Modelling by Shepard-type curves and surfaces

First parametric curves of Shepard-type are studied, which overcome some of the original Shepard operator's drawbacks, have some advantages with respect to the Bezier case and are optimal in some sense. Bounds for the deviation and approximation results for Shepard-type operators faster converging than the original one are proved. As an application a weighted progressive iterative approximation technique interesting in CAGD and an extension to tensor product surfaces case are given.