A fractal model for constrained curve and surface interpolation

In the literature, a rational cubic spline fractal interpolation function is developed using a rational iterated function system. The parameters (namely, scaling factors and shape parameters) of the rational iterated function system in each subinterval are identified befittingly so that the graph of the resulting rational cubic spline fractal interpolation function lies within a prescribed rectangle. Using a partially blending technique, a rational cubic spline fractal interpolation surface is developed in the literature. The stability analysis of the rational cubic spline fractal interpolation surface is studied with respect to a perturbation in the scaling factors. We investigate the sufficient conditions under which rational cubic spline fractal interpolation surface lies inside a stipulated cuboid. We illustrate our fractal interpolation models with some numerical examples.