《立体上直线的投影》由会员分享，可在线阅读，更多相关《立体上直线的投影（10页珍藏版）》请在金锄头文库上搜索。
1、Projection of linesProjection of lines 直线的投影直线的投影Characteristics of line projectionCharacteristics of line projection 直线的投影特性直线的投影特性ExercisesExercises 练习题练习题Projection of Lines for a Solid 立体上直线的投影 请点击相应标题显示其内容请点击相应标题显示其内容The result of projection is a line connecting the The result of projection is
2、a line connecting the projected points of the two end points of the lineprojected points of the two end points of the line. . 直线的投影由直线上两端点直线的投影由直线上两端点A A、B B同面投影的连线来确定。同面投影的连线来确定。Projection of linesProjection of lines 直线的投影直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bb“baa“aba“b“aVHWabThe partition of point on a
3、 line must be equal to on theThe partition of point on a line must be equal to on theprojected 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。Characteristics of line projectionCharacteristics of line projection 直线的投影特性直线的投影特性1. Linearity1. Linearity直线性：直线性：The projection of a lin
4、e produces a line.The projection of a line produces a line. 直线的投影仍然是直线直线的投影仍然是直线( (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：The parallelism of lines before and after projection does not change.The parallelism of lines before and after projection does not change. 平行直线的各同面投影仍然平行。平行直线的各
5、同面投影仍然平行。 3. 3. SubordinativeSubordinative从属性：从属性：The projection of a point on a line must be on theThe projection of a point on a line must be on theprojected line.projected line. 若点在线上若点在线上, ,则其投影应在线的投影上。则其投影应在线的投影上。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A4. Proportionality4. Proportionality定比性：定比性：VHx 0
6、 YwW-perpendicular lineW-perpendicular line 侧垂线侧垂线 Z efefe(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H H面的夹角面的夹角: : ；与；与V V 面的夹角面的夹角: : ；
7、与；与WW面的夹角面的夹角: : 。（均为（均为0 0 或或9090 ）H H-plane,-plane, H H-perpendicular-perpendicular ( (铅铅垂线垂线) ) If it is vertical to theIf it is vertical to theV V-plane, it is called a -plane, it is called a V V-perpendicular line-perpendicular line. . ( (正正垂线垂线) ) WW-plane,-plane, WW-perpendicular -perpendicul
8、ar ( (侧侧垂线垂线) ) 与某投影面垂直的直线称为该面的垂直线 与某投影面垂直的直线称为该面的垂直线Its projection on its vertical plane converges to a point. 投影面垂直线在所垂直的投影面上的投影积聚为一点投影面垂直线在所垂直的投影面上的投影积聚为一点。 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的投影均平行相应的投影轴，且反映实长
9、。在另外两个投影面上的投影均平行相应的投影轴，且反映实长。DefinitionDefinition定定 义义ObliquityObliquity倾倾 角角CharacteristicsCharacteristics投影特性投影特性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H-perpendicularH-perpendicularlineline 铅垂线铅垂线YWab
10、a(b)ab XZoYHABABABABV-perpendicular lineV-perpendicular line 正垂线正垂线c(d)cddcXZoYHYWCDCDCDCDEFEFEFEF2.2.Parallel line of a projection plane Parallel line of a projection plane 投影面平行线投影面平行线 Obliquity Obliquity倾倾 角角 horizontalhorizontal is the oblique angles of the corresponding line formed with the is
11、the oblique angles of the corresponding line formed with the f frontal plane.rontal plane. profileprofile 与与H H面的夹角面的夹角: : ; ;与与V V 面的夹角面的夹角: : ; ;与与WW面的夹角面的夹角: : 。 ( (总有一个为总有一个为0 0 ) )DefinitionDefinition 定定 义义Characteristics Characteristics 投影特性投影特性请请 点点 击击 鼠鼠 标标 左左 键键 显显 示示 后后 面面 内内 容容H H-plane,
12、horizontal-plane, horizontal ( (水水平线平线) ) If it is parallel with theIf it is parallel with theV V-plane, it is called a frontal line-plane, it is called a frontal line. . ( (正正平线平线) )WW-plane, profile-plane, profile ( (侧侧平线平线) )与某投影面平行的直线称为该面的平行线与某投影面平行的直线称为该面的平行线Shows its true length and the inclin
13、ation 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. 在所平行的面上的投影反映实长在所平行的面上的投影反映实长, ,且反映其对另外两投影面的倾角且反映其对另外两投影面的倾角。Its projections on the othe
