空间两射影对应点列形成的单叶双曲面

摘要

The One-Sheet Hyperbolid can be formed by connecting the correponding points of projection point ranges with two intersection lines as the basis in a space. When one line of them is moved to a new position, the One-Sheet Hyperbolid will generate change in a certain pattern. Through a systematic analysis to the shape of its intersection lines, it is for the first time to put forward the existence of the parabola-type intersection line in the One-Sheet Hyperbolid. Simplification of the drawing of projection point ranges provides theoretical support to further application of CAD software to automatically produce the Hyperbolid.%空间两条交叉直线为底的射影对应点列,对应点连线包络成单叶双曲面.如果移动其中任一点列的位置,单叶双曲面的形状变化有一定的规律.通过对单叶双曲面截交线形状的系统分析,首次提出单叶双曲面上存在抛物线型截交线.针对二射影对应点列作图法的简化,为我们进一步开发应用CAD软件自动生成该曲面提供了理论支持.