立体上直线的投影PPT课件市公开课一等奖百校联赛获奖课件.pptx

Projection of linesProjection of lines 直线投影直线投影Characteristics of line projectionCharacteristics of line projection 直线投影特征直线投影特征 ExercisesExercises 练习题练习题 Projection of Lines for a Solid 立体上直线投影 请点击对应标题显示其内容请点击对应标题显示其内容请点击对应标题显示其内容请点击对应标题显示其内容第1页 The result of projection is a line connecting the The result of projection is a line connecting the projected points of the two end points of the lineprojected points of the two end points of the line.直线投影由直线上两端点直线投影由直线上两端点直线投影由直线上两端点直线投影由直线上两端点A A A A、B B B B同面投影连线来确定。同面投影连线来确定。同面投影连线来确定。同面投影连线来确定。Projection of linesProjection of lines 直线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bbbaaababaVHWab第2页The partition of point on a line must be equal to on theThe partition of point on a line must be equal to on the projected line.projected line.点分线段长度之比等于其投影分线段投影长度之比。点分线段长度之比等于其投影分线段投影长度之比。点分线段长度之比等于其投影分线段投影长度之比。点分线段长度之比等于其投影分线段投影长度之比。Characteristics of line projectionCharacteristics of line projection 直线投影特征1.Linearity1.Linearity 直线性：直线性：直线性：直线性：The projection of a line produces a line.The projection of a line produces a line.直线投影依然是直线直线投影依然是直线直线投影依然是直线直线投影依然是直线(特殊情况积聚为点特殊情况积聚为点特殊情况积聚为点特殊情况积聚为点)。2.Parallelism2.Parallelism 平行性：平行性：平行性：平行性：The parallelism of lines before and after projection does not change.The parallelism of lines before and after projection does not change.平行直线各同面投影依然平行。平行直线各同面投影依然平行。平行直线各同面投影依然平行。平行直线各同面投影依然平行。3.Subordinative3.Subordinative 隶属性：隶属性：隶属性：隶属性：The projection of a point on a line must be on theThe projection of a point on a line must be on the projected line.projected line.若点在线上若点在线上若点在线上若点在线上,则其投影应在线投影上。则其投影应在线投影上。则其投影应在线投影上。则其投影应在线投影上。aaaaa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A4.Proportionality4.Proportionality 定比性：定比性：定比性：定比性：VHx 0 Yw第3页W-perpendicular lineW-perpendicular line 侧垂线侧垂线侧垂线侧垂线Ze f efe(f)XoYHYW horizontalhorizontal is the oblique angles of the corresponding line formed with the is the oblique angles of the corresponding line formed with the f frontal plane.rontal plane.profileprofile与与与与H H面夹角面夹角面夹角面夹角:；与；与；与；与V V 面夹角面夹角面夹角面夹角:；与；与；与；与WW面夹角面夹角面夹角面夹角:。（均为（均为（均为（均为0 0 或或或或9090 ）H H-plane,-plane,H H-perpendicular-perpendicular (铅铅铅铅垂线垂线垂线垂线)If it is vertical to theIf it is vertical to the V V-plane,it is called a -plane,it is called a V V-perpendicular line-perpendicular line.(正正正正垂线垂线垂线垂线)WW-plane,-plane,WW-perpendicular -perpendicular (侧侧侧侧垂垂垂垂线线线线)与某投影面垂直直线称为该面垂直线与某投影面垂直直线称为该面垂直线与某投影面垂直直线称为该面垂直线与某投影面垂直直线称为该面垂直线Its projection on its vertical plane converges to a point.投影面垂直线在所垂直投影面上投影积聚为一点投影面垂直线在所垂直投影面上投影积聚为一点投影面垂直线在所垂直投影面上投影积聚为一点投影面垂直线在所垂直投影面上投影积聚为一点。Its projections on the other two planes are both parallel with an axis of projection,and shows its true length.在另外两个投影面上投影均平行对应投影轴，且反应实长。在另外两个投影面上投影均平行对应投影轴，且反应实长。在另外两个投影面上投影均平行对应投影轴，且反应实长。在另外两个投影面上投影均平行对应投影轴，且反应实长。DefinitionDefinition 定定定定 义义义义ObliquityObliquity 倾倾倾倾 角角角角CharacteristicsCharacteristicsCharacteristicsCharacteristics 投影特征投影特征投影特征投影特征1.1.The vertical line of a projection plane The vertical line of a projection plane 投影面垂直线投影面垂直线投影面垂直线投影面垂直线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 H-perpendicularH-perpendicular lineline 铅垂线铅垂线铅垂线铅垂线YWa b a(b)a b XZoYHABABABABV-perpendicular lineV-perpendicular line 正垂线正垂线正垂线正垂线c(d)cdd c XZoYHYWCDCDCDCDEFEFEFEF第4页2.2.2.2.Parallel line of a projection plane Parallel line of a projection plane 投影面平行线投影面平行线投影面平行线投影面平行线 Obliquity Obliquity 倾倾倾倾 角角角角 horizontalhorizontal is the oblique angles of the corresponding line formed with the is the oblique angles of the corresponding line formed with the f frontal plane.rontal plane.profileprofile与与与与H H面夹角面夹角面夹角面夹角:;与与与与V V 面夹角面夹角面夹角面夹角:;与与与与WW面夹角面夹角面夹角面夹角:。(总有一个为总有一个为总有一个为总有一个为0 0 )DefinitionDefinition定定定定 义义义义Characteristics Characteristics 投影特征投影特征投影特征投影特征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 H H-plane,horizontal-plane,horizontal (水水水水平平平平线线线线)If it is parallel with theIf it is parallel with the V V-plane,it is called a frontal line-plane,it is called a frontal line.(正正正正平线平线平线平线)WW-plane,profile-plane,profile (侧侧侧侧平线平线平线平线)与某投影面平行直线称为该面平行线与某投影面平行直线称为该面平行线与某投影面平行直线称为该面平行线与某投影面平行直线称为该面平行线Shows its true length and the inclination angles formed with the axes of Shows its true length and the inclination angles formed with the axes of projection show the oblique formed with the other two planes of projection.projection show the oblique formed with the other two planes of projection.在所平行面上投影反应实长在所平行面上投影反应实长在所平行面上投影反应实长在所平行面上投影反应实长,且反应其对另外两投影面倾角且反应其对另外两投影面倾角且反应其对另外两投影面倾角且反应其对另外两投影面倾角。Its projections on the other two projection planes are shorter than its true Its projections on the other two projection planes are shorter than its true length,and are all vertical to the axis of projectionlength,and are all vertical to the axis of projection.在另外两个投影面上投影长度比实长短在另外两个投影面上投影长度比实长短在另外两个投影面上投影长度比实长短在另外两个投影面上投影长度比实长短,且垂直于对应投影轴且垂直于对应投影轴且垂直于对应投影轴且垂直于对应投影轴。b a bb aa XYWZYH Profile lineProfile line 侧平线侧平线侧平线侧平线Horizontal lineHorizontal line 水平线水平线水平线水平线XZYWYHba aa b b Frontal lineFrontal line 正平线正平线正平线正平线XYWb a aba b ZYHABABABABABAB 第5页3.3.A line in general position A line in general position 普通位置直线普通位置直线普通位置直线普通位置直线DefinitionDefinition 定定定定 义义义义 ObliquityObliquity 倾倾倾倾 角角角角Characteristics Characteristics 投影特征投影特征投影特征投影特征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X O YW YHZa ab bbaThe line being projected is oblique with the three planes of projection.The line being projected is oblique with the three planes of projection.与三个投影面都倾斜直线称为普通位置直线。与三个投影面都倾斜直线称为普通位置直线。与三个投影面都倾斜直线称为普通位置直线。与三个投影面都倾斜直线称为普通位置直线。horizontalhorizontal is the oblique angles of the corresponding line formed with the frontal planeis the oblique angles of the corresponding line formed with the frontal plane.profileprofile与与与与HH面夹角面夹角面夹角面夹角:;与与与与V V 面夹角面夹角面夹角面夹角:;与与与与WW面夹角面夹角面夹角面夹角:。The angleThe angle alwaysalways 0 0or or 0 0或或或或 9090)ThreeThree projections projections on on the the projection projection planes planes are are shorter shorter than than its its true true length,and all oblique angles are not true.length,and all oblique angles are not true.三投影均小于实长，其倾角均不反应真实大小三投影均小于实长，其倾角均不反应真实大小。第6页 1.Given positions of line 1.Given positions of line AB AB&CDCD,label its,label its projection in view and fill the vacancy.projection in view and fill the vacancy.已知立体上直线已知立体上直线已知立体上直线已知立体上直线ABABABAB、CDCDCDCD 空间位置空间位置空间位置空间位置,在投影图中标注其投影位置在投影图中标注其投影位置在投影图中标注其投影位置在投影图中标注其投影位置,并填空。并填空。并填空。并填空。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.Given two projections of lineGiven two projections of line AB AB&CDCD,draw,draw the third projection and fill the vacancy.the third projection and fill the vacancy.已知直线已知直线已知直线已知直线ABABABAB、ACACACAC 二投影二投影二投影二投影,求二直线求二直线求二直线求二直线 第三投影第三投影第三投影第三投影,并填空并填空并填空并填空。第7页 本 小 节 结 束谢谢您认真学习！前一页前一页前一页前一页第8页 1.Given positions of line 1.Given positions of line AB AB&CDCD,label its projection in view and fill in the blank.,label its projection in view and fill in the blank.已知立体上直线已知立体上直线已知立体上直线已知立体上直线ABABABAB、CDCDCDCD空间位置空间位置空间位置空间位置,在投影图中标注其投影位置在投影图中标注其投影位置在投影图中标注其投影位置在投影图中标注其投影位置,并填空。并填空。并填空。并填空。请请请请点点点点击击击击解解解解答答答答显显显显示示示示其其其其内内内内容容容容H H-perpendicular-perpendicular铅垂线铅垂线铅垂线铅垂线a line in general positiona line in general position 普通位置直线普通位置直线 aaa bbb c dc(d)cd第9页 ABAB ，=ABAB；ACAC ，=ACAC。请请请请点点点点击击击击解解解解答答答答显显显显示示示示其其其其内内内内容容容容 2.Given two projections of line 2.Given two projections of line ABAB&CDCD,draw the third projection and fill in the blank.,draw the third projection and fill in the blank.已知直线已知直线已知直线已知直线ABABABAB、ACACACAC 二投影二投影二投影二投影,求第三投影求第三投影求第三投影求第三投影,并填空。并填空。并填空。并填空。(它们是什么直线它们是什么直线它们是什么直线它们是什么直线?哪个投影反应实长哪个投影反应实长哪个投影反应实长哪个投影反应实长?)F Frontalrontal lineline正平正平正平正平线线HorizontalHorizontal lineline水平水平水平水平线线a a b b acac ABACabc第10页