SMOOTH SURFACE INTERPOLATION TO SCATTERED DATA USING INTERPOLATORY SUBDIVISION ALGORITHMS

In this paper, a smooth interpolatory subdivision algorithm for the ge neration of interpolatory surfaces (GC(1)) over arbitrary triangulatio ns is constructed and its convergence properties over nonuniform trian gulations studied. An immediate application of this algorithm to surfa ce interpolation to scattered data in R(n), n greater than or equal to 3 is also studied. For uniform data, this method is a generalization of the analyses for univariate subdivision algorithms, and for nonunif orm data, an extraordinary point analysis is proposed and a local subd ivision matrix analysis presented. (-)It is proved that the subdivisio n algorithm produces smooth surfaces over arbitrary networks provided the shape parameters of the algorithm are kept within an appropriate r ange. Some error estimates for both uniform and nonuniform triangulati ons are also investigated. Finally, three graphical examples of surfac e interpolations over nonuniform data are given to show the smoothing interpolating process of the algorithm.