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Curvature integrability of subdivision surfaces

Reif, Ulrich and Schröder, Peter (2001) Curvature integrability of subdivision surfaces. Advances in Computational Mathematics, 14 (2). pp. 157-174. ISSN 1019-7168. 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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1023/a:1016685104156DOIArticle
https://rdcu.be/bPRgCPublisherFree ReadCube access
ORCID:
AuthorORCID
Schröder, Peter0000-0002-0323-7674
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.
Funders:
Funding AgencyGrant Number
NSFACI-9624957
NSFACI-9721349
NSFDMS-9874082
NSFDMS-9872890
Alias|wavefrontUNSPECIFIED
David and Lucile Packard FoundationUNSPECIFIED
Subject Keywords:subdivision, smoothness, function spaces, approximation, thin shell equations
Issue or Number:2
Classification Code:AMS subject classification: 65D17, 65N30
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:03 Oct 2019 21:40

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