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

Vincent Nivoliers 1 Cédric Gérot 2 Victor Ostromoukhov 3 Neil Stewart 4
1 ALICE - Geometry and Lighting
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
GIPSA-DIS - Département Images et Signal
3 R3AM - Rendu Réaliste pour la Réalité Augmentée Mobile
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
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.
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Submitted on : Thursday, January 12, 2012 - 6:04:39 PM
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Vincent Nivoliers, Cédric Gérot, Victor Ostromoukhov, Neil Stewart. L-system specification of knot-insertion rules for non-uniform B-spline subdivision. Computer Aided Geometric Design, Elsevier, 2012, 29 (2), pp.150-161. ⟨10.1016/j.cagd.2011.11.004⟩. ⟨hal-00659465⟩



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