G1 quadratic trigonometric beta spline with a shape parameter

Munir, Nur Azliana Azlin; Yahya, Fatimah; Afrouzi, Hadi Nabipour

doi:10.1063/1.5041672

Cited by 3 publications

(2 citation statements)

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“…Due to some limitations in constructing free form curves using conventional methods based on polynomial, many researchers over the years proposed trigonometric splines based on trigonometric polynomials. Munir et al [16] generated a new quadratic trigonometric beta spline with one shape parameter in preserving characteristics of positive data. In constructing smooth spline, relevant shape parameter values are assigned in achieving geometric continuity, G 1 .…”

Section: Related Workmentioning

confidence: 99%

“…The proposed scheme succeeds to generate a positive interpolating curve elsewhere. Munir et al [15] developed G 1 cubic trigonometric spline with the presence of two shape parameters β 1 and β 2 in fitting positive data that results in an effective realistic approximation since it manages to retain features of the real data. A year later, [14] continued the work by generating schemes that interpolate curves and data that not only lie at the position y = 0 axis but also should be above, below or between line or constrained f i = mx i + c. Han et al [6] analyzed the problem of cubic trigonometric polynomial curves and state the conditions of the curve when having the loops, cusps and inflection points.…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

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

Munir¹,

Afrouzi²,

Nasir³

2022

MJMS

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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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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%