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Ck Continuity of Subdivision Surfaces

Zorin, Denis (1996) Ck Continuity of Subdivision Surfaces. California Institute of Technology , Pasadena, CA. (Unpublished)

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Stationary subdivision is an important tool for generating smooth free-form surfaces for CAGD and computer graphics. One of the challenges in construction of subdivision schemes for arbitrary meshes is to guarantee that the limit surface will have smooth regular parameterization in a neighborhood of any point. First results in this direction were obtained only recently. In this paper we derive necessary and sufficient criteria for Ck -continuity that generalize and extend most known conditions. We create a general mathematical framework that can be used for analysis of more general types of schemes. Finally, we prove a degree estimate for Ck -continuous polynomial schemes generalizing an estimate of Reif [20] and give a practical sufficient condition for smoothness.

Item Type:Report or Paper (Technical Report)
Additional Information:© 1996 California Institute of Technology. November 13, 1996. I would like to thank Peter Schröder and Wim Sweldens for their encouragement, advice and support; special thanks to Wim Sweldens for the opportunity to work at Bell Laboratories during the summer. I am also grateful to Jeff Lagarias for his attention to this work. This research was supported in part through grants from the Intel Corporation, the Charles Lee Powell Foundation, the Sloan Foundation. Part of this work was completed at the Bell Laboratories (Lucent Technologies).
Group:Computer Science Technical Reports
Funding AgencyGrant Number
Intel CorporationUNSPECIFIED
Charles Lee Powell FoundationUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Record Number:CaltechCSTR:1996.cs-tr-96-23
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ID Code:26802
Deposited By: Imported from CaltechCSTR
Deposited On:25 Apr 2001
Last Modified:03 Oct 2019 03:18

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