Volume 13, Issue 1
Monotonicity/Symmetricity Preserving Rational Quadratic Fractal Interpolation Surfaces

A.K.B. Chand & N. Vijender

DOI:

Int. J. Numer. Anal. Mod., 13 (2016), pp. 145-165

Published online: 2016-01

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  • Abstract

This paper presents the theory of C¹-rational quadratic fractal interpolation surfaces (FISs) over a rectangular grid. First we approximate the original function along the grid lines of interpolation domain by using the univariate C¹-rational quadratic fractal interpolation functions (fractal boundary curves). Then we construct the rational quadratic FIS as a blending combination with the x-direction and y-direction fractal boundary curves. The developed rational quadratic FISs are monotonic whenever the corresponding fractal boundary curves are monotonic. We derive the optimal range for the scaling parameters in both positive and negative directions such that the rational quadratic fractal boundary curves are monotonic in nature. The relation between x-direction and y-direction scaling matrices is deduced for symmetric rational quadratic FISs for symmetric surface data. The presence of scaling parameters in the fractal boundary curves helps us to get a wide variety of monotonic/symmetric rational quadratic FISs without altering the given surface data. Numerical examples are provided to demonstrate the comprehensive performance of the rational quadratic FIS in fitting a monotonic/symmetric surface data. The convergence analysis of the monotonic rational quadratic FIS to the original function is reported.

  • Keywords

Fractals Fractal Interpolation Functions Rational Quadratic Fractal Interpolation Surfaces Convergence Monotonicity Symmetricity

  • AMS Subject Headings

28A80 41A20 65D05 65D07 65D10 65D17 26A48

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-13-145, author = {A.K.B. Chand and N. Vijender}, title = {Monotonicity/Symmetricity Preserving Rational Quadratic Fractal Interpolation Surfaces}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {1}, pages = {145--165}, abstract = {This paper presents the theory of C¹-rational quadratic fractal interpolation surfaces (FISs) over a rectangular grid. First we approximate the original function along the grid lines of interpolation domain by using the univariate C¹-rational quadratic fractal interpolation functions (fractal boundary curves). Then we construct the rational quadratic FIS as a blending combination with the x-direction and y-direction fractal boundary curves. The developed rational quadratic FISs are monotonic whenever the corresponding fractal boundary curves are monotonic. We derive the optimal range for the scaling parameters in both positive and negative directions such that the rational quadratic fractal boundary curves are monotonic in nature. The relation between x-direction and y-direction scaling matrices is deduced for symmetric rational quadratic FISs for symmetric surface data. The presence of scaling parameters in the fractal boundary curves helps us to get a wide variety of monotonic/symmetric rational quadratic FISs without altering the given surface data. Numerical examples are provided to demonstrate the comprehensive performance of the rational quadratic FIS in fitting a monotonic/symmetric surface data. The convergence analysis of the monotonic rational quadratic FIS to the original function is reported.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/431.html} }
TY - JOUR T1 - Monotonicity/Symmetricity Preserving Rational Quadratic Fractal Interpolation Surfaces AU - A.K.B. Chand & N. Vijender JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 145 EP - 165 PY - 2016 DA - 2016/01 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/431.html KW - Fractals KW - Fractal Interpolation Functions KW - Rational Quadratic Fractal Interpolation Surfaces KW - Convergence KW - Monotonicity KW - Symmetricity AB - This paper presents the theory of C¹-rational quadratic fractal interpolation surfaces (FISs) over a rectangular grid. First we approximate the original function along the grid lines of interpolation domain by using the univariate C¹-rational quadratic fractal interpolation functions (fractal boundary curves). Then we construct the rational quadratic FIS as a blending combination with the x-direction and y-direction fractal boundary curves. The developed rational quadratic FISs are monotonic whenever the corresponding fractal boundary curves are monotonic. We derive the optimal range for the scaling parameters in both positive and negative directions such that the rational quadratic fractal boundary curves are monotonic in nature. The relation between x-direction and y-direction scaling matrices is deduced for symmetric rational quadratic FISs for symmetric surface data. The presence of scaling parameters in the fractal boundary curves helps us to get a wide variety of monotonic/symmetric rational quadratic FISs without altering the given surface data. Numerical examples are provided to demonstrate the comprehensive performance of the rational quadratic FIS in fitting a monotonic/symmetric surface data. The convergence analysis of the monotonic rational quadratic FIS to the original function is reported.
A.K.B. Chand & N. Vijender. (1970). Monotonicity/Symmetricity Preserving Rational Quadratic Fractal Interpolation Surfaces. International Journal of Numerical Analysis and Modeling. 13 (1). 145-165. doi:
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