de.mpg.escidoc.pubman.appbase.FacesBean
Deutsch
 
Hilfe Wegweiser Datenschutzhinweis Impressum Kontakt
  DetailsucheBrowse

Datensatz

DATENSATZ AKTIONENEXPORT

Freigegeben

Zeitschriftenartikel

Polygonal decompositions of quadrilateral subdivision meshes

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44685

Ivrissimtzis,  Ioannis
Computer Graphics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45789

Zayer,  Rhaleb
Computer Graphics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45449

Seidel,  Hans-Peter
Computer Graphics, MPI for Informatics, Max Planck Society;

Externe Ressourcen
Es sind keine Externen Ressourcen verfügbar
Volltexte (frei zugänglich)
Es sind keine frei zugänglichen Volltexte verfügbar
Ergänzendes Material (frei zugänglich)
Es sind keine frei zugänglichen Ergänzenden Materialien verfügbar
Zitation

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


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-000F-275F-F
Zusammenfassung
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.