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CE-Bézier 曲面光滑拼接的研究与实现

  

  • 出版日期:2012-10-31 发布日期:2015-07-28

Research on the continuity conditions for CE-Bézier surfaces

  • Online:2012-10-31 Published:2015-07-28

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摘要： 针对CE-Bézier 曲面造型中复杂曲面难以用单一曲面来表示的问题，通过
分析CE-Bézier 曲线的唯一性，提出了一种新的CE-Bézier 曲面的光滑拼接技术。首先，在
分析第1 类CE-Bézier 曲线基函数及其端点性质的基础上，对第1 类CE-Bézier 曲线的唯一
性进行了研究，得出了对于同一条第1 类CE-Bézier 曲线可以有很多组不相同的控制顶点和
形状参数与之对应的结论；其次，利用该结论进一步给出了两相邻第1 类CE-Bézier 曲面片
间G1 光滑拼接的一般几何条件，并通过合理地选取形状参数，进一步简化了该曲面的G1
拼接条件；最后，给出了第1 类CE-Bézier 曲面光滑拼接的几何造型实例。实例结果表明，
该方法简单、直观、易实现，有效地增强了CE-Bézier 方法表达复杂曲线曲面的能力，可广
泛地应用于工程复杂曲面的造型系统中。

关键词: CE-Bé, zier 曲线, CE-Bé, zier 曲面, 形状参数, 光滑拼接, 唯一性分析

Abstract: Focusing on the problem that the engineering complex surfaces can not be
described by using a single cubic extension Bézier (CE-Bézier) surfaces with multiple shape
parameters, the continuity conditions of CE-Bézier surfaces are proposed. Following the analysis
of basis functions and terminal properties, the unique property of CE-Bézier curves is investigated
and the corresponding conclusion that a CE-Bézier curve can be defined by many different groups
of control points and shape parameters is also obtained. And then, the geometric model of
CE-Bézier surfaces is constructed and the condition of G1 continuity between two adjacent
CE-Bézier surfaces in u and v directions is derived and simplified by choosing the control
parameters properly. The modeling examples illustrate that the continuity condition of CE-Bézier
surfaces can be widely applied to the complex surfaces modeling system.

Key words: CE-Bézier curve, CE-Bézier surface, shape parameter, continuity condition;
analysis of unique property