https://doi.org/10.1140/epjs/s11734-023-00862-0
Regular Article
A fractal model for constrained curve and surface interpolation
1
School of Advanced Sciences, VIT-AP University, 522020, Amaravati, Andhra Pradesh, India
2
Department of Mathematics, Visvesvaraya National Institute of Technology Nagpur, 440010, Nagpur, Maharashtra, India
Received:
27
September
2022
Accepted:
3
May
2023
Published online:
16
June
2023
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.
Framework of Fractals in Data Analysis: Theory and Interpretation. Guest editors: Santo Banerjee, A. Gowrisankar.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
