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  Polygonal decompositions of quadrilateral subdivision meshes

Ivrissimtzis, I., Zayer, R., & Seidel, H.-P. (2005). Polygonal decompositions of quadrilateral subdivision meshes. Computer Graphics & Geometry, 7, 16-30.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-275F-F Version Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-2760-9
Genre: Journal Article

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 Creators:
Ivrissimtzis, Ioannis1, Author           
Zayer, Rhaleb1, Author           
Seidel, Hans-Peter1, Author           
Affiliations:
1Computer Graphics, MPI for Informatics, Max Planck Society, ou_40047              

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 Abstract: We study a polygonal decomposition of the 1-ring neighborhood of a quadrilateral mesh. This decomposition corresponds to the eigenvectors of a matrix with circulant blocks, thus, it is suitable for the study of subdivision schemes. First, we calculate the extent of the local mesh area we have to consider in order to get a geometrically meaningful decomposition. Then we concentrate on the Catmull-Clark scheme and decompose the 1-ring neighborhood into 2n planar 2n-gons, which under subdivision scheme transform into 4n planar n-gons coming in pairs of coplanar polygons and quadruples of parallel polygons. We calculate the eigenvalues and eigenvectors of the transformations of these configurations showing their relation with the tangent plane and the curvature properties of the subdivision surface. Using direct computations on circulant-block matrices we show how the same eigenvalues can be analytically deduced from the subdivision matrix.

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Language(s): eng - English
 Dates: 2006-06-192005
 Publication Status: Issued
 Pages: -
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 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 278948
Other: Local-ID: C125675300671F7B-B462B3435182A3AEC1256FC1004E095F-izs2005a
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Title: Computer Graphics & Geometry
Source Genre: Journal
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Pages: - Volume / Issue: 7 Sequence Number: - Start / End Page: 16 - 30 Identifier: ISSN: 1811-8992