Bivariate Hermite Subdivision

摘要

A subdivision scheme for constructing smooth surfaces interpolating scattereddata in three-dimensional real numbers is proposed. It is also possible to impose derivative constraints in these points. 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(sup 2) if the data are not 'too irregular'. Finally, the approximation properties of the methods are investigated.