今天我们学习《机械制图》——点，直线，平面的投影第三部分的内容。今天的主要内容是平面的投影。Today we are studying Mechanical Drawing - Projection of Points, Lines and Planes Part 3. Today's main topic is the projection of planes.
No.1 平面的表示法
No.2 平面对投影面的各种相对位置
（1）一般位置平面的投影特性：它的三个投影都是平面图形，而且是面积缩小的类似形。倾斜于投影面的平面图形在该投影面上的正投影必定是这个平面图形的类似形，这样的投影特性通常称为类似性。
（2）投影面垂直面的投影特性：
A.在垂直的投影面上的投影，积聚成直线；它与投影轴的夹角，分别反映平面对另两投影的真实倾角。
B.在另两投影面上的投影为面积缩小的类似性。
（3）投影面平行面
A.在平面的投影面上的投影，反映真形。
B.在另两投影面上的投影，分别积聚成直线，平行于相应的投影轴。
(1) The projective property of the plane of general position: all three of its projections are planar figures and are similar shapes of reduced area. The orthographic projection of a plane figure inclined to the projection plane must be an analogue of this plane figure; such a projective property is usually called similarity.
(2) The projective properties of a perpendicular plane of projection.
A. The projection on the perpendicular projection plane, accumulating into a straight line; its angle with the projection axis, respectively, reflects the true inclination of the plane to the other two projections.
B. The projection on the other two projection planes as an analogy of area reduction.
(3) Projection plane parallel to plane
A. Projection on the projection plane of the plane reflecting the true form.
B. Projection on the other two projection planes that accumulate into straight lines, respectively, parallel to the corresponding projection axes.
No.3 平面的迹线表示法
（1）平面主要用几何元素表示，也可以用迹线表示。
（2）迹线是平面与投影面的交线。用迹线表示的平面称为迹线平面。平面与V面，H面，W面的交线，分别称为正面迹线，水平迹线，侧面迹线。
（3）迹线的符号用平面名称的大写字母附加投影面名称的注脚表示。
（4）投影特性：在垂直的投影面上的迹线与这个平面在该投影面上的有积聚性的投影相重合。它与投影轴的夹角，分别反映平面对另两投影面的真实倾角；在另两投影面上的迹线，分别垂直于相应的投影轴。
(1) The plane is mainly represented by geometric elements, but can also be represented by traces.
(2) The trace is the line of intersection between the plane and the projection plane. A plane represented by a trace is called a trace plane. The intersection of the plane with the V, H and W planes is called the frontal trace, the horizontal trace and the lateral trace respectively.
(3) The sign of the trace plane is indicated by a footnote with the name of the plane in capital letters attached to the name of the projection plane.
(4) Projection characteristics: a trace on a vertical projection plane coincides with the projection of this plane on that projection plane with accumulation. Its angle with the projection axis reflects the true inclination of the plane to the other two projection planes, respectively; the trace on the other two projection planes is perpendicular to the corresponding projection axis, respectively.
No.4 平面上的点和线
（1）点在平面上，则该点必定在这个平面的一条直线上
（2）直线在平面上，则该直线必定通过这个平面上的两个点；或者通过这个平面上的一个点，且平行于这个平面上的另一条直线。
(1) If a point is in the plane, the point must be on a line in the plane
(2) A line is in a plane, then the line must pass through two points in that plane; or through a point in that plane and parallel to another line in that plane.
参考资料：文字：百度；图片：微博；翻译：百度翻译
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