Rational fractal surface interpolating scheme with variable parameters

This paper presents a method of construction for Rational Fractal Surfaces (RFSs) on grids by using bivariate rational Fractal Interpolation Functions (FIFs) with function scaling factors. Further, analysis properties of bivariate rational FIFs are investigated, including the convergence, the stability and the box-counting dimension. Compared with the current interpolation, the developed bivariate rational interpolation can recapture the traditional non-recursive shape modifiable interpolation, and provide shape properties of the interpolant and fractality of the derivatives. Numerical examples show that the presented interpolation scheme can describe real phenomenon well.