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

1
School of Mathematics, Hefei University of Technology, Hefei 230009, China
2
School of Computer and Information, Hefei University of Technology, Hefei 230009, China
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2018, 23(4), 65; https://doi.org/10.3390/mca23040065
Received: 17 October 2018 / Accepted: 22 October 2018 / Published: 23 October 2018
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Abstract

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. View Full-Text
Keywords: subdivision scheme; rational mask; subdivision matrix; C2 continuity; fractal behavior subdivision scheme; rational mask; subdivision matrix; C2 continuity; fractal behavior
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Peng, K.; Tan, J.; Li, Z.; Zhang, L. Fractal Behavior of a Ternary 4-Point Rational Interpolation Subdivision Scheme. Math. Comput. Appl. 2018, 23, 65.

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