Parameter Identification of Constrained Data by a New Class of Rational Fractal Function
For researchers in fractal interpolation and data visualization, this provides a new constrained interpolation method, but the contribution is incremental as it extends existing rational spline FIFs with additional parameter control.
This paper develops rational cubic spline fractal interpolation functions with two shape parameters to ensure the interpolant lies within prescribed constraints (e.g., positivity or above a line). Numerical examples demonstrate the method's effectiveness for constrained data visualization.
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