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On Non-Tensor Product Bivariate Fractal Interpolation Surfaces on Rectangular Grids

Author

Listed:
  • Vasileios Drakopoulos

    (Department of Computer Science and Biomedical Informatics, University of Thessaly, 35131 Lamia, Greece
    These authors contributed equally to this work.)

  • Polychronis Manousopoulos

    (Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, 157 84 Athens, Greece
    These authors contributed equally to this work.)

Abstract

Some years ago, several authors tried to construct fractal surfaces which pass through a given set of data points. They used bivariable functions on rectangular grids, but the resulting surfaces failed to be continuous. A method based on their work for generating fractal interpolation surfaces is presented. Necessary conditions for the attractor of an iterated function system to be the graph of a continuous bivariable function which interpolates a given set of data are also presented here. Moreover, a comparative study for four of the most important constructions and attempts on rectangular grids is considered which points out some of their limitations and restrictions.

Suggested Citation

  • Vasileios Drakopoulos & Polychronis Manousopoulos, 2020. "On Non-Tensor Product Bivariate Fractal Interpolation Surfaces on Rectangular Grids," Mathematics, MDPI, vol. 8(4), pages 1-19, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:525-:d:340995
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    References listed on IDEAS

    as
    1. Ri, Songil, 2019. "New types of fractal interpolation surfaces," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 291-297.
    2. Ri, SongIl, 2019. "DUPLICATE: New types of fractal interpolation surfaces," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 52-58.
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    Cited by:

    1. Vasileios Drakopoulos & Dimitrios Matthes & Dimitrios Sgourdos & Nallapu Vijender, 2023. "Parameter Identification of Bivariate Fractal Interpolation Surfaces by Using Convex Hulls," Mathematics, MDPI, vol. 11(13), pages 1-16, June.

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