Bivariate hermite subdivision Original Research Article

A subdivision scheme for constructing smooth surfaces interpolating scattered data in R3 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 {(xi, yi)}i=1N from which none of the pairs (xi,yi) and (xj,yj) with i≠j coincide, it is proved that the resulting surface (function) is C1. 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 C2 if the data are not ‘too irregular’. Finally the approximation properties of the methods are investigated.