A new C2 rational interpolation based on function values and constrained control of the interpolant curves

In this paper a new method is developed to create a high-order smoothness interpolation using values of the function being interpolated. This is a kind of rational cubic interpolation with quadratic denominator. This rational spline not only belongs to C2 in the interpolating interval, but could also be used to constrain the shape of the interpolant curve such as to force it to be in the given region, all because of the selectable parameters in the rational spline itself. The more important achievement mathematically of this method is that the uniqueness of the interpolating function for the given data would be replaced by the uniqueness of the interpolating curve for the given data and the selected parameters.