Developable B-spline surface for interpolating two planar curves and it’s convexity analysis

doi:10.3778/j.issn.1002-8331.2008.29.013

Computer Engineering and Applications ›› 2008, Vol. 44 ›› Issue (29): 47-50.DOI: 10.3778/j.issn.1002-8331.2008.29.013

• 理论研究 • Previous Articles Next Articles

Developable B-spline surface for interpolating two planar curves and it’s convexity analysis

FANG Kui¹,TANG Tuo¹,TAN Jian-rong²

1.College of Information Science & Technology，Hunan Agricultural University，Changsha 410128，China
2.College of Mechanical and Energy Engineering，Zhejiang University，Hangzhou 310027，China

Received:2008-04-14 Revised:2008-07-04 Online:2008-10-11 Published:2008-10-11
Contact: FANG Kui

插值平面曲线的可展B样条曲面及凸性分析

方逵¹,唐妥¹,谭建荣²

1.湖南农业大学信息科学技术学院长沙 410128
2.浙江大学机械与能源工程学院，杭州310027

通讯作者: 方逵

Abstract

Abstract: When the two B-spline boundary curves of the ruled surface are in two arbitrary planes，a necessary and sufficient condition for the （n，n） degree developable B-spline ruled surface is obtained，and the （2，2） degree developable B-spline surfaces are constructed.Through the analysis of the convexity of the B-spline ruled surface，a necessary and sufficient condition for the convex （n，n） degree developable B-spline ruled surface is obtained.

Key words: Computer Aided Geometry Design（CAGD）, developable surface, b-spline curve surface, convex surface, characteristic polygon

摘要： 用两条位于两任意平面上的均匀B样条曲线作边界曲线，形成一个直纹面，得到了该直纹面为可展曲面的充要条件，解决了（n，n）次可展B样条曲面的设计问题，构造了（2，2）次B样条可展曲面。通过对以上可展B样条曲面进行凸性分析，得到了（n，n）次可展B样条曲面为凸曲面的充要条件。

关键词: 计算机辅助几何设计（CAGD）, 可展曲面, B－样条曲线曲面, 凸曲面, 特征多边形

FANG Kui¹,TANG Tuo¹,TAN Jian-rong². Developable B-spline surface for interpolating two planar curves and it’s convexity analysis[J]. Computer Engineering and Applications, 2008, 44(29): 47-50.

方逵¹,唐妥¹,谭建荣². 插值平面曲线的可展B样条曲面及凸性分析[J]. 计算机工程与应用, 2008, 44(29): 47-50.

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Developable B-spline surface for interpolating two planar curves and it’s convexity analysis

插值平面曲线的可展B样条曲面及凸性分析

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