两平面场仿射及其在工程上的应用

An Affine Transformation of Two Plane-fields and the Application in Solving Spatial Problems

本文使用两平面场仿射变换的方法来解决工程上的一些空间几何问题,对这些几何问题,使用普通画法几何的方法来解决有一定困难,有时甚至不可能。本文将依次介绍仿射变换的基本概念,在正投影中如何建立两平面场的仿射对应,以及它们在解空间几何问题上的应用。

This paper uses the method of an affine transformation of two plane- fields to solve certain spatial geometrical problems which need to be solved in the engineering practice.These problems are difficult or sometimes even impossible to solve by the use of common method of descriptive geometry. This paper will discuss in proper order the primary principle of the affine transformation of two plane-fields,and how to build up an affine correspon- dence of two plane-fields in the orthographic projection.The practical app- lications in solving spatial geometrical problems by means of the affine trans- formation of two plane-fields are also introduced.