Optimal multi-degree reduction of C-Bézier surfaces with constraints
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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 wordsC-Bézier surfaces Degree reduction Boundary constraints
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- Fan, J.H., Wu, Y.J., Lin, X., 2002. Subdivision algorithm and G1 condition for C-Bézier curves. J. Comput. Aided Des. Comput. Graph., 14(5):421–424 https://doi.org/10.3321/j.issn:1003-9775.2002.05.009Google Scholar
- Qin, X.Q., Wang, W.W., Hu, G., 2013. Degree reduction of C-Bézier curve based on genetic algorithm. Comput. Eng. Appl., 49(5):174–178. https://doi.org/10.3778/j.issn.1002-8331.1107-0346Google Scholar
- Zhou, L., 2012. Algorithm for explicit multi-degree reduction of C-Bézier curves. J. Shanghai Marit. Univ., 33(4):86–90. https://doi.org/10.3969/j.issn.1672-9498.2012.04.017Google Scholar