L-system specification of knot-insertion rules for non-uniform B-spline subdivision

Subdivision schemes are based on a hierarchy of knot grids in parameter space. A univariate grid hierarchy is regular if all knots are equidistant on each level, and irregular otherwise. We use L-systems to design a wide class of systematically described irregular grid hierarchies. Furthermore, we give sufficient conditions on the L-system which guarantee that the subdivision scheme, based on the non-uniform B-spline of degree d defined on the initial knot grid, is uniformly convergent. If n   is the number of symbols in the alphabet of the L-system, this subdivision scheme is defined with a finite set of masks (at most nd+1nd+1) which does not depend on the subdivision step. We provide an implementation of such schemes which is available as a worksheet for Sage software.

► We use L-systems to specify knot interval subdivision descriptors.
► They are applied to the design of non-uniform univariate subdivision schemes.
► Each scheme uses a finite set of masks which does not depend on the subdivision step.
► We give sufficient conditions on the L-system which guarantee uniform convergence.