Dimensions of spline spaces over unconstricted triangulations

Gerald Farin

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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 Sn r ( 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
Volume192
Issue number2
DOIs
StatePublished - Aug 1 2006

Fingerprint

Approximation theory
Triangulation
Splines
Spline
Computer aided design
Polynomials
Computer Aided Geometric Design
Approximation Theory
Denote
Polynomial

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

Dimensions of spline spaces over unconstricted triangulations. / Farin, Gerald.

In: Journal of Computational and Applied Mathematics, Vol. 192, No. 2, 01.08.2006, p. 320-327.

Research output: Contribution to journalArticle

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