Projection of Polyhedral Solids 平面立体的投影 Summary of Polyhedral Solids 平面立体慨述 Prism 棱柱 Pyramid 棱锥 Exercise 练习题 请点击相应标题显示其内容 总目录
Summary of Polyhedral Solids 平面立体概述 Prism 棱柱 Pyramid 棱锥 Exercise 练习题 Projection of Polyhedral Solids 平面立体的投影 请点击相应标题显示其内容
Summary of Polyhedral Solids平面立体概述 Polyhedral solids:The solids that are surrounded by planes are called polyhedral solids. 平面立体： 完全由平面围成的立体称为平面立体。 Prisms Polyhedral solids 棱柱 平面立体 Pyramids 棱锥 Intersection lines of edge planes are called edge lines.Intersection lines of edge planes and bases are called base edge lines.When drawing projections of polyhedral solids,we are actually drawing the projections of all edge lines and base edge lines followed by a visibility test of the projected edge lines and base edge lines. 各棱面的交线称为棱线，棱面与底面的交线称为底边画平面立 体的按影瘤，实质是画出所有棱线和底边的投影，并判别其可见性。 请点击鼠标左键显示后面内容
2 Summary of Polyhedral Solids 平面立体概述 Prisms 棱柱 Intersection lines of edge planes are called edge lines. Intersection lines of edge planes and bases are called base edge lines. When drawing projections of polyhedral solids, we are actually drawing the projections of all edge lines and base edge lines followed by a visibility test of the projected edge lines and base edge lines. 各棱面的交线称为棱线,棱面与底面的交线称为底边,画平面立 体的投影图,实质是画出所有棱线和底边的投影,并判别其可见性。 Pyramids 棱锥 Polyhedral solids 平面立体 请点击鼠标左键显示后面内容 Polyhedral solids: The solids that are surrounded by planes are called polyhedral solids. 平面立体: 完全由平面围成的立体称为平面立体
Prism 棱柱 1.Projection of a prism 棱柱的投影 Class by the bases of prisms 根据棱柱底面形状可分为： Triangular prism Square prism Pentagonal prism Hexagonal prism 三棱柱 四棱柱 五棱柱 六棱柱 Draw steps Draw centerlines and datum lines. 画图步骤： 先画中心线和基准线： Add lines for the upper and lower (end)faces. 再画反映顶部或底部（端面）形状的视图； Complete three views. 按三等规律画全三视图。 五棱柱的投影演示 请点击鼠标左键显示后面内空
3 Class by the bases of prisms 根据棱柱底面形状可分为: Triangular prism 三棱柱 Prism 棱柱 Square prism 四棱柱 Pentagonal prism 五棱柱 Hexagonal prism 六棱柱 Draw steps 画图步骤： Draw centerlines and datum lines. 先画中心线和基准线; Add lines for the upper and lower (end) faces. 再画反映顶部或底部(端面)形状的视图; Complete three views. 按三等规律画全三视图。 请点击鼠标左键显示后面内容 五棱柱的投影演示 1. Projection of a prism 棱柱的投影
Prism 棱柱 2.Getting points on the surface of a prism棱柱表面上取点 Method Getting points on surfaces of a prism can be based on the accumulation 方法： characteristics of edge lines or plane projection. 棱柱表面上的点可利角棱线或棱面的积聚性投影求之。 The projection of point is also visible when it is on visible edge or plane. ldentification 凡在可见表面及棱线上的点，其投影为可见： 判别： The projection of point is not visible when it is on invisible edge or plane. 凡在不可见表面及棱线上的点，其投影则为不可见。 Labeling All invisible points are written in brackets. 击 标注 对不可见的点加括号以示区别。 Example1.Draw the triangular prism and get points on the surface. 标左 画三棱柱及表面上各点的三视图。 显 Example2.Draw the square prism and get points on the surface. 示 画四棱柱及表面上各点的三视图。 面 Example3.Draw the pentagonal prism and get points on the surface. 画五棱柱及表面上各点的三视图
4 Example3. Draw the pentagonal prism and get points on the surface. 画五棱柱及表面上各点的三视图。 The projection of point is not visible when it is on invisible edge or plane. 凡在不可见表面及棱线上的点,其投影则为不可见。 Identification 判别: The projection of point is also visible when it is on visible edge or plane. 凡在可见表面及棱线上的点,其投影为可见; Method 方法: Getting points on surfaces of a prism can be based on the accumulation characteristics of edge lines or plane projection. 棱柱表面上的点可利用棱线或棱面的积聚性投影求之。 2.Getting points on the surface of a prism 棱柱表面上取点 Labeling 标注: All invisible points are written in brackets. 对不可见的点加括号以示区别。 请 点 击 鼠 标 左 键 显 示 后 面 内 容 Example1. Draw the triangular prism and get points on the surface. 画三棱柱及表面上各点的三视图。 Example2. Draw the square prism and get points on the surface. 画四棱柱及表面上各点的三视图。 Prism 棱柱
Pyramid 棱锥 1.Projection of pyramid 棱锥的投影 Class by the bases of a pyramid根据棱锥底面形状可分为： Triangular pyramid Square pyramid Pentagonal pyramid 】Hexagonal pyramid 三棱锥 四棱锥 五棱锥 六棱锥 Draw steps画图步骤： 1.Draw symmetry lines and the base of the pyramid. 先画锥底面形状的投影； 2.Add the vertex of the pyramid. 再画锥顶点的投影； 3.Complete three views after adding lines for the side faces.最后画各棱线的投影。 请点击鼠标左键显示后面内容
5 Class by the bases of a pyramid 根据棱锥底面形状可分为: Triangular pyramid 三棱锥 1. Projection of pyramid 棱锥的投影 Square pyramid 四棱锥 Pentagonal pyramid 五棱锥 Hexagonal pyramid 六棱锥 Draw steps画图步骤： 1.Draw symmetry lines and the base of the pyramid. 先画锥底面形状的投影; 2.Add the vertex of the pyramid. 再画锥顶点的投影; 3.Complete three views after adding lines for the side faces. 最后画各棱线的投影。 请点击鼠标左键显示后面内容 Pyramid 棱锥
Pyramid 棱锥 2.Getting points on the surface of a pyramid棱锥表面取点 Method Draw an auxiliary line or plane going through the point on the pyramid. 方法： 在棱面上过锥顶作一条包含该点的辅助线或辅助平面。 The projection of pointis also visible when it on visible edge or plane. Distinguish 凡在可见表面及棱线上的点，其投影为可见； 判别 The projection of point is not visible when it on invisible edge or plane. 凡在不可见表面及棱线上的点，其投影则为不可见。 Labeling All invisible points are written in brackets. 标注： 对不可见的点加括号以示区别。 Example4.Draw a regular triangular pyramid and get points on the surface.画正三棱维及表面上各点的三视图。 Example5.Draw a regular pentagonal pyramid and get points on the surface.画正五棱锥及表面上各点的三视图。 请点击鼠标左键显示后面内空
6 2.Getting points on the surface of a pyramid 棱锥表面取点 A K C B P E F Draw an auxiliary line or plane going through the point on the pyramid. 在棱面上过锥顶作一条包含该点的辅助线或辅助平面。 Distinguish 判别: Labeling 标注: All invisible points are written in brackets. 对不可见的点加括号以示区别。 请点击鼠标左键显示后面内容 Example4. Draw a regular triangular pyramid and get points on the surface. 画正三棱锥及表面上各点的三视图。 Example5. Draw a regular pentagonal pyramid and get points on the surface. 画正五棱锥及表面上各点的三视图。 Pyramid 棱锥 The projection of point is also visible when it on visible edge or plane. 凡在可见表面及棱线上的点,其投影为可见； The projection of point is not visible when it on invisible edge or plane. 凡在不可见表面及棱线上的点,其投影则为不可见。 Method 方法:
Exercise. Complete each drawing by adding the missing detail. 补全平面立体及其表面上各点的三投影。 (1)Draw a prism and get points on the surface(2)Draw a pyramid and get points on the surface. 画三棱柱及各点的三投影。 画五棱锥及各点的三投影。 Q (b) b" C 解答 解答 请点击解答显示其内容
7 a" Exercise. Complete each drawing by adding the missing detail. 补全平面立体及其表面上各点的三投影。 （1）Draw a prism and get points on the surface. 画三棱柱及各点的三投影。 c' a' (b') a a" b (c") c b" （2）Draw a pyramid and get points on the surface. 画五棱锥及各点的三投影。 a b c a' b' c" 请点击解答显示其内容 (c') (b")
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Example1.Draw the triangular prism and get points on the surface 画三棱柱及表面上各点的三视图。 动画 Steps作图步骤： Draw view of the end faces. 先画反映端面形状的视图； Complete three views. 再按三等规律画全三视图； Draw all views of points. 6 求各点的三投影。 a 请点击鼠标左键显示后面内容 返回
9 A B Example1. Draw the triangular prism and get points on the surface. 画三棱柱及表面上各点的三视图。 (b) a S Draw view of the end faces. 先画反映端面形状的视图; Complete three views. 再按三等规律画全三视图; Draw all views of points. 求各点的三投影。 请点击鼠标左键显示后面内容 Steps作图步骤： a" a' (b' ) b
Example2.Draw the square prism and get points on the surface 画四棱柱及表面上各点的三视图。 Steps作图步骤： Draw view of the end faces 先画反映端面形状的视图； Complete three views. 再按三等规律画全三视图； Draw all views of points. 求各点的三投影。 请点击鼠标左键显示后面内容返回
10 d" c d C D S Example2. Draw the square prism and get points on the surface. 画四棱柱及表面上各点的三视图。 请点击鼠标左键显示后面内容 Draw view of the end faces. 先画反映端面形状的视图; Complete three views. 再按三等规律画全三视图; Draw all views of points. 求各点的三投影。 Steps 作图步骤： c" d' （c")