hal-00659465, version 1

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

Vincent Nivoliers ¹, Cédric Gérot (, ) ², Victor Ostromoukhov ³, Neil F. Stewart ⁴

Computer Aided Geometric Design 29, 2 (2012) 150-161

• 1:  ALICE (INRIA Nancy - Grand Est / LORIA)
• 
  INRIA – CNRS : UMR7503 – Université de Lorraine France
• 2:  Grenoble Images Parole Signal Automatique (GIPSA-lab)
• http://www.gipsa-lab.inpg.fr/
  CNRS : UMR5216 – Université Joseph Fourier - Grenoble I – Université Pierre-Mendès-France - Grenoble II – Université Stendhal - Grenoble III – Institut Polytechnique de Grenoble - Grenoble Institute of Technology Gipsa-lab - 961 rue de la Houille Blanche - BP 46 - 38402 Grenoble cedex France
• 3:  Département d'Informatique et de Recherche Opérationnelle [Montreal] (DIRO)
• http://www.iro.umontreal.ca/
  Université de Montréal Département d'Informatique et de recherche opérationnelle Université de Montréal Pavillon André-Aisenstadt CP 6128 succ Centre-Ville Montréal QC H3C 3J7 Canada Canada
• 4:  Laboratoire d'Informatique Graphique de l'Université de Monréal (LIGUM)
• http://www.iro.umontreal.ca/labs/infographie/
  Université de Montréal DIRO, Université de Montréal, C.P. 6128, succursale Centre-ville, Montreal (Québec) Canada H3C 3J7 Canada

Bibliographic reference

• Type of document: Articles in peer-reviewed journal
• Subject:

  Computer Science/Computer Graphics and Virtual Reality

  Computer Science/Computational Geometry

• Title: 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.
• Fulltext language: English
• Production date: 2011-03
• DOI: 10.1016/j.cagd.2011.11.004
• Journal:

  Computer Aided Geometric Design
  Publisher	Elsevier
  ISSN	0167-8396

• Audience: international
• Publication date: 2012-02
• Volume: 29
• Issue: 2
• Page, identifiant, ...: 150-161
• Keyword(s): L-system – Subdivision – Non-uniform
• Internal note: Département Images et Signal

• hal-00659465, version 1
• http://hal.archives-ouvertes.fr/hal-00659465
• oai:hal.archives-ouvertes.fr:hal-00659465
• From: Cédric Gérot <>
• Submitted on: Thursday, 12 January 2012 18:04:39
• Updated on: Thursday, 25 October 2012 14:28:13