The Quartic Generalized C-B閦ier Surface with Multiple Shape Parameters and Continuity Condition
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摘要: 利用空间Φ=span{sint,cost,t2,t1,1}上一组正规B基,构造了一种新的含多形状参数的四次广义C-Bézier曲面。这种曲面不仅保留了传统Bézier曲面的性质,而且具有优良的形状可调性,特别当所有形状参数趋于0时其极限曲面就是四次Bézier曲面。此外,为了解决造型设计中复杂曲面难以用单一曲面表示的问题,进一步研究了该曲面的拼接技术,推导了两相邻四次广义CBézier曲面片间G0和G1光滑拼接的几何条件,并给出了光滑拼接的具体步骤与几何造型实例。
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关键词:
- 广义C-Bézier曲面 /
- 形状参数 /
- 光滑拼接 /
- 曲面设计
Abstract: A new geometric model for the quartic generalized C-B閦ier surface with multiple shape parameters is constructed by using the basis functions 1,t,t2,sint,cost. The proposed generalized C-B閦ier surface not only inherit the outstanding properties of the B閦ier surface,but also have a good performance on adjusting their shapes by changing shape control parameters. To tackle the problem that the engineering complex surfaces can not be constructed by using a single surface,the continuity condition of quartic generalized C-B閦ier surface with shape parameter are investigated. Based on the analysis of the basis functions,the conditions of G0 and G1continuity between two adjacent quartic generalized C-B閦ier surface are proposed. In addition,the application of the quartic generalized C-B閦ier surface design is discussed.-
Key words:
- continuity conditions /
- design /
- generalized C-B閦ier Surfaces /
- shape parameter
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