一种带参数的二次Bezier曲线的连续条件

Continuity conditions for a class of quadratic Bezier curve with parameters

针对计算机辅助几何设计中曲线的光滑拼接问题,研究了一种带参数的二次Bezier曲线的连续条件.利用曲线性质给出了两条带参数的二次Bezier曲线在连接点处实现光滑拼接的充要条件,并得到了该曲线间G^(l)、G^(2)、C^(l)、C^(2)光滑拼接的定理。利用实例计算表明,该连续条件易于实现复杂曲线的构造,可为参数曲线的设计提供良好参考。

Focusing on the problem of smooth splicing for curves in Computer-Aided Geometric Design,continuity conditions for a class of quadratic Bezier curve with parameters is studied.The necessary and sufficient conditions to realize smooth splicing for two quadratic Bezier curves with parameters at the connection pionts are given by using the properties of curves,and the G^(1),G^(2),C^(1)and C^(2)smooth splicing theorems between the curves are also obtained.The calculation examples show that the continuity conditions are easy to realize the construction of complex curves.This can provide good reference for thedesign of parameter curves.