TA Lecture at Indian institute of technology kanpur of bachelor of technology or bachelor of science in first year.

1. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra

2. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
TA 101: Engineering Graphics
2023 - 24 Sem – I
Lecture 15 – Sept 27, 2023
Space Geometry
Lines and Planes – I
Sudhir Misra
Department of Civil Engineering
IIT Kanpur, Kanpur 208 016
2
Room No.: WLE 303 C;
Phone – 7346
E-mail: sud@iitk.ac.in

3. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
• Space geometry helps in describing or
specifying an object completely, on a drawing
sheet
• It helps in determining the ‘true shape’ and
‘true size’ of objects and various inter-
relationships among different parts of an
object
Space Geometry

4. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
In order to describe an object completely, one needs to be
able to perform one or more of the following tasks
– Find the ‘Point View’ (PV) of a line
– Find the ‘Normal View’ of a line
– Find the ‘True Length (TL)’ of a line
– Find the ‘Edge View (EV)’ of a plane
– Find the ‘Normal View’ of a plane
– Find the true size and shape of a surface
– Find angle between lines and planes
– Find clearance/spacing between ‘elements’ of an object
Space Geometry

5. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
• A ‘Point View’ of a line is that view, which
shows the line as a ‘single point’
• The ‘direction of sight’ is parallel to the line in
the PV
• Similarly, an ‘Edge View’ of a plane is that
view, which shows the plane as a ‘line’
• Clearly, the ‘direction of sight’ should be
parallel to the plane in an EV
Point View and Edge View

6. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
• The term ‘Normal’ means ‘perpendicular’ or
at ‘right angles’
• A Normal View is one in which the ‘direction
of sight’ is perpendicular to a line/plane
• The normal view of a line shows its TL
• The normal view of a plane shows its true
shape/ surface
• A Normal View may or may not be in one of
the principal orthographic views/projections
Normal View or True Shape

7. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
Given information of a
Point or Line in two views,
their projection in the third
should be possible !
Important
Observations:
Lines
TL
TL
TL
TL
TL
TL
TL?
TL?
TL?
TL?
TL?
Oblique Line

8. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
• How to get a normal view of an oblique line?
• The most general case in space geometry is to
locate the normal view of an oblique line
• Once the normal view of an oblique line has been
found, it is easy to determine its true length
• Every design requires knowledge about true length
of its parts
Normal View of An ‘Oblique Line’

9. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
AH BH
A
B
AF
BF
Frontal
Profile
Horizontal
Normal View
Concepts
Notice the distances
from the hinge lines for
Front and Profile views
AP
BP
d1
d2
d1
d2
d1
d2
d1
d2

10. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
AH BH
A
B
AF
BF
Frontal
Profile
Horizontal
Auxiliary View -
Concepts
The distances from
the hinge lines
remain the same
AP
BP
d1
d2
d1
d2
d1
d2
d1
d2
Take any auxiliary plane
perpendicular to the
horizontal plane

11. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
LINE
OF
SIGHT
AH BH
A
B
BA
AA
AF
BF
F
P
A
H
Normal/Auxiliary
View - Concepts
Notice the distances
from the hinge lines
d1
d2
d1
d2
TL
BA
AA
AA
BA

12. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
• Normal view of a line occurs when the line of sight
is perpendicular to the line
• Point view of a line occurs when the line of sight is
parallel to the line
• In a point view, the line appears as a single point
• Point views are very useful in solving many
problems in space geometry
• A point view may be obtained through the use of
the same four step procedure
Point view of a line

13. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
F
H
bH
bF
aH
aF
d aA1
bA1
Notice the
direction of
Projectors
Notice the
distance
Measurements
along Projectors
bA2
, aA2
Normal View and PV of Oblique Lines
Projected from the Top/Horizontal View
PV

14. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
STEP-1: Determine a plane parallel to the line. It is
perpendicular to one of the projections of the line. It is
equivalent to one walking around in space until desired
line of sight is obtained
STEP-2: Establish a new projection plane (called Auxiliary
Plane-1 or A1) perpendicular to the line of sight. It is
placed at a convenient distance parallel to the line
STEP-3: Project all points of the object (two points of the
oblique line in this case) into the new view (A1) using
the principals of orthographic projections
STEP-4: Locate points on the object (points A & B of an
oblique line) along the projections in auxiliary plane
4-Step Procedure for Normal View/True
Length of an ‘oblique line’

15. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
F
H
bH
bF
aH
aF
d aA1
bA1
Notice the
direction of
Projectors
Notice the
distance
Measurements
along Projectors
bA2
, aA2
Normal View and PV of an Oblique Line
Projected from the Top/Horizontal View
PV
d1
d1

16. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
H
F
P
BH
AH
BF
AF
AP
BP
AA1
BA1
AA2 ,BA2
Notice the
direction of
Projectors
Notice the
distance
Measurements
along Projectors PV
d
d
d1
d1
Normal & point view of Oblique Line
Projected from the Front View

17. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
H
F
EDGE VIEW OF HORIZONTAL CEILING
EDGE VIEW OF HORIZONTAL GROUND
Y=RISE
X=RUN
C
D
H
Slope of a Line CD
Slope = Rise/Run = (y/x) = tan (θH)
θH is ‘slope angle’ of line CD
Grade of line CD = 100 tan (θH ) %

18. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
• Slope, slope angle, and grade of a line are considered
‘positive’ if the line rises upward as one travels along it
from beginning to end
• Slope, slope angle, and grade of a line are considered
‘negative’ if one travels downward from beginning to end
• Slope of a line would be visible in which view?
• In a Vertical Normal View in which the line is seen in TL!
Slope of an oblique line

19. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
F
H
AF
BF
AH
BH
AA
BA
Slope of an Oblique Line
Slope of Line
= Rise/Run
= Y/X
= - 0.5
= - 50 % Slope

20. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
• Bearing is used by engineers, pilots, and sailors on maps for
specifying the alignment of a line in 2-D space (horizontal
plane).
• Bearing of a line is its deviation (in terms of angle) from North
or South.
• The deviation angle is always an acute angle (less than 90o).
• Bearing can be seen in a horizontal view only.
• Four special cases of bearing
N0oE - Due North N90oE – Due East
S0oW – Due South S90oW – Due West
Bearing of a line

21. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
W
N
E
S
N 300 E
N 600 W
S 450 W
C
D
B
A
How many different
bearings are there in this
figure?
3
Plus 4 basic directions
Bearing of a line

22. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
Azimuth of a Line
W
N
E
S
B
C
A
D
N 300
N 2250
N 3000
Azimuth of a line is an
alternative way to
express the bearing of a
line
Azimuth is always read
clockwise from the North
arrow and uses only the
letter N together with the
clockwise angle

23. Department of Civil Engineering
Indian Institute of Technology Kanpur
TA 111 2023 – 2024 Sem - 1 Prof. Sudhir Misra
23
:: THANK YOU ::