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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U2 - 10.1080/01630560701564139
DO - 10.1080/01630560701564139
M3 - Article
AN - SCOPUS:35148873693
SN - 0163-0563
VL - 28
SP - 1179
EP - 1196
JO - Numerical Functional Analysis and Optimization
JF - Numerical Functional Analysis and Optimization
IS - 9-10
ER -