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Grenoble Images Parole Signal Automatique |
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Grenoble Images Parole Signal Automatique |
| HAL: hal-00659465, version 1 |
| DOI: 10.1016/j.cagd.2011.11.004 |
| Detailed view |  Export this paper |
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| Computer Aided Geometric Design 29, 2 (2012) 150-161 |
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| L-system specification of knot-insertion rules for non-uniform B-spline subdivision |
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| Vincent Nivoliers 1Cédric Gérot 2 |
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| (2012-02) |
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| 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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| 1: | ALICE (INRIA Nancy - Grand Est / LORIA) |
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INRIA – CNRS : UMR7503 – Université de Lorraine |
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| 2: | Grenoble Images Parole Signal Automatique (GIPSA-lab) |
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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 |
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| 3: | Département d'Informatique et de Recherche Opérationnelle [Montreal] (DIRO) |
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Université de Montréal |
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| 4: | Laboratoire d'Informatique Graphique de l'Université de Monréal (LIGUM) |
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Université de Montréal |
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| AGPIG |
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| Subject | : | Computer Science/Computer Graphics and Virtual Reality Computer Science/Computational Geometry |
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| L-system – Subdivision – Non-uniform |
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| 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 | |
