Subdivision and Spline Spaces

Hal Schenck, Tatyana Sorokina

Research output: Contribution to journalArticlepeer-review


A standard construction in approximation theory is mesh refinement. For a simplicial or polyhedral mesh Δ⊆ Rk, 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 languageEnglish (US)
Pages (from-to)237-247
Number of pages11
JournalConstructive Approximation
Issue number2
StatePublished - Apr 1 2018


  • Dimension formula
  • Spline
  • Subdivision

ASJC Scopus subject areas

  • Analysis
  • General Mathematics
  • Computational Mathematics


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