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四次帶參廣義Bézier曲面構(gòu)造與光滑拼接技術(shù)
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國(guó)家自然科學(xué)基金資助項(xiàng)目(51305344)、國(guó)家自然科學(xué)基金重大研究計(jì)劃培育項(xiàng)目(91120014)和陜西省教育廳基金資助項(xiàng)目(2013JK1029)


Quartic Generalized Bézier Surfaces with Multiple Shape Parameters and Its Continuity Conditions
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    摘要:

    基于一組帶參數(shù)的四次廣義Bernstein基函數(shù),構(gòu)造了一種帶多形狀參數(shù)λ、γi的四次廣義Bézier曲面,該曲面不僅保留了傳統(tǒng)Bézier曲面的性質(zhì),而且具有優(yōu)良的形狀可調(diào)性,同時(shí)還以四次Bézier曲面為其特殊情形;其次,詳細(xì)分析了該曲面的一些基本性質(zhì),以及討論了該曲面的一些特殊退化曲面的構(gòu)造;最后,為了解決造型設(shè)計(jì)中復(fù)雜曲面難以用單一曲面表示的問題,進(jìn)一步研究了該曲面的拼接技術(shù),推導(dǎo)了兩相鄰四次帶參廣義Bézier曲面片間G1和G2光滑拼接的幾何條件,并給出了具體的拼接步驟與幾何造型實(shí)例。實(shí)例結(jié)果表明,所提方法不僅簡(jiǎn)單有效且易實(shí)現(xiàn),可應(yīng)用于工程復(fù)雜曲面的構(gòu)造與外形設(shè)計(jì)中。

    Abstract:

    A new geometric model of quartic generalized Bézier surfaces with multiple shape parameters was constructed by using a class of quartic generalized Bernstein basis functions. The proposed quartic generalized Bézier surfaces inherit the outstanding properties of conventional Bézier Surfaces, have a good performance on adjusting their shapes by changing shape control parameters, and have quartic Bézier surfaces as their special cases. Some basic properties of the surfaces were analyzed, and the constructions of some special surfaces degenerated from the generalized surfaces were discussed. With the aim to tackle the problem that the engineering complex surfaces can not be constructed by a single surface, the continuity conditions of quartic generalized Bézier surfaces with shape parameter were investigated. Based on the analysis of the basis functions, the conditions of G1 and G2 continuity between two adjacent quartic generalized Bézier surfaces and the detail process to blend the two surfaces were proposed. In addition, some applications of the quartic generalized Bézier surfaces in geometric modeling were discussed. The modeling examples show that the proposed method is effective and easy to implement and has extensive applications in constructing engineering complex surface.

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胡 鋼,吉曉民,郭 磊.四次帶參廣義Bézier曲面構(gòu)造與光滑拼接技術(shù)[J].農(nóng)業(yè)機(jī)械學(xué)報(bào),2014,45(5):315-321. Hu Gang, Ji Xiaomin, Guo Lei. Quartic Generalized Bézier Surfaces with Multiple Shape Parameters and Its Continuity Conditions[J]. Transactions of the Chinese Society for Agricultural Machinery,2014,45(5):315-321.

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  • 收稿日期:2013-06-10
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  • 在線發(fā)布日期: 2014-05-10
  • 出版日期: 2014-05-10