A variational approach to subdivision

In this paper a new class of interpolatory re nement schemes is presented which in every re nement step determine the new points by solving an optimization problem. In general, these schemes are global, i.e., every new point depends on all points of the polygon to be re ned. By choosing appropriate quadratic functionals to be minimized iteratively during re nement, very e cient schemes producing limiting curves of high smoothness can be de ned. The well known class of stationary interpolatory re nement schemes turns out to be a special case of these variational schemes.