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Composite primal/dual √3-subdivision schemes

Oswald, Peter and Schröder, Peter (2003) Composite primal/dual √3-subdivision schemes. Computer Aided Geometric Design, 20 (3). pp. 135-164. ISSN 0167-8396. doi:10.1016/S0167-8396(03)00026-8.

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We present new families of primal and dual subdivision schemes for triangle meshes and 3-refinement. The proposed schemes use two simple local rules which cycle between primal and dual meshes a number of times. The resulting surfaces become very smooth at regular vertices if the number of cycles is ⩾2. The C^1-property is violated only at low-valence irregular vertices, and can be restored by slight modifications of the local rules used. As a generalization, we introduce a wide class of composite subdivision schemes suitable for arbitrary topologies and refinement rules. A composite scheme is defined by a simple upsampling from the coarse to a refined topology, embedded into a cascade of geometric averaging operators acting on coarse and/or refined topologies. We propose a small set of such averaging rules (and some of their parametric extensions) which allow for the switching between control nets associated with the same or different topologic elements (vertices, edges, faces), and show a number of examples, based on triangles, that the resulting class of composite subdivision schemes contains new and old, primal and dual schemes for 3-refinement as well as for quadrisection. As a common observation from the examples considered, we found that irregular vertex treatment is necessary only at vertices of low valence, and can easily be implemented by using generic modifications of some elementary averaging rules.

Item Type:Article
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URLURL TypeDescription ItemTechnical Report
Schröder, Peter0000-0002-0323-7674
Additional Information:© 2003 Elsevier Science. Received 15 October 2002, Revised 7 March 2003, Accepted 7 March 2003, Available online 10 April 2003. The work of the second author was supported in part by NSF (DMS-9874082, ACI-9721349, DMS-9872890, ACI-9982273), Lucent, Intel, Alias|Wavefront, Pixar, Microsoft, and the Packard Foundation.
Errata:Peter Oswald, Peter Schröder, Corrigendum to: ‘Composite primal/dual 3-subdivision schemes’: [COMAID 20 (2003) 135–164], Computer Aided Geometric Design, Volume 20, Issue 5, 2003, Page 295, ISSN 0167-8396,
Funding AgencyGrant Number
David and Lucile Packard FoundationUNSPECIFIED
Subject Keywords:Subdivision; Repeated averaging; Smooth surfaces; Arbitrary topology; Geometric modeling
Issue or Number:3
Record Number:CaltechAUTHORS:20170408-163038224
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Official Citation:Peter Oswald, Peter Schröder, Composite primal/dual 3-subdivision schemes, Computer Aided Geometric Design, Volume 20, Issue 3, 2003, Pages 135-164, ISSN 0167-8396,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:76198
Deposited By: 1Science Import
Deposited On:07 Mar 2018 18:41
Last Modified:01 Jun 2023 22:42

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