拟三次Bézier曲线曲面的拼接技术

Continuity Conditions for Cubic Quasi-Bézier Curves and Surfaces

针对工程中复杂自由曲线曲面难以用单一曲线曲面来表示的问题,研究了一种带形状参数的拟三次Bézier(三次Q-Bézier)曲线曲面的拼接技术.在对三次Q-Bézier曲线基函数及其端点性质分析的基础上,给出了两相邻三次Q-Bézier曲线间G1、G2和C1、C2拼接的充要条件,运用张量积的方法给出了双三次Q-Bézier曲面的几何模型,同时分析了两相邻双三次Q-Bézier曲面片间G1光滑拼接的几何条件,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,给出了三次Q-Bézier曲线曲面光滑拼接的几何造型实例.实例结果表明,所提方法简单、直观、易实现,有效地增强了三次Q-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线曲面的造型系统中.

Focusing on the fact that the engineering complex curves or surfaces can not be described by using a single curve or surface, the continuity conditions of cubic quasi-Bézier （cubic Q-Bézier） curves and surfaces with shape parameters are investigated. Following the analysis of basis functions and terminal properties, the necessary and sufficient conditions of G1 , G2 continuity and C1 , C2 continuity between two adjacent cubic Q-Bézier curves are proposed. And then, the geometric model of the cubic Q-Bézier surfaces is constructed and the condition of G1 continuity between two adjacent cubic Q-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 the cubic Q-Bézier curves and surfaces can be widely applied to the complex curves and surfaces modeling system.