Given a set of scattered data, we usually use a minimal energy method to find Lagrange interpolation based on bivariate spline spaces over a triangulation of the scattered data locations. It is known that the approximation order of the minimal energy spline interpolation is only 2 in terms of the size of triangulation. To improve this order of approximation, we propose several new schemes in th...

This paper is concerned with the nonnegativity preserving interpolation of data on rectangular grids. The function is a kind of bivariate rational interpolation spline with parameters, which is C1 in the whole interpolation region. Sufficient conditions are derived on coefficients in the rational spline to ensure that the surfaces are always nonnegative if the original data are nonnegative. The...

This article presents uniform B-spline interpolation, completely contained on the graphics processing unit (GPU). This implies that the CPU does not need to compute any lookup tables or B-spline basis functions. The cubic interpolation can be decomposed into several linear interpolations [Sigg and Hadwiger 05], which are hard-wired on the GPU and therefore very fast. Here it is demonstrated tha...

In this paper a rational cubic algebraic spline with two shape parameters is developed to create a high-order smoothness interpolation using function values and derivative values which are being interpolated. This is a kind of rational cubic interpolation with quadratic denominator. This rational spline interpolant is monotonic interpolant to given monotonic data. The more important achievement...