Constructive Approximation

, Volume 3, Issue 1, pp 131–141 | Cite as

Cones and recurrence relations for simplex splines

  • Elaine Cohen
  • T. Lyche
  • R. F. Riesenfeld
Article

Abstract

We prove some new relations between functions defined as shadows of cones (cone splines) and simplices (simplex splines). We use them to show how ans-variate simplex spline of some orderk can be written as a sum ofk+1 (s-l)-variate simplex splines of orderk-1. A recurrence relation on the spatial dimension of the simplex spline,s, is proposed as an interesting alternative to the recurrence relation in [17], where one uses the orderk for recursion, but not the spatial dimensions.

Key words and phrases

Multivariate cone and simplex splines Surfaces Approximation Algorithms Computation Spatial dimension 

AMS classification

41A15 41A63 65D07 

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Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • Elaine Cohen
    • 1
  • T. Lyche
    • 2
  • R. F. Riesenfeld
    • 1
  1. 1.Department of Civil EngineeringPrinceton UniversityPrincetonUSA
  2. 2.Institute for InformatikkUniversity of OsloOsloNorway

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