负高斯曲率曲面可见轮廓的临界投影方向

CRITICAL DIRECTION OF PROJECTION FOR THE VISIBLE CONTOUR OF A SMOOTH SURFACE WITH NEGATIVE GAUSSIAN CURVATUVE

本文的目的是探讨负高斯曲率曲面块轮廓的动态可见性的曲面几何条件。证明了下面两个命题:(1)设P_0为负高斯曲率曲面S的实廓线上的一点。在P_0的邻域内,S上P_0的渐近方向是P_0的可见轮廓的临界投影方向。(2)当P_0在S上具有对称性时,P_0的象为正常点;当P_0在S上不具有对称性时,P_0的象为尖点。

The following proposition are proved:Let P_0 be a point on the contour of a smooth surface withnegative gaussian curvature S,the asymptotic direction of P_0 on S is the critical direction for the visi-ble contour of S in the neighborhood of P_0.