Scattered data fitting with bivariate splines

We describe scattered data fitting by bivariate splines, i.e., splines defined w.r.t. triangulations in the plane. These spaces are powerful tools for the efficient approximation of large sets of scattered data which appear in many real world problems. Bernstein-Bezier techniques can be used for the efficient computation of bivariate splines and for analysing the complex structure of these spaces. We report on the classical approaches and we describe interpolation and approximation methods for bivariate splines that have been developed recently. For the latter methods, we give illustrative examples treating sets of geodetic data (consisting of Up to 10(6) points).