Reif, Ulrich and Schröder, Peter (2001) Curvature integrability of subdivision surfaces. Advances in Computational Mathematics, 14 (2). pp. 157-174. ISSN 1019-7168. doi:10.1023/a:1016685104156. https://resolver.caltech.edu/CaltechAUTHORS:20190829-131533096
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Abstract
We examine the smoothness properties of the principal curvatures of subdivision surfaces near irregular points. In particular we give an estimate of their L_p class based on the eigenstructure of the subdivision matrix. As a result we can show that the popular Loop and Catmull–Clark schemes (among many others) have square integrable principal curvatures enabling their use as shape functions in FEM treatments of the thin shell equations.
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| Additional Information: | © Kluwer Academic Publishers 2001. Received 2 February 2000; revised 9 September 2000; accepted 15 November 2000. Communicated by C. Micchelli. The second author was supported in part by NSF (ACI-9624957, ACI-9721349, DMS-9874082, DMS-9872890), Alias|Wavefront and through a Packard Fellowship. Special thanks for Cici Koenig for production help and Fehmi Cirak and Eitan Grinspun for the thin shell simulation of the cylinder. | ||||||||||||||
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| Subject Keywords: | subdivision, smoothness, function spaces, approximation, thin shell equations | ||||||||||||||
| Issue or Number: | 2 | ||||||||||||||
| Classification Code: | AMS subject classification: 65D17, 65N30 | ||||||||||||||
| DOI: | 10.1023/a:1016685104156 | ||||||||||||||
| Record Number: | CaltechAUTHORS:20190829-131533096 | ||||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20190829-131533096 | ||||||||||||||
| Official Citation: | Reif, U. & Schröder, P. Advances in Computational Mathematics (2001) 14: 157. https://doi.org/10.1023/A:1016685104156 | ||||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||||
| ID Code: | 98342 | ||||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||||
| Deposited By: | George Porter | ||||||||||||||
| Deposited On: | 30 Aug 2019 15:51 | ||||||||||||||
| Last Modified: | 16 Nov 2021 17:38 |
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