[formula omitted]-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. • The class of rational splines is generalized using a binary vector. • A novel class of zipper fractal rational surface interpolants is developed. • The proposed surface interpolants unify traditional rational and fractal surfaces as special cases. • Shape preservation theory is explored, with practical examples provided. [ABSTRACT FROM AUTHOR]