Constructive Approximation

, Volume 3, Issue 1, pp 189–197

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

  • Peter Alfeld
  • L. L. Schumaker

DOI: 10.1007/BF01890563

Cite this article as:
Alfeld, P. & Schumaker, L.L. Constr. Approx (1987) 3: 189. doi:10.1007/BF01890563


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 splinesSplinesPiecewise polynomial functionsTriangulations

AMS classification

Primary 65D07Secondary 41A6341A15

Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • Peter Alfeld
    • 1
  • L. L. Schumaker
    • 2
  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA
  2. 2.Center for Approximation TheoryTexas A & M UniversityCollege StationUSA