A new bivariate interpolation by rational triangular patch
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 interpolation function has a simple and explicit mathematical representation with some parameters alpha, beta, mu and nu; (2) the shape of the interpolating surface can be modified by using the parameters for the unchanged interpolating data. Moreover, a local shape control method is employed to control the shape of surfaces.
bivariate interpolation rational spline scattered data triangular surface shape constraint