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√2 Subdivision for quadrilateral meshes

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Abstract

This paper presents a \(\sqrt2\)subdivision scheme for quadrilateral meshes that can be regarded as an extension of a 4-8 subdivision with new subdivision rules and improved capability and performance. The proposed scheme adopts a so-called \(\sqrt2\)split operator to refine a control mesh such that the face number of the refined mesh generally equals the edge number and is thus about twice the face number of the coarse mesh. Smooth rules are designed in reference to the 4-8 subdivision, while a new set of weights is developed to balance the flatness of surfaces at vertices of different valences. Compared to the 4-8 subdivision, the presented scheme can be naturally generalized for arbitrary control nets and is more efficient in both space and computing time management. Analysis shows that limit surfaces produced by the scheme are C4 continuous for regular control meshes and G1 continuous at extraordinary vertices.

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Authors and Affiliations

  1. The State Key Lab of CAD&CG, Zhejiang University, Hangzhou, P.R. China

    Guiqing Li  & Hujun Bao

  2. Dept. of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Kowloon, Hong Kong, P.R. China

    Weiyin Ma

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  1. Guiqing Li
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  2. Weiyin Ma
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  3. Hujun Bao
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Correspondence to Weiyin Ma .

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Li , G., Ma , W. & Bao , H. √2 Subdivision for quadrilateral meshes. Visual Comp 20, 180–198 (2004). https://doi.org/10.1007/s00371-003-0238-7

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