Bivariate hermite subdivision

A subdivision scheme for constructing smooth surfaces interpolating scattered data in 1~3 is proposed. It is also possible to impose derivative constraints in these points. In the case of functional data, i,e., data are given in a properly triangulated set of points {(x~, y~)}~=~ from which none of the pairs (xi, Yi) and (x j, gj) with i ~ j coincide, it is proved that the resulting surface (function) is C t. The method is based on the construction of a sequence of continuous splines of degree 3. Another subdivision method, based on constructing a sequence of splines of degree 5 which are once differentiable, yields a function which is C 2 if the data are not 'too irregular'. Finally the approximation properties of the methods are investigated.