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Cube Decompositions by Eigenvectors of Quadratic Multivariate Splines

In: Geometric Modeling and Algebraic Geometry

Author

Listed:
  • Ioannis Ivrissimtzis

    (Durham University)

  • Hans-Peter Seidel

    (MPI-Informatik)

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.

Suggested Citation

  • Ioannis Ivrissimtzis & Hans-Peter Seidel, 2008. "Cube Decompositions by Eigenvectors of Quadratic Multivariate Splines," Springer Books, in: Bert Jüttler & Ragni Piene (ed.), Geometric Modeling and Algebraic Geometry, chapter 10, pages 181-197, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-72185-7_10
    DOI: 10.1007/978-3-540-72185-7_10
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