四次带参Bézier曲线曲面的光滑拼接

On Continuity Conditions for Quartic Bézier Curves and Surfaces with Shape Parameters

针对复杂自由曲线曲面难以用单一曲线曲面表示的问题,研究了一种四次带参Bézier曲线曲面的拼接技术.在对四次带参Bézier曲线基函数及端点性质分析的基础上,给出了该曲线间G1、G2和C1、C2光滑拼接的充要条件.利用四次带参Bézier曲线与C-Bézier曲线间的拼接技术,解决了该曲线造型中圆弧和椭圆弧的表示问题.分析了2张双四次带参Bézier曲面片间G1光滑拼接的几何条件,并通过合理选取形状参数,进一步简化了该曲面的拼接条件.实例结果表明,该方法简单、直观、易实现,有效增强了四次带参Bézier曲线曲面表达复杂曲线曲面的能力,可广泛应用于各种CAD/CAM造型系统中.

To tackle the problem that the engineering complex curves or surfaces can not be constructed by using a single curve or surface,the continuity condition of quartic quasi-Bézier（quartic q-Bézier） curves and surfaces with shape parameters was studied.Based on the analysis of the basis functions and terminal properties,the necessary and sufficient conditions of G^1 and G^2 continuity,and C^1 and C^2 continuity between two adjacent quartic q-Bézier curves were proposed.In order to overcome the shortcomings that the circular arc and ellipse can not be accurately represented by quartic q-Bézier curves,the continuity condition between quartic q-Bézier curves and C-Bézier curves was also presented.In addition,the geometric model of the quartic q-Bézier surfaces was constructed and the condition of G^1 continuity between two adjacent quartic q-Bézier surfaces in u and v directions was derived and simplified by choosing the control parameters properly. The modeling examples illustrated that the continuity condition of the quartic qBézier curves and surfaces could be widely applied to the complex curves and surfaces modeling system.