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浙江大学学报(理学版)  2016, Vol. 43 Issue (5): 554-559    DOI: 10.3785/j.issn.1008-9497.2016.05.011
数学与计算机科学     
有理三角Bézier曲线曲面光滑融合的构造
刘华勇, 李璐, 张大明, 谢新平, 王焕宝
安徽建筑大学 数理学院, 安徽 合肥 230601
Smooth blending of rational trigonometric Bézier curves and surfaces
LIU Huayong, LI Lu, ZHANG Daming, XIE Xinping, WANG Huanbao
School of Mathematic&Physics, Anhui Jianzhu University, Hefei 230601, China
 全文: PDF(1619 KB)  
摘要: 为了使自由曲线曲面在较为简单的条件下能够达到相对高阶的光滑拼接,并在不改变控制顶点的情况下自由调整曲线曲面的形状,构造了含多个形状参数的有理三角函数.基于该组基函数,定义了含多个形状参数的有理三角曲线曲面,并讨论了曲线曲面的光滑拼接条件.根据拼接条件,分别定义了由含多个形状参数的有理三角曲线曲面构成的分段组合曲线、分片组合曲面.这种新的曲线曲面能够自动保证组合曲线、曲面的连续性.数值实例的结果显示了该方法的有效性.
关键词: 三角Bézier曲线融合连续性封闭的曲线曲面    
Abstract: In order to achieve high level of smooth blending between the free form curves and surfaces in relatively simple conditions and easy shape adjustment of the curves and surfaces without changing their control vertices, a set of rational trigonometric Bézier basis functions with multiple shape parameters are constructed. Based on these basis functions, the rational trigonometric Bézier curves and surfaces with multiple shape parameters are defined, and the conditions for smooth joining of these curves and surfaces are derived. Following the above conditions of blending, the piecewise composite rational curves and surfaces with multiple shape parameters are defined, which automatically meet with the higher order continuity. The results of numerical examples show the effectiveness of the method.
Key words: trigonometric Bézier curve    blending    continuity    closed curves and surfaces
收稿日期: 2015-08-10 出版日期: 2016-05-01
CLC:  TP391  
基金资助: 国家自然科学基金资助项目(61402010,61471003); 安徽省高等学校自然科学研究项目(KJ2015A328; KJ2015JD16; KJ2016A151 ).
作者简介: 刘华勇(1972-),ORCID:http://orcid:org/0000-0002-9330-1149,男,硕士,副教授,主要从事计算机辅助几何设计研究,E-mail:aiaiwj@126.com.
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引用本文:

刘华勇, 李璐, 张大明, 谢新平, 王焕宝. 有理三角Bézier曲线曲面光滑融合的构造[J]. 浙江大学学报(理学版), 2016, 43(5): 554-559.

LIU Huayong, LI Lu, ZHANG Daming, XIE Xinping, WANG Huanbao. Smooth blending of rational trigonometric Bézier curves and surfaces. Journal of ZheJIang University(Science Edition), 2016, 43(5): 554-559.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2016.05.011        https://www.zjujournals.com/sci/CN/Y2016/V43/I5/554

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