一对B&#233;zier曲线基于控制顶点优化的显式<i>G</i><sup>2</sup>约束拼接

陆利正; 裘渔洋

doi:10.3724/SP.J.1004.2014.01505

一对Bézier曲线基于控制顶点优化的显式G²约束拼接

doi: 10.3724/SP.J.1004.2014.01505

1.
浙江工商大学统计与数学学院杭州 310018

基金项目:

Supported by National Natural Science Foundation of China (61272307, 11201422), Natural Science Foundation of Zhejiang Province (Y6110639, LQ13A010004, Y1110034)

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出版历程
- 收稿日期: 2013-06-07
- 修回日期: 2013-11-21
- 刊出日期: 2014-07-20

Explicit G²-constrained Merging of a Pair of Bézier Curves by Control Point Optimization

1.
School of Statistics and Mathematics, Zhejiang Gongshang Uni-versity, Hangzhou 310018, China

Funds:

Supported by National Natural Science Foundation of China (61272307, 11201422), Natural Science Foundation of Zhejiang Province (Y6110639, LQ13A010004, Y1110034)

More Information

Corresponding author: LU Li-Zheng Associate professor at Zhejiang GongshangUniversity. He received the bachelor and Ph. D. degrees fromZhejiang University, China in 2003 and 2008, respectively. Hisresearch interest covers geometric design and processing, com-puter graphics and image processing. E-mail：lulz99@163.com

摘要

摘要: 针对一对Bézier曲线的G2约束拼接，提出了通过最小化l2距离的一种简单且显式方法。将l2距离表示成具有两个参数的二次函数，最优的拼接曲线以优化控制顶点使得l2距离最小的方式得到。通过证明l2距离是凸的，说明了唯一解的存在性。由于该方法是非迭代的并且表示为已知的控制顶点，所以是显式和高效的。实例表明新方法的有效性。
- Bé /
- zier曲线 /
- 拼接 /
- l2距离 /
- G2连续 /
- 优化
Abstract: This paper presents a simple and explicit method for G2-constrained merging of a pair of Bézier curves by mini-mizing the l2 distance defined in terms of control points. After expressing the l2 distance as a quadratic function of two param-eters, the optimally merged curve can be explicitly obtained, which is achieved by control point optimization such that the l2 distance is minimized. The existence of the unique solution is shown by proving that the l2 distance is convex. The pro-posed method is explicit and effcient since it is non-iterative and expressed by known control points. Numerical examples demonstrate the effectiveness of the new method.
- Bé /
- zier curve /
- merging /
- l2 distance /
- G2 continuity /
- optimization

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参考文献(17)

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