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Composite \(\sqrt{2}\) Subdivision Surfaces

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Geometric Modeling and Processing - GMP 2006 (GMP 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4077))

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Abstract

This paper presents a new unified framework for subdivisions based on a \(\sqrt{2}\) splitting operator, the so-called composite \(\sqrt{2}\) subdivision. The composite subdivision scheme generalizes 4-direction box spline surfaces for processing irregular quadrilateral meshes and is realized through various atomic operators. Several well-known subdivisions based on both the \(\sqrt{2}\) splitting operator and 1-4 splitting for quadrilateral meshes are properly included in the newly proposed unified scheme. Typical examples include the midedge and 4-8 subdivisions based on the \(\sqrt{2}\) splitting operator that are now special cases of the unified scheme as the simplest dual and primal subdivisions, respectively. Variants of Catmull-Clark and Doo-Sabin subdivisions based on the 1-4 splitting operator also fall in the proposed unified framework. Furthermore, unified subdivisions as extension of tensor-product B-spline surfaces also become a subset of the proposed unified subdivision scheme. In addition, Kobbelt interpolatory subdivision can also be included into the unified framework using VV-type (vertex to vertex type) averaging operators.

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Author information

Authors and Affiliations

  1. School of Computer Science and Engineering, South China University of Technology, Guangzhou, 510641, China

    Guiqing Li

  2. Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Hong Kong (SAR), China

    Weiyin Ma

Authors
  1. Guiqing Li
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  2. Weiyin Ma
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Editor information

Editors and Affiliations

  1. Seoul National University, Korea

    Myung-Soo Kim

  2. Carnegie Mellon University, Pittsburgh, PA, USA

    Kenji Shimada

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© 2006 Springer-Verlag Berlin Heidelberg

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Li, G., Ma, W. (2006). Composite \(\sqrt{2}\) Subdivision Surfaces. In: Kim, MS., Shimada, K. (eds) Geometric Modeling and Processing - GMP 2006. GMP 2006. Lecture Notes in Computer Science, vol 4077. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11802914_30

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  • DOI: https://doi.org/10.1007/11802914_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-36711-6

  • Online ISBN: 978-3-540-36865-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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