• 虚拟现实与数字媒体 •

### T-Bézier曲线能量法的光顺计算

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

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

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.