Geometric degree reduction of Bézier curves

Abedallah Rababah; Salisu Ibrahim

doi:10.1007/978-981-13-2095-8_8

Geometric degree reduction of Bézier curves

Abedallah Rababah, Salisu Ibrahim

Department of Mathematical Sciences

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

We consider the weighted-multi-degree reduction of Bézier curves. Based on the fact that exact degree reduction is not possible, therefore approximative process to reduce a given Bézier curve of high degree n to a Bézier curve of lower degree m, m < n is needed. The weight function is used to better representing the approximative curve at some parts that need more details, and the error is greater than other parts. The L₂ norm is used in the degree reduction process. Numerical results and comparisons are supported by examples. The numerical results obtained from the new method yield minimum approximation error, improve the approximation in some parts of the curve, and show up possible applications in science and engineering.

Original language	English
Title of host publication	Springer Proceedings in Mathematics and Statistics
Publisher	Springer New York LLC
Pages	87-95
Number of pages	9
DOIs	https://doi.org/10.1007/978-981-13-2095-8_8
Publication status	Published - 2018

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	253
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Keywords

Bézier curves
Geometric continuity
Multiple degree reduction

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1007/978-981-13-2095-8_8

Cite this

@inbook{c3cceae57f6d4418a6b9f139f74037f0,

title = "Geometric degree reduction of B{\'e}zier curves",

abstract = "We consider the weighted-multi-degree reduction of B{\'e}zier curves. Based on the fact that exact degree reduction is not possible, therefore approximative process to reduce a given B{\'e}zier curve of high degree n to a B{\'e}zier curve of lower degree m, m < n is needed. The weight function is used to better representing the approximative curve at some parts that need more details, and the error is greater than other parts. The L2 norm is used in the degree reduction process. Numerical results and comparisons are supported by examples. The numerical results obtained from the new method yield minimum approximation error, improve the approximation in some parts of the curve, and show up possible applications in science and engineering.",

keywords = "B{\'e}zier curves, Geometric continuity, Multiple degree reduction",

author = "Abedallah Rababah and Salisu Ibrahim",

note = "Publisher Copyright: {\textcopyright} Springer Nature Singapore Pte Ltd. 2018.",

year = "2018",

doi = "10.1007/978-981-13-2095-8_8",

language = "English",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer New York LLC",

pages = "87--95",

booktitle = "Springer Proceedings in Mathematics and Statistics",

}

TY - CHAP

T1 - Geometric degree reduction of Bézier curves

AU - Rababah, Abedallah

AU - Ibrahim, Salisu

N1 - Publisher Copyright: © Springer Nature Singapore Pte Ltd. 2018.

PY - 2018

Y1 - 2018

N2 - We consider the weighted-multi-degree reduction of Bézier curves. Based on the fact that exact degree reduction is not possible, therefore approximative process to reduce a given Bézier curve of high degree n to a Bézier curve of lower degree m, m < n is needed. The weight function is used to better representing the approximative curve at some parts that need more details, and the error is greater than other parts. The L2 norm is used in the degree reduction process. Numerical results and comparisons are supported by examples. The numerical results obtained from the new method yield minimum approximation error, improve the approximation in some parts of the curve, and show up possible applications in science and engineering.

AB - We consider the weighted-multi-degree reduction of Bézier curves. Based on the fact that exact degree reduction is not possible, therefore approximative process to reduce a given Bézier curve of high degree n to a Bézier curve of lower degree m, m < n is needed. The weight function is used to better representing the approximative curve at some parts that need more details, and the error is greater than other parts. The L2 norm is used in the degree reduction process. Numerical results and comparisons are supported by examples. The numerical results obtained from the new method yield minimum approximation error, improve the approximation in some parts of the curve, and show up possible applications in science and engineering.

KW - Bézier curves

KW - Geometric continuity

KW - Multiple degree reduction

UR - http://www.scopus.com/inward/record.url?scp=85054758963&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85054758963&partnerID=8YFLogxK

U2 - 10.1007/978-981-13-2095-8_8

DO - 10.1007/978-981-13-2095-8_8

M3 - Chapter

AN - SCOPUS:85054758963

T3 - Springer Proceedings in Mathematics and Statistics

SP - 87

EP - 95

BT - Springer Proceedings in Mathematics and Statistics

PB - Springer New York LLC

ER -

Geometric degree reduction of Bézier curves

Abstract

Publication series

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this