| Constrained multi-degree reduction of rational Bezier curves using reparametenzation |
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| 作者姓名： | CAI Hong-jie WANG Guo-jin |
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| 作者单位： | Institute of Computer Images and Graphics, State Key Laboratory of CAD ＆ CG, Zhejiang University, Hangzhou 310027, China |
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| 基金项目： | Project supported by the National Basic Research Program （973） of China （No. 2004CB719400）, the National Natural Science Foundation of China （Nos. 60673031 and 60333010）, and the National Natural Science Foundation for Innovative Research Groups of China （No. 60021201） |
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| 摘 要： | Applying homogeneous coordinates, we extend a newly appeared algorithm of best constrained multi-degree reduction for polynomial Bezier curves to the algorithms of constrained multi-degree reduction for rational Bezier curves. The idea is introducing two criteria, variance criterion and ratio criterion, for reparameterization of rational Bezier curves, which are used to make uniform the weights of the rational Bezier curves as accordant as possible, and then do multi-degree reduction for each component in homogeneous coordinates. Compared with the two traditional algorithms of ＂cancelling the best linear common divisor＂ and ＂shifted Chebyshev polynomial＂, the two new algorithms presented here using reparameterization have advantages of simplicity and fast computing, being able to preserve high degrees continuity at the end points of the curves, do multi-degree reduction at one time, and have good approximating effect.
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| 关 键 词： | 有理贝济埃曲线 多级还原技术 再参量化 计算机技术 |
| 收稿时间： | 2006-12-13 |
| 修稿时间： | 2007-03-07 |
Constrained multi-degree reduction of rational Bézier curves using reparameterization |
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| CAI Hong-jie WANG Guo-jin.Constrained multi-degree reduction of rational Bezier curves using reparametenzation[J].Journal of Zhejiang University Science,2007,8(10):1650-1656. |
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| Authors: | Cai Hong-jie Wang Guo-jin |
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| Institution: | (1) Institute of Computer Images and Graphics, State Key Laboratory of CAD & CG, Zhejiang University, Hangzhou, 310027, China |
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| Abstract: | Applying homogeneous coordinates, we extend a newly appeared algorithm of best constrained multi-degree reduction for polynomial
Bézier curves to the algorithms of constrained multi-degree reduction for rational Bézier curves. The idea is introducing
two criteria, variance criterion and ratio criterion, for reparameterization of rational Bézier curves, which are used to
make uniform the weights of the rational Bézier curves as accordant as possible, and then do multi-degree reduction for each
component in homogeneous coordinates. Compared with the two traditional algorithms of “cancelling the best linear common divisor”
and “shifted Chebyshev polynomial”, the two new algorithms presented here using reparameterization have advantages of simplicity
and fast computing, being able to preserve high degrees continuity at the end points of the curves, do multi-degree reduction
at one time, and have good approximating effect.
Project supported by the National Basic Research Program (973) of China (No. 2004CB719400), the National Natural Science Foundation
of China (Nos. 60673031 and 60333010), and the National Natural Science Foundation for Innovative Research Groups of China
(No. 60021201) |
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| Keywords: | Rational Bezier curves Constrained multi-degree reduction Reparameterization |
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