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Author, Editor

Author(s):

Ivrissimtzis, Ioannis
Zayer, Rhaleb
Seidel, Hans-Peter

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BibTeX cite key*:

izs2005a

Title

Title*:

Polygonal decompositions of quadrilateral subdivision meshes

Journal

Journal Title*:

Computer Graphics & Geometry

Journal's URL:

http://www.cgg.ru/

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Language:

English

Publisher

Publisher's
Name:

Moscow Engineering Physics Institute (MEPhI)

Publisher's URL:

http://elibrary.ru/cgg

Publisher's
Address:

Moscow, Russia

ISSN:

1811-8992

Vol, No, Year, pp.

Volume:

7

Number:

1

Month:


Year*:

2005

Pages:

16-30

Number of VG Pages:


Sequence Number:


DOI:


Abstract, Links, (C)

Note:


(LaTeX) 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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Access Level:

Public

Correlation

MPG Unit:

Max-Planck-Institut für Informatik



MPG Subunit:

Computer Graphics Group

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MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat, VG Wort



BibTeX Entry:

@MISC{izs2005a,
AUTHOR = {Ivrissimtzis, Ioannis and Zayer, Rhaleb and Seidel, Hans-Peter},
TITLE = {Polygonal decompositions of quadrilateral subdivision meshes},
JOURNAL = {Computer Graphics & Geometry},
PUBLISHER = {Moscow Engineering Physics Institute (MEPhI)},
YEAR = {2005},
NUMBER = {1},
VOLUME = {7},
PAGES = {16--30},
ADDRESS = {Moscow, Russia},
ISBN = {1811-8992},
}


Entry last modified by Christine Kiesel, 06/19/2006
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Editor(s)
Ioannis Ivrissimtzis
Created
03/11/2005 03:12:22 PM
Revisions
3.
2.
1.
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Editor(s)
Christine Kiesel
Christine Kiesel
Ioannis Ivrissimtzis
Ioannis Ivrissimtzis
Edit Dates
19.06.2006 16:15:01
25.04.2006 18:07:41
01/12/2006 02:43:13 PM
03/11/2005 03:12:22 PM
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