Cell reducing and the dimension of the C1 bivariate spline space

Gašper Jaklič

Abstract


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.


Keywords


Dimension, spline space, triangulation, cell

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DOI: https://doi.org/10.26493/1855-3974.2646.c07

ISSN: 1855-3974

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