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Fractal Interpolation Algorithms For Complex Curves And Surfaces

Author

Listed:
  • ZHONG DAI

    (School of Control Science and Engineering, Shandong University, Jinan 250061, Shandong, P. R. China)

  • SHUTANG LIU

    (School of Control Science and Engineering, Shandong University, Jinan 250061, Shandong, P. R. China)

Abstract

This paper provides a new idea for interpolating complex curves and surfaces by fractal interpolation. A type of bivariate fractal interpolation functions with function vertical scaling factors for the special interpolation data set is presented. The interpolation algorithm is proposed for complex curves by contour lines of two types of fractal interpolation functions which are proposed by this paper and Navascués et al. [Construction of fractal surfaces, Fractals 28(2) (2020) 2050033], respectively. Meanwhile, some properties of the interpolation algorithm are introduced. Then, the two classes of fractal interpolation functions are extended to the cases of trivariate functions. We also introduce the interpolation algorithm for complex surfaces based on iso-surfaces of fractal interpolation functions constructed. Finally, several examples are provided.

Suggested Citation

  • Zhong Dai & Shutang Liu, 2023. "Fractal Interpolation Algorithms For Complex Curves And Surfaces," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(05), pages 1-14.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:05:n:s0218348x23500408
    DOI: 10.1142/S0218348X23500408
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