B-Form Basics

Abstract

The basic facts about the B(arycentric, -ernstein, -ezier)-form of a multivariate polynomial are recorded and, in part, proved. These include: evaluation (de Casteliau's algorithm), differentiation and integration, product, degree raising, change of the underlying simplex, and the behavior on the boundary of the underlying simplex, with application to the construction of smooth pp functions on a given "triangulation". Some effort has gone into making the notation fully reflect the symmetries and structure of this form. In particular, the description of this form in terms of difference operators is stressed. Keywords: Piecewise polynomials; Linear interpolation.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1986
Accession Number
ADA180769

Entities

People

  • C. De Boor

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Coefficients
  • Construction
  • Interpolation
  • Linear Systems
  • Mathematics
  • Military Research
  • North Carolina
  • Notation
  • Numerical Analysis
  • Polynomials
  • Test And Evaluation
  • Triangles
  • Triangulation
  • United States
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Theoretical Analysis.