Spline Approximations for an Arbitrarv Simplex Mesh.’

In this paper we develop a polynomial spline approximation for data in Euclidean space. The approach considered involves generating an abstract set which provides a unique parametrization of the geometry of the data considered. Polynomial functions from this set to Euclidean space are considered which provide an interpolation function whose computational cost grows at worst iineruly with the dimension of the problem. Coefficients for the polynomial functions are determined via the solution of a constrained linear system generated by imposing continuity, differentiability and convexity requirements on the interpolation. Once a suitable choice of polynomial coefficients has been made the quality of the approximation can be improved with low computational overheads.