L 1 Spline Methods for Scattered Data Interpolation and Approximation

We generalize the L ₁ spline methods proposed in 4, 5] for scattered data interpolation and fitting using bivariate spline spaces of any degree d and any smoothness r (of course, r<d) over any triangulation. Some numerical experiments are presented to illustrate the better performance of the L ₁ spline methods as compared to the minimal energy method. We include some extensions for dealing with other surface design problems.