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Journal Articles Computer Aided Geometric Design Year : 2012

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

Abstract

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+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.

Dates and versions

hal-00659465 , version 1 (12-01-2012)

Identifiers

Cite

Vincent Nivoliers, Cédric Gérot, Victor Ostromoukhov, Neil F. Stewart. L-system specification of knot-insertion rules for non-uniform B-spline subdivision. Computer Aided Geometric Design, 2012, 29 (2), pp.150-161. ⟨10.1016/j.cagd.2011.11.004⟩. ⟨hal-00659465⟩
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