Rational Spline Function And Its Application

Interpolation of rational spline is a natural extension of polynomial spline. Owing to the practical background of modeling by curves and surfaces, it has been widely focused by people. The research in this field is very productive. Firstly, this paper briefly summarizes theory and structural means of one variable rational spline interpolation, especially discusses the monotonicity preserving, convexity preserving and error analysis of piecewise rational cubic spline function involving two tension parameters. And on the basis of it, this paper constructs rational cubic spline function based on function values and elaborates the construction's feasibility through numerical example. Then the paper constructs weighted rational cubic spline interpolation function and discusses region control and approximation properties by using the above-mentioned rational cubic spline function involving two tension parameters.Secondly, this paper introduces some basic theories and problems on kinds of special partition of bivariate rational spline function.Finally, an application on the rational cubic spline involving one parameter in the modeling of curves and surfaces is introduced in the paper, and the tension parameter make the curves and surfaces have global and local tension properties.