计算机应用 ›› 2015, Vol. 35 ›› Issue (7): 2047-2050.DOI: 10.11772/j.issn.1001-9081.2015.07.2047

• 虚拟现实与数字媒体 • 上一篇    下一篇

T-Bézier曲线能量法的光顺计算

方永锋1, 陈建军2, 邱泽阳3   

  1. 1. 贵州工程应用技术学院 机械工程学院, 贵州 毕节 551700;
    2. 西安电子科技大学 电子装备结构设计教育部重点实验室, 西安 710071;
    3. 兰州交通大学 工业设计研究所, 兰州 730001
  • 收稿日期:2015-01-21 修回日期:2015-03-25 出版日期:2015-07-10 发布日期:2015-07-17
  • 通讯作者: 方永锋(1975-),男,甘肃宁县人,副教授,博士,主要研究方向:计算机辅助几何设计、结构可靠性,fangyf_9707@126.com
  • 作者简介:邱泽阳(1968-),男,江苏沭阳人,教授,博士,主要研究方向:计算机辅助几何设计、逆向计算; 陈建军(1952-),男,河北保定人,教授,博士生导师,主要研究方向:结构可靠性、随机振动。
  • 基金资助:

    国家自然科学基金资助项目(61473331);贵州省自然科学基金资助项目(黔科合J字[2014]2001);贵州省省级实验示范教学中心项目;贵州省高等学校新能源汽车产学研基地项目(黔教科KY[2014]238);贵州工程应用技术学院高层次人才项目(院科合字G2013007号)。

Fairing computation for T-Bézier curves based on energy method

FANG Yongfeng1, CHEN Jianjun2, QIU Zeyang3   

  1. 1. School of Mechanical Engineering, Guizhou University of Engineering Science, Bijie Guizhou 551700, China;
    2. Key Laboratory of Electronic Equipment Structure Design, Ministry of Education (Xidian University), Xi'an Shaanxi 710071, China;
    3. Institute of Industry Design, Lanzhou Jiaotong University, Lanzhou Gansu 730001, China
  • Received:2015-01-21 Revised:2015-03-25 Online:2015-07-10 Published:2015-07-17

摘要:

针对T-Bézier曲线的光顺要求,提出了用能量法对T-Bézier曲线进行光顺。首先通过能量法对T-Bézier曲线修改一个控制顶点使之达到光顺,同时给出了扰动因子α对曲线的影响,由此得到欲移动T-Bézier曲线的一个控制顶点达到光顺,可先确定α,再确定新的控制顶点,就可得到光顺后的新的T-Bézier曲线。对整条曲线进行光顺时先确定扰动因子{αi}i=1n,然后求解一个系数矩阵为实对称三对角矩阵的方程组,再依次确定新的控制点列{Pi}i=0n,最后由控制顶点确定光顺后的三次T-Bézier插值曲线,从而使T-Bézier曲线不仅达到整体光顺而且在数据点实现C2连续。最后,给出了3个实例,说明该算法是简单、实用和有效的。

关键词: 能量法, T-Bé, zier曲线, 光顺, 连续

Abstract:

For fairing requirements of the T-Bézier curve, the T-Bézier curve was smoothed by using the energy method. A control point of the T-Bézier curve was modified by using the energy method to make the T-Bézier curve smooth, while it was shown how the interference factor α influenced the smoothness of the T-Bézier curve. It was obtained a method that a fairing T-Bézier curve would be obtained by moving a control point: the α could be determined before the new control point would be found out, the new T-Bézier curve was produced by these new control points. The whole curve would be smoothed: firstly, the interference factors {αi}i=1n were determined; secondly, the equation system whose coefficient matrix was a real symmetric matrix tridiagonal was solved; thirdly, the new control points {Pi}i=0n were obtained; finally, the new T-Bézier curve could be produced. Not only overall fairness of the T-Bézier curve but also C2 continuity of data points was achieved. Finally, it was shown that the proposed algorithm is simple, practical and effective by three examples.

Key words: energy method, T-Bé, zier curve, fairing, continuation

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