning

confidence: 99%

Rational cubic Ball curves for monotone data

Tahat¹,

Piah²,

Yahya³

2016

AIP Conference Proceedings

Self Cite

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Positivity Preserving Interpolation by Using Rational Cubic Ball Spline

Karim

2016

Jurnal Teknologi

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This paper discusses the positivity preserving by using rational cubic Ball interpolant of the form cubic/quadratic with two parameters. The sufficient condition for the positivity is derived on one parameter meanwhile the other one is a free parameter to control the final shape of the interpolating curves. The degree smoothness achieved is . From numerical results, the rational cubic Ball spline with two parameters gives smooth interpolating positive curves as well as visually pleasing for computer graphics visualization. Furthermore the scheme is better than existing schemes i.e. its easiness to use and less computation. All numerical results are produced by using Mathematica.

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Positivity preserving curves using rational cubic Ball interpolant

Cited by 2 publications

References 13 publications

Rational cubic Ball curves for monotone data

Rational cubic Ball curves for monotone data

Positivity Preserving Interpolation by Using Rational Cubic Ball Spline

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