轴测参数图解正轴测坐标系的新方法

A New Graphic Method of Constructing an Orthogonal Axonometric System of Coordinates by the Use of Axonometric Parameters

在正轴测投影理论中,由轴向变形系数p、q、r中的任意两个可确定轴测轴X、Y、Z 及其轴测单位i、j、k。这是图解正轴测坐标系的一种典型解法。但是至今为止,尚未见到,以一个轴向变形系数和一个轴间角(r和∠XOY或P和∠YOZ或q和∠XOZ)来图解正轴测坐标系的方法。本文提出了,在一个单位圆中,利用轨迹相交来解决这个问题的一种极为简便的图解法。实际上,这个方法也解决了在不画出椭圆的情况下,就能确定椭圆中夹角为某个角度的一对共轭直径的位置以及椭圆中任意一对共轭直径所夹角度的取值范围问题。

In the theory of orthogonal axonometric projection, axonometric axes X, Y, Z and axonometric units i, j, k can be determined by any two of distortion factors along axonometric axes p, q, r. This is a typical graphic method of constructing an orthogonal axonometric system of coordinates. But up to now, we have not seen a graphic method of constructing an orthogonal axonometric system of coordinates by the use of a distortion factor and an angle between two axonometric axes(r,∠XOY or p,∠YOZ or q,∠XOZ). This paper describes a very simple graphic method for this problem by means of intersec-tion of locus in a unit circle. By the way, it also solves the problem of determining the position of a pair of conjugate diameters at a certain angle and the extent of the angle between any pair of conjugate diameters in an ellipse, needless to construct the ellipse itself.