Mathematical and Computational Applications (Oct 2018)

Fractal Behavior of a Ternary 4-Point Rational Interpolation Subdivision Scheme

  • Kaijun Peng,
  • Jieqing Tan,
  • Zhiming Li,
  • Li Zhang

DOI
https://doi.org/10.3390/mca23040065
Journal volume & issue
Vol. 23, no. 4
p. 65

Abstract

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In this paper, a ternary 4-point rational interpolation subdivision scheme is presented, and the necessary and sufficient conditions of the continuity are analyzed. The generalization incorporates existing schemes as special cases: Hassan⁻Ivrissimtzis’s scheme, Siddiqi⁻Rehan’s scheme, and Siddiqi⁻Ahmad’s scheme. Furthermore, the fractal behavior of the scheme is investigated and analyzed, and the range of the parameter of the fractal curve is the neighborhood of the singular point of the rational scheme. When the fractal curve and surface are reconstructed, it is convenient for the selection of parameter values.

Keywords