Cube Decompositions by Eigenvectors of Quadratic Multivariate Splines

Ioannis Ivrissimtzis () and Hans-Peter Seidel ()
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Ioannis Ivrissimtzis: Durham University
Hans-Peter Seidel: MPI-Informatik

Chapter 10 in Geometric Modeling and Algebraic Geometry, 2008, pp 181-197 from Springer

Abstract: A matrix is called G-circulant if its columns and rows are indexed by the elements of a group G. When G is cyclic we obtain the usual circulant matrices, which appear in the study of linear transformations of polygons. In this paper, we study linear transformations of cubes and prisms using G-circulant matrices, where G is the direct product of cyclic groups. As application, we study the evolution of a single cell of an n-dimensional grid under the subdivision algorithm of the multivariate quadratic B-spline. Regarding the prism, we study its evolution under a tensor extension of the Doo-Sabin subdivision scheme.

Keywords: Subdivision Scheme; Limit Shape; Subdivision Surface; Circulant Matrice; Subdivision Algorithm (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-72185-7_10

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DOI: 10.1007/978-3-540-72185-7_10

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