Degree reduction of B-spline curves

Degree reduction of B-spline curves

In this paper, we propose the generalized B divided difference, with which the (k−1)th derivative of B-spline curves of order k can be obtained directly without the need to compute the first (k−2) derivatives as before. Based on the generalized B divided difference, the necessary and sufficient cond...

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Veröffentlicht in:Computer aided geometric design 2001-03, Vol.18 (2), p.117-127
Hauptverfasser: Yong, Jun-Hai, Hu, Shi-Min, Sun, Jia-Guang, Tan, Xing-Yu
Format: Artikel
Sprache:eng
Schlagworte:
Applied sciences
B-spline curve
Computer aided design
Computer science
control theory
systems
Constrained optimization
Degenerate condition
Degree reduction
Exact sciences and technology
Generalized B divided difference
Software
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Zusammenfassung:In this paper, we propose the generalized B divided difference, with which the (k−1)th derivative of B-spline curves of order k can be obtained directly without the need to compute the first (k−2) derivatives as before. Based on the generalized B divided difference, the necessary and sufficient condition for degree-reducible B-spline curves is presented. Algorithms for degree reduction of B-spline curves are proposed using the constrained optimization methods.
ISSN:0167-8396
1879-2332
DOI:10.1016/S0167-8396(01)00017-6