轨迹曲面的构造与分析

根据点,线、面的运动轨迹可以形成曲面的原理,应用投影方法将空间轨迹降低为平面上的轨迹,再使平面轨迹按规律运动形成空间曲面,在此基础上获取曲面上点的主曲率和主方向。

The Construction and Analysis of Trace Curved Surface

The trace is a space collection which the geometric elements are moved on given conditions. To find out the trace law of moving geometric elements, the projection method can be used to describe trace in the space. Due to principles of the trajectory of point, line and plane can form a curved surface, a trace in the space can be projected to different planes. The plane trajectories can return to space curved surface according to its moving regularities. The principal curvatures and principal directions at a given point on the curved surface can be obtained.