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1、abcABC2.2 Projection of Points2.3 Projection of Lines2.4 relationship of two linesChapter 2 Projection of Point、Line and PlaneAssignments:P4/2-5,2-6，2-7，2-8;P5/2-9，2-10,xHOWaazayayzyHyWaaxVaReview:projections of a point three projections of a pointWOxVzaaAaaxyyxzxyzazaya a The horizontal projection
2、of the point A A a a The frontal projection of the point A A a a The profile projection of the point A A。b b(c(c)aab b c cab bc cab b c c 1.Draw the third projection from its two others shown.1.Draw the third projection from its two others shown.(1)(1)(1)(1)(2)(2)(2)(2)b ba(c)(c)ab bc cRelative posi
3、tion of two pointsRelative position of two points Relative positions of point Relative positions of point A A B B Up and down Up and down Z ZFront and back Front and back Y Y Left and right Left and right X Xaa abbAX X Line projection can be made of the line connecting between the same plane project
4、ion of its two end points.2.3 Projection of Lines2.3.1 Position of lines&types of Line2.3.2 Relationship of two lines2.3.1 Position of lines&types of Line 1）Lines parallel to a projection plane Parallel to one of the projection planes and inclined to the other two.(1)Horizontal lines(2)Frontal lines
5、(3)Profile lines 2）Lines perpendicular to the projection planes Perpendicular to one of the projection planes and parallel to the other two.(1)H-perpendicular lines(2)V-perpendicular lines(3)W-perpendicular lines 3）General position lines Inclined to all three projection planes.(1)Horizontal lines：pa
6、rallel to H-planes and inclined to the other twoCharacteristic：1 1a a b b OX OX;a a b b OYOYW W 2 2 abab=AB=TL(True length),real shapeAB=TL(True length),real shape xa b ab baOzyHyW 1）Lines parallel to the projection planes (2)Frontal lines：parallel to V-planes and inclined to the other twoCharacteri
7、stic：1 ab OX;a b OZ 2 a b=AB=TL(True length),real shape=TL(True length),real shapexa b ab baO z yHyW 1）Lines parallel to the projection planes (3)Profile lines：parallel to W-planes and inclined to the other twoCharacteristic：1 1 a a b b OZOZ;ab ab OYOYH H 2 2 a a b b =AB=TL(True length),real shapeAB
8、=TL(True length),real shape yW xa b ab baO zyH 1）Lines parallel to the projection planesTry to find the lines three projections on cube surface Horizontal line Frontal line Profile lineExample xab ab(b)aO zyHyWCharacteristic：1 1a ba b accumulate to a pointaccumulate to a point 2 2a a b bOXOX ;a a b
9、b OYOYW W 3 3a a b b =a a b b =ABAB(1)H-perpendicular lines：Perpendicular H-planes and parallel to the other two2）Lines perpendicular to the projection planes x(a)b ab baO zyHyW (2)V-perpendicular lines：Perpendicular V-planes and parallel to the other two Characteristic：1 1a a b b accumulate to a ac
10、cumulate to a pointpoint 2 2abab OXOX ;a a b b O OZ Z 3 3abab=a a b b =ABAB2）Lines perpendicular to the projection planes xab a(b)baO z yHyWCharacteristic：1 a b accumulate to a pointaccumulate to a point 2 ab OYH ;a b OZ 3 ab=a b =AB (3)W-perpendicular lines：Perpendicular W-planes and parallel to th
11、e other two2）Lines perpendicular to the projection planes2）Lines perpendicular to the projection planesHperp.lineperp.line perp.LineTry to find the lines three projections on cube surface ABDefinition:H-、V-、W-Inclined to all three projection planes.babaab xzabaO yHyWabb3）General position lines Incli
12、ned to all three projection planes.3）General position lines2.3.1 Position of lines&types of Line Given positions of line AB&CD,label its projection in views and fill in the blank.aa bbb c dc(d)cd a Relationship of two lines：2.4 Relationship of two lines1.Parallel 2.intersection 3.SkewABCD ABCDCDCDAB
13、ABabcdabcdcdababcdEeEe1(2)4.Perpendicular If two lines in space are parallel,their projection will be parallel.ABCDabcdxOyHyWzabcdabcdabcd Characteristic:AB/CD ab/cd and ab/cd and ab/cd 1)Parallel lines1)Parallel linesExample ABCDabcdxOyHyWzabcdabcdabcdkkkCharacteristic：If two lines in space are int
14、ersection,their projection will be intersection also,and their intersection point is accord with point projection rule,as shown in Figure.2)Intersection linesExample The given lines are neither parallel nor intersection,so they are skew lines.(the point in one projection plane is not a intersection
15、point projection,it is a projection of a coinciding point.)ABCDababcdcdO1(2)3(4)xOabcdabcd13(4)3421(2)3)SkewEX.Judge the relative position of two lines EF and MNxOef mnefnmyWzyHfenm3)Skew lines Here,we only discuss the situation that at least one of two intersecting perpendicular lines is parallel t
16、o a projection plane.BCAabcabcabcxO 1)Both two intersecting perpendicular lines are parallel to a projection plane,then the projections of both lines on that plane will be perpendicular to each other,as shown in above figures.4)PerpendicularBACDabcdxOabcdabcd2)If one of two perpendicular lines is pa
17、rallel to a projection plane,the projections of both lines on that plane will be at a right angle,as shown in above figure.(both skew and intersection lines)4)Perpendicular Example Example Try to make a line AB perpendicular to CD,and get the two Try to make a line AB perpendicular to CD,and get the
18、 two projections of projections of abab and and ababxOcdaacdbbStepsSteps：make make ab c d pass pass through through a,get b,get b get ab in H projection get ab in H projection Steps Steps：make make efefcd cd pass through pass through a a(b b),get point),get point f f Example Example Try to get commo
19、n perpendicular line Try to get common perpendicular line EF of the skew lines of the skew lines AB、CDa(b)cdcdabxOBCAa(e,b)cDFEdf through through f f get get f,then make then make fefeOxOxa(e,b)True lengthffeabcABC2.2 Projection of Points2.3 Projection of Lines2.4 relationship of two linesChapter 2 Projection of Point、Line and PlaneAssignments:P4/2-5,2-6，2-7，2-8;P5/2-9，2-10,