C1-Positivity preserving Bi-quintic blended rational quartic zipper fractal interpolation surfaces

In this article, we introduce a new class of bi-quintic partially blended rational quartic zipper fractal interpolation surfaces (RQZFISs) tailored for surface data over a rectangular grid. The construction of these surfaces begins with the generation of a network of curves using univariable rational quartic spline zipper fractal interpolation functions (RQS ZFIFs) with variable scalings. These fractal curves are then blended with quintic blended functions. The proposed RQZFISs encompass traditional rational surfaces and a class of fractal surfaces as particular cases. We demonstrate that the bivariable interpolant uniformly converges to the data- generating function. Additionally, the theory of positivity preservation for these interpolants is explored, with practical examples provided to illustrate positivity-preserving bivariable interpolants.