Jacobi-Bernstein Basis Transformation

Abedallah Rababah

doi:10.2478/cmam-2004-0012

Jacobi-Bernstein Basis Transformation

Abedallah Rababah

Research output: Contribution to journal › Article › peer-review

33 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 language	English
Pages (from-to)	206-214
Number of pages	9
Journal	Computational Methods in Applied Mathematics
Volume	4
Issue number	2
DOIs	https://doi.org/10.2478/cmam-2004-0012
Publication status	Published - 2004
Externally published	Yes

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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10.2478/cmam-2004-0012

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KW - Bernstein polynomials

KW - Jacobi polynomials

KW - basis transformation

KW - computer aided geometric design

KW - inversion of Bézier curves

KW - least-squares approximation

KW - orthogonal polynomials

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Jacobi-Bernstein Basis Transformation

Abstract

Keywords

ASJC Scopus subject areas

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