Computing curves invariant under halving (Q1091743)

This paper unifies and extends some of the most important subdivision algorithms in the one-dimensional case of Computer Aided Geometric Design. This theory permits a general insight to get limit theorems and error estimates in computing curves. Several basic theorems are presented. For the corresponding proofs the authors refer to a forthcoming paper. Further results concern the differentiability and polynomial structure of the functions produced by these algorithms. It is emphasized that similar ideas are applicable for surface generation.