平面体的投影Projection of  Planar Solids

       识读平面体三视图，就是依据平面体三视图的图形特征想象出它的立体形状的过程。由上述可知，平面体三视图中，两个视图外轮廓是矩形，所表示的形体一定是柱体，对应的多边形是什么形状就是什么棱柱；两个视图外轮廓是三角形，所表示的形体一定是锥体，对应的多边形是几边形就是几棱锥；两个视图外轮廓是梯形，所表示的形体一定是台体，对应的多边形是几边形就是几棱台。无论是完整的还是部分的平面体的三视都具有此图形特征。

       Reading three views of basic solids is to imagine the solid in space based on its three views. As we know, if its two views are both rectangles, the solid must be a prism. The name depends on the polygon. If two views are both triangles, solid must be a pyramid. If the two views are both trapeziums[trә'pi:ziәm],  the views show frustum of a pyramid. Whenever the planar solid is complete or part , it should follow the feature characteristics.

【例 4-1】逐一分析图 4-1 所示平面体的三视图，想象出它们的立体形状。 Please produce the solid based on three views of planar solid.

分析 analyze

      图 4-1(a)所示三视图，左视图和俯视图两个视图为矩形，一定是柱体，特征图主视图为“凸”字形（底面实形），可知该形体是前后底面为凸字形的“凸形柱”，立体形状如图 4-2 (a)所示。

      According to the given three views, left and top views are both rectangles, one can make sure it is a prism. The feature view is the front view and the shape is 凸( show the true shape of front and back faces), the solid as shown in fig 4-2.

      图 4-1 (b)所示三视图，主视图和俯视图两个视图都是三角形，一定是锥体，特征图左视图为四边形，可知该形体是锥尖向左，底面平行于 W 投影面的四棱锥，立体形状如图 4-2 (b)所示。

      Figure 4-1 (b) shows that the left and top views both triangles, it indicates that the solid is a cone. The feature view is a quadrangle; the solid is a cone tip to the left, bottom surface is parallel to the W projection plane, three-dimensional shape as shown in Figure 4-2 (b).

      图 4-1 (c)所示三视图，有两个视图为梯形，一定是台体，特征图是 1/2 四棱台底面形状。可知该形体为左半四棱台，立体形状如图 4-2 (c)所示。

      Figure 4-1 (c) shows that there are two views are both trapezoids[ˈtræpəzɔɪd], must be a frustum of a pyramid, feature view is 1/2 frustum of a rectangular pyramid. The solid is the left semi frustum of a rectangular pyramid. Three-dimensional shape is shown in Figure 4-2(c).

                          图4-1 平面体三视图的识读举例  Fig 4-1 samples of reading planar solids

                              图4-2 平面体三视图识读示例对应的立体形状  Fig 4-2 solids in space

2.曲面体三视图的识读 reading of curved solids

曲面体三视图的读图依据是曲面体三视图的图形特征。无论是完整还是部分曲面体

的三视图都具有上述的图形特征。

The rule of reading curved solids is the projection feature of curved solids. Whenever the

solid is complete or partial [ˈpɑ:ʃəl].

【例 4-2】识读图 4-3 所示曲面体的三视图。Please imagine the solids based on given views.

                        图4-3 曲面体三视图的识读举例  Fig 4-3 samples of reading curved solids

分析 analyze

       图 4-3(a)所示三视图，主视图和俯视图两个视图为矩形，是柱体，特征图左视图是圆，可知该形体是轴线垂直 W 投影面的圆柱。

       Figure 4-3 (a) shows that the front and top views are both rectangles and the solid must be a column. The feature view is a circle. So the solid is a cylinder and its axis is perpendicular to the W – projection plane. 

       图 4-3(b)所示三视图，俯视图和左视图都是梯形，主视图是特征图为上半圆，可知该形体是轴线垂直 V 投影面的上半圆台。

       Figure 4-3 (b) shows the front and left views are both trapezoids, and its feature view is a semi- circle, so the solid is a frustum of cone and its axis is perpendicular to the V–projection plane.

       图 4-3(c)所示三视图是直径相等的三个圆形线框，但主视图、俯视图为半圆，是左半部，可知该形体是左半圆球。

       Figure 4-3 (c) shows the front and top views are both half circles and the left view is a circle,so the solid is a semi-sphere.

       基本体三视图的图形特征是今后画图和读图的依据之一，必须熟记。

       Feature characteristics of basic solids are not only the fundamental of drawing but also the basis of reading. One needs to keep them in mind during learning engineering drawing.