Dimensions of spline spaces over unconstricted triangulations

  • Authors:

  • Gerald Farin

  • Affiliations:

  • Department of Computer Science, Arizona State University, Tempe, AZ

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2006

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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 Irn(Ω). In this note, we restrict Ω to have a special structure, namely to be unconstricted. This will allow for several exact dimension formulas.