Published February 2001
| public
Journal Article
Curvature integrability of subdivision surfaces
- Creators
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Reif, Ulrich
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Schröder, Peter
Chicago
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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.
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.Additional details
- Eprint ID
- 98342
- DOI
- 10.1023/a:1016685104156
- Resolver ID
- CaltechAUTHORS:20190829-131533096
- NSF
- ACI-9624957
- NSF
- ACI-9721349
- NSF
- DMS-9874082
- NSF
- DMS-9872890
- Alias|wavefront
- David and Lucile Packard Foundation
- Created
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2019-08-30Created from EPrint's datestamp field
- Updated
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2023-09-28Created from EPrint's last_modified field