Subdivision schemes are iterative procedures to construct curves and constitute fundamental tools in Computer Aided Design. Starting with an initial control polygon, a subdivision scheme refines the
computed values at the previous step according to some basic rules.
The scheme is said to be convergent if there exists a limit curve. The computed values define a control polygon in each step. This paper is devoted to estimate error bounds between the “ideal” limit curve and
the control polygon defined after k subdivision stages. In particular,
a stop criteria of convergence is obtained. The considered refinement rules in the paper are widely used in practice and are associated to the well known two-scale refinement equation including as particular
examples Daubechies’ schemes. Companies such as Pixar have made subdivision schemes the basic tool for much of their computer graphicsmodelling software.Research supported in part by MTM2007-62945
