Descriptive Geometry Eng. Areej Afeefy

1
Descriptive GeometryEng. Areej Afeefy

• Ref. Descriptive Geometry Metric
• PARE/LOVING/HILL
• Fifth edition

2
Descriptive Geometry

• Descriptive Geometry
• is the science of graphic representation and
  solution and space problems

3
projections

• Tow common types of projections
• 1) perspective projections (used by architects
  or artists)
• 2) orthographic projections (perpendicular to
  the object)

4
Principal Views
5
Draw the profile
6
Steps to obtain a view

• Establish the line of sight.
• Introduce the folding line
• Transfer distances to the new view
• Determine visibility and complete the view

7
Step 1 Establish the line of sight.
Primary Auxiliary Views
Step 2 Introduce the folding line
Step 3 transfer distances
a,e
d,h
y
b,f
c,g
H
Step 4 determine visibility and complete view
1
D2
1
D1
D
y
h
d
g
k1
e
D2
c
y
f
a
D1
f,e
g,h
b
b,a
c,d
8
All views projected from top view has the same
height dimension
9
Primary Auxiliary Views
10
View 1 is an auxiliary view projected from the
front View
11
All the views projected from front view have the
same depth dimension
12
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13
Edge View of a plane
14
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15
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16
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17
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18
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21
Chapter 3 LINES
22
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23
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24
Frontal Line
25
Frontal Line
26
the true angel between a line and any
projection plane appears in any view shows
the line in true length and the projection plane
in Edge View.
27
Level (Horizontal) Line
28
Level Line
29
Profile Line
30
Profile Line
31
True Length of an Oblique Line
32
True Length of an Oblique Line
33
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34
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35
Bearing , Slope, and Grade
N
N
aH
aH
S55oE
55
b
b
Bearing a term used to describe the direction of
a line on the earths surface
36
Azimuth Bearing
N
aH
aH
125o
N125o
b
b
37
problem

• A 160-m segment AB of a power line has a bearing
  of N 60o and a downward slope of 20o from the
  given point A. Complete the front and top views.

ah
aF
38
b
1
20o
H
160 m
N
b
N 60o
a1
ah
H
F
aF
b
39
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40
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41
Grade
Grade another way to describe the inclination of
a line from the horizontal Plane
42
Grade
43
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44
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45
Chapter 4

• Planes

46
Points and lines in Planes
47
Locating a Point in a Plane

• Problem Given the front and side views of a
  plane MON and the front view of a point A in the
  plane. Determine the side view

n
n
m
m
aF x
oF
oP
48
Solution
n
n
m
Y
m
Y
aF x
aPx
X
X
oF
oP
49
Lines in Planes
b
g
c
aH
e
b
aF
c
e
Complete the front view
50
Lines in Planes
b
x
g
c
aH
e
b
aF
x
g
c
e
51
Principal Lines in Planes
52
Frontal Line
All frontal lines in the same plane are parallel
unless the plane it self is frontal
53
Horizontal or Level Lines
54
Horizontal or Level Lines
All horizontal lines in the same plane are
parallel unless the plane it self is horizontal
55
Profile Line
56
Profile Line
All profile lines in the same plane are parallel
unless the plane it self is profile
57
Locus

• The Locus is the path of a point, line or curve
  moving is some specified manner.
• Or it is the assemblage of all possible positions
  of a moving point, line or curve
• The locus of a point moving in a plane with a
  specified distance from another point is circle.

58
Locus

• Problem in the given plane ABC locate a point K
  that lies 6 mm above horizontal line AB and 5 mm
  in front of frontal line AC. Scale full size

59
Solution
h
c
aH
K
f
f
h
b
c
f
h
h
K
aF
b
f
60
Pictorial Intersection
A
B
H
D
N
E
C
K
M
Tow principles to solve the problem
1) Lines in a single plane must either be
parallel or intersect.
2) If tow planes are parallel, any lines on the
planes in question are parallel.
61
Pictorial Intersection
62
Pictorial Intersection
63
Chapter 5

• Successive Auxiliary Views

64
Construction of successive Auxiliary Views

• Step 1 Establish the line of sight.
• Step 2 Introduce the necessary folding
• lines.
• Step 3 transfer distance to the new view.
• Step 4 Complete view.

65
Point View of a Line

• A line will appear in point view if the line of
  sight is parallel to the line in space..
• In the drawing sheet, the line of sight should be
  parallel to the true length of the line.

66
Point View of a Line
2
b
a2
ah
b
H
a1,b
F
b
T.L.
Point View (P.V)
aF
1
67
Problem I

• Find the true clearance between the point O and
  the line AB.

b
a2,b
1
Clearance
o
b
o
T.L.
ah
2
H
o
F
ah
aF
b
o
68
Edge View of a Plane

• A plane will appear in edge view in any view for
  which the line of sight is parallel to the plane.
• In the drawing sheet, a plane will appear in edge
  view in any view for which the line of sight is
  parallel to a true length line in the plane.

69
Edge View of a Plane
c
c
h
ah
E.V.
b
a
H
b
F
c
h
b
T.L.
1
aF
70
Normal Views of a Plane

• A normal view or TRUE SIZE and shape of a plane
  is obtained in any view for which the line of
  sight is perpendicular to the plane.
• In the drawing sheet the line of sight appear
  perpendicular to the Edge View of the plane.

71
Edge View of a Plane
c
2
c
h
ah
E.V.
Normal View T.S.
b
a
H
b
F
c
h
b
T.L.
1
aF
72
Uses of Auxiliary and additional Views
Use Position of line of sight Position of line of sight
Use In space On the drawing sheet
1) True length of line (TL) Perpendicular to line Perpendicular to any view of the line or directed to a point view of the line
2) Point view of line Parallel to line Parallel to the true length of the line
3) Edge view of plane (EV) Parallel to plane Parallel to true length of line in plane OR directed toward a true size view of plane
4) Normal or true size view of plane (TS) Perpendicular to plane Perpendicular to edge view of plane
73
problem

• Find the front and top views of a 2.5m radius
  curve joining tow intersecting lines BA BC.

74
b
a
f
b
c
c
a
c
c
b
b
f
TL
a
a
75
b
a
2
1
3
5
4
f
3
4
b
c
5
2
c
1
a
c
c
1
1
2
2
b
3
b
3
f
TL
4
4
5
5
a
a
76
Chapter 6

• Piercing Points

77
Piercing point

• The intersection of a line with a plane is called
  Piercing Point.
• If the line is not in or parallel to a plane, it
  must intersect the plane.

78
Piercing point - Auxiliary View Method
1.
e
b1,c
p
c
e
TL
a
bH
g
p
g
a
a
e
g
p
c
bF
79
Piercing point- Tow View Method

• A piercing point could be found using the given
  views as follows (see the following Fig.)
• Any convenient cutting plane containing line EG
  is introduced, it appears EV in a principal view.
  
• The line of intersection between the tow planes
  is determined.
• Since line EG and line 1 - 2 both lies in the
  cutting plane they intersect, locating point P.
• Since line 1 2 also lies in Plane ABC, point P
  is the required Piercing Point.

80
Piercing point- Tow View Method
A
Vertical cutting plane N
1
E
P
G
C
2
B
81
Piercing point- Tow View Method
a
e
1
p
Vertical cutting plane N
c
2
bH
g
a
1
e
p
g
c
bF
2
82
Chapter 7

• Intersection of Planes

83
Intersection of Planes

• Any tow planes either parallel or must intersect.
  
• Even the intersection beyond the limits of
  planes.
• The intersection of planes result a line common
  to both of them.

84
Intersection of Planes Auxiliary view Method
bH
e
x
k
z
b1
a
y
f
k
e
g
J
x
c
y
a
j
a
c
k
g
c
e
x
z
y
f
J
g
bF
85
Intersection of Planes Auxiliary view Method
bH
e
k
z
bH
a
y
k
e
g
J
x
c
y
a
j
a
c
k
c
g
e
z
y
J
g
bF
86
Intersection of Planes Tow View - Piercing point
Method
b
b
d
d
a
a
x
x
g
g
y
y
eF
eP
cF
cP
87
Intersection of Planes Tow View - Piercing point
Method
E.V.
b
b
d
d
L1
L1
2
2
a
a
x
x
E.V.
1
1
g
g
4
y
y
4
3
3
eF
eP
cF
cP
88
Intersection of Planes Tow View - Piercing point
Method
b
b
d
d
a
a
g
g
eF
eP
cF
cP
89
Intersection of Planes Cutting Plane Method
Line of intersection
m
c
H1
P1
3
2
1
4
H2
7
6
P2
5
8
b
n
a
o
90
Intersection of Planes Cutting Plane Method
cH
m
P1
2
4
1
3
6
P2
7
8
b
nH
o
LI
5
a
cF
m
1
2
EV of HI
4
P1
3
EV of H2
8
5
6
7
P2
o
a
b
nH
LI
91
Pictorial Intersection Of Planes
n
3
a
d
s
c
k
b
e
2
m
o
92
Pictorial Intersection Of Planes
n
3
a
v
c
k
b
2
m
93
Chapter 8

• Angle between Planes

94
Angle between Planes
B
?
m
?
n
E.V. of m
E.V. of n
A
P.V. of line of intersection AB
Line of sight
95
Dihedral Angle Line of Intersection given
g
A
eH
B
e1
A
TL LI
eF
g
B
LI
e2g
E.V. of A
?
E.V. of B
g
96
Dihedral Angle Line of Intersection is NOT given
a
n
4
o
x
3
2
m
kH
y
bH
c
1
a
o
n
EV.1
3
4
x
bF
2
EV.2
y
m
1
kF
c
97
Dihedral Angle Line of Intersection is NOT given
b2
a
n
o
X,y
x
?
c
m
n
kH
y
m
bH
c
a
x
o
b1
a
n
TL
o
n
x
y
k1
bF
m
y
m
kF
c
c
98
Dihedral Angle Line of Intersection is NOT given

• Alternative solution You can find the Edge View
  for both planes without resorting to find the
  line of intersection.
• See next slide

99
Dihedral Angle Line of Intersection is NOT given
Both Planes will Appear EV.
a
b2
n
a
o
TS
m
kH
o
bH
c
c
n
TL
k2
3
a
o
n
m
2
bF
TL
m
n
kF
c
m
o
k1
EV
a
b1,c
1
100
Angle between Oblique Plane and Principal Plane
EV of frontal plane
b
aH
f
c
H
F
1
F
c
a1
b
?f
c
f
TL
b
aF
Angle between plane and frontal plane
101
Angle between Oblique Plane and Principal Plane
b
aH
c
H
F
P
1
c
c
TL
b
b
f
f
aF
b
aP
EV of Profile plane
?P
c
a1
Angle between plane and Profile plane
102
Angle between Oblique Plane and Principal Plane

• Angle between a plane and a horizontal plane can
  be measured in the similar fashion.
• The angle between sloping plane and a horizontal
  plane is called DIP ANGLE.

103
Angle between Oblique Plane and Principal Plane
1
aH
b
?H
b
aH
c
TL
f
c
H
F
c
f
b
aF
Angle between plane and horizontal plane
104
Chapter 9

• Parallelism

105
Parallel Lines

• Oblique Lines that appears parallel in tow or
  more principal views are parallel in space.

106
Parallel Lines
d
b
c
aH
H
P
F
aP
aF
b
b
c
c
d
d
107
Parallel Lines
c
b
d
aH
H
P
F
F
aF
aP
b
b
c
d
d
c
108
Principal Line

• Tow horizontal, tow frontal, or tow profile lines
  that appears to be parallel in tow principal
  views may or may not be parallel in space.
• non intersecting, non parallel lines are called
  SKEW LINES.

109
Parallel Lines
aH
X a1b
e c X
b
1
X c
P
H
P
F
F
aF
aP
X c
X c
b
b
110
Parallel Lines
aH
X e
X a1b
e c X
b
D2
1
X c
P
D1
H
P
F
F
D1
D2
aF
aP
e X
X e
X c
X c
b
b
111
Parallel Planes
n
c
mH
f
b
aH
o
H
1
F
o
aF
b
a1
o
b
c
TL
f
mF
c
m1
n
n
112
Parallel Planes

• If tow planes are parallel, any view showing one
  of the planes in edge view must also show the
  other plane as parallel edge view.
• Parallel edge views prove that planes are
  parallel.

113
Lines parallel to planesPlanes parallel to lines

• If tow lines are parallel, any plane containing
  one of the lines is parallel to the other line.
• A line may be drawn parallel to a plane by making
  it parallel to any line in the plane.

114
Lines parallel to planesPlanes parallel to lines
o
y
r
m
x
q
p
q
x
m
o
y
p
r
115
Chapter 10

• Perpendicularity

116
Perpendicular Lines

• If a line is perpendicular to a plane, it is
  perpendicular to every line in the Plane.

e
y1
g
90
90
y
f
j
x1
x
Perpendicular lines are not necessarily
intersecting lines and they do not
necessarily Lie in the same plane.
117
Perpendicular Lines

• If tow lines are perpendicular, they appear
  perpendicular in any view showing at least one of
  the lines in true length.
• If tow lines appear perpendicular in a view, they
  are actually perpendicular in space if at least
  one of the lines is true length in the same view.
  

118
Perpendicular Lines
H
n
1
s
m
o
n
s
o
H
F
TL
o
n
s
m
m
119
Plane Perpendicular to LineTow-View Method

• A plane is perpendicular to a line if the plane
  contains tow intersecting lines each of which is
  perpendicular to the given line.

120
Plane Perpendicular to LineTow-View Method
y
h
TL
z
x
f
H
x
F
h
z
TL
z
f
y
xf
EV
h
F
TL
1
y
121
Plane Perpendicular to LineAuxiliary-View Method
y
h
k
z
x
H
h
x
F
z
k
z
y
x
EV
F
k
h
TL
1
y
122
Line Perpendicular to PlaneTow-View Method

• A line perpendicular to a plane is perpendicular
  to all lines in the plane.

123
Line Perpendicular to PlaneTow-View Method
n
a
h
f
TL
o
m
k
H
F
o
a
TL
k
m
h
f
k
n
124
Line Perpendicular to PlaneAuxiliary-View Method
n
a
TL
EV
n
m
a
k
h
TL
o
o
m
H
k
o
F
a
k
m
h
k
n
125
Common Perpendicular Point View Method

• The shortest distance from a point to a line is
  measured along the perpendicular from the point
  to a line.
• The shortest distance between tow skew lines is
  measured by a line perpendicular to each of them.
  

126
Common Perpendicular Point View Method
c
b
e
1
2
a
e
H
e
ab x
b
TL
F
c
a
e
a
c
c
b
127
Common Perpendicular Point View Method
c
b
x
e
1
y
2
a
e
x
TL
H
e
ab x
x
b
TL
F
c
a
y
e
x
a
y
c
c
b
128
Common Perpendicular Plane Method

• Another method to find the shortest distance
  between skew lines, specially when the
  perpendicular view are not required.

129
Common Perpendicular plane Method
1
c
b
Shortest Distance
x kh
k
EV
TL
c
b
h
e
e
a
H
a
F
e
a
h
k
c
b
130
Shortest line at specified Grade connecting Tow
Skew Lines
1
c
h
TL
c
p
e
EV
x ph
b
b
a
e
H
Shortest Horizontal Distance
F
b
h
a
c
p
h
a
e
131
Shortest line at specified Grade connecting Tow
Skew Lines
1
c
h
TL
c
p
e
EV
x ph
b
b
100
a
e
H
F
b
h
a
15
c
p
h
a
e
132
Projection of line on a Plane

• The projection of a point on a plane is the point
  in which a perpendicular from the point to the
  plane pierces the plane.

133
Projection of line on a Plane
a
a
m
m
1
ap
ap
TL
b
b
n
n
a
bp
bp
h
h
b
TL
o
o
ev
F
o
P
m
bp
ap
n
134
Second exam Solution
A
1
E
P
G
C
2
B
135
o
2
1
b
k
X v
3
a
4
n
m
o
k
2
b
X v
1
a
4
3
m
n