Projections of Lines : Lecture No 01

1. Unit No:03
Projections of Points & Lines
Yash B. Parikh
M.Tech. (CIM)
Assistant Professor
Department of Mechanical Engineering
Symbiosis Institute of Technology

2. 2
What is a point????
Prof. Yash Parikh

3. 3
What is a point????
A French word meaning "dot, point, period (the punctuation
mark)”
 When you puncture something, you use a sharp object to make a
tiny hole in it.
 That tiny hole, especially from a distance, looks like a dot, so a
point is a dot.
 In mathematics a point is assumed to be dimensionless, but of
course any physical representation of a point must be of some
size.
 A point is often represented in textbooks by the smallest of all
printing symbols, the period.
 In fact printers' type sizes are measured in units called points.
Prof. Yash Parikh

4. 4
Introduction
 Point, together with line, is a basic concept of elementary
geometry.
 You can't get too wrong if you say that point is a mere location,
location without width, breadth or length.
 It makes no point to give a definition without a purpose.
Prof. Yash Parikh

5. 5
Introduction
 It is practically impossible to define point without mentioning
the joints that may go between the points.
 And this is how we come around to talking about points and -
simultaneously - lines.
”It takes line to know point -- and vice versa.”
The common practice is to leave the terms point and line
undefined but just start using them in the first principles:
1. There is a single line through two points.
2. There is a single point at the intersection of two lines.
Prof. Yash Parikh

6. 6
Principal Planes of Projections
 The principal planes of projections are:
Prof. Yash Parikh

7. 7
Positions of a Point
Prof. Yash Parikh

8. 8
Notations of a Point
 Following Notations should be followed while naming different
views in orthographic projections.
Prof. Yash Parikh
IT’S FRONT VIEW a’ a’ b’
OBJECT POINT A LINE AB
IT’S TOP VIEW a a b
IT’S SIDE VIEW a” a” b”

9. 9
Positions of a Point
1. Point is above H.P. & in front of V.P.
2. Point is above H.P. & behind V.P.
3. Point is below H.P. & behind V.P..
4. Point is below H.P. & in front of V.P.
5. Point is in H.P. & in front of V.P.
6. Point is in H.P. & behind V.P.
7. Point is above H.P. & in V.P.
8. Point is below H.P. & in V.P.
9. Point is in both H.P. & V.P.
Prof. Yash Parikh

10. 10
HP
VP
a’
a
A
POINT A IN
1ST QUADRANT
OBSERVER
VP
HP
POINT A IN
2ND QUADRANT
OBSERVER
a’
a
A
OBSERVER
a
a’
POINT A IN
3RD QUADRANT
HP
VP
A
OBSERVER
a
a’
POINT A IN
4TH QUADRANT
HP
VP
A
Point A is
Placed In
different
quadrants
and it’s Fv & Tv
are brought in
same plane for
Observer to see
clearly.
Fv is visible as
t is a view on
VP. But as Tv
is a view on Hp,
t is rotated
downward 900,
n clockwise
Direction (in 1st
quadrant).The
n front part of
Hp comes below
xy line.
The HP behind the
Vp is also rotated
clockwise, and
herefore
comes above the xy
ine.
Observe and
note the
process.
Convention: Horizontal plane is always rotated clockwise

11. 11
PROJECTIONS OF A POINT IN THE 4 QUADRANTS
HP
VP
POINT IN 2nd QUADRANT
VPHP
PT
PF
HP
VP
POINT IN 3rd QUADRANT
HP
VP
POINT IN 4th QUADRANT
VP VP
HP
HP
PT: TOP VIEW
PF: FRONT VIEW
PF
PT
PF
HP
VP
POINT IN 1st QUADRANT
VP
HP
PT
PF
PT
P
P
P
P

12. 12
How you will draw on the sheet
POINT IN 2nd QUADRANT
PT
PF
POINT IN 3rd QUADRANT POINT IN 4th QUADRANT
PT: TOP VIEW
PF: FRONT VIEW
PF
PT
PF
POINT IN 1st QUADRANT
PT
PF
PT
y
y
y
y
xx
xx

13. 13
A
a
a’
A
a
a’
A
a
a’
X
Y
X
Y
X
Y
For Tv
For Tv
For Tv
POINT A ABOVE HP
& INFRONT OF VP
POINT A IN HP
& INFRONT OF VP
POINT A ABOVE HP
& IN VP
PROJECTIONS OF A POINT IN FIRST QUADRANT.
ORTHOGRAPHIC PRESENTATIONS
OF ALL ABOVE CASES.
X Y
a
a’
VP
HP
X Y
a’
VP
HP
a X Y
a
VP
HP
a’
Fv above xy,
Tv below xy.
Fv above xy,
Tv on xy.
Fv on xy,
Tv below xy.

14. 14
Problem on Projections of Point
Question: 01
Draw the projections of the following points on a common XY line.
Keep the distance between two consecutive projectors as 20 mm;
# A, 30 mm above the HP and 40 mm in front of VP.
# B, 80 mm above the HP and 40 mm behind the VP.
# C, 30 mm below the HP and 40 mm behind the VP.
# D, 30 mm below the HP and 40 mm in front of the VP.
# E, in the HP and 40 mm behind the VP.
# F, in the VP and 40 mm below the HP.
# G, in both the HP and VP.
Prof. Yash Parikh

15. 15
Thank You
Prof. Yash Parikh