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A fractal model for constrained curve and surface interpolation

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Abstract

In the literature, a rational cubic spline fractal interpolation function is developed using a rational iterated function system. The parameters (namely, scaling factors and shape parameters) of the rational iterated function system in each subinterval are identified befittingly so that the graph of the resulting rational cubic spline fractal interpolation function lies within a prescribed rectangle. Using a partially blending technique, a rational cubic spline fractal interpolation surface is developed in the literature. The stability analysis of the rational cubic spline fractal interpolation surface is studied with respect to a perturbation in the scaling factors. We investigate the sufficient conditions under which rational cubic spline fractal interpolation surface lies inside a stipulated cuboid. We illustrate our fractal interpolation models with some numerical examples.

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Acknowledgements

The authors are grateful to the anonymous referees for extensive comments that improved the presentation of the paper.

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Authors and Affiliations

  1. School of Advanced Sciences, VIT-AP University, Amaravati, Andhra Pradesh, 522020, India

    K. Mahipal Reddy

  2. Department of Mathematics, Visvesvaraya National Institute of Technology Nagpur, Nagpur, Maharashtra, 440010, India

    N. Vijender

Authors
  1. K. Mahipal Reddy
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  2. N. Vijender
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Correspondence to K. Mahipal Reddy.

Additional information

Framework of Fractals in Data Analysis: Theory and Interpretation. Guest editors: Santo Banerjee, A. Gowrisankar.

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Reddy, K.M., Vijender, N. A fractal model for constrained curve and surface interpolation. Eur. Phys. J. Spec. Top. 232, 1015–1025 (2023). https://doi.org/10.1140/epjs/s11734-023-00862-0

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