1. Descriptive Geometry Eng. 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
By Arch. Areej Afeefy

3. projections Two common types of projections:
1) perspective projections (used by architects or artists)
2) orthographic projections (perpendicular to the object)

4. Perspective Projection
Screen
Human eye

5. Orthographic Projection
Screen

6. Orthographic Projection
Horizontal
Front
Profil

7. Horizontal
Profil
Front

8. Principal Views

9. Draw the profile

10. 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

11. Primary Auxiliary Views
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 1
Step 4: determine visibility and
complete view 1 D2 D1 D y h d g k1 e D2 c y f a
f,e
g,h D1 b
b,a
c,d

12. All views projected from top view has the same height dimension

13. Primary Auxiliary Views

14. View 1 is an auxiliary view projected from the front View

15. All the views projected from front view have the same depth dimension

17. Edge View of a plane

25. Chapter 3: LINES

28. Frontal Line

29. Frontal Line

30. 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.

31. Level (Horizontal) Line

32. Level Line

33. Profile Line

34. Profile Line

35. True Length of an Oblique Line

36. True Length of an Oblique Line

39. Bearing , Slope, and GradeaH aH
S55oE 55 b b
Bearing: a term used to describe the direction of a line on
the earth’s surface

40. Azimuth Bearing N aH aH
125o
N125o b b

41. 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

42. D1 b 1
20o H
160 m N b
N 60o a1 D1 ah H F D1 D1 aF b

45. Grade
Grade: another way to describe the inclination of a line from the horizontal
Plane

46. Grade

49. Chapter 4
Planes

50. Points and lines in Planes

51. 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

52. Solution n n m Y m Y
aF x
aPx X X oF oP

53. Lines in Planes b g c aH e b aF c e
Complete the front view

54. Lines in Planes b x g c aH e b aF x g c e

55. Principal Lines in Planes

56. Frontal Line
All frontal lines in the same plane are parallel unless the plane it self is frontal

57. Horizontal or Level Lines

58. Horizontal or Level Lines
All horizontal lines in the same plane are parallel unless the plane it self is horizontal

59. Profile Line

60. Profile Line
All profile lines in the same plane are parallel unless the plane it self is profile

61. 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.

62. 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

63. Solution h c aH K
5 mm f f h b c f h h K
6 mm aF f b

64. Pictorial IntersectionB H D N E C K M
Two principles to solve the problem:
1) Lines in a single plane must either be parallel or intersect.
2) If two planes are parallel, any lines on the planes in question are parallel.

65. Pictorial Intersection

66. Pictorial Intersection

67. Successive Auxiliary Views
Chapter 5
Successive Auxiliary Views

68. 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.

69. 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.

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

71. Problem I Find the true clearance between the point O and the line AB.1
a2,b
Clearance b o o ah
T.L. 2 H o F aF ah b o

72. 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.

73. Edge View of a Plane c c h ah
E.V. b a H F b c h b
T.L. 1 aF

74. 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.

75. Edge View of a Plane c 2 c h E.V. ah b a H b F c h b T.L. 1 aF
Normal View
T.S. b a H F b c h b
T.L. 1 aF

76. Uses of Auxiliary and additional Views
Position of line of sight
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

77. problem
Find the front and top views of a 2.5m radius curve joining two intersecting lines BA & BC.

78. b a f b c c a c c b b TL f a a

79. b a 2 1 3 5 4 3 f 4 b c 2 5 c 1 a c c 1 1 2 2 b 3 b 3 TL f 4 4 5 5 a a

80. Chapter 6
Piercing Points

81. 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.

82. Piercing point - Auxiliary View Method1. e
b1,c c p e TL bH a p g g a a e p g c bF

83. Piercing point- Two 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 two planes is determined.
Since line EG and line 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.

84. Piercing point- Two View MethodA
Vertical cutting plane N 1 E P G C 2 B

85. Piercing point- Two View Methoda e 1 p c
Vertical cutting plane N 2 bH g a 1 e p g c bF 2

86. Intersection of Planes
Chapter 7
Intersection of Planes

87. Intersection of Planes
Any two 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.

88. Intersection of Planes Auxiliary view MethodbH e x k z a b1 f y k e g J x c a y j a c k g e c x z y f J g bF

89. Intersection of Planes Auxiliary view MethodbH e k z a bH y k e g J x c a y j a c k c g e z y J g bF

90. Intersection of Planes Two View - Piercing point Methodb b d d a a x x g g y y eF eP cF cP

91. Intersection of Planes Two View - Piercing point Methodb
E.V. b d d L1 L1 2 a 2 a x x
E.V. 1 1 g g 4 y y 4 3 3 eF eP cF cP

92. Intersection of Planes Two View - Piercing point Methodb b d d a a g g eF eP cF cP

93. Intersection of Planes Cutting Plane Method
Line of intersection m c H1 P1 2 3 1 4 H2 6 7 P2 5 b 8 n a o

94. Intersection of Planes Cutting Plane MethodcH m P1 2 1 3 4 6 P2 7 8 b nH LI o 5 a cF m 1 2
EV of HI P1 4 3 5 6 8
EV of H2 a P2 7 o b nH LI

95. Pictorial Intersection of Planes3 a d s c k b e m 2 o

96. Pictorial Intersection Of Planes3 a v c k b m 2

97. Chapter 8
Angle between Planes

98. Angle between Planes B θ m E.V. of m θ n E.V. of n A
P.V. of line of intersection AB
Line of sight

99. Dihedral Angle Line of Intersection giveneH B e1 A
TL LI eF g B LI
e2g
E.V. of A
E.V. of B θ g

100. Dihedral Angle Line of Intersection is NOT given4 o x 3 2 m kH y bH c 1 a
EV.1 o n 3 4 x bF
EV.2 2 y m 1 kF c

101. Dihedral Angle Line of Intersection is NOT givenb2 a n o
X,y x m c θ kH n y bH m c a x o b1 a n TL o n x y k1 bF m y m kF c c

102. 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

103. Dihedral Angle Line of Intersection is NOT given
Both Planes will
Appear EV. a b2 n o a TS m kH o bH c c k2 TL n 3 a o n m 2 bF TL m kF n c m o k1 EV a
b1,c 1

104. Angle between Oblique Plane and Principal Plane
EV of frontal plane b aH f c H F 1 F c a1 b θf c f TL b aF
Angle between plane and frontal plane

105. Angle between Oblique Plane and Principal PlaneaH c H F P 1 c c TL b b aF f f b aP
EV of Profile plane θP c a1
Angle between plane and Profile plane

106. 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.

107. Angle between Oblique Plane and Principal Plane1 aH b b θH aH TL c f c H F c f b aF
Angle between plane and horizontal plane

108. Chapter 9
Parallelism

109. Parallel Lines
Oblique Lines that appears parallel in two or more principal views are parallel in space.

110. Parallel Lines d b c aH H P F aF aP b b c c d d

111. Parallel Lines c b d aH H F F P aF b aP b c d d c

112. Principal Line
Two horizontal, two frontal, or two profile lines that appears to be parallel in two principal views may or may not be parallel in space.
non intersecting, non parallel lines are called SKEW LINES.

113. Parallel Lines aH
X a1b
e c X b 1
X c P H F F P aF aP
X c
X c b b

114. Parallel Lines aH X e X a1b e c X b D2 1 X c P D1 H F F P aF D1 D2 aP

115. Parallel Planes n c mH f b aH o H 1 F o b aF a1 o b TL c mF f c m1 n n

116. Parallel Planes
If two 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.

117. Lines parallel to planes Planes parallel to lines
If two 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.

118. Lines parallel to planes Planes parallel to linesy r m x q p x q m o y p r

119. Chapter 10
Perpendicularity

120. 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.

121. Perpendicular Lines
If two lines are perpendicular, they appear perpendicular in any view showing at least one of the lines in true length.
If two 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.

122. Perpendicular Lines n H 1 s m o n s H o F o TL n s m m

123. Plane Perpendicular to Line Two-View Method
A plane is perpendicular to a line if the plane contains two intersecting lines each of which is perpendicular to the given line.

124. Plane Perpendicular to Line Two-View Methody h TL z x f H F x h z TL z f y xf EV F h TL 1 y

125. Plane Perpendicular to Line Auxiliary-View Methodk z x H h F x z k z y x EV F k h TL 1 y

126. Line Perpendicular to Plane Two-View Method
A line perpendicular to a plane is perpendicular to all lines in the plane.

127. Line Perpendicular to Plane Two-View Methodf TL o m k H F o a TL k m h f k n

128. Line Perpendicular to Plane Auxiliary-View MethodTL EV n m a k h TL o o m H k F o a k m h k n

129. 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 two skew lines is measured by a line perpendicular to each of them.

130. Common Perpendicular Point View Methodb e 1 2 a e H e
ab x b F TL a c a e c c b

131. Common Perpendicular Point View Methodb x e 1 y 2 a e x TL H e
ab x x b F TL a c y a x e c y c b

132. Common Perpendicular Plane Method
Another method to find the shortest distance between skew lines, specially when the perpendicular view are not required.

133. Common Perpendicular plane Method1 c
x kh
Shortest Distance b k EV TL c h b e e a H a F a e h k c b

134. Shortest line at specified Grade connecting Two Skew Lines1 c h TL p c e EV b
x ph b a e H
Shortest Horizontal Distance F b h a c h p a e

135. Shortest line at specified Grade connecting Two Skew Lines1 c h TL p c e EV b
x ph b a
100 e H F b h a c 15 h p a e

136. 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.

137. Projection of line on a Planem m 1 ap ap TL b b n n a bp bp h h b TL o o ev F P o m bp ap n

138. o 2 1 b k
X v 3 a 4 n m k 2 o b
X v 1 a 4 3 m n