Multiple degree reduction and elevation of bzier curves using Jacobi-Bernstein basis transformations

Abedallah Rababah; Byung Gook Lee; Jaechil Yoo

doi:10.1080/01630560701564139

Multiple degree reduction and elevation of bzier curves using Jacobi-Bernstein basis transformations

Abedallah Rababah
, Byung Gook Lee
, Jaechil Yoo

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

19 Citations (Scopus)

Abstract

In this article, we find the optimal r times degree reduction of Bzier curves with respect to the Jacobi-weighted L2-norm on the interval [0, 1]. This method describes a simple and efficient algorithm based on matrix computations. Also, our method includes many previous results for the best approximation with L1, L2, and L-norms. We give some examples and figures to demonstrate these methods.

Original language	English
Pages (from-to)	1179-1196
Number of pages	18
Journal	Numerical Functional Analysis and Optimization
Volume	28
Issue number	9-10
DOIs	https://doi.org/10.1080/01630560701564139
Publication status	Published - Sept 2007
Externally published	Yes

Keywords

Basis transformation
Bernstein polynomials
Bzier curves
Degree reduction
Jacobi polynomials
Least-squares approximation
Orthogonal polynomials

ASJC Scopus subject areas

Analysis
Signal Processing
Computer Science Applications
Control and Optimization

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10.1080/01630560701564139

Cite this

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title = "Multiple degree reduction and elevation of bzier curves using Jacobi-Bernstein basis transformations",

abstract = "In this article, we find the optimal r times degree reduction of Bzier curves with respect to the Jacobi-weighted L2-norm on the interval [0, 1]. This method describes a simple and efficient algorithm based on matrix computations. Also, our method includes many previous results for the best approximation with L1, L2, and L-norms. We give some examples and figures to demonstrate these methods.",

keywords = "Basis transformation, Bernstein polynomials, Bzier curves, Degree reduction, Jacobi polynomials, Least-squares approximation, Orthogonal polynomials",

author = "Abedallah Rababah and Lee, \{Byung Gook\} and Jaechil Yoo",

note = "Funding Information: The authors thank the referee for the valuable comments. B.-G. Lee was supported by Korea Science and Engineering Foundation Grant (R05-2004-000-10968-0), and J. Yoo was supported by Dongeui University.",

year = "2007",

month = sep,

doi = "10.1080/01630560701564139",

language = "English",

volume = "28",

pages = "1179--1196",

journal = "Numerical Functional Analysis and Optimization",

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publisher = "Taylor and Francis Ltd.",

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TY - JOUR

T1 - Multiple degree reduction and elevation of bzier curves using Jacobi-Bernstein basis transformations

AU - Rababah, Abedallah

AU - Lee, Byung Gook

AU - Yoo, Jaechil

N1 - Funding Information: The authors thank the referee for the valuable comments. B.-G. Lee was supported by Korea Science and Engineering Foundation Grant (R05-2004-000-10968-0), and J. Yoo was supported by Dongeui University.

PY - 2007/9

Y1 - 2007/9

N2 - In this article, we find the optimal r times degree reduction of Bzier curves with respect to the Jacobi-weighted L2-norm on the interval [0, 1]. This method describes a simple and efficient algorithm based on matrix computations. Also, our method includes many previous results for the best approximation with L1, L2, and L-norms. We give some examples and figures to demonstrate these methods.

AB - In this article, we find the optimal r times degree reduction of Bzier curves with respect to the Jacobi-weighted L2-norm on the interval [0, 1]. This method describes a simple and efficient algorithm based on matrix computations. Also, our method includes many previous results for the best approximation with L1, L2, and L-norms. We give some examples and figures to demonstrate these methods.

KW - Basis transformation

KW - Bernstein polynomials

KW - Bzier curves

KW - Degree reduction

KW - Jacobi polynomials

KW - Least-squares approximation

KW - Orthogonal polynomials

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VL - 28

SP - 1179

EP - 1196

JO - Numerical Functional Analysis and Optimization

JF - Numerical Functional Analysis and Optimization

IS - 9-10

ER -

Multiple degree reduction and elevation of bzier curves using Jacobi-Bernstein basis transformations

Abstract

Keywords

ASJC Scopus subject areas

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