A new bivariate interpolation by rational triangular patch

摘要

In this paper, a new approach is proposed to construct bivariate rational spline interpolation over triangulation, based on scattered data in parallel lines. The main advantage of this method have two points: (1) the inter-polation function has a simple and explicit mathematical representation with some parameters α,β,μ,and v; (2) the shape of the interpolating surface can be modified by using the parameters for the unchanged in-terpolating data. Moreover, a local shape control method is employed to control the shape of surfaces.