平面立体的投影.pptx

平面立体的投影平面立体的投影 Summary of Polyhedral Solids 平面立体概述平面立体概述Prisms 棱柱棱柱棱柱棱柱 Intersection lines of edge planes are called edge lines.Intersection Intersection lines of edge planes are called edge lines.Intersection lines of edge planes and bases are called base edge lines.When lines of edge planes and bases are called base edge lines.When drawing projections of polyhedral solids,we are actually drawing drawing projections of polyhedral solids,we are actually drawing the projections of all edge lines and base edge lines followed the projections of all edge lines and base edge lines followed by a visibility test of the projected edge lines and base edge lines.by a visibility test of the projected edge lines and base edge lines.各棱面的交线称为棱线各棱面的交线称为棱线各棱面的交线称为棱线各棱面的交线称为棱线,棱面与底面的交线称为底边棱面与底面的交线称为底边棱面与底面的交线称为底边棱面与底面的交线称为底边,画平面立画平面立画平面立画平面立体的投影图体的投影图体的投影图体的投影图,实质是画出所有棱线和底边的投影实质是画出所有棱线和底边的投影实质是画出所有棱线和底边的投影实质是画出所有棱线和底边的投影,并判别其可见性并判别其可见性并判别其可见性并判别其可见性。Pyramids棱锥棱锥棱锥棱锥 Polyhedral solids 平面立体平面立体平面立体平面立体请点击鼠标左键显示后面内容请点击鼠标左键显示后面内容请点击鼠标左键显示后面内容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.平面立体平面立体平面立体平面立体:完全由平面围成的立体称为平面立体。完全由平面围成的立体称为平面立体。完全由平面围成的立体称为平面立体。完全由平面围成的立体称为平面立体。第1页/共17页 Class by the Class by the bases of bases of prismsprisms 根据棱柱底面形状可分为根据棱柱底面形状可分为:Triangular Triangular prismprism三棱柱三棱柱三棱柱三棱柱 Prism 棱柱Square prismSquare prism四棱柱四棱柱四棱柱四棱柱PentagonalPentagonal prism prism 五棱柱五棱柱五棱柱五棱柱HexagonalHexagonal prismprism六棱柱六棱柱六棱柱六棱柱Draw stepsDraw steps画图步骤画图步骤：Draw centerlines and Draw centerlines and datum datum lines.lines.先画中心线和基准线先画中心线和基准线先画中心线和基准线先画中心线和基准线;Add lines for the upper and lower(end)faces.Add lines for the upper and lower(end)faces.再画反映顶部或底部再画反映顶部或底部再画反映顶部或底部再画反映顶部或底部(端面端面端面端面)形状的视图形状的视图形状的视图形状的视图;Complete three views.Complete three views.按三等规律画全三视图。按三等规律画全三视图。按三等规律画全三视图。按三等规律画全三视图。请点击鼠标左键显示后面内容请点击鼠标左键显示后面内容请点击鼠标左键显示后面内容请点击鼠标左键显示后面内容五棱柱的投影演示五棱柱的投影演示1.Projection of a prism1.Projection of a prism 棱柱的投影棱柱的投影棱柱的投影棱柱的投影第2页/共17页 Example3.Draw the pentagonal prism and get points on the surface.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画五棱柱及表面上各点的三视图画五棱柱及表面上各点的三视图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.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凡在不可见表面及棱线上的点凡在不可见表面及棱线上的点凡在不可见表面及棱线上的点,其投影则为不可见。其投影则为不可见。其投影则为不可见。其投影则为不可见。IdentificationIdentification 判别判别判别判别:The projection of point is also visible when it is on visible edge or plane.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凡在可见表面及棱线上的点凡在可见表面及棱线上的点凡在可见表面及棱线上的点,其投影为可见其投影为可见其投影为可见其投影为可见;MethodMethod 方法方法方法方法:Getting points on surfaces of a prism can be based on the accumulation Getting points on surfaces of a prism can be based on the accumulation characteristics of edge lines or plane projection.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棱柱表面上的点可利用棱线或棱面的积聚性投影棱柱表面上的点可利用棱线或棱面的积聚性投影棱柱表面上的点可利用棱线或棱面的积聚性投影求之。求之。求之。求之。2.2.2.2.Getting points on the surface of a prismGetting points on the surface of a prism 棱柱表面上取点棱柱表面上取点棱柱表面上取点棱柱表面上取点 Labeling Labeling 标注标注标注标注:All invisible points are written in brackets.All invisible points are written in brackets.对不可见的点加括号以示区别。对不可见的点加括号以示区别。对不可见的点加括号以示区别。对不可见的点加括号以示区别。请请请请点点点点击击击击鼠鼠鼠鼠标标标标左左左左键键键键显显显显示示示示后后后后面面面面内内内内容容容容 Example1.Draw the triangular prism and get points on the surface.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画三棱柱及表面上各点的三视图画三棱柱及表面上各点的三视图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.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画四棱柱及表面上各点的三视图画四棱柱及表面上各点的三视图画四棱柱及表面上各点的三视图。Prism 棱柱第3页/共17页Class by the Class by the bases of a pyramid bases of a pyramid 根据棱锥底面形状可分为根据棱锥底面形状可分为:TriangularTriangular pyramidpyramid 三棱锥三棱锥三棱锥三棱锥1.1.Projection of pyramid Projection of pyramid 棱锥棱锥棱锥棱锥的投影的投影的投影的投影SquareSquare pyramidpyramid 四棱锥四棱锥四棱锥四棱锥Pentagonal Pentagonal pyramidpyramid五棱锥五棱锥五棱锥五棱锥Hexagonal pyramidHexagonal pyramid六棱锥六棱锥六棱锥六棱锥Draw stepsDraw steps画图步骤画图步骤画图步骤画图步骤：1.Draw symmetry lines and the base of the pyramid.1.Draw symmetry lines and the base of the pyramid.先画锥底面形状的投先画锥底面形状的投影影;2.Add the vertex of the pyramid.2.Add the vertex of the pyramid.再画锥顶点的投影再画锥顶点的投影;3.Complete three views after3.Complete three views after adding lines for the side faces.adding lines for the side faces.最后画各棱线的投影最后画各棱线的投影。请点击鼠标左键显示后面内容请点击鼠标左键显示后面内容请点击鼠标左键显示后面内容请点击鼠标左键显示后面内容 Pyramid 棱锥第4页/共17页2.2.2.2.Getting points on the surface of a pyramid Getting points on the surface of a pyramid 棱锥表面取点棱锥表面取点棱锥表面取点棱锥表面取点A AK KEFDraw an auxiliary line Draw an auxiliary line or planeor plane going through the point on the pyramid.going through the point on the pyramid.在棱面上过锥顶作一条包含该点在棱面上过锥顶作一条包含该点在棱面上过锥顶作一条包含该点在棱面上过锥顶作一条包含该点的辅助线或的辅助线或的辅助线或的辅助线或辅助平面辅助平面辅助平面辅助平面。Distinguish Distinguish 判别判别判别判别:Labeling Labeling 标注标注标注标注:All invisible points are written in brackets.All invisible points are written in brackets.对不可见的点加括号以示区别。对不可见的点加括号以示区别。对不可见的点加括号以示区别。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请点击鼠标左键显示后面内容请点击鼠标左键显示后面内容请点击鼠标左键显示后面内容Example4.Draw a regular triangular pyramid and get points on the Example4.Draw a regular triangular pyramid and get points on the surface.surface.画正三棱锥及表面上各点的三视图画正三棱锥及表面上各点的三视图画正三棱锥及表面上各点的三视图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 Example5.Draw a regular pentagonal pyramid and get points on the surface surface.画正五棱锥及表面上各点的三视图画正五棱锥及表面上各点的三视图画正五棱锥及表面上各点的三视图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.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凡在可见表面及棱线上的点凡在可见表面及棱线上的点凡在可见表面及棱线上的点,其投影为可见；其投影为可见；其投影为可见；其投影为可见；The projection of point is not visible when it on invisible edge or plane.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凡在不可见表面及棱线上的点凡在不可见表面及棱线上的点凡在不可见表面及棱线上的点,其投影则为不可见。其投影则为不可见。其投影则为不可见。其投影则为不可见。MethodMethod 方法方法方法方法:第5页/共17页aExercise.Complete each drawing by adding the missing detail.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。补全平面立体及其表面上各点的三投影。补全平面立体及其表面上各点的三投影。补全平面立体及其表面上各点的三投影。（1 1）Draw a prism and get points on the surface.Draw a prism and get points on the surface.画三棱柱及各点的三投影。画三棱柱及各点的三投影。画三棱柱及各点的三投影。画三棱柱及各点的三投影。ca(b)aab(c)cb （2 2）Draw a pyramid and get points on the surface.Draw a pyramid and get points on the surface.画五棱锥及各点的三投影。画五棱锥及各点的三投影。画五棱锥及各点的三投影。画五棱锥及各点的三投影。abcabc请点击解答显示其内容请点击解答显示其内容请点击解答显示其内容请点击解答显示其内容(c)(b)第6页/共17页 本 小 节 结 束谢谢您的认真学习！谢谢您的认真学习！退出退出退出退出前一页前一页前一页前一页第7页/共17页 Example1Example1.Draw the triangular prism and get points on the surface.Draw the triangular prism and get points on the surface.画三棱柱及表面上各点的三视图。画三棱柱及表面上各点的三视图。画三棱柱及表面上各点的三视图。画三棱柱及表面上各点的三视图。Draw view of the end faces.Draw view of the end faces.先画反映端面形状的视图先画反映端面形状的视图;Complete three views.Complete three views.再按三等规律画全三视图再按三等规律画全三视图;Draw all views of points.Draw all views of points.求各点的三投影求各点的三投影。请点击鼠标左键显示后面内容请点击鼠标左键显示后面内容请点击鼠标左键显示后面内容请点击鼠标左键显示后面内容Steps作图步骤：作图步骤：aa(b)b第8页/共17页d Example2.Draw the square prism and get points on the surface.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。画四棱柱及表面上各点的三视图。画四棱柱及表面上各点的三视图。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请点击鼠标左键显示后面内容请点击鼠标左键显示后面内容请点击鼠标左键显示后面内容Draw view of the end faces.Draw view of the end faces.先画反映端面形状的视图先画反映端面形状的视图;Complete three views.Complete three views.再按三等规律画全三视图再按三等规律画全三视图;Draw all views of points.Draw all views of points.求各点的三投影求各点的三投影。Steps 作图步骤作图步骤：cd（c)第9页/共17页Example3.Draw the pentagonal prism and get points on the surface.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。画五棱柱及表面上各点的三视图。画五棱柱及表面上各点的三视图。画五棱柱及表面上各点的三视图。Steps作图步骤作图步骤：（1 1）DrawDraw thethe accumulation top view.accumulation top view.先画有积聚性的俯视图先画有积聚性的俯视图;（2 2）DrawDraw thethe limit elements.limit elements.再画主视图各棱线的投影再画主视图各棱线的投影;（3 3）Draw all views of prism.Draw all views of prism.根据投影规律求第三投影根据投影规律求第三投影;（4 4）Draw all views of points.Draw all views of points.求各点的三投影求各点的三投影。请点击鼠标左键显示后面内容请点击鼠标左键显示后面内容请点击鼠标左键显示后面内容请点击鼠标左键显示后面内容ee（f)f fe第10页/共17页a b cSteps 作图步骤：Example4.Draw a regular triangular pyramid and get points on the Example4.Draw a regular triangular pyramid and get points on the surface.surface.画正三棱锥及表面上各点的三视图。画正三棱锥及表面上各点的三视图。画正三棱锥及表面上各点的三视图。画正三棱锥及表面上各点的三视图。（1 1）DrawDraw thethe top view.top view.先画俯视图先画俯视图;（2 2）DrawDraw thethe limit elements.limit elements.再画主视图各棱线的投影再画主视图各棱线的投影;（3 3）Draw all views of Draw all views of pyramid pyramid.根据投影规律求第三投影根据投影规律求第三投影;（4 4）Draw all views of point Draw all views of point D D.用辅助素线法求用辅助素线法求D D点的三投影点的三投影;（5 5）Draw all views of point Draw all views of point E E.用辅助平面法求用辅助平面法求E E点的三投影。点的三投影。请点击鼠标左键显示后面内请点击鼠标左键显示后面内请点击鼠标左键显示后面内请点击鼠标左键显示后面内容容容容 a(c)bd（d)eeedkk pp第11页/共17页 Example5.Draw a regular pentagonal pyramid and get points on Example5.Draw a regular pentagonal pyramid and get points on the surface.the surface.画正五棱锥及表面上各点的三视图。画正五棱锥及表面上各点的三视图。画正五棱锥及表面上各点的三视图。画正五棱锥及表面上各点的三视图。Steps 作图步骤作图步骤：1 1）DrawDraw the topthe top view.view.先画俯视图先画俯视图;2 2）DrawDraw thethe limit elements.limit elements.再画主视图各棱线的投影。再画主视图各棱线的投影。3 3）Draw all views of Draw all views of pyramid.pyramid.根据投影规律求第三投影根据投影规律求第三投影;4 4）Draw all views of point Draw all views of point G G.求求G G点的三投影点的三投影(用棱线法用棱线法)。5 5）Draw all views of point Draw all views of point F.F.求求F F点的三投影点的三投影(用辅助平面法用辅助平面法)。请请请请点点点点击击击击鼠鼠鼠鼠标标标标左左左左键键键键显显显显示示示示后后后后面面面面内内内内容容容容gg（f)f gb (a)c (e)d a(e)b(d)c kk pp第12页/共17页第13页/共17页在图片上点击鼠标左键可以在图片上点击鼠标左键可以在图片上点击鼠标左键可以在图片上点击鼠标左键可以“暂停暂停暂停暂停”或再次或再次或再次或再次“播放播放播放播放”第14页/共17页在图片上点击鼠标左键可以在图片上点击鼠标左键可以在图片上点击鼠标左键可以在图片上点击鼠标左键可以“暂停暂停暂停暂停”或再次或再次或再次或再次“播放播放播放播放”第15页/共17页在图片上点击鼠标左键可以在图片上点击鼠标左键可以在图片上点击鼠标左键可以在图片上点击鼠标左键可以“暂停暂停暂停暂停”或再次或再次或再次或再次“播放播放播放播放”第16页/共17页