Visualization of constrained data by smooth rational fractal interpolation

Abstract

A family of smooth rational spline fractal interpolation function (SRFIF) is presented with the help of classical rational cubic spline. Each SRFIF of the family is identified uniquely by the values of vertical scaling factor s i and shape parameters α i and β i , and the shape of the fractal interpolating curves can be constrained and modified by selecting suitable parameters and vertical scaling factor. In order to meet the needs of practical design, a new method is developed to visualize constrained data in the view of constrained curves. In the special case, the methods of linear constraint and quadratic constraint are discussed. Also, convergence analysis shows that SRFIF gives a good approximation to the original function.