Polygonal decomposition of the 1-ring neighborhood of the Catmull-Clark scheme | IEEE Conference Publication | IEEE Xplore

Polygonal decomposition of the 1-ring neighborhood of the Catmull-Clark scheme


Abstract:

We propose a polygonal decomposition of the 1-ring neighborhood of a quadrilateral mesh, which is suitable for the study of the Catmull-Clark subdivision scheme. The init...Show More

Abstract:

We propose a polygonal decomposition of the 1-ring neighborhood of a quadrilateral mesh, which is suitable for the study of the Catmull-Clark subdivision scheme. The initial configuration consists of 2n planar 2n-gons and under the Catmull-Clark subdivision they 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.
Date of Conference: 07-09 June 2004
Date Added to IEEE Xplore: 04 October 2004
Print ISBN:0-7695-2075-8
Conference Location: Genova, Italy

References

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