CE-Bézier曲面光滑拼接的研究与实现

摘要

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