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浙江大学学报（理学版）
浙江大学学报（理学版）  2019, Vol. 46 Issue (4): 422-430    DOI: 10.3785/j.issn.1008-9497.2019.04.007
数学与计算机科学     
保参数方向的形状可调过渡曲线与曲面
李军成1, 李兵2, 易叶青3
1.湖南人文科技学院 数学与金融学院， 湖南 娄底 417000
2.四川航天技术研究院 总体部， 四川 成都 610100
3.湖南人文科技学院 信息学院， 湖南 娄底 417000
The shape-adjustable transition curves and surfaces with parameter direction preserving
LI Juncheng1, LI Bing2, YI Yeqing3
1.College of Mathematics and Finances， Hunan University of Humanities， Science and Technology， Loudi 417000， Hunan Province， China
2.The General Design Department， Sichuan Academy of Aerospace Technology， Chengdu 610100， China
3.College of Information， Hunan University of Humanities， Science and Technology， Loudi 417000， Hunan Province， China
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摘要： 针对保参数方向构造过渡曲线曲面方法的不足， 构造了任意参数曲线曲面间既保持参数方向又具有形状可调性的C1与C2连续过渡曲线曲面。首先，基于2类带1个自由参数的调配函数，分别构造满足C1与C2连续的过渡曲线，并讨论基于能量优化模型的最佳过渡曲线构造问题；然后，将所提出的方法推广到过渡曲面的构造。 实例结果表明，2被过渡曲线曲面为任意参数曲线曲面时，利用该方法构造的过渡曲线曲面不仅与2被过渡曲线曲面的参数方向保持一致，而且可利用所带的自由参数对其形状进行调整。通过能量优化模型确定自由参数的取值，可获得尽可能光顺的过渡曲线曲面。 所提方法弥补了保参数方向构造过渡曲线曲面方法的不足，是一种实用的过渡曲线曲面构造方法。
关键词： 过渡曲线曲面;  形状可调;  保参数方向;  光顺    
Abstract: In view of the deficiency of the methods for constructing the transition curve and surface with parameter direction preserving， the C1 and C2 transition curves and surfaces with adjustable shape and parameter direction preserving between arbitrary parametric curves and surfaces are constructed. Firstly， the C1 and C2 transition curves are established on the base of two blending functions with a free parameter， and construction of the optimal transition curves based on energy optimization models is discussed. Then， the transition surfaces are similarly presented. Examples show that， the two transited curves and surfaces can be arbitrary parametric curves and surfaces when the proposed methods are used to construct transition curves and surfaces. The transition curves and surfaces not only maintain the parameter direction with the two transited curves and surfaces， but also can be adjusted by the free parameter. The value of the free parameters can be determined by the energy optimization model， which would obtain the transition curves and surfaces as smooth as possible. The proposed method is a practical method which overcomes the disadvantages of the methods for constructing the transition curve and surface with parameter direction preserving.
Key words: transition curves and surfaces    shape adjustment    parameter direction preserving    smoothness
收稿日期: 2018-04-20 出版日期: 2019-07-25
CLC:  TP391  
基金资助: 国家自然科学基金资助项目(61472135); 湖南省自然科学基金资助项目(2017JJ3124);湖南省教育厅资助科研项目(18A415).
作者简介: 李军成(1982—),ORCID:http://orcid.org.0000-0000-0002-1904-4068 ， 男, 博士, 副教授, 主要从事计算机辅助几何设计及其应用研究， E-mail:lijuncheng82@126.com.
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引用本文:

李军成, 李兵, 易叶青. 保参数方向的形状可调过渡曲线与曲面[J]. 浙江大学学报（理学版）, 2019, 46(4): 422-430.

LI Juncheng, LI Bing, YI Yeqing. The shape-adjustable transition curves and surfaces with parameter direction preserving. Journal of Zhejiang University (Science Edition), 2019, 46(4): 422-430.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2019.04.007    或    https://www.zjujournals.com/sci/CN/Y2019/V46/I4/422

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