BIVARIATE HERMITE SUBDIVISION

A subdivision scheme for constructing smooth surfaces interpolating sc attered data in R-3 is proposed. It is also possible to impose derivat ive constraints in these points. In the case of functional data, i.e., data are given in a properly triangulated set of points {(x(i), y(i)) }(i=1)(N) from which none of the pairs (x(i), y(i)) and (x(j), y(j)) w ith i not equal j coincide, it is proved that the resulting surface (f unction) is C-1. 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 diffe rentiable, yields a function which is C-2 if the data are not 'too irr egular'. Finally the approximation properties of the methods are inves tigated. (C) 1997 Elsevier Science B.V.