Projection of lines

Characteristics of line projection

Exercises

Projection of LinesLines

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..

ab a´b´ a"b"

Projection of linesProjection of lines

YH

z

x 0 Yw

b´ b"

b

a´ a"

a

B

Ab´

a"

b"

a´V

H

W

ab

YH

z

x 0 Yw

ABAB

Characteristics of line projectionCharacteristics of line projection

1. The vertical line of a projection plane1. The vertical line of a projection plane

2. The parallel line of a projection plane2. The parallel line of a projection plane

3. A line in general position3. A line in general position

　　　　　　　　　　　　　　　　　　　　　　 HH-plane,-plane, HH-perpendicular-perpendicular 　　　　　　　　　　　　

If it is vertical to theIf it is vertical to the VV-plane, it is called a -plane, it is called a VV-perpendicular line-perpendicular line .. 　　　　　　　　　　　　　　　　　　　　 　　　　　　　　　　 　　　　　　　　　　 WW-plane,-plane, WW-perpendicular-perpendicular 　　　　　　　　　　　　

DefinitionDefinition

11. The vertical line of a projection plane. The vertical line of a projection plane

Z

b

X

a

b

a(b)

O

YH

YW

a

b

a(b)

a

a

b

A

B

H-perpendicular lineH-perpendicular line

b

ab

a

b

a

A

B

z

X

ab b

a

O

YH

YW

a

b

V-perpendicular lineV-perpendicular line

A B

b

a

ab

a

b

Z

X

abb

a

O

YH

YW

a

b

W-perpendicular lineW-perpendicular line

CharacteristicsCharacteristics Its projection on its vertical plane converges to a point.

Its projections on the other two planes are both parallel with an axis of projection, and shows its true length.

1. The vertical line of a projection plane1. The vertical line of a projection plane

W-perpendicular lineW-perpendicular lineZ

●e f

e f

e(f)

Xo

YH

YW

H-perpendicularH-perpendicular lineline

YW

●

a

b

a(b)

a

bX

Z

o

YH

ABAB ABAB

V-perpendicular lineV-perpendicular line

●c(d)

c

d

d c

X

Z

o

YH

YW

CDCD

CDCD EFEF

EFEF

2.2.Parallel line of a projection planeParallel line of a projection plane

ObliquityObliquity αα horizontalhorizontalββis the oblique angles of the corresponding line formed with the is the oblique angles of the corresponding line formed with the ffrontal plane.rontal plane.γγ profileprofile

DefinitionDefinition HH-plane, horizontal-plane, horizontalIf it is parallel with theIf it is parallel with the VV-plane, it is called a frontal line-plane, it is called a frontal line.. WW-plane, profile-plane, profile　　　　　　　　

a

a ba

b

b

A

B

a

a ba

b

b

A

B

a

a

b

a

b

b

A

B

a

a ba

b

b X

a b a b

b

a

O

z

YH

YW

A

B

a

a

b

a

b

b

X

a

b

a

b

ba

O

Z

YH

YWA

B

a

a

b

a

b

b

A

B

X

Za

b b

b

a

O

YH

YW

a

2.2.Parallel line of a projection planeParallel line of a projection plane

ββαα

CharacteristicsCharacteristics

Shows its true length and the inclination angles formed Shows its true length and the inclination angles formed with the axes of projection show the oblique formed with the axes of projection show the oblique formed with the other two planes of projection.with the other two planes of projection.

Its projections on the other two projection planes are Its projections on the other two projection planes are shorter than its true length, and are all vertical to the shorter than its true length, and are all vertical to the axis of projectionaxis of projection..

b

a

b

b

a

a

X YW

Z

YH

Profile lineProfile lineHorizontal lineHorizontal line

X

Z

YW

YHb

a

a

a b bFrontal lineFrontal line

X YW

b

a

ab

a

b

Z

YH

ABABABAB

ABABββ γγ

αα γγ

V Z

b´

B b"

W

a´

X 0

A a" b

a

H Y

3. A line in general position3. A line in general position

DefinitionDefinition

ObliquityObliquity

CharacteristicsCharacteristics

X O YW

YH

Z

a´

a

b´

b

b"

a"

The line being projected is oblique with the three planes of projection.The line being projected is oblique with the three planes of projection.

αα horizontalhorizontalββis the oblique angles of the corresponding line formed with the frontal planeis the oblique angles of the corresponding line formed with the frontal plane..γγ profileprofile

The angleThe angle always > 0°or < 90°always > 0°or < 90°

ThreeThree projections on the projection planes are shorter than its true projections on the projection planes are shorter than its true length, and all oblique angles are not true. length, and all oblique angles are not true.

1. Given positions of line AB & CD, label its projection in view and fill the vacancy.

ExercisesExercises

2. Given two projections of line AB & CD, draw the third projection and fill the vacancy.

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.

HH-perpendicular-perpendiculara line in general positiona line in general position

a´

a

a"

b´

b

b" c´

d´

c(d)

c"

d"

Z

b´

a´ c´ X 0 Yw c a b

YH

ABAB ，， = = ABAB ；；

ACAC ，， == ACAC 。。

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.

FFrontal linerontal line

　　 Horizontal lineHorizontal line

aa´́bb´́

acac

AB

AC

a"

b"

c"