TY - JOUR
T1 - Monotonicity/Symmetricity Preserving Rational Quadratic Fractal Interpolation Surfaces
AU - Chand , A. K. B.
AU - Vijender , N.
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, Fractal Interpolation Functions, Rational Quadratic Fractal Interpolation Surfaces, Convergence, Monotonicity, Symmetricity.
AB - <p style="text-align: justify;">This paper presents the theory of $\mathcal{C}^1$-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 $\mathcal{C}^1$-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.</p>