立体上点的投影优秀文档.ppt

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1、Projection of a point Projection of a point 点的投影点的投影 Relative position of two points onRelative position of two points on a solida solid立体上二点的相对位置立体上二点的相对位置Identification and labeling of coincident point Identification and labeling of coincident point 重影点的判别与标注重影点的判别与标注 Exercises Exercises 练习题练习题 Pr

2、ojection of Points for a Solid 立体上点的投影请点击相应标题显示其内容请点击相应标题显示其内容请点击相应标题显示其内容请点击相应标题显示其内容2O Projection of a point 点的投影1.1.Projection of the point Projection of the point A A 空间空间 A A A A 点的投影点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a a The horizontal projection of the point The horizonta

3、l projection of the point A A 点点A A在在水水平面平面平面平面 HH上的投影；上的投影；上的投影；上的投影；a a The frontal projection of the pointThe frontal projection of the point A A 点点A A在正平面在正平面 V V上的投影；上的投影；a a The profile projection of the pointThe profile projection of the point A A 点点A A在侧平面在侧平面 WW上的投影。上的投影。a a a3（2）According

4、to coordinate of point A,construct projection a,a;Draw projection of point D投影在W面上重合时，左遮右(X坐标大的可见)。aa OY The width equality,Y equal.Draw projection of point A已知C 点距W 面5mm、距V 面10mm、距H 面10mm,D点距W 面15mm、距V 面10mm、距H 面5mm，求C、D 二点的三面投影,并判别其可见性。points will be the same point and the two points areDraw proje

5、ction of point B求C点投影Relative positions of point A B (A与B两点的相对位置)Draw projection of point ASteps 作图步骤：A(20、15、10)；Z=a ax=a a aYw The distance of A to H.(A点到水平面H的距离)a a a a OZOZ The The height alignmentheight alignment,Z Z equal.equal.即即高平齐高平齐,Z Z相等相等XYYZ 2.2.The The principleprinciple of points of p

6、oints 点的投影规律点的投影规律 3.3.Relation of points projection Relation of points projection&coordinatecoordinate 点的坐标与投影的关系点的坐标与投影的关系 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 Projection of a point 点的投影aaaa OXOX The The length alignmentlength alignment,X X equal.equal.即即长对正长对正,X X相等相等aaaa OYOY The

7、 The width equality width equality,Y Y equal.equal.即即宽相等宽相等,Y Y相等相等 X=a az=aaYH The distance of A to W.(A点到侧平面W的距离)Y=aax =a a az The distance of A to V.(A点到正平面V的距离)a a a aa a axaZ ZaYH aY YW 4a aa aa aStepsSteps 作图步骤作图步骤：（1）Drawing coordinate origin and axis.画出坐标原点及各轴;（2）According to coordinate of p

8、oint A,construct projection a a,a a;根据A点的坐标求其V、H面的投影 a a,a a;（3）According to rules projections of point,draw projection a a.根据点的投影规律求出第三投影 a a。Example1.The point Example1.The point A A (5 5,10,15,10,15).construct three projections of).construct three projections of A A.已知已知已知已知A A A A点的坐标为点的坐标为点的坐标为

9、点的坐标为(5 5 5 5，10101010，15151515),),),),求求求求A A A A点的三面投影。点的三面投影。点的三面投影。点的三面投影。A A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由于投影面的大小与视图由于投影面的大小与视图无关。因此无关。因此,在画三视图时在画三视图时,不必画出投影面的边框。不必画出投影面的边框。5 Relative position of two points Relative position of two points 二点的相对位置 Relative positions of poi

10、nt Relative positions of point A A B B (A A与与与与B B两点的相对位置两点的相对位置两点的相对位置两点的相对位置)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 Up and down Up and down Z Z上、下上、下 在在V、W面上看坐标差面上看坐标差 ZFront and back Front and back Y Y前、后前、后 在在H、W面上看坐标差面上看坐标差 Y Left and right Left and right X X左、右左、右 在在V、H面上看坐标差面上看坐

11、标差 Xaa abbAX X6请点击鼠标左键显示后面内容Draw projection of point A已知各点的坐标,画出点A、B、C、D的三面投影。Draw the third-view from its two other views shown.aa OY The width equality,Y equal.Projection of the point A 空间 A 点的投影Steps 作图步骤：Draw projection of point AIdentification and labeling of coincident pointExercises 练习题即高平齐,Z

12、相等Example2.投影在V面上重合时，前遮后(Y坐标大的可见)。到投影面的距离,画出点A、B、C、D 的三面投影。投影在W面上重合时，左遮右(X坐标大的可见)。Construct the three projections of points A,B,C,D.aaaStepsSteps 作图步骤：作图步骤：（2 2 2 2）Construct projection b b b b.根据点的投影规律求b b b b。Example2.Point Example2.Point B B below below A10A10,after,after A A5 5,left left A10A10.

13、construct projections of.construct projections of B B.已知点已知点已知点已知点B B B B在在在在A A A A下下下下10101010mmmmmmmm,A A A A后后后后5 5 5 5mmmmmmmm,A A A A左左左左10101010mmmmmmmm处处处处,求求求求B B B B点的三投影。点的三投影。点的三投影。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A AB B （1 1 1 1）Construct projection b b b b,b,b,

14、b,b.根据B的相对位置求投影b b b b,b b b b。b b 7IdentificationIdentification 判别判别When projected to the H-Plane,up covering down.投影在投影在投影在投影在H H H H面上重合时，面上重合时，面上重合时，面上重合时，上上上上遮下遮下遮下遮下(Z Z Z Z坐标坐标坐标坐标大大大大的的的的可见可见可见可见)。Identification and labeling of coincident point Identification and labeling of coincident point

15、 重影点的判别与标注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LabelingLabeling标注标注DefiningDefining定义定义 when two points on the solid are on the same vertical line of a projection plane,the two projected points will be the same point and the two points are called the coincident point of the projection

16、.当两点在某一投影面上的投影重合时称为该面的当两点在某一投影面上的投影重合时称为该面的当两点在某一投影面上的投影重合时称为该面的当两点在某一投影面上的投影重合时称为该面的重影点重影点重影点重影点。When projected to the V-Plane,front covering back.投影在投影在投影在投影在V V V V面上重合时，面上重合时，面上重合时，面上重合时，前遮后前遮后前遮后前遮后(Y Y Y Y坐标坐标坐标坐标大大大大的的的的可见可见可见可见)。When projected to the W-Plane,left covering right.投影在投影在投影在投影在W

17、 W W W面上重合时，面上重合时，面上重合时，面上重合时，左遮右左遮右左遮右左遮右(X X X X坐标坐标坐标坐标大大大大的的的的可见可见可见可见)。All invisible projections of points are written in brackets.将将将将点点点点在某投影面上在某投影面上在某投影面上在某投影面上的的的的不可见投影加括号不可见投影加括号不可见投影加括号不可见投影加括号标注标注标注标注以示区别。以示区别。以示区别。以示区别。8b A AB BSteps Steps 作图步骤作图步骤作图步骤作图步骤：2.Construct projections D D,d

18、d d d,d d d d ,d d d d ;求求D D D D点的三投影点的三投影d d d d、d d d d 、d d d d 。1.Construct projections C C,c c,c c,cc;求求C C C C点的三投影点的三投影 c c c c、c c c c 、c c c c。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C CD D(c)Example3.Point Example3.Point C C from from WW 5mm,from 5mm,from V V10mm,from10mm,from

19、H H10mm.point10mm.point D D from from WW1 15 5mmmm,from from V V 10mm,from 10mm,from H H 5mm.construct three projections of point and distinguish its visibility.5mm.construct three projections of point and distinguish its visibility.已知已知已知已知C C C C 点距点距点距点距W W W W 面面面面5 5 5 5mmmmmmmm、距、距、距、距V V V V

20、面面面面10101010mmmmmmmm、距、距、距、距H H H H 面面面面10101010mm,mm,mm,mm,D D D D点距点距点距点距W W W W 面面面面15151515mmmmmmmm、距、距、距、距V V V V 面面面面10101010mmmmmmmm、距、距、距、距H H H H 面面面面5 5 5 5mmmmmmmm，求求求求C C C C、D D D D 二点的三面投影二点的三面投影二点的三面投影二点的三面投影,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。a a b abc c d ()()d 91.Draw the third-view f

21、rom its two other views shownDraw the third-view from its two other views shown.已知各点的两个投影，求其第三投影已知各点的两个投影，求其第三投影已知各点的两个投影，求其第三投影已知各点的两个投影，求其第三投影。请点击题目显示其内容请点击题目显示其内容请点击题目显示其内容请点击题目显示其内容 Exercises 练习题2.2.Construct the three projections of points Construct the three projections of points A,B,C,DA,B,C,

22、D.from.from its coordinate and distance.its coordinate and distance.根据所给定点的坐标或点到投影面的距离根据所给定点的坐标或点到投影面的距离根据所给定点的坐标或点到投影面的距离根据所给定点的坐标或点到投影面的距离,画出点画出点画出点画出点A A A A、B B B B、C C C C、D D D D 的三面投影的三面投影的三面投影的三面投影。3.The point The point A A (3030,15,0,15,0).according to request draw the three .according to r

23、equest draw the three 4.projections of points projections of points A,B,CA,B,C.已知已知已知已知A A A A点的坐点的坐点的坐点的坐标标标标为为为为(30303030、15151515、0 0 0 0)，按要求画出点，按要求画出点，按要求画出点，按要求画出点 A A A A、B B B B、C C C C 的三的三的三的三面投影面投影面投影面投影。4.4.Draw three projections of points Draw three projections of points A,B,C,DA,B,C,D,

24、from its coordinate.,from its coordinate.已知各点的坐标已知各点的坐标已知各点的坐标已知各点的坐标,画出点画出点画出点画出点A A A A、B B B B、C C C C、D D D D的三面投影的三面投影的三面投影的三面投影。本 小 节 结 束谢谢您的认真学习！退出退出退出退出前一页前一页前一页前一页11b b(c(c)aab b c cab bc cab b c c 1.Draw the third view from its two other views shown.1.Draw the third view from its two other

25、 views shown.已知各点的两个投影，求其第三投影。已知各点的两个投影，求其第三投影。已知各点的两个投影，求其第三投影。已知各点的两个投影，求其第三投影。(1)(1)(1)(1)(2)(2)(2)(2)b ba c cab bc c()()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12 2.Construct the three projections of points 2.Construct the three projections of points A,B,C,DA,B,C,D.from its coordinate and distan

26、ce.from its coordinate and distance.根据所给定的点的坐标或点到投影面的距离，画出根据所给定的点的坐标或点到投影面的距离，画出根据所给定的点的坐标或点到投影面的距离，画出根据所给定的点的坐标或点到投影面的距离，画出 点点点点A A A A、B B B B、C C C C、D D D D 的三面投影。的三面投影。的三面投影。的三面投影。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 Point Point 点点distancedistance H H 距距H H面面distance distance V V 距距V V面面dis

27、tance distance WW 距距WW面面 X Y Z A 15 10 20 B 10 0 10 C 15 15 0 D 0 20 2013 3.The point 3.The point A A (30,15,030,15,0).according to request draw.according to request draw thethe three projections of points three projections of points A,B,CA,B,C.已知已知已知已知A A A A点的坐标为点的坐标为点的坐标为点的坐标为(30,15,030,15,030,15

28、,030,15,0)，按下述要求画出点，按下述要求画出点，按下述要求画出点，按下述要求画出点 A A A A、B B B B、C C C C 的三面投影。的三面投影。的三面投影。的三面投影。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(1)(1)(1)(1)点点点点B B B B在在在在A A A A之右之右之右之右20202020mmmmmmmm，A A A A之前之前之前之前15151515mmmmmmmm，A A A A之上之上之上之上20202020mmmmmmmm。点点点点C C C C在在在在A A A A之左之左之左之左5 5 5 5mmmmm

29、mmm，A A A A之后之后之后之后10101010mmmmmmmm，A A A A之上之上之上之上25252525mmmmmmmm。(2)(2)(2)(2)点点点点B B B B在在在在A A A A之左之左之左之左5 5 5 5mmmmmmmm，A A A A之后之后之后之后5 5 5 5mmmmmmmm，A A A A之上之上之上之上15151515mmmmmmmm。点点点点C C C C在在在在A A A A之右之右之右之右1 1 1 15 5 5 5mmmmmmmm，A A A A之前之前之前之前10101010mmmmmmmm，A A A A之上之上之上之上30303030mmm

30、mmmmm。14projections of points A,B,C.The point A(30,15,0).Draw the third view from its two other views shown.When projected to the W-Plane,left covering right.Construct the three projections of points A,B,C,D.请点击鼠标左键显示后面内容D(10、25、10)。Draw projection of point CThe point A(30,15,0),according to request

31、 draw the three（2）Construct projection b.按下述要求画出点A、B、C 的三面投影。A(20、15、10)；重影点的判别与标注Steps 作图步骤：The point A(30,15,0).when two points on the solid are on the same请点击鼠标左键显示后面内容4.Draw three projections of points Draw three projections of points A,B,C,DA,B,C,D,from its coordinate.,from its coordinate.已知各点的

32、坐标，求点已知各点的坐标，求点已知各点的坐标，求点已知各点的坐标，求点A A A A、B B B B、C C C C、D D D D 的三面的三面的三面的三面投影投影投影投影。A A(2020、1515、1010)；B B(2020、1515、2525)；C C(1010、1515、1010)；D D(1010、2525、1010)。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15dddcccbbb 2.Construct the three projections of points 2.Construct the three projections of

33、 points A,B,C,D.A,B,C,D.from its from its coordinate and distance.coordinate and distance.根据所给定的点的坐标或点根据所给定的点的坐标或点根据所给定的点的坐标或点根据所给定的点的坐标或点 到投影面的距离到投影面的距离到投影面的距离到投影面的距离,画出点画出点画出点画出点A A A A、B B B B、C C C C、D D D D 的三面投影。的三面投影。的三面投影。的三面投影。aaa1.Draw projection of point Draw projection of point A A求求A A点

34、投影点投影2.Draw projection of point Draw projection of point B B求求B B点投影点投影3.Draw projection of point Draw projection of point C C求求C C点投影点投影4.Draw projection of point Draw projection of point D D求求D D点投影点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 Steps 作图步骤作图步骤：16cc 3.The point 3.The p

35、oint A A (30,15,030,15,0),according to request draw the three ,according to request draw the three projections of points projections of points A,B,CA,B,C.已知已知A A点的坐标为点的坐标为(30,15,030,15,0),),按下述要求画出点按下述要求画出点A A、B B、C C 的三面投影。的三面投影。(1)(1)(1)(1)点点点点B B B B在在在在A A A A之右之右之右之右20202020mmmmmmmm，A A A A之前之前

36、之前之前15151515mmmmmmmm，A A A A之上之上之上之上20202020mmmmmmmm。点点点点C C C C在在在在A A A A之左之左之左之左5 5 5 5mmmmmmmm，A A A A之后之后之后之后10101010mmmmmmmm，A A A A之上之上之上之上25252525mmmmmmmm。1.Draw projection of point Draw projection of point A A 求求A A点投影点投影 2.Draw projection of pointDraw projection of point B B求求B B点投影点投影 3.D

37、raw projection of pointDraw projection of point C C求求C C点投影点投影 aaabbbc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 Steps 作图步骤作图步骤：17cc1 1.Draw projection of point Draw projection of point A A求求求求A A A A点投影点投影点投影点投影2.Draw projection of point Draw projection of point B B 求求求求B B B B点投影点投影

38、点投影点投影 3.Draw projection of point Draw projection of point C C 求求求求C C C C点投影点投影点投影点投影 aaabbbc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(2)(2)(2)(2)点点点点B B B B在在在在A A A A之左之左之左之左5 5 5 5mmmmmmmm，A A A A之后之后之后之后5 5 5 5mmmmmmmm，A A A A之上之上之上之上15151515mmmmmmmm。点点点点C C C C在在在在A A A A之右之右之右之右1 1

39、 1 15 5 5 5mmmmmmmm，A A A A之前之前之前之前10101010mmmmmmmm，A A A A之上之上之上之上30303030mmmmmmmm。Steps Steps 作图步骤作图步骤作图步骤作图步骤：3.The point 3.The point A A (30,15,030,15,0),according to request draw the three ,according to request draw the three projections of points projections of points A,B,CA,B,C.已知已知A A点的坐标为点的

40、坐标为(30,15,030,15,0),),按下述要求画出点按下述要求画出点A A、B B、C C 的三面投影。的三面投影。18b()d()ab4.Draw three projections of points4.Draw three projections of points A,B,C,D A,B,C,D,from its coordinate.,from its coordinate.已知各点的坐标，求点已知各点的坐标，求点已知各点的坐标，求点已知各点的坐标，求点A A A A、B B B B、C C C C、D D D D 的三面投影。的三面投影。的三面投影。的三面投影。A A A

41、A(20202020、15151515、10101010)；B B B B (20202020、15151515、25252525)；C C C C (10101010、15151515、10101010)；D D D D (10101010、25252525、10101010)。cc1.Draw projection of point Draw projection of point A A 求求A点投影点投影 2.Draw projection of point Draw projection of point B B 求求B点投影点投影 3.Draw projection of point Draw projection of point C C求求C点投影点投影aab(c)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dd4.Draw projection of point Draw projection of point D D求求D点投影点投影 Steps Steps 作图步骤作图步骤：