Degree reduction of B-spline curves

Jun-Hai Yong Tsinghua University Shi-Min Hu Tsinghua University Jia-Guang Sun Tsinghua University

Geometric Modeling and Processing mathscidoc:1608.16081

Computer Aided Geometric Design, 13, (2), 117-127, 2001
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.
Degree reduction, B-spline curves
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@inproceedings{jun-hai2001degree,
  title={Degree reduction of B-spline curves},
  author={Jun-Hai Yong, Shi-Min Hu, and Jia-Guang Sun},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160826224230040618464},
  booktitle={Computer Aided Geometric Design},
  volume={13},
  number={2},
  pages={117-127},
  year={2001},
}
Jun-Hai Yong, Shi-Min Hu, and Jia-Guang Sun. Degree reduction of B-spline curves. 2001. Vol. 13. In Computer Aided Geometric Design. pp.117-127. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160826224230040618464.
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