3.
1. Introduction of the course1. Introduction of the course
Task: How to represent a 3D objectTask: How to represent a 3D object
with a 2D drawingwith a 2D drawing
4.
2. Form of Projection2. Form of Projection
Projection method :Projection method :
When the lines of projection pass through the object and the pre -When the lines of projection pass through the object and the pre -
established plane, there will be graphics produced on the plane.established plane, there will be graphics produced on the plane.
This method is called projection.This method is called projection.
Center of projectionCenter of projection
Plane of projectionPlane of projection
ObjectObject
Lines of projectionLines of projection
ProjectionProjection
5.
Types of ProjectionTypes of Projection
Projection methodProjection method
Central projectionCentral projection methodmethod
(( The central projection is mainly used for the pictorialThe central projection is mainly used for the pictorial
drawings of buildings.drawings of buildings.))
Parallel projection methodParallel projection method
(( It is used in most engineering drawings.It is used in most engineering drawings.))
6.
a
b
c
SS
（（ Sight or centerSight or center
of projectionof projection ））
A
B
C
Central projectionCentral projection ：： When the lines of projection meet at a point,When the lines of projection meet at a point,
it is called central projection.it is called central projection.
Central projection methodCentral projection method
Projection linesProjection lines
ObjectObject
PP Projection planeProjection plane
ProjectionProjection
7.
Lines of projection will be parallelLines of projection will be parallel
a
b
c
A
B
C
Parallel projection: When the lines of projection are parallel withParallel projection: When the lines of projection are parallel with
each other, it is called parallel projection.each other, it is called parallel projection.
Parallel projection methodParallel projection method
ObjectObject
PP Projection planeProjection plane
ProjectionProjection
SS
9.
3. Similarity: When planar features or lines are inclined to the3. Similarity: When planar features or lines are inclined to the
projection plane , the projection producesprojection plane , the projection produces
similar shapes of the original feature. The length ofsimilar shapes of the original feature. The length of
projected lines will be shorter than the real length.projected lines will be shorter than the real length.
2.2. Accumulation: When planar features or lines are orthogonal to theAccumulation: When planar features or lines are orthogonal to the
projection plane, the projection accumulates to aprojection plane, the projection accumulates to a
line or a point.line or a point.
1.1. Authenticity: When planar features or lines are in parallel with theAuthenticity: When planar features or lines are in parallel with the
projection plane, the projection shows the real shapeprojection plane, the projection shows the real shape
or true length of the features being projected.or true length of the features being projected.
Features of Orthographic ProjectionFeatures of Orthographic Projection
10.
These axes meet at a pointThese axes meet at a point
which is called the origin.which is called the origin.
Y-axis
0X
Y
Z
V
H
W
Three-Planes Projection SystemThree-Planes Projection System
1) Set up three-planes projection system
The three projection planes are orthogonal fromThe three projection planes are orthogonal from
each other.each other. Make up of one projection system.Make up of one projection system.
V-plane → Vertical (Frontal) plane
H-plane → Horizontal plane
W-plane→Profile (Wall) plane
The intersection lines of theThe intersection lines of the
three projection planes arethree projection planes are
called the axes of projection.called the axes of projection.
X-axis
Z-axis
11.
To draw three-view drawings on a drawing sheetTo draw three-view drawings on a drawing sheet
The V-Plane is first fixed.
TheThe HH-Plane turns down 90-Plane turns down 90°°..
TheThe WW-Plane turns right 90-Plane turns right 90°°..
X
Y
Z
V
H
W
Three-Planes Projection SystemThree-Planes Projection System
12.
Projection of a pointProjection of a point
Relative position of two pointsRelative position of two points
Identification and labeling of coincident pointIdentification and labeling of coincident point
ExercisesExercises
3. Projection of Points3. Projection of Points
13.
W
Y
V
H
x
Z
O
A
Projection of a pointProjection of a point
1. Projection of the point1. Projection of the point AA
aa ———— The horizontal projection of the pointThe horizontal projection of the point AA
aa'' ———— The frontal projection of the pointThe frontal projection of the point AA
aa""———— The profile projection of the pointThe profile projection of the point AA
aa'' aa""
aa
14.
Z = a''ax
= aa""aYw
→ The distance of A to H.
aa''aa""⊥⊥OZOZ The height alignment,The height alignment, ZZ equalequal..
H
X 0 Yw
YH
Z
V W
X Y
Y
Z
2. The2. The principleprinciple of pointsof points
3. Relation of points projection & coordinate3. Relation of points projection & coordinate
Projection of a pointProjection of a point
aaaa'' ⊥⊥ OXOX The length alignment,The length alignment, XX equalequal..
aaaa""⊥⊥ OYOY The width equality ,The width equality , YY equal.equal.
X = a''az
= aaYH
→ The distance of A to W.
Y = aax
= aa""az
→ The distance of A to V.
aa''
aa
aa""
ax
aZ
aYH
aYW
15.
15
10
5
aa'
aa
aa"
45°
x
z
YH
Yw
0
StepsSteps
（ 1 ） Drawing coordinate origin and
axis.
（ 2 ） According to coordinate of point A, construct projection aa'',,aa;;
（ 3 ） According to rules projections of point, draw projection aa"".
Example1. The pointExample1. The point AA ((5, 10, 155, 10, 15) . construct three projections of) . construct three projections of AA..
AA
16.
Y
Z
WV
H
WV
H
∆ Z ∆ Z
∆ Y
∆Y
∆ X
∆X
Relative position of two pointsRelative position of two points
Relative positions of pointRelative positions of point AA && BB
Up and downUp and down →→ ∆ZZ
Front and backFront and back →→
∆YY
Left and rightLeft and right →→ ∆XX
b
aa' aa"
aa
B bb"
bb'
A
X
17.
x 0 YW
YH
z
a' a"
a
Bel ow10
Lef t 10
Af t er
5
b
StepsSteps
（（ 22 ）） Construct projection bb""..
Example2. PointExample2. Point BB belowbelow A10A10, after, after A5A5,left,left A10A10.construct projections of.construct projections of BB..
AA
BB
（（ 11 ）） Construct projection bb'',b,b..
b' b"
18.
IdentificationIdentification When projected to the H-Plane, up covering down.
Identification and labeling of coincident pointIdentification and labeling of coincident point
LabelingLabeling
DefiningDefining when two points 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.
When projected to the V-Plane, front covering back.
When projected to the W-Plane, left covering right.
All invisible projections of points are written in brackets.
19.
b'
AA
BB
5
10 10
15
1 0
5
d
StepsSteps
2. Construct projections DD, dd, dd '',dd "";
1. Construct projections CC , cc,, c'c',,c"c";
CC
DD
(c)
Example3. PointExample3. Point CC fromfrom WW 5mm, from5mm, from VV10mm, from10mm, fromHH10mm. point10mm. point DD fromfrom WW15mm, from15mm, from
VV 10mm, from10mm, from HH 5mm.construct three projections of point5mm.construct three projections of point C.DC.D and distinguish itsand distinguish its
visibility.visibility.
a' a"
x 0 Yw
YH
z
b"
a
b
c' c"
d"
( )d'
20.
1.Draw the third-view from its two other views shown1.Draw the third-view from its two other views shown..
ExercisesExercises
2.2.Construct the three projections of pointsConstruct the three projections of points A, B, C, DA, B, C, D. from. from
its coordinate and distance.its coordinate and distance.
3.3.Draw three projections of pointsDraw three projections of points A, B, C, DA, B, C, D, from its coordinate., from its coordinate.
21.
b"(c")
a"
a b c
a"
b"
c"
a'
b'
c'
1. Draw the third view from its two other views shown.1. Draw the third view from its two other views shown.
(1)(1) (2)(2)
b a c
a'
b' c'
( )
22.
2. Construct the three projections of points2. Construct the three projections of points A,B,C,DA,B,C,D..
from its coordinate and distance.from its coordinate and distance.
PointPoint distancedistance HH distancedistance VV distancedistance WW X Y Z
A 15 10 20
B 10 0 10
C 15 10 0
D 0 20 20
23.
3.3. Draw three projections of pointsDraw three projections of points A,B,C,DA,B,C,D, from its coordinate., from its coordinate.
AA
((2020 、、 1515 、、 1010))
；；
BB
((2020 、、 1515 、、 2525))
；；
CC
((1010 、、 1515 、、 1010))
；；
24.
d
d"d'
c'
c
c"
b"
b
b'
2. Construct the three projections of points2. Construct the three projections of points A,B,C,D.A,B,C,D. from itsfrom its
coordinate and distance.coordinate and distance.
a'
45°
0x
z
YH
Yw
a
a"
poi nt Di st anc
e H
Di st an
ce V
Di st an
ce W
X Y Z
A 15 10 20
B 10 0 10
C 15 15 0
D 0 20 20
1. Draw projection of pointDraw projection of point AA
2. Draw projection of pointDraw projection of point BB
3. Draw projection of pointDraw projection of point CC
4. Draw projection of pointDraw projection of point DD
StepsSteps
25.
b( )
d'( )
a
b'
4. Draw three projections of points4. Draw three projections of points A,B,C,DA,B,C,D, from its coordinate., from its coordinate.
AA
((2020 、、 1515 、、 1010))
；；
BB
((2020 、、 1515 、、 2525))
；；
CC
((1010 、、 1515 、、 1010))
；；
DD
((1010 、、 2525 、、 1010))
。。
c'
c
0x
z
YH
Yw
1. Draw projection of pointDraw projection of point AA
2. Draw projection of pointDraw projection of point BB
3. Draw projection of pointDraw projection of point CC
a'
a"
b"
(c")
45°
d"
d
4. Draw projection of pointDraw projection of point DD
StepsSteps
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