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四次帶參Bézier旋轉(zhuǎn)曲面設(shè)計
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國家自然科學(xué)基金資助項目(51305344),、國家自然科學(xué)基金重大研究計劃培育資助項目(91120014)和陜西省教育廳基金資助項目(2013JK1029)


Quickly Construction of Quartic λ-Bézier Rotation Surfaces with Shape Parameters
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    摘要:

    針對傳統(tǒng)旋轉(zhuǎn)曲面繪制中存在計算復(fù)雜和形狀難以調(diào)節(jié)的問題,,提出了一種帶形狀參數(shù)的旋轉(zhuǎn)曲面設(shè)計方法。該方法基于超限向量值有理插值函數(shù)的基本思想,,利用帶形狀參數(shù)的四次Bézier曲線來進行旋轉(zhuǎn)曲面的設(shè)計,并得到生成整個旋轉(zhuǎn)曲面的一個顯式函數(shù)表達式,。所生成的旋轉(zhuǎn)曲面不僅計算簡單,,而且具有靈活的局部形狀可調(diào)性。最后,,對所設(shè)計的旋轉(zhuǎn)曲面進行形狀與性質(zhì)分析,,并給出了一些旋轉(zhuǎn)曲面的幾何造型實例。實例結(jié)果表明,,所提方法不僅直觀,、有效,而且易于修改旋轉(zhuǎn)曲面的形狀,,可以在工程旋轉(zhuǎn)曲面的構(gòu)造與外形設(shè)計中得到應(yīng)用,。

    Abstract:

    A method for constructing rotation surfaces with local shape parameters was proposed to solve the problems in adjusting and controlling shapes of rotation surfaces. Based on the transfinite vectored rational interpolating function, the quartic λ-Bézier rotation surfaces with multiple shape parameters were constructed using a quartic λ-Bézier curve. Then, the explicit function expression of the quartic λ-Bézier rotation surfaces was presented. The proposed quartic λ-Bézier rotation surfaces inherited the outstanding properties of the Bézier rotation surfaces, and had a good performance on adjusting their local shapes by changing the value of shape parameters. Finally, some properties of the quartic λ-Bézier rotation surfaces and applications in rotation surfaces design were discussed. The modeling examples showed that the proposed method was simple and effective, and easy to control the shape of rotation surfaces, which provided a valuable way for the design of rotation surfaces.

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胡 鋼,吉曉民,秦新強.四次帶參Bézier旋轉(zhuǎn)曲面設(shè)計[J].農(nóng)業(yè)機械學(xué)報,2014,45(4):304-309. Hu Gang, Ji Xiaomin, Qin Xinqiang. Quickly Construction of Quartic λ-Bézier Rotation Surfaces with Shape Parameters[J]. Transactions of the Chinese Society for Agricultural Machinery,2014,45(4):304-309.

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  • 收稿日期:2013-09-29
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  • 在線發(fā)布日期: 2014-04-10
  • 出版日期: 2014-04-10
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