Subdivision and Spline Spaces

Hal Schenck; Tatyana Sorokina

doi:10.1007/s00365-017-9367-5

Subdivision and Spline Spaces

Hal Schenck, Tatyana Sorokina

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A standard construction in approximation theory is mesh refinement. For a simplicial or polyhedral mesh Δ⊆ R^k, we study the subdivision Δ^′ obtained by subdividing a maximal cell of Δ. We give sufficient conditions for the module of splines on Δ^′ to split as the direct sum of splines on Δ 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.

Original language	English (US)
Pages (from-to)	237-247
Number of pages	11
Journal	Constructive Approximation
Volume	47
Issue number	2
DOIs	https://doi.org/10.1007/s00365-017-9367-5
State	Published - Apr 1 2018

Keywords

Dimension formula
Spline
Subdivision

ASJC Scopus subject areas

Analysis
General Mathematics
Computational Mathematics

Online availability

10.1007/s00365-017-9367-5

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Subdivision and Spline Spaces

Abstract

Keywords

ASJC Scopus subject areas

Online availability

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