A New Bivariate Rational Interpolation over Triangulation

摘要

In many practical problems, it has been detected that the scattered data are usually arranged in parallel lines. Thus, it is necessary to construct the bivariate spline interpolation function over the triangulation lattice. In this paper, we present a new approach to construct bivariate rational spline interpolation over triangulation, based on scattered data in parallel lines. The main advantage of the method is that the interpolation function has a simple and explicit mathematical representation with parameters a and /?, and the shape of the interpolating surface can be modified by using the suitable parameters for the unchanged interpolating data. Moreover, a shape control method is employed to control the shape of surfaces, and numerical examples are presented to show the performance of the method.