Isometric Projections (正等轴测图)

Construction of isometric projection(正等轴测图的形成)

To produce an isometric projection, it is necessary to view an object such that its   principal edges are equally inclined to the viewer and hence are foreshortened equally.

当空间的直角坐标轴向轴测投影面倾斜的角度相同时,用正投影法得到的投影图称为正等轴测图。

Angle between isometric axes and coefficient of axial deformation (正等轴测图的轴间角和轴向伸缩系数)

 With an isometric projection, coordinate axes (O1X1-axis, O1Y1-axis and O1Z1-axis) are equally inclined to the P-plane and the isometric axes form angles of 120°from each other (see Fig. 5-2). It can be shown that, in this case, the coefficient of axial deformation for the three axes are p=q=r=0.82. However,as the utilization of such a ratio is quite complicated for drawing preparation, we often use a simplified ratio with p=q=r=1 and the drawing produced with such a simplified ratio is called an isometric drawing. It results in a view that is (1/0.82=)1.22 percent larger than that produced with the isometric projection, but conveys the same pictorial presentation of the object. Fig. 5-3 b and c show different views produced with isometric projections and isometric views, respectively.

在正等轴测图中,三根坐标轴与轴测投影面倾斜的角度相同,其三个轴间角相等,都是120°(图5-2),其中将O1Z1沿铅垂方向放置,O1X1轴位于左下边,O1Y1轴位于右下边。由于轴间角都相等,可以证明:轴向伸缩系数p=q=r=0.82。也就是在画图时物体在长、宽、高三个方向的尺寸均要缩小0.82倍。由于按这一轴向伸缩系数作图繁琐,在制图中常采用简化的轴向伸缩系数,即取p=q=r=1。也就是在作图时,沿各轴方向取相应的实长,其放大的倍数为(1/0.82=)1.22倍,这样作图方便快捷,也不影响对物体形状的理解。图5-3b、c分别为根据两种轴向伸缩系数画出的轴测图。