零阶连续曲线包络的计算*

包络理论中通常采用速度与法矢正交的条件来判断曲线族上的点是否为特征点,它要求曲线至少C1连续,而对于C0连续的曲线则无能为力。在此背景下,提出了扩展的包络条件来适应C0连续的曲线包络的计算,并证明了在C1连续条件下扩展包络条件是传统包络条件的充分非必要条件;在此基础上,提出了一种新的任意非凸平面多边形变形包络的计算方法。最后,通过实例验证了理论和方法的正确性。

Calculation of envelope of curves with C0 continuity

The traditional envelope condition that the velocity is perpendicular to the normal is usually used to determine gra-zing points on a family of curves. It only can be used for curves that have C1 continuity at least. If they have Co continuity, thiscondition is useless. In this situation, this paper proposed an extended envelope condition for the curves with C0 continuity.Further, it proved that the extended envelope condition was a sufficient and not necessary condition of traditional envelope con-dition. Based on this conclusion,it presented a new calculation of envelope for deformed non-convex polygon with any shape.Finally, it verified the correctness of this method by using cases.