Intersection of plane surfaces and curved solids 平面与曲面立体相交平面与曲面立体相交Exercises 练习题练习题Characteristics of intersection lines截交线的特性截交线的特性请点击相应标题显示其内容请点击相应标题显示其内容The method of finding intersections 求截交线的方法求截交线的方法 Procedure of drawing intersections 求截交线的步骤求截交线的步骤21. Characteristics of intersection lines截交线的特性截交线的特性Cutting plane 截平面截平面Intersection line 截交线截交线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Intersection of plane surfaces and curved solids 平面与曲面立体相交平面与曲面立体相交 Every point on the segments of an intersection line is common Every point on the segments of an intersection line is common segments to both the intersecting plane and surfaces of the solid.segments to both the intersecting plane and surfaces of the solid.截交线是截平面与立体表面的共有点的连线截交线是截平面与立体表面的共有点的连线; ; Segments of the intersection line also form a closed plane area.Segments of the intersection line also form a closed plane area.截交线是一条封闭的平面图形。截交线是一条封闭的平面图形。3(3)Rectangle: Parallel cutting plane with respect to the axis.矩形矩形 截平面截平面P P平行于轴线。平行于轴线。(2)Ellipse: Inclined cutting plane with respect to the axis.椭圆椭圆 截平面截平面P P倾斜于轴线；倾斜于轴线；(1)Circularity: Perpendicular cutting plane with respect to the axis. 圆形圆形 截平面截平面P P垂直垂直于轴线；于轴线； 1)1)Analyze right cylinder intersection 圆柱体截交线分析圆柱体截交线分析请请 点点 击击 鼠鼠 标标 左左 键键 显显 示示 后后 面面 内内 容容4IsocelesIsoceles triangle triangle: :Going through the apex point. Going through the apex point. 等腰三角形等腰三角形 P P通过锥尖通过锥尖。 ParabolaParabola: :Parallel with one element line. Parallel with one element line.抛物线抛物线 P P平行于一条轮廓素线；平行于一条轮廓素线；HyperbolaHyperbola: :Parallel with the axis lines.Parallel with the axis lines.双曲线双曲线 P P平行于轴线；平行于轴线； EllipseEllipse: : Inclined cutting plane with respect to the axis.Inclined cutting plane with respect to the axis.椭圆椭圆 P P倾斜于轴线；倾斜于轴线； Circularity:Circularity: Perpendicular cutting plane.Perpendicular cutting plane. 圆形圆形 P P垂直垂直于轴线；于轴线；2)2)Analyze cone intersection 圆锥体截交线分析圆锥体截交线分析Intersection 截交线形状截交线形状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5 EllipseEllipse: : Inclined cutting plane with respect to the axis.Inclined cutting plane with respect to the axis.椭圆椭圆椭圆椭圆 P P 倾倾倾倾斜于斜于轴线轴线轴线轴线 。 Circularity:Circularity: Perpendicular cutting plane.Perpendicular cutting plane.圆圆圆圆 P P 平行平行或垂直于轴线。或垂直于轴线。 IntersectionIntersection ： 截交线形状截交线形状3)3)Analyze spheresphere intersection 圆球体截交线分析圆球体截交线分析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6(1)(1)Using the accumulation method. 积积积积聚性法聚性法利用有利用有积积积积聚性的投影求截交聚性的投影求截交线线线线( (适合适合圆圆圆圆柱柱) ); ; 2.2.The method of finding intersections. 求截交线的方法求截交线的方法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Intersection of plane surfaces and curved solids 平面与曲面立体相交平面与曲面立体相交(2)(2)Using the element method. 辅辅辅辅助素助素线线线线法法利用立体表面的素利用立体表面的素线线线线求截交求截交线线线线( (适合适合圆锥圆锥圆锥圆锥 );); (3)(3)Using the circle method. 辅辅辅辅助助纬圆纬圆纬圆纬圆 法法利用所作的利用所作的辅辅辅辅助助纬圆纬圆纬圆纬圆 求截交求截交线线线线( (适合适合锥锥锥锥、球、球) )。 7请请 点点 击击 鼠鼠 标标 左左 键键 显显 示示 后后 面面 内内 容容Example1. Draw Example1. Draw V V，H H views of the cutting views of the cutting right cylinderright cylinder. .求圆柱体被截切后的求圆柱体被截切后的H H、WW面投影面投影。 Example2. Draw Example2. Draw V V，H H views of the cutting views of the cutting right cylinderright cylinder. .求圆柱筒被截切后的求圆柱筒被截切后的H H 、WW面投影面投影。Example3. Draw Example3. Draw V V，H H views of the cutting views of the cutting conecone. . 求圆锥体被截切后的求圆锥体被截切后的H H、WW面投影面投影。Example4. Example4. Draw V，H views of the cutting half spheresphere。求半圆球体被截切后的求半圆球体被截切后的H H、WW面投影面投影。Intersection of plane surfaces and curved solids 平面与曲面立体相交平面与曲面立体相交(1) Analyze. 根据立体与截平面的位置分析截交线的形状；根据立体与截平面的位置分析截交线的形状；3.3.Procedure of drawing intersections 求截交线一般步骤求截交线一般步骤(2) Draw special points. 求截交线上特殊位置各点（顶、拐点）的投影；求截交线上特殊位置各点（顶、拐点）的投影； (3) Distinguish its visibility. 判别可见性后，按顺序连接各点的投影；判别可见性后，按顺序连接各点的投影； (4) Complete the projection. 根据立体和截交线的二投影求出第三投影；根据立体和截交线的二投影求出第三投影；(5)Erase redundant lines and draw deeply. 擦去被截掉部分擦去被截掉部分, ,加深图线。加深图线。82. Draw V, H views of the cutting cone.求圆锥被截切后的求圆锥被截切后的V V、H H 投影。投影。 Exercises 练习题练习题请点击题目显示其内容请点击题目显示其内容1. Which one is correctly drawn of the left view指出哪个左视图是正确的。指出哪个左视图是正确的。本 小 节 结 束谢谢您的认真学习！谢谢您的认真学习！退出退出前一页前一页10CorrectCorrectCorrectCorrect请点击解答显示其内容请点击解答显示其内容1. Which one is correctly drawn of the left view. 指出哪个左视图是正确的。指出哪个左视图是正确的。11请点击解答显示其内容请点击解答显示其内容2.Draw V, H views of the cutting cone.求圆锥被截切后的求圆锥被截切后的V V、H H面投影。面投影。12(2)(2) Analyze.Analyze.分析各截交线形状分析各截交线形状: :1. Draw V, H views of the cutting right cylinder.求圆柱体被截切后的求圆柱体被截切后的H H、WW面投影。面投影。(1)(1) Draw uncut of Draw uncut of V, HV, H. .先求出圆柱先求出圆柱未截切未截切时的时的V V、H H 投影投影。(3)(3) Draw special points.Draw special points.利用利用圆柱圆柱积聚性投影积聚性投影, ,求截求截 交线上交线上特殊位置点特殊位置点的投影。的投影。(4) (4) Draw all views of points.Draw all views of points.求各截交线上求各截交线上特殊位置点特殊位置点的的 第三投影第三投影。 (5) (5) Complete the projection.Complete the projection. 判别判别可见性后可见性后, ,根据截交线的根据截交线的 形状形状, ,依次连接各点的投影依次连接各点的投影。倾斜倾斜于轴线切于轴线切椭圆椭圆/ / 于轴线切于轴线切 矩形矩形