The document describes different types of projections of points and lines in space. There are 9 types of point projections depending on whether the point lies in one of the 4 quadrants, or on one of the planes. Line projections can be parallel to two planes and perpendicular to the third, inclined to one plane and parallel to the other, or inclined to both planes. Examples of problems involving drawing the projections of lines in various orientations are presented.

1. Projection of Points
• There are basically nine type of projections of point is space :
1. In FIRST Quadrant (Above H.P. , In front of V.P.)
2. In SECOND Quadrant (Above H.P. , Behind V.P.)
3. In THIRD Quadrant (Below H.P. , Behind V.P.)
4. In FOURTH Quadrant (Below H.P. , In front of V.P.)
5. In PLANE (On V.P. , Above H.P.)
6. In PLANE (On H.P. , Behind V.P.)
7. In PLANE (On V.P. , Below H.P.)
8. In PLANE (On H.P. In front of V.P.)
9. In PLANE (On both H.P. & V.P.)

2. V.P.
H.P.
.
.
.
.
.
X
Y
a1’
A1
a1
a1’
a1
Y
X
X
Y
A1- Point
a1’- F.V.
a1 - T.V.
(3D)
(2D)
In 3D In 2D
Above H.P. Front View Above Reference Line
In front of V.P. Top View Below Reference Line
Position 1

3. H.P.
V.P.
.
.
.
.
.
(3D)
(2D)
X
Y
X Y
A2
a2
a2’
a2
a2’
A2- Point
X
a2’- F.V.
Y a2 - T.V.
In 3D In 2D
Above H.P. Front View Above Reference Line
Behind V.P. Top View Above Reference Line
Position 2

4. a3
A3
a3’
X
Y
.
.a3
a3’
X
Y
X Y
(2D)
(3D)
A3- Point
a3’- F.V.
a3- T.V.
.
.
.
In 3D In 2D
Below H.P. Front View Below Reference Line
Behind V.P. Top View Above Reference Line
Position 3

5. A4
a4
.
a4’
.
a4’
X
Y
X
Y
X Y
.
(2D)
(3D)
A4- Point
a4’- F.V.
a4- T.V.
.
.
a4
In 3D In 2D
Below H.P. Front View Below Reference Line
In front of V.P. Top View Below Reference Line
Position 4

6. H.P.
H.P. V.P.
.
.
.
.
Y
X
a5’
A5
a5
a5’
a5
X Y
A5
X
Y
(3D)
(2D)
A5- Point
a5’- F.V.
a5 - T.V.
In 3D In 2D
Above H.P. Front View Above Reference Line
On V.P. Top View On Reference Line
Position 5

7. .
X
Y
X
Y
A6
a6
a6’
a6’
.
X Y
(2D)
a6
.
A6
(3D)
.
A6- Point
a6’- F.V.
a6- T.V.
In 3D In 2D
Below H.P. Front View Below Reference Line
On V.P. Top View On Reference Line
Position 6

8. A7
.
.
A7
a7
a7’
X
Y
Y
X
(3D)
(2D)
Y
X
A7 Point
.
.
a7’- F.V.
a7’
a7
a7 - T.V.
In 3D In 2D
On H.P. Front View On Reference Line
In Front of V.P. Top View Below Reference Line
Position 7

9. A8
.
.
Y
X
Y
X
A8
a8
a8’
X Y
(3D)
(2D)
a8
.
.a8’
A8- Point
a8’- F.V.
a8 - T.V.
In 3D In 2D
On H.P. Front View On Reference Line
Behind V.P. Top View Above Reference Line
Position 8

10. V.P.
H.P.
(3D)
(2D)
X
Y
Y
X
.
A9
A9- Point
X
a9’
a9’- F.V.
.a9’
a9
a9
A9
a9 - T.V.
Y
In 3D In 2D
On H.P. Front View On Reference Line
On V.P. Top View On Reference Line
Position 9

11. Projection Of Lines
• A straight line is the shortest distance between two
points.
• Top views of two end points of a straight line, when
joined, give the top view of the straight line.
• Front views of the two end points of a straight line,
when joined, give the front view of the straight line.
• Both the above projections are straight lines.

12. Notations for : Projection Of Lines
• True length of the line:
Denoted by Capital letters. e.g. AB=100 mm, means that true length of the
line is 100 mm.
• Front View Length:
Denoted by small letters. e.g. a’b’=70 mm, means that Front View Length
is 70 mm.
• Top View Length:
Denoted by small letters. e.g. ab=80 mm, means that Top View Length is
80 mm.
• Inclination of True Length of Line with H.P.:
It is denoted by θ. e.g. Inclination of the line with H.P. (or Ground) is given
as 30º means that θ = 30º.

13. Notations for : Projection Of Lines
• Inclination of True Length of Line with V.P.:
It is denoted by Φ. e.g. Inclination of the line with V.P. is given as 40º
means that Φ = 40º.
• Inclination of Front View Length with XY :
It is denoted by α. e.g. Inclination of the Front View of the line with XY is
given as 50º means that α = 50º.
• Inclination of Top View Length with XY :
It is denoted by β. e.g. Inclination of the Top View of the line with XY is
given as 30º means that β = 30º.
• End Projector Distance:
It is the distance between two projectors passing through end points of
F.V. & T.V. measured parallel to XY line.

14. Projection Of Lines
There are cases of projections of line :-
1.Line Parallel to two Planes and Perpendicular
to the third plane.
2.Line Inclined to one Plane and Parallel to
another
3.Line Inclined to both the Planes.

15. X Y
H.P.
V.P.
a b
a’ b’
Fv
TV
Position 1: Parallel to two planes & perpendicular to the other
P.P.
.
H.P.
V.P.
Y
X
B
A
a’
b’
b
a
b”
a”
z x
Y
a’’ b’’
P.P.
In 3D In 2D
Parallel to H.P. Front View – Parallel line to reference line
Parallel to V.P. Top View – Parallel Line to reference line
Perpendicular to P.P. Side View – Point on the side of front view

16. X
Y
V.P.
A
B
b’
a’
b
a
θ
θ
F
.
V
.
T.V.
X Y
H.P.
V.P.
F.V.
T.V.
a b
a’
b’
θ
True Length
Position 1: Parallel to one plane and inclined to the other
In 3D In 2D
Inclined to H.P. Front View – Line inclined by to reference line
Parallel to V.P. Top View – Parallel Line to reference line
θ

17. H.P.
V.P.
X
Y
a b
a’
b’


Y
X
B
A
X Y
α
β
H.P.
V.P.
a
b
FV
TV
a’
b’
Position 1: Inclined to both the planes
In 3D In 2D
Inclined to H.P. Front View – Line inclined by to reference line
Parallel to V.P. Top View – Line inclined by to reference line
α
β

18. Problem 1 : A line PJ, 50 mm long is perpendicular to H.P. & t is below H.P.
Point P is on H.P. & 30 mm behind V.P. Draw projections of line PJ.
50
30
j’
j
p
p’
50
50
30
30
pj
p’
j’
X Y

19. Problem 2 :A line MJ, 35 mm long, is perpendicular to the profile plane. The
end M is 20 mm below H.P., 30 mm behind V.P. Draw projections on H.P. &
V.P.
j m
j’ m’
X Y
30
20
35
35
35
30
20
m’
j’
j
m

20. Problem 3 : A line KP, 70 mm long, is parallel to H.P. & inclined to V.P. by
60O
. Point P is 20 mm above H.P. and 30 mm in front of V.P. Point K is
behind V.P. Draw to projection of line KP.
k’
k
p’
p
X Y
20
70
6
0

21. 25
15
Φ
α
β
a’
a
b’ b1’
Y
X
b b2
θ
Locus of b’
Locus of b
Data Given :-
(1) T.L.=90 mm
(2) Θ =30°
(3) Φ =45°
(4) Point A
15 above H.P.
25 mm in Front of
V.P.
F.V.
T.V.
Answers :-
(1) F.V.= 64 mm
(2) T.V = 78 mm
(3)  = 45° (4)  = 55°
T.L.= 90
b2’
b1
.
.
.
.
Problem 4 : A Line AB, 90 mm long, is inclined to H.P. by 30° and
inclined to V.P. by 45º. The line is in first quadrant with Point A 15 mm
above H.P. and 25 mm in front of V.P. Draw the projection of line AB.