Subdivision and spline spaces
Numerical Analysis
2016-10-18 v1
Abstract
A standard construction in approximation theory is mesh refinement. For a simplicial or polyhedral mesh D in R^k, we study the subdivision D' obtained by subdividing a maximal cell of D. We give sufficient conditions for the module of splines on D' to split as the direct sum of splines on D and splines on the subdivided cell. As a consequence, we obtain dimension formulas and explicit bases for several commonly used subdivisions and their multivariate generalizations.
Cite
@article{arxiv.1610.05188,
title = {Subdivision and spline spaces},
author = {Hal Schenck and Tatyana Sorokina},
journal= {arXiv preprint arXiv:1610.05188},
year = {2016}
}
Comments
8 pages, 8 figures