Cell reducing and the dimension of the C1 bivariate spline space
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
Full Text:
MANUSCRIPTDOI: https://doi.org/10.26493/1855-3974.2646.c07
ISSN: 1855-3974
Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications