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 -