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Composite primal/dual √3-subdivision schemes

Oswald, Peter and Schröder, Peter (2003) Composite primal/dual √3-subdivision schemes. ASCI Technical Report, ASCI-TR157. . (Unpublished)

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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 C¹-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:Report or Paper (Technical Report)
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URLURL TypeDescription ItemJournal Article
Schröder, Peter0000-0002-0323-7674
Additional Information: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.
Group:Accelerated Strategic Computing Initiative
Funding AgencyGrant Number
David and Lucile Packard FoundationUNSPECIFIED
Series Name:ASCI Technical Report
Issue or Number:ASCI-TR157
Record Number:CaltechAUTHORS:20230210-191814502
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:119197
Deposited By: George Porter
Deposited On:11 Feb 2023 00:41
Last Modified:11 Feb 2023 00:41

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