n次λ-Bézier曲线光滑拼接的连续性条件  

Continuity Conditions for λ-Bézier Curves of Degree n

作　　者：胡钢[1,2] Wei Guo 吉晓民[1] 

机构地区：[1]西安理工大学机械与精密仪器工程学院,西安710048 [2]西安理工大学理学院,西安710054 [3]北卡罗来纳大学彭布罗克分校,彭布罗克28372

出　　处：《农业机械学报》2015年第4期351-359,337,共10页Transactions of the Chinese Society for Agricultural Machinery

基　　金：国家自然科学基金资助项目(51305344);陕西省科技计划(工业攻关)资助项目(2014K05-22);陕西省教育厅基金资助项目(2013JK1029)

摘　　要：针对n次λ-Bézier曲线造型中的复杂曲线难以用单一曲线来构造的问题,研究了该曲线光滑拼接时的连续性条件。通过分析λ-Bézier曲线的基函数及其端点性质,给出了相邻两段λ-Bézier曲线间C1、C2和G1、G2光滑拼接的充要条件;最后,给出了λ-Bézier曲线光滑拼接的具体步骤与几何造型实例,并分析了形状参数对拼接后曲线形状的影响规律。实例结果表明,所提方法不仅易实现且简单有效,在工程复杂曲面的构造与外形设计中将有一定的应用价值。With the aim to tackle the problem that the engineering complex curves can not be constructed by using a single curve,the continuity condition of the λ-Bézier curves of degree n with shape control parameters were investigated.The λ-Bézier curves of degree n not only inherit the outstanding properties of the corresponding classical Bézier curve of degree n,but also have a good performance on adjusting their shapes by changing shape control parameters.In the particular case where the shape control parameter equals to zero,the λ-Bézier curves degenerate to the classical Bézier curve.Firstly,the Bernstein-like basis functions of arbitrary order n were constructed by using a recursive formula from the initial basis functions,and the geometric property at the endpoints of the λ-Bézier curves were obtained,such as interpolation at the corners,the derivative at end-points and the second derivative at end-points.Secondly,based on the analysis of basis functions and terminal properties,the necessary and sufficient conditions of G1,G2 continuity and C1,C2 continuity between two adjacent λ-Bézier curves were proposed.Finally,some properties of the continuity condition for the λ-Bézier curves and applications inλ-Bézier curves design were discussed.In addition,the influence rules of the shape parameters on the complex λ-Bézier curves shape were studied.The modeling examples showed that the proposed method was effective and easy to implement,which greatly enhanced the ability to construct complex curves by using λ-Bézier curves.

关 键 词：λ-Bézier曲线 形状参数 几何连续 曲线设计 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]