  This paper sets a theoretical foundation for the applications of the fractal
interpolation functions (FIFs). We construct rational cubic spline FIFs
(RCSFIFs) with quadratic denominator involving two shape parameters. The
elements of the iterated function system (IFS) in each subinterval are
identified befittingly so that the graph of the resulting
$\mathcal{C}^1$-RCSFIF lies within a prescribed rectangle. These parameters
include, in particular, conditions on the positivity of the
$\mathcal{C}^1$-RCSFIF. The problem of visualization of constrained data is
also addressed when the data is lying above a straight line, the proposed
fractal curve is required to lie on the same side of the line. We illustrate
our interpolation scheme with some numerical examples
