Constructive Approximation

, Volume 3, Issue 1, pp 189-197

First online:

The dimension of bivariate spline spaces of smoothnessr for degreed≥4r+1

  • Peter AlfeldAffiliated withDepartment of Mathematics, University of Utah
  • , L. L. SchumakerAffiliated withCenter for Approximation Theory, Texas A & M University

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We consider spaces of piecewise polynomials of degreed defined over a triangulation of a polygonal domain and possessingr continuous derivatives globally. Morgan and Scott constructed a basis in the case wherer=1 andd≥5. The purpose of this paper is to extend the dimension part of their result tor≥0 andd≥4r+l. We use Bézier nets as a crucial tool in deriving the dimension of such spaces.

Key words and phrases

Multivariate splines Splines Piecewise polynomial functions Triangulations

AMS classification

Primary 65D07 Secondary 41A63 41A15