用平行轴旋转法解决空间几何问题  

Solving space geometry problems with the mode of revolving on parallel axis

作　　者：彭慧敏[1] 雷光明[1] 文佩芳[1] 王明海[1] 成彬[1] 

机构地区：[1]西安建筑科技大学理学院,陕西西安710055

出　　处：《西安建筑科技大学学报（自然科学版）》2006年第5期724-727,共4页Journal of Xi'an University of Architecture & Technology(Natural Science Edition)

基　　金：陕西省高等教育教改立项资助项目(2005-47)

摘　　要：在画法几何投影变换中,不论用换面法或旋转法,一般位置直线均需两次变换才能变成投影面垂直线.给出了一般位置直线绕平行轴经一次旋转成为投影面垂直线的方法,从而使平行轴旋转法的应用范围由平面扩展到空间.使其不仅可以解决有关同一平面的几何问题,也可方便地求解空间几何元素间的定位与度量问题.其作图原理及方法是对旋转法内容的重要补充,给求解空间几何问题提供了又一基本工具.In the transformation of descriptive geometry, no matter the method of change plane or revolve, the oblique line can be changed to a vertical line in two successive transformations. The paper introduces a new method of transforming an oblique line into a vertical line. To complete the transformation, the oblique line has to revolve only once on the parallel axis. Thus the scope of applying the mode of revolving on parallel axis will be expanded. This mode of revolution can be used not only to solve the problems in plane geometry, but to deal easily with orientation and measurement of space geometry elements. The principle and method of drawing are an important supplement for mode of revolving on paralled axis contents. It provides another basic means to slove the space geometry problems.

关 键 词：投影变换 平行轴旋转法 一般位置直线 

分 类 号：O185.2[理学—数学]