Geodesic
Cell reducing and the dimension of the C^1 bivariate spline space
Ars Mathematica Contemporanea, Tome 22 (2022) no. 3, article no. 06, 18 p.

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In this paper, the problem of determining the dimension of the space Sn1(△), n ≥ 3 of bivariate C1 splines of degree ≤ n over a triangulation △ is considered. The piecewise polynomials are represented as blossoms, and the smoothness conditions are written as a system of linear equations. The rank of the system matrix is analysed by repeatedly reducing small subtriangulations (cells) at the boundary of a triangulation. It is shown that the dimension of the bivariate spline space Sn1(△), n ≥ 3 is equal to Schumaker’s lower bound for a large class of triangulations.
DOI : 10.26493/1855-3974.2646.c07
Keywords: Dimension, spline space, triangulation, cell 
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Gašper Jaklič. Cell reducing and the dimension of the C^1 bivariate spline space. Ars Mathematica Contemporanea, Tome 22 (2022) no. 3, article  no. 06, 18 p. doi : 10.26493/1855-3974.2646.c07. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2646.c07/

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