Preserving Monotonicity of Two-Dimensional Data Using a Three-Parameter Rational Cubic Spline
Keywords:
Fractional Spline, Data Interpolation, Shape PreservationAbstract
Preserving the original form of the data whilst inserting new data is a fundamental challenge in many applications, particularly as a number of common insertion methods used in practical applications result in distortions in the graphical representation of the data. This research proposes a fractional spline function as an interpolation function designed to ensure the smoothness of two-dimensional data whilst avoiding certain physical artefacts such as oscillation, as well as providing the ability to control the shape of sub-intervals locally. The proposed function features three positive parameters that can be adjusted manually, thereby allowing control over the tension or curvature of the graphical curve as required. The method relies on the use of the first derivative in its mathematical sense to ensure a smooth transition between each sub-interval of the function’s curve, resulting in a final shape that is smooth and free from physical artefacts. The research includes numerical examples and comparisons demonstrating that the proposed method offers high efficiency in maintaining the regularity of the function, whilst also providing flexibility, reliability and computational efficiency.
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