Jacobi-Bernstein Basis Transformation

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31 Citations (Scopus)

Abstract

In this paper we derive the matrix of transformation of the Jacobi polynomial basis form into the Bernstein polynomial basis of the same degree n and vice versa. This enables us to combine the superior least-squares performance of the Jacobi polynomials with the geometrical insight of the Bernstein form. Application to the inversion of the Bézier curves is given.

Original languageEnglish
Pages (from-to)206-214
Number of pages9
JournalComputational Methods in Applied Mathematics
Volume4
Issue number2
DOIs
Publication statusPublished - 2004
Externally publishedYes

Keywords

  • Bernstein polynomials
  • Jacobi polynomials
  • basis transformation
  • computer aided geometric design
  • inversion of Bézier curves
  • least-squares approximation
  • orthogonal polynomials

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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