This document discusses the projection of straight lines. It defines projection of lines and notes that the top and front views of a straight line are also straight lines. It describes different positions a line can have with respect to the horizontal and vertical planes, including being perpendicular to one plane, parallel to one plane and inclined to both. Notations used for projecting lines are explained. Examples of different line positions are illustrated with diagrams. The concept of traces, where a line intersects the planes, is defined and important points regarding traces are provided.

1. Engineering Graphics
Projection of Lines
Submitted By:
Akabari Nirali(130130116002)
Bhut Vidhi(130120116013)
Bavasar Mausam(130120116012)

2. Projection of straight lines
Definition :
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.

3. Orientation of Straight Line in Space
• A line in space may be parallel, perpendicular or
inclined to either the H.P. or V.P. or both.
• It may be in one or both the reference Planes.
• Line ends may be in different Quadrants.
• Position of Straight Line in space can be fixed by various
combinations of data like distance of its end points from
reference planes, inclinations of the line with the
reference planes, distance between end projectors of the
line etc.

4. Notations used for Straight Line
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.

5. 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.

6. Line in Different Positions with
respect to H.P. & V.P.
CLASS A: Line perpendicular to (or in) one
reference plane & hence parallel to both the other
planes
(1) Line perpendicular to P.P. & (hence) parallel
to both H.P. & V.P.
(2) Line perpendicular to V.P. & (hence) parallel
to both H.P. & P.P.
(3) Line perpendicular to H.P. & (hence) parallel
to both V.P. & P.P.

7. Line in Different Positions with
respect to H.P. & V.P.
CLASS B: Line parallel to (or in) one
reference plane & inclined to other two
planes
(1) Line parallel to ( or in) V.P. & inclined to H.P.
by  .
(2) Line parallel to ( or in) H.P. & inclined to V.P.
by  .
(3) Line parallel to ( or in) P.P. & inclined to H.P.
by  & V.P. by  .

8. Line in Different Positions with
respect to H.P. & V.P.
CLASS C: Line inclined to all three reference
planes ( Oblique lines )
Line inclined to H.P. by  , to V.P. by  and also inclined to profile
plane.

9. Class A(1) : Line perpendicular to P.P. &
hence parallel to both the other
planes
Y
a”
P.P.
.
H.P.
V.P.
Y
X
B
A
a’
b’
b
a
b”
z x

10. Class A(1) : Line perpendicular to P.P. &
hence parallel to both the other
planes
X
Y
a’
V.P.
b’
H.P.
a
b

11. V.P.
H.P.
Y
X
a’,. b’
A
B
b
a
Y
Class A(2):Line perpendicular to V.P. &X (hence)
parallel to both the other Planes
(i.e. H.P. & P.P.)

12. Class A(2):Line perpendicular to V.P. &
(hence) parallel to both the other
Planes
a’, b’
X
Y
V.P.
H.P.
a
b
.

13. H.P.
Y X
.
V.P.
B
A
a,b
b’
a’
X
Y
Class A(3):Line perpendicular to H.P. &
(hence) parallel to both the other
Planes

14. Class A(3):Line perpendicular to H.P. &
(hence) parallel to both the other
Planes
b’
Y X
a.,b
V.P.
H.P.
a’

15. Class B(1): Line contained by ( or parallel
to) V.P. & inclined to H.P. by Ө
H.P.
V.P.
a’
b’
X
Y
a
b
X
Y
A
B
θθ

16. Class B(1): Line contained by ( or parallel to)
V.P. & inclined to H.P. by Ө
Y
X
V.P.
b’
a’
a
θθ b
H.P.

17. Class B(2) : Line parallel to (or contained by) H.P. &
V.P.
b’ a’ b’
H.P.
a’ A B
V.P.
H.P.
b=f
a b
a
b
X
Y
ø
X Y
b
X
Y
inclined to V.P. by 

18. Class B(3): Line parallel to (or contained by) P.P.,
inclined to H.P. by Ө & to V.P. by 
H.P.
V.P.
P.P.
Y
a’
b’
X
A
B
a”
 b”

Y
b
a


Z X

19. Class B(3): Line parallel to (or contained by) P.P.,
V.P.
H.P.
inclined to H.P. by Ө & to V.P. by 
P.P.


a’
b’
X Y
a
b
b”
a”

20. Class C:Line inclined to H.P. by θ & V.P.
by  ( i.e. Line inclined to both the
planes)
H.P.
V.P.
X Y
a b
a’
b’


Y
X
B
A

21. Class C:Line inclined to H.P. by Ө & V.P. by
 ( i.e. Line inclined to both the
planes)
V.P.
X Y
a
b

H.P.

a’
b’

22. TRACES OF A LINE
Definition: When a line is inclined to a plane, it will meet that
plane, produced if necessary. The point where the line or
line produced meets the plane is called trace.
Horizontal Trace: The point of intersection of the inclined line
with the H.P. is called Horizontal Trace or simply H.T.
Vertical Trace: The point of intersection of the inclined line
with the V.P. is called Vertical Trace or simply V.T.

23. V.P.
.
b’
a b
H.P.
.
V.P. a’
B
A
Y
X
Example to illustrate
the concept of traces


F.V.
T.V.
H.T.
h
v
V.T.

24. IMPORTANT POINTS REGARDING
TRACES OF A LINE
• If a line is inclined to both H.P. & V.P. then its
Front view, h’ and V.T. must be on the same
straight line.
e.g. if front view of a line AB is a’b’, then
h,a’,b’ and V.T. must be on a same straight
line.
• If a line is inclined to both H.P. & V.P. then its
Top view, v and H.T. must be on the same
straight line.
e.g. if Top View of a line AB is ab, then v, a, b
and H.T. must be on a same straight line.

25. IMPORTANT POINTS REGARDING
TRACES OF A LINE
(1) If a line is parallel to any of the plane, it has no trace
upon that plane.
e.g. If the line is parallel to
V.P.
horizontal plane then that
line will not meet H.P and
hence there will be no H.T.
and only V.T.
H.P.
a’,. b’
A
B
b
a
V.T.
Y

26. IMPORTANT POINTS REGARDING
TRACES OF A LINE
e.g. If the line is parallel to
Vertical Plane then that
line will not meet V.P and
hence there will be no V.T.
and only H.T.
V.P.
B
b’
Y X
H.P.
.
A
a,b
a’
H.T.