C1 Cubic Trigonometric Spline with a Shape Parameter for Positive Shape Preservation

IF 0.5 Q3 MATHEMATICS

Malaysian Journal of Mathematical Sciences Pub Date : 2022-01-31 DOI:10.47836/mjms.16.1.05

N. A. A. Munir, N. A. Hadi, M. Nasir

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Abstract

This paper presents a new construction of C1 cubic trigonometric spline interpolation. Instead of repositioning control points, a shape parameter is introduced in the spline to control the shape and behaviour of the curves. The built basis functions fulfil all the geometric properties of the standard cubic Bezier curve, and the proof is included in this paper. Then, the interpolation of the spline is illustrated using suitable parameter values. Every curve segment comprises four successive control points with a cubic trigonometric spline that carries out all the curve properties. The result showed effective approximation since the developed C1 cubic trigonometric spline produced a smooth and pleasant interpolating curve while preserving the positive data features. The flexibility of the developed spline is compared with the other two existing works: b-spline and bezier-like curves. The analysis shows that the proposed spline gives greater flexibility since it has a broader parameter value range. Therefore, this helps the spline interpolation build opened and closed curves, as incorporated in the paper.Munir, N. A. A. A

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具有正形状保存参数的C1三次三角样条

提出了C1三次三角样条插值的一种新构造。在样条中引入形状参数来控制曲线的形状和行为，而不是重新定位控制点。所建立的基函数满足标准三次贝塞尔曲线的所有几何性质，并给出了证明。然后，利用合适的参数值对样条曲线进行插值。每个曲线段由四个连续的控制点组成，具有执行所有曲线属性的三次三角样条。结果表明，所建立的C1三次三角样条曲线在保留正数据特征的情况下，产生了光滑宜人的插值曲线，是一种有效的逼近。将所建立的样条曲线的柔度与现有的b样条曲线和贝塞尔曲线进行了比较。分析表明，所提出的样条曲线具有更大的参数取值范围，具有更大的灵活性。因此，这有助于样条插值建立开放和封闭的曲线，在论文中纳入。慕尼尔，n.a.a.a

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来源期刊

Malaysian Journal of Mathematical Sciences MATHEMATICS-

CiteScore

1.10

自引率

20.00%

发文量

期刊介绍： The Research Bulletin of Institute for Mathematical Research (MathDigest) publishes light expository articles on mathematical sciences and research abstracts. It is published twice yearly by the Institute for Mathematical Research, Universiti Putra Malaysia. MathDigest is targeted at mathematically informed general readers on research of interest to the Institute. Articles are sought by invitation to the members, visitors and friends of the Institute. MathDigest also includes abstracts of thesis by postgraduate students of the Institute.