Regularized smoothing spline with tension is a radial basis function method for interpolation from scattered data. The interpolation is flexible through the choice of the tension parameter which controls the properties of the interpolation function and smoothing parameter which enables to filter out the noise. The function has regular derivatives of arbitrary order and can be used for interpolation in arbitrary dimension (2D, 3D, 4D and higher). These methods have been developed by Lubos Mitas at NCSA , (see also Mitasova and Mitas 1993, Mitasova et al. 1995) and Mitas and Mitasova 1988, Computers and Mathematics with Applications, v16, p. 983.

Further enhancements will include a new parameter which enables independent tuning of the impact of higher derivatives on the interpolation function, generalizing tension from a scalar to a tensor and regularized spline with tension for interpolation on a sphere ( Mitas and Mitasova, in preparation).