Dimensions of spline spaces over unconstricted triangulations

Gerald Farin

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


One of the puzzlingly hard problems in Computer Aided Geometric Design and Approximation Theory is that of finding the dimension of the spline space of Cr piecewise degree n polynomials over a 2D triangulation Ω. We denote such spaces by Snr ( Ω ). In this note, we restrict Ω to have a special structure, namely to be unconstricted. This will allow for several exact dimension formulas.

Original languageEnglish (US)
Pages (from-to)320-327
Number of pages8
JournalJournal of Computational and Applied Mathematics
Issue number2
StatePublished - Aug 1 2006


  • Bernstein-Bézier form
  • Bivariate spline spaces
  • Dimensions
  • Minimal determining sets
  • Unconstricted triangulations

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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