Projection of Lines

The shortest distance between two

points is called a straight line. The
projectors of a straight line are drawn
therefore by joining the projections of its
end points.
 VARIOUS ORIENTATIONS OF THE STRAIGHT LINES 2

Sl. Orientation/ Front view/ Top view/ plan Horizontal Vertical trace
No. Position of line Elevation trace

1 Line parallel to both True length, parallel True length, parallel Does not exist Does not exist
HP and VP to xy to xy
2 Line perpendicular to True length, Point Coincides with Does not exist
HP perpendicular to xy top view
3 Line perpendicular to Point True length, Does not exist Coincides with
VP perpendicular to xy front view
4 Line inclined at Ɵ to True length inclined Shorter than the true Exists Does not exist
HP and parallel to at Ɵ to xy length, parallel to xy
VP

5 Line inclined at Φ to Shorter than the true True length inclined Does not exist Exists
VP and parallel to length, parallel to xy at Φ to xy
HP

6 Line situated in HP Shorter than the true True length inclined Does not exist Exists on xy
and inclined at Φ to length, lying on xy at Φ to xy
VP

7 Line situated in VP True length inclined Shorter than the true Exists on xy Does not exist
and inclined at Ɵ at Ɵ to xy length, lying on xy

8 Line situated both in Both front and top views are true length and Does not exist Does not exist
HP and VP coincide on xy
 Projection of Lines

The possible projections of straight. lines with

respect to V.P and H.P in the first quadrant
are as follows:
I. Perpendicular to one plane and parallel to the other.

2. Parallel to both the planes

3. Parallel to one plane and inclined to the other.

4. Inclined to both the planes

I. Perpendicular to one plane and parallel to the other.
a. Line perpendicular to H.P and parallel to V.P
I. Perpendicular to one plane and parallel to the other.
b. Line perpendicular to v.p and parallel to H.P.
2. Line parallel to both the planes
3. Parallel to one plane and inclined to the other.
a. Line parallel to V.P and inclined to H.P.
3. Parallel to one plane and inclined to the other.
b- Line Parallel to H.P and Inclined to V.P.
4. Inclined to both the planes
 For TV For TV
A Line inclined to both
b’’ HP and VP b’’

B
B

 Y
Y
On removal of object a’´
a’’´ i.e. Line AB
FV as a image on VP.
TV as a image on HP, A
A 
 Y
Y a’ T.V. b’
a’ T.V. b’
V.P.
b’´
FV
a’´ 

Orthographic Projections Y Y
FV is seen on VP clearly. Note:-
To see TV clearly, HP is rotated Both FV & TV are inclined to
900 downwards, XY.
a’  (No view is parallel to XY)
Hence it comes below XY.
Both FV & TV are reduced
TV
lengths
H.P. b (No view shows True Length)
 Note the procedure
Orthographic Projections When FV & TV known,
Means FV & TV of Line AB How to find True Length.
are shown below, with their (Views are rotated to determine
apparent inclinations  &  True Length & it’s inclinations
with HP & VP).
V.P. V.P.
b’´ b1’´’
b’´
FV FV
TL
a’´  a’´ 

Y Y Y Y

a’  b2’
a’  TV

TV TV

H.P. b’ H.P. b’

In this sketch, TV is rotated

Here TV (ab) is not // to XY and made // to XY line.
line Hence it’s corresponding
Hence it’s corresponding FV FV, a’ b1’ is showing
a’ b’ is not showing True Length
True Length & &
True Inclination with HP. True Inclination with HP.
Obtaining True Length and Angles
 Note the procedure
When True Length is known,
How to locate FV & TV.
(Component a-1 of TL is drawn
which is further rotated
to determine FV)

V.P.
b’´ b1´’’


a’´  1´

Y Y

1
a’ Ø


Here a -1 is component
of TL ab1 gives length of FV.
Hence it is brought upto H.P. b’ b1’
Locus of a’ and further rotated
to get point b’. a’ b’ will be FV.
Similarly drawing component
of other TL (a’ b1‘) TV can be drawn.
 Relations Between Two Lines in Space

1- Parallel lines
2- Intersect lines
3- Un-intersect lines
1- Parallel lines
2- Intersect lines
3- Un-intersect lines