Optimal multi-degree reduction of C-Bézier surfaces with constraints

  • Lian Zhou
  • Xin-hui Lin
  • Hong-yan Zhao
  • Jun Chen


We propose an optimal approach to solve the problem of multi-degree reduction of C-Bézier surfaces in the norm L2 with prescribed constraints. The control points of the degree-reduced C-Bézier surfaces can be explicitly obtained by using a matrix operation that is based on the transfer matrix of the C-Bézier basis. With prescribed boundary constraints, this method can be applied to piecewise continuous patches or to a single patch with the combination of surface subdivision. The resulting piecewise approximating patches are globally G1 continuous. Finally, numerical examples are presented to show the effectiveness of the method.

Key words

C-Bézier surfaces Degree reduction Boundary constraints 

CLC number



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Copyright information

© Zhejiang University and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Maritime UniversityShanghaiChina
  2. 2.Zhejiang Institute of Economics and TradeHangzhouChina
  3. 3.College of Fundamental StudiesShanghai University of Engineering ScienceShanghaiChina
  4. 4.Faculty of ScienceNingbo University of TechnologyNingboChina

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