上海交通大学学报(自然版) ›› 2012, Vol. 46 ›› Issue (04): 601-606.

• 自动化技术、计算机技术 • 上一篇    下一篇

4次带参Bézier可展曲面的设计

胡钢a,b,吉晓民b,c,秦新强a,沈晓芹a   

  1. (西安理工大学a. 理学院, b. 机械与精密仪器工程学院, c. 艺术设计学院,西安 710048)
  • 收稿日期:2011-05-03 出版日期:2012-04-28 发布日期:2012-04-28
  • 基金资助:

    国家自然科学基金资助项目(11101330;60971127),陕西省自然科学基金资助项目(2011JM1006),陕西省教育厅基金资助项目(11JK1052)

Geometric Design and Adjustment of Shape for Developable Quartic λBézier Surfaces with Shape Parameters

 HU  Gang-a, b , JI  Xiao-Min-b, c , QIN  Xin-Qiang-a, SHEN  Xiao-Qin-a   

  1. (a. School of Science, b. Faculty of Mechanical and Precision Instrument Engineering, c. College of the Arts, Xi’an University of Technology, Xi’an 710048, China)
  • Received:2011-05-03 Online:2012-04-28 Published:2012-04-28

摘要: 摘要: 为了方便解决工程中可展曲面位置与形状难以调节和控制的问题,提出了2种带形状参数的Bézier可展曲面设计新方法. 基于3D射影空间中点和平面间的对偶性,利用一种带形状参数的4次λBézier调配函数生成了具有4次λBézier基的控制平面,并由该平面进行包络和脊线可展曲面的设计,同时给出了在4次λBézier基函数下2种可展曲面的参数表示形式. 该方法生成的可展曲面不仅具有良好的形状可调性,而且保留了Bézier曲面的许多特性, 特别当参数λ取值为0时, 所生成的可展曲面即为3次Bézier可展曲面. 最后,对所设计的可展曲面进行了形状与性质分析,并给出了可展曲面间G2光滑拼接的条件. 实例结果表明,所提方法不仅直接、简单有效,而且易于控制可展曲面的形状,从而为可展曲面的设计提供了一种有效的新途径.
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Abstract:

关键词: Bé, zier曲线, 形状参数, 可展曲面, 对偶性, 控制平面, 光滑拼接

Abstract: To solve the problems in adjusting and controlling shapes of developable surfaces, two direct explicit and efficient methods of computeraided design for developable surfaces with local shape parameters were proposed. Firstly, following the important idea of duality between points and planes in 3D projective space, the developable quartic λBézier surfaces with shape parameters were represented using control planes with quartic λBézier basis functions. The developable quartic λBézier surfaces inherit the outstanding properties of the Bézier surfaces, with a good performance on adjusting their local shapes by changing the shape parameters. In the particular case where λ is equal to 0, the developable quartic λBézier surface is a developable Bézie surface. And then, the conditions of G2 continuity and C2 continuity between two adjacent developable quartic λBézier surfaces were presented. Finally, some properties of the developable quartic λBézier surfaces and applications in developable surfaces design were discussed. The modeling examples illustrate that the developable quartic λBézier surfaces provide two valuable ways for the design of developable surfaces.

Key words: Bézier curve, shape parameter, developable surface, duality, control plane, continuity conditionBézier

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