带多形状参数的三次Bézier曲线曲面的光滑拼接

Research on the Smooth Splice for Cubic Bézier Curves and Surfaces with Multiple Shape Parameters

研究了一种带多形状参数的三次扩展Bézier(CE-Bézier)曲线曲面的拼接技术。在对CE-Bézier曲线基函数及端点性质分析的基础上,给出了第二类CE-Bézier曲线间G1、G2和C1、C2拼接的充要条件;同时,分析了两张CE-Bézier曲面片间G1、C1光滑拼接的几何条件,通过合理选取形状参数,进一步简化了曲面的拼接条件,并给出了几何造型的实例。实例结果表明,CE-Bézier曲线曲面的光滑拼接技术可广泛地应用于工程复杂曲线、曲面的造型系统中。

The splicing technology of cubic extension Bézier（CE-Bézier） curves and surfaces with multiple shape parameters is studied in this paper.Based on the analysis of the basis functions and terminal properties for CE-Bézier curve,the necessary and sufficient splicing conditions of G1,G2 and C1,C2 between two CE-Bézier curves are proposed.And at the same time,G1,C1 smooth splicing condition between two CE-Bézier surfaces in u and v directions is derived and the curved surface splicing condition is further simplified by choosing the control parameters properly with some geometric modeling examples given.The results from real examples indicate that the smooth splicing technology of CE-Bézier curves and surfaces can be widely applied to the engineering complex curves and surfaces modeling system.