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.
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Ivrissimtzis, I., Seidel, HP. (2008). Cube Decompositions by Eigenvectors of Quadratic Multivariate Splines. In: Jüttler, B., Piene, R. (eds) Geometric Modeling and Algebraic Geometry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72185-7_10
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DOI: https://doi.org/10.1007/978-3-540-72185-7_10
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