  This paper presents a description and analysis of a rational cubic spline FIF
(RCSFIF) that has two shape parameters in each subinterval when it is defined
implicitly. To be precise, we consider the iterated function system (IFS) with
$q_n=\frac{P_n}{Q_n}$, $n \in \mathbb{N}_{N-1}$, where $P_n(x)$ are cubic
polynomials to be determined through interpolatory conditions of the
corresponding FIF and $Q_n(x)$ are preassigned quadratic polynomials each
containing two free shape/rationality parameters. We establish the convergence
of the proposed RCSFIF $g$ to the original function $\Phi \in \mathcal{C}^3(I)$
with respect to the uniform norm. We also provide the sufficient conditions for
an automatic selection of the rational IFS parameters to preserve monotonicity
and convexity of a prescribed set of data points. We consider some examples to
illustrate the developed fractal interpolation scheme and its shape preserving
aspects.
