直线绕直线的旋转曲面怎么求，《机械制图》——立体投影（1）

今天我们学习《机械制图》——立体投影第一部分的内容。主要的学习内容是立体及其表面上的点与线。Today we are studying Mechanical Drawing - Stereographic Projection Part 1. The main topic of study is the stereoscope and the points and lines on its surface.

No.1 平面立体

一.平面立体

1.立体可分为两类：表面都是平面的平面立体和表面是曲面或曲面与平面的曲面立体。

2.平面立体的表面是若干个平面多边形，因此，绘制平面立体的投影，可归结为绘制它的所有平面多边形表面的投影，也就是绘制这些多边形的边和顶点的投影。常见的有棱柱和棱锥两种。

I. Planar stereo

1. Stereoscopic can be divided into two categories: flat stereoscopic whose surfaces are all flat and curved stereoscopic whose surfaces are curved or curved and flat.

2. The surface of a planar stereo is a number of planar polygons, so that the projection of a planar stereo can be reduced to the projection of the surface of all its planar polygons, that is, the projection of the sides and vertices of these polygons. Two common types are prisms and prismatic cones.

棱柱由两个形状、大小相同且平行的顶、底面和若干个矩形棱面围成。The prism is enclosed by two top and bottom faces of the same shape, size and parallel, and a number of rectangular prism faces.

棱锥是由一个多边形底面和若干个共顶点的三角形棱面所围成的。从棱锥顶点到底面的距离叫做棱锥的高。当棱锥底面为正多边形，各棱面是全等的等腰三角形时，称之为正棱锥。A prism is enclosed by a polygonal base and a number of triangular prism faces with a common vertex. The distance from the apex of the prism to the base is called the height of the prism. When the base of a prism is a regular polygon and the prism faces are congruent isosceles triangles, it is called a regular prism.

No.2曲面立体

1.回转面的形成

回转面可以看作是一任意动线（母线）绕一定直线（轴线）旋转一周后形成的曲面。如圆柱面，圆锥面，球面等。

2.常见回转体

常见的回转体有圆柱体，圆锥体和圆球体等。

对于回转体的回转面，若按某一投射方向看，有一部分可见，有一部分不可见，把其可见与不可见的分界线称为转向线。

1. The formation of a rotary surface

A rotary surface can be seen as an arbitrary line of motion (bus) around a certain line (axis) after a week of rotation to form the surface. Such as cylindrical surface, conical surface, spherical surface, etc.

2. Common rotating bodies

Common rotating bodies are cylinders, cones and spheres.

For the rotary surface of the body, if a certain projection direction, part of the visible, part of the invisible, the visible and invisible line of demarcation is called the steering line.

圆柱表面有圆柱面，顶面和底面。圆柱面由直线绕与它平行的轴线旋转而成。The cylindrical surface has a cylindrical face, a top face and a bottom face. The cylindrical surface is formed by rotating a straight line around an axis parallel to it.

圆锥的表面有圆锥面和底面。圆锥面由直线绕与它相交的轴线旋转而成。The surface of a cone has a conical face and a base. The conical surface is formed by rotating a straight line around an axis that intersects it.

球的表面是球面。球面由圆绕其直径为轴线旋转而成。The surface of a ball is a sphere. The spherical surface consists of a circle rotating around its diameter as its axis.

环的表面是环面。环面由圆绕圆平面上不与圆心共线且在圆外的直线为轴旋转而成。The surface of a ring is the ring surface. The ring surface consists of a circle rotating on its axis around a line in the circular plane that is not co-linear with the centre of the circle and is outside the circle.

参考资料：文字：百度；图片：微博；翻译：百度翻译

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