Bivariate Box Splines and Smooth pp Functions on a Three Direction Mesh.
Abstract
This report investigates the use of translates of certain bivariate box-splines in the construction of a unified theory for piecewise polynomial functions on regular meshes. A simple mesh is considered, derived from a square mesh by drawing in the same diagonal into every square. The space S of piecewise polynomial functions of a given degree and smoothness, and with discontinuities (in some derivative) only across lines of that mesh is considered. We show that the box splines and their translates provide a basis for the local part of S and use the techniques of (BH sub 1) to analyse the approximation properties of S. The report stresses the importance of local support bases which are desirable for applications such as finite element methods, smoothing of data and approximation in general. Our results should be useful for the further investigation of smooth piecewise polynomials, in particular on regular meshes (c.f. (CW), (Si), S1) for related work).
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1982
- Accession Number
- ADA120989
Entities
People
- C. De Boor
- K. Hoellig
Organizations
- University of Wisconsin–Madison