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
This paper presented the G1 cubic trigonometric spline function with three shape parameters that generate a constrained curve that interpolates 2D data. The purpose of this research is to ensure the generated curve passes through all data point yet satisfied the three cases of line constraints given. The three cases are: the data must lie above line Li the data must lie below line Li and lastly, the data must lie between two lines Li,1 and Li,2. A simpler theorem is implemented involving the roles of shape parameters. Two of the shape parameters are set free, while another parameter is fixed to fulfil all the three cases stated. The results show that a smooth curve of the G1 cubic trigonometric spline function can be produced within the constrained line by using the theorem developed while the hereditary shape of the data is preserved. Numerical examples are illustrated and discussed.
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